Finite Group Databasebeta

← C2×#21457705 #30556419

Subgroups — C2×#21457705 #30556419

Order 15616.

2146 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840450C211yesmaximal, characteristic, complemented
2C2×#16840420C211yesmaximal, characteristic
3#21457705C2116yesmaximal, direct product factor
4C2×#16840102C211yesmaximal, characteristic, complemented
5C2×#16840074C211yesmaximal, characteristic, complemented
6C2×#16840066C211yesmaximal, characteristic, complemented
7C2×#16840002C211yesmaximal, characteristic, complemented
8C2×#16839990C211yesmaximal, characteristic, complemented
9C2×#16839981C211yesmaximal, characteristic, complemented
10C2×#16839925C211yesmaximal, characteristic, complemented
11C2×#16839919C211yesmaximal, characteristic, complemented
12C2×C4×Dic244C211yesmaximal, characteristic, complemented
13C2×C8×D244C211yesmaximal, characteristic, complemented
14C2×#16839755C211yesmaximal, characteristic, complemented
15C2×#103×D61C211yesmaximal, characteristic, complemented
16C2×C61×#488C211yesmaximal, characteristic, complemented
17C22×#11758224C2211yescharacteristic
18C22×Q8×D61C2211yescharacteristic
19C22×Dic244C2211yescharacteristic
20C22×#11758202C2211yescharacteristic
21C22×#11758200C2211yescharacteristic
22C22×C8×D61C2211yescharacteristic
23C22×C8×D61C2211yescharacteristic
24#16840450—24no—
25#16840450C2218yescomplemented
26#16840420—24no—
27#16840420C2218yes—
28C2×#14519772—21no—
29C2×#14519768—21no—
30C2×#14519763—21no—
31C2×#14519762—21no—
32C2×#14519757C2211yescharacteristic
33C2×#14519757C2211yescharacteristic
34C2×#14519754—21no—
35C2×#14519753C2211yescharacteristic
36C2×#14519750—21no—
37C2×#14519748C2211yescharacteristic
38C2×C4×Dic122C2211yescharacteristic
39C2×C4×Dic122C2211yescharacteristic
40C2×C4×D244C2211yescharacteristic
41C2×#14519737—21no—
42C2×#14519735—21no—
43C2×#14519735C2211yescharacteristic
44C2×C4⋊C4×D61C2211yescharacteristic
45#16840102C2218yescomplemented
46#16840074C2218yescomplemented
47#16840066C2218yescomplemented
48#16840002C2218yescomplemented
49#16839990C2218yescomplemented
50#16839981C2218yescomplemented
51#16839925C2218yescomplemented
52#16839919C2218yescomplemented
53C4×Dic244C2218yescomplemented
54C8×D244C2218yescomplemented
55C2×#14519711C2211yescharacteristic
56C2×#14519710C2211yescharacteristic
57C2×#14519708C2211yescharacteristic
58C2×C4⋊#92418C2211yescharacteristic
59#16839755C2218yescomplemented
60C2×#14519702C2211yescharacteristic
61C2×#14519702C2211yescharacteristic
62C2×#14519701C2211yescharacteristic
63C2×#14519700C2211yescharacteristic
64C2×#14519700C2211yescharacteristic
65#103×D61C2218yescomplemented
66C2×#14519698C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×#14519689C2211yescharacteristic
69C2×#125×C61C2211yescharacteristic
70C2×#124×C61C2211yescharacteristic
71C61×#488C2218yescomplemented
72C2×#103×C61C2211yescharacteristic
73C2×#103×C61C2211yescharacteristic
74C2×#102×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×C4×C8×C61C2211yescharacteristic
77C2×#11758224—22no—
78C2×#11758224—24no—
79C2×#11758224—42no—
80C2×#11758224C2314yes—
81C22×Dic122—21no—
82C22×Dic122C2311yescharacteristic
83C22×Dic122C2311yescharacteristic
84C2×Q8×D61—22no—
85C2×Q8×D61—24no—
86C2×Q8×D61—42no—
87C2×Q8×D61C2314yes—
88C22×D244D411yescharacteristic
89C22×C22⋊D61—21no—
90C22×C22⋊D61—21no—
91C23×Dic61—21no—
92C22×C4×D61—21no—
93C22×C4×D61—21no—
94C22×C4×D61C2311yescharacteristic
95C22×C4×D61C2311yescharacteristic
96C2×Dic244—24no—
97C2×Dic244C2314yes—
98C2×#11758202—42no—
99C2×#11758202C2314yes—
100C2×#11758200—42no—
101C2×#11758200C2314yes—
102C22×#92418C2311yescharacteristic
103C22×#92418C2311yescharacteristic
104C2×C8×D61—42no—
105C2×C8×D61—42no—
106C2×C8×D61C2314yes—
107C2×C8×D61C2314yes—
108#14519772—28no—
109#14519768—28no—
110#14519763—28no—
111#14519762—28no—
112#14519757—22no—
113#14519757—22no—
114#14519757C2314yes—
115#14519757C2314yes—
116#14519754—28no—
117#14519753—22no—
118#14519753C2314yes—
119#14519750—28no—
120#14519748—22no—
121#14519748C2314yes—
122C4×Dic122—22no—
123C4×Dic122—22no—
124C4×Dic122C2314yes—
125C4×Dic122C2314yes—
126C4×D244D414yes—
127C4×D244C2314yes—
128#14519737—28no—
129#14519735—22no—
130#14519735—28no—
131#14519735C2314yes—
132C2×C4⋊Dic61—21no—
133C2×C4⋊Dic61—21no—
134C2×C4⋊Dic61D411yescharacteristic
135C2×C4⋊Dic61C2311yescharacteristic
136C2×C4⋊Dic61C2311yescharacteristic
137C2×#11758196—21no—
138C2×#11758196—21no—
139C2×#11758196—21no—
140C2×#11758196—21no—
141C4⋊C4×D61—22no—
142C4⋊C4×D61C2314yes—
143C2×C22⋊Dic61—21no—
144C2×#11758198—21no—
145C2×#11758198—21no—
146C2×#11758198—21no—
147C2×#11758198—21no—
148C2×#11758198D411yescharacteristic
149C2×#11758198D411yescharacteristic
150C2×C4×Dic61—21no—
151C2×C4×Dic61—21no—
152C2×C4×Dic61—21no—
153#14519711C2314yes—
154#14519710C2314yes—
155#14519708C2314yes—
156C4⋊#92418C2314yes—
157#14519702C2314yes—
158#14519702C2314yes—
159#14519701C2314yes—
160#14519700C2314yes—
161#14519700C2314yes—
162#14519698C2314yes—
163#14519689C2314yes—
164#14519689C2314yes—
165C22×Q8×C61C2311yescharacteristic
166C22×D4×C61C2311yescharacteristic
167C22×C8×C61C2311yescharacteristic
168C22×C8×C61C2311yescharacteristic
169#125×C61—22no—
170#125×C61C2314yes—
171#124×C61—22no—
172#124×C61C2314yes—
173C2×C4⋊C4×C61—21no—
174C2×C4⋊C4×C61—21no—
175C2×C4⋊C4×C61C2311yescharacteristic
176C2×C4⋊C4×C61C2311yescharacteristic
177C2×C22⋊C4×C61—21no—
178C2×C22⋊C4×C61—21no—
179C2×C42×C61C2311yescharacteristic
180#103×C61C2314yes—
181#103×C61C2314yes—
182#102×C61C2314yes—
183#102×C61C2314yes—
184C4×C8×C61C2314yes—
185C24×C61—21no—
186C23×D61C2×D411yescharacteristic
187C23×D61C2×D411yescharacteristic
188C2×Q8×C61—21no—
189C2×Q8×C61—22no—
190C2×Q8×C61—22no—
191C2×Q8×C61C2412yes—
192C2×D4×C61—21no—
193C2×D4×C61—22no—
194C2×D4×C61—22no—
195C2×D4×C61C2412yes—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61C2×D411yescharacteristic
200C22×C4×C61C2×D411yescharacteristic
201C22×C4×C61C2411yescharacteristic
202C2×C22⋊D61—24no—
203C2×C22⋊D61—24no—
204C2×C22⋊D61—44no—
205C2×C22⋊D61—44no—
206C22×Dic61—21no—
207C22×Dic61—21no—
208C22×Dic61—21no—
209C22×Dic61—21no—
210C22×Dic61—24no—
211C22×Dic61—44no—
212C22×Dic61C2×D411yescharacteristic
213C22×Dic61C2×D411yescharacteristic
214Q8×D61—28no—
215Q8×D61—44no—
216Q8×D61—48no—
217#11758224—28no—
218#11758224—44no—
219#11758224—48no—
220C2×D244—24no—
221C2×D244C2×D414yes—
222C2×C4×D61—22no—
223C2×C4×D61—22no—
224C2×C4×D61—22no—
225C2×C4×D61—22no—
226C2×C4×D61—24no—
227C2×C4×D61—24no—
228C2×C4×D61—44no—
229C2×C4×D61—44no—
230C2×C4×D61C2×D412yes—
231C2×C4×D61C2×D412yes—
232C2×C4×D61C2412yes—
233C2×C4×D61C2412yes—
234C2×Dic122—21no—
235C2×Dic122—22no—
236C2×Dic122—22no—
237C2×Dic122—22no—
238C2×Dic122—21no—
239C2×Dic122—24no—
240C2×Dic122—44no—
241C2×Dic122#4114yes—
242C2×Dic122C2412yes—
243C2×Dic122C2412yes—
244C2×C8×C61—22no—
245C2×C8×C61—22no—
246C2×C8×C61C2412yes—
247C2×C8×C61C2412yes—
248C4⋊C4×C61—24no—
249C4⋊C4×C61—24no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61C2412yes—
253C4⋊C4×C61C2412yes—
254C22⋊C4×C61—24no—
255C22⋊C4×C61—24no—
256C42×C61C2×D412yes—
257C42×C61C2412yes—
258C22⋊Dic61—24no—
259#11758202—44no—
260#11758200—44no—
261#11758198—24no—
262#11758198—24no—
263#11758198—24no—
264#11758198—24no—
265#11758198C2×D414yes—
266#11758198C2×D414yes—
267C4⋊Dic61—21no—
268C4⋊Dic61—21no—
269C4⋊Dic61—24no—
270C4⋊Dic61—24no—
271C4⋊Dic61C2×D414yes—
272C4⋊Dic61C2412yes—
273C4⋊Dic61C2412yes—
274#11758196—24no—
275#11758196—24no—
276#11758196—24no—
277#11758196—24no—
278C4×Dic61—24no—
279C4×Dic61—24no—
280C4×Dic61—24no—
281C2×#92418—22no—
282C2×#92418—22no—
283C2×#92418C2412yes—
284C2×#92418C2412yes—
285Dic244—28no—
286C8×D61—44no—
287C8×D61—44no—
288C23×C61—22no—
289C23×C61—42no—
290C23×C61—42no—
291C23×C61—42no—
292C23×C61C22×D411yescharacteristic
293C22×D61—22no—
294C22×D61—22no—
295C22×D61—22no—
296C22×D61—22no—
297C22×D61—22no—
298C22×D61#13514yes—
299C22×D61C22×D412yes—
300C22×D61C22×D412yes—
301Q8×C61—22no—
302Q8×C61—22no—
303Q8×C61—42no—
304D4×C61—22no—
305D4×C61—22no—
306D4×C61—42no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—42no—
313C2×C4×C61—42no—
314C2×C4×C61—42no—
315C2×C4×C61C22×D412yes—
316C2×C4×C61C22×D412yes—
317C2×C4×C61C22×D411yescharacteristic
318C2×C4×C61C2×#4112yes—
319C2×C4×C61H(5,𝔽2)12yes—
320C2×C4×C61C2511yescharacteristic
321C22⋊D61—48no—
322C22⋊D61—48no—
323C2×Dic61—24no—
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—48no—
331C2×Dic61—42no—
332C2×Dic61—42no—
333C2×Dic61—42no—
334C2×Dic61C22×D412yes—
335C2×Dic61C22×D412yes—
336D244—28no—
337C4×D61—24no—
338C4×D61—24no—
339C4×D61—22no—
340C4×D61—22no—
341C4×D61—22no—
342C4×D61—22no—
343C4×D61—48no—
344C4×D61—48no—
345Dic122—24no—
346Dic122—22no—
347Dic122—22no—
348Dic122—22no—
349Dic122—48no—
350Dic122—42no—
351Dic122C2×#4114yes—
352C8×C61—22no—
353C8×C61—22no—
354#92418—22no—
355#92418—22no—
356C2×#3300—611nomaximal, Sylow
357C22×C61—42no—
358C22×C61—42no—
359C22×C61—42no—
360C22×C61—84no—
361C22×C61#54612yes—
362C22×C61C2×#13512yes—
363C22×C61#57812yes—
364C22×C61C23×D411yescharacteristic
365C2×D61—22no—
366C2×D61—28no—
367C2×D61—22no—
368C2×D61—22no—
369C2×D61—22no—
370C2×D61—22no—
371C2×D61—44no—
372C2×D61C2×#13514yes—
373C4×C61—22no—
374C4×C61—22no—
375C4×C61—42no—
376C4×C61—42no—
377C4×C61—42no—
378C4×C61#54612yes—
379C4×C61C22×#4111yescharacteristic
380C4×C61C2×H(5,𝔽2)11yescharacteristic
381Dic61—24no—
382Dic61—22no—
383Dic61—22no—
384Dic61—42no—
385Dic61—42no—
386Dic61—42no—
387C2×#552—611no—
388C2×#548—611no—
389#3300—6116no—
390C2×#488D6111yescharacteristic, complemented
391C2×#485—611no—
392C2×#480—611no—
393C2×#479—611no—
394C2×#467—611no—
395C2×#465—611no—
396C2×#464—611no—
397C2×#452—611no—
398C2×#451—611no—
399C2×C4×Q16—611no—
400C2×C8×D4—611no—
401C2×#416—611no—
402C22×#103—611no—
403C2×C61—82no—
404C2×C61#330014yescomplemented
405C2×C61C2×#54611yescharacteristic
406C2×C61C22×#13511yescharacteristic
407C2×C61C2×#57811yescharacteristic
408D61—24no—
409D61—42no—
410C22×#41—611no—
411C23×Q8—611no—
412C22×Q16—611no—
413C22×Q16—611no—
414C22×SD16—611no—
415C23×C8—611no—
416C23×C8—611no—
417#552—618no—
418#552—1224no—
419#548—618no—
420#548—1224no—
421C2×#126—1221no—
422C2×#125—1221no—
423C2×#125C2×D6111yescharacteristic
424C2×#124—1221no—
425C2×#124C2×D6111yescharacteristic
426C2×#123—1221no—
427C2×C22⋊Q8—611no—
428C2×C22⋊Q8—611no—
429C2×C22⋊Q8—611no—
430C2×C22⋊Q8—1221no—
431C2×#121—611no—
432C2×#121—1221no—
433C2×C4×Q8—611no—
434C2×C4×Q8—611no—
435C2×C4×D4—611no—
436C2×C4×D4—1221no—
437C2×#117—611no—
438C2×#117—1221no—
439C22×C4⋊C4—611no—
440#488C2×D6118yescomplemented
441#485—618no—
442#480—618no—
443#479—618no—
444#467—618no—
445#465—618no—
446#464—618no—
447#452—618no—
448#451—618no—
449C4×Q16—618no—
450C8×D4—618no—
451C2×#107—611no—
452C2×#107—611no—
453C2×#106—611no—
454C2×C4⋊C8—611no—
455#416—618no—
456C2×#103—611no—
457C2×#103—611no—
458C2×#103—611no—
459C2×#103—611no—
460C2×#103—611no—
461C2×#103—618no—
462C2×#103C2×D6111yescharacteristic
463C2×#103C2×D6111yescharacteristic
464C2×#102—611no—
465C2×#102C2×D6111yescharacteristic
466C2×#102C2×D6111yescharacteristic
467C2×C22⋊C8—611no—
468C2×C22⋊C8—611no—
469C2×C4×C8C2×D6111yescharacteristic
470C61C2×#330011yescharacteristic, complemented, Sylow
471C2×#41—614no—
472C2×#41—1222no—
473C2×#41—1224no—
474C2×#41—2442no—
475C22×Q8—614no—
476C22×Q8—611no—
477C22×Q8—611no—
478C22×Q8—1221no—
479C22×Q8—1222no—
480C22×Q8—1224no—
481C22×Q8—2442no—
482C22×Q8C22×D6111yescharacteristic
483C22×D4—611no—
484C22×D4—1221no—
485C22×D4—1221no—
486C22×D4C22×D6111yescharacteristic
487C23×C4—611no—
488C23×C4—611no—
489C23×C4—1221no—
490C23×C4—1221no—
491C23×C4—1221no—
492C2×Q16—614no—
493C2×Q16—614no—
494C2×Q16—1224no—
495C2×Q16—2442no—
496C2×SD16—614no—
497C2×SD16—2442no—
498C22×C8—611no—
499C22×C8—611no—
500C22×C8—614no—
501C22×C8—614no—
502C22×C8—2442no—
503C22×C8—2442no—
504C22×C8C22×D6111yescharacteristic
505C22×C8C22×D6111yescharacteristic
506#126—1228no—
507#125—22no—
508#125—1228no—
509#125C22×D6114yes—
510#124—22no—
511#124—1228no—
512#124C22×D6114yes—
513#123—1228no—
514C22⋊Q8—614no—
515C22⋊Q8—614no—
516C22⋊Q8—614no—
517C22⋊Q8—1228no—
518C22⋊Q8—1222no—
519C22⋊Q8—1222no—
520C22⋊Q8—1222no—
521#121—614no—
522#121—1228no—
523#121—1222no—
524C4×Q8—614no—
525C4×Q8—614no—
526C4×Q8—1222no—
527C4×Q8—1222no—
528C4×D4—614no—
529C4×D4—614no—
530C4×D4—1228no—
531#117—614no—
532#117—1228no—
533#117—1222no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—611no—
537C2×C4⋊C4—611no—
538C2×C4⋊C4—611no—
539C2×C4⋊C4—614no—
540C2×C4⋊C4—1222no—
541C2×C4⋊C4—1221no—
542C2×C4⋊C4—1221no—
543C2×C4⋊C4—1221no—
544C2×C4⋊C4—1221no—
545C2×C4⋊C4—1221no—
546C2×C4⋊C4—1221no—
547C2×C4⋊C4C22×D6111yescharacteristic
548C2×C4⋊C4C22×D6111yescharacteristic
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—611no—
552C2×C22⋊C4—611no—
553C2×C22⋊C4—1221no—
554C2×C22⋊C4—1221no—
555C2×C22⋊C4—1221no—
556C2×C22⋊C4—1221no—
557C2×C22⋊C4—1221no—
558C2×C42—1221no—
559C2×C42—1221no—
560C2×C42—1221no—
561C2×C42C22×D6111yescharacteristic
562#107—614no—
563#107—614no—
564#106—614no—
565C4⋊C8—614no—
566#103—614no—
567#103—614no—
568#103—614no—
569#103—614no—
570#103—614no—
571#103C22×D6114yes—
572#103C22×D6114yes—
573#102—614no—
574#102C22×D6114yes—
575#102C22×D6114yes—
576C22⋊C8—614no—
577C22⋊C8—614no—
578C4×C8C22×D6114yes—
579C24—21no—
580C24—611no—
581C24—611no—
582#41—1228no—
583#41—2444no—
584#41—2448no—
585C2×Q8—21no—
586C2×Q8—22no—
587C2×Q8—22no—
588C2×Q8—614no—
589C2×Q8—612no—
590C2×Q8—612no—
591C2×Q8—1224no—
592C2×Q8—1221no—
593C2×Q8—1221no—
594C2×Q8—1222no—
595C2×Q8—1228no—
596C2×Q8—1222no—
597C2×Q8—1222no—
598C2×Q8—2444no—
599C2×Q8—2444no—
600C2×Q8—2448no—
601C2×Q8C23×D6112yes—
602C2×D4—21no—
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—614no—
606C2×D4—1224no—
607C2×D4—1224no—
608C2×D4—1224no—
609C2×D4—2444no—
610C2×D4—2444no—
611C2×D4C23×D6112yes—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—611no—
616C22×C4—611no—
617C22×C4—612no—
618C22×C4—612no—
619C22×C4—612no—
620C22×C4—612no—
621C22×C4—1224no—
622C22×C4—1224no—
623C22×C4—1224no—
624C22×C4—1221no—
625C22×C4—1222no—
626C22×C4—1222no—
627C22×C4—1222no—
628C22×C4—1222no—
629C22×C4—1221no—
630C22×C4—1221no—
631C22×C4—1221no—
632C22×C4—2444no—
633C22×C4—2444no—
634C22×C4—2444no—
635C22×C4D4×D6111yescharacteristic
636C22×C4D4×D6111yescharacteristic
637C22×C4C23×D6111yescharacteristic
638Q16—1228no—
639Q16—2444no—
640SD16—2444no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—612no—
644C2×C8—612no—
645C2×C8—1222no—
646C2×C8—1222no—
647C2×C8—2444no—
648C2×C8—2444no—
649C2×C8C23×D6112yes—
650C2×C8C23×D6112yes—
651C4⋊C4—24no—
652C4⋊C4—24no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—614no—
656C4⋊C4—612no—
657C4⋊C4—612no—
658C4⋊C4—1224no—
659C4⋊C4—1224no—
660C4⋊C4—1224no—
661C4⋊C4—1224no—
662C4⋊C4—1221no—
663C4⋊C4—1221no—
664C4⋊C4—1224no—
665C4⋊C4—1224no—
666C4⋊C4C23×D6112yes—
667C4⋊C4C23×D6112yes—
668C22⋊C4—24no—
669C22⋊C4—24no—
670C22⋊C4—614no—
671C22⋊C4—614no—
672C22⋊C4—1224no—
673C22⋊C4—1224no—
674C22⋊C4—1224no—
675C22⋊C4—1224no—
676C22⋊C4—1224no—
677C42—1224no—
678C42—1224no—
679C42—1224no—
680C42D4×D6112yes—
681C42C23×D6112yes—
682C23—22no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—614no—
687C23—612no—
688C23—612no—
689C23—1222no—
690C23—1222no—
691C23—1222no—
692C23—1222no—
693C23—1222no—
694C23C2×D4×D6111yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—42no—
698Q8—614no—
699Q8—1222no—
700Q8—1224no—
701Q8—1222no—
702Q8—1222no—
703Q8—2448no—
704Q8—2442no—
705D4—22no—
706D4—22no—
707D4—42no—
708D4—1228no—
709D4—2448no—
710D4—2448no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—612no—
720C2×C4—612no—
721C2×C4—1222no—
722C2×C4—1222no—
723C2×C4—1222no—
724C2×C4—1224no—
725C2×C4—1222no—
726C2×C4—1222no—
727C2×C4—1222no—
728C2×C4—1222no—
729C2×C4—1224no—
730C2×C4—1224no—
731C2×C4—1222no—
732C2×C4—1222no—
733C2×C4—1222no—
734C2×C4—2448no—
735C2×C4—2448no—
736C2×C4—2448no—
737C2×C4—2442no—
738C2×C4—2442no—
739C2×C4—2442no—
740C2×C4C2×D4×D6112yes—
741C2×C4C2×D4×D6112yes—
742C2×C4C2×D4×D6111yescharacteristic
743C2×C4#41×D6112yes—
744C2×C4#1451982312yes—
745C2×C4C24×D6111yescharacteristic
746C8—22no—
747C8—22no—
748C8—1222no—
749C8—1222no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—84no—
754C22—614no—
755C22—1228no—
756C22—1222no—
757C22—1222no—
758C22—1222no—
759C22—1222no—
760C22—1222no—
761C22—2444no—
762C22#1684040512yes—
763C22#135×D6112yes—
764C22#1684057612yes—
765C22C22×D4×D6111yescharacteristic
766C4—22no—
767C4—22no—
768C4—42no—
769C4—42no—
770C4—42no—
771C4—1222no—
772C4—1222no—
773C4—1224no—
774C4—2442no—
775C4—2442no—
776C4—2442no—
777C4#1684040512yes—
778C4C2×#41×D6111yescharacteristic
779C4C2×#1451982311yescharacteristic
780C2—82no—
781C2—1224no—
782C2—2442no—
783C2#2145770514yesdirect product factor
784C2C2×#1684040511yescharacteristic
785C2C2×#135×D6111yescharacteristic
786C2C2×#1684057611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#488C2
socleC23×C61C22×D4
prime radicalC2×#16840420C2
hypercenterC2×#488D61
hypocenterC61C2×#3300
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#488

Complements

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

NH ≅ G/Ntype
1. C2×#16840450C2semidirect
3. #21457705C2direct (N × H)
4. C2×#16840102C2semidirect
5. C2×#16840074C2semidirect
6. C2×#16840066C2semidirect
7. C2×#16840002C2semidirect
8. C2×#16839990C2semidirect
9. C2×#16839981C2semidirect
10. C2×#16839925C2semidirect
11. C2×#16839919C2semidirect
12. C2×C4×Dic244C2semidirect
13. C2×C8×D244C2semidirect
14. C2×#16839755C2semidirect
15. C2×#103×D61C2semidirect
16. C2×C61×#488C2semidirect
25. #16840450C22semidirect
45. #16840102C22semidirect
46. #16840074C22semidirect
47. #16840066C22semidirect
48. #16840002C22semidirect
49. #16839990C22semidirect
50. #16839981C22semidirect
51. #16839925C22semidirect
52. #16839919C22semidirect
53. C4×Dic244C22semidirect
54. C8×D244C22semidirect
59. #16839755C22semidirect
65. #103×D61C22semidirect
71. C61×#488C22semidirect
390. C2×#488D61semidirect
404. C2×C61#3300semidirect
440. #488C2×D61semidirect
470. C61C2×#3300semidirect
783. C2#21457705direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404502
C2×#168404202
#214577052
C2×#168401022
C2×#168400742
C2×#168400662
C2×#168400022
C2×#168399902
C2×#168399812
C2×#168399252
C2×#168399192
C2×C4×Dic2442
C2×C8×D2442
C2×#168397552
C2×#103×D612
C2×C61×#4882
C2×#330061