Finite Group Databasebeta

← C2×#24913435 #35570847

Subgroups — C2×#24913435 #35570847

Order 21248.

2374 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24913435C2116yesmaximal, direct product factor
2C2×#19127642C211yesmaximal, characteristic, complemented
3C2×#19127642C211yesmaximal, characteristic, complemented
4C2×#19127641C211yesmaximal, characteristic, complemented
5C2×#19127639C211yesmaximal, characteristic, complemented
6C2×#19127635C211yesmaximal, characteristic, complemented
7C2×#19127634C211yesmaximal, characteristic, complemented
8C2×#19127632C211yesmaximal, characteristic, complemented
9C2×#19127631C211yesmaximal, characteristic, complemented
10C2×#19127576C211yesmaximal, characteristic
11C2×#19127574C211yesmaximal, characteristic
12C2×#19127573C211yesmaximal, characteristic
13C2×#19127559C211yesmaximal, characteristic
14C2×#19127559C211yesmaximal, characteristic
15C22×C83⋊#95C211yesmaximal, characteristic
16C2×#385×C83C211yesmaximal, characteristic
17C24×Dic83C2211yescharacteristic
18C24×Dic83C2211yescharacteristic
19C22×C4⋊Dic83C2211yescharacteristic
20C22×C4⋊Dic83C2211yescharacteristic
21C22×Dic83⋊C4C2211yescharacteristic
22C22×Dic83⋊C4C2211yescharacteristic
23C22×Dic83⋊C4C2211yescharacteristic
24C22×Dic83⋊C4C2211yescharacteristic
25C22×Dic83⋊C4C2211yescharacteristic
26C22×Dic83⋊C4C2211yescharacteristic
27C22×Dic83⋊C4C2211yescharacteristic
28C22×Dic83⋊C4C2211yescharacteristic
29C22×C22⋊Dic83C2211yescharacteristic
30C22×C22⋊Dic83C2211yescharacteristic
31#19127642C2218yescomplemented
32#19127642C2218yescomplemented
33#19127641C2218yescomplemented
34#19127639C2218yescomplemented
35#19127635C2218yescomplemented
36#19127634C2218yescomplemented
37#19127632C2218yescomplemented
38#19127631C2218yescomplemented
39#19127576C2218yes—
40#19127574C2218yes—
41#19127573C2218yes—
42#19127559C2218yes—
43#19127559C2218yes—
44C2×C83⋊#95C2211yescharacteristic
45C2×C83⋊#95C2211yescharacteristic
46C2×C83⋊#95C2211yescharacteristic
47C2×C83⋊#95C2211yescharacteristic
48C2×C83⋊#95C2218yes—
49C2×C83⋊#95C2211yescharacteristic
50C2×C83⋊#95C2211yescharacteristic
51C2×C83⋊#95C2211yescharacteristic
52C2×C83⋊#95C2211yescharacteristic
53C2×C83⋊#95C2211yescharacteristic
54C2×C83⋊#95C2211yescharacteristic
55C2×C83⋊#95C2211yescharacteristic
56C2×C83⋊#95C2211yescharacteristic
57C2×C83⋊#95C2211yescharacteristic
58C2×C83⋊#95C2211yescharacteristic
59C24×C4×C83C2211yescharacteristic
60C22×C4⋊C4×C83C2211yescharacteristic
61C22×C4⋊C4×C83C2211yescharacteristic
62C22×C22⋊C4×C83C2211yescharacteristic
63C22×C22⋊C4×C83C2211yescharacteristic
64#385×C83C2218yes—
65C2×#95×C83C2211yescharacteristic
66C2×#95×C83C2211yescharacteristic
67C23×Dic83—24no—
68C23×Dic83—42no—
69C23×Dic83—42no—
70C23×Dic83—42no—
71C23×Dic83—42no—
72C23×Dic83Q818yes—
73C23×Dic83C2311yescharacteristic
74C23×Dic83C2311yescharacteristic
75C23×Dic83C2311yescharacteristic
76C23×Dic83C2311yescharacteristic
77C23×Dic83C2311yescharacteristic
78C23×Dic83C2311yescharacteristic
79C23×Dic83C2311yescharacteristic
80C23×Dic83C2311yescharacteristic
81C23×Dic83C2314yes—
82C23×Dic83C2314yes—
83C2×C4⋊Dic83—42no—
84C2×C4⋊Dic83—42no—
85C2×C4⋊Dic83C2314yes—
86C2×C4⋊Dic83C2314yes—
87C2×Dic83⋊C4—42no—
88C2×Dic83⋊C4—42no—
89C2×Dic83⋊C4—42no—
90C2×Dic83⋊C4—42no—
91C2×Dic83⋊C4—42no—
92C2×Dic83⋊C4—42no—
93C2×Dic83⋊C4—42no—
94C2×Dic83⋊C4—42no—
95C2×Dic83⋊C4C2314yes—
96C2×Dic83⋊C4C2314yes—
97C2×Dic83⋊C4C2314yes—
98C2×Dic83⋊C4C2314yes—
99C2×Dic83⋊C4C2314yes—
100C2×Dic83⋊C4C2314yes—
101C2×Dic83⋊C4C2314yes—
102C2×Dic83⋊C4C2314yes—
103C2×C22⋊Dic83—24no—
104C2×C22⋊Dic83—24no—
105C2×C22⋊Dic83C2314yes—
106C2×C22⋊Dic83C2314yes—
107C83⋊#95C2314yes—
108C83⋊#95C2314yes—
109C83⋊#95C2314yes—
110C83⋊#95C2314yes—
111C83⋊#95C2314yes—
112C83⋊#95C2314yes—
113C83⋊#95C2314yes—
114C83⋊#95C2314yes—
115C83⋊#95C2314yes—
116C83⋊#95C2314yes—
117C83⋊#95C2314yes—
118C83⋊#95C2314yes—
119C83⋊#95C2314yes—
120C83⋊#95C2314yes—
121C25×C83C2311yescharacteristic
122C23×C4×C83—24no—
123C23×C4×C83—42no—
124C23×C4×C83—42no—
125C23×C4×C83C2311yescharacteristic
126C23×C4×C83C2311yescharacteristic
127C23×C4×C83C2311yescharacteristic
128C23×C4×C83C2311yescharacteristic
129C23×C4×C83C2311yescharacteristic
130C23×C4×C83C2311yescharacteristic
131C23×C4×C83C2314yes—
132C2×C4⋊C4×C83—42no—
133C2×C4⋊C4×C83—42no—
134C2×C4⋊C4×C83C2314yes—
135C2×C4⋊C4×C83C2314yes—
136C2×C22⋊C4×C83—24no—
137C2×C22⋊C4×C83—24no—
138C2×C22⋊C4×C83C2314yes—
139C2×C22⋊C4×C83C2314yes—
140#95×C83C2314yes—
141#95×C83C2314yes—
142C22×Dic83—22no—
143C22×Dic83—22no—
144C22×Dic83—22no—
145C22×Dic83—22no—
146C22×Dic83—28no—
147C22×Dic83—22no—
148C22×Dic83—22no—
149C22×Dic83—22no—
150C22×Dic83—22no—
151C22×Dic83—22no—
152C22×Dic83—22no—
153C22×Dic83—22no—
154C22×Dic83—22no—
155C22×Dic83—22no—
156C22×Dic83—22no—
157C22×Dic83—22no—
158C22×Dic83—22no—
159C22×Dic83—22no—
160C22×Dic83—22no—
161C22×Dic83—22no—
162C22×Dic83—22no—
163C22×Dic83—22no—
164C22×Dic83—22no—
165C22×Dic83—416no—
166C22×Dic83—44no—
167C22×Dic83—44no—
168C22×Dic83—44no—
169C22×Dic83—44no—
170C22×Dic83—416no—
171C22×Dic83C2×Q814yes—
172C22×Dic83C2×Q814yes—
173C22×Dic83C2×Q8116yes—
174C22×Dic83C2412yes—
175C22×Dic83C2412yes—
176C22×Dic83C2412yes—
177C22×Dic83C2412yes—
178C22×Dic83C2412yes—
179C22×Dic83C2412yes—
180C22×Dic83C2412yes—
181C22×Dic83C2412yes—
182C4⋊Dic83—44no—
183C4⋊Dic83—44no—
184Dic83⋊C4—44no—
185Dic83⋊C4—44no—
186Dic83⋊C4—44no—
187Dic83⋊C4—44no—
188Dic83⋊C4—44no—
189Dic83⋊C4—44no—
190Dic83⋊C4—44no—
191Dic83⋊C4—44no—
192C22⋊Dic83—28no—
193C22⋊Dic83—28no—
194C24×C83—22no—
195C24×C83—22no—
196C24×C83—22no—
197C24×C83—22no—
198C24×C83C2×Q814yes—
199C24×C83#4114yes—
200C24×C83#4114yes—
201C24×C83C2412yes—
202C24×C83C2411yescharacteristic
203C22×C4×C83—22no—
204C22×C4×C83—22no—
205C22×C4×C83—22no—
206C22×C4×C83—22no—
207C22×C4×C83—28no—
208C22×C4×C83—22no—
209C22×C4×C83—22no—
210C22×C4×C83—22no—
211C22×C4×C83—22no—
212C22×C4×C83—22no—
213C22×C4×C83—22no—
214C22×C4×C83—22no—
215C22×C4×C83—22no—
216C22×C4×C83—22no—
217C22×C4×C83—22no—
218C22×C4×C83—22no—
219C22×C4×C83—22no—
220C22×C4×C83—22no—
221C22×C4×C83—22no—
222C22×C4×C83—44no—
223C22×C4×C83—44no—
224C22×C4×C83—416no—
225C22×C4×C83C2412yes—
226C22×C4×C83C2412yes—
227C22×C4×C83C2412yes—
228C22×C4×C83C2412yes—
229C22×C4×C83C2412yes—
230C22×C4×C83C2412yes—
231C4⋊C4×C83—44no—
232C4⋊C4×C83—44no—
233C22⋊C4×C83—28no—
234C22⋊C4×C83—28no—
235C23×C83—28no—
236C23×C83—28no—
237C23×C83—28no—
238C23×C83—28no—
239C23×C83—28no—
240C23×C83—28no—
241C23×C83—22no—
242C23×C83—22no—
243C23×C83—22no—
244C23×C83—22no—
245C23×C83#125116yes—
246C23×C83C22×Q814yes—
247C23×C83C22×Q812yes—
248C23×C83C2×#4114yes—
249C23×C83C2×#4112yes—
250C23×C83C2×#4114yes—
251C23×C83C2×#4112yes—
252C23×C83H(5,𝔽2)12yes—
253C23×C83H(5,𝔽2)12yes—
254C23×C83H(5,𝔽2)12yes—
255C23×C832−1+412yes—
256C23×C83C2511yescharacteristic
257C2×C4×C83—22no—
258C2×C4×C83—22no—
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×C83—22no—
269C2×C4×C83—22no—
270C2×C4×C83—22no—
271C2×C4×C83—22no—
272C2×C4×C83—22no—
273C2×C4×C83—22no—
274C2×C4×C83—22no—
275C2×C4×C83—416no—
276C2×C4×C83—44no—
277C2×C4×C83—44no—
278C2×C4×C83—44no—
279C2×C4×C83—44no—
280C2×C4×C83—44no—
281C2×C4×C83—44no—
282C2×Dic83—28no—
283C2×Dic83—28no—
284C2×Dic83—22no—
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×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×Dic83—22no—
306C2×Dic83—416no—
307C2×Dic83—416no—
308C2×Dic83—44no—
309C2×Dic83—44no—
310C2×Dic83—44no—
311C2×Dic83—44no—
312C2×Dic83—44no—
313C2×Dic83—44no—
314C2×Dic83C22×Q814yes—
315C2×Dic83C22×Q814yes—
316C22×C83—232no—
317C22×C83—24no—
318C22×C83—24no—
319C22×C83—24no—
320C22×C83—24no—
321C22×C83—24no—
322C22×C83—24no—
323C22×C83C2×#12518yes—
324C22×C83C2×#12514yes—
325C22×C83#53814yes—
326C22×C83#53814yes—
327C22×C83#53914yes—
328C22×C83#53914yes—
329C22×C83#54314yes—
330C22×C83#54414yes—
331C22×C83C23×Q811yescharacteristic
332C22×C83C22×#4111yescharacteristic
333C22×C83C22×#4111yescharacteristic
334C22×C83C2×H(5,𝔽2)11yescharacteristic
335C22×C83C2×H(5,𝔽2)11yescharacteristic
336C22×C83C2×H(5,𝔽2)11yescharacteristic
337C22×C83C2×2−1+411yescharacteristic
338C4×C83—42no—
339C4×C83—42no—
340C4×C83—42no—
341C4×C83—42no—
342C4×C83—42no—
343C4×C83—42no—
344Dic83—24no—
345Dic83—24no—
346Dic83—42no—
347Dic83—42no—
348Dic83—42no—
349Dic83—42no—
350Dic83—42no—
351Dic83—42no—
352C2×#2646—831nomaximal, Sylow
353C2×C83—28no—
354C2×C83#264618yescomplemented
355C2×C83C22×#12511yescharacteristic
356C2×C83C2×#53811yescharacteristic
357C2×C83C2×#53811yescharacteristic
358C2×C83C2×#53911yescharacteristic
359C2×C83C2×#53911yescharacteristic
360C2×C83C2×#54311yescharacteristic
361C2×C83C2×#54411yescharacteristic
362#2646—8316no—
363C2×#400—831no—
364C2×#400—831no—
365C2×#400—831no—
366C2×#400—831no—
367C2×#398—831no—
368C2×#398—831no—
369C2×#398—831no—
370C2×#398—831no—
371C2×#385—831no—
372C2×#385—831no—
373C2×#385—831no—
374C2×#385D8311yescharacteristic
375C2×#380—831no—
376C2×#380—831no—
377C22×#95—831no—
378C83C2×#264611yescharacteristic, complemented, Sylow
379C24×C4—831no—
380C24×C4—831no—
381C24×C4C2×D8311yescharacteristic
382C22×C4⋊C4—831no—
383C22×C4⋊C4—831no—
384C22×C4⋊C4—831no—
385C22×C4⋊C4—831no—
386C22×C4⋊C4—831no—
387C22×C4⋊C4—831no—
388C22×C4⋊C4—831no—
389C22×C4⋊C4—831no—
390C22×C4⋊C4—831no—
391C22×C4⋊C4—831no—
392C22×C4⋊C4C2×D8311yescharacteristic
393C22×C4⋊C4C2×D8311yescharacteristic
394C22×C22⋊C4—831no—
395C22×C22⋊C4—831no—
396C22×C22⋊C4C2×D8311yescharacteristic
397C22×C22⋊C4C2×D8311yescharacteristic
398#400—838no—
399#400—838no—
400#400—838no—
401#400—838no—
402#398—838no—
403#398—838no—
404#398—838no—
405#398—838no—
406#385—838no—
407#385—838no—
408#385—838no—
409#385C2×D8318yes—
410#380—838no—
411#380—838no—
412C2×#95—838no—
413C2×#95—831no—
414C2×#95—831no—
415C2×#95—831no—
416C2×#95—831no—
417C2×#95—831no—
418C2×#95—831no—
419C2×#95—831no—
420C2×#95—831no—
421C2×#95—831no—
422C2×#95—831no—
423C2×#95—831no—
424C2×#95—831no—
425C2×#95—831no—
426C2×#95—831no—
427C2×#95C2×D8311yescharacteristic
428C2×#95C2×D8311yescharacteristic
429C25C22×D8311yescharacteristic
430C23×C4—24no—
431C23×C4—42no—
432C23×C4—42no—
433C23×C4—3322no—
434C23×C4—3322no—
435C23×C4—3322no—
436C23×C4—3322no—
437C23×C4—838no—
438C23×C4—834no—
439C23×C4—834no—
440C23×C4—831no—
441C23×C4—831no—
442C23×C4—831no—
443C23×C4—831no—
444C23×C4—831no—
445C23×C4—831no—
446C23×C4—831no—
447C23×C4—831no—
448C23×C4—1664no—
449C23×C4C22×D8311yescharacteristic
450C23×C4C22×D8311yescharacteristic
451C23×C4C22×D8311yescharacteristic
452C23×C4C22×D8311yescharacteristic
453C23×C4C22×D8311yescharacteristic
454C23×C4C22×D8311yescharacteristic
455C23×C4C22×D8314yes—
456C2×C4⋊C4—42no—
457C2×C4⋊C4—42no—
458C2×C4⋊C4—3322no—
459C2×C4⋊C4—3322no—
460C2×C4⋊C4—3322no—
461C2×C4⋊C4—3322no—
462C2×C4⋊C4—3322no—
463C2×C4⋊C4—3322no—
464C2×C4⋊C4—3322no—
465C2×C4⋊C4—3322no—
466C2×C4⋊C4—3322no—
467C2×C4⋊C4—3322no—
468C2×C4⋊C4—834no—
469C2×C4⋊C4—834no—
470C2×C4⋊C4—834no—
471C2×C4⋊C4—834no—
472C2×C4⋊C4—834no—
473C2×C4⋊C4—834no—
474C2×C4⋊C4—834no—
475C2×C4⋊C4—834no—
476C2×C4⋊C4—834no—
477C2×C4⋊C4—834no—
478C2×C4⋊C4C22×D8314yes—
479C2×C4⋊C4C22×D8314yes—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—834no—
483C2×C22⋊C4—834no—
484C2×C22⋊C4—1664no—
485C2×C22⋊C4—1664no—
486C2×C22⋊C4C22×D8314yes—
487C2×C22⋊C4C22×D8314yes—
488#95—834no—
489#95—834no—
490#95—834no—
491#95—834no—
492#95—834no—
493#95—834no—
494#95—834no—
495#95—834no—
496#95—834no—
497#95—834no—
498#95—834no—
499#95—834no—
500#95—834no—
501#95—834no—
502#95C22×D8314yes—
503#95C22×D8314yes—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24Q8×D8314yes—
509C24#1305058914yes—
510C24#1305059014yes—
511C24C23×D8312yes—
512C24C23×D8311yescharacteristic
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—28no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—416no—
535C22×C4—33216no—
536C22×C4—3324no—
537C22×C4—3324no—
538C22×C4—33216no—
539C22×C4—3324no—
540C22×C4—3324no—
541C22×C4—8316no—
542C22×C4—834no—
543C22×C4—834no—
544C22×C4—832no—
545C22×C4—832no—
546C22×C4—832no—
547C22×C4—832no—
548C22×C4—832no—
549C22×C4—832no—
550C22×C4—832no—
551C22×C4—832no—
552C22×C4—1662no—
553C22×C4—1662no—
554C22×C4—1662no—
555C22×C4—1662no—
556C22×C4—1668no—
557C22×C4—1662no—
558C22×C4—1662no—
559C22×C4—1662no—
560C22×C4—1662no—
561C22×C4—1662no—
562C22×C4—1662no—
563C22×C4—1662no—
564C22×C4—1662no—
565C22×C4—1662no—
566C22×C4—1662no—
567C22×C4—1662no—
568C22×C4—1662no—
569C22×C4—1662no—
570C22×C4—1662no—
571C22×C4—1662no—
572C22×C4—1662no—
573C22×C4—1662no—
574C22×C4—1662no—
575C22×C4C23×D8312yes—
576C22×C4C23×D8312yes—
577C22×C4C23×D8312yes—
578C22×C4C23×D8312yes—
579C22×C4C23×D8312yes—
580C22×C4C23×D8312yes—
581C4⋊C4—44no—
582C4⋊C4—44no—
583C4⋊C4—3324no—
584C4⋊C4—3324no—
585C4⋊C4—3324no—
586C4⋊C4—3324no—
587C4⋊C4—3324no—
588C4⋊C4—3324no—
589C4⋊C4—3324no—
590C4⋊C4—3324no—
591C4⋊C4—3324no—
592C4⋊C4—3324no—
593C22⋊C4—28no—
594C22⋊C4—28no—
595C22⋊C4—1668no—
596C22⋊C4—1668no—
597C23—28no—
598C23—28no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—28no—
604C23—28no—
605C23—28no—
606C23—28no—
607C23#14581782116yes—
608C23C2×Q8×D8314yes—
609C23C2×Q8×D8312yes—
610C23C2×#1305058914yes—
611C23C2×#1305058912yes—
612C23C2×#1305059014yes—
613C23C2×#1305059012yes—
614C23#1458183712yes—
615C23#1458183712yes—
616C23#1458183812yes—
617C23#1458183912yes—
618C23C24×D8311yescharacteristic
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—416no—
638C2×C4—44no—
639C2×C4—44no—
640C2×C4—44no—
641C2×C4—44no—
642C2×C4—44no—
643C2×C4—44no—
644C2×C4—33216no—
645C2×C4—3324no—
646C2×C4—3324no—
647C2×C4—3324no—
648C2×C4—3324no—
649C2×C4—3324no—
650C2×C4—3324no—
651C2×C4—33216no—
652C2×C4—834no—
653C2×C4—834no—
654C2×C4—1662no—
655C2×C4—1662no—
656C2×C4—1662no—
657C2×C4—1662no—
658C2×C4—1662no—
659C2×C4—1662no—
660C2×C4—1662no—
661C2×C4—1662no—
662C2×C4—1662no—
663C2×C4—1662no—
664C2×C4—1662no—
665C2×C4—1662no—
666C2×C4—1662no—
667C2×C4—1662no—
668C2×C4—1662no—
669C2×C4—1662no—
670C2×C4—1662no—
671C2×C4—1662no—
672C2×C4—1668no—
673C2×C4—1668no—
674C2×C4—1662no—
675C2×C4—1662no—
676C2×C4—1662no—
677C2×C4—1662no—
678C22—24no—
679C22—232no—
680C22—24no—
681C22—24no—
682C22—24no—
683C22—24no—
684C22—24no—
685C22C2×#1458178218yes—
686C22C2×#1458178214yes—
687C22#1912828414yes—
688C22#1912828614yes—
689C22#1912829314yes—
690C22#1912829514yes—
691C22#1912832614yes—
692C22#1912833014yes—
693C22C22×Q8×D8311yescharacteristic
694C22C22×#1305058911yescharacteristic
695C22C22×#1305059011yescharacteristic
696C22C2×#1458183711yescharacteristic
697C22C2×#1458183711yescharacteristic
698C22C2×#1458183811yescharacteristic
699C22C2×#1458183911yescharacteristic
700C4—42no—
701C4—42no—
702C4—42no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—3322no—
707C4—3322no—
708C4—3322no—
709C4—3322no—
710C4—3322no—
711C4—3322no—
712C4—1664no—
713C4—1664no—
714C2—28no—
715C2#2491343518yesdirect product factor
716C2C22×#1458178211yescharacteristic
717C2C2×#1912828411yescharacteristic
718C2C2×#1912828611yescharacteristic
719C2C2×#1912829311yescharacteristic
720C2C2×#1912829511yescharacteristic
721C2C2×#1912832611yescharacteristic
722C2C2×#1912833011yescharacteristic
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×#385×C83C2
socleC24×C83C24
prime radicalC25×C83C23
hypercenterC2×#385D83
hypocenterC83C2×#2646
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. #24913435C2direct (N × H)
2. C2×#19127642C2semidirect
3. C2×#19127642C2semidirect
4. C2×#19127641C2semidirect
5. C2×#19127639C2semidirect
6. C2×#19127635C2semidirect
7. C2×#19127634C2semidirect
8. C2×#19127632C2semidirect
9. C2×#19127631C2semidirect
31. #19127642C22semidirect
32. #19127642C22semidirect
33. #19127641C22semidirect
34. #19127639C22semidirect
35. #19127635C22semidirect
36. #19127634C22semidirect
37. #19127632C22semidirect
38. #19127631C22semidirect
354. C2×C83#2646semidirect
378. C83C2×#2646semidirect
715. C2#24913435direct (N × H)

Maximal subgroups

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

subgroupindex
#249134352
C2×#191276422
C2×#191276412
C2×#191276392
C2×#191276352
C2×#191276342
C2×#191276322
C2×#191276312
C2×#191275762
C2×#191275742
C2×#191275732
C2×#191275592
C22×C83⋊#952
C2×#385×C832
C2×#264683