Finite Group Databasebeta

← #35569058

Subgroups — #35569058

Order 21248.

2368 conjugacy classes of subgroups.

The subgroup lattice has 1544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128400C211yesmaximal, characteristic
2#24910656C211yesmaximal, characteristic, complemented
3#24910651C211yesmaximal, characteristic, complemented
4#24910608C211yesmaximal, characteristic, complemented
5#24910607C211yesmaximal, characteristic, complemented
6#24910562C211yesmaximal, characteristic, complemented
7#24910482C211yesmaximal, characteristic, complemented
8#24910480C211yesmaximal, characteristic, complemented
9#24910480C211yesmaximal, characteristic, complemented
10#24910479C211yesmaximal, characteristic, complemented
11C4⋊C4×C22⋊D83C211yesmaximal, characteristic, complemented
12#24910361C211yesmaximal, characteristic, complemented
13#24910361C211yesmaximal, characteristic, complemented
14#24910357C211yesmaximal, characteristic, complemented
15#24910335C211yesmaximal, characteristic, complemented
16#24910238C211yesmaximal, characteristic, complemented
17#24910233C211yesmaximal, characteristic, complemented
18#24910201C211yesmaximal, characteristic, complemented
19#24910163C211yesmaximal, characteristic, complemented
20#24910161C211yesmaximal, characteristic, complemented
21#24910155C211yesmaximal, characteristic, complemented
22#24910132C211yesmaximal, characteristic, complemented
23#24910127C211yesmaximal, characteristic, complemented
24#24910105C211yesmaximal, characteristic, complemented
25#24910096C211yesmaximal, characteristic, complemented
26#24910091C211yesmaximal, characteristic, complemented
27#24910084C211yesmaximal, characteristic, complemented
28C4×#14581764C211yesmaximal, characteristic, complemented
29C2×#19127596C211yesmaximal, characteristic, complemented
30#24909899C211yesmaximal, characteristic, complemented
31D4×C4⋊C4×C83C211yesmaximal, characteristic, complemented
32#19128400C4116yescomplemented
33C2×#14581786C2211yescharacteristic
34C2×#14581785C2211yescharacteristic
35C2×#14581782C2211yescharacteristic
36C2×#14581777C2211yescharacteristic
37C2×#14581775C2211yescharacteristic
38C2×#14581766C2211yescharacteristic
39C2×#14581765C2211yescharacteristic
40C2×#14581764C2211yescharacteristic
41C2×#14581764C2211yescharacteristic
42C2×#14581754C2211yescharacteristic
43C2×C4×C22⋊D83C2211yescharacteristic
44C2×C4×C22⋊D83C2211yescharacteristic
45C2×C4×C22⋊D83C2211yescharacteristic
46C2×C4×C22⋊D83C2211yescharacteristic
47C2×C4×C22⋊D83C2211yescharacteristic
48C2×C4×C22⋊D83C2211yescharacteristic
49C2×(C22⋊D83)⋊C4C2211yescharacteristic
50C2×(C22⋊D83)⋊C4C2211yescharacteristic
51C2×(C22⋊D83)⋊C4C2211yescharacteristic
52C2×(C22⋊D83)⋊C4C2211yescharacteristic
53C2×#14581750C2211yescharacteristic
54C2×#14581749C2211yescharacteristic
55C22×Dic83⋊C4C2211yescharacteristic
56C22×Dic83⋊C4C2211yescharacteristic
57C22×Dic83⋊C4C2211yescharacteristic
58C2×C4⋊C4×D83C2211yescharacteristic
59C2×C4⋊C4×D83C2211yescharacteristic
60C22×C4×Dic83C2211yescharacteristic
61#19127602C2211yescharacteristic
62#19127601C2211yescharacteristic
63#19127601C2211yescharacteristic
64#19127601C2211yescharacteristic
65#19127598C2211yescharacteristic
66#19127598C2211yescharacteristic
67#19127597C2211yescharacteristic
68#19127596C2211yescharacteristic
69#19127596C2211yescharacteristic
70#19127596C2211yescharacteristic
71#19127596C2211yescharacteristic
72#19127596C2211yescharacteristic
73#19127596C2211yescharacteristic
74#19127596C2211yescharacteristic
75#19127596C2211yescharacteristic
76#19127596C2211yescharacteristic
77#19127596C2211yescharacteristic
78#19127596C2211yescharacteristic
79#19127596C2211yescharacteristic
80#19127596C2211yescharacteristic
81#19127596C2211yescharacteristic
82#19127596C2211yescharacteristic
83#19127595C2211yescharacteristic
84#19127594C2211yescharacteristic
85#19127594C2211yescharacteristic
86#19127593C2211yescharacteristic
87#19127593C2211yescharacteristic
88#19127592C2211yescharacteristic
89#19127592C2211yescharacteristic
90#19127592C2211yescharacteristic
91#19127591C2211yescharacteristic
92#19127591C2211yescharacteristic
93#19127591C2211yescharacteristic
94#19127591C2211yescharacteristic
95#19127591C2211yescharacteristic
96#19127591C2211yescharacteristic
97#19127591C2211yescharacteristic
98#19127589C2211yescharacteristic
99#19127589C2211yescharacteristic
100#19127589C2211yescharacteristic
101#19127588C2211yescharacteristic
102#19127588C2211yescharacteristic
103#19127587C2211yescharacteristic
104#19127587C2211yescharacteristic
105#19127585C2211yescharacteristic
106#19127584C2211yescharacteristic
107#19127584C2211yescharacteristic
108#19127583C2211yescharacteristic
109#19127583C2211yescharacteristic
110#19127582C2211yescharacteristic
111#19127582C2211yescharacteristic
112#19127582C2211yescharacteristic
113#19127582C2211yescharacteristic
114#19127582C2211yescharacteristic
115#19127581C2211yescharacteristic
116#19127581C2211yescharacteristic
117#19127580C2211yescharacteristic
118#19127580C2211yescharacteristic
119#19127580C2211yescharacteristic
120#19127579C2211yescharacteristic
121#19127579C2211yescharacteristic
122#19127578C2211yescharacteristic
123#19127578C2211yescharacteristic
124#19127577C2211yescharacteristic
125#19127576C2211yescharacteristic
126#19127576C2211yescharacteristic
127#19127575C2211yescharacteristic
128#19127575C2211yescharacteristic
129#19127574C2211yescharacteristic
130#19127574C2211yescharacteristic
131#19127574C2211yescharacteristic
132#19127572C2211yescharacteristic
133#19127572C2211yescharacteristic
134#19127572C2211yescharacteristic
135#19127572C2211yescharacteristic
136#19127572C2211yescharacteristic
137#19127572C2211yescharacteristic
138#19127572C2211yescharacteristic
139#19127572C2211yescharacteristic
140#19127572C2211yescharacteristic
141#19127570C2211yescharacteristic
142#19127570C2211yescharacteristic
143#19127569C2211yescharacteristic
144#19127568C2211yescharacteristic
145#19127567C2211yescharacteristic
146#19127566C2211yescharacteristic
147#19127564C2211yescharacteristic
148#19127563C2211yescharacteristic
149#19127561C2211yescharacteristic
150#19127560C2211yescharacteristic
151#19127560C2211yescharacteristic
152#19127559C2211yescharacteristic
153#19127559C2211yescharacteristic
154#19127558C2211yescharacteristic
155C4⋊C4×Dic83C2211yescharacteristic
156C4⋊C4×Dic83C2211yescharacteristic
157C4×Dic83⋊C4C2211yescharacteristic
158C4×Dic83⋊C4C2211yescharacteristic
159C4×Dic83⋊C4C2211yescharacteristic
160#19127552C2211yescharacteristic
161#19127552C2211yescharacteristic
162#19127552C2211yescharacteristic
163#19127552C2211yescharacteristic
164C22⋊C4×Dic83C2211yescharacteristic
165C22⋊C4×Dic83C2211yescharacteristic
166C4×(C2×D83)⋊C4C2211yescharacteristic
167C4×C22⋊Dic83C2211yescharacteristic
168C4×C22⋊Dic83C2211yescharacteristic
169#19127548C2211yescharacteristic
170#19127546C2211yescharacteristic
171C2×C83⋊#95C2211yescharacteristic
172C2×C83⋊#95C2211yescharacteristic
173C2×C4×D4×C83C2211yescharacteristic
174C2×C4×D4×C83C2211yescharacteristic
175C2×C4×D4×C83C2211yescharacteristic
176C22×C4⋊C4×C83C2211yescharacteristic
177C22×C4⋊C4×C83C2211yescharacteristic
178#389×C83C2211yescharacteristic
179#389×C83C2211yescharacteristic
180#385×C83C2211yescharacteristic
181#385×C83C2211yescharacteristic
182#385×C83C2211yescharacteristic
183#385×C83C2211yescharacteristic
184#384×C83C2211yescharacteristic
185#380×C83C2211yescharacteristic
186#380×C83C2211yescharacteristic
187C4×C4⋊C4×C83C2211yescharacteristic
188C22×D332C2311yescharacteristic
189C22×C22⋊D83C2311yescharacteristic
190C22×C22⋊D83C2311yescharacteristic
191C22×C22⋊D83C2311yescharacteristic
192C22×C22⋊D83C2311yescharacteristic
193C23×Dic83C2311yescharacteristic
194C23×Dic83C2311yescharacteristic
195C23×Dic83C2311yescharacteristic
196C23×Dic83C2311yescharacteristic
197C22×C4×D83C2311yescharacteristic
198C22×C4×D83C2311yescharacteristic
199C22×C4×D83C2311yescharacteristic
200C22×C4×D83C2311yescharacteristic
201C22×C4×D83C2311yescharacteristic
202C22×C4×D83C2311yescharacteristic
203#14581786C2×C418yescomplemented
204#14581785C2×C418yescomplemented
205#14581782C2×C418yescomplemented
206#14581777C2×C418yescomplemented
207#14581775C2×C418yescomplemented
208#14581766C2×C418yescomplemented
209#14581765C2×C418yescomplemented
210#14581764C2×C418yescomplemented
211#14581764C2×C418yescomplemented
212#14581754—42no—
213C4×C22⋊D83—42no—
214C4×C22⋊D83—42no—
215C4×C22⋊D83—42no—
216C4×C22⋊D83—42no—
217C4×C22⋊D83—42no—
218C4×C22⋊D83C2×C418yescomplemented
219(C22⋊D83)⋊C4—42no—
220(C22⋊D83)⋊C4—42no—
221(C22⋊D83)⋊C4C2×C418yescomplemented
222(C22⋊D83)⋊C4C2×C418yescomplemented
223#14581750—42no—
224#14581749C2×C418yescomplemented
225C2×C4⋊Dic83C2311yescharacteristic
226C2×C4⋊Dic83C2311yescharacteristic
227C2×C4⋊Dic83C2311yescharacteristic
228C2×C4⋊Dic83C2311yescharacteristic
229C2×C4⋊Dic83C2311yescharacteristic
230C2×Dic83⋊C4—42no—
231C2×Dic83⋊C4—42no—
232C2×Dic83⋊C4C2×C418yescomplemented
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×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
254C2×Dic83⋊C4C2311yescharacteristic
255C2×Dic83⋊C4C2311yescharacteristic
256C2×Dic83⋊C4C2311yescharacteristic
257C4⋊C4×D83—42no—
258C4⋊C4×D83—42no—
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)⋊C4C2311yescharacteristic
268C2×(C2×D83)⋊C4C2311yescharacteristic
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×C4×Dic83—42no—
286C2×C4×Dic83C2311yescharacteristic
287C2×C4×Dic83C2311yescharacteristic
288C2×C4×Dic83C2311yescharacteristic
289C2×C4×Dic83C2311yescharacteristic
290C2×C4×Dic83C2311yescharacteristic
291C2×C4×Dic83C2311yescharacteristic
292C2×C4×Dic83C2311yescharacteristic
293C2×C4×Dic83C2311yescharacteristic
294C2×C4×Dic83C2311yescharacteristic
295C2×C4×Dic83C2311yescharacteristic
296C2×C4×Dic83C2311yescharacteristic
297C2×C4×Dic83C2311yescharacteristic
298C2×C4×Dic83C2311yescharacteristic
299C2×C4×Dic83C2311yescharacteristic
300C2×C4×Dic83C2311yescharacteristic
301C2×C4×Dic83C2311yescharacteristic
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
332C83⋊#95C2311yescharacteristic
333C83⋊#95C2311yescharacteristic
334C83⋊#95C2311yescharacteristic
335C83⋊#95C2311yescharacteristic
336C22×D4×C83C2311yescharacteristic
337C23×C4×C83C2311yescharacteristic
338C23×C4×C83C2311yescharacteristic
339C23×C4×C83C2311yescharacteristic
340C23×C4×C83C2311yescharacteristic
341C23×C4×C83C2311yescharacteristic
342C23×C4×C83C2311yescharacteristic
343C4×D4×C83—42no—
344C4×D4×C83—42no—
345C4×D4×C83C2×C418yescomplemented
346C2×C4⋊C4×C83—42no—
347C2×C4⋊C4×C83—42no—
348C2×C4⋊C4×C83C2311yescharacteristic
349C2×C4⋊C4×C83C2311yescharacteristic
350C2×C4⋊C4×C83C2311yescharacteristic
351C2×C4⋊C4×C83C2311yescharacteristic
352C2×C4⋊C4×C83C2311yescharacteristic
353C2×C4⋊C4×C83C2311yescharacteristic
354C2×C4⋊C4×C83C2311yescharacteristic
355C2×C4⋊C4×C83C2311yescharacteristic
356C2×C4⋊C4×C83C2311yescharacteristic
357C2×C4⋊C4×C83C2311yescharacteristic
358C2×C4⋊C4×C83C2311yescharacteristic
359C2×C4⋊C4×C83C2311yescharacteristic
360C2×C4⋊C4×C83C2311yescharacteristic
361C2×C22⋊C4×C83C2311yescharacteristic
362C2×C22⋊C4×C83C2311yescharacteristic
363C2×C22⋊C4×C83C2311yescharacteristic
364C2×C22⋊C4×C83C2311yescharacteristic
365C2×C22⋊C4×C83C2311yescharacteristic
366C2×C22⋊C4×C83C2311yescharacteristic
367C2×C42×C83C2311yescharacteristic
368C2×C42×C83C2311yescharacteristic
369C2×C42×C83C2311yescharacteristic
370#95×C83C2311yescharacteristic
371#95×C83C2311yescharacteristic
372#95×C83C2311yescharacteristic
373#95×C83C2311yescharacteristic
374#95×C83C2311yescharacteristic
375#95×C83C2311yescharacteristic
376C23×D83C2411yescharacteristic
377C23×D83C2411yescharacteristic
378C2×D332—41no—
379C2×D332—41no—
380C2×D332C22×C414yes—
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—41no—
388C2×C22⋊D83—41no—
389C2×C22⋊D83C22×C414yes—
390C2×C22⋊D83C22×C414yes—
391C2×C22⋊D83C22×C414yes—
392C2×C22⋊D83C22×C414yes—
393C22×Dic83—22no—
394C22×Dic83—22no—
395C22×Dic83—22no—
396C22×Dic83—22no—
397C22×Dic83—41no—
398C22×Dic83—41no—
399C22×Dic83—41no—
400C22×Dic83—41no—
401C22×Dic83—41no—
402C22×Dic83—41no—
403C22×Dic83C22×C414yes—
404C22×Dic83C22×C414yes—
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—41no—
423C2×C4×D83—41no—
424C2×C4×D83—41no—
425C2×C4×D83—41no—
426C2×C4×D83—41no—
427C2×C4×D83—41no—
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×D83C22×C414yes—
436C2×C4×D83C22×C414yes—
437C4⋊Dic83—41no—
438C4⋊Dic83—41no—
439C4⋊Dic83—41no—
440C4⋊Dic83—41no—
441C4⋊Dic83C22×C414yes—
442Dic83⋊C4—22no—
443Dic83⋊C4—22no—
444Dic83⋊C4—22no—
445Dic83⋊C4—22no—
446Dic83⋊C4—22no—
447Dic83⋊C4—22no—
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⋊C4C22×C414yes—
459Dic83⋊C4C22×C414yes—
460Dic83⋊C4C22×C414yes—
461Dic83⋊C4C22×C414yes—
462Dic83⋊C4C22×C414yes—
463Dic83⋊C4C22×C414yes—
464Dic83⋊C4C22×C414yes—
465Dic83⋊C4C22×C414yes—
466C22⋊Dic83—22no—
467C22⋊Dic83—22no—
468C22⋊Dic83—41no—
469C22⋊Dic83—41no—
470C22⋊Dic83—41no—
471C22⋊Dic83—41no—
472C22⋊Dic83C22×C414yes—
473C22⋊Dic83C22×C414yes—
474(C2×D83)⋊C4—22no—
475(C2×D83)⋊C4—41no—
476(C2×D83)⋊C4—41no—
477(C2×D83)⋊C4—41no—
478(C2×D83)⋊C4—41no—
479(C2×D83)⋊C4—41no—
480(C2×D83)⋊C4—41no—
481(C2×D83)⋊C4—41no—
482(C2×D83)⋊C4—41no—
483(C2×D83)⋊C4—41no—
484(C2×D83)⋊C4—41no—
485(C2×D83)⋊C4—41no—
486(C2×D83)⋊C4C22×C414yes—
487(C2×D83)⋊C4C22×C414yes—
488(C2×D83)⋊C4C22×C414yes—
489(C2×D83)⋊C4C22×C414yes—
490(C2×D83)⋊C4C22×C414yes—
491(C2×D83)⋊C4C22×C414yes—
492C4×Dic83—22no—
493C4×Dic83—22no—
494C4×Dic83—22no—
495C4×Dic83—22no—
496C4×Dic83—41no—
497C4×Dic83—41no—
498C4×Dic83—41no—
499C4×Dic83—41no—
500C4×Dic83—41no—
501C4×Dic83—41no—
502C4×Dic83—41no—
503C4×Dic83—41no—
504C4×Dic83—41no—
505C4×Dic83—41no—
506C4×Dic83C22×C414yes—
507C4×Dic83C22×C414yes—
508C24×C83C2411yescharacteristic
509C24×C83C2411yescharacteristic
510C2×D4×C83—22no—
511C2×D4×C83—22no—
512C2×D4×C83C22×C414yes—
513C22×C4×C83—22no—
514C22×C4×C83—22no—
515C22×C4×C83—22no—
516C22×C4×C83—22no—
517C22×C4×C83—41no—
518C22×C4×C83—41no—
519C22×C4×C83—41no—
520C22×C4×C83—41no—
521C22×C4×C83—41no—
522C22×C4×C83—41no—
523C22×C4×C83—41no—
524C22×C4×C83—41no—
525C22×C4×C83—41no—
526C22×C4×C83—41no—
527C22×C4×C83—41no—
528C22×C4×C83—41no—
529C22×C4×C83C22×C414yes—
530C22×C4×C83C22×C414yes—
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
540C22×C4×C83C2411yescharacteristic
541C22×C4×C83C2411yescharacteristic
542C22×C4×C83C2411yescharacteristic
543C22×C4×C83C2411yescharacteristic
544C4⋊C4×C83—22no—
545C4⋊C4×C83—22no—
546C4⋊C4×C83—22no—
547C4⋊C4×C83—41no—
548C4⋊C4×C83—41no—
549C4⋊C4×C83—41no—
550C4⋊C4×C83—41no—
551C4⋊C4×C83—41no—
552C4⋊C4×C83—41no—
553C4⋊C4×C83—41no—
554C4⋊C4×C83—41no—
555C4⋊C4×C83—41no—
556C4⋊C4×C83C22×C414yes—
557C22⋊C4×C83—22no—
558C22⋊C4×C83—22no—
559C22⋊C4×C83—41no—
560C22⋊C4×C83—41no—
561C22⋊C4×C83C22×C414yes—
562C22⋊C4×C83C22×C414yes—
563C42×C83—41no—
564C42×C83—41no—
565C42×C83C22×C414yes—
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×C83C23×C412yes—
577C23×C83C23×C412yes—
578C23×C83H(5,𝔽2)12yes—
579C23×C832−1+412yes—
580C23×C83C2511yescharacteristic
581C22×D83—21no—
582C22×D83—21no—
583C22×D83—21no—
584C22×D83—21no—
585C22×D83—21no—
586C22×D83—21no—
587C22×D83—21no—
588C22×D83—21no—
589C22×D83—21no—
590C22×D83—21no—
591C22×D83—21no—
592C22×D83—21no—
593C22×D83C23×C412yes—
594C22×D83C23×C412yes—
595D4×C83—28no—
596C2×C4×C83—21no—
597C2×C4×C83—21no—
598C2×C4×C83—21no—
599C2×C4×C83—21no—
600C2×C4×C83—21no—
601C2×C4×C83—21no—
602C2×C4×C83—21no—
603C2×C4×C83—21no—
604C2×C4×C83—21no—
605C2×C4×C83—21no—
606C2×C4×C83—21no—
607C2×C4×C83—21no—
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—44no—
630C2×C4×C83—44no—
631C2×C4×C83—44no—
632C2×C4×C83—82no—
633C2×C4×C83—82no—
634C2×C4×C83—82no—
635C2×C4×C83C23×C412yes—
636C2×C4×C83C23×C412yes—
637C2×C4×C83C23×C412yes—
638C2×C4×C83C23×C412yes—
639C2×C4×C83C23×C412yes—
640C2×C4×C83H(5,𝔽2)12yes—
641C22⋊D83—28no—
642C22⋊D83—28no—
643C22⋊D83—28no—
644C22⋊D83—44no—
645C2×Dic83—21no—
646C2×Dic83—21no—
647C2×Dic83—21no—
648C2×Dic83—21no—
649C2×Dic83—21no—
650C2×Dic83—21no—
651C2×Dic83—21no—
652C2×Dic83—21no—
653C2×Dic83—21no—
654C2×Dic83—21no—
655C2×Dic83—28no—
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—44no—
681C2×Dic83—44no—
682C2×Dic83—82no—
683C2×Dic83C23×C412yes—
684C2×Dic83C23×C412yes—
685C2×Dic83C23×C412yes—
686C2×Dic83C23×C412yes—
687C2×Dic83C23×C412yes—
688C2×Dic83C23×C412yes—
689C2×Dic83H(5,𝔽2)12yes—
690C2×Dic832−1+412yes—
691D332—44no—
692C4×D83—28no—
693C4×D83—44no—
694C4×D83—82no—
695C4×D83—82no—
696C4×D83—82no—
697C4×D83—82no—
698C22×C83—22no—
699C22×C83—22no—
700C22×C83—22no—
701C22×C83—22no—
702C22×C83—22no—
703C22×C83—22no—
704C22×C83—22no—
705C22×C83—22no—
706C22×C83—22no—
707C22×C83—41no—
708C22×C83—41no—
709C22×C83—41no—
710C22×C83—41no—
711C22×C83#52014yes—
712C22×C83C24×C411yescharacteristic
713C22×C83C2×H(5,𝔽2)11yescharacteristic
714C22×C83C2×H(5,𝔽2)11yescharacteristic
715C22×C83C2×H(5,𝔽2)11yescharacteristic
716C22×C83C2×2−1+411yescharacteristic
717C22×C83C2×2−1+411yescharacteristic
718C22×C83#58511yescharacteristic
719C2×D83—22no—
720C2×D83—22no—
721C2×D83—22no—
722C2×D83—22no—
723C2×D83—22no—
724C2×D83—22no—
725C2×D83—41no—
726C2×D83—41no—
727C2×D83—41no—
728C2×D83—41no—
729C2×D83—41no—
730C2×D83—41no—
731C2×D83—41no—
732C2×D83—41no—
733C4×C83—22no—
734C4×C83—22no—
735C4×C83—22no—
736C4×C83—22no—
737C4×C83—22no—
738C4×C83—22no—
739C4×C83—41no—
740C4×C83—41no—
741C4×C83—41no—
742C4×C83—41no—
743C4×C83—41no—
744C4×C83—41no—
745C4×C83—41no—
746Dic83—22no—
747Dic83—22no—
748Dic83—22no—
749Dic83—22no—
750Dic83—22no—
751Dic83—41no—
752Dic83—41no—
753Dic83—41no—
754Dic83—41no—
755Dic83—41no—
756Dic83—41no—
757Dic83—41no—
758Dic83—41no—
759Dic83#52014yes—
760#34461—831nomaximal, Sylow
761C2×C83—24no—
762C2×C83—42no—
763C2×C83C2×#52011yescharacteristic
764C2×C83C2×#52011yescharacteristic
765C2×C83C4×H(5,𝔽2)11yescharacteristic
766C2×C83#353711yescharacteristic
767C2×C83#354111yescharacteristic
768C2×C83#355211yescharacteristic
769C2×C83#355911yescharacteristic
770D83—42no—
771D83—42no—
772C2×#553—831no—
773#2383—831no—
774#2383—831no—
775#2376—831no—
776#2376—831no—
777#2370—831no—
778#2361—831no—
779#2361—831no—
780#2361—831no—
781#2361—831no—
782D4×C4⋊C4—831no—
783D4×C4⋊C4—831no—
784D4×C4⋊C4—831no—
785D4×C4⋊C4D8311yescharacteristic, complemented
786#2347—831no—
787#2345—831no—
788#2334—831no—
789#2334—831no—
790#2330—831no—
791#2325—831no—
792#2325—831no—
793#2324—831no—
794#2322—831no—
795#2322—831no—
796#2319—831no—
797#2318—831no—
798#2318—831no—
799#2317—831no—
800C4×#121—831no—
801C2×#389—831no—
802#2290—831no—
803C83#3446111yescharacteristic, complemented, Sylow
804#553—8316no—
805C2×#126—831no—
806C2×#126—831no—
807C2×#125—831no—
808C2×#123—831no—
809C2×#123—831no—
810C2×#121—831no—
811C2×#121—831no—
812C2×#121—831no—
813C2×#121—831no—
814C2×C4×D4—831no—
815C2×C4×D4—831no—
816C2×C4×D4—831no—
817C2×C4×D4—831no—
818C2×C4×D4—831no—
819C2×C4×D4—831no—
820C2×C4×D4—831no—
821C2×C4×D4—831no—
822C2×C4×D4—831no—
823C2×C4×D4—831no—
824C2×C4×D4—831no—
825C2×C4×D4C2×D8311yescharacteristic
826C2×C4×D4C2×D8311yescharacteristic
827C2×C4×D4C2×D8311yescharacteristic
828C2×#117—831no—
829C2×#117—831no—
830C22×C4⋊C4—831no—
831C22×C4⋊C4—831no—
832C22×C4⋊C4—831no—
833C22×C4⋊C4—831no—
834C22×C4⋊C4—831no—
835C22×C4⋊C4C2×D8311yescharacteristic
836C22×C4⋊C4C2×D8311yescharacteristic
837C22×C42—831no—
838#390—831no—
839#390—831no—
840#390—831no—
841#390—831no—
842#389—831no—
843#389—831no—
844#389—831no—
845#389—831no—
846#389—831no—
847#389—831no—
848#389—831no—
849#389—831no—
850#389—831no—
851#389—831no—
852#389—831no—
853#389—831no—
854#389—831no—
855#389—831no—
856#389—831no—
857#389—831no—
858#389—831no—
859#389—831no—
860#389C2×D8311yescharacteristic
861#389C2×D8311yescharacteristic
862#388—831no—
863#388—831no—
864#388—831no—
865#388—831no—
866#388—831no—
867#388—831no—
868#388—831no—
869#388—831no—
870#388—831no—
871#388—831no—
872#388—831no—
873#388—831no—
874#388—831no—
875#388—831no—
876#388—831no—
877#388—831no—
878#388—831no—
879#388—831no—
880#387—831no—
881#387—831no—
882#387—831no—
883#387—831no—
884#387—831no—
885#387—831no—
886#387—831no—
887#387—831no—
888#387—831no—
889#387—831no—
890#387—831no—
891#387—831no—
892#387—831no—
893#387—831no—
894#386—831no—
895#386—831no—
896#386—831no—
897#386—831no—
898#386—831no—
899#386—831no—
900#386—831no—
901#386—831no—
902#386—831no—
903#386—831no—
904#385—831no—
905#385—831no—
906#385—831no—
907#385—831no—
908#385—831no—
909#385—831no—
910#385—831no—
911#385—831no—
912#385—831no—
913#385—831no—
914#385—831no—
915#385—831no—
916#385—831no—
917#385—831no—
918#385—831no—
919#385—831no—
920#385C2×D8311yescharacteristic
921#385C2×D8311yescharacteristic
922#385C2×D8311yescharacteristic
923#385C2×D8311yescharacteristic
924#384—831no—
925#384—831no—
926#384C2×D8311yescharacteristic
927#383—831no—
928#383—831no—
929#382—831no—
930#382—831no—
931#381—831no—
932#381—831no—
933#380—831no—
934#380—831no—
935#380—831no—
936#380—831no—
937#380—831no—
938#380—831no—
939#380C2×D8311yescharacteristic
940#380C2×D8311yescharacteristic
941C4×C4⋊C4—831no—
942C4×C4⋊C4—831no—
943C4×C4⋊C4—831no—
944C4×C4⋊C4—831no—
945C4×C4⋊C4—831no—
946C4×C4⋊C4—831no—
947C4×C4⋊C4—831no—
948C4×C4⋊C4—831no—
949C4×C4⋊C4—831no—
950C4×C4⋊C4C2×D8311yescharacteristic
951C4×C22⋊C4—831no—
952C4×C22⋊C4—831no—
953C4×C22⋊C4—831no—
954C4×C22⋊C4—831no—
955C4×C22⋊C4—831no—
956C4×C22⋊C4—831no—
957#376—831no—
958C2×#95—831no—
959C2×#95—831no—
960C22×D4—831no—
961C22×D4—831no—
962C22×D4—831no—
963C22×D4—831no—
964C22×D4—831no—
965C22×D4C22×D8311yescharacteristic
966C23×C4—831no—
967C23×C4—831no—
968C23×C4—831no—
969C23×C4—831no—
970C23×C4—831no—
971C23×C4—831no—
972C23×C4—831no—
973C23×C4—831no—
974C23×C4—831no—
975C23×C4—831no—
976C23×C4C22×D8311yescharacteristic
977C23×C4C22×D8311yescharacteristic
978C23×C4C22×D8311yescharacteristic
979C23×C4C22×D8311yescharacteristic
980C23×C4C22×D8311yescharacteristic
981C23×C4C22×D8311yescharacteristic
982#126—838no—
983#126—838no—
984#125—838no—
985#123—838no—
986#123—838no—
987#121—838no—
988#121—838no—
989#121—838no—
990#121—838no—
991C4×D4—42no—
992C4×D4—42no—
993C4×D4—3322no—
994C4×D4—3322no—
995C4×D4—3322no—
996C4×D4—3322no—
997C4×D4—3322no—
998C4×D4—3322no—
999C4×D4—3322no—
1000C4×D4—3322no—
1001C4×D4—838no—
1002C4×D4—838no—
1003C4×D4—838no—
1004C4×D4C4×D8318yescomplemented
1005#117—3322no—
1006#117—838no—
1007C2×C4⋊C4—42no—
1008C2×C4⋊C4—42no—
1009C2×C4⋊C4—3322no—
1010C2×C4⋊C4—3322no—
1011C2×C4⋊C4—3322no—
1012C2×C4⋊C4—3322no—
1013C2×C4⋊C4—831no—
1014C2×C4⋊C4—831no—
1015C2×C4⋊C4—831no—
1016C2×C4⋊C4—831no—
1017C2×C4⋊C4—831no—
1018C2×C4⋊C4—831no—
1019C2×C4⋊C4—831no—
1020C2×C4⋊C4—831no—
1021C2×C4⋊C4—831no—
1022C2×C4⋊C4—831no—
1023C2×C4⋊C4—831no—
1024C2×C4⋊C4—831no—
1025C2×C4⋊C4—831no—
1026C2×C4⋊C4—831no—
1027C2×C4⋊C4—838no—
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⋊C4C22×D8311yescharacteristic
1044C2×C4⋊C4C22×D8311yescharacteristic
1045C2×C4⋊C4C22×D8311yescharacteristic
1046C2×C4⋊C4C22×D8311yescharacteristic
1047C2×C4⋊C4C22×D8311yescharacteristic
1048C2×C4⋊C4C22×D8311yescharacteristic
1049C2×C4⋊C4C22×D8311yescharacteristic
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×C22⋊C4—831no—
1057C2×C22⋊C4—831no—
1058C2×C22⋊C4—831no—
1059C2×C22⋊C4—831no—
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⋊C4C22×D8311yescharacteristic
1083C2×C22⋊C4C22×D8311yescharacteristic
1084C2×C22⋊C4C22×D8311yescharacteristic
1085C2×C22⋊C4C22×D8311yescharacteristic
1086C2×C22⋊C4C22×D8311yescharacteristic
1087C2×C22⋊C4C22×D8311yescharacteristic
1088C2×C42—3322no—
1089C2×C42—831no—
1090C2×C42—831no—
1091C2×C42—831no—
1092C2×C42—831no—
1093C2×C42—831no—
1094C2×C42—831no—
1095C2×C42—831no—
1096C2×C42—831no—
1097C2×C42—831no—
1098C2×C42—831no—
1099C2×C42—831no—
1100C2×C42—831no—
1101C2×C42—831no—
1102C2×C42—831no—
1103C2×C42—831no—
1104C2×C42—831no—
1105C2×C42C22×D8311yescharacteristic
1106C2×C42C22×D8311yescharacteristic
1107C2×C42C22×D8311yescharacteristic
1108#95—831no—
1109#95—831no—
1110#95—831no—
1111#95—831no—
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#95C22×D8311yescharacteristic
1143#95C22×D8311yescharacteristic
1144#95C22×D8311yescharacteristic
1145#95C22×D8311yescharacteristic
1146#95C22×D8311yescharacteristic
1147#95C22×D8311yescharacteristic
1148C24—831no—
1149C24—831no—
1150C24C23×D8311yescharacteristic
1151C24C23×D8311yescharacteristic
1152C2×D4—22no—
1153C2×D4—22no—
1154C2×D4—3321no—
1155C2×D4—3321no—
1156C2×D4—3321no—
1157C2×D4—3321no—
1158C2×D4—834no—
1159C2×D4—834no—
1160C2×D4—834no—
1161C2×D4—834no—
1162C2×D4—834no—
1163C2×D4—1662no—
1164C2×D4—1662no—
1165C2×D4—1662no—
1166C2×D4—1662no—
1167C2×D4—1662no—
1168C2×D4—1662no—
1169C2×D4C2×C4×D8314yes—
1170C22×C4—22no—
1171C22×C4—22no—
1172C22×C4—22no—
1173C22×C4—22no—
1174C22×C4—41no—
1175C22×C4—41no—
1176C22×C4—41no—
1177C22×C4—41no—
1178C22×C4—41no—
1179C22×C4—41no—
1180C22×C4—41no—
1181C22×C4—41no—
1182C22×C4—41no—
1183C22×C4—41no—
1184C22×C4—41no—
1185C22×C4—41no—
1186C22×C4—3321no—
1187C22×C4—3321no—
1188C22×C4—3321no—
1189C22×C4—3321no—
1190C22×C4—3321no—
1191C22×C4—3321no—
1192C22×C4—3321no—
1193C22×C4—3321no—
1194C22×C4—3321no—
1195C22×C4—3321no—
1196C22×C4—3321no—
1197C22×C4—3321no—
1198C22×C4—3321no—
1199C22×C4—3321no—
1200C22×C4—3321no—
1201C22×C4—3321no—
1202C22×C4—3321no—
1203C22×C4—3321no—
1204C22×C4—3321no—
1205C22×C4—834no—
1206C22×C4—834no—
1207C22×C4—831no—
1208C22×C4—834no—
1209C22×C4—831no—
1210C22×C4—831no—
1211C22×C4—831no—
1212C22×C4—831no—
1213C22×C4—831no—
1214C22×C4—834no—
1215C22×C4—831no—
1216C22×C4—831no—
1217C22×C4—831no—
1218C22×C4—831no—
1219C22×C4—831no—
1220C22×C4—831no—
1221C22×C4—831no—
1222C22×C4—831no—
1223C22×C4—1662no—
1224C22×C4—1662no—
1225C22×C4—1662no—
1226C22×C4—1662no—
1227C22×C4—1662no—
1228C22×C4—1662no—
1229C22×C4—1662no—
1230C22×C4C2×C4×D8314yes—
1231C22×C4C2×C4×D8314yes—
1232C22×C4C23×D8311yescharacteristic
1233C22×C4C23×D8311yescharacteristic
1234C22×C4C23×D8311yescharacteristic
1235C22×C4C23×D8311yescharacteristic
1236C22×C4C23×D8311yescharacteristic
1237C22×C4C23×D8311yescharacteristic
1238C22×C4C23×D8311yescharacteristic
1239C22×C4C23×D8311yescharacteristic
1240C22×C4C23×D8311yescharacteristic
1241C22×C4C23×D8311yescharacteristic
1242C22×C4C23×D8311yescharacteristic
1243C22×C4C23×D8311yescharacteristic
1244C22×C4C23×D8311yescharacteristic
1245C4⋊C4—22no—
1246C4⋊C4—22no—
1247C4⋊C4—22no—
1248C4⋊C4—41no—
1249C4⋊C4—41no—
1250C4⋊C4—41no—
1251C4⋊C4—41no—
1252C4⋊C4—41no—
1253C4⋊C4—41no—
1254C4⋊C4—41no—
1255C4⋊C4—41no—
1256C4⋊C4—41no—
1257C4⋊C4—3321no—
1258C4⋊C4—3321no—
1259C4⋊C4—3321no—
1260C4⋊C4—3321no—
1261C4⋊C4—3321no—
1262C4⋊C4—3321no—
1263C4⋊C4—3321no—
1264C4⋊C4—3321no—
1265C4⋊C4—3321no—
1266C4⋊C4—3321no—
1267C4⋊C4—3321no—
1268C4⋊C4—3321no—
1269C4⋊C4—3321no—
1270C4⋊C4—3321no—
1271C4⋊C4—834no—
1272C4⋊C4—834no—
1273C4⋊C4—834no—
1274C4⋊C4—834no—
1275C4⋊C4—834no—
1276C4⋊C4—834no—
1277C4⋊C4—834no—
1278C4⋊C4—834no—
1279C4⋊C4—834no—
1280C4⋊C4—1662no—
1281C4⋊C4—1662no—
1282C4⋊C4—1662no—
1283C4⋊C4—1662no—
1284C4⋊C4—1662no—
1285C4⋊C4—1662no—
1286C4⋊C4C2×C4×D8314yes—
1287C22⋊C4—22no—
1288C22⋊C4—22no—
1289C22⋊C4—41no—
1290C22⋊C4—41no—
1291C22⋊C4—3321no—
1292C22⋊C4—3321no—
1293C22⋊C4—3321no—
1294C22⋊C4—3321no—
1295C22⋊C4—3321no—
1296C22⋊C4—3321no—
1297C22⋊C4—3321no—
1298C22⋊C4—3321no—
1299C22⋊C4—3321no—
1300C22⋊C4—3321no—
1301C22⋊C4—3321no—
1302C22⋊C4—3321no—
1303C22⋊C4—3321no—
1304C22⋊C4—3321no—
1305C22⋊C4—3321no—
1306C22⋊C4—834no—
1307C22⋊C4—834no—
1308C22⋊C4—834no—
1309C22⋊C4—834no—
1310C22⋊C4—834no—
1311C22⋊C4—834no—
1312C22⋊C4—834no—
1313C22⋊C4—834no—
1314C22⋊C4—1662no—
1315C22⋊C4—1662no—
1316C22⋊C4—1662no—
1317C22⋊C4C2×C4×D8314yes—
1318C22⋊C4C2×C4×D8314yes—
1319C42—41no—
1320C42—41no—
1321C42—3321no—
1322C42—3321no—
1323C42—3321no—
1324C42—3321no—
1325C42—3321no—
1326C42—3321no—
1327C42—3321no—
1328C42—3321no—
1329C42—3321no—
1330C42—3321no—
1331C42—834no—
1332C42—834no—
1333C42—1662no—
1334C42—1662no—
1335C42—1662no—
1336C42—1662no—
1337C42C2×C4×D8314yes—
1338C23—21no—
1339C23—21no—
1340C23—21no—
1341C23—21no—
1342C23—21no—
1343C23—21no—
1344C23—21no—
1345C23—21no—
1346C23—21no—
1347C23—21no—
1348C23—832no—
1349C23—832no—
1350C23—1661no—
1351C23—1661no—
1352C23—1661no—
1353C23—1661no—
1354C23—1661no—
1355C23—1661no—
1356C23—1661no—
1357C23—1661no—
1358C23—1661no—
1359C23—1661no—
1360C23—1661no—
1361C23—1661no—
1362C23C22×C4×D8312yes—
1363C23C22×C4×D8312yes—
1364C23#1458183712yes—
1365C23#1458184012yes—
1366C23C24×D8311yescharacteristic
1367D4—28no—
1368D4—3324no—
1369D4—3324no—
1370D4—1668no—
1371D4—1668no—
1372D4—1668no—
1373C2×C4—21no—
1374C2×C4—21no—
1375C2×C4—21no—
1376C2×C4—21no—
1377C2×C4—21no—
1378C2×C4—21no—
1379C2×C4—21no—
1380C2×C4—21no—
1381C2×C4—21no—
1382C2×C4—21no—
1383C2×C4—21no—
1384C2×C4—21no—
1385C2×C4—21no—
1386C2×C4—21no—
1387C2×C4—21no—
1388C2×C4—21no—
1389C2×C4—21no—
1390C2×C4—21no—
1391C2×C4—21no—
1392C2×C4—21no—
1393C2×C4—21no—
1394C2×C4—21no—
1395C2×C4—21no—
1396C2×C4—21no—
1397C2×C4—21no—
1398C2×C4—21no—
1399C2×C4—21no—
1400C2×C4—21no—
1401C2×C4—21no—
1402C2×C4—21no—
1403C2×C4—21no—
1404C2×C4—21no—
1405C2×C4—21no—
1406C2×C4—44no—
1407C2×C4—44no—
1408C2×C4—44no—
1409C2×C4—82no—
1410C2×C4—82no—
1411C2×C4—82no—
1412C2×C4—3324no—
1413C2×C4—3324no—
1414C2×C4—3324no—
1415C2×C4—832no—
1416C2×C4—832no—
1417C2×C4—832no—
1418C2×C4—832no—
1419C2×C4—832no—
1420C2×C4—832no—
1421C2×C4—832no—
1422C2×C4—832no—
1423C2×C4—6642no—
1424C2×C4—6642no—
1425C2×C4—6642no—
1426C2×C4—6642no—
1427C2×C4—6642no—
1428C2×C4—1668no—
1429C2×C4—1661no—
1430C2×C4—1661no—
1431C2×C4—1661no—
1432C2×C4—1661no—
1433C2×C4—1661no—
1434C2×C4—1661no—
1435C2×C4—1661no—
1436C2×C4—1661no—
1437C2×C4—1661no—
1438C2×C4—1661no—
1439C2×C4—1661no—
1440C2×C4—1661no—
1441C2×C4—1661no—
1442C2×C4—1661no—
1443C2×C4—1661no—
1444C2×C4—1661no—
1445C2×C4—1661no—
1446C2×C4—1661no—
1447C2×C4—1661no—
1448C2×C4—1661no—
1449C2×C4—1661no—
1450C2×C4—1661no—
1451C2×C4—1661no—
1452C2×C4—1661no—
1453C2×C4—1668no—
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×C4C22×C4×D8312yes—
1465C2×C4C22×C4×D8312yes—
1466C2×C4C22×C4×D8312yes—
1467C2×C4C22×C4×D8312yes—
1468C2×C4C22×C4×D8312yes—
1469C2×C4#1458183712yes—
1470C22—22no—
1471C22—22no—
1472C22—22no—
1473C22—22no—
1474C22—22no—
1475C22—22no—
1476C22—22no—
1477C22—22no—
1478C22—22no—
1479C22—41no—
1480C22—41no—
1481C22—41no—
1482C22—41no—
1483C22—3321no—
1484C22—3321no—
1485C22—3321no—
1486C22—3321no—
1487C22—3321no—
1488C22—3321no—
1489C22—3321no—
1490C22—3321no—
1491C22—1662no—
1492C22—1662no—
1493C22—1662no—
1494C22—1662no—
1495C22—1662no—
1496C22—1662no—
1497C22#1912818214yes—
1498C22C23×C4×D8311yescharacteristic
1499C22H(5,𝔽2)×D8311yescharacteristic
1500C22C2×#1458183711yescharacteristic
1501C22C2×#1458183711yescharacteristic
1502C222−1+4×D8311yescharacteristic
1503C22C2×#1458184011yescharacteristic
1504C22#1912853711yescharacteristic
1505C4—22no—
1506C4—22no—
1507C4—22no—
1508C4—22no—
1509C4—22no—
1510C4—22no—
1511C4—41no—
1512C4—41no—
1513C4—41no—
1514C4—41no—
1515C4—41no—
1516C4—41no—
1517C4—41no—
1518C4—3321no—
1519C4—3321no—
1520C4—3321no—
1521C4—3321no—
1522C4—3321no—
1523C4—3321no—
1524C4—3321no—
1525C4—3321no—
1526C4—834no—
1527C4—1662no—
1528C4—1662no—
1529C4—1662no—
1530C4—1662no—
1531C4—1662no—
1532C2—24no—
1533C2—42no—
1534C2—3322no—
1535C2—3322no—
1536C2#520×D8311yescharacteristic
1537C2C2×#1912818211yescharacteristic
1538C2C4×#1458183711yescharacteristic
1539C2#2492169311yescharacteristic
1540C2#2492174911yescharacteristic
1541C2#2492190611yescharacteristic
1542C2#2492198811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingD4×C4⋊C4×C83C2
socle, cosocleC23×C83C25
prime radicalC2×#19128400C2
hypercenterD4×C4⋊C4D83
hypocenterC83#34461
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #24910656C2semidirect
3. #24910651C2semidirect
4. #24910608C2semidirect
5. #24910607C2semidirect
6. #24910562C2semidirect
7. #24910482C2semidirect
8. #24910480C2semidirect
9. #24910480C2semidirect
10. #24910479C2semidirect
11. C4⋊C4×C22⋊D83C2semidirect
12. #24910361C2semidirect
13. #24910361C2semidirect
14. #24910357C2semidirect
15. #24910335C2semidirect
16. #24910238C2semidirect
17. #24910233C2semidirect
18. #24910201C2semidirect
19. #24910163C2semidirect
20. #24910161C2semidirect
21. #24910155C2semidirect
22. #24910132C2semidirect
23. #24910127C2semidirect
24. #24910105C2semidirect
25. #24910096C2semidirect
26. #24910091C2semidirect
27. #24910084C2semidirect
28. C4×#14581764C2semidirect
29. C2×#19127596C2semidirect
30. #24909899C2semidirect
31. D4×C4⋊C4×C83C2semidirect
32. #19128400C4semidirect
203. #14581786C2×C4semidirect
204. #14581785C2×C4semidirect
205. #14581782C2×C4semidirect
206. #14581777C2×C4semidirect
207. #14581775C2×C4semidirect
208. #14581766C2×C4semidirect
209. #14581765C2×C4semidirect
210. #14581764C2×C4semidirect
211. #14581764C2×C4semidirect
218. C4×C22⋊D83C2×C4semidirect
221. (C22⋊D83)⋊C4C2×C4semidirect
222. (C22⋊D83)⋊C4C2×C4semidirect
224. #14581749C2×C4semidirect
232. C2×Dic83⋊C4C2×C4semidirect
345. C4×D4×C83C2×C4semidirect
785. D4×C4⋊C4D83semidirect
803. C83#34461semidirect
1004. C4×D4C4×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#191284002
#249106562
#249106512
#249106082
#249106072
#249105622
#249104822
#249104802
#249104792
C4⋊C4×C22⋊D832
#249103612
#249103572
#249103352
#249102382
#249102332
#249102012
#249101632
#249101612
#249101552
#249101322
#249101272
#249101052
#249100962
#249100912
#249100842
C4×#145817642
C2×#191275962
#249098992
D4×C4⋊C4×C832
#3446183