Finite Group Databasebeta

← #35565269

Subgroups — #35565269

Order 21248.

2430 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128238C211yesmaximal, characteristic
2#24910564C212yesmaximal, complemented
3#24910530C212yesmaximal, complemented
4#24910450C214yesmaximal, complemented
5#24910420C211yesmaximal, characteristic, complemented
6#24910410C211yesmaximal, characteristic, complemented
7#24910395C212yesmaximal, complemented
8#24910363C211yesmaximal, characteristic, complemented
9#24910363C212yesmaximal, complemented
10#24910237C214yesmaximal, complemented
11#24910071C212yesmaximal, complemented
12C4×#14581768C212yesmaximal, complemented
13#24909971C212yesmaximal
14#24909868C211yesmaximal, characteristic, complemented
15#24909817C212yesmaximal, complemented
16C4×C4⋊C4×D83C211yesmaximal, characteristic, complemented
17Q8×C4⋊C4×C83C211yesmaximal, characteristic, complemented
18#19128238C4116yescomplemented
19C2×#14581787C2212yes—
20C2×#14581783C2211yescharacteristic
21C2×#14581781C2211yescharacteristic
22C2×#14581777C2212yes—
23C2×#14581768C2211yescharacteristic
24C2×#14581767C2211yescharacteristic
25C2×C4×D332C2212yes—
26C2×C4×D332C2211yescharacteristic
27C2×#14581754C2214yes—
28C2×#14581754C2212yes—
29C2×#14581750C2212yes—
30C2×#14581750C2212yes—
31C2×#14581749C2212yes—
32C2×C4⋊C4×D83C2211yescharacteristic
33C2×C4⋊C4×D83C2212yes—
34C2×C4⋊C4×D83C2211yescharacteristic
35C2×C42×D83C2212yes—
36C2×C42×D83C2211yescharacteristic
37#19127608C2212yes—
38#19127603C2212yes—
39#19127597C2214yes—
40#19127597C2212yes—
41#19127593C2214yes—
42#19127592C2214yes—
43#19127591C2214yes—
44#19127591C2214yes—
45#19127587C2214yes—
46#19127586C2214yes—
47#19127582C2214yes—
48#19127582C2214yes—
49#19127579C2214yes—
50#19127572C2214yes—
51#19127572C2214yes—
52#19127572C2214yes—
53#19127571C2211yescharacteristic
54#19127567C2212yes—
55#19127566C2212yes—
56#19127558C2212yes—
57#19127558C2212yes—
58#19127558C2212yes—
59#19127558C2212yes—
60C4⋊C4×Dic83C2212yes—
61C4⋊C4×Dic83C2212yes—
62C4⋊C4×Dic83C2212yes—
63C4⋊C4×Dic83C2211yescharacteristic
64C4⋊C4×Dic83C2211yescharacteristic
65C4×Dic83⋊C4C2214yes—
66C4×Dic83⋊C4C2212yes—
67C4×C4⋊Dic83C2211yescharacteristic
68C4×C4⋊Dic83C2212yes—
69C4×C4⋊Dic83C2212yes—
70#19127552C2214yes—
71#19127552C2212yes—
72C4×(C2×D83)⋊C4C2214yes—
73C4×(C2×D83)⋊C4C2214yes—
74#19127548C2214yes—
75#95×D83C2212yes—
76C2×C4×Q8×C83C2212yes—
77C2×C4×Q8×C83C2211yescharacteristic
78#389×C83C2214yes—
79#389×C83C2212yes—
80#384×C83C2211yescharacteristic
81#384×C83C2212yes—
82C4×C4⋊C4×C83C2212yes—
83C4×C4⋊C4×C83C2211yescharacteristic
84C22×D332C2312yes—
85C22×D332C2311yescharacteristic
86C22×C4×D83C2312yes—
87C22×C4×D83C2312yes—
88C22×C4×D83C2311yescharacteristic
89C22×C4×D83C2311yescharacteristic
90C22×C4×D83C2312yes—
91C22×C4×D83C2311yescharacteristic
92C22×C4×D83C2314yes—
93#14581787C2×C4116yescomplemented
94#14581783C2×C418yescomplemented
95#14581781C2×C418yescomplemented
96#14581777C2×C4116yescomplemented
97#14581768C2×C418yescomplemented
98#14581767C2×C418yes—
99C4×D332C2×C418yescomplemented
100C4×D332C2×C4116yescomplemented
101#14581754—44no—
102#14581754—48no—
103#14581750—28no—
104#14581750—44no—
105#14581749C2×C4116yescomplemented
106C2×C4⋊Dic83C2312yes—
107C2×C4⋊Dic83C2311yescharacteristic
108C2×C4⋊Dic83C2312yes—
109C2×C4⋊Dic83C2312yes—
110C2×C4⋊Dic83C2311yescharacteristic
111C2×C4⋊Dic83C2312yes—
112C2×C4⋊Dic83C2311yescharacteristic
113C2×Dic83⋊C4C2314yes—
114C2×Dic83⋊C4C2312yes—
115C2×Dic83⋊C4C2312yes—
116C2×Dic83⋊C4C2312yes—
117C2×Dic83⋊C4C2312yes—
118C4⋊C4×D83—24no—
119C4⋊C4×D83—28no—
120C4⋊C4×D83—24no—
121C2×(C2×D83)⋊C4C2314yes—
122C2×(C2×D83)⋊C4C2314yes—
123C2×(C2×D83)⋊C4C2314yes—
124C2×(C2×D83)⋊C4C2314yes—
125C2×(C2×D83)⋊C4C2312yes—
126C2×(C2×D83)⋊C4C2312yes—
127C2×(C2×D83)⋊C4C2312yes—
128C2×(C2×D83)⋊C4C2312yes—
129C2×(C2×D83)⋊C4C2312yes—
130C2×C4×Dic83C2314yes—
131C2×C4×Dic83C2312yes—
132C2×C4×Dic83C2314yes—
133C2×C4×Dic83C2312yes—
134C2×C4×Dic83C2314yes—
135C2×C4×Dic83C2312yes—
136C2×C4×Dic83C2311yescharacteristic
137C2×C4×Dic83C2311yescharacteristic
138C2×C4×Dic83C2311yescharacteristic
139C42×D83—44no—
140C42×D83C2×C418yescomplemented
141C83⋊#95C2312yes—
142C83⋊#95C2312yes—
143C83⋊#95C2314yes—
144C83⋊#95C2314yes—
145C83⋊#95C2314yes—
146C83⋊#95C2312yes—
147C83⋊#95C2314yes—
148C83⋊#95C2314yes—
149C83⋊#95C2314yes—
150C83⋊#95C2314yes—
151C22×Q8×C83C2311yescharacteristic
152C4×Q8×C83—44no—
153C4×Q8×C83C2×C418yescomplemented
154C2×C4⋊C4×C83C2312yes—
155C2×C4⋊C4×C83C2311yescharacteristic
156C2×C4⋊C4×C83C2312yes—
157C2×C4⋊C4×C83C2312yes—
158C2×C4⋊C4×C83C2314yes—
159C2×C4⋊C4×C83C2314yes—
160C2×C4⋊C4×C83C2311yescharacteristic
161C2×C4⋊C4×C83C2312yes—
162C2×C4⋊C4×C83C2311yescharacteristic
163C2×C42×C83C2312yes—
164C2×C42×C83C2314yes—
165C2×C42×C83C2312yes—
166C2×C42×C83C2311yescharacteristic
167#95×C83C2314yes—
168#95×C83C2312yes—
169C23×D83C2412yes—
170C23×D83C2411yescharacteristic
171C2×D332—24no—
172C2×D332—24no—
173C2×D332—22no—
174C2×D332—22no—
175C2×D332C22×C418yes—
176C2×D332C22×C414yes—
177C22×Dic83C2412yes—
178C22×Dic83C2414yes—
179C22×Dic83C2411yescharacteristic
180C22×Dic83C2411yescharacteristic
181C22×Dic83C2412yes—
182C22×Dic83C2411yescharacteristic
183C22×Dic83C2412yes—
184C2×C4×D83—22no—
185C2×C4×D83—22no—
186C2×C4×D83—22no—
187C2×C4×D83—24no—
188C2×C4×D83—22no—
189C2×C4×D83—24no—
190C2×C4×D83—22no—
191C2×C4×D83—22no—
192C2×C4×D83—24no—
193C2×C4×D83—24no—
194C2×C4×D83—24no—
195C2×C4×D83—24no—
196C2×C4×D83—28no—
197C2×C4×D83—42no—
198C2×C4×D83—42no—
199C2×C4×D83—44no—
200C2×C4×D83—44no—
201C2×C4×D83C22×C414yes—
202C2×C4×D83C22×C414yes—
203C2×C4×D83C22×C414yes—
204C2×C4×D83C22×C418yes—
205C4⋊Dic83—22no—
206C4⋊Dic83—24no—
207C4⋊Dic83—24no—
208C4⋊Dic83—42no—
209C4⋊Dic83C22×C414yes—
210C4⋊Dic83C22×C418yes—
211C4⋊Dic83#4114yes—
212Dic83⋊C4—24no—
213Dic83⋊C4—24no—
214Dic83⋊C4—28no—
215Dic83⋊C4C22×C418yes—
216Dic83⋊C4C22×C418yes—
217(C2×D83)⋊C4—28no—
218(C2×D83)⋊C4—28no—
219(C2×D83)⋊C4—44no—
220(C2×D83)⋊C4—44no—
221(C2×D83)⋊C4C22×C418yes—
222(C2×D83)⋊C4C22×C418yes—
223(C2×D83)⋊C4C22×C418yes—
224(C2×D83)⋊C4C22×C418yes—
225(C2×D83)⋊C4C22×C418yes—
226C4×Dic83—28no—
227C4×Dic83—24no—
228C4×Dic83—42no—
229C4×Dic83—42no—
230C4×Dic83—44no—
231C4×Dic83—44no—
232C4×Dic83C22×C414yes—
233C4×Dic83C22×C414yes—
234C4×Dic83C22×C414yes—
235C2×Q8×C83—22no—
236C2×Q8×C83—22no—
237C2×Q8×C83C22×C414yes—
238C22×C4×C83C2412yes—
239C22×C4×C83C2414yes—
240C22×C4×C83C2411yescharacteristic
241C22×C4×C83C2412yes—
242C22×C4×C83C2412yes—
243C22×C4×C83C2412yes—
244C22×C4×C83C2411yescharacteristic
245C22×C4×C83C2411yescharacteristic
246C4⋊C4×C83—22no—
247C4⋊C4×C83—24no—
248C4⋊C4×C83—24no—
249C4⋊C4×C83—44no—
250C4⋊C4×C83—42no—
251C4⋊C4×C83—44no—
252C4⋊C4×C83C22×C414yes—
253C4⋊C4×C83C22×C418yes—
254C4⋊C4×C83#4114yes—
255C42×C83—24no—
256C42×C83—44no—
257C42×C83C22×C414yes—
258C42×C83C22×C418yes—
259C23×C83C2511yescharacteristic
260C22×D83—21no—
261C22×D83—21no—
262C22×D83—21no—
263C22×D83—21no—
264C22×D83—22no—
265C22×D83—22no—
266C22×D83—22no—
267C22×D83—22no—
268C22×D83—22no—
269C22×D83—22no—
270C22×D83C23×C414yes—
271C22×D83C23×C412yes—
272C22×D83H(5,𝔽2)12yes—
273C22×D832−1+412yes—
274Q8×C83—28no—
275C2×C4×C83—22no—
276C2×C4×C83—22no—
277C2×C4×C83—22no—
278C2×C4×C83—21no—
279C2×C4×C83—22no—
280C2×C4×C83—21no—
281C2×C4×C83—22no—
282C2×C4×C83—22no—
283C2×C4×C83—22no—
284C2×C4×C83—24no—
285C2×C4×C83—22no—
286C2×C4×C83—24no—
287C2×C4×C83—24no—
288C2×C4×C83—22no—
289C2×C4×C83C23×C412yes—
290C2×C4×C83C23×C414yes—
291C2×C4×C83C23×C414yes—
292C2×C4×C83C23×C412yes—
293C2×C4×C83C23×C412yes—
294C2×C4×C83C2×#4112yes—
295C2×C4×C83C2×#4114yes—
296C2×C4×C83C2×#4112yes—
297C2×C4×C83H(5,𝔽2)12yes—
298C2×C4×C832−1+412yes—
299C2×Dic83—22no—
300C2×Dic83—22no—
301C2×Dic83—21no—
302C2×Dic83—21no—
303C2×Dic83—22no—
304C2×Dic83—21no—
305C2×Dic83—21no—
306C2×Dic83—22no—
307C2×Dic83—21no—
308C2×Dic83—21no—
309C2×Dic83—24no—
310C2×Dic83—22no—
311C2×Dic83—22no—
312C2×Dic83—24no—
313C2×Dic83—24no—
314C2×Dic83—22no—
315C2×Dic83C23×C412yes—
316C2×Dic83C23×C412yes—
317C2×Dic83C23×C412yes—
318C2×Dic83C23×C414yes—
319C2×Dic83C2×#4114yes—
320D332—216no—
321D332—28no—
322C4×D83—28no—
323C4×D83—28no—
324C4×D83—216no—
325C4×D83—28no—
326C4×D83—48no—
327C4×D83—48no—
328C4×D83—88no—
329C22×C83C24×C411yescharacteristic
330C22×C83C22×#4111yescharacteristic
331C22×C83C22×#4111yescharacteristic
332C22×C83C2×H(5,𝔽2)11yescharacteristic
333C22×C83C2×H(5,𝔽2)11yescharacteristic
334C22×C83C2×2−1+411yescharacteristic
335C22×C83C2×2−1+411yescharacteristic
336C2×D83—22no—
337C2×D83—22no—
338C2×D83—22no—
339C2×D83—22no—
340C2×D83—22no—
341C2×D83—22no—
342C2×D83—24no—
343C2×D83—24no—
344C2×D83—24no—
345C2×D83—42no—
346C2×D83—42no—
347C2×D83—42no—
348C2×D83—42no—
349C2×D83#52014yes—
350C4×C83—22no—
351C4×C83—24no—
352C4×C83—24no—
353C4×C83—24no—
354C4×C83—42no—
355C4×C83—44no—
356C4×C83C4×#4114yes—
357C4×C83#52014yes—
358Dic83—24no—
359Dic83—22no—
360Dic83—22no—
361Dic83—22no—
362Dic83—24no—
363Dic83—42no—
364Dic83—44no—
365#34243—831nomaximal, Sylow
366C2×C83C2×C4×#4111yescharacteristic
367C2×C83C2×#52011yescharacteristic
368C2×C83C2×#52011yescharacteristic
369C2×C83#351911yescharacteristic
370C2×C83#352011yescharacteristic
371C2×C83#352211yescharacteristic
372C2×C83#352311yescharacteristic
373D83—24no—
374D83—44no—
375C2×#529—831no—
376#2370—832no—
377#2367—832no—
378#2359—834no—
379#2355—831no—
380#2354—831no—
381#2352—832no—
382Q8×C4⋊C4D8311yescharacteristic, complemented
383D4×C4⋊C4—832no—
384D4×C4⋊C4—831no—
385#2334—834no—
386#2314—832no—
387C4×C22⋊Q8—832no—
388C4×#121—832no—
389#2285—831no—
390#2274—832no—
391C2×C4×C4⋊C4—831no—
392C83#3424311yescharacteristic, complemented, Sylow
393#529—8316no—
394C2×#126—832no—
395C2×#125—831no—
396C2×#124—831no—
397C2×#123—832no—
398C2×C22⋊Q8—831no—
399C2×#121—831no—
400C2×C4×Q8C2×D8312yes—
401C2×C4×Q8C2×D8311yescharacteristic
402C2×C4×D4—834no—
403C2×C4×D4—832no—
404C2×C4×D4—832no—
405C2×C4×D4—831no—
406C2×#117—832no—
407C2×#117—832no—
408C2×#117—832no—
409C22×C4⋊C4—831no—
410C22×C4⋊C4—832no—
411C22×C4⋊C4—831no—
412C22×C42—832no—
413C22×C42—831no—
414#391—832no—
415#390—832no—
416#389—834no—
417#389—832no—
418#389C2×D8314yes—
419#389C2×D8312yes—
420#388—834no—
421#388—834no—
422#388—834no—
423#388—834no—
424#387—834no—
425#387—834no—
426#387—834no—
427#387—834no—
428#386—834no—
429#385—834no—
430#385—834no—
431#385—834no—
432#384—831no—
433#384C2×D8312yes—
434#384C2×D8311yescharacteristic
435#382—832no—
436#382—832no—
437#380—832no—
438#380—832no—
439#380—832no—
440#380—832no—
441C4×C4⋊C4—831no—
442C4×C4⋊C4—832no—
443C4×C4⋊C4—832no—
444C4×C4⋊C4—832no—
445C4×C4⋊C4—831no—
446C4×C4⋊C4—831no—
447C4×C4⋊C4—832no—
448C4×C4⋊C4—832no—
449C4×C4⋊C4—834no—
450C4×C4⋊C4—832no—
451C4×C4⋊C4—832no—
452C4×C4⋊C4—834no—
453C4×C4⋊C4C2×D8312yes—
454C4×C4⋊C4C2×D8311yescharacteristic
455C4×C22⋊C4—834no—
456C4×C22⋊C4—834no—
457C4×C22⋊C4—834no—
458C2×#95—832no—
459C22×Q8C22×D8311yescharacteristic
460C22×D4—832no—
461C22×D4—831no—
462C23×C4—834no—
463C23×C4—832no—
464C23×C4—832no—
465C23×C4—831no—
466C23×C4—832no—
467C23×C4—831no—
468C23×C4—831no—
469#126—8316no—
470#125—838no—
471#124—838no—
472#123—8316no—
473C22⋊Q8—838no—
474#121—838no—
475C4×Q8—44no—
476C4×Q8C4×D8318yescomplemented
477C4×D4—3328no—
478C4×D4—3324no—
479C4×D4—838no—
480C4×D4—8316no—
481#117—3324no—
482#117—8316no—
483#117—1668no—
484C2×C4⋊C4—832no—
485C2×C4⋊C4—831no—
486C2×C4⋊C4—832no—
487C2×C4⋊C4—832no—
488C2×C4⋊C4—831no—
489C2×C4⋊C4—832no—
490C2×C4⋊C4—831no—
491C2×C4⋊C4—832no—
492C2×C4⋊C4—834no—
493C2×C4⋊C4—832no—
494C2×C4⋊C4—832no—
495C2×C4⋊C4—832no—
496C2×C4⋊C4—1664no—
497C2×C4⋊C4—1668no—
498C2×C4⋊C4—1664no—
499C2×C4⋊C4C22×D8311yescharacteristic
500C2×C4⋊C4C22×D8312yes—
501C2×C4⋊C4C22×D8312yes—
502C2×C4⋊C4C22×D8312yes—
503C2×C4⋊C4C22×D8314yes—
504C2×C4⋊C4C22×D8314yes—
505C2×C4⋊C4C22×D8311yescharacteristic
506C2×C4⋊C4C22×D8312yes—
507C2×C4⋊C4C22×D8311yescharacteristic
508C2×C22⋊C4—834no—
509C2×C22⋊C4—834no—
510C2×C22⋊C4—832no—
511C2×C22⋊C4—832no—
512C2×C22⋊C4—832no—
513C2×C22⋊C4—832no—
514C2×C22⋊C4—832no—
515C2×C22⋊C4—834no—
516C2×C22⋊C4—834no—
517C2×C42—3324no—
518C2×C42—834no—
519C2×C42—834no—
520C2×C42—832no—
521C2×C42—832no—
522C2×C42—831no—
523C2×C42—831no—
524C2×C42—831no—
525C2×C42—838no—
526C2×C42—834no—
527C2×C42—832no—
528C2×C42C22×D8312yes—
529C2×C42C22×D8314yes—
530C2×C42C22×D8312yes—
531C2×C42C22×D8311yescharacteristic
532#95—832no—
533#95—832no—
534#95—832no—
535#95—834no—
536#95—834no—
537#95—834no—
538#95—834no—
539#95—834no—
540#95—834no—
541#95—834no—
542#95C22×D8312yes—
543#95C22×D8314yes—
544C24—831no—
545C24—832no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8C2×C4×D8314yes—
549C2×D4—838no—
550C2×D4—834no—
551C2×D4—1664no—
552C2×D4—1664no—
553C2×D4—1662no—
554C2×D4—1662no—
555C22×C4—3322no—
556C22×C4—3322no—
557C22×C4—3324no—
558C22×C4—3324no—
559C22×C4—831no—
560C22×C4—831no—
561C22×C4—832no—
562C22×C4—831no—
563C22×C4—832no—
564C22×C4—834no—
565C22×C4—834no—
566C22×C4—834no—
567C22×C4—838no—
568C22×C4—832no—
569C22×C4—834no—
570C22×C4—1664no—
571C22×C4—1664no—
572C22×C4—1664no—
573C22×C4—1668no—
574C22×C4—1662no—
575C22×C4—1662no—
576C22×C4—1664no—
577C22×C4—1664no—
578C22×C4—1662no—
579C22×C4—1662no—
580C22×C4—1664no—
581C22×C4—1662no—
582C22×C4—1662no—
583C22×C4C23×D8314yes—
584C22×C4C23×D8312yes—
585C22×C4C23×D8312yes—
586C22×C4C23×D8312yes—
587C22×C4C23×D8311yescharacteristic
588C22×C4C23×D8312yes—
589C22×C4C23×D8311yescharacteristic
590C22×C4C23×D8311yescharacteristic
591C4⋊C4—22no—
592C4⋊C4—24no—
593C4⋊C4—24no—
594C4⋊C4—42no—
595C4⋊C4—44no—
596C4⋊C4—44no—
597C4⋊C4—3322no—
598C4⋊C4—838no—
599C4⋊C4—838no—
600C4⋊C4—834no—
601C4⋊C4—838no—
602C4⋊C4—834no—
603C4⋊C4—1664no—
604C4⋊C4—1668no—
605C4⋊C4—1664no—
606C4⋊C4—1662no—
607C4⋊C4—1664no—
608C4⋊C4—1664no—
609C4⋊C4C2×C4×D8314yes—
610C4⋊C4C2×C4×D8318yes—
611C4⋊C4#1305059114yes—
612C22⋊C4—3324no—
613C22⋊C4—3324no—
614C22⋊C4—838no—
615C22⋊C4—838no—
616C22⋊C4—838no—
617C22⋊C4—838no—
618C22⋊C4—838no—
619C22⋊C4—1668no—
620C22⋊C4—1668no—
621C42—24no—
622C42—44no—
623C42—3322no—
624C42—3322no—
625C42—3324no—
626C42—3324no—
627C42—834no—
628C42—834no—
629C42—834no—
630C42—1668no—
631C42—1664no—
632C42C2×C4×D8314yes—
633C42C2×C4×D8318yes—
634C23—832no—
635C23—832no—
636C23—832no—
637C23—834no—
638C23—1662no—
639C23—1662no—
640C23—1662no—
641C23—1662no—
642C23—1662no—
643C23—1662no—
644C23—1661no—
645C23—1661no—
646C23—1661no—
647C23—1661no—
648C23C24×D8311yescharacteristic
649Q8—28no—
650D4—16616no—
651D4—1668no—
652C2×C4—22no—
653C2×C4—21no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—21no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—24no—
666C2×C4—3328no—
667C2×C4—3328no—
668C2×C4—832no—
669C2×C4—832no—
670C2×C4—832no—
671C2×C4—834no—
672C2×C4—834no—
673C2×C4—6648no—
674C2×C4—1668no—
675C2×C4—1664no—
676C2×C4—1662no—
677C2×C4—1664no—
678C2×C4—1662no—
679C2×C4—1662no—
680C2×C4—1664no—
681C2×C4—1661no—
682C2×C4—1662no—
683C2×C4—1662no—
684C2×C4—1661no—
685C2×C4—1661no—
686C2×C4—1662no—
687C2×C4—1661no—
688C2×C4—1662no—
689C2×C4—1661no—
690C2×C4—1661no—
691C2×C4—16616no—
692C2×C4—1668no—
693C2×C4—1668no—
694C2×C4C22×C4×D8312yes—
695C2×C4C22×C4×D8314yes—
696C2×C4C22×C4×D8314yes—
697C2×C4C22×C4×D8312yes—
698C2×C4C22×C4×D8312yes—
699C2×C4#41×D8312yes—
700C2×C4C2×#1305059114yes—
701C2×C4C2×#1305059112yes—
702C2×C4#1458183712yes—
703C2×C4#1458184012yes—
704C22—3322no—
705C22—3322no—
706C22—3322no—
707C22—3322no—
708C22—834no—
709C22—1664no—
710C22—1664no—
711C22—1664no—
712C22—1662no—
713C22—1662no—
714C22—1662no—
715C22—1662no—
716C22—1662no—
717C22—1662no—
718C22C23×C4×D8311yescharacteristic
719C22C2×#41×D8311yescharacteristic
720C22C22×#1305059111yescharacteristic
721C22H(5,𝔽2)×D8311yescharacteristic
722C22C2×#1458183711yescharacteristic
723C222−1+4×D8311yescharacteristic
724C22C2×#1458184011yescharacteristic
725C4—22no—
726C4—24no—
727C4—24no—
728C4—24no—
729C4—42no—
730C4—44no—
731C4—3322no—
732C4—3324no—
733C4—1662no—
734C4—1664no—
735C4—1662no—
736C4—1662no—
737C4—1664no—
738C4C4×#1305059114yes—
739C4#1912818214yes—
740C2—3324no—
741C2—1664no—
742C2C2×C4×#1305059111yescharacteristic
743C2#520×D8311yescharacteristic
744C2C2×#1912818211yescharacteristic
745C2#2492149411yescharacteristic
746C2#2492151311yescharacteristic
747C2#2492154911yescharacteristic
748C2#2492155611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingQ8×C4⋊C4×C83C2
socle, cosocleC23×C83C25
prime radicalC2×#14581767C22
hypercenterQ8×C4⋊C4D83
hypocenterC83#34243
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ Q8×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #24910564C2semidirect
3. #24910530C2semidirect
4. #24910450C2semidirect
5. #24910420C2semidirect
6. #24910410C2semidirect
7. #24910395C2semidirect
8. #24910363C2semidirect
9. #24910363C2semidirect
10. #24910237C2semidirect
11. #24910071C2semidirect
12. C4×#14581768C2semidirect
14. #24909868C2semidirect
15. #24909817C2semidirect
16. C4×C4⋊C4×D83C2semidirect
17. Q8×C4⋊C4×C83C2semidirect
18. #19128238C4semidirect
93. #14581787C2×C4semidirect
94. #14581783C2×C4semidirect
95. #14581781C2×C4semidirect
96. #14581777C2×C4semidirect
97. #14581768C2×C4semidirect
99. C4×D332C2×C4semidirect
100. C4×D332C2×C4semidirect
105. #14581749C2×C4semidirect
140. C42×D83C2×C4semidirect
153. C4×Q8×C83C2×C4semidirect
382. Q8×C4⋊C4D83semidirect
392. C83#34243semidirect
476. C4×Q8C4×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#191282382
#249105642
#249105302
#249104502
#249104202
#249104102
#249103952
#249103632
#249102372
#249100712
C4×#145817682
#249099712
#249098682
#249098172
C4×C4⋊C4×D832
Q8×C4⋊C4×C832
#3424383