Finite Group Databasebeta

← #35612700

Subgroups — #35612700

Order 21248.

2186 conjugacy classes of subgroups.

The subgroup lattice has 1638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24915750C211yesmaximal, characteristic, complemented
2#24915135C211yesmaximal, characteristic, complemented
3#24914697C211yesmaximal, characteristic, complemented
4#24914647C211yesmaximal, characteristic, complemented
5#24914642C211yesmaximal, characteristic, complemented
6#24914599C211yesmaximal, characteristic, complemented
7#24914436C211yesmaximal, characteristic, complemented
8#24914179C211yesmaximal, characteristic, complemented
9#24914177C211yesmaximal, characteristic, complemented
10#24914145C211yesmaximal, characteristic, complemented
11#24914014C211yesmaximal, characteristic, complemented
12#24913996C211yesmaximal, characteristic, complemented
13#24913969C211yesmaximal, characteristic, complemented
14#24913968C211yesmaximal, characteristic, complemented
15#24913939C211yesmaximal, characteristic, complemented
16#24913884C211yesmaximal, characteristic, complemented
17#24913815C211yesmaximal, characteristic, complemented
18#24913435C211yesmaximal, characteristic, complemented
19#24913418C211yesmaximal, characteristic, complemented
20#24911968C211yesmaximal, characteristic, complemented
21#24911708C211yesmaximal, characteristic, complemented
22#24911291C211yesmaximal, characteristic, complemented
23#24911128C211yesmaximal, characteristic, complemented
24#24910921C211yesmaximal, characteristic, complemented
25#24910858C211yesmaximal, characteristic, complemented
26#24910833C211yesmaximal, characteristic
27#24910788C211yesmaximal, characteristic, complemented
28#24910126C211yesmaximal, characteristic, complemented
29#24910074C211yesmaximal, characteristic, complemented
30C2×#19127580C211yesmaximal, characteristic, complemented
31C83×#2849C211yesmaximal, characteristic, complemented
32C23×C22⋊D83C2211yescharacteristic
33C2×#14581785C2211yescharacteristic, complemented
34C2×#14581774C2211yescharacteristic
35C2×#14581774C2211yescharacteristic
36C2×#14581774C2211yescharacteristic, complemented
37C2×#14581773C2211yescharacteristic, complemented
38C2×#14581771C2211yescharacteristic
39C2×#14581771C2211yescharacteristic, complemented
40C2×#14581771C2211yescharacteristic, complemented
41C2×#14581770C2211yescharacteristic, complemented
42C2×#14581763C2211yescharacteristic
43C2×#14581763C2211yescharacteristic
44C2×#14581760C2211yescharacteristic
45C2×D4×Dic83C2211yescharacteristic
46C22×C22⋊Dic83C2211yescharacteristic
47C22×(C2×D83)⋊C4C2211yescharacteristic
48C22×(C2×D83)⋊C4C2211yescharacteristic
49C2×C22⋊C4×D83C2211yescharacteristic
50C2×C22⋊C4×D83C2211yescharacteristic
51C83⋊#401C2211yescharacteristic, complemented
52#19127643C2211yescharacteristic, complemented
53#19127643C2211yescharacteristic, complemented
54#19127643C2211yescharacteristic, complemented
55#19127642C2211yescharacteristic, complemented
56#19127642C2211yescharacteristic, complemented
57#19127642C2211yescharacteristic, complemented
58#19127641C2211yescharacteristic, complemented
59#19127641C2211yescharacteristic, complemented
60#19127640C2211yescharacteristic, complemented
61#19127640C2211yescharacteristic, complemented
62#19127639C2211yescharacteristic, complemented
63#19127637C2211yescharacteristic, complemented
64#19127636C2211yescharacteristic, complemented
65#19127635C2211yescharacteristic, complemented
66#19127634C2211yescharacteristic, complemented
67#19127633C2211yescharacteristic, complemented
68#19127633C2211yescharacteristic, complemented
69#19127632C2211yescharacteristic, complemented
70#19127631C2211yescharacteristic, complemented
71#19127630C2211yescharacteristic, complemented
72#19127629C2211yescharacteristic, complemented
73#19127629C2211yescharacteristic, complemented
74#19127629C2211yescharacteristic, complemented
75#19127629C2211yescharacteristic, complemented
76#19127628C2211yescharacteristic, complemented
77#19127626C2211yescharacteristic, complemented
78#19127626C2211yescharacteristic, complemented
79#19127626C2211yescharacteristic, complemented
80#19127625C2211yescharacteristic, complemented
81#19127624C2211yescharacteristic, complemented
82#19127624C2211yescharacteristic, complemented
83#19127624C2211yescharacteristic, complemented
84#19127623C2211yescharacteristic, complemented
85#19127617C2211yescharacteristic
86#19127617C2211yescharacteristic
87#19127617C2211yescharacteristic
88#19127617C2211yescharacteristic
89#19127617C2211yescharacteristic, complemented
90#19127616C2211yescharacteristic
91#19127616C2211yescharacteristic
92#19127616C2211yescharacteristic, complemented
93#19127615C2211yescharacteristic, complemented
94#19127615C2211yescharacteristic, complemented
95#19127614C2211yescharacteristic, complemented
96#19127613C2211yescharacteristic, complemented
97#19127609C2211yescharacteristic
98#19127609C2211yescharacteristic
99#19127605C2211yescharacteristic, complemented
100#19127601C2211yescharacteristic, complemented
101#19127601C2211yescharacteristic, complemented
102#19127600C2211yescharacteristic, complemented
103#19127595C2211yescharacteristic, complemented
104#19127594C2211yescharacteristic, complemented
105#19127593C2211yescharacteristic, complemented
106#19127593C2211yescharacteristic, complemented
107#19127590C2211yescharacteristic, complemented
108#19127590C2211yescharacteristic, complemented
109#19127589C2211yescharacteristic, complemented
110#19127589C2211yescharacteristic, complemented
111#19127589C2211yescharacteristic, complemented
112#19127588C2211yescharacteristic, complemented
113#19127584C2211yescharacteristic, complemented
114#19127584C2211yescharacteristic, complemented
115#19127581C2211yescharacteristic
116#19127581C2211yescharacteristic
117#19127581C2211yescharacteristic, complemented
118#19127580C2211yescharacteristic
119#19127580C2211yescharacteristic
120#19127580C2211yescharacteristic
121#19127580C2211yescharacteristic
122#19127580C2211yescharacteristic
123#19127580C2211yescharacteristic
124#19127580C2211yescharacteristic
125#19127580C2211yescharacteristic
126#19127578C2211yescharacteristic, complemented
127#19127578C2211yescharacteristic, complemented
128#19127577C2211yescharacteristic
129#19127577C2211yescharacteristic
130#19127577C2211yescharacteristic
131#19127577C2211yescharacteristic
132#19127577C2211yescharacteristic, complemented
133#19127576C2211yescharacteristic
134#19127576C2211yescharacteristic
135#19127576C2211yescharacteristic
136#19127576C2211yescharacteristic, complemented
137#19127575C2211yescharacteristic, complemented
138#19127575C2211yescharacteristic, complemented
139#19127575C2211yescharacteristic, complemented
140#19127575C2211yescharacteristic, complemented
141#19127574C2211yescharacteristic
142#19127574C2211yescharacteristic
143#19127574C2211yescharacteristic, complemented
144#19127574C2211yescharacteristic, complemented
145#19127574C2211yescharacteristic, complemented
146#19127574C2211yescharacteristic, complemented
147#19127573C2211yescharacteristic
148#19127573C2211yescharacteristic
149#19127573C2211yescharacteristic
150#19127572C2211yescharacteristic, complemented
151#19127572C2211yescharacteristic, complemented
152#19127572C2211yescharacteristic, complemented
153#19127566C2211yescharacteristic, complemented
154#19127563C2211yescharacteristic, complemented
155#19127561C2211yescharacteristic
156#19127561C2211yescharacteristic, complemented
157#19127561C2211yescharacteristic, complemented
158#19127560C2211yescharacteristic, complemented
159#19127560C2211yescharacteristic, complemented
160#19127560C2211yescharacteristic, complemented
161#19127559C2211yescharacteristic
162#19127559C2211yescharacteristic
163#19127559C2211yescharacteristic, complemented
164#19127558C2211yescharacteristic, complemented
165#19127558C2211yescharacteristic, complemented
166#19127557C2211yescharacteristic
167#19127557C2211yescharacteristic
168#19127556C2211yescharacteristic
169C22⋊C4×Dic83C2211yescharacteristic
170C2×C83⋊#95C2211yescharacteristic
171C2×C83⋊#95C2211yescharacteristic
172C24×C4×C83C2211yescharacteristic
173C2×#123×C83C2211yescharacteristic, complemented
174C2×#123×C83C2211yescharacteristic, complemented
175C2×#120×C83C2211yescharacteristic
176#386×C83C2211yescharacteristic
177#386×C83C2211yescharacteristic
178#386×C83C2211yescharacteristic, complemented
179#386×C83C2211yescharacteristic, complemented
180#385×C83C2211yescharacteristic
181#385×C83C2211yescharacteristic
182#385×C83C2211yescharacteristic, complemented
183#385×C83C2211yescharacteristic, complemented
184#381×C83C2211yescharacteristic, complemented
185#381×C83C2211yescharacteristic, complemented
186#379×C83C2211yescharacteristic
187C24×D83C2311yescharacteristic
188C22×Dic166C2311yescharacteristic
189C22×C22⋊D83—24no—
190C22×C22⋊D83—42no—
191C22×C22⋊D83—42no—
192C22×C22⋊D83C2311yescharacteristic
193C22×C22⋊D83C2311yescharacteristic
194C22×C22⋊D83C2311yescharacteristic
195C22×C22⋊D83C2311yescharacteristic
196C22×C22⋊D83C2311yescharacteristic
197C22×C22⋊D83C2311yescharacteristic
198C23×Dic83C2311yescharacteristic
199C23×Dic83C2311yescharacteristic
200C23×Dic83C2311yescharacteristic
201C23×Dic83C2311yescharacteristic
202C22×C4×D83C2311yescharacteristic
203C22×C4×D83C2311yescharacteristic
204C22×C4×D83C2311yescharacteristic
205C22×C4×D83C2311yescharacteristic
206#14581785—42no—
207#14581774—42no—
208#14581774—42no—
209#14581774—42no—
210#14581773—42no—
211#14581771—42no—
212#14581771—42no—
213#14581771—42no—
214#14581770—42no—
215#14581763—42no—
216#14581763—42no—
217#14581760—24no—
218D4×Dic83—42no—
219C2×C4⋊Dic83C2311yescharacteristic
220C2×C4⋊Dic83C2311yescharacteristic
221C2×C4⋊Dic83C2311yescharacteristic
222C2×C4⋊Dic83C2311yescharacteristic
223C2×C4⋊Dic83C2311yescharacteristic
224C2×C4⋊Dic83C2311yescharacteristic
225C2×C4⋊Dic83C2311yescharacteristic
226C2×C4⋊Dic83C2311yescharacteristic
227C2×C4⋊Dic83C2311yescharacteristic
228C2×C4⋊Dic83C2311yescharacteristic
229C2×Dic83⋊C4C2311yescharacteristic
230C2×Dic83⋊C4C2311yescharacteristic
231C2×Dic83⋊C4C2311yescharacteristic
232C2×Dic83⋊C4C2311yescharacteristic
233C2×Dic83⋊C4C2311yescharacteristic
234C2×Dic83⋊C4C2311yescharacteristic
235C2×Dic83⋊C4C2311yescharacteristic
236C2×Dic83⋊C4C2311yescharacteristic
237C2×Dic83⋊C4C2311yescharacteristic
238C2×Dic83⋊C4C2311yescharacteristic
239C2×Dic83⋊C4C2311yescharacteristic
240C2×Dic83⋊C4C2311yescharacteristic
241C2×Dic83⋊C4C2311yescharacteristic
242C2×Dic83⋊C4C2311yescharacteristic
243C2×Dic83⋊C4C2311yescharacteristic
244C2×Dic83⋊C4C2311yescharacteristic
245C2×C22⋊Dic83—42no—
246C2×C22⋊Dic83C2311yescharacteristic
247C2×C22⋊Dic83C2311yescharacteristic
248C2×C22⋊Dic83C2311yescharacteristic
249C2×C22⋊Dic83C2311yescharacteristic
250C2×C22⋊Dic83C2311yescharacteristic
251C2×C22⋊Dic83C2311yescharacteristic
252C2×C22⋊Dic83C2311yescharacteristic
253C2×C22⋊Dic83C2311yescharacteristic
254C2×C22⋊Dic83C2311yescharacteristic
255C2×C22⋊Dic83C2311yescharacteristic
256C2×C22⋊Dic83C2311yescharacteristic
257C2×C22⋊Dic83C2311yescharacteristic
258C2×C22⋊Dic83C2311yescharacteristic
259C2×C22⋊Dic83C2311yescharacteristic
260C2×C22⋊Dic83C2311yescharacteristic
261C2×C22⋊Dic83C2311yescharacteristic
262C2×C22⋊Dic83C2311yescharacteristic
263C2×C22⋊Dic83C2311yescharacteristic
264C2×C22⋊Dic83C2311yescharacteristic
265C2×C22⋊Dic83C2311yescharacteristic
266C2×C22⋊Dic83C2311yescharacteristic
267C2×(C2×D83)⋊C4—42no—
268C2×(C2×D83)⋊C4—42no—
269C2×(C2×D83)⋊C4C2311yescharacteristic
270C2×(C2×D83)⋊C4C2311yescharacteristic
271C2×(C2×D83)⋊C4C2311yescharacteristic
272C2×(C2×D83)⋊C4C2311yescharacteristic
273C2×(C2×D83)⋊C4C2311yescharacteristic
274C2×(C2×D83)⋊C4C2311yescharacteristic
275C2×(C2×D83)⋊C4C2311yescharacteristic
276C2×(C2×D83)⋊C4C2311yescharacteristic
277C2×(C2×D83)⋊C4C2311yescharacteristic
278C2×(C2×D83)⋊C4C2311yescharacteristic
279C2×(C2×D83)⋊C4C2311yescharacteristic
280C2×(C2×D83)⋊C4C2311yescharacteristic
281C2×(C2×D83)⋊C4C2311yescharacteristic
282C2×(C2×D83)⋊C4C2311yescharacteristic
283C2×(C2×D83)⋊C4C2311yescharacteristic
284C2×(C2×D83)⋊C4C2311yescharacteristic
285C2×(C2×D83)⋊C4C2311yescharacteristic
286C2×(C2×D83)⋊C4C2311yescharacteristic
287C22⋊C4×D83—24no—
288C22⋊C4×D83—42no—
289C2×C4×Dic83C2311yescharacteristic
290C2×C4×Dic83C2311yescharacteristic
291C2×C4×Dic83C2311yescharacteristic
292C83⋊#95C2311yescharacteristic
293C83⋊#95C2311yescharacteristic
294C83⋊#95C2311yescharacteristic
295C83⋊#95C2311yescharacteristic
296C83⋊#95C2311yescharacteristic
297C83⋊#95C2311yescharacteristic
298C83⋊#95C2311yescharacteristic
299C83⋊#95C2311yescharacteristic
300C83⋊#95C2311yescharacteristic
301C83⋊#95C2311yescharacteristic
302C83⋊#95C2311yescharacteristic
303C83⋊#95C2311yescharacteristic
304C83⋊#95C2311yescharacteristic
305C83⋊#95C2311yescharacteristic
306C83⋊#95C2311yescharacteristic
307C83⋊#95C2311yescharacteristic
308C83⋊#95C2311yescharacteristic
309C83⋊#95C2311yescharacteristic
310C83⋊#95C2311yescharacteristic
311C83⋊#95C2311yescharacteristic
312C83⋊#95C2311yescharacteristic
313C83⋊#95C2311yescharacteristic
314C83⋊#95C2311yescharacteristic
315C83⋊#95C2311yescharacteristic
316C83⋊#95C2311yescharacteristic
317C83⋊#95C2311yescharacteristic
318C83⋊#95C2311yescharacteristic
319C83⋊#95C2311yescharacteristic
320C83⋊#95C2311yescharacteristic
321C83⋊#95C2311yescharacteristic
322C83⋊#95C2311yescharacteristic
323C83⋊#95C2311yescharacteristic
324C83⋊#95C2311yescharacteristic
325C83⋊#95C2311yescharacteristic
326C83⋊#95C2311yescharacteristic
327C83⋊#95C2311yescharacteristic
328C25×C83C2311yescharacteristic
329C22×D4×C83C2311yescharacteristic
330C22×D4×C83C2311yescharacteristic
331C22×D4×C83C2311yescharacteristic
332C23×C4×C83—42no—
333C23×C4×C83—42no—
334C23×C4×C83—42no—
335C23×C4×C83C2311yescharacteristic
336C23×C4×C83C2311yescharacteristic
337C23×C4×C83C2311yescharacteristic
338C23×C4×C83C2311yescharacteristic
339C23×C4×C83C2311yescharacteristic
340C23×C4×C83C2311yescharacteristic
341#123×C83—42no—
342#123×C83—42no—
343#120×C83—42no—
344C2×C4⋊C4×C83C2311yescharacteristic
345C2×C4⋊C4×C83C2311yescharacteristic
346C2×C4⋊C4×C83C2311yescharacteristic
347C2×C4⋊C4×C83C2311yescharacteristic
348C2×C22⋊C4×C83C2311yescharacteristic
349C2×C22⋊C4×C83C2311yescharacteristic
350C2×C22⋊C4×C83C2311yescharacteristic
351C2×C22⋊C4×C83C2311yescharacteristic
352C2×C22⋊C4×C83C2311yescharacteristic
353C2×C22⋊C4×C83C2311yescharacteristic
354C2×C22⋊C4×C83C2311yescharacteristic
355C2×C22⋊C4×C83C2311yescharacteristic
356C2×C22⋊C4×C83C2311yescharacteristic
357C2×C22⋊C4×C83C2311yescharacteristic
358C2×C22⋊C4×C83C2311yescharacteristic
359C2×C22⋊C4×C83C2311yescharacteristic
360C2×C22⋊C4×C83C2311yescharacteristic
361#95×C83C2311yescharacteristic
362#95×C83C2311yescharacteristic
363#95×C83C2311yescharacteristic
364#95×C83C2311yescharacteristic
365#95×C83C2311yescharacteristic
366#95×C83C2311yescharacteristic
367#95×C83C2311yescharacteristic
368#95×C83C2311yescharacteristic
369C23×D83—22no—
370C23×D83—22no—
371C23×D83—41no—
372C23×D83—41no—
373C23×D83—41no—
374C23×D83—41no—
375C23×D83#4114yes—
376C23×D83C2411yescharacteristic
377C23×D83C2411yescharacteristic
378C2×Dic166—22no—
379C2×Dic166—41no—
380C2×Dic166—41no—
381C2×C22⋊D83—22no—
382C2×C22⋊D83—22no—
383C2×C22⋊D83—22no—
384C2×C22⋊D83—22no—
385C2×C22⋊D83—22no—
386C2×C22⋊D83—22no—
387C2×C22⋊D83—22no—
388C2×C22⋊D83—22no—
389C2×C22⋊D83—22no—
390C2×C22⋊D83—22no—
391C2×C22⋊D83—41no—
392C2×C22⋊D83—41no—
393C2×C22⋊D83—41no—
394C2×C22⋊D83—41no—
395C2×C22⋊D83—41no—
396C2×C22⋊D83—41no—
397C2×C22⋊D83—41no—
398C2×C22⋊D83—41no—
399C2×C22⋊D83—416no—
400C22×Dic83—22no—
401C22×Dic83—22no—
402C22×Dic83—22no—
403C22×Dic83—41no—
404C22×Dic83—41no—
405C22×Dic83—41no—
406C22×Dic83—41no—
407C22×Dic83—41no—
408C22×Dic83—41no—
409C22×Dic83—41no—
410C22×Dic83—41no—
411C22×Dic83—41no—
412C22×Dic83C2411yescharacteristic
413C22×Dic83C2411yescharacteristic
414C22×Dic83C2411yescharacteristic
415C22×Dic83C2411yescharacteristic
416C22×Dic83C2411yescharacteristic
417C22×Dic83C2411yescharacteristic
418C22×Dic83C2411yescharacteristic
419C22×Dic83C2411yescharacteristic
420C22×Dic83C2411yescharacteristic
421C22×Dic83C2411yescharacteristic
422C22×Dic83C2411yescharacteristic
423C22×Dic83C2411yescharacteristic
424C22×Dic83C2411yescharacteristic
425C22×Dic83C2411yescharacteristic
426C2×C4×D83—22no—
427C2×C4×D83—22no—
428C2×C4×D83—41no—
429C2×C4×D83—41no—
430C2×C4×D83—41no—
431C2×C4×D83—41no—
432C2×C4×D83—41no—
433C2×C4×D83—41no—
434C2×C4×D83—41no—
435C2×C4×D83—41no—
436C2×C4×D83—41no—
437C2×C4×D83—41no—
438C4⋊Dic83—22no—
439C4⋊Dic83—41no—
440C4⋊Dic83—41no—
441C4⋊Dic83—41no—
442C4⋊Dic83—41no—
443C4⋊Dic83—41no—
444C4⋊Dic83—41no—
445C4⋊Dic83—41no—
446C4⋊Dic83—41no—
447C4⋊Dic83—41no—
448Dic83⋊C4—41no—
449Dic83⋊C4—41no—
450Dic83⋊C4—41no—
451Dic83⋊C4—41no—
452Dic83⋊C4—41no—
453Dic83⋊C4—41no—
454Dic83⋊C4—41no—
455Dic83⋊C4—41no—
456Dic83⋊C4—41no—
457Dic83⋊C4—41no—
458Dic83⋊C4—41no—
459Dic83⋊C4—41no—
460Dic83⋊C4—41no—
461Dic83⋊C4—41no—
462Dic83⋊C4—41no—
463Dic83⋊C4—41no—
464C22⋊Dic83—22no—
465C22⋊Dic83—22no—
466C22⋊Dic83—22no—
467C22⋊Dic83—22no—
468C22⋊Dic83—22no—
469C22⋊Dic83—22no—
470C22⋊Dic83—22no—
471C22⋊Dic83—22no—
472C22⋊Dic83—22no—
473C22⋊Dic83—22no—
474C22⋊Dic83—41no—
475C22⋊Dic83—41no—
476C22⋊Dic83—41no—
477C22⋊Dic83—41no—
478C22⋊Dic83—41no—
479C22⋊Dic83—41no—
480C22⋊Dic83—41no—
481C22⋊Dic83—41no—
482C22⋊Dic83—41no—
483C22⋊Dic83—41no—
484C22⋊Dic83—41no—
485(C2×D83)⋊C4—22no—
486(C2×D83)⋊C4—22no—
487(C2×D83)⋊C4—22no—
488(C2×D83)⋊C4—22no—
489(C2×D83)⋊C4—22no—
490(C2×D83)⋊C4—22no—
491(C2×D83)⋊C4—41no—
492(C2×D83)⋊C4—41no—
493(C2×D83)⋊C4—41no—
494(C2×D83)⋊C4—41no—
495(C2×D83)⋊C4—41no—
496(C2×D83)⋊C4—41no—
497(C2×D83)⋊C4—41no—
498(C2×D83)⋊C4—41no—
499(C2×D83)⋊C4—41no—
500(C2×D83)⋊C4—41no—
501(C2×D83)⋊C4—41no—
502(C2×D83)⋊C4—41no—
503C4×Dic83—41no—
504C4×Dic83—41no—
505C4×Dic83—41no—
506C24×C83—22no—
507C24×C83—22no—
508C24×C83—22no—
509C24×C83—22no—
510C24×C83—22no—
511C24×C83—41no—
512C24×C83—41no—
513C24×C83C2411yescharacteristic
514C24×C83C2411yescharacteristic
515C24×C83C2411yescharacteristic
516C24×C83C2411yescharacteristic
517C2×D4×C83—22no—
518C2×D4×C83—22no—
519C2×D4×C83—22no—
520C2×D4×C83—22no—
521C2×D4×C83—22no—
522C2×D4×C83—41no—
523C2×D4×C83—41no—
524C2×D4×C83—41no—
525C2×D4×C83—41no—
526C22×C4×C83—22no—
527C22×C4×C83—22no—
528C22×C4×C83—22no—
529C22×C4×C83—22no—
530C22×C4×C83—22no—
531C22×C4×C83—22no—
532C22×C4×C83—22no—
533C22×C4×C83—41no—
534C22×C4×C83—41no—
535C22×C4×C83—41no—
536C22×C4×C83—41no—
537C22×C4×C83—41no—
538C22×C4×C83—41no—
539C22×C4×C83—41no—
540C22×C4×C83—41no—
541C22×C4×C83—41no—
542C22×C4×C83—41no—
543C22×C4×C83—41no—
544C22×C4×C83—416no—
545C22×C4×C83C2411yescharacteristic
546C22×C4×C83C2411yescharacteristic
547C22×C4×C83C2411yescharacteristic
548C22×C4×C83C2411yescharacteristic
549C22×C4×C83C2411yescharacteristic
550C22×C4×C83C2411yescharacteristic
551C22×C4×C83C2411yescharacteristic
552C22×C4×C83C2411yescharacteristic
553C22×C4×C83C2411yescharacteristic
554C22×C4×C83C2411yescharacteristic
555C22×C4×C83C2411yescharacteristic
556C4⋊C4×C83—22no—
557C4⋊C4×C83—41no—
558C4⋊C4×C83—41no—
559C4⋊C4×C83—41no—
560C22⋊C4×C83—22no—
561C22⋊C4×C83—22no—
562C22⋊C4×C83—22no—
563C22⋊C4×C83—22no—
564C22⋊C4×C83—22no—
565C22⋊C4×C83—22no—
566C22⋊C4×C83—41no—
567C22⋊C4×C83—41no—
568C22⋊C4×C83—41no—
569C22⋊C4×C83—41no—
570C22⋊C4×C83—41no—
571C22⋊C4×C83—41no—
572C22⋊C4×C83—41no—
573C23×C83—21no—
574C23×C83—21no—
575C23×C83—21no—
576C23×C83—21no—
577C23×C83—28no—
578C23×C83—21no—
579C23×C83—21no—
580C23×C83—21no—
581C23×C83—21no—
582C23×C83—21no—
583C23×C83—21no—
584C23×C83—21no—
585C23×C83—21no—
586C23×C83—21no—
587C23×C83—21no—
588C23×C83—21no—
589C23×C83—21no—
590C23×C83—21no—
591C23×C83—21no—
592C23×C83—21no—
593C23×C83—21no—
594C23×C83—21no—
595C23×C83—21no—
596C23×C83—21no—
597C23×C83—44no—
598C23×C83—44no—
599C23×C83—44no—
600C23×C83—44no—
601C23×C83—44no—
602C23×C83—44no—
603C23×C83C2×#4112yes—
604C23×C83H(5,𝔽2)12yes—
605C23×C83H(5,𝔽2)12yes—
606C23×C83H(5,𝔽2)12yes—
607C23×C832−1+412yes—
608C23×C83C2511yescharacteristic
609C22×D83—21no—
610C22×D83—21no—
611C22×D83—21no—
612C22×D83—21no—
613C22×D83—21no—
614C22×D83—21no—
615C22×D83—21no—
616C22×D83—21no—
617C22×D83—21no—
618C22×D83—21no—
619C22×D83—21no—
620C22×D83—21no—
621C22×D83—28no—
622C22×D83—44no—
623C22×D83—44no—
624C22×D83—82no—
625C22×D83—82no—
626C22×D83—82no—
627C22×D83—82no—
628C22×D83C2×#4112yes—
629C22×D83C2×#4112yes—
630D4×C83—44no—
631D4×C83—82no—
632D4×C83—82no—
633C2×C4×C83—21no—
634C2×C4×C83—21no—
635C2×C4×C83—21no—
636C2×C4×C83—21no—
637C2×C4×C83—21no—
638C2×C4×C83—21no—
639C2×C4×C83—21no—
640C2×C4×C83—21no—
641C2×C4×C83—21no—
642C2×C4×C83—21no—
643C2×C4×C83—21no—
644C2×C4×C83—21no—
645C2×C4×C83—21no—
646C2×C4×C83—21no—
647C2×C4×C83—21no—
648C2×C4×C83—21no—
649C2×C4×C83—21no—
650C2×C4×C83—21no—
651C2×C4×C83—21no—
652C2×C4×C83—21no—
653C2×C4×C83—21no—
654C2×C4×C83—21no—
655C2×C4×C83—21no—
656C2×C4×C83—21no—
657C2×C4×C83—21no—
658C2×C4×C83—21no—
659C2×C4×C83—21no—
660C2×C4×C83—21no—
661C2×C4×C83—21no—
662C2×C4×C83—21no—
663C2×C4×C83—21no—
664C2×C4×C83—21no—
665C2×C4×C83—44no—
666C2×C4×C83—44no—
667C2×C4×C83—44no—
668C2×C4×C83—44no—
669C2×C4×C83—44no—
670C2×C4×C83—44no—
671C2×C4×C83H(5,𝔽2)12yes—
672C22⋊D83—44no—
673C22⋊D83—44no—
674C22⋊D83—44no—
675C22⋊D83—44no—
676C22⋊D83—82no—
677C22⋊D83—82no—
678C2×Dic83—21no—
679C2×Dic83—21no—
680C2×Dic83—21no—
681C2×Dic83—21no—
682C2×Dic83—21no—
683C2×Dic83—21no—
684C2×Dic83—21no—
685C2×Dic83—21no—
686C2×Dic83—21no—
687C2×Dic83—21no—
688C2×Dic83—21no—
689C2×Dic83—21no—
690C2×Dic83—21no—
691C2×Dic83—21no—
692C2×Dic83—21no—
693C2×Dic83—21no—
694C2×Dic83—21no—
695C2×Dic83—21no—
696C2×Dic83—21no—
697C2×Dic83—21no—
698C2×Dic83—21no—
699C2×Dic83—21no—
700C2×Dic83—21no—
701C2×Dic83—21no—
702C2×Dic83—21no—
703C2×Dic83—21no—
704C2×Dic83—21no—
705C2×Dic83—21no—
706C2×Dic83—21no—
707C2×Dic83—21no—
708C2×Dic83—21no—
709C2×Dic83—21no—
710C2×Dic83—21no—
711C2×Dic83—21no—
712C2×Dic83—21no—
713C2×Dic83—21no—
714C2×Dic83—21no—
715C2×Dic83—21no—
716C2×Dic83—21no—
717C2×Dic83—21no—
718C2×Dic83—21no—
719C2×Dic83—21no—
720C2×Dic83—44no—
721C2×Dic83—82no—
722C2×Dic83—82no—
723C2×Dic83—82no—
724C4×D83—82no—
725C4×D83—82no—
726C4×D83—82no—
727C4×D83—82no—
728Dic166—82no—
729C22×C83—22no—
730C22×C83—22no—
731C22×C83—22no—
732C22×C83—22no—
733C22×C83—22no—
734C22×C83—22no—
735C22×C83—22no—
736C22×C83—22no—
737C22×C83—22no—
738C22×C83—22no—
739C22×C83—22no—
740C22×C83—22no—
741C22×C83—416no—
742C22×C83—41no—
743C22×C83—41no—
744C22×C83—41no—
745C22×C83—41no—
746C22×C83—41no—
747C22×C83—41no—
748C22×C83—41no—
749C22×C83—41no—
750C22×C83—41no—
751C22×C83—41no—
752C22×C83—41no—
753C22×C83—41no—
754C22×C83—41no—
755C22×C83—41no—
756C22×C83—41no—
757C22×C83#53914yes—
758C22×C83C22×#4111yescharacteristic
759C22×C83C2×H(5,𝔽2)11yescharacteristic
760C22×C83C2×H(5,𝔽2)11yescharacteristic
761C22×C83C2×H(5,𝔽2)11yescharacteristic
762C22×C83C2×H(5,𝔽2)11yescharacteristic
763C22×C83C2×2−1+411yescharacteristic
764C22×C83#58511yescharacteristic
765C2×D83—22no—
766C2×D83—22no—
767C2×D83—22no—
768C2×D83—22no—
769C2×D83—22no—
770C2×D83—22no—
771C2×D83—41no—
772C2×D83—41no—
773C2×D83—41no—
774C2×D83—41no—
775C2×D83—41no—
776C2×D83—41no—
777C2×D83—41no—
778C2×D83—41no—
779C2×D83—88no—
780C4×C83—22no—
781C4×C83—41no—
782C4×C83—41no—
783C4×C83—41no—
784C4×C83—41no—
785C4×C83—41no—
786C4×C83—41no—
787C4×C83—41no—
788C4×C83—41no—
789C4×C83—41no—
790C4×C83—41no—
791Dic83—41no—
792Dic83—41no—
793Dic83—41no—
794Dic83—41no—
795Dic83—41no—
796Dic83—41no—
797Dic83—41no—
798Dic83—41no—
799Dic83—41no—
800Dic83—41no—
801Dic83—41no—
802Dic83—41no—
803Dic83—41no—
804Dic83—41no—
805#36775—831nomaximal, Sylow
806C2×C83—24no—
807C2×C83—42no—
808C2×C83—42no—
809C2×C83—81no—
810C2×C83C2×#53911yescharacteristic
811C2×C83#349011yescharacteristic
812C2×C83#350511yescharacteristic
813C2×C83#353211yescharacteristic
814C2×C83#353411yescharacteristic
815C2×C83#353511yescharacteristic
816C2×C83#353611yescharacteristic
817D83—42no—
818D83—42no—
819#2849D8311yescharacteristic, complemented
820#2848—831no—
821#2782—831no—
822#2750—831no—
823#2746—831no—
824#2746—831no—
825#2743—831no—
826#2728—831no—
827#2708—831no—
828#2708—831no—
829#2706—831no—
830#2696—831no—
831#2695—831no—
832#2693—831no—
833#2693—831no—
834#2691—831no—
835#2687—831no—
836#2681—831no—
837#2646—831no—
838#2643—831no—
839#2505—831no—
840#2480—831no—
841#2450—831no—
842#2437—831no—
843#2418—831no—
844#2412—831no—
845#2410—831no—
846#2405—831no—
847#2321—831no—
848#2315—831no—
849C2×#386—831no—
850C83#3677511yescharacteristic, complemented, Sylow
851C23×D4—831no—
852C24×C4C2×D8311yescharacteristic
853C2×#126—831no—
854C2×#123—831no—
855C2×#123—831no—
856C2×#123—831no—
857C2×#123—831no—
858C2×#123C2×D8311yescharacteristic, complemented
859C2×#123C2×D8311yescharacteristic, complemented
860C2×C22⋊Q8—831no—
861C2×C22⋊Q8—831no—
862C2×C22⋊Q8—831no—
863C2×C22⋊Q8—831no—
864C2×#121—831no—
865C2×#121—831no—
866C2×#120—831no—
867C2×#120C2×D8311yescharacteristic
868C2×C4×D4—831no—
869C22×C22⋊C4—831no—
870C22×C22⋊C4—831no—
871C22×C22⋊C4—831no—
872C22×C22⋊C4—831no—
873C22×C22⋊C4—831no—
874#401—831no—
875#400—831no—
876#400—831no—
877#400—831no—
878#400—831no—
879#400—831no—
880#400—831no—
881#400—831no—
882#400—831no—
883#400—831no—
884#400—831no—
885#400—831no—
886#399—831no—
887#399—831no—
888#398—831no—
889#398—831no—
890#398—831no—
891#398—831no—
892#398—831no—
893#398—831no—
894#397—831no—
895#397—831no—
896#397—831no—
897#397—831no—
898#397—831no—
899#397—831no—
900#397—831no—
901#397—831no—
902#397—831no—
903#396—831no—
904#396—831no—
905#396—831no—
906#396—831no—
907#396—831no—
908#394—831no—
909#394—831no—
910#394—831no—
911#394—831no—
912#394—831no—
913#394—831no—
914#394—831no—
915#394—831no—
916#394—831no—
917#394—831no—
918#393—831no—
919#393—831no—
920#392—831no—
921#392—831no—
922#391—831no—
923#390—831no—
924#390—831no—
925#389—831no—
926#388—831no—
927#388—831no—
928#388—831no—
929#388—831no—
930#388—831no—
931#388—831no—
932#388—831no—
933#388—831no—
934#388—831no—
935#387—831no—
936#387—831no—
937#387—831no—
938#386—831no—
939#386—831no—
940#386—831no—
941#386—831no—
942#386—831no—
943#386—831no—
944#386—831no—
945#386—831no—
946#386—831no—
947#386—831no—
948#386—831no—
949#386—831no—
950#386—831no—
951#386—831no—
952#386—831no—
953#386—831no—
954#386—831no—
955#386—831no—
956#386C2×D8311yescharacteristic
957#386C2×D8311yescharacteristic
958#386C2×D8311yescharacteristic, complemented
959#386C2×D8311yescharacteristic, complemented
960#385—831no—
961#385—831no—
962#385—831no—
963#385—831no—
964#385—831no—
965#385—831no—
966#385—831no—
967#385—831no—
968#385—831no—
969#385—831no—
970#385—831no—
971#385—831no—
972#385—831no—
973#385—831no—
974#385—831no—
975#385—831no—
976#385—831no—
977#385—831no—
978#385—831no—
979#385—831no—
980#385C2×D8311yescharacteristic
981#385C2×D8311yescharacteristic
982#385C2×D8311yescharacteristic, complemented
983#385C2×D8311yescharacteristic, complemented
984#382—831no—
985#381—831no—
986#381C2×D8311yescharacteristic, complemented
987#381C2×D8311yescharacteristic, complemented
988#380—831no—
989#380—831no—
990#380—831no—
991#380—831no—
992#380—831no—
993#380—831no—
994#380—831no—
995#380—831no—
996#380—831no—
997#380—831no—
998#380—831no—
999#379—831no—
1000#379—831no—
1001#379—831no—
1002#379C2×D8311yescharacteristic
1003C4×C22⋊C4—831no—
1004C2×#95—831no—
1005C2×#95—831no—
1006C25—831no—
1007C25C22×D8311yescharacteristic
1008C22×Q8—831no—
1009C22×D4—3322no—
1010C22×D4—3322no—
1011C22×D4—831no—
1012C22×D4—831no—
1013C22×D4—831no—
1014C22×D4—831no—
1015C22×D4—831no—
1016C22×D4—831no—
1017C22×D4—1664no—
1018C22×D4C22×D8311yescharacteristic
1019C22×D4C22×D8311yescharacteristic
1020C22×D4C22×D8311yescharacteristic
1021C23×C4—42no—
1022C23×C4—42no—
1023C23×C4—42no—
1024C23×C4—831no—
1025C23×C4—831no—
1026C23×C4—831no—
1027C23×C4—831no—
1028C23×C4—831no—
1029C23×C4—831no—
1030C23×C4—831no—
1031C23×C4—831no—
1032C23×C4C22×D8311yescharacteristic
1033C23×C4C22×D8311yescharacteristic
1034C23×C4C22×D8311yescharacteristic
1035C23×C4C22×D8311yescharacteristic
1036C23×C4C22×D8311yescharacteristic
1037C23×C4C22×D8311yescharacteristic
1038#126—3322no—
1039#123—42no—
1040#123—42no—
1041#123—3322no—
1042#123—3322no—
1043#123—3322no—
1044#123—3322no—
1045C22⋊Q8—3322no—
1046C22⋊Q8—3322no—
1047C22⋊Q8—3322no—
1048C22⋊Q8—3322no—
1049#121—3322no—
1050#121—3322no—
1051#120—42no—
1052#120—1664no—
1053C4×D4—3322no—
1054C2×C4⋊C4—831no—
1055C2×C4⋊C4—831no—
1056C2×C4⋊C4—831no—
1057C2×C4⋊C4—831no—
1058C2×C4⋊C4—831no—
1059C2×C4⋊C4—831no—
1060C2×C4⋊C4—831no—
1061C2×C4⋊C4—831no—
1062C2×C4⋊C4—831no—
1063C2×C4⋊C4—831no—
1064C2×C4⋊C4—831no—
1065C2×C4⋊C4—831no—
1066C2×C4⋊C4—831no—
1067C2×C4⋊C4—831no—
1068C2×C4⋊C4—831no—
1069C2×C4⋊C4—831no—
1070C2×C4⋊C4—831no—
1071C2×C4⋊C4—831no—
1072C2×C4⋊C4—831no—
1073C2×C4⋊C4—831no—
1074C2×C4⋊C4—831no—
1075C2×C4⋊C4—831no—
1076C2×C4⋊C4—831no—
1077C2×C4⋊C4—831no—
1078C2×C4⋊C4—831no—
1079C2×C4⋊C4—831no—
1080C2×C4⋊C4C22×D8311yescharacteristic
1081C2×C4⋊C4C22×D8311yescharacteristic
1082C2×C4⋊C4C22×D8311yescharacteristic
1083C2×C4⋊C4C22×D8311yescharacteristic
1084C2×C22⋊C4—3322no—
1085C2×C22⋊C4—3322no—
1086C2×C22⋊C4—3322no—
1087C2×C22⋊C4—3322no—
1088C2×C22⋊C4—831no—
1089C2×C22⋊C4—831no—
1090C2×C22⋊C4—831no—
1091C2×C22⋊C4—831no—
1092C2×C22⋊C4—831no—
1093C2×C22⋊C4—831no—
1094C2×C22⋊C4—831no—
1095C2×C22⋊C4—831no—
1096C2×C22⋊C4—831no—
1097C2×C22⋊C4—831no—
1098C2×C22⋊C4—831no—
1099C2×C22⋊C4—831no—
1100C2×C22⋊C4—831no—
1101C2×C22⋊C4—831no—
1102C2×C22⋊C4—831no—
1103C2×C22⋊C4—831no—
1104C2×C22⋊C4—831no—
1105C2×C22⋊C4—831no—
1106C2×C22⋊C4—831no—
1107C2×C22⋊C4—831no—
1108C2×C22⋊C4—831no—
1109C2×C22⋊C4—831no—
1110C2×C22⋊C4—831no—
1111C2×C22⋊C4—831no—
1112C2×C22⋊C4—831no—
1113C2×C22⋊C4—831no—
1114C2×C22⋊C4—831no—
1115C2×C22⋊C4—831no—
1116C2×C22⋊C4—831no—
1117C2×C22⋊C4—831no—
1118C2×C22⋊C4—831no—
1119C2×C22⋊C4—831no—
1120C2×C22⋊C4—831no—
1121C2×C22⋊C4—831no—
1122C2×C22⋊C4—831no—
1123C2×C22⋊C4—831no—
1124C2×C22⋊C4—831no—
1125C2×C22⋊C4—831no—
1126C2×C22⋊C4—831no—
1127C2×C22⋊C4—1664no—
1128C2×C22⋊C4C22×D8311yescharacteristic
1129C2×C22⋊C4C22×D8311yescharacteristic
1130C2×C22⋊C4C22×D8311yescharacteristic
1131C2×C22⋊C4C22×D8311yescharacteristic
1132C2×C22⋊C4C22×D8311yescharacteristic
1133C2×C22⋊C4C22×D8311yescharacteristic
1134C2×C22⋊C4C22×D8311yescharacteristic
1135C2×C22⋊C4C22×D8311yescharacteristic
1136C2×C22⋊C4C22×D8311yescharacteristic
1137C2×C22⋊C4C22×D8311yescharacteristic
1138C2×C22⋊C4C22×D8311yescharacteristic
1139C2×C22⋊C4C22×D8311yescharacteristic
1140C2×C22⋊C4C22×D8311yescharacteristic
1141C2×C42—831no—
1142C2×C42—831no—
1143C2×C42—831no—
1144#95—831no—
1145#95—831no—
1146#95—831no—
1147#95—831no—
1148#95—831no—
1149#95—831no—
1150#95—831no—
1151#95—831no—
1152#95—831no—
1153#95—831no—
1154#95—831no—
1155#95—831no—
1156#95—831no—
1157#95—831no—
1158#95—831no—
1159#95—831no—
1160#95—831no—
1161#95—831no—
1162#95—831no—
1163#95—831no—
1164#95—831no—
1165#95—831no—
1166#95—831no—
1167#95—831no—
1168#95—831no—
1169#95—831no—
1170#95—831no—
1171#95—831no—
1172#95—831no—
1173#95—831no—
1174#95—831no—
1175#95—831no—
1176#95—831no—
1177#95—831no—
1178#95—831no—
1179#95—831no—
1180#95C22×D8311yescharacteristic
1181#95C22×D8311yescharacteristic
1182#95C22×D8311yescharacteristic
1183#95C22×D8311yescharacteristic
1184#95C22×D8311yescharacteristic
1185#95C22×D8311yescharacteristic
1186#95C22×D8311yescharacteristic
1187#95C22×D8311yescharacteristic
1188C24—22no—
1189C24—22no—
1190C24—22no—
1191C24—22no—
1192C24—22no—
1193C24—41no—
1194C24—41no—
1195C24—3321no—
1196C24—3321no—
1197C24—3321no—
1198C24—3321no—
1199C24—834no—
1200C24—831no—
1201C24—831no—
1202C24—1662no—
1203C24—1662no—
1204C24C23×D8311yescharacteristic
1205C24C23×D8311yescharacteristic
1206C24C23×D8311yescharacteristic
1207C24C23×D8311yescharacteristic
1208C2×Q8—3321no—
1209C2×Q8—3321no—
1210C2×Q8—1662no—
1211C2×D4—22no—
1212C2×D4—22no—
1213C2×D4—22no—
1214C2×D4—22no—
1215C2×D4—22no—
1216C2×D4—41no—
1217C2×D4—41no—
1218C2×D4—41no—
1219C2×D4—41no—
1220C2×D4—33216no—
1221C2×D4—3321no—
1222C2×D4—3321no—
1223C2×D4—3321no—
1224C2×D4—3321no—
1225C2×D4—3321no—
1226C2×D4—3321no—
1227C2×D4—3321no—
1228C2×D4—3321no—
1229C2×D4—1662no—
1230C2×D4—1662no—
1231C2×D4—1662no—
1232C2×D4—1662no—
1233C2×D4—1662no—
1234C2×D4—1662no—
1235C2×D4—1662no—
1236C2×D4—1662no—
1237C2×D4—1662no—
1238C2×D4—1662no—
1239C22×C4—22no—
1240C22×C4—22no—
1241C22×C4—22no—
1242C22×C4—22no—
1243C22×C4—22no—
1244C22×C4—22no—
1245C22×C4—22no—
1246C22×C4—41no—
1247C22×C4—41no—
1248C22×C4—41no—
1249C22×C4—41no—
1250C22×C4—41no—
1251C22×C4—41no—
1252C22×C4—41no—
1253C22×C4—41no—
1254C22×C4—41no—
1255C22×C4—41no—
1256C22×C4—41no—
1257C22×C4—416no—
1258C22×C4—3321no—
1259C22×C4—3321no—
1260C22×C4—3321no—
1261C22×C4—3321no—
1262C22×C4—3321no—
1263C22×C4—3321no—
1264C22×C4—3321no—
1265C22×C4—3321no—
1266C22×C4—3321no—
1267C22×C4—3321no—
1268C22×C4—3321no—
1269C22×C4—3321no—
1270C22×C4—3321no—
1271C22×C4—3321no—
1272C22×C4—3321no—
1273C22×C4—3321no—
1274C22×C4—3321no—
1275C22×C4—3321no—
1276C22×C4—3321no—
1277C22×C4—831no—
1278C22×C4—831no—
1279C22×C4—831no—
1280C22×C4—831no—
1281C22×C4—831no—
1282C22×C4—831no—
1283C22×C4—831no—
1284C22×C4—831no—
1285C22×C4—831no—
1286C22×C4—831no—
1287C22×C4—831no—
1288C22×C4—831no—
1289C22×C4—831no—
1290C22×C4—831no—
1291C22×C4—1662no—
1292C22×C4—1662no—
1293C22×C4—1662no—
1294C22×C4—1662no—
1295C22×C4—1662no—
1296C22×C4C23×D8311yescharacteristic
1297C22×C4C23×D8311yescharacteristic
1298C22×C4C23×D8311yescharacteristic
1299C22×C4C23×D8311yescharacteristic
1300C22×C4C23×D8311yescharacteristic
1301C22×C4C23×D8311yescharacteristic
1302C22×C4C23×D8311yescharacteristic
1303C22×C4C23×D8311yescharacteristic
1304C22×C4C23×D8311yescharacteristic
1305C22×C4C23×D8311yescharacteristic
1306C22×C4C23×D8311yescharacteristic
1307C4⋊C4—22no—
1308C4⋊C4—41no—
1309C4⋊C4—41no—
1310C4⋊C4—41no—
1311C4⋊C4—3321no—
1312C4⋊C4—3321no—
1313C4⋊C4—3321no—
1314C4⋊C4—3321no—
1315C4⋊C4—3321no—
1316C4⋊C4—3321no—
1317C4⋊C4—3321no—
1318C4⋊C4—3321no—
1319C4⋊C4—3321no—
1320C4⋊C4—3321no—
1321C4⋊C4—3321no—
1322C4⋊C4—3321no—
1323C4⋊C4—3321no—
1324C4⋊C4—3321no—
1325C4⋊C4—3321no—
1326C4⋊C4—3321no—
1327C4⋊C4—3321no—
1328C4⋊C4—3321no—
1329C4⋊C4—3321no—
1330C4⋊C4—3321no—
1331C4⋊C4—3321no—
1332C4⋊C4—3321no—
1333C4⋊C4—3321no—
1334C4⋊C4—3321no—
1335C4⋊C4—3321no—
1336C4⋊C4—1662no—
1337C22⋊C4—22no—
1338C22⋊C4—22no—
1339C22⋊C4—22no—
1340C22⋊C4—22no—
1341C22⋊C4—22no—
1342C22⋊C4—22no—
1343C22⋊C4—41no—
1344C22⋊C4—41no—
1345C22⋊C4—41no—
1346C22⋊C4—41no—
1347C22⋊C4—41no—
1348C22⋊C4—41no—
1349C22⋊C4—41no—
1350C22⋊C4—3321no—
1351C22⋊C4—3321no—
1352C22⋊C4—3321no—
1353C22⋊C4—3321no—
1354C22⋊C4—3321no—
1355C22⋊C4—3321no—
1356C22⋊C4—3321no—
1357C22⋊C4—3321no—
1358C22⋊C4—3321no—
1359C22⋊C4—3321no—
1360C22⋊C4—3321no—
1361C22⋊C4—3321no—
1362C22⋊C4—3321no—
1363C22⋊C4—3321no—
1364C22⋊C4—3321no—
1365C22⋊C4—3321no—
1366C22⋊C4—3321no—
1367C22⋊C4—3321no—
1368C22⋊C4—3321no—
1369C22⋊C4—3321no—
1370C22⋊C4—3321no—
1371C22⋊C4—3321no—
1372C22⋊C4—3321no—
1373C22⋊C4—1662no—
1374C22⋊C4—1662no—
1375C22⋊C4—1662no—
1376C22⋊C4—1662no—
1377C22⋊C4—1662no—
1378C22⋊C4—1662no—
1379C22⋊C4—1662no—
1380C22⋊C4—1662no—
1381C22⋊C4—1662no—
1382C22⋊C4—1662no—
1383C22⋊C4—1662no—
1384C22⋊C4—1662no—
1385C22⋊C4—1662no—
1386C22⋊C4—1662no—
1387C22⋊C4—1662no—
1388C22⋊C4—1662no—
1389C42—3321no—
1390C42—3321no—
1391C42—3321no—
1392C23—21no—
1393C23—21no—
1394C23—21no—
1395C23—21no—
1396C23—28no—
1397C23—21no—
1398C23—21no—
1399C23—21no—
1400C23—21no—
1401C23—21no—
1402C23—21no—
1403C23—21no—
1404C23—21no—
1405C23—21no—
1406C23—21no—
1407C23—21no—
1408C23—21no—
1409C23—21no—
1410C23—21no—
1411C23—21no—
1412C23—21no—
1413C23—21no—
1414C23—21no—
1415C23—21no—
1416C23—44no—
1417C23—44no—
1418C23—44no—
1419C23—44no—
1420C23—44no—
1421C23—44no—
1422C23—3324no—
1423C23—3324no—
1424C23—832no—
1425C23—832no—
1426C23—6642no—
1427C23—6642no—
1428C23—6642no—
1429C23—6642no—
1430C23—1661no—
1431C23—1661no—
1432C23—1661no—
1433C23—1661no—
1434C23—1661no—
1435C23—1661no—
1436C23—1661no—
1437C23—1661no—
1438C23—1661no—
1439C23—1661no—
1440C23—1661no—
1441C23—1661no—
1442C23—1668no—
1443C23#41×D8312yes—
1444C23#1458183712yes—
1445C23#1458183712yes—
1446C23#1458183812yes—
1447C23#1458183912yes—
1448C23C24×D8311yescharacteristic
1449Q8—6642no—
1450D4—44no—
1451D4—82no—
1452D4—82no—
1453D4—3324no—
1454D4—3324no—
1455D4—3324no—
1456D4—3324no—
1457D4—6642no—
1458D4—6642no—
1459C2×C4—21no—
1460C2×C4—21no—
1461C2×C4—21no—
1462C2×C4—21no—
1463C2×C4—21no—
1464C2×C4—21no—
1465C2×C4—21no—
1466C2×C4—21no—
1467C2×C4—21no—
1468C2×C4—21no—
1469C2×C4—21no—
1470C2×C4—21no—
1471C2×C4—21no—
1472C2×C4—21no—
1473C2×C4—21no—
1474C2×C4—21no—
1475C2×C4—21no—
1476C2×C4—21no—
1477C2×C4—21no—
1478C2×C4—21no—
1479C2×C4—21no—
1480C2×C4—21no—
1481C2×C4—21no—
1482C2×C4—21no—
1483C2×C4—21no—
1484C2×C4—21no—
1485C2×C4—21no—
1486C2×C4—21no—
1487C2×C4—21no—
1488C2×C4—21no—
1489C2×C4—21no—
1490C2×C4—21no—
1491C2×C4—44no—
1492C2×C4—44no—
1493C2×C4—44no—
1494C2×C4—44no—
1495C2×C4—44no—
1496C2×C4—44no—
1497C2×C4—3324no—
1498C2×C4—6642no—
1499C2×C4—6642no—
1500C2×C4—6642no—
1501C2×C4—6642no—
1502C2×C4—6642no—
1503C2×C4—6642no—
1504C2×C4—6642no—
1505C2×C4—1661no—
1506C2×C4—1661no—
1507C2×C4—1661no—
1508C2×C4—1661no—
1509C2×C4—1661no—
1510C2×C4—1661no—
1511C2×C4—1661no—
1512C2×C4—1661no—
1513C2×C4—1661no—
1514C2×C4—1661no—
1515C2×C4—1661no—
1516C2×C4—1661no—
1517C2×C4—1661no—
1518C2×C4—1661no—
1519C2×C4—1661no—
1520C2×C4—1661no—
1521C2×C4—1661no—
1522C2×C4—1661no—
1523C2×C4—1661no—
1524C2×C4—1661no—
1525C2×C4—1661no—
1526C2×C4—1661no—
1527C2×C4—1661no—
1528C2×C4—1661no—
1529C2×C4—1661no—
1530C2×C4—1661no—
1531C2×C4—1661no—
1532C2×C4—1661no—
1533C2×C4—1661no—
1534C2×C4—1661no—
1535C2×C4—1661no—
1536C2×C4—1661no—
1537C2×C4—1661no—
1538C2×C4—1661no—
1539C2×C4—1661no—
1540C2×C4—1661no—
1541C2×C4—1661no—
1542C2×C4—1661no—
1543C2×C4—1661no—
1544C2×C4—1661no—
1545C2×C4—1661no—
1546C2×C4—1661no—
1547C2×C4#1458183712yes—
1548C22—22no—
1549C22—22no—
1550C22—22no—
1551C22—22no—
1552C22—22no—
1553C22—22no—
1554C22—22no—
1555C22—22no—
1556C22—22no—
1557C22—22no—
1558C22—22no—
1559C22—22no—
1560C22—416no—
1561C22—41no—
1562C22—41no—
1563C22—41no—
1564C22—41no—
1565C22—41no—
1566C22—41no—
1567C22—41no—
1568C22—41no—
1569C22—41no—
1570C22—41no—
1571C22—41no—
1572C22—41no—
1573C22—41no—
1574C22—41no—
1575C22—41no—
1576C22—3321no—
1577C22—3321no—
1578C22—3321no—
1579C22—3321no—
1580C22—3321no—
1581C22—3321no—
1582C22—3321no—
1583C22—3321no—
1584C22—6648no—
1585C22—1662no—
1586C22—1662no—
1587C22—1662no—
1588C22—1662no—
1589C22—1662no—
1590C22—1662no—
1591C22#1912829414yes—
1592C22C2×#41×D8311yescharacteristic
1593C22C2×#1458183711yescharacteristic
1594C22C2×#1458183711yescharacteristic
1595C22C2×#1458183711yescharacteristic
1596C22C2×#1458183811yescharacteristic
1597C22C2×#1458183911yescharacteristic
1598C22#1912853711yescharacteristic
1599C4—22no—
1600C4—41no—
1601C4—41no—
1602C4—41no—
1603C4—41no—
1604C4—41no—
1605C4—41no—
1606C4—41no—
1607C4—41no—
1608C4—41no—
1609C4—41no—
1610C4—3321no—
1611C4—3321no—
1612C4—3321no—
1613C4—3321no—
1614C4—3321no—
1615C4—3321no—
1616C4—3321no—
1617C4—3321no—
1618C4—3321no—
1619C4—3321no—
1620C4—3321no—
1621C4—3321no—
1622C4—3321no—
1623C4—3321no—
1624C2—24no—
1625C2—42no—
1626C2—42no—
1627C2—81no—
1628C2—3322no—
1629C2—3322no—
1630C2C2×#1912829411yescharacteristic
1631C2#2492114611yescharacteristic
1632C2#2492129111yescharacteristic
1633C2#2492161811yescharacteristic
1634C2#2492165711yescharacteristic
1635C2#2492166611yescharacteristic
1636C2#2492169011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutator, socle, cosocleC23×C83C25
FittingC83×#2849C2
prime radical#24910833C2
hypercenter#2849D83
hypocenterC83#36775
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2849

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #24915750C2semidirect
2. #24915135C2semidirect
3. #24914697C2semidirect
4. #24914647C2semidirect
5. #24914642C2semidirect
6. #24914599C2semidirect
7. #24914436C2semidirect
8. #24914179C2semidirect
9. #24914177C2semidirect
10. #24914145C2semidirect
11. #24914014C2semidirect
12. #24913996C2semidirect
13. #24913969C2semidirect
14. #24913968C2semidirect
15. #24913939C2semidirect
16. #24913884C2semidirect
17. #24913815C2semidirect
18. #24913435C2semidirect
19. #24913418C2semidirect
20. #24911968C2semidirect
21. #24911708C2semidirect
22. #24911291C2semidirect
23. #24911128C2semidirect
24. #24910921C2semidirect
25. #24910858C2semidirect
27. #24910788C2semidirect
28. #24910126C2semidirect
29. #24910074C2semidirect
30. C2×#19127580C2semidirect
31. C83×#2849C2semidirect
33. C2×#14581785C22semidirect
36. C2×#14581774C22semidirect
37. C2×#14581773C22semidirect
39. C2×#14581771C22semidirect
40. C2×#14581771C22semidirect
41. C2×#14581770C22semidirect
51. C83⋊#401C22semidirect
52. #19127643C22semidirect
53. #19127643C22semidirect
54. #19127643C22semidirect
55. #19127642C22semidirect
56. #19127642C22semidirect
57. #19127642C22semidirect
58. #19127641C22semidirect
59. #19127641C22semidirect
60. #19127640C22semidirect
61. #19127640C22semidirect
62. #19127639C22semidirect
63. #19127637C22semidirect
64. #19127636C22semidirect
65. #19127635C22semidirect
66. #19127634C22semidirect
67. #19127633C22semidirect
68. #19127633C22semidirect
69. #19127632C22semidirect
70. #19127631C22semidirect
71. #19127630C22semidirect
72. #19127629C22semidirect
73. #19127629C22semidirect
74. #19127629C22semidirect
75. #19127629C22semidirect
76. #19127628C22semidirect
77. #19127626C22semidirect
78. #19127626C22semidirect
79. #19127626C22semidirect
80. #19127625C22semidirect
81. #19127624C22semidirect
82. #19127624C22semidirect
83. #19127624C22semidirect
84. #19127623C22semidirect
89. #19127617C22semidirect
92. #19127616C22semidirect
93. #19127615C22semidirect
94. #19127615C22semidirect
95. #19127614C22semidirect
96. #19127613C22semidirect
99. #19127605C22semidirect
100. #19127601C22semidirect
101. #19127601C22semidirect
102. #19127600C22semidirect
103. #19127595C22semidirect
104. #19127594C22semidirect
105. #19127593C22semidirect
106. #19127593C22semidirect
107. #19127590C22semidirect
108. #19127590C22semidirect
109. #19127589C22semidirect
110. #19127589C22semidirect
111. #19127589C22semidirect
112. #19127588C22semidirect
113. #19127584C22semidirect
114. #19127584C22semidirect
117. #19127581C22semidirect
126. #19127578C22semidirect
127. #19127578C22semidirect
132. #19127577C22semidirect
136. #19127576C22semidirect
137. #19127575C22semidirect
138. #19127575C22semidirect
139. #19127575C22semidirect
140. #19127575C22semidirect
143. #19127574C22semidirect
144. #19127574C22semidirect
145. #19127574C22semidirect
146. #19127574C22semidirect
150. #19127572C22semidirect
151. #19127572C22semidirect
152. #19127572C22semidirect
153. #19127566C22semidirect
154. #19127563C22semidirect
156. #19127561C22semidirect
157. #19127561C22semidirect
158. #19127560C22semidirect
159. #19127560C22semidirect
160. #19127560C22semidirect
163. #19127559C22semidirect
164. #19127558C22semidirect
165. #19127558C22semidirect
173. C2×#123×C83C22semidirect
174. C2×#123×C83C22semidirect
178. #386×C83C22semidirect
179. #386×C83C22semidirect
182. #385×C83C22semidirect
183. #385×C83C22semidirect
184. #381×C83C22semidirect
185. #381×C83C22semidirect
819. #2849D83semidirect
850. C83#36775semidirect
858. C2×#123C2×D83semidirect
859. C2×#123C2×D83semidirect
958. #386C2×D83semidirect
959. #386C2×D83semidirect
982. #385C2×D83semidirect
983. #385C2×D83semidirect
986. #381C2×D83semidirect
987. #381C2×D83semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#249157502
#249151352
#249146972
#249146472
#249146422
#249145992
#249144362
#249141792
#249141772
#249141452
#249140142
#249139962
#249139692
#249139682
#249139392
#249138842
#249138152
#249134352
#249134182
#249119682
#249117082
#249112912
#249111282
#249109212
#249108582
#249108332
#249107882
#249101262
#249100742
C2×#191275802
C83×#28492
#3677583