Finite Group Databasebeta

← #35563831

Subgroups — #35563831

Order 21248.

2434 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×C4×Q8×D83C211yesmaximal, characteristic
2#24910421C212yesmaximal, complemented
3#24910420C211yesmaximal, characteristic, complemented
4#24910415C212yesmaximal, complemented
5C4⋊C4×Dic166C211yesmaximal, characteristic, complemented
6#24910375C211yesmaximal, characteristic, complemented
7#24910337C214yesmaximal
8#24910336C212yesmaximal
9#24910297C212yesmaximal
10#24909938C212yesmaximal, complemented
11#24909936C214yesmaximal, complemented
12#24909869C212yesmaximal
13#24909868C211yesmaximal, characteristic
14C4×#14581757C212yesmaximal, complemented
15C4×#14581750C211yesmaximal, characteristic
16C4×#14581750C212yesmaximal
17C83×#2355C211yesmaximal, characteristic, complemented
18C22×Q8×D83C2211yescharacteristic
19C2×Q8×Dic83C2211yescharacteristic
20C2×C4×Dic166C2212yes—
21C2×C4×Dic166C2211yescharacteristic
22C2×C4×Dic166C2212yes—
23C2×#14581757C2212yes—
24C2×#14581757C2212yes—
25C2×#14581757C2211yescharacteristic
26C4×Q8×D83C4116yescomplemented
27C2×#14581750C2212yes—
28C2×#14581750C2211yescharacteristic
29C2×#14581750C2211yescharacteristic
30C2×C4⋊C4×D83C2211yescharacteristic
31C2×C4⋊C4×D83C2212yes—
32C2×C42×D83C2211yescharacteristic
33C2×C42×D83C2212yes—
34#19127608C2212yes—
35#19127605C2214yes—
36#19127605C2214yes—
37#19127599C2212yes—
38#19127598C2214yes—
39#19127597C2212yes—
40#19127596C2214yes—
41#19127587C2214yes—
42#19127586C2214yes—
43#19127585C2214yes—
44#19127584C2214yes—
45#19127583C2214yes—
46#19127571C2211yescharacteristic
47#19127570C2212yes—
48#19127570C2212yes—
49#19127567C2212yes—
50#19127566C2212yes—
51#19127560C2214yes—
52#19127560C2214yes—
53#19127558C2212yes—
54#19127558C2212yes—
55C4⋊C4×Dic83C2212yes—
56C4⋊C4×Dic83C2212yes—
57C4⋊C4×Dic83C2212yes—
58C4⋊C4×Dic83C2212yes—
59C4⋊C4×Dic83C2212yes—
60C4⋊C4×Dic83C2211yescharacteristic
61C4⋊C4×Dic83C2211yescharacteristic
62C4×Dic83⋊C4C2214yes—
63C4×C4⋊Dic83C2211yescharacteristic
64C4×C4⋊Dic83C2212yes—
65#19127552C2214yes—
66#19127552C2214yes—
67#19127552C2214yes—
68C4×(C2×D83)⋊C4C2214yes—
69C4×(C2×D83)⋊C4C2212yes—
70#19127548C2212yes—
71#19127548C2214yes—
72#19127546C2212yes—
73#19127546C2214yes—
74C42×Dic83C2214yes—
75C42×Dic83C2212yes—
76C2×C4×Q8×C83C2211yescharacteristic
77#391×C83C2212yes—
78#387×C83C2214yes—
79#384×C83C2211yescharacteristic
80#382×C83C2212yes—
81C4×C4⋊C4×C83C2212yes—
82C4×C4⋊C4×C83C2211yescharacteristic
83C4×C4⋊C4×C83C2212yes—
84C22×Dic166C2312yes—
85C22×Dic166C2311yescharacteristic
86C2×Q8×D83—24no—
87C2×Q8×D83—24no—
88C2×Q8×D83C2×C418yes—
89C22×C4×D83C2311yescharacteristic
90C22×C4×D83C2312yes—
91C22×C4×D83C2311yescharacteristic
92C22×C4×D83C2312yes—
93C22×C4×D83C2311yescharacteristic
94Q8×Dic83C2×C418yes—
95C4×Dic166—28no—
96C4×Dic166C2×C4116yes—
97C4×Dic166C2×C418yes—
98#14581757—28no—
99#14581757C2×C4116yes—
100#14581757C2×C418yes—
101#14581750—28no—
102#14581750—24no—
103#14581750Q818yescomplemented
104C2×C4⋊Dic83C2312yes—
105C2×C4⋊Dic83C2311yescharacteristic
106C2×C4⋊Dic83C2312yes—
107C2×C4⋊Dic83C2312yes—
108C2×C4⋊Dic83C2312yes—
109C2×C4⋊Dic83C2311yescharacteristic
110C2×C4⋊Dic83C2311yescharacteristic
111C2×Dic83⋊C4C2314yes—
112C2×Dic83⋊C4C2314yes—
113C2×Dic83⋊C4C2314yes—
114C2×Dic83⋊C4C2314yes—
115C2×Dic83⋊C4C2312yes—
116C2×Dic83⋊C4C2312yes—
117C2×Dic83⋊C4C2312yes—
118C4⋊C4×D83C2×C418yes—
119C4⋊C4×D83C2×C4116yes—
120C2×(C2×D83)⋊C4C2314yes—
121C2×(C2×D83)⋊C4C2312yes—
122C2×(C2×D83)⋊C4C2312yes—
123C2×C4×Dic83C2312yes—
124C2×C4×Dic83C2314yes—
125C2×C4×Dic83C2314yes—
126C2×C4×Dic83C2312yes—
127C2×C4×Dic83C2314yes—
128C2×C4×Dic83C2312yes—
129C2×C4×Dic83C2314yes—
130C2×C4×Dic83C2312yes—
131C2×C4×Dic83C2312yes—
132C2×C4×Dic83C2312yes—
133C2×C4×Dic83C2311yescharacteristic
134C2×C4×Dic83C2312yes—
135C2×C4×Dic83C2311yescharacteristic
136C2×C4×Dic83C2311yescharacteristic
137C2×C4×Dic83C2312yes—
138C42×D83C2×C418yes—
139C42×D83C2×C4116yes—
140C83⋊#95C2314yes—
141C83⋊#95C2314yes—
142C83⋊#95C2314yes—
143C83⋊#95C2314yes—
144C83⋊#95C2312yes—
145C83⋊#95C2314yes—
146C83⋊#95C2312yes—
147C83⋊#95C2314yes—
148C83⋊#95C2314yes—
149C83⋊#95C2312yes—
150C22×Q8×C83C2311yescharacteristic
151C4×Q8×C83C2×C418yes—
152C2×C4⋊C4×C83C2312yes—
153C2×C4⋊C4×C83C2312yes—
154C2×C4⋊C4×C83C2311yescharacteristic
155C2×C4⋊C4×C83C2312yes—
156C2×C4⋊C4×C83C2311yescharacteristic
157C2×C4⋊C4×C83C2312yes—
158C2×C4⋊C4×C83C2311yescharacteristic
159C2×C42×C83C2312yes—
160C2×C42×C83C2314yes—
161C2×C42×C83C2312yes—
162C2×C42×C83C2311yescharacteristic
163#95×C83C2314yes—
164#95×C83C2314yes—
165#95×C83C2314yes—
166#95×C83C2312yes—
167C23×D83C2411yescharacteristic
168C2×Dic166—24no—
169C2×Dic166—24no—
170C2×Dic166C22×C418yes—
171C2×Dic166C22×C414yes—
172C2×Dic166#4114yes—
173C2×Dic166#4114yes—
174Q8×D83—232no—
175C22×Dic83C2412yes—
176C22×Dic83C2414yes—
177C22×Dic83C2411yescharacteristic
178C22×Dic83C2411yescharacteristic
179C22×Dic83C2412yes—
180C22×Dic83C2412yes—
181C22×Dic83C2411yescharacteristic
182C22×Dic83C2412yes—
183C2×C4×D83—22no—
184C2×C4×D83—22no—
185C2×C4×D83—24no—
186C2×C4×D83—24no—
187C2×C4×D83—41no—
188C2×C4×D83—41no—
189C2×C4×D83—42no—
190C2×C4×D83—42no—
191C2×C4×D83C22×C414yes—
192C2×C4×D83C22×C418yes—
193C2×C4×D83C22×C414yes—
194C2×C4×D83C22×C418yes—
195C2×C4×D83C22×C414yes—
196C2×C4×D83C2×Q814yes—
197C2×C4×D83#4114yes—
198C4⋊Dic83—24no—
199C4⋊Dic83—22no—
200C4⋊Dic83—24no—
201C4⋊Dic83—42no—
202C4⋊Dic83C22×C418yes—
203C4⋊Dic83C22×C414yes—
204C4⋊Dic83C2×Q814yescomplemented
205Dic83⋊C4—28no—
206Dic83⋊C4—28no—
207Dic83⋊C4—44no—
208Dic83⋊C4—44no—
209Dic83⋊C4C22×C418yes—
210Dic83⋊C4C22×C418yes—
211Dic83⋊C4C22×C418yes—
212(C2×D83)⋊C4—28no—
213(C2×D83)⋊C4—24no—
214(C2×D83)⋊C4C2×Q818yes—
215C4×Dic83—24no—
216C4×Dic83—24no—
217C4×Dic83—28no—
218C4×Dic83—28no—
219C4×Dic83—28no—
220C4×Dic83—42no—
221C4×Dic83—44no—
222C4×Dic83—42no—
223C4×Dic83C22×C414yes—
224C4×Dic83C22×C418yes—
225C4×Dic83C22×C418yes—
226C4×Dic83C22×C414yes—
227C4×Dic83C22×C414yes—
228C4×Dic83C22×C418yes—
229C4×Dic83C2×Q818yescomplemented
230C2×Q8×C83—22no—
231C2×Q8×C83—22no—
232C2×Q8×C83C22×C414yes—
233C22×C4×C83C2412yes—
234C22×C4×C83C2414yes—
235C22×C4×C83C2412yes—
236C22×C4×C83C2412yes—
237C22×C4×C83C2411yescharacteristic
238C22×C4×C83C2412yes—
239C22×C4×C83C2411yescharacteristic
240C22×C4×C83C2411yescharacteristic
241C4⋊C4×C83—24no—
242C4⋊C4×C83—22no—
243C4⋊C4×C83—24no—
244C4⋊C4×C83—42no—
245C4⋊C4×C83C22×C418yes—
246C4⋊C4×C83C22×C414yes—
247C4⋊C4×C83C2×Q814yescomplemented
248C42×C83—24no—
249C42×C83—44no—
250C42×C83C22×C418yes—
251C42×C83C22×C414yes—
252C23×C83C2511yescharacteristic
253C22×D83—21no—
254C22×D83—21no—
255C22×D83—21no—
256C22×D83—21no—
257C22×D83C23×C412yes—
258C22×D83C22×Q812yes—
259C22×D83C2×#4112yes—
260Q8×C83—28no—
261C2×C4×C83—22no—
262C2×C4×C83—22no—
263C2×C4×C83—22no—
264C2×C4×C83—22no—
265C2×C4×C83—22no—
266C2×C4×C83—21no—
267C2×C4×C83—22no—
268C2×C4×C83—21no—
269C2×C4×C83—22no—
270C2×C4×C83—22no—
271C2×C4×C83—24no—
272C2×C4×C83—24no—
273C2×C4×C83—24no—
274C2×C4×C83—22no—
275C2×C4×C83C23×C414yes—
276C2×C4×C83C23×C412yes—
277C2×C4×C83C23×C414yes—
278C2×C4×C83C23×C412yes—
279C2×C4×C83C23×C412yes—
280C2×C4×C83C22×Q814yes—
281C2×C4×C83C22×Q812yes—
282C2×C4×C83C2×#4112yes—
283C2×C4×C83C2×#4112yes—
284C2×C4×C83C2×#4112yes—
285C2×Dic83—22no—
286C2×Dic83—21no—
287C2×Dic83—21no—
288C2×Dic83—22no—
289C2×Dic83—21no—
290C2×Dic83—21no—
291C2×Dic83—22no—
292C2×Dic83—22no—
293C2×Dic83—22no—
294C2×Dic83—24no—
295C2×Dic83—22no—
296C2×Dic83—24no—
297C2×Dic83—22no—
298C2×Dic83—24no—
299C2×Dic83C23×C412yes—
300C2×Dic83C23×C414yes—
301C2×Dic83C23×C412yes—
302C2×Dic83C23×C414yes—
303C2×Dic83C23×C412yes—
304C2×Dic83C22×Q814yes—
305C2×Dic83C22×Q812yes—
306C2×Dic83C2×#4114yes—
307C2×Dic83C2×#4114yes—
308C2×Dic83C2×#4112yes—
309C4×D83—28no—
310C4×D83—216no—
311C4×D83—44no—
312C4×D83—48no—
313C4×D83C4×Q8116yescomplemented
314Dic166—216no—
315Dic166#117116yescomplemented
316C22×C83C24×C411yescharacteristic
317C22×C83C23×Q811yescharacteristic
318C22×C83C22×#4111yescharacteristic
319C22×C83C22×#4111yescharacteristic
320C22×C83C22×#4111yescharacteristic
321C22×C83#58511yescharacteristic
322C22×C83#58511yescharacteristic
323C2×D83—22no—
324C2×D83—22no—
325C2×D83—22no—
326C2×D83—22no—
327C2×D83—22no—
328C2×D83—22no—
329C2×D83C2×C4×Q814yes—
330C4×C83—24no—
331C4×C83—24no—
332C4×C83—22no—
333C4×C83—24no—
334C4×C83—42no—
335C4×C83—44no—
336C4×C83C2×#11714yes—
337C4×C83C2×C4×Q814yes—
338Dic83—22no—
339Dic83—22no—
340Dic83—24no—
341Dic83—24no—
342Dic83—44no—
343Dic83—42no—
344Dic83C2×#11718yes—
345Dic83C2×C4×Q814yes—
346Q8×#117—831nomaximal, Sylow
347C2×C83C22×#11711yescharacteristic
348C2×C83C22×C4×Q811yescharacteristic
349C2×C83#342811yescharacteristic
350C2×C83Q8×#4111yescharacteristic
351C2×C83Q8×#4111yescharacteristic
352C2×C83#348011yescharacteristic
353C2×C83#348011yescharacteristic
354D83—24no—
355C22×C4×Q8—831no—
356#2355—832no—
357#2355—832no—
358#2355—831no—
359#2355D8311yescharacteristic, complemented
360Q8×C4⋊C4—831no—
361Q8×C4⋊C4—831no—
362#2345—834no—
363#2345—832no—
364Q8×C22⋊C4—832no—
365#2295—832no—
366#2295—834no—
367#2285—831no—
368#2285—832no—
369C42×Q8—832no—
370C4×#117—831no—
371C4×#117—832no—
372C83Q8×#11711yescharacteristic, complemented, Sylow
373C23×Q8—831no—
374C2×C4×Q8—831no—
375C2×C4×Q8—8316no—
376C2×C4×Q8—831no—
377C2×C4×Q8—832no—
378C2×C4×Q8—832no—
379C2×C4×Q8—831no—
380C2×C4×Q8—832no—
381C2×C4×Q8—832no—
382C2×C4×Q8C2×D8311yescharacteristic
383C2×#117—831no—
384C2×#117—832no—
385C2×#117—831no—
386C22×C4⋊C4—832no—
387C22×C4⋊C4—831no—
388C22×C42—831no—
389C22×C42—832no—
390#391—832no—
391#391—834no—
392#391—834no—
393#391C2×D8312yes—
394#389—834no—
395#389—832no—
396#389—832no—
397#389—834no—
398#387—834no—
399#387—834no—
400#387—834no—
401#387—834no—
402#387—834no—
403#387C2×D8314yes—
404#384—832no—
405#384—832no—
406#384—831no—
407#384C2×D8311yescharacteristic
408#382—832no—
409#382—832no—
410#382C2×D8312yes—
411#380—832no—
412#380—832no—
413#380—834no—
414#380—834no—
415C4×C4⋊C4—832no—
416C4×C4⋊C4—832no—
417C4×C4⋊C4—832no—
418C4×C4⋊C4—831no—
419C4×C4⋊C4—831no—
420C4×C4⋊C4—832no—
421C4×C4⋊C4—832no—
422C4×C4⋊C4—831no—
423C4×C4⋊C4—832no—
424C4×C4⋊C4—834no—
425C4×C4⋊C4—834no—
426C4×C4⋊C4—834no—
427C4×C4⋊C4—834no—
428C4×C4⋊C4C2×D8312yes—
429C4×C4⋊C4C2×D8311yescharacteristic
430C4×C4⋊C4C2×D8312yes—
431C4×C22⋊C4—832no—
432C4×C22⋊C4—834no—
433C4×C22⋊C4—834no—
434C4×C22⋊C4—832no—
435#376—834no—
436#376—832no—
437C43—832no—
438C43—834no—
439C22×Q8—838no—
440C22×Q8—831no—
441C22×Q8—832no—
442C22×Q8—1664no—
443C22×Q8—1664no—
444C22×Q8C22×D8311yescharacteristic
445C23×C4—831no—
446C23×C4—832no—
447C23×C4—831no—
448C23×C4—832no—
449C23×C4—831no—
450C4×Q8—838no—
451C4×Q8—838no—
452C4×Q8—8316no—
453C4×Q8—838no—
454C4×Q8—8316no—
455C4×Q8—1668no—
456C4×Q8—1668no—
457C4×Q8C4×D8318yes—
458#117—838no—
459#117—1668no—
460#117—1664no—
461C2×C4⋊C4—834no—
462C2×C4⋊C4—834no—
463C2×C4⋊C4—832no—
464C2×C4⋊C4—832no—
465C2×C4⋊C4—832no—
466C2×C4⋊C4—832no—
467C2×C4⋊C4—832no—
468C2×C4⋊C4—831no—
469C2×C4⋊C4—831no—
470C2×C4⋊C4—8316no—
471C2×C4⋊C4—838no—
472C2×C4⋊C4—832no—
473C2×C4⋊C4—831no—
474C2×C4⋊C4—834no—
475C2×C4⋊C4—834no—
476C2×C4⋊C4—832no—
477C2×C4⋊C4C22×D8312yes—
478C2×C4⋊C4C22×D8311yescharacteristic
479C2×C4⋊C4C22×D8312yes—
480C2×C4⋊C4C22×D8312yes—
481C2×C4⋊C4C22×D8311yescharacteristic
482C2×C4⋊C4C22×D8312yes—
483C2×C4⋊C4C22×D8311yescharacteristic
484C2×C22⋊C4—832no—
485C2×C22⋊C4—834no—
486C2×C22⋊C4—832no—
487C2×C42—832no—
488C2×C42—834no—
489C2×C42—832no—
490C2×C42—832no—
491C2×C42—832no—
492C2×C42—831no—
493C2×C42—831no—
494C2×C42—832no—
495C2×C42—831no—
496C2×C42—832no—
497C2×C42—8316no—
498C2×C42—838no—
499C2×C42—834no—
500C2×C42—832no—
501C2×C42—834no—
502C2×C42—834no—
503C2×C42—832no—
504C2×C42C22×D8312yes—
505C2×C42C22×D8314yes—
506C2×C42C22×D8312yes—
507C2×C42C22×D8311yescharacteristic
508#95—834no—
509#95—832no—
510#95—834no—
511#95—832no—
512#95—832no—
513#95—834no—
514#95—834no—
515#95—834no—
516#95—834no—
517#95—834no—
518#95C22×D8314yes—
519#95C22×D8312yes—
520#95C22×D8314yes—
521#95C22×D8314yes—
522C24—831no—
523C2×Q8—22no—
524C2×Q8—22no—
525C2×Q8—834no—
526C2×Q8—838no—
527C2×Q8—834no—
528C2×Q8—834no—
529C2×Q8—1664no—
530C2×Q8—1664no—
531C2×Q8—16632no—
532C2×Q8C2×C4×D8314yes—
533C22×C4—3322no—
534C22×C4—3321no—
535C22×C4—3322no—
536C22×C4—3321no—
537C22×C4—834no—
538C22×C4—838no—
539C22×C4—831no—
540C22×C4—832no—
541C22×C4—834no—
542C22×C4—834no—
543C22×C4—834no—
544C22×C4—831no—
545C22×C4—832no—
546C22×C4—831no—
547C22×C4—832no—
548C22×C4—838no—
549C22×C4—834no—
550C22×C4—832no—
551C22×C4—834no—
552C22×C4—1664no—
553C22×C4—1664no—
554C22×C4—1662no—
555C22×C4—1662no—
556C22×C4C23×D8314yes—
557C22×C4C23×D8312yes—
558C22×C4C23×D8312yes—
559C22×C4C23×D8312yes—
560C22×C4C23×D8311yescharacteristic
561C22×C4C23×D8312yes—
562C22×C4C23×D8311yescharacteristic
563C22×C4C23×D8311yescharacteristic
564C4⋊C4—24no—
565C4⋊C4—22no—
566C4⋊C4—24no—
567C4⋊C4—42no—
568C4⋊C4—3324no—
569C4⋊C4—3324no—
570C4⋊C4—3322no—
571C4⋊C4—838no—
572C4⋊C4—838no—
573C4⋊C4—838no—
574C4⋊C4—838no—
575C4⋊C4—834no—
576C4⋊C4—834no—
577C4⋊C4—1668no—
578C4⋊C4—1668no—
579C4⋊C4—1664no—
580C4⋊C4—1662no—
581C4⋊C4—1664no—
582C4⋊C4C2×C4×D8318yes—
583C4⋊C4C2×C4×D8314yes—
584C4⋊C4Q8×D8314yescomplemented
585C22⋊C4—838no—
586C22⋊C4—1664no—
587C22⋊C4—1668no—
588C42—24no—
589C42—44no—
590C42—3322no—
591C42—3324no—
592C42—3322no—
593C42—838no—
594C42—838no—
595C42—834no—
596C42—834no—
597C42—838no—
598C42—834no—
599C42—838no—
600C42—1664no—
601C42—1668no—
602C42—1668no—
603C42—1668no—
604C42—1664no—
605C42C2×C4×D8318yes—
606C42C2×C4×D8314yes—
607C23—832no—
608C23—832no—
609C23—832no—
610C23—1661no—
611C23—1661no—
612C23—1661no—
613C23—1661no—
614C23C24×D8311yescharacteristic
615Q8—28no—
616Q8—8316no—
617Q8—16616no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—21no—
624C2×C4—22no—
625C2×C4—21no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—22no—
632C2×C4—3328no—
633C2×C4—3324no—
634C2×C4—832no—
635C2×C4—834no—
636C2×C4—832no—
637C2×C4—832no—
638C2×C4—834no—
639C2×C4—834no—
640C2×C4—8316no—
641C2×C4—832no—
642C2×C4—834no—
643C2×C4—832no—
644C2×C4—834no—
645C2×C4—16616no—
646C2×C4—1664no—
647C2×C4—1662no—
648C2×C4—1664no—
649C2×C4—1662no—
650C2×C4—1662no—
651C2×C4—1664no—
652C2×C4—1662no—
653C2×C4—1661no—
654C2×C4—1661no—
655C2×C4—1661no—
656C2×C4—1662no—
657C2×C4—1662no—
658C2×C4—1661no—
659C2×C4—1662no—
660C2×C4—1668no—
661C2×C4C22×C4×D8314yes—
662C2×C4C22×C4×D8312yes—
663C2×C4C22×C4×D8314yes—
664C2×C4C22×C4×D8312yes—
665C2×C4C22×C4×D8312yes—
666C2×C4C2×Q8×D8314yes—
667C2×C4C2×Q8×D8312yes—
668C2×C4#41×D8312yes—
669C2×C4#41×D8312yes—
670C2×C4#41×D8312yes—
671C22—834no—
672C22—1662no—
673C22—1662no—
674C22—1662no—
675C22—1662no—
676C22—1662no—
677C22—1662no—
678C22C23×C4×D8311yescharacteristic
679C22C22×Q8×D8311yescharacteristic
680C22C2×#41×D8311yescharacteristic
681C22C2×#41×D8311yescharacteristic
682C22C2×#41×D8311yescharacteristic
683C22#1912853611yescharacteristic
684C22#1912853811yescharacteristic
685C4—24no—
686C4—24no—
687C4—22no—
688C4—24no—
689C4—42no—
690C4—44no—
691C4—3324no—
692C4—3322no—
693C4—838no—
694C4—834no—
695C4—1662no—
696C4—1662no—
697C4—1664no—
698C4—1664no—
699C4#117×D8314yes—
700C4C4×Q8×D8314yes—
701C2—1664no—
702C2C2×#117×D8311yescharacteristic
703C2C2×C4×Q8×D8311yescharacteristic
704C2#2492066311yescharacteristic
705C2#2492104211yescharacteristic
706C2#2492104511yescharacteristic
707C2#2492105511yescharacteristic
708C2#2492105911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingC83×#2355C2
socle, cosocleC23×C83C25
prime radicalC23×D83C24
hypercenter#2355D83
hypocenterC83Q8×#117
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2355

Complements

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

NH ≅ G/Ntype
2. #24910421C2semidirect
3. #24910420C2semidirect
4. #24910415C2semidirect
5. C4⋊C4×Dic166C2semidirect
6. #24910375C2semidirect
10. #24909938C2semidirect
11. #24909936C2semidirect
14. C4×#14581757C2semidirect
17. C83×#2355C2semidirect
26. C4×Q8×D83C4semidirect
103. #14581750Q8semidirect
204. C4⋊Dic83C2×Q8semidirect
229. C4×Dic83C2×Q8semidirect
247. C4⋊C4×C83C2×Q8semidirect
313. C4×D83C4×Q8semidirect
315. Dic166#117semidirect
359. #2355D83semidirect
372. C83Q8×#117semidirect
584. C4⋊C4Q8×D83semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D832
#249104212
#249104202
#249104152
C4⋊C4×Dic1662
#249103752
#249103372
#249103362
#249102972
#249099382
#249099362
#249098692
#249098682
C4×#145817572
C4×#145817502
C83×#23552
Q8×#11783