Finite Group Databasebeta

← #35611571

Subgroups — #35611571

Order 21248.

2034 conjugacy classes of subgroups.

The subgroup lattice has 1574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24915749C211yesmaximal, characteristic, complemented
2#24915742C211yesmaximal, characteristic
3#24914661C211yesmaximal, characteristic, complemented
4#24914657C211yesmaximal, characteristic, complemented
5#24914592C211yesmaximal, characteristic, complemented
6#24914588C211yesmaximal, characteristic, complemented
7#24914583C211yesmaximal, characteristic, complemented
8#24914571C211yesmaximal, characteristic, complemented
9#24914304C211yesmaximal, characteristic, complemented
10#24914302C211yesmaximal, characteristic, complemented
11#24914097C211yesmaximal, characteristic, complemented
12#24914085C211yesmaximal, characteristic, complemented
13#24913960C211yesmaximal, characteristic, complemented
14#24913956C211yesmaximal, characteristic, complemented
15#24913940C211yesmaximal, characteristic, complemented
16#24913720C211yesmaximal, characteristic, complemented
17#24913718C211yesmaximal, characteristic, complemented
18#24913578C211yesmaximal, characteristic, complemented
19#24913394C211yesmaximal, characteristic, complemented
20#24911720C211yesmaximal, characteristic, complemented
21#24911719C211yesmaximal, characteristic, complemented
22#24911595C211yesmaximal, characteristic, complemented
23#24911590C211yesmaximal, characteristic, complemented
24#24911273C211yesmaximal, characteristic, complemented
25#24911271C211yesmaximal, characteristic, complemented
26#24910924C211yesmaximal, characteristic, complemented
27#24910920C211yesmaximal, characteristic, complemented
28#24910190C211yesmaximal, characteristic, complemented
29#24910165C211yesmaximal, characteristic, complemented
30#380×D83C211yesmaximal, characteristic, complemented
31C83×#2691C211yesmaximal, characteristic, complemented
32C23×C4×D83C2211yescharacteristic
33C2×#14581785C2211yescharacteristic, complemented
34C2×#14581778C2211yescharacteristic
35C2×#14581778C2211yescharacteristic
36C2×#14581776C2211yescharacteristic
37C2×#14581775C2211yescharacteristic
38C2×#14581772C2211yescharacteristic
39C2×#14581771C2211yescharacteristic, complemented
40C2×#14581770C2211yescharacteristic
41C2×#14581770C2211yescharacteristic
42C2×#14581770C2211yescharacteristic
43C2×#14581769C2211yescharacteristic
44C2×#14581769C2211yescharacteristic, complemented
45C2×#14581763C2211yescharacteristic
46C2×#14581763C2211yescharacteristic
47C2×#14581760C2211yescharacteristic
48C2×#14581760C2211yescharacteristic
49C2×C4×C22⋊D83C2211yescharacteristic
50C2×(C22⋊D83)⋊C4C2211yescharacteristic
51C2×C4⋊C4×D83C2211yescharacteristic
52C2×C4⋊C4×D83C2211yescharacteristic
53C2×C22⋊C4×D83C2211yescharacteristic
54C2×C22⋊C4×D83C2211yescharacteristic
55#19127642C2211yescharacteristic, complemented
56#19127641C2211yescharacteristic, complemented
57#19127640C2211yescharacteristic, complemented
58#19127640C2211yescharacteristic, complemented
59#19127639C2211yescharacteristic, complemented
60#19127639C2211yescharacteristic, complemented
61#19127637C2211yescharacteristic
62#19127637C2211yescharacteristic
63#19127637C2211yescharacteristic, complemented
64#19127637C2211yescharacteristic, complemented
65#19127635C2211yescharacteristic, complemented
66#19127634C2211yescharacteristic, complemented
67#19127634C2211yescharacteristic, complemented
68#19127634C2211yescharacteristic, complemented
69#19127632C2211yescharacteristic, complemented
70#19127630C2211yescharacteristic
71#19127630C2211yescharacteristic
72#19127629C2211yescharacteristic, complemented
73#19127629C2211yescharacteristic, complemented
74#19127628C2211yescharacteristic
75#19127627C2211yescharacteristic
76#19127626C2211yescharacteristic, complemented
77#19127624C2211yescharacteristic, complemented
78#19127624C2211yescharacteristic, complemented
79#19127624C2211yescharacteristic, complemented
80#19127622C2211yescharacteristic, complemented
81#19127622C2211yescharacteristic, complemented
82#19127622C2211yescharacteristic, complemented
83#19127622C2211yescharacteristic, complemented
84#19127621C2211yescharacteristic, complemented
85#19127621C2211yescharacteristic, complemented
86#19127617C2211yescharacteristic
87#19127617C2211yescharacteristic
88#19127616C2211yescharacteristic
89#19127616C2211yescharacteristic
90#19127615C2211yescharacteristic
91#19127615C2211yescharacteristic
92#19127615C2211yescharacteristic, complemented
93#19127613C2211yescharacteristic
94#19127613C2211yescharacteristic
95#19127613C2211yescharacteristic, complemented
96#19127613C2211yescharacteristic, complemented
97#19127607C2211yescharacteristic, complemented
98#19127605C2211yescharacteristic, complemented
99#19127604C2211yescharacteristic
100#19127600C2211yescharacteristic, complemented
101#19127600C2211yescharacteristic, complemented
102#19127598C2211yescharacteristic, complemented
103#19127596C2211yescharacteristic, complemented
104#19127595C2211yescharacteristic
105#19127595C2211yescharacteristic, complemented
106#19127595C2211yescharacteristic, complemented
107#19127594C2211yescharacteristic
108#19127594C2211yescharacteristic
109#19127592C2211yescharacteristic
110#19127591C2211yescharacteristic
111#19127591C2211yescharacteristic
112#19127590C2211yescharacteristic
113#19127589C2211yescharacteristic
114#19127589C2211yescharacteristic, complemented
115#19127589C2211yescharacteristic, complemented
116#19127588C2211yescharacteristic, complemented
117#19127587C2211yescharacteristic, complemented
118#19127586C2211yescharacteristic, complemented
119#19127585C2211yescharacteristic, complemented
120#19127584C2211yescharacteristic, complemented
121#19127584C2211yescharacteristic, complemented
122#19127584C2211yescharacteristic, complemented
123#19127583C2211yescharacteristic, complemented
124#19127583C2211yescharacteristic, complemented
125#19127582C2211yescharacteristic, complemented
126#19127582C2211yescharacteristic, complemented
127#19127581C2211yescharacteristic
128#19127581C2211yescharacteristic
129#19127581C2211yescharacteristic
130#19127581C2211yescharacteristic, complemented
131#19127577C2211yescharacteristic
132#19127577C2211yescharacteristic
133#19127577C2211yescharacteristic
134#19127577C2211yescharacteristic
135#19127577C2211yescharacteristic
136#19127577C2211yescharacteristic
137#19127577C2211yescharacteristic
138#19127577C2211yescharacteristic
139#19127577C2211yescharacteristic
140#19127577C2211yescharacteristic
141#19127576C2211yescharacteristic, complemented
142#19127575C2211yescharacteristic
143#19127575C2211yescharacteristic
144#19127575C2211yescharacteristic
145#19127575C2211yescharacteristic
146#19127574C2211yescharacteristic
147#19127574C2211yescharacteristic, complemented
148#19127573C2211yescharacteristic, complemented
149#19127572C2211yescharacteristic
150#19127572C2211yescharacteristic
151#19127561C2211yescharacteristic
152#19127561C2211yescharacteristic
153#19127560C2211yescharacteristic
154#19127560C2211yescharacteristic
155#19127560C2211yescharacteristic
156#19127560C2211yescharacteristic
157#19127560C2211yescharacteristic
158#19127559C2211yescharacteristic
159#19127559C2211yescharacteristic
160#19127559C2211yescharacteristic
161#19127558C2211yescharacteristic
162#19127558C2211yescharacteristic
163#19127558C2211yescharacteristic
164#19127558C2211yescharacteristic
165#19127558C2211yescharacteristic
166#19127556C2211yescharacteristic
167#19127556C2211yescharacteristic
168C4×(C2×D83)⋊C4C2211yescharacteristic
169#19127548C2211yescharacteristic
170#95×D83C2211yescharacteristic
171#95×D83C2211yescharacteristic
172C2×#126×C83C2211yescharacteristic, complemented
173C2×#121×C83C2211yescharacteristic
174#398×C83C2211yescharacteristic, complemented
175#397×C83C2211yescharacteristic, complemented
176#396×C83C2211yescharacteristic, complemented
177#394×C83C2211yescharacteristic
178#394×C83C2211yescharacteristic
179#394×C83C2211yescharacteristic, complemented
180#390×C83C2211yescharacteristic
181#387×C83C2211yescharacteristic, complemented
182#386×C83C2211yescharacteristic
183#386×C83C2211yescharacteristic, complemented
184#385×C83C2211yescharacteristic
185#385×C83C2211yescharacteristic, complemented
186#380×C83C2211yescharacteristic
187C24×D83C2311yescharacteristic
188C22×Dic166C2311yescharacteristic
189C22×Dic166C2311yescharacteristic
190C22×Dic166C2311yescharacteristic
191C22×C22⋊D83C2311yescharacteristic
192C22×C22⋊D83C2311yescharacteristic
193C22×C22⋊D83C2311yescharacteristic
194C22×C22⋊D83C2311yescharacteristic
195C23×Dic83C2311yescharacteristic
196C23×Dic83C2311yescharacteristic
197C22×C4×D83—24no—
198C22×C4×D83—42no—
199C22×C4×D83—42no—
200C22×C4×D83C2311yescharacteristic
201C22×C4×D83C2311yescharacteristic
202C22×C4×D83C2311yescharacteristic
203C22×C4×D83C2311yescharacteristic
204C22×C4×D83C2311yescharacteristic
205C22×C4×D83C2311yescharacteristic
206C22×C4×D83C2311yescharacteristic
207C22×C4×D83C2311yescharacteristic
208#14581785—42no—
209#14581778—42no—
210#14581778—42no—
211#14581776—42no—
212#14581775—42no—
213#14581772—42no—
214#14581771—42no—
215#14581770—24no—
216#14581770—42no—
217#14581770—42no—
218#14581769—42no—
219#14581769—42no—
220#14581763—24no—
221#14581763—42no—
222#14581760—42no—
223#14581760—42no—
224C4×C22⋊D83—42no—
225(C22⋊D83)⋊C4—42no—
226C2×C4⋊Dic83C2311yescharacteristic
227C2×C4⋊Dic83C2311yescharacteristic
228C2×C4⋊Dic83C2311yescharacteristic
229C2×C4⋊Dic83C2311yescharacteristic
230C2×C4⋊Dic83C2311yescharacteristic
231C2×C4⋊Dic83C2311yescharacteristic
232C2×C4⋊Dic83C2311yescharacteristic
233C2×C4⋊Dic83C2311yescharacteristic
234C2×C4⋊Dic83C2311yescharacteristic
235C2×C4⋊Dic83C2311yescharacteristic
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×Dic83⋊C4C2311yescharacteristic
246C2×Dic83⋊C4C2311yescharacteristic
247C2×Dic83⋊C4C2311yescharacteristic
248C2×Dic83⋊C4C2311yescharacteristic
249C2×Dic83⋊C4C2311yescharacteristic
250C2×Dic83⋊C4C2311yescharacteristic
251C2×Dic83⋊C4C2311yescharacteristic
252C2×Dic83⋊C4C2311yescharacteristic
253C2×Dic83⋊C4C2311yescharacteristic
254C4⋊C4×D83—42no—
255C4⋊C4×D83—42no—
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×C22⋊Dic83C2311yescharacteristic
268C2×C22⋊Dic83C2311yescharacteristic
269C2×C22⋊Dic83C2311yescharacteristic
270C2×C22⋊Dic83C2311yescharacteristic
271C2×C22⋊Dic83C2311yescharacteristic
272C2×C22⋊Dic83C2311yescharacteristic
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
287C2×(C2×D83)⋊C4C2311yescharacteristic
288C2×(C2×D83)⋊C4C2311yescharacteristic
289C22⋊C4×D83—42no—
290C22⋊C4×D83—42no—
291C2×C4×Dic83C2311yescharacteristic
292C2×C4×Dic83C2311yescharacteristic
293C2×C4×Dic83C2311yescharacteristic
294C2×C4×Dic83C2311yescharacteristic
295C2×C4×Dic83C2311yescharacteristic
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
328C83⋊#95C2311yescharacteristic
329C83⋊#95C2311yescharacteristic
330C83⋊#95C2311yescharacteristic
331C83⋊#95C2311yescharacteristic
332C22×D4×C83C2311yescharacteristic
333C22×D4×C83C2311yescharacteristic
334C22×D4×C83C2311yescharacteristic
335C23×C4×C83C2311yescharacteristic
336C23×C4×C83C2311yescharacteristic
337#126×C83—42no—
338#121×C83—42no—
339C2×C4⋊C4×C83C2311yescharacteristic
340C2×C4⋊C4×C83C2311yescharacteristic
341C2×C4⋊C4×C83C2311yescharacteristic
342C2×C4⋊C4×C83C2311yescharacteristic
343C2×C4⋊C4×C83C2311yescharacteristic
344C2×C4⋊C4×C83C2311yescharacteristic
345C2×C4⋊C4×C83C2311yescharacteristic
346C2×C4⋊C4×C83C2311yescharacteristic
347C2×C22⋊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×C42×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—22no—
372C23×D83—22no—
373C23×D83—22no—
374C23×D83—41no—
375C23×D83—41no—
376C23×D83C2411yescharacteristic
377C23×D83C2411yescharacteristic
378C2×Dic166—22no—
379C2×Dic166—41no—
380C2×Dic166—41no—
381C2×Dic166—41no—
382C2×Dic166—41no—
383C2×Dic166—41no—
384C2×Dic166—41no—
385C2×Dic166—41no—
386C2×Dic166—41no—
387C2×C22⋊D83—22no—
388C2×C22⋊D83—22no—
389C2×C22⋊D83—22no—
390C2×C22⋊D83—22no—
391C2×C22⋊D83—22no—
392C2×C22⋊D83—22no—
393C2×C22⋊D83—22no—
394C2×C22⋊D83—22no—
395C2×C22⋊D83—41no—
396C2×C22⋊D83—41no—
397C2×C22⋊D83—41no—
398C2×C22⋊D83—41no—
399C22×Dic83—22no—
400C22×Dic83—22no—
401C22×Dic83—41no—
402C22×Dic83—41no—
403C22×Dic83—41no—
404C22×Dic83—41no—
405C22×Dic83C2411yescharacteristic
406C22×Dic83C2411yescharacteristic
407C22×Dic83C2411yescharacteristic
408C22×Dic83C2411yescharacteristic
409C22×Dic83C2411yescharacteristic
410C22×Dic83C2411yescharacteristic
411C22×Dic83C2411yescharacteristic
412C22×Dic83C2411yescharacteristic
413C22×Dic83C2411yescharacteristic
414C22×Dic83C2411yescharacteristic
415C22×Dic83C2411yescharacteristic
416C22×Dic83C2411yescharacteristic
417C22×Dic83C2411yescharacteristic
418C22×Dic83C2411yescharacteristic
419C2×C4×D83—22no—
420C2×C4×D83—22no—
421C2×C4×D83—22no—
422C2×C4×D83—22no—
423C2×C4×D83—22no—
424C2×C4×D83—22no—
425C2×C4×D83—22no—
426C2×C4×D83—22no—
427C2×C4×D83—22no—
428C2×C4×D83—22no—
429C2×C4×D83—22no—
430C2×C4×D83—416no—
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—
438C2×C4×D83—41no—
439C2×C4×D83—41no—
440C2×C4×D83—41no—
441C2×C4×D83—41no—
442C2×C4×D83—41no—
443C2×C4×D83#4114yes—
444C4⋊Dic83—22no—
445C4⋊Dic83—22no—
446C4⋊Dic83—22no—
447C4⋊Dic83—41no—
448C4⋊Dic83—41no—
449C4⋊Dic83—41no—
450C4⋊Dic83—41no—
451C4⋊Dic83—41no—
452C4⋊Dic83—41no—
453C4⋊Dic83—41no—
454Dic83⋊C4—22no—
455Dic83⋊C4—22no—
456Dic83⋊C4—22no—
457Dic83⋊C4—22no—
458Dic83⋊C4—22no—
459Dic83⋊C4—22no—
460Dic83⋊C4—41no—
461Dic83⋊C4—41no—
462Dic83⋊C4—41no—
463Dic83⋊C4—41no—
464Dic83⋊C4—41no—
465Dic83⋊C4—41no—
466Dic83⋊C4—41no—
467Dic83⋊C4—41no—
468Dic83⋊C4—41no—
469Dic83⋊C4—41no—
470Dic83⋊C4—41no—
471Dic83⋊C4—41no—
472C22⋊Dic83—22no—
473C22⋊Dic83—22no—
474C22⋊Dic83—22no—
475C22⋊Dic83—22no—
476C22⋊Dic83—22no—
477C22⋊Dic83—41no—
478C22⋊Dic83—41no—
479C22⋊Dic83—41no—
480C22⋊Dic83—41no—
481C22⋊Dic83—41no—
482C22⋊Dic83—41no—
483C22⋊Dic83—41no—
484C22⋊Dic83—41no—
485C22⋊Dic83—41no—
486C22⋊Dic83—41no—
487C22⋊Dic83—41no—
488C22⋊Dic83—41no—
489(C2×D83)⋊C4—22no—
490(C2×D83)⋊C4—22no—
491(C2×D83)⋊C4—22no—
492(C2×D83)⋊C4—22no—
493(C2×D83)⋊C4—22no—
494(C2×D83)⋊C4—22no—
495(C2×D83)⋊C4—22no—
496(C2×D83)⋊C4—22no—
497(C2×D83)⋊C4—22no—
498(C2×D83)⋊C4—22no—
499(C2×D83)⋊C4—22no—
500(C2×D83)⋊C4—22no—
501(C2×D83)⋊C4—41no—
502(C2×D83)⋊C4—41no—
503(C2×D83)⋊C4—41no—
504(C2×D83)⋊C4—41no—
505C4×Dic83—41no—
506C4×Dic83—41no—
507C4×Dic83—41no—
508C4×Dic83—41no—
509C4×Dic83—41no—
510C24×C83C2411yescharacteristic
511C24×C83C2411yescharacteristic
512C24×C83C2411yescharacteristic
513C2×D4×C83—22no—
514C2×D4×C83—22no—
515C2×D4×C83—22no—
516C2×D4×C83—41no—
517C2×D4×C83—41no—
518C2×D4×C83—41no—
519C2×D4×C83—41no—
520C2×D4×C83—41no—
521C2×D4×C83—41no—
522C22×C4×C83—22no—
523C22×C4×C83—22no—
524C22×C4×C83—41no—
525C22×C4×C83—41no—
526C22×C4×C83—41no—
527C22×C4×C83—41no—
528C22×C4×C83C2411yescharacteristic
529C22×C4×C83C2411yescharacteristic
530C22×C4×C83C2411yescharacteristic
531C22×C4×C83C2411yescharacteristic
532C22×C4×C83C2411yescharacteristic
533C22×C4×C83C2411yescharacteristic
534C22×C4×C83C2411yescharacteristic
535C22×C4×C83C2411yescharacteristic
536C22×C4×C83C2411yescharacteristic
537C22×C4×C83C2411yescharacteristic
538C22×C4×C83C2411yescharacteristic
539C22×C4×C83C2411yescharacteristic
540C4⋊C4×C83—22no—
541C4⋊C4×C83—22no—
542C4⋊C4×C83—22no—
543C4⋊C4×C83—41no—
544C4⋊C4×C83—41no—
545C4⋊C4×C83—41no—
546C4⋊C4×C83—41no—
547C4⋊C4×C83—41no—
548C22⋊C4×C83—22no—
549C22⋊C4×C83—22no—
550C22⋊C4×C83—22no—
551C22⋊C4×C83—41no—
552C22⋊C4×C83—41no—
553C22⋊C4×C83—41no—
554C22⋊C4×C83—41no—
555C22⋊C4×C83—41no—
556C22⋊C4×C83—41no—
557C22⋊C4×C83—41no—
558C22⋊C4×C83—41no—
559C22⋊C4×C83—41no—
560C22⋊C4×C83—41no—
561C42×C83—41no—
562C23×C83—21no—
563C23×C83—21no—
564C23×C83—21no—
565C23×C83—21no—
566C23×C83—21no—
567C23×C83—21no—
568C23×C83—21no—
569C23×C83—21no—
570C23×C83—21no—
571C23×C83—21no—
572C23×C83—21no—
573C23×C83—21no—
574C23×C83—21no—
575C23×C83—21no—
576C23×C83—21no—
577C23×C83—21no—
578C23×C83—21no—
579C23×C83—21no—
580C23×C83—21no—
581C23×C83—21no—
582C23×C832−1+412yes—
583C23×C83C2511yescharacteristic
584C22×D83—21no—
585C22×D83—21no—
586C22×D83—21no—
587C22×D83—21no—
588C22×D83—28no—
589C22×D83—21no—
590C22×D83—21no—
591C22×D83—21no—
592C22×D83—21no—
593C22×D83—21no—
594C22×D83—21no—
595C22×D83—44no—
596C22×D83—44no—
597C22×D83—44no—
598C22×D83—44no—
599C22×D83—44no—
600C22×D83—44no—
601C22×D83C2×#4112yes—
602C22×D83H(5,𝔽2)12yes—
603C22×D83H(5,𝔽2)12yes—
604C22×D832−1+412yes—
605D4×C83—82no—
606D4×C83—82no—
607D4×C83—82no—
608C2×C4×C83—21no—
609C2×C4×C83—21no—
610C2×C4×C83—21no—
611C2×C4×C83—21no—
612C2×C4×C83—21no—
613C2×C4×C83—21no—
614C2×C4×C83—21no—
615C2×C4×C83—21no—
616C2×C4×C83—21no—
617C2×C4×C83—21no—
618C2×C4×C83—21no—
619C2×C4×C83—21no—
620C2×C4×C83—21no—
621C2×C4×C83—21no—
622C2×C4×C83—21no—
623C2×C4×C83—21no—
624C2×C4×C83—21no—
625C2×C4×C83—21no—
626C2×C4×C83—21no—
627C2×C4×C83—21no—
628C2×C4×C83—21no—
629C2×C4×C83—21no—
630C2×C4×C83—21no—
631C2×C4×C83—21no—
632C2×C4×C83—21no—
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—44no—
643C2×C4×C83—82no—
644C2×C4×C83C2×#4112yes—
645C2×C4×C83H(5,𝔽2)12yes—
646C22⋊D83—44no—
647C22⋊D83—44no—
648C22⋊D83—82no—
649C22⋊D83—82no—
650C2×Dic83—21no—
651C2×Dic83—21no—
652C2×Dic83—21no—
653C2×Dic83—21no—
654C2×Dic83—21no—
655C2×Dic83—21no—
656C2×Dic83—21no—
657C2×Dic83—21no—
658C2×Dic83—21no—
659C2×Dic83—21no—
660C2×Dic83—21no—
661C2×Dic83—21no—
662C2×Dic83—21no—
663C2×Dic83—21no—
664C2×Dic83—21no—
665C2×Dic83—21no—
666C2×Dic83—21no—
667C2×Dic83—21no—
668C2×Dic83—21no—
669C2×Dic83—21no—
670C2×Dic83—21no—
671C2×Dic83—21no—
672C2×Dic83—21no—
673C2×Dic83—21no—
674C2×Dic83—21no—
675C2×Dic83—21no—
676C2×Dic83—21no—
677C2×Dic83—21no—
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—44no—
691C2×Dic83—82no—
692C2×Dic83C2×#4112yes—
693C2×Dic83H(5,𝔽2)12yes—
694C4×D83—28no—
695C4×D83—44no—
696C4×D83—44no—
697C4×D83—44no—
698C4×D83—82no—
699C4×D83—82no—
700C4×D83—82no—
701C4×D83—82no—
702Dic166—82no—
703Dic166—82no—
704Dic166—82no—
705C22×C83—22no—
706C22×C83—22no—
707C22×C83—22no—
708C22×C83—41no—
709C22×C83—41no—
710C22×C83—41no—
711C22×C83—41no—
712C22×C83—41no—
713C22×C83—41no—
714C22×C83—41no—
715C22×C83—41no—
716C22×C83—41no—
717C22×C83—41no—
718C22×C83—41no—
719C22×C83—41no—
720C22×C83—41no—
721C22×C83—41no—
722C22×C83—41no—
723C22×C83—41no—
724C22×C83—41no—
725C22×C83—41no—
726C22×C83C22×#4111yescharacteristic
727C22×C83C2×H(5,𝔽2)11yescharacteristic
728C22×C83C2×H(5,𝔽2)11yescharacteristic
729C22×C83C2×H(5,𝔽2)11yescharacteristic
730C22×C83C2×H(5,𝔽2)11yescharacteristic
731C22×C83C2×2−1+411yescharacteristic
732C22×C83C2×2−1+411yescharacteristic
733C2×D83—22no—
734C2×D83—22no—
735C2×D83—22no—
736C2×D83—22no—
737C2×D83—22no—
738C2×D83—22no—
739C2×D83—22no—
740C2×D83—22no—
741C2×D83—22no—
742C2×D83—416no—
743C2×D83—41no—
744C2×D83—41no—
745C2×D83—41no—
746C2×D83—41no—
747C2×D83#54214yes—
748C4×C83—22no—
749C4×C83—22no—
750C4×C83—41no—
751C4×C83—41no—
752C4×C83—41no—
753C4×C83—41no—
754C4×C83—41no—
755C4×C83—41no—
756C4×C83—41no—
757C4×C83—41no—
758C4×C83—41no—
759C4×C83—41no—
760Dic83—22no—
761Dic83—22no—
762Dic83—41no—
763Dic83—41no—
764Dic83—41no—
765Dic83—41no—
766Dic83—41no—
767Dic83—41no—
768Dic83—41no—
769Dic83—41no—
770Dic83—41no—
771Dic83—41no—
772Dic83—41no—
773Dic83—41no—
774#36729—831nomaximal, Sylow
775C2×C83—42no—
776C2×C83—81no—
777C2×C83—81no—
778C2×C83C2×#54211yescharacteristic
779C2×C83#349011yescharacteristic
780C2×C83#349211yescharacteristic
781C2×C83#353611yescharacteristic
782C2×C83#353611yescharacteristic
783C2×C83#353711yescharacteristic
784C2×C83#353811yescharacteristic
785D83—24no—
786D83—42no—
787#2848—831no—
788#2847—831no—
789#2747—831no—
790#2747—831no—
791#2742—831no—
792#2742—831no—
793#2741—831no—
794#2741—831no—
795#2717—831no—
796#2717—831no—
797#2702—831no—
798#2702—831no—
799#2692—831no—
800#2692—831no—
801#2691—831no—
802#2691D8311yescharacteristic, complemented
803#2672—831no—
804#2672—831no—
805#2659—831no—
806#2639—831no—
807#2481—831no—
808#2481—831no—
809#2472—831no—
810#2472—831no—
811#2449—831no—
812#2449—831no—
813#2418—831no—
814#2418—831no—
815#2329—831no—
816#2325—831no—
817C2×#380—831no—
818C83#3672911yescharacteristic, complemented, Sylow
819C24×C4—831no—
820C2×#126—831no—
821C2×#126C2×D8311yescharacteristic, complemented
822C2×#124—831no—
823C2×#124—831no—
824C2×#123—831no—
825C2×#123—831no—
826C2×C22⋊Q8—831no—
827C2×C22⋊Q8—831no—
828C2×C22⋊Q8—831no—
829C2×C22⋊Q8—831no—
830C2×C22⋊Q8—831no—
831C2×C22⋊Q8—831no—
832C2×C22⋊Q8—831no—
833C2×#121—831no—
834C2×#121—831no—
835C2×#121C2×D8311yescharacteristic
836C2×#120—831no—
837C2×#120—831no—
838C2×C4×D4—831no—
839C2×C4×D4—831no—
840C22×C4⋊C4—831no—
841C22×C4⋊C4—831no—
842C22×C22⋊C4—831no—
843C22×C22⋊C4—831no—
844#400—831no—
845#400—831no—
846#400—831no—
847#400—831no—
848#400—831no—
849#400—831no—
850#399—831no—
851#399—831no—
852#399—831no—
853#399—831no—
854#398—831no—
855#398—831no—
856#398—831no—
857#398—831no—
858#398—831no—
859#398C2×D8311yescharacteristic, complemented
860#397—831no—
861#397—831no—
862#397—831no—
863#397—831no—
864#397—831no—
865#397—831no—
866#397—831no—
867#397C2×D8311yescharacteristic, complemented
868#396—831no—
869#396—831no—
870#396—831no—
871#396C2×D8311yescharacteristic, complemented
872#395—831no—
873#395—831no—
874#395—831no—
875#395—831no—
876#395—831no—
877#395—831no—
878#394—831no—
879#394—831no—
880#394—831no—
881#394—831no—
882#394—831no—
883#394—831no—
884#394—831no—
885#394C2×D8311yescharacteristic
886#394C2×D8311yescharacteristic
887#394C2×D8311yescharacteristic, complemented
888#393—831no—
889#393—831no—
890#393—831no—
891#393—831no—
892#391—831no—
893#391—831no—
894#390—831no—
895#390C2×D8311yescharacteristic
896#389—831no—
897#389—831no—
898#389—831no—
899#389—831no—
900#388—831no—
901#388—831no—
902#388—831no—
903#388—831no—
904#388—831no—
905#388—831no—
906#388—831no—
907#388—831no—
908#388—831no—
909#388—831no—
910#388—831no—
911#388—831no—
912#387—831no—
913#387—831no—
914#387—831no—
915#387—831no—
916#387—831no—
917#387—831no—
918#387—831no—
919#387—831no—
920#387—831no—
921#387—831no—
922#387—831no—
923#387C2×D8311yescharacteristic, complemented
924#386—831no—
925#386—831no—
926#386—831no—
927#386—831no—
928#386—831no—
929#386—831no—
930#386—831no—
931#386—831no—
932#386—831no—
933#386—831no—
934#386—831no—
935#386—831no—
936#386—831no—
937#386—831no—
938#386C2×D8311yescharacteristic
939#386C2×D8311yescharacteristic, complemented
940#385—831no—
941#385—831no—
942#385—831no—
943#385—831no—
944#385—831no—
945#385—831no—
946#385—831no—
947#385—831no—
948#385—831no—
949#385—831no—
950#385C2×D8311yescharacteristic
951#385C2×D8311yescharacteristic, complemented
952#380—831no—
953#380—831no—
954#380—831no—
955#380—831no—
956#380—831no—
957#380—831no—
958#380—831no—
959#380—831no—
960#380—831no—
961#380—831no—
962#380—831no—
963#380—831no—
964#380—831no—
965#380—831no—
966#380—831no—
967#380C2×D8311yescharacteristic
968#379—831no—
969#379—831no—
970C4×C22⋊C4—831no—
971C4×C22⋊C4—831no—
972C2×#95—831no—
973C2×#95—831no—
974C25—831no—
975C22×Q8—831no—
976C22×Q8—831no—
977C22×Q8—831no—
978C22×D4—831no—
979C22×D4—831no—
980C22×D4—831no—
981C22×D4—831no—
982C22×D4C22×D8311yescharacteristic
983C22×D4C22×D8311yescharacteristic
984C22×D4C22×D8311yescharacteristic
985C23×C4—3322no—
986C23×C4—3322no—
987C23×C4—831no—
988C23×C4—831no—
989C23×C4—831no—
990C23×C4—831no—
991C23×C4—831no—
992C23×C4—831no—
993C23×C4—831no—
994C23×C4—831no—
995C23×C4—831no—
996C23×C4—831no—
997C23×C4—1664no—
998C23×C4C22×D8311yescharacteristic
999C23×C4C22×D8311yescharacteristic
1000#126—42no—
1001#126—3322no—
1002#124—3322no—
1003#124—3322no—
1004#123—3322no—
1005#123—3322no—
1006C22⋊Q8—3322no—
1007C22⋊Q8—3322no—
1008C22⋊Q8—3322no—
1009C22⋊Q8—3322no—
1010C22⋊Q8—3322no—
1011C22⋊Q8—3322no—
1012C22⋊Q8—1664no—
1013#121—42no—
1014#121—3322no—
1015#121—1664no—
1016#120—3322no—
1017#120—3322no—
1018C4×D4—3322no—
1019C4×D4—3322no—
1020C2×C4⋊C4—3322no—
1021C2×C4⋊C4—3322no—
1022C2×C4⋊C4—831no—
1023C2×C4⋊C4—831no—
1024C2×C4⋊C4—831no—
1025C2×C4⋊C4—831no—
1026C2×C4⋊C4—831no—
1027C2×C4⋊C4—831no—
1028C2×C4⋊C4—831no—
1029C2×C4⋊C4—831no—
1030C2×C4⋊C4—831no—
1031C2×C4⋊C4—831no—
1032C2×C4⋊C4—831no—
1033C2×C4⋊C4—831no—
1034C2×C4⋊C4—831no—
1035C2×C4⋊C4—831no—
1036C2×C4⋊C4—831no—
1037C2×C4⋊C4—831no—
1038C2×C4⋊C4—831no—
1039C2×C4⋊C4—831no—
1040C2×C4⋊C4—831no—
1041C2×C4⋊C4—831no—
1042C2×C4⋊C4—831no—
1043C2×C4⋊C4—831no—
1044C2×C4⋊C4—831no—
1045C2×C4⋊C4—831no—
1046C2×C4⋊C4—831no—
1047C2×C4⋊C4—831no—
1048C2×C4⋊C4—831no—
1049C2×C4⋊C4—831no—
1050C2×C4⋊C4C22×D8311yescharacteristic
1051C2×C4⋊C4C22×D8311yescharacteristic
1052C2×C4⋊C4C22×D8311yescharacteristic
1053C2×C4⋊C4C22×D8311yescharacteristic
1054C2×C4⋊C4C22×D8311yescharacteristic
1055C2×C4⋊C4C22×D8311yescharacteristic
1056C2×C4⋊C4C22×D8311yescharacteristic
1057C2×C4⋊C4C22×D8311yescharacteristic
1058C2×C22⋊C4—3322no—
1059C2×C22⋊C4—3322no—
1060C2×C22⋊C4—831no—
1061C2×C22⋊C4—831no—
1062C2×C22⋊C4—831no—
1063C2×C22⋊C4—831no—
1064C2×C22⋊C4—831no—
1065C2×C22⋊C4—831no—
1066C2×C22⋊C4—831no—
1067C2×C22⋊C4—831no—
1068C2×C22⋊C4—831no—
1069C2×C22⋊C4—831no—
1070C2×C22⋊C4—831no—
1071C2×C22⋊C4—831no—
1072C2×C22⋊C4—831no—
1073C2×C22⋊C4—831no—
1074C2×C22⋊C4—831no—
1075C2×C22⋊C4—831no—
1076C2×C22⋊C4—831no—
1077C2×C22⋊C4—831no—
1078C2×C22⋊C4—831no—
1079C2×C22⋊C4—831no—
1080C2×C22⋊C4—831no—
1081C2×C22⋊C4—831no—
1082C2×C22⋊C4—831no—
1083C2×C22⋊C4—831no—
1084C2×C22⋊C4—831no—
1085C2×C22⋊C4—831no—
1086C2×C22⋊C4—831no—
1087C2×C22⋊C4—831no—
1088C2×C22⋊C4—831no—
1089C2×C22⋊C4—831no—
1090C2×C22⋊C4—831no—
1091C2×C22⋊C4—831no—
1092C2×C22⋊C4—831no—
1093C2×C22⋊C4C22×D8311yescharacteristic
1094C2×C22⋊C4C22×D8311yescharacteristic
1095C2×C22⋊C4C22×D8311yescharacteristic
1096C2×C22⋊C4C22×D8311yescharacteristic
1097C2×C22⋊C4C22×D8311yescharacteristic
1098C2×C22⋊C4C22×D8311yescharacteristic
1099C2×C22⋊C4C22×D8311yescharacteristic
1100C2×C22⋊C4C22×D8311yescharacteristic
1101C2×C22⋊C4C22×D8311yescharacteristic
1102C2×C22⋊C4C22×D8311yescharacteristic
1103C2×C22⋊C4C22×D8311yescharacteristic
1104C2×C22⋊C4C22×D8311yescharacteristic
1105C2×C22⋊C4C22×D8311yescharacteristic
1106C2×C42—831no—
1107C2×C42—831no—
1108C2×C42—831no—
1109C2×C42—831no—
1110C2×C42—831no—
1111C2×C42C22×D8311yescharacteristic
1112#95—831no—
1113#95—831no—
1114#95—831no—
1115#95—831no—
1116#95—831no—
1117#95—831no—
1118#95—831no—
1119#95—831no—
1120#95—831no—
1121#95—831no—
1122#95—831no—
1123#95—831no—
1124#95—831no—
1125#95—831no—
1126#95—831no—
1127#95—831no—
1128#95—831no—
1129#95—831no—
1130#95—831no—
1131#95—831no—
1132#95—831no—
1133#95—831no—
1134#95—831no—
1135#95—831no—
1136#95—831no—
1137#95—831no—
1138#95—831no—
1139#95—831no—
1140#95—831no—
1141#95—831no—
1142#95—831no—
1143#95—831no—
1144#95—831no—
1145#95—831no—
1146#95—831no—
1147#95—831no—
1148#95C22×D8311yescharacteristic
1149#95C22×D8311yescharacteristic
1150#95C22×D8311yescharacteristic
1151#95C22×D8311yescharacteristic
1152#95C22×D8311yescharacteristic
1153#95C22×D8311yescharacteristic
1154#95C22×D8311yescharacteristic
1155#95C22×D8311yescharacteristic
1156C24—3321no—
1157C24—3321no—
1158C24—831no—
1159C24—831no—
1160C24—1662no—
1161C24—1662no—
1162C24—1662no—
1163C24—1662no—
1164C24—1662no—
1165C24C23×D8311yescharacteristic
1166C24C23×D8311yescharacteristic
1167C24C23×D8311yescharacteristic
1168C2×Q8—3321no—
1169C2×Q8—3321no—
1170C2×Q8—3321no—
1171C2×Q8—3321no—
1172C2×Q8—3321no—
1173C2×Q8—3321no—
1174C2×Q8—3321no—
1175C2×Q8—3321no—
1176C2×Q8—1662no—
1177C2×D4—22no—
1178C2×D4—22no—
1179C2×D4—22no—
1180C2×D4—41no—
1181C2×D4—41no—
1182C2×D4—41no—
1183C2×D4—41no—
1184C2×D4—41no—
1185C2×D4—41no—
1186C2×D4—3321no—
1187C2×D4—3321no—
1188C2×D4—3321no—
1189C2×D4—3321no—
1190C2×D4—1662no—
1191C2×D4—1662no—
1192C2×D4—1662no—
1193C2×D4—1662no—
1194C2×D4—1662no—
1195C2×D4—1662no—
1196C2×D4—1662no—
1197C2×D4—1662no—
1198C22×C4—22no—
1199C22×C4—22no—
1200C22×C4—41no—
1201C22×C4—41no—
1202C22×C4—41no—
1203C22×C4—41no—
1204C22×C4—3321no—
1205C22×C4—3321no—
1206C22×C4—3321no—
1207C22×C4—3321no—
1208C22×C4—3321no—
1209C22×C4—3321no—
1210C22×C4—3321no—
1211C22×C4—3321no—
1212C22×C4—3321no—
1213C22×C4—3321no—
1214C22×C4—3321no—
1215C22×C4—3321no—
1216C22×C4—33216no—
1217C22×C4—3321no—
1218C22×C4—3321no—
1219C22×C4—3321no—
1220C22×C4—3321no—
1221C22×C4—834no—
1222C22×C4—831no—
1223C22×C4—831no—
1224C22×C4—831no—
1225C22×C4—831no—
1226C22×C4—831no—
1227C22×C4—831no—
1228C22×C4—831no—
1229C22×C4—831no—
1230C22×C4—831no—
1231C22×C4—831no—
1232C22×C4—831no—
1233C22×C4—831no—
1234C22×C4—831no—
1235C22×C4—831no—
1236C22×C4—1662no—
1237C22×C4—1662no—
1238C22×C4—1662no—
1239C22×C4—1662no—
1240C22×C4—1662no—
1241C22×C4—1662no—
1242C22×C4—1662no—
1243C22×C4—1662no—
1244C22×C4—1662no—
1245C22×C4—1662no—
1246C22×C4—1662no—
1247C22×C4—1662no—
1248C22×C4—1662no—
1249C22×C4C23×D8311yescharacteristic
1250C22×C4C23×D8311yescharacteristic
1251C22×C4C23×D8311yescharacteristic
1252C22×C4C23×D8311yescharacteristic
1253C22×C4C23×D8311yescharacteristic
1254C22×C4C23×D8311yescharacteristic
1255C22×C4C23×D8311yescharacteristic
1256C22×C4C23×D8311yescharacteristic
1257C22×C4C23×D8311yescharacteristic
1258C22×C4C23×D8311yescharacteristic
1259C22×C4C23×D8311yescharacteristic
1260C22×C4C23×D8311yescharacteristic
1261C4⋊C4—22no—
1262C4⋊C4—22no—
1263C4⋊C4—22no—
1264C4⋊C4—41no—
1265C4⋊C4—41no—
1266C4⋊C4—41no—
1267C4⋊C4—41no—
1268C4⋊C4—41no—
1269C4⋊C4—3321no—
1270C4⋊C4—3321no—
1271C4⋊C4—3321no—
1272C4⋊C4—3321no—
1273C4⋊C4—3321no—
1274C4⋊C4—3321no—
1275C4⋊C4—3321no—
1276C4⋊C4—3321no—
1277C4⋊C4—3321no—
1278C4⋊C4—3321no—
1279C4⋊C4—3321no—
1280C4⋊C4—3321no—
1281C4⋊C4—3321no—
1282C4⋊C4—3321no—
1283C4⋊C4—3321no—
1284C4⋊C4—3321no—
1285C4⋊C4—3321no—
1286C4⋊C4—3321no—
1287C4⋊C4—3321no—
1288C4⋊C4—1662no—
1289C4⋊C4—1662no—
1290C4⋊C4—1662no—
1291C4⋊C4—1662no—
1292C4⋊C4—1662no—
1293C4⋊C4—1662no—
1294C4⋊C4—1662no—
1295C4⋊C4—1662no—
1296C4⋊C4—1662no—
1297C22⋊C4—22no—
1298C22⋊C4—22no—
1299C22⋊C4—22no—
1300C22⋊C4—41no—
1301C22⋊C4—41no—
1302C22⋊C4—41no—
1303C22⋊C4—41no—
1304C22⋊C4—41no—
1305C22⋊C4—41no—
1306C22⋊C4—41no—
1307C22⋊C4—41no—
1308C22⋊C4—41no—
1309C22⋊C4—41no—
1310C22⋊C4—3321no—
1311C22⋊C4—3321no—
1312C22⋊C4—3321no—
1313C22⋊C4—3321no—
1314C22⋊C4—3321no—
1315C22⋊C4—3321no—
1316C22⋊C4—3321no—
1317C22⋊C4—3321no—
1318C22⋊C4—3321no—
1319C22⋊C4—3321no—
1320C22⋊C4—3321no—
1321C22⋊C4—3321no—
1322C22⋊C4—3321no—
1323C22⋊C4—3321no—
1324C22⋊C4—3321no—
1325C22⋊C4—3321no—
1326C22⋊C4—1662no—
1327C22⋊C4—1662no—
1328C22⋊C4—1662no—
1329C22⋊C4—1662no—
1330C22⋊C4—1662no—
1331C22⋊C4—1662no—
1332C22⋊C4—1662no—
1333C22⋊C4—1662no—
1334C22⋊C4—1662no—
1335C22⋊C4—1662no—
1336C22⋊C4—1662no—
1337C22⋊C4—1662no—
1338C22⋊C4—1662no—
1339C22⋊C4—1662no—
1340C22⋊C4—1662no—
1341C22⋊C4—1662no—
1342C22⋊C4—1662no—
1343C42—41no—
1344C42—3321no—
1345C42—3321no—
1346C42—3321no—
1347C42—3321no—
1348C42—3321no—
1349C23—21no—
1350C23—21no—
1351C23—21no—
1352C23—21no—
1353C23—21no—
1354C23—21no—
1355C23—21no—
1356C23—21no—
1357C23—21no—
1358C23—21no—
1359C23—21no—
1360C23—21no—
1361C23—21no—
1362C23—21no—
1363C23—21no—
1364C23—21no—
1365C23—21no—
1366C23—21no—
1367C23—21no—
1368C23—21no—
1369C23—3324no—
1370C23—3324no—
1371C23—3324no—
1372C23—3324no—
1373C23—3324no—
1374C23—3324no—
1375C23—832no—
1376C23—832no—
1377C23—832no—
1378C23—832no—
1379C23—1668no—
1380C23—1661no—
1381C23—1661no—
1382C23—1661no—
1383C23—1661no—
1384C23—1661no—
1385C23—1661no—
1386C23—1661no—
1387C23—1661no—
1388C23—1661no—
1389C23—1661no—
1390C23#1458183912yes—
1391C23C24×D8311yescharacteristic
1392Q8—6642no—
1393Q8—6642no—
1394Q8—6642no—
1395D4—82no—
1396D4—82no—
1397D4—82no—
1398D4—3324no—
1399D4—3324no—
1400D4—6642no—
1401D4—6642no—
1402C2×C4—21no—
1403C2×C4—21no—
1404C2×C4—21no—
1405C2×C4—21no—
1406C2×C4—21no—
1407C2×C4—21no—
1408C2×C4—21no—
1409C2×C4—21no—
1410C2×C4—21no—
1411C2×C4—21no—
1412C2×C4—21no—
1413C2×C4—21no—
1414C2×C4—21no—
1415C2×C4—21no—
1416C2×C4—21no—
1417C2×C4—21no—
1418C2×C4—21no—
1419C2×C4—21no—
1420C2×C4—21no—
1421C2×C4—21no—
1422C2×C4—21no—
1423C2×C4—21no—
1424C2×C4—21no—
1425C2×C4—21no—
1426C2×C4—21no—
1427C2×C4—21no—
1428C2×C4—21no—
1429C2×C4—21no—
1430C2×C4—21no—
1431C2×C4—21no—
1432C2×C4—21no—
1433C2×C4—21no—
1434C2×C4—21no—
1435C2×C4—21no—
1436C2×C4—44no—
1437C2×C4—82no—
1438C2×C4—3324no—
1439C2×C4—3324no—
1440C2×C4—3324no—
1441C2×C4—3324no—
1442C2×C4—832no—
1443C2×C4—832no—
1444C2×C4—6642no—
1445C2×C4—6642no—
1446C2×C4—6642no—
1447C2×C4—6642no—
1448C2×C4—6642no—
1449C2×C4—1668no—
1450C2×C4—1661no—
1451C2×C4—1661no—
1452C2×C4—1661no—
1453C2×C4—1661no—
1454C2×C4—1661no—
1455C2×C4—1661no—
1456C2×C4—1661no—
1457C2×C4—1661no—
1458C2×C4—1661no—
1459C2×C4—1661no—
1460C2×C4—1661no—
1461C2×C4—1661no—
1462C2×C4—1661no—
1463C2×C4—1661no—
1464C2×C4—1661no—
1465C2×C4—1661no—
1466C2×C4—1661no—
1467C2×C4—1661no—
1468C2×C4—1661no—
1469C2×C4—1661no—
1470C2×C4—1661no—
1471C2×C4—1661no—
1472C2×C4—1661no—
1473C2×C4—1661no—
1474C2×C4—1661no—
1475C2×C4—1661no—
1476C2×C4—1661no—
1477C2×C4—1661no—
1478C2×C4—1661no—
1479C2×C4—1661no—
1480C2×C4—1661no—
1481C2×C4—1661no—
1482C2×C4—1661no—
1483C2×C4—1661no—
1484C2×C4—1661no—
1485C2×C4—1661no—
1486C2×C4—1661no—
1487C2×C4—1661no—
1488C2×C4—1661no—
1489C2×C4—1661no—
1490C2×C4#41×D8312yes—
1491C2×C4#1458183712yes—
1492C22—22no—
1493C22—22no—
1494C22—22no—
1495C22—41no—
1496C22—41no—
1497C22—41no—
1498C22—41no—
1499C22—41no—
1500C22—41no—
1501C22—41no—
1502C22—41no—
1503C22—41no—
1504C22—41no—
1505C22—41no—
1506C22—41no—
1507C22—41no—
1508C22—41no—
1509C22—41no—
1510C22—41no—
1511C22—41no—
1512C22—41no—
1513C22—33216no—
1514C22—3321no—
1515C22—3321no—
1516C22—3321no—
1517C22—3321no—
1518C22—834no—
1519C22—1662no—
1520C22—1662no—
1521C22—1662no—
1522C22—1662no—
1523C22—1662no—
1524C22—1662no—
1525C22—1662no—
1526C22—1662no—
1527C22—1662no—
1528C22C2×#41×D8311yescharacteristic
1529C22H(5,𝔽2)×D8311yescharacteristic
1530C22H(5,𝔽2)×D8311yescharacteristic
1531C22H(5,𝔽2)×D8311yescharacteristic
1532C22C2×#1458183711yescharacteristic
1533C222−1+4×D8311yescharacteristic
1534C22C2×#1458183911yescharacteristic
1535C4—22no—
1536C4—22no—
1537C4—41no—
1538C4—41no—
1539C4—41no—
1540C4—41no—
1541C4—41no—
1542C4—41no—
1543C4—41no—
1544C4—41no—
1545C4—41no—
1546C4—41no—
1547C4—3321no—
1548C4—3321no—
1549C4—3321no—
1550C4—3321no—
1551C4—3321no—
1552C4—3321no—
1553C4—3321no—
1554C4—3321no—
1555C4—3321no—
1556C4—3321no—
1557C4—3321no—
1558C4—3321no—
1559C4—1662no—
1560C4—1662no—
1561C2—42no—
1562C2—81no—
1563C2—81no—
1564C2—3322no—
1565C2—1664no—
1566C2#542×D8311yescharacteristic
1567C2#2492114511yescharacteristic
1568C2#2492116711yescharacteristic
1569C2#2492168111yescharacteristic
1570C2#2492168311yescharacteristic
1571C2#2492169711yescharacteristic
1572C2#2492171011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutator, socle, cosocleC23×C83C25
FittingC83×#2691C2
prime radical#24915742C2
hypercenter#2691D83
hypocenterC83#36729
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2691

Complements

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

NH ≅ G/Ntype
1. #24915749C2semidirect
3. #24914661C2semidirect
4. #24914657C2semidirect
5. #24914592C2semidirect
6. #24914588C2semidirect
7. #24914583C2semidirect
8. #24914571C2semidirect
9. #24914304C2semidirect
10. #24914302C2semidirect
11. #24914097C2semidirect
12. #24914085C2semidirect
13. #24913960C2semidirect
14. #24913956C2semidirect
15. #24913940C2semidirect
16. #24913720C2semidirect
17. #24913718C2semidirect
18. #24913578C2semidirect
19. #24913394C2semidirect
20. #24911720C2semidirect
21. #24911719C2semidirect
22. #24911595C2semidirect
23. #24911590C2semidirect
24. #24911273C2semidirect
25. #24911271C2semidirect
26. #24910924C2semidirect
27. #24910920C2semidirect
28. #24910190C2semidirect
29. #24910165C2semidirect
30. #380×D83C2semidirect
31. C83×#2691C2semidirect
33. C2×#14581785C22semidirect
39. C2×#14581771C22semidirect
44. C2×#14581769C22semidirect
55. #19127642C22semidirect
56. #19127641C22semidirect
57. #19127640C22semidirect
58. #19127640C22semidirect
59. #19127639C22semidirect
60. #19127639C22semidirect
63. #19127637C22semidirect
64. #19127637C22semidirect
65. #19127635C22semidirect
66. #19127634C22semidirect
67. #19127634C22semidirect
68. #19127634C22semidirect
69. #19127632C22semidirect
72. #19127629C22semidirect
73. #19127629C22semidirect
76. #19127626C22semidirect
77. #19127624C22semidirect
78. #19127624C22semidirect
79. #19127624C22semidirect
80. #19127622C22semidirect
81. #19127622C22semidirect
82. #19127622C22semidirect
83. #19127622C22semidirect
84. #19127621C22semidirect
85. #19127621C22semidirect
92. #19127615C22semidirect
95. #19127613C22semidirect
96. #19127613C22semidirect
97. #19127607C22semidirect
98. #19127605C22semidirect
100. #19127600C22semidirect
101. #19127600C22semidirect
102. #19127598C22semidirect
103. #19127596C22semidirect
105. #19127595C22semidirect
106. #19127595C22semidirect
114. #19127589C22semidirect
115. #19127589C22semidirect
116. #19127588C22semidirect
117. #19127587C22semidirect
118. #19127586C22semidirect
119. #19127585C22semidirect
120. #19127584C22semidirect
121. #19127584C22semidirect
122. #19127584C22semidirect
123. #19127583C22semidirect
124. #19127583C22semidirect
125. #19127582C22semidirect
126. #19127582C22semidirect
130. #19127581C22semidirect
141. #19127576C22semidirect
147. #19127574C22semidirect
148. #19127573C22semidirect
172. C2×#126×C83C22semidirect
174. #398×C83C22semidirect
175. #397×C83C22semidirect
176. #396×C83C22semidirect
179. #394×C83C22semidirect
181. #387×C83C22semidirect
183. #386×C83C22semidirect
185. #385×C83C22semidirect
802. #2691D83semidirect
818. C83#36729semidirect
821. C2×#126C2×D83semidirect
859. #398C2×D83semidirect
867. #397C2×D83semidirect
871. #396C2×D83semidirect
887. #394C2×D83semidirect
923. #387C2×D83semidirect
939. #386C2×D83semidirect
951. #385C2×D83semidirect

Maximal subgroups

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

subgroupindex
#249157492
#249157422
#249146612
#249146572
#249145922
#249145882
#249145832
#249145712
#249143042
#249143022
#249140972
#249140852
#249139602
#249139562
#249139402
#249137202
#249137182
#249135782
#249133942
#249117202
#249117192
#249115952
#249115902
#249112732
#249112712
#249109242
#249109202
#249101902
#249101652
#380×D832
C83×#26912
#3672983