Finite Group Databasebeta

← C2×#24919993 #36283031

Subgroups — C2×#24919993 #36283031

Order 21248.

1834 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128421C211yesmaximal, characteristic
2#24919993C2116yesmaximal, direct product factor
3C2×#19128111C211yesmaximal, characteristic, complemented
4C2×#19128036C211yesmaximal, characteristic, complemented
5C2×#19128042C211yesmaximal, characteristic, complemented
6C2×#19128039C211yesmaximal, characteristic, complemented
7C2×#19128039C211yesmaximal, characteristic, complemented
8C2×#19128005C211yesmaximal, characteristic, complemented
9C2×#19127996C211yesmaximal, characteristic, complemented
10C2×#19127957C211yesmaximal, characteristic, complemented
11C2×#19127940C211yesmaximal, characteristic, complemented
12C2×#19127806C211yesmaximal, characteristic, complemented
13C2×#19127773C211yesmaximal, characteristic
14C2×#19127741C211yesmaximal, characteristic, complemented
15C2×#19127737C211yesmaximal, characteristic, complemented
16C2×#552×C83C211yesmaximal, characteristic
17C22×#13050580C2211yescharacteristic
18C22×#13050574C2211yescharacteristic
19C23×C83⋊C8C2211yescharacteristic
20#19128421—24no—
21#19128421C2218yes—
22C2×#14581792C2211yescharacteristic
23C2×#14581785—21no—
24C2×#14581785—21no—
25C2×#14581779—21no—
26C2×#14581771C2211yescharacteristic
27C2×#14581771C2211yescharacteristic
28C2×C4×Dic166C2211yescharacteristic
29C2×#14581757—21no—
30C2×#14581751C2211yescharacteristic
31C2×#14581751C2211yescharacteristic
32#19128111C2218yescomplemented
33#19128042C2218yescomplemented
34#19128039C2218yescomplemented
35#19128039C2218yescomplemented
36#19128036C2218yescomplemented
37#19128005C2218yescomplemented
38#19127996C2218yescomplemented
39#19127957C2218yescomplemented
40#19127940C2218yescomplemented
41#19127806C2218yescomplemented
42#19127773C2218yes—
43#19127741C2218yescomplemented
44#19127737C2218yescomplemented
45C2×#14581725C2211yescharacteristic
46C2×#14581725C2211yescharacteristic
47C2×#14581725C2211yescharacteristic
48C2×#14581725C2211yescharacteristic
49C2×#14581725C2211yescharacteristic
50C2×#14581723C2211yescharacteristic
51C2×#14581723C2211yescharacteristic
52C2×#14581723C2211yescharacteristic
53C2×#14581723C2211yescharacteristic
54C2×C4⋊(C83⋊C8)C2211yescharacteristic
55C2×#14581716C2211yescharacteristic
56C2×#14581716C2211yescharacteristic
57C2×#14581716C2211yescharacteristic
58C2×#14581715C2211yescharacteristic
59C2×#14581715C2211yescharacteristic
60C2×#14581715C2211yescharacteristic
61C2×C22⋊(C83⋊C8)C2211yescharacteristic
62C2×C22⋊(C83⋊C8)C2211yescharacteristic
63C2×#14581703C2211yescharacteristic
64#552×C83—24no—
65#552×C83C2218yes—
66C2×#126×C83—21no—
67C2×#125×C83—21no—
68C2×#125×C83C2211yescharacteristic
69C2×#123×C83—21no—
70C2×C22⋊Q8×C83C2211yescharacteristic
71C2×C22⋊Q8×C83C2211yescharacteristic
72C2×C4×Q8×C83C2211yescharacteristic
73C2×C4×D4×C83C2211yescharacteristic
74C2×#117×C83—21no—
75C2×#117×C83C2211yescharacteristic
76C22×C4⋊C4×C83C2211yescharacteristic
77C22×Dic166—21no—
78C22×Dic166C2311yescharacteristic
79C2×#13050580—24no—
80C2×#13050580C2314yes—
81C2×#13050574—24no—
82C2×#13050574C2314yes—
83C22×C83⋊C8—24no—
84C22×C83⋊C8C2311yescharacteristic
85C22×C83⋊C8C2311yescharacteristic
86C22×C83⋊C8C2311yescharacteristic
87C22×C83⋊C8C2314yes—
88C22×C83⋊C8C2311yescharacteristic
89#14581792—22no—
90#14581792C2314yes—
91#14581785—28no—
92#14581785—28no—
93#14581779—28no—
94#14581771—22no—
95#14581771—22no—
96#14581771C2314yes—
97#14581771C2314yes—
98C4×Dic166—22no—
99C4×Dic166C2314yes—
100#14581757—28no—
101#14581751—22no—
102#14581751—22no—
103#14581751C2314yes—
104#14581751C2314yes—
105C2×C4⋊Dic83—21no—
106C2×C4⋊Dic83C2311yescharacteristic
107C2×C4⋊Dic83C2311yescharacteristic
108C2×C4⋊Dic83C2311yescharacteristic
109C2×Dic83⋊C4—21no—
110C2×Dic83⋊C4—21no—
111C2×Dic83⋊C4—21no—
112C2×C22⋊Dic83—21no—
113C2×C22⋊Dic83—21no—
114C2×C22⋊Dic83—21no—
115C2×C22⋊Dic83—21no—
116C2×C4×Dic83—21no—
117C2×C4×Dic83—21no—
118C2×C4×Dic83—21no—
119#14581725C2314yes—
120#14581725C2314yes—
121#14581725C2314yes—
122#14581725C2314yes—
123#14581725C2314yes—
124#14581723C2314yes—
125#14581723C2314yes—
126#14581723C2314yes—
127#14581723C2314yes—
128C4⋊(C83⋊C8)C2314yes—
129#14581716C2314yes—
130#14581716C2314yes—
131#14581716C2314yes—
132#14581715C2314yes—
133#14581715C2314yes—
134#14581715C2314yes—
135C22⋊(C83⋊C8)C2314yes—
136C22⋊(C83⋊C8)C2314yes—
137#14581703C2314yes—
138C22×Q8×C83C2311yescharacteristic
139C22×D4×C83D411yescharacteristic
140C23×C4×C83—21no—
141C23×C4×C83C2311yescharacteristic
142C23×C4×C83C2311yescharacteristic
143#126×C83—28no—
144#125×C83—28no—
145#125×C83—22no—
146#125×C83C2314yes—
147#123×C83—28no—
148C22⋊Q8×C83—22no—
149C22⋊Q8×C83—22no—
150C22⋊Q8×C83C2314yes—
151C22⋊Q8×C83C2314yes—
152C4×Q8×C83—22no—
153C4×Q8×C83C2314yes—
154C4×D4×C83D414yes—
155C4×D4×C83C2314yes—
156#117×C83—22no—
157#117×C83—28no—
158#117×C83C2314yes—
159C2×C4⋊C4×C83—21no—
160C2×C4⋊C4×C83—22no—
161C2×C4⋊C4×C83—21no—
162C2×C4⋊C4×C83—21no—
163C2×C4⋊C4×C83—21no—
164C2×C4⋊C4×C83—21no—
165C2×C4⋊C4×C83—21no—
166C2×C4⋊C4×C83D411yescharacteristic
167C2×C4⋊C4×C83C2311yescharacteristic
168C2×C4⋊C4×C83C2311yescharacteristic
169C2×C4⋊C4×C83C2314yes—
170C2×C4⋊C4×C83C2311yescharacteristic
171C2×C22⋊C4×C83—21no—
172C2×C22⋊C4×C83—21no—
173C2×C22⋊C4×C83—21no—
174C2×C22⋊C4×C83D411yescharacteristic
175C2×C22⋊C4×C83D411yescharacteristic
176C2×C42×C83—21no—
177C2×C42×C83—21no—
178C2×C42×C83C2311yescharacteristic
179C2×Dic166—22no—
180C2×Dic166—22no—
181C2×Dic166—21no—
182C2×Dic166—24no—
183C2×Dic166—44no—
184C2×Dic166C2412yes—
185C22×Dic83—21no—
186C22×Dic83—21no—
187C22×Dic83—21no—
188C22×Dic83—21no—
189#13050580—28no—
190#13050574—28no—
191C2×C83⋊C8—22no—
192C2×C83⋊C8—22no—
193C2×C83⋊C8—22no—
194C2×C83⋊C8—28no—
195C2×C83⋊C8#4114yes—
196C2×C83⋊C8C2412yes—
197C2×C83⋊C8C2412yes—
198C2×C83⋊C8C2412yes—
199C2×C83⋊C8C2412yes—
200C4⋊Dic83—21no—
201C4⋊Dic83—21no—
202C4⋊Dic83—24no—
203C4⋊Dic83—21no—
204C4⋊Dic83C2412yes—
205C4⋊Dic83C2412yes—
206C4⋊Dic83C2412yes—
207Dic83⋊C4—24no—
208Dic83⋊C4—24no—
209Dic83⋊C4—24no—
210C22⋊Dic83—24no—
211C22⋊Dic83—24no—
212C22⋊Dic83—24no—
213C22⋊Dic83—24no—
214C4×Dic83—24no—
215C4×Dic83—24no—
216C4×Dic83—24no—
217C24×C83C2×D411yescharacteristic
218C24×C83C2×D411yescharacteristic
219C2×Q8×C83—21no—
220C2×Q8×C83—22no—
221C2×Q8×C83—22no—
222C2×Q8×C83C2412yes—
223C2×D4×C83—42no—
224C2×D4×C83C2×D414yes—
225C22×C4×C83—22no—
226C22×C4×C83—22no—
227C22×C4×C83—22no—
228C22×C4×C83—22no—
229C22×C4×C83—21no—
230C22×C4×C83—21no—
231C22×C4×C83—21no—
232C22×C4×C83—21no—
233C22×C4×C83—24no—
234C22×C4×C83—44no—
235C22×C4×C83C2×D412yes—
236C22×C4×C83C2×D412yes—
237C22×C4×C83C2×D411yescharacteristic
238C22×C4×C83C2×D411yescharacteristic
239C22×C4×C83C2×D411yescharacteristic
240C22×C4×C83C2×D411yescharacteristic
241C22×C4×C83C2412yes—
242C22×C4×C83C2412yes—
243C22×C4×C83C2411yescharacteristic
244C4⋊C4×C83—21no—
245C4⋊C4×C83—21no—
246C4⋊C4×C83—24no—
247C4⋊C4×C83—24no—
248C4⋊C4×C83—24no—
249C4⋊C4×C83—24no—
250C4⋊C4×C83—24no—
251C4⋊C4×C83—24no—
252C4⋊C4×C83—21no—
253C4⋊C4×C83C2×D414yes—
254C4⋊C4×C83C2412yes—
255C4⋊C4×C83C2412yes—
256C4⋊C4×C83C2412yes—
257C22⋊C4×C83—24no—
258C22⋊C4×C83—24no—
259C22⋊C4×C83—24no—
260C22⋊C4×C83C2×D414yes—
261C22⋊C4×C83C2×D414yes—
262C42×C83—24no—
263C42×C83—24no—
264C42×C83C2×D412yes—
265C42×C83C2412yes—
266C23×C83—22no—
267C23×C83—22no—
268C23×C83—22no—
269C23×C83—22no—
270C23×C83—22no—
271C23×C83—22no—
272C23×C83C22×D412yes—
273C23×C83C22×D412yes—
274C23×C83C22×D411yescharacteristic
275Q8×C83—22no—
276Q8×C83—22no—
277Q8×C83—42no—
278D4×C83—44no—
279C2×C4×C83—22no—
280C2×C4×C83—22no—
281C2×C4×C83—22no—
282C2×C4×C83—22no—
283C2×C4×C83—24no—
284C2×C4×C83—24no—
285C2×C4×C83—22no—
286C2×C4×C83—22no—
287C2×C4×C83—22no—
288C2×C4×C83—22no—
289C2×C4×C83—22no—
290C2×C4×C83—22no—
291C2×C4×C83—22no—
292C2×C4×C83—22no—
293C2×C4×C83—48no—
294C2×C4×C83—42no—
295C2×C4×C83—42no—
296C2×C4×C83—42no—
297C2×C4×C83—42no—
298C2×C4×C83C22×D412yes—
299C2×C4×C83C22×D412yes—
300C2×C4×C83C22×D412yes—
301C2×C4×C83C22×D412yes—
302C2×C4×C83C22×D411yescharacteristic
303C2×C4×C83C2×#4112yes—
304C2×C4×C832−1+412yes—
305C2×C4×C83C2511yescharacteristic
306C2×Dic83—22no—
307C2×Dic83—22no—
308C2×Dic83—22no—
309C2×Dic83—22no—
310C2×Dic83—42no—
311C2×Dic83—42no—
312C2×Dic83—42no—
313C2×Dic83—42no—
314Dic166—22no—
315Dic166—22no—
316Dic166—48no—
317Dic166—42no—
318C83⋊C8—22no—
319C83⋊C8—22no—
320C83⋊C8—22no—
321C83⋊C8C2×#4114yes—
322C22×C83—22no—
323C22×C83—22no—
324C22×C83—22no—
325C22×C83—22no—
326C22×C83—22no—
327C22×C83—22no—
328C22×C83—44no—
329C22×C83—44no—
330C22×C83#54712yes—
331C22×C83#57512yes—
332C22×C83#57812yes—
333C22×C83C23×D411yescharacteristic
334C4×C83—22no—
335C4×C83—22no—
336C4×C83—22no—
337C4×C83—22no—
338C4×C83—42no—
339C4×C83—42no—
340C4×C83—42no—
341C4×C83—42no—
342C4×C83#54712yes—
343C4×C83C22×#4111yescharacteristic
344C4×C83C2×2−1+411yescharacteristic
345Dic83—42no—
346Dic83—42no—
347Dic83—42no—
348Dic83—42no—
349C2×#3349—831nomaximal, Sylow
350C2×C83—42no—
351C2×C83—42no—
352C2×C83#334914yescomplemented
353C2×C83C2×#54711yescharacteristic
354C2×C83C2×#57511yescharacteristic
355C2×C83C2×#57811yescharacteristic
356C2×#556—831no—
357C2×#552D8311yescharacteristic
358#3349—8316no—
359C2×#501—831no—
360C2×#484—831no—
361C2×#485—831no—
362C2×#485—831no—
363C2×#485—831no—
364C2×#479—831no—
365C2×#477—831no—
366C2×#470—831no—
367C2×#467—831no—
368C2×#441—831no—
369C2×#435—831no—
370C2×#428—831no—
371C2×#427—831no—
372C83C2×#334911yescharacteristic, complemented, Sylow
373C22×Q16—831no—
374C22×M16—831no—
375C23×C8—831no—
376#556—838no—
377#556—1664no—
378#552—24no—
379#552C2×D8318yes—
380C2×C4⋊Q8—831no—
381C2×#126—21no—
382C2×#126—1661no—
383C2×#126—1661no—
384C2×#125—21no—
385C2×#125C2×D8311yescharacteristic
386C2×#124—1661no—
387C2×#123—21no—
388C2×C22⋊Q8—831no—
389C2×C22⋊Q8—831no—
390C2×C22⋊Q8C2×D8311yescharacteristic
391C2×C22⋊Q8C2×D8311yescharacteristic
392C2×C4×Q8—831no—
393C2×C4×Q8—1661no—
394C2×C4×Q8C2×D8311yescharacteristic
395C2×C4×D4C2×D8311yescharacteristic
396C2×#117—21no—
397C2×#117—831no—
398C2×#117—831no—
399C2×#117C2×D8311yescharacteristic
400C22×C4⋊C4C2×D8311yescharacteristic
401#501—838no—
402#485—838no—
403#485—838no—
404#485—838no—
405#484—838no—
406#479—838no—
407#477—838no—
408#470—838no—
409#467—838no—
410#441—838no—
411#435—838no—
412#428—838no—
413#427—838no—
414C2×#107—831no—
415C2×#107—831no—
416C2×#107—831no—
417C2×#107—831no—
418C2×#107—831no—
419C2×#106—831no—
420C2×#106—831no—
421C2×#106—831no—
422C2×#106—831no—
423C2×C4⋊C8—831no—
424C2×#103—831no—
425C2×#103—831no—
426C2×#103—831no—
427C2×#103—831no—
428C2×#103—831no—
429C2×#103—831no—
430C2×C22⋊C8—831no—
431C2×C22⋊C8—831no—
432C2×#97—831no—
433C22×Q8—831no—
434C22×Q8—1661no—
435C22×Q8C22×D8311yescharacteristic
436C22×D4C22⋊D8311yescharacteristic
437C23×C4—21no—
438C23×C4C22×D8311yescharacteristic
439C23×C4C22×D8311yescharacteristic
440C2×Q16—834no—
441C2×Q16—1664no—
442C2×M16—834no—
443C2×M16—1664no—
444C22×C8—831no—
445C22×C8—831no—
446C22×C8—834no—
447C22×C8—831no—
448C22×C8—831no—
449C22×C8—1664no—
450C4⋊Q8—834no—
451C4⋊Q8—1662no—
452#126—28no—
453#126—1668no—
454#126—1668no—
455#125—28no—
456#125—22no—
457#125C22×D8314yes—
458#124—1668no—
459#123—28no—
460C22⋊Q8—22no—
461C22⋊Q8—22no—
462C22⋊Q8—834no—
463C22⋊Q8—834no—
464C22⋊Q8—1662no—
465C22⋊Q8—1662no—
466C22⋊Q8C22×D8314yes—
467C22⋊Q8C22×D8314yes—
468C4×Q8—22no—
469C4×Q8—834no—
470C4×Q8—1668no—
471C4×Q8—1662no—
472C4×Q8C22×D8314yes—
473C4×D4C22⋊D8314yes—
474C4×D4C22×D8314yes—
475#117—22no—
476#117—28no—
477#117—834no—
478#117—834no—
479#117—1662no—
480#117—1662no—
481#117C22×D8314yes—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—831no—
490C2×C4⋊C4—831no—
491C2×C4⋊C4—831no—
492C2×C4⋊C4—1661no—
493C2×C4⋊C4—1661no—
494C2×C4⋊C4—1661no—
495C2×C4⋊C4—1661no—
496C2×C4⋊C4C22⋊D8311yescharacteristic
497C2×C4⋊C4C22×D8311yescharacteristic
498C2×C4⋊C4C22×D8311yescharacteristic
499C2×C4⋊C4C22×D8314yes—
500C2×C4⋊C4C22×D8311yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—1661no—
505C2×C22⋊C4—1661no—
506C2×C22⋊C4—1661no—
507C2×C22⋊C4—1661no—
508C2×C22⋊C4C22⋊D8311yescharacteristic
509C2×C22⋊C4C22⋊D8311yescharacteristic
510C2×C42—21no—
511C2×C42—21no—
512C2×C42—1661no—
513C2×C42—1661no—
514C2×C42—1661no—
515C2×C42C22×D8311yescharacteristic
516#107—834no—
517#107—834no—
518#107—834no—
519#107—834no—
520#107—834no—
521#106—834no—
522#106—834no—
523#106—834no—
524#106—834no—
525C4⋊C8—834no—
526#103—834no—
527#103—834no—
528#103—834no—
529#103—834no—
530#103—834no—
531#103—834no—
532C22⋊C8—834no—
533C22⋊C8—834no—
534#97—834no—
535C24C2×C22⋊D8311yescharacteristic
536C24C2×C22⋊D8311yescharacteristic
537C2×Q8—21no—
538C2×Q8—22no—
539C2×Q8—22no—
540C2×Q8—3324no—
541C2×Q8—832no—
542C2×Q8—1662no—
543C2×Q8—1662no—
544C2×Q8—1661no—
545C2×Q8—1664no—
546C2×Q8C23×D8312yes—
547C2×D4—42no—
548C2×D4C2×C22⋊D8314yes—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—24no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—44no—
559C22×C4—1661no—
560C22×C4—1661no—
561C22×C4—1661no—
562C22×C4—1661no—
563C22×C4C2×C22⋊D8312yes—
564C22×C4C2×C22⋊D8312yes—
565C22×C4C2×C22⋊D8311yescharacteristic
566C22×C4C2×C22⋊D8311yescharacteristic
567C22×C4C2×C22⋊D8311yescharacteristic
568C22×C4C2×C22⋊D8311yescharacteristic
569C22×C4C23×D8312yes—
570C22×C4C23×D8312yes—
571C22×C4C23×D8311yescharacteristic
572Q16—1668no—
573M16—1668no—
574C2×C8—834no—
575C2×C8—832no—
576C2×C8—832no—
577C2×C8—832no—
578C2×C8—832no—
579C2×C8—1668no—
580C2×C8—1662no—
581C2×C8—1662no—
582C2×C8—1662no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—24no—
586C4⋊C4—24no—
587C4⋊C4—24no—
588C4⋊C4—24no—
589C4⋊C4—24no—
590C4⋊C4—24no—
591C4⋊C4—21no—
592C4⋊C4—832no—
593C4⋊C4—832no—
594C4⋊C4—832no—
595C4⋊C4—1661no—
596C4⋊C4—1661no—
597C4⋊C4—1661no—
598C4⋊C4—1664no—
599C4⋊C4—1664no—
600C4⋊C4—1664no—
601C4⋊C4—1664no—
602C4⋊C4C2×C22⋊D8314yes—
603C4⋊C4C23×D8312yes—
604C4⋊C4C23×D8312yes—
605C4⋊C4C23×D8312yes—
606C22⋊C4—24no—
607C22⋊C4—24no—
608C22⋊C4—24no—
609C22⋊C4—1664no—
610C22⋊C4—1664no—
611C22⋊C4—1664no—
612C22⋊C4—1664no—
613C22⋊C4C2×C22⋊D8314yes—
614C22⋊C4C2×C22⋊D8314yes—
615C42—24no—
616C42—24no—
617C42—1664no—
618C42—1664no—
619C42—1664no—
620C42C2×C22⋊D8312yes—
621C42C23×D8312yes—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23C22×C22⋊D8312yes—
629C23C22×C22⋊D8312yes—
630C23C22×C22⋊D8311yescharacteristic
631Q8—22no—
632Q8—22no—
633Q8—42no—
634Q8—3328no—
635Q8—3322no—
636Q8—1662no—
637Q8—1662no—
638D4—44no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—48no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—3322no—
659C2×C4—3322no—
660C2×C4—3322no—
661C2×C4—3322no—
662C2×C4—1662no—
663C2×C4—1662no—
664C2×C4—1662no—
665C2×C4—1662no—
666C2×C4C22×C22⋊D8312yes—
667C2×C4C22×C22⋊D8312yes—
668C2×C4C22×C22⋊D8312yes—
669C2×C4C22×C22⋊D8312yes—
670C2×C4C22×C22⋊D8311yescharacteristic
671C2×C4#41×D8312yes—
672C2×C4#1458183912yes—
673C2×C4C24×D8311yescharacteristic
674C8—834no—
675C8—1662no—
676C8—1662no—
677C8—1662no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—44no—
685C22—44no—
686C22#1912835012yes—
687C22#1912849912yes—
688C22#1912851612yes—
689C22C23×C22⋊D8311yescharacteristic
690C4—22no—
691C4—22no—
692C4—22no—
693C4—22no—
694C4—42no—
695C4—42no—
696C4—42no—
697C4—42no—
698C4—3322no—
699C4—3322no—
700C4—3322no—
701C4—3322no—
702C4#1912835012yes—
703C4C2×#41×D8311yescharacteristic
704C4C2×#1458183911yescharacteristic
705C2—42no—
706C2—42no—
707C2#2491999314yesdirect product factor
708C2C2×#1912835011yescharacteristic
709C2C2×#1912849911yescharacteristic
710C2C2×#1912851611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#552×C83C2
socleC23×C83C22×D4
prime radicalC22×D4×C83D4
hypercenterC2×#552D83
hypocenterC83C2×#3349
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
2. #24919993C2direct (N × H)
3. C2×#19128111C2semidirect
4. C2×#19128036C2semidirect
5. C2×#19128042C2semidirect
6. C2×#19128039C2semidirect
7. C2×#19128039C2semidirect
8. C2×#19128005C2semidirect
9. C2×#19127996C2semidirect
10. C2×#19127957C2semidirect
11. C2×#19127940C2semidirect
12. C2×#19127806C2semidirect
14. C2×#19127741C2semidirect
15. C2×#19127737C2semidirect
32. #19128111C22semidirect
33. #19128042C22semidirect
34. #19128039C22semidirect
35. #19128039C22semidirect
36. #19128036C22semidirect
37. #19128005C22semidirect
38. #19127996C22semidirect
39. #19127957C22semidirect
40. #19127940C22semidirect
41. #19127806C22semidirect
43. #19127741C22semidirect
44. #19127737C22semidirect
352. C2×C83#3349semidirect
372. C83C2×#3349semidirect
707. C2#24919993direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191284212
#249199932
C2×#191281112
C2×#191280362
C2×#191280422
C2×#191280392
C2×#191280052
C2×#191279962
C2×#191279572
C2×#191279402
C2×#191278062
C2×#191277732
C2×#191277412
C2×#191277372
C2×#552×C832
C2×#334983