Finite Group Databasebeta

← #35564842

Subgroups — #35564842

Order 21248.

2226 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128256C211yesmaximal, characteristic
2#24910564C212yesmaximal, complemented
3#24910555C212yesmaximal, complemented
4#24910552C211yesmaximal, characteristic, complemented
5#24910552C211yesmaximal, characteristic, complemented
6#24910523C211yesmaximal, characteristic, complemented
7#24910419C212yesmaximal, complemented
8#24910417C214yesmaximal, complemented
9Q8×Dic83⋊C4C212yesmaximal, complemented
10#24910192C214yesmaximal
11#24910085C212yesmaximal
12#24910001C212yesmaximal
13C4×#14581768C212yesmaximal
14#24909867C211yesmaximal, characteristic
15#24909817C212yesmaximal
16C4×C4⋊C4×D83C211yesmaximal, characteristic
17C83×#2365C211yesmaximal, characteristic, complemented
18#19128256C4116yescomplemented
19C2×#14581792C2211yescharacteristic
20C2×#14581783C2212yes—
21C2×#14581772C2212yes—
22C2×#14581768C2212yes—
23C2×Q8×Dic83C2212yes—
24C2×Q8×Dic83C2212yes—
25C2×#14581757C2212yes—
26C2×#14581750C2212yes—
27C2×#14581749C2212yes—
28C2×C4⋊C4×D83C2211yescharacteristic
29C2×C4⋊C4×D83C2211yescharacteristic
30C2×C42×D83C2212yes—
31C2×C42×D83C2211yescharacteristic
32#19127608C2212yes—
33#19127605C2214yes—
34#19127605C2214yes—
35#19127600C2212yes—
36#19127599C2212yes—
37#19127599C2214yes—
38#19127599C2212yes—
39#19127597C2212yes—
40#19127597C2214yes—
41#19127597C2212yes—
42#19127588C2214yes—
43#19127587C2214yes—
44#19127586C2214yes—
45#19127584C2214yes—
46#19127582C2214yes—
47#19127575C2214yes—
48#19127572C2214yes—
49#19127570C2214yes—
50#19127570C2211yescharacteristic
51#19127570C2211yescharacteristic
52#19127565C2214yes—
53#19127565C2212yes—
54#19127560C2212yes—
55#19127558C2211yescharacteristic
56#19127558C2211yescharacteristic
57C4⋊C4×Dic83C2212yes—
58C4⋊C4×Dic83C2212yes—
59C4⋊C4×Dic83C2212yes—
60C4⋊C4×Dic83C2211yescharacteristic
61C4⋊C4×Dic83C2211yescharacteristic
62C4×Dic83⋊C4C2214yes—
63C4×Dic83⋊C4C2212yes—
64C4×Dic83⋊C4C2212yes—
65C4×Dic83⋊C4C2214yes—
66C4×C4⋊Dic83C2211yescharacteristic
67C4×C4⋊Dic83C2212yes—
68C4×C4⋊Dic83C2211yescharacteristic
69C4×C4⋊Dic83C2212yes—
70#19127552C2212yes—
71#19127552C2214yes—
72#19127552C2214yes—
73C4×(C2×D83)⋊C4C2214yes—
74#19127548C2214yes—
75#95×D83C2212yes—
76C2×C4⋊Q8×C83C2211yescharacteristic
77C2×C4×Q8×C83C2212yes—
78#391×C83C2212yes—
79#389×C83C2212yes—
80#387×C83C2214yes—
81C4×C4⋊C4×C83C2211yescharacteristic
82C4×C4⋊C4×C83C2211yescharacteristic
83C4×C4⋊C4×C83C2212yes—
84C22×Dic166C2312yes—
85C22×C4×D83C2311yescharacteristic
86C22×C4×D83C2312yes—
87C22×C4×D83C2311yescharacteristic
88C22×C4×D83C2312yes—
89C22×C4×D83C2311yescharacteristic
90#14581792C2×C418yescomplemented
91#14581783C2×C4116yescomplemented
92#14581772C2×C4116yes—
93#14581768C2×C4116yes—
94Q8×Dic83—44no—
95Q8×Dic83C2×C4116yescomplemented
96#14581757C2×C4116yescomplemented
97#14581750C2×C4116yes—
98#14581749—28no—
99C2×C4⋊Dic83C2311yescharacteristic
100C2×C4⋊Dic83C2311yescharacteristic
101C2×C4⋊Dic83C2311yescharacteristic
102C2×C4⋊Dic83C2314yes—
103C2×C4⋊Dic83C2312yes—
104C2×C4⋊Dic83C2312yes—
105C2×C4⋊Dic83C2314yes—
106C2×C4⋊Dic83C2311yescharacteristic
107C2×Dic83⋊C4C2312yes—
108C2×Dic83⋊C4C2312yes—
109C2×Dic83⋊C4C2312yes—
110C2×Dic83⋊C4C2314yes—
111C2×Dic83⋊C4C2312yes—
112C2×Dic83⋊C4C2312yes—
113C2×Dic83⋊C4C2314yes—
114C2×Dic83⋊C4C2314yes—
115C2×Dic83⋊C4C2312yes—
116C4⋊C4×D83—24no—
117C4⋊C4×D83Q818yescomplemented
118C2×(C2×D83)⋊C4C2312yes—
119C2×(C2×D83)⋊C4C2312yes—
120C2×(C2×D83)⋊C4C2314yes—
121C2×C4×Dic83C2312yes—
122C2×C4×Dic83C2312yes—
123C2×C4×Dic83C2312yes—
124C2×C4×Dic83C2314yes—
125C2×C4×Dic83C2314yes—
126C2×C4×Dic83C2312yes—
127C2×C4×Dic83C2314yes—
128C2×C4×Dic83C2311yescharacteristic
129C2×C4×Dic83C2314yes—
130C2×C4×Dic83C2311yescharacteristic
131C2×C4×Dic83C2311yescharacteristic
132C42×D83—44no—
133C42×D83C2×C418yes—
134C83⋊#95C2312yes—
135C83⋊#95C2312yes—
136C83⋊#95C2314yes—
137C83⋊#95C2314yes—
138C83⋊#95C2312yes—
139C83⋊#95C2314yes—
140C83⋊#95C2312yes—
141C83⋊#95C2312yes—
142C83⋊#95C2312yes—
143C83⋊#95C2314yes—
144C83⋊#95C2314yes—
145C83⋊#95C2314yes—
146C22×Q8×C83C2312yes—
147C4⋊Q8×C83C2×C418yescomplemented
148C4×Q8×C83—44no—
149C2×C4⋊C4×C83C2311yescharacteristic
150C2×C4⋊C4×C83C2311yescharacteristic
151C2×C4⋊C4×C83C2311yescharacteristic
152C2×C4⋊C4×C83C2314yes—
153C2×C4⋊C4×C83C2312yes—
154C2×C4⋊C4×C83C2312yes—
155C2×C4⋊C4×C83C2311yescharacteristic
156C2×C42×C83C2312yes—
157C2×C42×C83C2312yes—
158C2×C42×C83C2314yes—
159C2×C42×C83C2311yescharacteristic
160#95×C83C2314yes—
161#95×C83C2314yes—
162#95×C83C2312yes—
163#95×C83C2312yes—
164C23×D83C2411yescharacteristic
165C2×Dic166—42no—
166C2×Dic166—42no—
167C2×Dic166C22×C418yes—
168C22×Dic83C2412yes—
169C22×Dic83C2412yes—
170C22×Dic83C2412yes—
171C22×Dic83C2411yescharacteristic
172C22×Dic83C2411yescharacteristic
173C22×Dic83C2414yes—
174C22×Dic83C2412yes—
175C22×Dic83C2411yescharacteristic
176C2×C4×D83—22no—
177C2×C4×D83—22no—
178C2×C4×D83—24no—
179C2×C4×D83—41no—
180C2×C4×D83—41no—
181C2×C4×D83—42no—
182C2×C4×D83—42no—
183C2×C4×D83—42no—
184C2×C4×D83—42no—
185C2×C4×D83C22×C414yes—
186C2×C4×D83C22×C414yes—
187C2×C4×D83C22×C414yes—
188C2×C4×D83C2×Q818yes—
189C2×C4×D83C2×Q814yes—
190C2×C4×D83#4114yes—
191C4⋊Dic83—22no—
192C4⋊Dic83—22no—
193C4⋊Dic83—22no—
194C4⋊Dic83—44no—
195C4⋊Dic83C22×C418yes—
196C4⋊Dic83C22×C4116yes—
197C4⋊Dic83C22×C418yes—
198C4⋊Dic83C2×Q814yes—
199Dic83⋊C4—24no—
200Dic83⋊C4—24no—
201Dic83⋊C4—24no—
202Dic83⋊C4—42no—
203Dic83⋊C4—42no—
204Dic83⋊C4—44no—
205Dic83⋊C4—44no—
206Dic83⋊C4C22×C4116yes—
207Dic83⋊C4C2×Q818yes—
208(C2×D83)⋊C4—24no—
209(C2×D83)⋊C4—24no—
210(C2×D83)⋊C4C22×C4116yes—
211C4×Dic83—24no—
212C4×Dic83—24no—
213C4×Dic83—42no—
214C4×Dic83—42no—
215C4×Dic83—44no—
216C4×Dic83—44no—
217C4×Dic83—44no—
218C4×Dic83C22×C414yes—
219C4×Dic83C22×C414yes—
220C4×Dic83C22×C414yes—
221C4×Dic83C22×C4116yes—
222C2×Q8×C83—24no—
223C2×Q8×C83—24no—
224C2×Q8×C83C22×C418yes—
225C22×C4×C83C2412yes—
226C22×C4×C83C2412yes—
227C22×C4×C83C2412yes—
228C22×C4×C83C2411yescharacteristic
229C22×C4×C83C2414yes—
230C22×C4×C83C2412yes—
231C22×C4×C83C2411yescharacteristic
232C22×C4×C83C2411yescharacteristic
233C4⋊C4×C83—22no—
234C4⋊C4×C83—22no—
235C4⋊C4×C83—22no—
236C4⋊C4×C83—44no—
237C4⋊C4×C83C22×C418yes—
238C4⋊C4×C83C22×C418yes—
239C4⋊C4×C83C2×Q814yes—
240C42×C83—24no—
241C42×C83—24no—
242C42×C83—44no—
243C42×C83C22×C414yes—
244C23×C83C2511yescharacteristic
245C22×D83—21no—
246C22×D83—21no—
247C22×D83—21no—
248C22×D83—21no—
249C22×D83C23×C412yes—
250C22×D83C22×Q812yes—
251C22×D83C2×#4112yes—
252Q8×C83—216no—
253C2×C4×C83—22no—
254C2×C4×C83—24no—
255C2×C4×C83—24no—
256C2×C4×C83—22no—
257C2×C4×C83—21no—
258C2×C4×C83—21no—
259C2×C4×C83—22no—
260C2×C4×C83—22no—
261C2×C4×C83—22no—
262C2×C4×C83—22no—
263C2×C4×C83—22no—
264C2×C4×C83—22no—
265C2×C4×C83—22no—
266C2×C4×C83—22no—
267C2×C4×C83—22no—
268C2×C4×C83C23×C412yes—
269C2×C4×C83C23×C418yes—
270C2×C4×C83C23×C412yes—
271C2×C4×C83C23×C412yes—
272C2×C4×C83C22×Q814yes—
273C2×C4×C83C22×Q812yes—
274C2×C4×C83C2×#4112yes—
275C2×C4×C83H(5,𝔽2)12yes—
276C2×C4×C832−1+412yes—
277C2×Dic83—22no—
278C2×Dic83—21no—
279C2×Dic83—21no—
280C2×Dic83—22no—
281C2×Dic83—24no—
282C2×Dic83—21no—
283C2×Dic83—21no—
284C2×Dic83—24no—
285C2×Dic83—22no—
286C2×Dic83—22no—
287C2×Dic83—22no—
288C2×Dic83—22no—
289C2×Dic83—22no—
290C2×Dic83—22no—
291C2×Dic83—22no—
292C2×Dic83—22no—
293C2×Dic83—22no—
294C2×Dic83C23×C412yes—
295C2×Dic83C23×C412yes—
296C2×Dic83C23×C418yes—
297C2×Dic83C23×C412yes—
298C2×Dic83C22×Q814yes—
299C2×Dic83C22×Q812yes—
300C2×Dic83C2×#4112yes—
301C4×D83—28no—
302C4×D83—44no—
303C4×D83—48no—
304C4×D83—48no—
305C4×D83C4×Q8116yescomplemented
306Dic166—48no—
307C22×C83C24×C411yescharacteristic
308C22×C83C23×Q811yescharacteristic
309C22×C83C22×#4111yescharacteristic
310C22×C83C2×H(5,𝔽2)11yescharacteristic
311C22×C83C2×2−1+411yescharacteristic
312C22×C83#58511yescharacteristic
313C22×C83#58511yescharacteristic
314C2×D83—22no—
315C2×D83—22no—
316C2×D83—22no—
317C2×D83—22no—
318C2×D83—22no—
319C2×D83—22no—
320C2×D83C2×C4×Q814yes—
321C4×C83—28no—
322C4×C83—22no—
323C4×C83—24no—
324C4×C83—42no—
325C4×C83—42no—
326C4×C83—42no—
327C4×C83C2×C4×Q814yes—
328C4×C83#52014yes—
329Dic83—22no—
330Dic83—28no—
331Dic83—22no—
332Dic83—24no—
333Dic83—42no—
334Dic83—42no—
335Dic83—42no—
336Dic83C2×C4×Q814yes—
337#34213—831nomaximal, Sylow
338C2×C83C22×C4×Q811yescharacteristic
339C2×C83C2×#52011yescharacteristic
340C2×C83#342811yescharacteristic
341C2×C83#350111yescharacteristic
342C2×C83#350211yescharacteristic
343C2×C83#350611yescharacteristic
344C2×C83#350711yescharacteristic
345D83—24no—
346C2×#533—831no—
347#2370—832no—
348#2370—832no—
349#2369—831no—
350#2369—831no—
351#2365—831no—
352#2365D8311yescharacteristic, complemented
353#2355—832no—
354#2355—834no—
355Q8×C4⋊C4—832no—
356#2329—834no—
357#2317—832no—
358C4×C22⋊Q8—832no—
359C4×C22⋊Q8—832no—
360#2285—831no—
361#2274—832no—
362C2×C4×C4⋊C4—831no—
363C83#3421311yescharacteristic, complemented, Sylow
364#533—8316no—
365C2×C4⋊Q8—831no—
366C2×C4⋊Q8C2×D8311yescharacteristic
367C2×#125—832no—
368C2×C22⋊Q8—832no—
369C2×C22⋊Q8—832no—
370C2×C4×Q8—832no—
371C2×C4×Q8—832no—
372C2×C4×Q8—832no—
373C2×C4×Q8C2×D8312yes—
374C2×#117—832no—
375C2×#117—832no—
376C22×C4⋊C4—831no—
377C22×C4⋊C4—831no—
378C22×C42—832no—
379C22×C42—831no—
380#391—832no—
381#391—834no—
382#391—834no—
383#391C2×D8312yes—
384#389—832no—
385#389—832no—
386#389—834no—
387#389—832no—
388#389—832no—
389#389—834no—
390#389—832no—
391#389C2×D8312yes—
392#387—834no—
393#387—834no—
394#387—834no—
395#387—834no—
396#387—834no—
397#387C2×D8314yes—
398#385—834no—
399#385—834no—
400#384—834no—
401#384—831no—
402#384—831no—
403#382—834no—
404#382—832no—
405#380—831no—
406#380—831no—
407#380—832no—
408C4×C4⋊C4—832no—
409C4×C4⋊C4—832no—
410C4×C4⋊C4—832no—
411C4×C4⋊C4—831no—
412C4×C4⋊C4—831no—
413C4×C4⋊C4—832no—
414C4×C4⋊C4—831no—
415C4×C4⋊C4—831no—
416C4×C4⋊C4—832no—
417C4×C4⋊C4—832no—
418C4×C4⋊C4—834no—
419C4×C4⋊C4—834no—
420C4×C4⋊C4—832no—
421C4×C4⋊C4—832no—
422C4×C4⋊C4—834no—
423C4×C4⋊C4—834no—
424C4×C4⋊C4C2×D8311yescharacteristic
425C4×C4⋊C4C2×D8311yescharacteristic
426C4×C4⋊C4C2×D8312yes—
427C4×C22⋊C4—834no—
428C4×C22⋊C4—834no—
429C2×#95—832no—
430C22×Q8—832no—
431C22×Q8C22×D8312yes—
432C23×C4—832no—
433C23×C4—831no—
434C23×C4—832no—
435C23×C4—831no—
436C23×C4—831no—
437C4⋊Q8—838no—
438C4⋊Q8C4×D8318yescomplemented
439#125—8316no—
440C22⋊Q8—8316no—
441C22⋊Q8—8316no—
442C4×Q8—44no—
443C4×Q8—3324no—
444C4×Q8—8316no—
445C4×Q8—8316no—
446#117—8316no—
447#117—1668no—
448C2×C4⋊C4—834no—
449C2×C4⋊C4—832no—
450C2×C4⋊C4—832no—
451C2×C4⋊C4—834no—
452C2×C4⋊C4—834no—
453C2×C4⋊C4—832no—
454C2×C4⋊C4—831no—
455C2×C4⋊C4—832no—
456C2×C4⋊C4—834no—
457C2×C4⋊C4—834no—
458C2×C4⋊C4—832no—
459C2×C4⋊C4—838no—
460C2×C4⋊C4—832no—
461C2×C4⋊C4—831no—
462C2×C4⋊C4—832no—
463C2×C4⋊C4—832no—
464C2×C4⋊C4—831no—
465C2×C4⋊C4—831no—
466C2×C4⋊C4—1664no—
467C2×C4⋊C4C22×D8311yescharacteristic
468C2×C4⋊C4C22×D8311yescharacteristic
469C2×C4⋊C4C22×D8311yescharacteristic
470C2×C4⋊C4C22×D8314yes—
471C2×C4⋊C4C22×D8312yes—
472C2×C4⋊C4C22×D8312yes—
473C2×C4⋊C4C22×D8311yescharacteristic
474C2×C22⋊C4—834no—
475C2×C22⋊C4—832no—
476C2×C22⋊C4—832no—
477C2×C42—3324no—
478C2×C42—834no—
479C2×C42—834no—
480C2×C42—834no—
481C2×C42—832no—
482C2×C42—832no—
483C2×C42—834no—
484C2×C42—831no—
485C2×C42—831no—
486C2×C42—831no—
487C2×C42—838no—
488C2×C42—832no—
489C2×C42—832no—
490C2×C42C22×D8312yes—
491C2×C42C22×D8312yes—
492C2×C42C22×D8314yes—
493C2×C42C22×D8311yescharacteristic
494#95—832no—
495#95—832no—
496#95—832no—
497#95—834no—
498#95—834no—
499#95—834no—
500#95—832no—
501#95—832no—
502#95—832no—
503#95—834no—
504#95—834no—
505#95—834no—
506#95C22×D8312yes—
507#95C22×D8314yes—
508#95C22×D8314yes—
509#95C22×D8312yes—
510C24—831no—
511C2×Q8—24no—
512C2×Q8—24no—
513C2×Q8—3322no—
514C2×Q8—3322no—
515C2×Q8—838no—
516C2×Q8C2×C4×D8318yes—
517C22×C4—3322no—
518C22×C4—3322no—
519C22×C4—3322no—
520C22×C4—3321no—
521C22×C4—3321no—
522C22×C4—3322no—
523C22×C4—834no—
524C22×C4—838no—
525C22×C4—831no—
526C22×C4—834no—
527C22×C4—834no—
528C22×C4—834no—
529C22×C4—832no—
530C22×C4—831no—
531C22×C4—834no—
532C22×C4—831no—
533C22×C4—834no—
534C22×C4—832no—
535C22×C4—832no—
536C22×C4—832no—
537C22×C4—1664no—
538C22×C4—1662no—
539C22×C4—1662no—
540C22×C4C23×D8312yes—
541C22×C4C23×D8312yes—
542C22×C4C23×D8312yes—
543C22×C4C23×D8311yescharacteristic
544C22×C4C23×D8314yes—
545C22×C4C23×D8312yes—
546C22×C4C23×D8311yescharacteristic
547C22×C4C23×D8311yescharacteristic
548C4⋊C4—22no—
549C4⋊C4—22no—
550C4⋊C4—22no—
551C4⋊C4—44no—
552C4⋊C4—3324no—
553C4⋊C4—3322no—
554C4⋊C4—3322no—
555C4⋊C4—3324no—
556C4⋊C4—3324no—
557C4⋊C4—838no—
558C4⋊C4—8316no—
559C4⋊C4—8316no—
560C4⋊C4—838no—
561C4⋊C4—838no—
562C4⋊C4—834no—
563C4⋊C4—1664no—
564C4⋊C4—1664no—
565C4⋊C4—1664no—
566C4⋊C4—1662no—
567C4⋊C4—1662no—
568C4⋊C4—1662no—
569C4⋊C4C2×C4×D8318yes—
570C4⋊C4C2×C4×D8318yes—
571C4⋊C4Q8×D8314yes—
572C22⋊C4—8316no—
573C22⋊C4—1664no—
574C22⋊C4—1664no—
575C42—24no—
576C42—24no—
577C42—44no—
578C42—3322no—
579C42—3322no—
580C42—3324no—
581C42—3324no—
582C42—3324no—
583C42—834no—
584C42—834no—
585C42—834no—
586C42—8316no—
587C42—1664no—
588C42—1664no—
589C42C2×C4×D8314yes—
590C23—832no—
591C23—832no—
592C23—832no—
593C23—1661no—
594C23—1661no—
595C23—1661no—
596C23—1661no—
597C23C24×D8311yescharacteristic
598Q8—216no—
599Q8—3328no—
600C2×C4—22no—
601C2×C4—24no—
602C2×C4—24no—
603C2×C4—22no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—3324no—
616C2×C4—3328no—
617C2×C4—3328no—
618C2×C4—832no—
619C2×C4—832no—
620C2×C4—832no—
621C2×C4—8316no—
622C2×C4—832no—
623C2×C4—832no—
624C2×C4—838no—
625C2×C4—834no—
626C2×C4—1662no—
627C2×C4—1662no—
628C2×C4—1662no—
629C2×C4—1662no—
630C2×C4—1662no—
631C2×C4—1662no—
632C2×C4—1662no—
633C2×C4—1662no—
634C2×C4—1662no—
635C2×C4—1661no—
636C2×C4—1662no—
637C2×C4—1661no—
638C2×C4—1662no—
639C2×C4—1664no—
640C2×C4—1661no—
641C2×C4—1661no—
642C2×C4—1664no—
643C2×C4—1668no—
644C2×C4C22×C4×D8312yes—
645C2×C4C22×C4×D8318yes—
646C2×C4C22×C4×D8312yes—
647C2×C4C22×C4×D8312yes—
648C2×C4C2×Q8×D8314yes—
649C2×C4C2×Q8×D8312yes—
650C2×C4#41×D8312yes—
651C2×C4#1458183712yes—
652C2×C4#1458183912yes—
653C22—834no—
654C22—1662no—
655C22—1662no—
656C22—1662no—
657C22—1662no—
658C22—1662no—
659C22—1662no—
660C22C23×C4×D8311yescharacteristic
661C22C22×Q8×D8311yescharacteristic
662C22C2×#41×D8311yescharacteristic
663C22C2×#1458183711yescharacteristic
664C22C2×#1458183911yescharacteristic
665C22#1912853811yescharacteristic
666C22#1912853811yescharacteristic
667C4—28no—
668C4—22no—
669C4—24no—
670C4—42no—
671C4—42no—
672C4—42no—
673C4—3322no—
674C4—3322no—
675C4—3322no—
676C4—834no—
677C4—1662no—
678C4—1662no—
679C4—1668no—
680C4—1664no—
681C4C4×Q8×D8314yes—
682C4#1912818014yes—
683C2—1664no—
684C2C2×C4×Q8×D8311yescharacteristic
685C2C2×#1912818011yescharacteristic
686C2#2492066511yescharacteristic
687C2#2492125811yescharacteristic
688C2#2492126711yescharacteristic
689C2#2492131311yescharacteristic
690C2#2492131811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingC83×#2365C2
socle, cosocleC23×C83C25
prime radicalC23×D83C24
hypercenter#2365D83
hypocenterC83#34213
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2365

Complements

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

NH ≅ G/Ntype
2. #24910564C2semidirect
3. #24910555C2semidirect
4. #24910552C2semidirect
5. #24910552C2semidirect
6. #24910523C2semidirect
7. #24910419C2semidirect
8. #24910417C2semidirect
9. Q8×Dic83⋊C4C2semidirect
17. C83×#2365C2semidirect
18. #19128256C4semidirect
90. #14581792C2×C4semidirect
91. #14581783C2×C4semidirect
95. Q8×Dic83C2×C4semidirect
96. #14581757C2×C4semidirect
117. C4⋊C4×D83Q8semidirect
147. C4⋊Q8×C83C2×C4semidirect
305. C4×D83C4×Q8semidirect
352. #2365D83semidirect
363. C83#34213semidirect
438. C4⋊Q8C4×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#191282562
#249105642
#249105552
#249105522
#249105232
#249104192
#249104172
Q8×Dic83⋊C42
#249101922
#249100852
#249100012
C4×#145817682
#249098672
#249098172
C4×C4⋊C4×D832
C83×#23652
#3421383