Finite Group Databasebeta

← #35566466

Subgroups — #35566466

Order 21248.

2860 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128366C211yesmaximal, characteristic
2C2×#19128177C212yesmaximal, complemented
3#24910523C211yesmaximal, characteristic, complemented
4#24910522C212yesmaximal, complemented
5#24910495C212yesmaximal, complemented
6#24910491C214yesmaximal, complemented
7#24910414C211yesmaximal, characteristic
8#24910408C212yesmaximal
9#24910375C211yesmaximal, characteristic, complemented
10#24910297C212yesmaximal, complemented
11#24910140C214yesmaximal, complemented
12#24910139C212yesmaximal, complemented
13#24910034C212yesmaximal, complemented
14#24909927C211yesmaximal, characteristic
15#24909921C212yesmaximal
16C42×Dic166C211yesmaximal, characteristic, complemented
17C4×C4⋊Q8×C83C211yesmaximal, characteristic, complemented
18C22×Q8×D83C2212yes—
19#19128366C4116yescomplemented
20C2×#14581791C2212yes—
21C2×#14581770C2214yes—
22C2×#14581768C2212yes—
23#19128177—216no—
24C2×Q8×Dic83C2212yes—
25C2×C4×Dic166C2214yes—
26C2×C4×Dic166C2211yescharacteristic
27C2×C4×Dic166C2211yescharacteristic
28C2×C4×Dic166C2211yescharacteristic
29C2×#14581757C2212yes—
30C2×#14581757C2214yes—
31C2×C4×D332C2211yescharacteristic
32C2×#14581754C2212yes—
33C2×#14581750C2214yes—
34C2×#14581750C2212yes—
35C2×#14581749C2212yes—
36C2×#14581749C2214yes—
37#19127608C2212yes—
38#19127605C2214yes—
39#19127605C2214yes—
40#19127603C2211yescharacteristic
41#19127603C2211yescharacteristic
42#19127602C2212yes—
43#19127600C2212yes—
44#19127599C2211yescharacteristic
45#19127599C2211yescharacteristic
46#19127597C2212yes—
47#19127596C2214yes—
48#19127596C2214yes—
49#19127593C2214yes—
50#19127592C2214yes—
51#19127592C2212yes—
52#19127592C2212yes—
53#19127591C2214yes—
54#19127591C2214yes—
55#19127590C2214yes—
56#19127588C2214yes—
57#19127587C2214yes—
58#19127585C2214yes—
59#19127570C2212yes—
60#19127560C2214yes—
61#19127558C2212yes—
62C4⋊C4×Dic83C2212yes—
63C4⋊C4×Dic83C2212yes—
64C4⋊C4×Dic83C2212yes—
65C4×Dic83⋊C4C2212yes—
66C4×Dic83⋊C4C2212yes—
67C4×Dic83⋊C4C2212yes—
68C4×C4⋊Dic83C2211yescharacteristic
69C4×C4⋊Dic83C2211yescharacteristic
70C4×C4⋊Dic83C2211yescharacteristic
71C4×C4⋊Dic83C2211yescharacteristic
72#19127552C2214yes—
73C4×(C2×D83)⋊C4C2212yes—
74#19127548C2214yes—
75C42×Dic83C2212yes—
76C2×C4⋊Q8×C83C2211yescharacteristic
77C2×C4×Q8×C83C2212yes—
78#391×C83C2212yes—
79#389×C83C2212yes—
80#389×C83C2212yes—
81#384×C83C2211yescharacteristic
82C4×C4⋊C4×C83C2212yes—
83C4×C4⋊C4×C83C2212yes—
84C43×C83C2211yescharacteristic
85C22×Dic166C2314yes—
86C22×Dic166C2311yescharacteristic
87C2×Q8×D83—28no—
88C2×Q8×D83—28no—
89C2×Q8×D83C2×C4116yes—
90C22×D332C2311yescharacteristic
91C22×C4×D83C2312yes—
92C22×C4×D83C2314yes—
93#14581791C2×C4116yes—
94#14581770C2×C4132yes—
95#14581768C2×C4116yes—
96Q8×Dic83—28no—
97C4×Dic166—24no—
98C4×Dic166—216no—
99C4×Dic166C2×C418yes—
100C4×Dic166D418yescomplemented
101#14581757—28no—
102#14581757—216no—
103C4×D332C2×C418yes—
104#14581754C2×C4116yes—
105#14581750—28no—
106#14581750—216no—
107#14581749—216no—
108#14581749—28no—
109C2×C4⋊Dic83C2311yescharacteristic
110C2×C4⋊Dic83C2311yescharacteristic
111C2×C4⋊Dic83C2311yescharacteristic
112C2×C4⋊Dic83C2314yes—
113C2×C4⋊Dic83C2311yescharacteristic
114C2×C4⋊Dic83C2311yescharacteristic
115C2×C4⋊Dic83C2311yescharacteristic
116C2×Dic83⋊C4C2312yes—
117C2×Dic83⋊C4C2314yes—
118C2×Dic83⋊C4C2312yes—
119C2×Dic83⋊C4C2312yes—
120C2×Dic83⋊C4C2314yes—
121C2×Dic83⋊C4C2314yes—
122C2×Dic83⋊C4C2312yes—
123C2×Dic83⋊C4C2312yes—
124C2×(C2×D83)⋊C4C2314yes—
125C2×(C2×D83)⋊C4C2312yes—
126C2×(C2×D83)⋊C4C2312yes—
127C2×(C2×D83)⋊C4C2312yes—
128C2×(C2×D83)⋊C4C2314yes—
129C2×(C2×D83)⋊C4C2312yes—
130C2×(C2×D83)⋊C4C2314yes—
131C2×(C2×D83)⋊C4C2312yes—
132C2×C4×Dic83C2312yes—
133C2×C4×Dic83C2314yes—
134C2×C4×Dic83C2314yes—
135C2×C4×Dic83C2312yes—
136C2×C4×Dic83C2312yes—
137C2×C4×Dic83C2312yes—
138C2×C4×Dic83C2314yes—
139C2×C4×Dic83C2312yes—
140C2×C4×Dic83C2312yes—
141C2×C4×Dic83C2312yes—
142C83⋊#95C2312yes—
143C83⋊#95C2312yes—
144C83⋊#95C2312yes—
145C83⋊#95C2312yes—
146C83⋊#95C2312yes—
147C83⋊#95C2314yes—
148C83⋊#95C2314yes—
149C83⋊#95C2314yes—
150C83⋊#95C2314yes—
151C83⋊#95C2312yes—
152C22×Q8×C83C2312yes—
153C4⋊Q8×C83C2×C418yes—
154C4×Q8×C83—28no—
155C2×C4⋊C4×C83C2312yes—
156C2×C4⋊C4×C83C2312yes—
157C2×C4⋊C4×C83C2314yes—
158C2×C4⋊C4×C83C2312yes—
159C2×C4⋊C4×C83C2312yes—
160C2×C4⋊C4×C83C2312yes—
161C2×C42×C83C2311yescharacteristic
162C2×C42×C83C2311yescharacteristic
163C2×C42×C83C2311yescharacteristic
164C2×C42×C83C2314yes—
165C2×C42×C83C2311yescharacteristic
166C2×C42×C83C2311yescharacteristic
167C2×C42×C83C2311yescharacteristic
168C2×C42×C83C2311yescharacteristic
169#95×C83C2314yes—
170#95×C83C2314yes—
171C23×D83C2412yes—
172C2×Dic166—28no—
173C2×Dic166—28no—
174C2×Dic166C22×C4116yes—
175C2×Dic166C22×C414yes—
176C2×Dic166C2×D414yes—
177C2×Dic166#4114yes—
178Q8×D83—264no—
179C2×D332—22no—
180C2×D332—22no—
181C2×D332C22×C414yes—
182C22×Dic83C2412yes—
183C22×Dic83C2412yes—
184C22×Dic83C2412yes—
185C22×Dic83C2412yes—
186C22×Dic83C2412yes—
187C22×Dic83C2412yes—
188C22×Dic83C2412yes—
189C2×C4×D83—24no—
190C2×C4×D83—24no—
191C2×C4×D83—28no—
192C2×C4×D83—28no—
193C2×C4×D83C22×C418yes—
194C2×C4×D83C22×C4116yes—
195C4⋊Dic83—22no—
196C4⋊Dic83—22no—
197C4⋊Dic83—22no—
198C4⋊Dic83—28no—
199C4⋊Dic83C22×C414yes—
200C4⋊Dic83C22×C414yes—
201C4⋊Dic83C2×D414yes—
202Dic83⋊C4—24no—
203Dic83⋊C4—24no—
204Dic83⋊C4—28no—
205Dic83⋊C4—24no—
206Dic83⋊C4—44no—
207Dic83⋊C4C22×C4116yes—
208Dic83⋊C4C22×C418yes—
209Dic83⋊C4C2×D418yes—
210(C2×D83)⋊C4—24no—
211(C2×D83)⋊C4—24no—
212(C2×D83)⋊C4—24no—
213(C2×D83)⋊C4—28no—
214(C2×D83)⋊C4—44no—
215(C2×D83)⋊C4—42no—
216(C2×D83)⋊C4C22×C4116yes—
217(C2×D83)⋊C4C22×C418yes—
218C4×Dic83—24no—
219C4×Dic83—24no—
220C4×Dic83—24no—
221C4×Dic83—28no—
222C4×Dic83—28no—
223C4×Dic83—28no—
224C4×Dic83—24no—
225C4×Dic83—42no—
226C4×Dic83C22×C418yes—
227C4×Dic83C2×D418yes—
228C2×Q8×C83—24no—
229C2×Q8×C83—24no—
230C2×Q8×C83C22×C418yes—
231C22×C4×C83C2411yescharacteristic
232C22×C4×C83C2414yes—
233C22×C4×C83C2414yes—
234C22×C4×C83C2411yescharacteristic
235C22×C4×C83C2411yescharacteristic
236C22×C4×C83C2411yescharacteristic
237C22×C4×C83C2411yescharacteristic
238C22×C4×C83C2411yescharacteristic
239C22×C4×C83C2411yescharacteristic
240C4⋊C4×C83—28no—
241C4⋊C4×C83—24no—
242C4⋊C4×C83—24no—
243C4⋊C4×C83—42no—
244C4⋊C4×C83C22×C418yes—
245C4⋊C4×C83C22×C418yes—
246C42×C83—28no—
247C42×C83—22no—
248C42×C83—22no—
249C42×C83—22no—
250C42×C83—22no—
251C42×C83—41no—
252C42×C83C22×C414yes—
253C42×C83C2×D414yes—
254C23×C83C2511yescharacteristic
255C22×D83—22no—
256C22×D83—22no—
257C22×D83—22no—
258C22×D83—22no—
259C22×D83—22no—
260C22×D83—22no—
261C22×D83C23×C414yes—
262Q8×C83—216no—
263C2×C4×C83—24no—
264C2×C4×C83—21no—
265C2×C4×C83—24no—
266C2×C4×C83—21no—
267C2×C4×C83—21no—
268C2×C4×C83—21no—
269C2×C4×C83—21no—
270C2×C4×C83—21no—
271C2×C4×C83—21no—
272C2×C4×C83—21no—
273C2×C4×C83—24no—
274C2×C4×C83—21no—
275C2×C4×C83—21no—
276C2×C4×C83—24no—
277C2×C4×C83—21no—
278C2×C4×C83—24no—
279C2×C4×C83C23×C412yes—
280C2×C4×C83C23×C418yes—
281C2×C4×C83C23×C412yes—
282C2×C4×C83C23×C412yes—
283C2×C4×C83C22×D412yes—
284C2×C4×C83C22×D412yes—
285C2×C4×C83C22×D412yes—
286C2×C4×C83C2×#4112yes—
287C2×C4×C832−1+412yes—
288C2×C4×C832−1+412yes—
289C2×C4×C832−1+412yes—
290C2×Dic83—22no—
291C2×Dic83—22no—
292C2×Dic83—22no—
293C2×Dic83—22no—
294C2×Dic83—22no—
295C2×Dic83—22no—
296C2×Dic83—22no—
297C2×Dic83—22no—
298C2×Dic83—22no—
299C2×Dic83—22no—
300C2×Dic83—22no—
301C2×Dic83—22no—
302C2×Dic83—22no—
303C2×Dic83—22no—
304C2×Dic83—22no—
305C2×Dic83C23×C414yes—
306C2×Dic83C23×C414yes—
307C2×Dic83C23×C414yes—
308C2×Dic83C22×D414yes—
309C2×Dic83C22×D414yes—
310C2×Dic83C2×#4114yes—
311D332—28no—
312C4×D83—216no—
313C4×D83—232no—
314Dic166—232no—
315Dic166C4×D4116yes—
316C22×C83C24×C411yescharacteristic
317C22×C83C23×D411yescharacteristic
318C22×C83C22×#4111yescharacteristic
319C22×C83C2×2−1+411yescharacteristic
320C22×C83C2×2−1+411yescharacteristic
321C22×C83C2×2−1+411yescharacteristic
322C22×C83#58511yescharacteristic
323C2×D83—24no—
324C2×D83—24no—
325C2×D83—24no—
326C2×D83—42no—
327C2×D83—42no—
328C2×D83—42no—
329C2×D83—42no—
330C4×C83—28no—
331C4×C83—22no—
332C4×C83—22no—
333C4×C83—22no—
334C4×C83—22no—
335C4×C83—44no—
336C4×C83—41no—
337C4×C83C2×C4×D414yes—
338C4×C83#51914yescomplemented
339Dic83—24no—
340Dic83—24no—
341Dic83—24no—
342Dic83—42no—
343Dic83—42no—
344Dic83—42no—
345Dic83C2×C4×D418yes—
346#34311—831nomaximal, Sylow
347C2×C83C22×C4×D411yescharacteristic
348C2×C83C2×#51911yescharacteristic
349C2×C83C4×2−1+411yescharacteristic
350C2×C83#349711yescharacteristic
351C2×C83#349911yescharacteristic
352C2×C83#351811yescharacteristic
353C2×C83#352311yescharacteristic
354D83—44no—
355C2×D4×Q8—831no—
356C2×#519—832no—
357#2365—832no—
358#2365—831no—
359#2362—832no—
360#2362—834no—
361#2354—831no—
362#2354—832no—
363Q8×C4⋊C4—831no—
364Q8×C22⋊C4—832no—
365#2323—834no—
366#2323—832no—
367C4×C4⋊Q8—832no—
368C4×C4⋊Q8D8311yescharacteristic, complemented
369#2293—832no—
370#2293—831no—
371C42×Q8—831no—
372C83#3431111yescharacteristic, complemented, Sylow
373C23×Q8—832no—
374D4×Q8—8316no—
375C2×C4⋊Q8—832no—
376C2×C4⋊Q8C2×D8311yescharacteristic
377C2×C22⋊Q8—832no—
378C2×C22⋊Q8—834no—
379#519—16616no—
380C2×C4×Q8—832no—
381C2×C4×Q8—834no—
382C2×C4×Q8—832no—
383C2×C4×Q8—831no—
384C2×C4×Q8—831no—
385C2×C4×Q8—831no—
386C2×C4×Q8—834no—
387C2×C4×Q8C2×D8312yes—
388C2×C4×D4—832no—
389C2×C4×D4—831no—
390C2×#117—834no—
391C2×#117—832no—
392C2×#117—832no—
393C2×#117—834no—
394#391—832no—
395#391—834no—
396#391—834no—
397#391C2×D8312yes—
398#390—832no—
399#390—831no—
400#390—831no—
401#389—834no—
402#389—834no—
403#389—832no—
404#389—832no—
405#389—831no—
406#389—831no—
407#389C2×D8312yes—
408#389C2×D8312yes—
409#388—834no—
410#388—834no—
411#388—832no—
412#388—834no—
413#388—832no—
414#388—834no—
415#388—834no—
416#387—834no—
417#387—834no—
418#387—834no—
419#384—832no—
420#384C2×D8311yescharacteristic
421#380—832no—
422#380—834no—
423C4×C4⋊C4—832no—
424C4×C4⋊C4—832no—
425C4×C4⋊C4—832no—
426C4×C4⋊C4—831no—
427C4×C4⋊C4—831no—
428C4×C4⋊C4—831no—
429C4×C4⋊C4—831no—
430C4×C4⋊C4—832no—
431C4×C4⋊C4—832no—
432C4×C4⋊C4—832no—
433C4×C4⋊C4—834no—
434C4×C4⋊C4C2×D8312yes—
435C4×C4⋊C4C2×D8312yes—
436C4×C22⋊C4—832no—
437C4×C22⋊C4—834no—
438C43—832no—
439C43C2×D8311yescharacteristic
440C22×Q8—8316no—
441C22×Q8—831no—
442C22×Q8—834no—
443C22×Q8—1668no—
444C22×Q8—1668no—
445C22×Q8C22×D8312yes—
446C22×D4—831no—
447C23×C4—834no—
448C23×C4—832no—
449C4⋊Q8—8316no—
450C4⋊Q8C4×D8318yes—
451C22⋊Q8—8316no—
452C22⋊Q8—8332no—
453C4×Q8—28no—
454C4×Q8—838no—
455C4×Q8—838no—
456C4×Q8—16616no—
457C4×Q8—1664no—
458C4×Q8—16616no—
459C4×Q8—1668no—
460C4×Q8—1668no—
461C4×D4—8316no—
462C4×D4—838no—
463#117—16616no—
464#117—16616no—
465#117—1668no—
466#117—1668no—
467C2×C4⋊C4—834no—
468C2×C4⋊C4—832no—
469C2×C4⋊C4—831no—
470C2×C4⋊C4—831no—
471C2×C4⋊C4—832no—
472C2×C4⋊C4—831no—
473C2×C4⋊C4—834no—
474C2×C4⋊C4—834no—
475C2×C4⋊C4—832no—
476C2×C4⋊C4—834no—
477C2×C4⋊C4—832no—
478C2×C4⋊C4—832no—
479C2×C4⋊C4—831no—
480C2×C4⋊C4—831no—
481C2×C4⋊C4—831no—
482C2×C4⋊C4C22×D8312yes—
483C2×C4⋊C4C22×D8314yes—
484C2×C4⋊C4C22×D8312yes—
485C2×C4⋊C4C22×D8312yes—
486C2×C4⋊C4C22×D8312yes—
487C2×C4⋊C4C22×D8312yes—
488C2×C22⋊C4—834no—
489C2×C22⋊C4—832no—
490C2×C22⋊C4—834no—
491C2×C22⋊C4—832no—
492C2×C22⋊C4—834no—
493C2×C22⋊C4—832no—
494C2×C22⋊C4—832no—
495C2×C22⋊C4—832no—
496C2×C42—832no—
497C2×C42—832no—
498C2×C42—832no—
499C2×C42—834no—
500C2×C42—832no—
501C2×C42—834no—
502C2×C42—834no—
503C2×C42—832no—
504C2×C42—832no—
505C2×C42—832no—
506C2×C42C22×D8314yes—
507C2×C42C22×D8311yescharacteristic
508C2×C42C22×D8311yescharacteristic
509C2×C42C22×D8311yescharacteristic
510C2×C42C22×D8311yescharacteristic
511C2×C42C22×D8311yescharacteristic
512C2×C42C22×D8311yescharacteristic
513C2×C42C22×D8311yescharacteristic
514#95—832no—
515#95—832no—
516#95—834no—
517#95—832no—
518#95—832no—
519#95—832no—
520#95—834no—
521#95—834no—
522#95—834no—
523#95—832no—
524#95C22×D8314yes—
525#95C22×D8314yes—
526C24—832no—
527C2×Q8—24no—
528C2×Q8—24no—
529C2×Q8—834no—
530C2×Q8—8316no—
531C2×Q8—834no—
532C2×Q8—834no—
533C2×Q8—1668no—
534C2×Q8—1668no—
535C2×Q8—16664no—
536C2×Q8C2×C4×D8318yes—
537C2×D4—834no—
538C2×D4—1662no—
539C2×D4—1662no—
540C22×C4—832no—
541C22×C4—832no—
542C22×C4—832no—
543C22×C4—832no—
544C22×C4—8316no—
545C22×C4—838no—
546C22×C4—832no—
547C22×C4—832no—
548C22×C4—832no—
549C22×C4—1668no—
550C22×C4—1668no—
551C22×C4—1664no—
552C22×C4—1664no—
553C22×C4C23×D8311yescharacteristic
554C22×C4C23×D8314yes—
555C22×C4C23×D8311yescharacteristic
556C22×C4C23×D8314yes—
557C22×C4C23×D8311yescharacteristic
558C22×C4C23×D8311yescharacteristic
559C22×C4C23×D8311yescharacteristic
560C22×C4C23×D8311yescharacteristic
561C22×C4C23×D8311yescharacteristic
562C4⋊C4—28no—
563C4⋊C4—24no—
564C4⋊C4—24no—
565C4⋊C4—42no—
566C4⋊C4—3324no—
567C4⋊C4—834no—
568C4⋊C4—838no—
569C4⋊C4—834no—
570C4⋊C4—8316no—
571C4⋊C4—838no—
572C4⋊C4—834no—
573C4⋊C4—1668no—
574C4⋊C4—1668no—
575C4⋊C4—1664no—
576C4⋊C4—1664no—
577C4⋊C4—1664no—
578C4⋊C4—1662no—
579C4⋊C4—1662no—
580C4⋊C4—1662no—
581C4⋊C4C2×C4×D8318yes—
582C4⋊C4C2×C4×D8318yes—
583C22⋊C4—3322no—
584C22⋊C4—3324no—
585C22⋊C4—8316no—
586C22⋊C4—838no—
587C22⋊C4—1668no—
588C22⋊C4—1664no—
589C22⋊C4—1664no—
590C22⋊C4—1664no—
591C42—28no—
592C42—22no—
593C42—22no—
594C42—22no—
595C42—22no—
596C42—41no—
597C42—3322no—
598C42—838no—
599C42—838no—
600C42—1668no—
601C42—1668no—
602C42—1668no—
603C42—1664no—
604C42—1664no—
605C42—1664no—
606C42—1664no—
607C42C2×C4×D8314yes—
608C42D4×D8314yes—
609C23—834no—
610C23—1662no—
611C23—1662no—
612C23—1662no—
613C23—1662no—
614C23—1662no—
615C23—1662no—
616C23C24×D8311yescharacteristic
617Q8—216no—
618Q8—8316no—
619Q8—16632no—
620D4—1668no—
621C2×C4—24no—
622C2×C4—21no—
623C2×C4—24no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—24no—
632C2×C4—21no—
633C2×C4—24no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—24no—
637C2×C4—834no—
638C2×C4—834no—
639C2×C4—834no—
640C2×C4—834no—
641C2×C4—834no—
642C2×C4—834no—
643C2×C4—16632no—
644C2×C4—1662no—
645C2×C4—1662no—
646C2×C4—1662no—
647C2×C4—1662no—
648C2×C4—1662no—
649C2×C4—1662no—
650C2×C4—1662no—
651C2×C4—1662no—
652C2×C4—1662no—
653C2×C4—1662no—
654C2×C4—1662no—
655C2×C4—1662no—
656C2×C4—1662no—
657C2×C4—1662no—
658C2×C4—1662no—
659C2×C4—16616no—
660C2×C4C22×C4×D8312yes—
661C2×C4C22×C4×D8318yes—
662C2×C4C22×C4×D8312yes—
663C2×C4C22×C4×D8312yes—
664C2×C4C2×D4×D8312yes—
665C2×C4C2×D4×D8312yes—
666C2×C4C2×D4×D8312yes—
667C2×C4#41×D8312yes—
668C2×C4#1458183912yes—
669C2×C4#1458184012yes—
670C2×C4#1458184012yes—
671C22—3322no—
672C22—3322no—
673C22—3322no—
674C22—3322no—
675C22—1664no—
676C22—1664no—
677C22—1664no—
678C22C23×C4×D8311yescharacteristic
679C22C22×D4×D8311yescharacteristic
680C22C2×#41×D8311yescharacteristic
681C22C2×#1458183911yescharacteristic
682C22C2×#1458184011yescharacteristic
683C22C2×#1458184011yescharacteristic
684C22#1912853711yescharacteristic
685C4—28no—
686C4—22no—
687C4—22no—
688C4—22no—
689C4—22no—
690C4—41no—
691C4—44no—
692C4—3322no—
693C4—3322no—
694C4—3322no—
695C4—838no—
696C4—1664no—
697C4—1664no—
698C4—1664no—
699C4C4×D4×D8314yes—
700C4#1912817714yescomplemented
701C2—3324no—
702C2C2×C4×D4×D8311yescharacteristic
703C2C2×#1912817711yescharacteristic
704C2C4×#1458184011yescharacteristic
705C2#2492122911yescharacteristic
706C2#2492124611yescharacteristic
707C2#2492147211yescharacteristic
708C2#2492155111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingC4×C4⋊Q8×C83C2
socle, cosocleC23×C83C25
prime radicalC22×D332C23
hypercenterC4×C4⋊Q8D83
hypocenterC83#34311
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C4×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#19128177C2semidirect
3. #24910523C2semidirect
4. #24910522C2semidirect
5. #24910495C2semidirect
6. #24910491C2semidirect
9. #24910375C2semidirect
10. #24910297C2semidirect
11. #24910140C2semidirect
12. #24910139C2semidirect
13. #24910034C2semidirect
16. C42×Dic166C2semidirect
17. C4×C4⋊Q8×C83C2semidirect
19. #19128366C4semidirect
100. C4×Dic166D4semidirect
338. C4×C83#519semidirect
368. C4×C4⋊Q8D83semidirect
372. C83#34311semidirect
700. C4#19128177semidirect

Maximal subgroups

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

subgroupindex
C2×#191283662
C2×#191281772
#249105232
#249105222
#249104952
#249104912
#249104142
#249104082
#249103752
#249102972
#249101402
#249101392
#249100342
#249099272
#249099212
C42×Dic1662
C4×C4⋊Q8×C832
#3431183