Finite Group Databasebeta

← #35564477

Subgroups — #35564477

Order 21248.

2518 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#117×D83C211yesmaximal, characteristic
2#24910352C212yesmaximal, complemented
3#24910344C212yesmaximal, complemented
4#24910336C212yesmaximal, complemented
5#24910328C212yesmaximal, complemented
6#24910317C214yesmaximal, complemented
7#24910306C214yesmaximal
8#24910087C211yesmaximal, characteristic, complemented
9#24910083C211yesmaximal, characteristic, complemented
10#24910068C212yesmaximal, complemented
11#24910068C212yesmaximal, complemented
12#24909867C212yesmaximal, complemented
13#24909859C212yesmaximal, complemented
14#24909842C211yesmaximal, characteristic
15C2×#19127558C211yesmaximal, characteristic
16#24909819C211yesmaximal, characteristic, complemented
17C83×#2274C211yesmaximal, characteristic, complemented
18C23×C4×D83C2211yescharacteristic
19C2×#14581751C2211yescharacteristic
20C2×#14581751C2211yescharacteristic
21C2×#14581750C2211yescharacteristic
22C2×#14581750C2211yescharacteristic
23C2×#14581749C2214yes—
24C2×#14581749C2212yes—
25C2×#14581748C2212yes—
26#117×D83C4116yescomplemented
27C22×C4⋊Dic83C2211yescharacteristic
28C2×C4⋊C4×D83C2211yescharacteristic
29C2×C4⋊C4×D83C2211yescharacteristic
30C22×(C2×D83)⋊C4C2212yes—
31C2×C22⋊C4×D83C2212yes—
32C2×C42×D83C2212yes—
33#19127599C2212yescomplemented
34#19127599C2212yescomplemented
35#19127597C2212yescomplemented
36#19127597C2212yescomplemented
37#19127592C2214yes—
38#19127592C2214yes—
39#19127590C2214yes—
40#19127590C2214yes—
41#19127585C2214yescomplemented
42#19127585C2214yescomplemented
43#19127583C2214yescomplemented
44#19127583C2214yescomplemented
45#19127574C2214yes—
46#19127573C2214yes—
47#19127570C2212yescomplemented
48#19127570C2212yescomplemented
49#19127568C2214yescomplemented
50#19127566C2212yescomplemented
51#19127566C2212yescomplemented
52#19127565C2214yescomplemented
53#19127563C2214yes—
54#19127562C2212yes—
55#19127560C2214yes—
56#19127558C2212yes—
57#19127558C2212yes—
58#19127558C2212yes—
59#19127558C2212yes—
60#19127558C2211yescharacteristic
61#19127558C2211yescharacteristic
62#19127558C2211yescharacteristic
63#19127558C2211yescharacteristic
64#19127556C2212yes—
65C4⋊C4×Dic83C2212yescomplemented
66C4⋊C4×Dic83C2212yescomplemented
67C4×Dic83⋊C4C2214yescomplemented
68C4×C4⋊Dic83C2212yescomplemented
69C4×C4⋊Dic83C2212yescomplemented
70C22⋊C4×Dic83C2214yes—
71C4×(C2×D83)⋊C4C2212yes—
72C4×(C2×D83)⋊C4C2214yes—
73C4×(C2×D83)⋊C4C2212yes—
74#19127547C2214yescomplemented
75C2×C83⋊#95C2212yes—
76C2×#117×C83C2211yescharacteristic
77C2×#117×C83C2211yescharacteristic
78C22×C4⋊C4×C83C2211yescharacteristic
79C4×C4⋊C4×C83C2212yescomplemented
80C4×C4⋊C4×C83C2212yescomplemented
81C4×C4⋊C4×C83C2212yescomplemented
82C4×C4⋊C4×C83C2212yescomplemented
83C4×C22⋊C4×C83C2214yes—
84C24×D83C2311yescharacteristic
85C23×Dic83C2311yescharacteristic
86C23×Dic83C2312yes—
87C22×C4×D83—24no—
88C22×C4×D83—24no—
89C22×C4×D83C2×C418yes—
90C22×C4×D83C2311yescharacteristic
91C22×C4×D83C2311yescharacteristic
92C22×C4×D83C2311yescharacteristic
93C22×C4×D83C2311yescharacteristic
94C22×C4×D83C2312yes—
95C22×C4×D83C2312yes—
96#14581751—24no—
97#14581751C2×C418yes—
98#14581750C2×C418yescomplemented
99#14581750C2×C418yescomplemented
100#14581749—48no—
101#14581749C2×C4116yescomplemented
102#14581748C2×C4116yes—
103C2×C4⋊Dic83—24no—
104C2×C4⋊Dic83C2311yescharacteristic
105C2×C4⋊Dic83C2312yes—
106C2×C4⋊Dic83C2311yescharacteristic
107C2×C4⋊Dic83C2312yes—
108C2×C4⋊Dic83C2311yescharacteristic
109C2×C4⋊Dic83C2311yescharacteristic
110C2×Dic83⋊C4C2314yes—
111C2×Dic83⋊C4C2314yes—
112C2×Dic83⋊C4C2314yes—
113C2×Dic83⋊C4C2314yes—
114C2×Dic83⋊C4C2312yes—
115C2×Dic83⋊C4C2312yes—
116C4⋊C4×D83C2×C418yescomplemented
117C4⋊C4×D83C2×C418yescomplemented
118C2×C22⋊Dic83C2312yes—
119C2×C22⋊Dic83C2312yes—
120C2×(C2×D83)⋊C4—44no—
121C2×(C2×D83)⋊C4C2312yes—
122C2×(C2×D83)⋊C4C2312yes—
123C2×(C2×D83)⋊C4C2314yes—
124C2×(C2×D83)⋊C4C2312yes—
125C2×(C2×D83)⋊C4C2312yes—
126C2×(C2×D83)⋊C4C2314yes—
127C2×(C2×D83)⋊C4C2312yes—
128C2×(C2×D83)⋊C4C2312yes—
129C22⋊C4×D83C2×C4116yes—
130C2×C4×Dic83C2312yes—
131C2×C4×Dic83C2314yes—
132C2×C4×Dic83C2314yes—
133C2×C4×Dic83C2312yes—
134C2×C4×Dic83C2312yes—
135C2×C4×Dic83C2312yes—
136C42×D83C2×C4116yescomplemented
137C83⋊#95C2314yes—
138C83⋊#95C2314yes—
139C83⋊#95C2312yes—
140C83⋊#95C2314yes—
141C83⋊#95C2314yes—
142C83⋊#95C2312yes—
143C83⋊#95C2312yes—
144C83⋊#95C2312yes—
145C83⋊#95C2314yes—
146C83⋊#95C2314yes—
147C83⋊#95C2314yes—
148C83⋊#95C2314yes—
149C23×C4×C83C2312yes—
150C23×C4×C83C2311yescharacteristic
151#117×C83—24no—
152#117×C83C2×C418yes—
153C2×C4⋊C4×C83—24no—
154C2×C4⋊C4×C83C2311yescharacteristic
155C2×C4⋊C4×C83C2312yes—
156C2×C4⋊C4×C83C2311yescharacteristic
157C2×C4⋊C4×C83C2312yes—
158C2×C4⋊C4×C83C2311yescharacteristic
159C2×C4⋊C4×C83C2311yescharacteristic
160C2×C22⋊C4×C83C2312yes—
161C2×C22⋊C4×C83C2312yes—
162C2×C42×C83C2312yes—
163C2×C42×C83C2314yes—
164C2×C42×C83C2314yes—
165C2×C42×C83C2312yes—
166#95×C83C2314yes—
167#95×C83C2314yes—
168C23×D83—22no—
169C23×D83—22no—
170C23×D83—22no—
171C23×D83—22no—
172C23×D83—41no—
173C23×D83—41no—
174C23×D83C22×C414yes—
175C23×D83C2411yescharacteristic
176C23×D83C2411yescharacteristic
177C22×Dic83—22no—
178C22×Dic83—22no—
179C22×Dic83—24no—
180C22×Dic83—42no—
181C22×Dic83—42no—
182C22×Dic83C22×C414yes—
183C22×Dic83C2414yes—
184C22×Dic83C2412yes—
185C22×Dic83C2412yes—
186C22×Dic83C2411yescharacteristic
187C22×Dic83C2411yescharacteristic
188C22×Dic83C2412yes—
189C22×Dic83C2412yes—
190C2×C4×D83—24no—
191C2×C4×D83—24no—
192C2×C4×D83—232no—
193C2×C4×D83—22no—
194C2×C4×D83—22no—
195C2×C4×D83—22no—
196C2×C4×D83—22no—
197C2×C4×D83—22no—
198C2×C4×D83—22no—
199C2×C4×D83—22no—
200C2×C4×D83—22no—
201C2×C4×D83—42no—
202C2×C4×D83—42no—
203C2×C4×D83C22×C414yes—
204C2×C4×D83C22×C414yes—
205C2×C4×D83C22×C414yes—
206C2×C4×D83C22×C414yes—
207C2×C4×D83C22×C418yes—
208C2×C4×D83C22×C418yes—
209C4⋊Dic83—24no—
210C4⋊Dic83—24no—
211C4⋊Dic83—22no—
212C4⋊Dic83—22no—
213C4⋊Dic83C22×C414yes—
214C4⋊Dic83C22×C414yes—
215Dic83⋊C4—44no—
216Dic83⋊C4—44no—
217Dic83⋊C4—44no—
218Dic83⋊C4—44no—
219Dic83⋊C4C22×C418yes—
220Dic83⋊C4C22×C418yes—
221C22⋊Dic83—24no—
222C22⋊Dic83C22×C418yes—
223(C2×D83)⋊C4—28no—
224(C2×D83)⋊C4—24no—
225(C2×D83)⋊C4—24no—
226(C2×D83)⋊C4—44no—
227(C2×D83)⋊C4—42no—
228(C2×D83)⋊C4—42no—
229(C2×D83)⋊C4C22×C418yes—
230(C2×D83)⋊C4C22×C418yes—
231C4×Dic83—24no—
232C4×Dic83—44no—
233C4×Dic83—44no—
234C4×Dic83C22×C418yes—
235C4×Dic83C22×C418yes—
236C4×Dic83C22×C418yes—
237C24×C83C2411yescharacteristic
238C22×C4×C83—24no—
239C22×C4×C83—42no—
240C22×C4×C83—42no—
241C22×C4×C83C22×C414yes—
242C22×C4×C83#4114yes—
243C22×C4×C83#4114yes—
244C22×C4×C83C2412yes—
245C22×C4×C83C2412yes—
246C22×C4×C83C2414yes—
247C22×C4×C83C2412yes—
248C22×C4×C83C2412yes—
249C22×C4×C83C2411yescharacteristic
250C22×C4×C83C2411yescharacteristic
251C4⋊C4×C83—24no—
252C4⋊C4×C83—24no—
253C4⋊C4×C83—22no—
254C4⋊C4×C83—22no—
255C4⋊C4×C83C22×C414yes—
256C4⋊C4×C83C22×C414yes—
257C22⋊C4×C83—24no—
258C22⋊C4×C83C22×C418yes—
259C42×C83—24no—
260C42×C83—44no—
261C42×C83—44no—
262C42×C83C22×C418yes—
263C23×C83—21no—
264C23×C83—21no—
265C23×C83—21no—
266C23×C83—21no—
267C23×C83C23×C412yes—
268C23×C83C2×#4112yes—
269C23×C83C2×#4112yes—
270C23×C83C2511yescharacteristic
271C22×D83—21no—
272C22×D83—21no—
273C22×D83—21no—
274C22×D83—21no—
275C22×D83—28no—
276C22×D83—21no—
277C22×D83—21no—
278C22×D83—21no—
279C22×D83—21no—
280C22×D83—21no—
281C22×D83—21no—
282C22×D83—28no—
283C22×D83—44no—
284C22×D83—44no—
285C22×D83—44no—
286C22×D83—44no—
287C22×D83—44no—
288C22×D83C23×C412yes—
289C22×D83C23×C412yes—
290C22×D83H(5,𝔽2)12yes—
291C22×D832−1+412yes—
292C2×C4×C83—22no—
293C2×C4×C83—22no—
294C2×C4×C83—22no—
295C2×C4×C83—22no—
296C2×C4×C83—22no—
297C2×C4×C83—22no—
298C2×C4×C83—24no—
299C2×C4×C83—22no—
300C2×C4×C83—24no—
301C2×C4×C83—22no—
302C2×C4×C83—22no—
303C2×C4×C83—24no—
304C2×C4×C83—22no—
305C2×C4×C83—84no—
306C2×C4×C83#117116yescomplemented
307C2×C4×C83C23×C414yes—
308C2×C4×C83C23×C414yes—
309C2×C4×C83C23×C412yes—
310C2×C4×C83C23×C412yes—
311C2×C4×C83C2×#4112yes—
312C2×C4×C83C2×#4112yes—
313C2×C4×C83C2×#4112yes—
314C2×C4×C83C2×#4112yes—
315C2×Dic83—28no—
316C2×Dic83—21no—
317C2×Dic83—21no—
318C2×Dic83—21no—
319C2×Dic83—21no—
320C2×Dic83—22no—
321C2×Dic83—22no—
322C2×Dic83—22no—
323C2×Dic83—22no—
324C2×Dic83—22no—
325C2×Dic83—22no—
326C2×Dic83—24no—
327C2×Dic83—22no—
328C2×Dic83—24no—
329C2×Dic83—22no—
330C2×Dic83—22no—
331C2×Dic83—24no—
332C2×Dic83—22no—
333C2×Dic83—84no—
334C2×Dic83C23×C412yes—
335C2×Dic83C23×C414yes—
336C2×Dic83C23×C414yes—
337C2×Dic83C23×C412yes—
338C4×D83—216no—
339C4×D83—28no—
340C4×D83—28no—
341C4×D83—28no—
342C4×D83—28no—
343C4×D83—48no—
344C22×C83—22no—
345C22×C83—22no—
346C22×C83—22no—
347C22×C83—22no—
348C22×C83—22no—
349C22×C83—22no—
350C22×C83C2×#11714yes—
351C22×C83C24×C411yescharacteristic
352C22×C83C22×#4111yescharacteristic
353C22×C83C22×#4111yescharacteristic
354C22×C83C2×H(5,𝔽2)11yescharacteristic
355C22×C83C2×2−1+411yescharacteristic
356C22×C83#58511yescharacteristic
357C22×C83#58511yescharacteristic
358C2×D83—22no—
359C2×D83—22no—
360C2×D83—22no—
361C2×D83—22no—
362C2×D83—22no—
363C2×D83—22no—
364C2×D83—22no—
365C2×D83—22no—
366C2×D83—22no—
367C2×D83—416no—
368C2×D83—41no—
369C2×D83—41no—
370C2×D83—41no—
371C2×D83—41no—
372C2×D83#52014yes—
373C4×C83—24no—
374C4×C83—24no—
375C4×C83—42no—
376C4×C83—44no—
377C4×C83—42no—
378C4×C83C2×#11714yes—
379C4×C83C2×#11714yes—
380Dic83—22no—
381Dic83—22no—
382Dic83—24no—
383Dic83—24no—
384Dic83—42no—
385Dic83—44no—
386Dic83—42no—
387#34180—831nomaximal, Sylow
388C2×C83—24no—
389C2×C83C22×#11711yescharacteristic
390C2×C83C2×#52011yescharacteristic
391C2×C83#342811yescharacteristic
392C2×C83#349411yescharacteristic
393C2×C83#349411yescharacteristic
394C2×C83#349511yescharacteristic
395C2×C83#349511yescharacteristic
396D83—24no—
397D83—42no—
398C22×#117—831no—
399#2347—832no—
400#2346—832no—
401#2345—832no—
402#2344—832no—
403#2343—834no—
404#2342—834no—
405#2317—831no—
406#2317—831no—
407#2314—832no—
408#2314—832no—
409#2285—832no—
410#2283—832no—
411#2280—831no—
412C2×#380—831no—
413#2274—831no—
414#2274D8311yescharacteristic, complemented
415C83#3418011yescharacteristic, complemented, Sylow
416C24×C4—831no—
417C2×#117—831no—
418C2×#117—8316no—
419C2×#117—831no—
420C2×#117—831no—
421C2×#117—831no—
422C2×#117—832no—
423C2×#117—834no—
424C2×#117—832no—
425C2×#117C2×D8311yescharacteristic
426C2×#117C2×D8311yescharacteristic
427C22×C4⋊C4—831no—
428C22×C4⋊C4—831no—
429C22×C4⋊C4—831no—
430C22×C4⋊C4C2×D8311yescharacteristic
431C22×C22⋊C4—832no—
432C22×C22⋊C4—832no—
433C22×C42—832no—
434#389—832no—
435#389—832no—
436#389—832no—
437#389—832no—
438#388—834no—
439#388—834no—
440#388—834no—
441#388—834no—
442#387—834no—
443#387—834no—
444#387—834no—
445#387—834no—
446#385—834no—
447#385—834no—
448#384—832no—
449#384—832no—
450#383—834no—
451#382—832no—
452#382—832no—
453#382—834no—
454#381—832no—
455#381—834no—
456#380—832no—
457#380—831no—
458#380—831no—
459#380—832no—
460#380—832no—
461#380—832no—
462#380—831no—
463#380—831no—
464#380—834no—
465#379—832no—
466C4×C4⋊C4—832no—
467C4×C4⋊C4—832no—
468C4×C4⋊C4—832no—
469C4×C4⋊C4—832no—
470C4×C4⋊C4—834no—
471C4×C4⋊C4C2×D8312yescomplemented
472C4×C4⋊C4C2×D8312yescomplemented
473C4×C4⋊C4C2×D8312yescomplemented
474C4×C4⋊C4C2×D8312yescomplemented
475C4×C22⋊C4—834no—
476C4×C22⋊C4—834no—
477C4×C22⋊C4—832no—
478C4×C22⋊C4—832no—
479C4×C22⋊C4C2×D8314yes—
480#376—834no—
481C2×#95—832no—
482C25—831no—
483C23×C4—832no—
484C23×C4—832no—
485C23×C4—831no—
486C23×C4—838no—
487C23×C4—832no—
488C23×C4—831no—
489C23×C4—831no—
490C23×C4—831no—
491C23×C4—831no—
492C23×C4—1664no—
493C23×C4—1664no—
494C23×C4C22×D8312yes—
495C23×C4C22×D8311yescharacteristic
496#117—24no—
497#117—3328no—
498#117—838no—
499#117—838no—
500#117—838no—
501#117—8316no—
502#117—8316no—
503#117—1664no—
504#117C4×D8318yes—
505C2×C4⋊C4—24no—
506C2×C4⋊C4—834no—
507C2×C4⋊C4—834no—
508C2×C4⋊C4—834no—
509C2×C4⋊C4—834no—
510C2×C4⋊C4—832no—
511C2×C4⋊C4—832no—
512C2×C4⋊C4—831no—
513C2×C4⋊C4—831no—
514C2×C4⋊C4—838no—
515C2×C4⋊C4—838no—
516C2×C4⋊C4—832no—
517C2×C4⋊C4—832no—
518C2×C4⋊C4—831no—
519C2×C4⋊C4—831no—
520C2×C4⋊C4—1664no—
521C2×C4⋊C4C22×D8312yes—
522C2×C4⋊C4C22×D8312yes—
523C2×C4⋊C4C22×D8311yescharacteristic
524C2×C4⋊C4C22×D8311yescharacteristic
525C2×C4⋊C4C22×D8311yescharacteristic
526C2×C4⋊C4C22×D8311yescharacteristic
527C2×C22⋊C4—3324no—
528C2×C22⋊C4—834no—
529C2×C22⋊C4—832no—
530C2×C22⋊C4—832no—
531C2×C22⋊C4—832no—
532C2×C22⋊C4—832no—
533C2×C22⋊C4—832no—
534C2×C22⋊C4—8316no—
535C2×C22⋊C4—832no—
536C2×C22⋊C4—834no—
537C2×C22⋊C4—832no—
538C2×C22⋊C4—832no—
539C2×C22⋊C4C22×D8312yes—
540C2×C22⋊C4C22×D8312yes—
541C2×C42—834no—
542C2×C42—834no—
543C2×C42—832no—
544C2×C42—832no—
545C2×C42—832no—
546C2×C42—8316no—
547C2×C42—832no—
548C2×C42C22×D8312yes—
549C2×C42C22×D8314yes—
550C2×C42C22×D8314yes—
551C2×C42C22×D8312yes—
552#95—834no—
553#95—834no—
554#95—832no—
555#95—834no—
556#95—834no—
557#95—832no—
558#95—834no—
559#95—834no—
560#95—832no—
561#95—832no—
562#95—834no—
563#95—834no—
564#95C22×D8314yes—
565#95C22×D8314yes—
566C24—3321no—
567C24—3321no—
568C24—834no—
569C24—831no—
570C24—831no—
571C24—1662no—
572C24—1662no—
573C24—1662no—
574C24—1662no—
575C24C23×D8311yescharacteristic
576C22×C4—24no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—3322no—
580C22×C4—3322no—
581C22×C4—3322no—
582C22×C4—3322no—
583C22×C4—838no—
584C22×C4—834no—
585C22×C4—831no—
586C22×C4—831no—
587C22×C4—832no—
588C22×C4—832no—
589C22×C4—834no—
590C22×C4—838no—
591C22×C4—834no—
592C22×C4—834no—
593C22×C4—834no—
594C22×C4—832no—
595C22×C4—834no—
596C22×C4—832no—
597C22×C4—1664no—
598C22×C4—1664no—
599C22×C4—1664no—
600C22×C4—1662no—
601C22×C4—1662no—
602C22×C4—1662no—
603C22×C4—1662no—
604C22×C4—1662no—
605C22×C4—1662no—
606C22×C4—1662no—
607C22×C4—1662no—
608C22×C4—1662no—
609C22×C4—1662no—
610C22×C4—16632no—
611C22×C4C2×C4×D8314yes—
612C22×C4#1305059014yes—
613C22×C4#1305059014yes—
614C22×C4C23×D8312yes—
615C22×C4C23×D8314yes—
616C22×C4C23×D8312yes—
617C22×C4C23×D8312yes—
618C22×C4C23×D8312yes—
619C22×C4C23×D8311yescharacteristic
620C22×C4C23×D8311yescharacteristic
621C4⋊C4—24no—
622C4⋊C4—24no—
623C4⋊C4—22no—
624C4⋊C4—22no—
625C4⋊C4—3324no—
626C4⋊C4—3324no—
627C4⋊C4—3324no—
628C4⋊C4—3324no—
629C4⋊C4—838no—
630C4⋊C4—838no—
631C4⋊C4—834no—
632C4⋊C4—834no—
633C4⋊C4—1664no—
634C4⋊C4—1664no—
635C4⋊C4—1662no—
636C4⋊C4—1662no—
637C4⋊C4C2×C4×D8314yes—
638C4⋊C4C2×C4×D8314yes—
639C22⋊C4—24no—
640C22⋊C4—3324no—
641C22⋊C4—3322no—
642C22⋊C4—3322no—
643C22⋊C4—838no—
644C22⋊C4—838no—
645C22⋊C4—838no—
646C22⋊C4—1668no—
647C22⋊C4—1664no—
648C22⋊C4—1664no—
649C22⋊C4—1664no—
650C22⋊C4C2×C4×D8318yes—
651C42—24no—
652C42—44no—
653C42—44no—
654C42—3324no—
655C42—3324no—
656C42—838no—
657C42—838no—
658C42—838no—
659C42—1664no—
660C42C2×C4×D8318yes—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—3324no—
666C23—3324no—
667C23—3324no—
668C23—3324no—
669C23—3324no—
670C23—832no—
671C23—832no—
672C23—832no—
673C23—832no—
674C23—1668no—
675C23—1668no—
676C23—1661no—
677C23—1661no—
678C23—1661no—
679C23—1661no—
680C23—1661no—
681C23—1661no—
682C23—1661no—
683C23—1661no—
684C23—1661no—
685C23—1661no—
686C23C22×C4×D8312yes—
687C23C2×#1305059012yes—
688C23C2×#1305059012yes—
689C23C24×D8311yescharacteristic
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—84no—
704C2×C4—3328no—
705C2×C4—832no—
706C2×C4—834no—
707C2×C4—834no—
708C2×C4—832no—
709C2×C4—6644no—
710C2×C4—16616no—
711C2×C4—1662no—
712C2×C4—1662no—
713C2×C4—1664no—
714C2×C4—1662no—
715C2×C4—1664no—
716C2×C4—1662no—
717C2×C4—1662no—
718C2×C4—1662no—
719C2×C4—1664no—
720C2×C4—1668no—
721C2×C4—1661no—
722C2×C4—1661no—
723C2×C4—1661no—
724C2×C4—1661no—
725C2×C4—1662no—
726C2×C4—1662no—
727C2×C4—1662no—
728C2×C4—1662no—
729C2×C4—1668no—
730C2×C4—1668no—
731C2×C4—1668no—
732C2×C4—1668no—
733C2×C4#14581749116yescomplemented
734C2×C4C22×C4×D8314yes—
735C2×C4C22×C4×D8314yes—
736C2×C4C22×C4×D8312yes—
737C2×C4C22×C4×D8312yes—
738C2×C4C2×#1305059012yes—
739C2×C4C2×#1305059012yes—
740C2×C4C2×#1305059012yes—
741C2×C4C2×#1305059012yes—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—33216no—
749C22—3321no—
750C22—3321no—
751C22—3321no—
752C22—3321no—
753C22—834no—
754C22—1662no—
755C22—1662no—
756C22—1662no—
757C22—1662no—
758C22—1662no—
759C22—1662no—
760C22—1662no—
761C22—1662no—
762C22—1662no—
763C22C2×#1458174914yes—
764C22C23×C4×D8311yescharacteristic
765C22C22×#1305059011yescharacteristic
766C22C22×#1305059011yescharacteristic
767C22H(5,𝔽2)×D8311yescharacteristic
768C222−1+4×D8311yescharacteristic
769C22#1912853611yescharacteristic
770C22#1912853811yescharacteristic
771C4—24no—
772C4—24no—
773C4—44no—
774C4—42no—
775C4—42no—
776C4—3322no—
777C4—3324no—
778C4—3322no—
779C4—1662no—
780C4—1662no—
781C4—1664no—
782C4—1664no—
783C4C2×#1458174914yes—
784C4C2×#1458174914yes—
785C2—24no—
786C2—3322no—
787C2—1664no—
788C2C22×#1458174911yescharacteristic
789C2#520×D8311yescharacteristic
790C2#2492066311yescharacteristic
791C2#2492118811yescharacteristic
792C2#2492119911yescharacteristic
793C2#2492120511yescharacteristic
794C2#2492121611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingC83×#2274C2
socle, cosocleC23×C83C25
prime radicalC24×D83C23
hypercenter#2274D83
hypocenterC83#34180
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2274

Complements

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

NH ≅ G/Ntype
2. #24910352C2semidirect
3. #24910344C2semidirect
4. #24910336C2semidirect
5. #24910328C2semidirect
6. #24910317C2semidirect
8. #24910087C2semidirect
9. #24910083C2semidirect
10. #24910068C2semidirect
11. #24910068C2semidirect
12. #24909867C2semidirect
13. #24909859C2semidirect
16. #24909819C2semidirect
17. C83×#2274C2semidirect
26. #117×D83C4semidirect
33. #19127599C22semidirect
34. #19127599C22semidirect
35. #19127597C22semidirect
36. #19127597C22semidirect
41. #19127585C22semidirect
42. #19127585C22semidirect
43. #19127583C22semidirect
44. #19127583C22semidirect
47. #19127570C22semidirect
48. #19127570C22semidirect
49. #19127568C22semidirect
50. #19127566C22semidirect
51. #19127566C22semidirect
52. #19127565C22semidirect
65. C4⋊C4×Dic83C22semidirect
66. C4⋊C4×Dic83C22semidirect
67. C4×Dic83⋊C4C22semidirect
68. C4×C4⋊Dic83C22semidirect
69. C4×C4⋊Dic83C22semidirect
74. #19127547C22semidirect
79. C4×C4⋊C4×C83C22semidirect
80. C4×C4⋊C4×C83C22semidirect
81. C4×C4⋊C4×C83C22semidirect
82. C4×C4⋊C4×C83C22semidirect
98. #14581750C2×C4semidirect
99. #14581750C2×C4semidirect
101. #14581749C2×C4semidirect
116. C4⋊C4×D83C2×C4semidirect
117. C4⋊C4×D83C2×C4semidirect
136. C42×D83C2×C4semidirect
306. C2×C4×C83#117semidirect
414. #2274D83semidirect
415. C83#34180semidirect
471. C4×C4⋊C4C2×D83semidirect
472. C4×C4⋊C4C2×D83semidirect
473. C4×C4⋊C4C2×D83semidirect
474. C4×C4⋊C4C2×D83semidirect
733. C2×C4#14581749semidirect

Maximal subgroups

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

subgroupindex
C2×#117×D832
#249103522
#249103442
#249103362
#249103282
#249103172
#249103062
#249100872
#249100832
#249100682
#249098672
#249098592
#249098422
C2×#191275582
#249098192
C83×#22742
#3418083