Finite Group Databasebeta

← C2×#21455939 #30548205

Subgroups — C2×#21455939 #30548205

Order 15616.

2398 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×#16840309C211yesmaximal, characteristic
2C2×C4×Q8×D61C211yesmaximal, characteristic, complemented
3#21455939C2116yesmaximal, direct product factor
4C2×#16840077C211yesmaximal, characteristic, complemented
5C2×#16840074C211yesmaximal, characteristic, complemented
6C2×#16840056C211yesmaximal, characteristic, complemented
7C2×#16840055C211yesmaximal, characteristic, complemented
8C2×#16839961C211yesmaximal, characteristic, complemented
9C2×#16839960C211yesmaximal, characteristic, complemented
10C2×#16839902C211yesmaximal, characteristic, complemented
11C2×#16839899C211yesmaximal, characteristic, complemented
12C2×#16839864C211yesmaximal, characteristic, complemented
13C2×#16839862C211yesmaximal, characteristic, complemented
14C2×#16839860C211yesmaximal, characteristic, complemented
15C2×#16839817C211yesmaximal, characteristic, complemented
16C2×C61×#440C211yesmaximal, characteristic, complemented
17C22×#11758222—21no—
18C22×Q8×D61C2211yescharacteristic
19C22×#11758190C2211yescharacteristic
20C22×#11758200C2211yescharacteristic
21C22×#11758201C2211yescharacteristic
22#16840309—24no—
23#16840309C2218yes—
24C2×#14519776C2211yescharacteristic
25C2×#14519773C2211yescharacteristic
26C2×#14519763—21no—
27C2×#14519752C2211yescharacteristic
28C2×#14519750—21no—
29C2×#14519748C2211yescharacteristic
30C2×Q8×Dic61C2211yescharacteristic
31C2×C4×Dic122—21no—
32C2×C4×Dic122C2211yescharacteristic
33C2×#14519742—21no—
34C2×#14519742C2211yescharacteristic
35C4×Q8×D61—24no—
36C4×Q8×D61C2218yescomplemented
37C2×C4×D244C2211yescharacteristic
38C2×C4×C22⋊D61—21no—
39C2×C4⋊C4×D61—21no—
40C2×C4⋊C4×D61C2211yescharacteristic
41C2×C42×D61—21no—
42C2×C42×D61C2211yescharacteristic
43#16840077C2218yescomplemented
44#16840074C2218yescomplemented
45#16840056C2218yescomplemented
46#16840055C2218yescomplemented
47#16839961C2218yescomplemented
48#16839960C2218yescomplemented
49#16839902C2218yescomplemented
50#16839899C2218yescomplemented
51#16839864C2218yescomplemented
52#16839862C2218yescomplemented
53#16839860C2218yescomplemented
54#16839817C2218yescomplemented
55C2×#14519711C2211yescharacteristic
56C2×#14519710C2211yescharacteristic
57C2×#14519710C2211yescharacteristic
58C2×#14519706C2211yescharacteristic
59C2×#14519706C2211yescharacteristic
60C2×#14519702C2211yescharacteristic
61C2×#14519701C2211yescharacteristic
62C2×#14519700C2211yescharacteristic
63C2×#14519699C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×#14519689C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×#14519688C2211yescharacteristic
69C22×SD16×C61C2211yescharacteristic
70C2×C4×Q8×C61C2211yescharacteristic
71C2×C4×D4×C61C2211yescharacteristic
72C61×#440C2218yescomplemented
73C2×#107×C61C2211yescharacteristic
74C2×#103×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×#97×C61C2211yescharacteristic
77C2×#11758222—28no—
78C2×#11758222—48no—
79C22×Dic122—21no—
80C22×Dic122—21no—
81C22×Dic122C2311yescharacteristic
82C2×Q8×D61—24no—
83C2×Q8×D61—22no—
84C2×Q8×D61—24no—
85C2×Q8×D61C2314yes—
86C22×D244—21no—
87C22×D244C2311yescharacteristic
88C22×C22⋊D61—21no—
89C22×C22⋊D61—21no—
90C22×C22⋊D61—21no—
91C22×C4×D61—21no—
92C22×C4×D61—21no—
93C22×C4×D61—21no—
94C22×C4×D61D411yescharacteristic
95C22×C4×D61D411yescharacteristic
96C22×C4×D61C2311yescharacteristic
97C2×#11758190—24no—
98C2×#11758190C2314yes—
99C2×#11758200—24no—
100C2×#11758200C2314yes—
101C2×#11758201—24no—
102C2×#11758201C2314yes—
103C22×#92418C2311yescharacteristic
104C22×#92418C2311yescharacteristic
105#14519776—22no—
106#14519776C2314yes—
107#14519773—22no—
108#14519773C2314yes—
109#14519763—28no—
110#14519752—22no—
111#14519752C2314yes—
112#14519750—28no—
113#14519748—22no—
114#14519748C2314yes—
115Q8×Dic61—22no—
116Q8×Dic61C2314yes—
117C4×Dic122—22no—
118C4×Dic122—28no—
119C4×Dic122C2314yes—
120#14519742—22no—
121#14519742—28no—
122#14519742C2314yes—
123C4×D244—22no—
124C4×D244C2314yes—
125C4×C22⋊D61—28no—
126C2×C4⋊Dic61—21no—
127C2×C4⋊Dic61C2311yescharacteristic
128C2×C4⋊Dic61C2311yescharacteristic
129C2×#11758196—21no—
130C2×#11758196—21no—
131C2×#11758196—21no—
132C2×#11758196—21no—
133C4⋊C4×D61—28no—
134C4⋊C4×D61—22no—
135C4⋊C4×D61C2314yes—
136C2×C22⋊Dic61—21no—
137C2×#11758198—21no—
138C2×#11758198—21no—
139C2×C4×Dic61—21no—
140C2×C4×Dic61—21no—
141C2×C4×Dic61—21no—
142C2×C4×Dic61D411yescharacteristic
143C2×C4×Dic61D411yescharacteristic
144C2×C4×Dic61C2311yescharacteristic
145C42×D61—28no—
146C42×D61D414yes—
147C42×D61C2314yes—
148#14519711C2314yes—
149#14519710C2314yes—
150#14519710C2314yes—
151#14519706C2314yes—
152#14519706C2314yes—
153#14519702C2314yes—
154#14519701C2314yes—
155#14519700C2314yes—
156#14519699C2314yes—
157#14519698C2314yes—
158#14519697C2314yes—
159#14519689C2314yes—
160#14519689C2314yes—
161#14519688C2314yes—
162C22×Q8×C61C2311yescharacteristic
163C22×D4×C61C2311yescharacteristic
164C23×C4×C61—21no—
165C2×SD16×C61—24no—
166C2×SD16×C61C2314yes—
167C22×C8×C61C2311yescharacteristic
168C22×C8×C61C2311yescharacteristic
169C4×Q8×C61—22no—
170C4×Q8×C61C2314yes—
171C4×D4×C61—22no—
172C4×D4×C61C2314yes—
173C2×C4⋊C4×C61—21no—
174C2×C4⋊C4×C61C2311yescharacteristic
175C2×C4⋊C4×C61C2311yescharacteristic
176C2×C22⋊C4×C61—21no—
177C2×C42×C61—21no—
178C2×C42×C61C2311yescharacteristic
179#107×C61C2314yes—
180#103×C61C2314yes—
181#102×C61C2314yes—
182#97×C61C2314yes—
183C24×C61—21no—
184C23×D61—21no—
185C23×D61C2×D411yescharacteristic
186C2×Q8×C61—21no—
187C2×Q8×C61—22no—
188C2×Q8×C61#4114yescomplemented
189C2×Q8×C61C2412yes—
190C2×D4×C61—21no—
191C2×D4×C61—22no—
192C2×D4×C61—22no—
193C2×D4×C61C2412yes—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—24no—
198C22×C4×C61—44no—
199C22×C4×C61C2×D411yescharacteristic
200C22×C4×C61C2×D411yescharacteristic
201C22×C4×C61C2411yescharacteristic
202C2×C22⋊D61—24no—
203C2×C22⋊D61—24no—
204C2×C22⋊D61—24no—
205C2×C22⋊D61—44no—
206C2×C22⋊D61—44no—
207C2×C22⋊D61—44no—
208C22×Dic61—21no—
209C22×Dic61—21no—
210C22×Dic61—21no—
211C22×Dic61C2×D411yescharacteristic
212C22×Dic61C2×D411yescharacteristic
213C22×Dic61C2×D411yescharacteristic
214Q8×D61—216no—
215Q8×D61—28no—
216Q8×D61—28no—
217#11758222—432no—
218C2×D244—22no—
219C2×D244—22no—
220C2×D244—24no—
221C2×D244—21no—
222C2×D244—44no—
223C2×D244C2412yes—
224C2×C4×D61—28no—
225C2×C4×D61—24no—
226C2×C4×D61—24no—
227C2×C4×D61—22no—
228C2×C4×D61—22no—
229C2×C4×D61—24no—
230C2×C4×D61—24no—
231C2×C4×D61—24no—
232C2×C4×D61—44no—
233C2×C4×D61—44no—
234C2×C4×D61C2×D414yes—
235C2×C4×D61C2×D414yes—
236C2×C4×D61C2×D412yes—
237C2×C4×D61C2412yes—
238C2×Dic122—28no—
239C2×Dic122—21no—
240C2×Dic122—22no—
241C2×Dic122—24no—
242C2×Dic122—24no—
243C2×Dic122—44no—
244C2×Dic122#4114yescomplemented
245C2×Dic122C2412yes—
246SD16×C61—28no—
247C2×C8×C61—22no—
248C2×C8×C61—22no—
249C2×C8×C61C2412yes—
250C2×C8×C61C2412yes—
251C4⋊C4×C61—24no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61—21no—
254C4⋊C4×C61C2412yes—
255C4⋊C4×C61C2412yes—
256C22⋊C4×C61—24no—
257C42×C61—24no—
258C42×C61C2×D412yes—
259C42×C61C2412yes—
260C22⋊Dic61—24no—
261#11758201—28no—
262#11758200—28no—
263#11758198—24no—
264#11758198—24no—
265C4⋊Dic61—21no—
266C4⋊Dic61—21no—
267C4⋊Dic61—24no—
268C4⋊Dic61C2412yes—
269C4⋊Dic61C2412yes—
270#11758196—24no—
271#11758196—24no—
272#11758196—24no—
273#11758196—24no—
274C4×Dic61—24no—
275C4×Dic61—24no—
276C4×Dic61—24no—
277C4×Dic61C2×D412yes—
278C4×Dic61C2×D414yes—
279C4×Dic61C2×D414yes—
280C4×Dic61C2412yes—
281C2×#92418—22no—
282C2×#92418—22no—
283C2×#92418C2412yes—
284C2×#92418C2412yes—
285#11758190—28no—
286C23×C61—22no—
287C23×C61—42no—
288C23×C61—42no—
289C23×C61—42no—
290C23×C61C22×D411yescharacteristic
291C22×D61—22no—
292C22×D61—22no—
293C22×D61—22no—
294C22×D61—42no—
295C22×D61—42no—
296C22×D61—42no—
297C22×D61AGL(1,ℤ/8)14yes—
298C22×D61C22×D412yes—
299Q8×C61—24no—
300Q8×C61—22no—
301Q8×C61C2×#4114yescomplemented
302D4×C61—22no—
303D4×C61—22no—
304D4×C61—42no—
305C2×C4×C61—24no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—22no—
311C2×C4×C61—48no—
312C2×C4×C61—42no—
313C2×C4×C61—42no—
314C2×C4×C61C22×D412yes—
315C2×C4×C61C22×D412yes—
316C2×C4×C61C22×D411yescharacteristic
317C2×C4×C61C2×#4112yes—
318C2×C4×C61C2×#4112yes—
319C2×C4×C61C2511yescharacteristic
320C22⋊D61—48no—
321C22⋊D61—48no—
322C22⋊D61—48no—
323C2×Dic61—22no—
324C2×Dic61—24no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—22no—
329C2×Dic61—42no—
330C2×Dic61—42no—
331C2×Dic61#13714yes—
332C2×Dic61C22×D412yes—
333C2×Dic61C22×D412yes—
334C2×Dic61C22×D412yes—
335D244—22no—
336D244—22no—
337D244—48no—
338D244—42no—
339C4×D61—216no—
340C4×D61—28no—
341C4×D61—24no—
342C4×D61—22no—
343C4×D61—22no—
344C4×D61—28no—
345C4×D61—48no—
346C4×D61—48no—
347Dic122—216no—
348Dic122—24no—
349Dic122—22no—
350Dic122—48no—
351Dic122C2×#4114yescomplemented
352C8×C61—22no—
353C8×C61—22no—
354#92418—22no—
355#92418—22no—
356C2×#3112—611nomaximal, Sylow
357C22×C61—42no—
358C22×C61—42no—
359C22×C61—42no—
360C22×C61—84no—
361C22×C61#52512yes—
362C22×C61C2×AGL(1,ℤ/8)12yes—
363C22×C61C2×#13712yes—
364C22×C61C23×D411yescharacteristic
365C2×D61—28no—
366C2×D61—22no—
367C2×D61—22no—
368C2×D61—42no—
369C2×D61—42no—
370C2×D61—42no—
371C2×D61—84no—
372C2×D61C2×AGL(1,ℤ/8)14yes—
373C4×C61—24no—
374C4×C61—22no—
375C4×C61—22no—
376C4×C61—42no—
377C4×C61—42no—
378C4×C61#52512yes—
379C4×C61C22×#4111yescharacteristic
380C4×C61C22×#4111yescharacteristic
381Dic61—22no—
382Dic61—24no—
383Dic61—22no—
384Dic61—42no—
385Dic61—42no—
386Dic61C2×#13714yes—
387C2×#532—611no—
388C22×C4×Q8—611no—
389#3112—6116no—
390C2×#480—611no—
391C2×#480—611no—
392C2×#477—611no—
393C2×#477—611no—
394C2×#460—611no—
395C2×#460—611no—
396C2×#448—611no—
397C2×#448—611no—
398C2×#440—611no—
399C2×#440—611no—
400C2×#440—611no—
401C2×#440D6111yescharacteristic, complemented
402C2×#432—611no—
403C2×C61—82no—
404C2×C61#311214yescomplemented
405C2×C61C2×#52511yescharacteristic
406C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
407C2×C61C22×#13711yescharacteristic
408D61—24no—
409D61—82no—
410C22×#41—1221no—
411C23×Q8—611no—
412C22×SD16—611no—
413C22×SD16—611no—
414C22×SD16—611no—
415C22×SD16C2×D6111yescharacteristic
416#532—618no—
417#532—1224no—
418C2×C4⋊Q8—611no—
419C2×#127—611no—
420C2×#124—1221no—
421C2×#121—611no—
422C2×#121—611no—
423C2×#121—1221no—
424C2×C4×Q8—611no—
425C2×C4×Q8—618no—
426C2×C4×Q8—611no—
427C2×C4×Q8—611no—
428C2×C4×Q8—1221no—
429C2×C4×Q8—1221no—
430C2×C4×Q8—1224no—
431C2×C4×Q8C2×D6111yescharacteristic
432C2×C4×D4—611no—
433C2×C4×D4—1221no—
434C2×C4×D4C2×D6111yescharacteristic
435C22×C4⋊C4—611no—
436C22×C4⋊C4—1221no—
437C22×C42—611no—
438C22×C42—1221no—
439#480—618no—
440#480—618no—
441#477—618no—
442#477—618no—
443#460—618no—
444#460—618no—
445#448—618no—
446#448—618no—
447#440—618no—
448#440—618no—
449#440—618no—
450#440C2×D6118yescomplemented
451#432—618no—
452C2×#107—611no—
453C2×#107—611no—
454C2×#107—611no—
455C2×#107C2×D6111yescharacteristic
456C2×C4⋊C8—611no—
457C2×C4⋊C8—611no—
458C2×#103—611no—
459C2×#103—611no—
460C2×#103—611no—
461C2×#103C2×D6111yescharacteristic
462C2×#102—611no—
463C2×#102—611no—
464C2×#102—611no—
465C2×#102C2×D6111yescharacteristic
466C2×C22⋊C8—611no—
467C2×C22⋊C8—611no—
468C2×#97—611no—
469C2×#97C2×D6111yescharacteristic
470C61C2×#311211yescharacteristic, complemented, Sylow
471C2×#41—1228no—
472C2×#41—2448no—
473C22×Q8—614no—
474C22×Q8—611no—
475C22×Q8—1221no—
476C22×Q8—1221no—
477C22×Q8—1222no—
478C22×Q8—1224no—
479C22×Q8—1224no—
480C22×Q8C22×D6111yescharacteristic
481C22×D4—611no—
482C22×D4—1221no—
483C22×D4—1221no—
484C22×D4—1221no—
485C22×D4—1221no—
486C22×D4C22×D6111yescharacteristic
487C23×C4—21no—
488C23×C4—611no—
489C23×C4—611no—
490C23×C4—611no—
491C23×C4—1221no—
492C23×C4—1221no—
493C23×C4—1221no—
494C2×SD16—24no—
495C2×SD16—614no—
496C2×SD16—614no—
497C2×SD16—614no—
498C2×SD16—1224no—
499C2×SD16—1224no—
500C2×SD16—1224no—
501C2×SD16C22×D6114yes—
502C22×C8—611no—
503C22×C8—611no—
504C22×C8C22×D6111yescharacteristic
505C22×C8C22×D6111yescharacteristic
506C4⋊Q8—614no—
507C4⋊Q8—1222no—
508#127—614no—
509#127—1222no—
510#124—1228no—
511#121—614no—
512#121—614no—
513#121—1228no—
514#121—1222no—
515#121—1222no—
516C4×Q8—22no—
517C4×Q8—614no—
518C4×Q8—614no—
519C4×Q8—614no—
520C4×Q8—1228no—
521C4×Q8—1228no—
522C4×Q8—1222no—
523C4×Q8—1222no—
524C4×Q8—1222no—
525C4×Q8C22×D6114yes—
526C4×D4—22no—
527C4×D4—614no—
528C4×D4—1228no—
529C4×D4—1222no—
530C4×D4C22×D6114yes—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—611no—
533C2×C4⋊C4—611no—
534C2×C4⋊C4—614no—
535C2×C4⋊C4—1222no—
536C2×C4⋊C4—1228no—
537C2×C4⋊C4—1221no—
538C2×C4⋊C4—1221no—
539C2×C4⋊C4—1221no—
540C2×C4⋊C4—1221no—
541C2×C4⋊C4—1221no—
542C2×C4⋊C4C22×D6111yescharacteristic
543C2×C4⋊C4C22×D6111yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—1221no—
546C2×C22⋊C4—1221no—
547C2×C22⋊C4—1221no—
548C2×C42—21no—
549C2×C42—611no—
550C2×C42—611no—
551C2×C42—611no—
552C2×C42—614no—
553C2×C42—614no—
554C2×C42—1228no—
555C2×C42—1221no—
556C2×C42—1221no—
557C2×C42—1221no—
558C2×C42C22×D6111yescharacteristic
559#107—614no—
560#107—614no—
561#107—614no—
562#107C22×D6114yes—
563C4⋊C8—614no—
564C4⋊C8—614no—
565#103—614no—
566#103—614no—
567#103—614no—
568#103C22×D6114yes—
569#102—614no—
570#102—614no—
571#102—614no—
572#102C22×D6114yes—
573C22⋊C8—614no—
574C22⋊C8—614no—
575#97—614no—
576#97C22×D6114yes—
577C24—21no—
578C24—611no—
579C24—1221no—
580#41—24432no—
581C2×Q8—21no—
582C2×Q8—22no—
583C2×Q8—614no—
584C2×Q8—612no—
585C2×Q8—1224no—
586C2×Q8—1224no—
587C2×Q8—1228no—
588C2×Q8—1228no—
589C2×Q8—12216no—
590C2×Q8—1228no—
591C2×Q8—1221no—
592C2×Q8—1222no—
593C2×Q8—2444no—
594C2×Q8#1175822214yescomplemented
595C2×Q8C23×D6112yes—
596C2×D4—21no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—612no—
600C2×D4—1224no—
601C2×D4—1224no—
602C2×D4—1224no—
603C2×D4—1224no—
604C2×D4—1221no—
605C2×D4—1222no—
606C2×D4—1222no—
607C2×D4—2444no—
608C2×D4—2444no—
609C2×D4—2444no—
610C2×D4—2444no—
611C2×D4C23×D6112yes—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—24no—
616C22×C4—44no—
617C22×C4—611no—
618C22×C4—611no—
619C22×C4—611no—
620C22×C4—614no—
621C22×C4—614no—
622C22×C4—612no—
623C22×C4—612no—
624C22×C4—1224no—
625C22×C4—1224no—
626C22×C4—1224no—
627C22×C4—1228no—
628C22×C4—1224no—
629C22×C4—1221no—
630C22×C4—1222no—
631C22×C4—1222no—
632C22×C4—1221no—
633C22×C4—1221no—
634C22×C4—1224no—
635C22×C4—2444no—
636C22×C4—2444no—
637C22×C4D4×D6111yescharacteristic
638C22×C4D4×D6111yescharacteristic
639C22×C4C23×D6111yescharacteristic
640SD16—28no—
641SD16—1228no—
642SD16—1228no—
643SD16—1228no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8—612no—
647C2×C8—612no—
648C2×C8—1222no—
649C2×C8—1222no—
650C2×C8C23×D6112yes—
651C2×C8C23×D6112yes—
652C4⋊C4—24no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—612no—
656C4⋊C4—612no—
657C4⋊C4—1224no—
658C4⋊C4—1224no—
659C4⋊C4—1224no—
660C4⋊C4—1224no—
661C4⋊C4—1221no—
662C4⋊C4—1221no—
663C4⋊C4—1224no—
664C4⋊C4C23×D6112yes—
665C4⋊C4C23×D6112yes—
666C22⋊C4—24no—
667C22⋊C4—1224no—
668C22⋊C4—1224no—
669C22⋊C4—1224no—
670C42—24no—
671C42—614no—
672C42—614no—
673C42—612no—
674C42—612no—
675C42—1224no—
676C42—1224no—
677C42—1224no—
678C42D4×D6112yes—
679C42C23×D6112yes—
680C23—22no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—614no—
685C23—612no—
686C23—1222no—
687C23—1222no—
688C23—1222no—
689C23—2442no—
690C23—2442no—
691C23—2442no—
692C23C2×D4×D6111yescharacteristic
693Q8—24no—
694Q8—22no—
695Q8—614no—
696Q8—12216no—
697Q8—1224no—
698Q8—1222no—
699Q8—2448no—
700Q8C2×#1175822214yescomplemented
701D4—22no—
702D4—22no—
703D4—42no—
704D4—1222no—
705D4—1222no—
706D4—2448no—
707D4—2448no—
708D4—2448no—
709D4—2448no—
710D4—2442no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—48no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—614no—
721C2×C4—612no—
722C2×C4—612no—
723C2×C4—612no—
724C2×C4—1228no—
725C2×C4—1228no—
726C2×C4—12216no—
727C2×C4—1222no—
728C2×C4—1224no—
729C2×C4—1222no—
730C2×C4—1222no—
731C2×C4—1224no—
732C2×C4—1222no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—2448no—
737C2×C4—2448no—
738C2×C4—2442no—
739C2×C4—2442no—
740C2×C4C2×D4×D6112yes—
741C2×C4C2×D4×D6112yes—
742C2×C4C2×D4×D6111yescharacteristic
743C2×C4#41×D6112yes—
744C2×C4C2×#1175822212yes—
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—4884no—
759C22—2442no—
760C22—2442no—
761C22—2442no—
762C22#1684027112yes—
763C22AGL(1,ℤ/8)×D6112yes—
764C22#137×D6112yes—
765C22C22×D4×D6111yescharacteristic
766C4—22no—
767C4—22no—
768C4—24no—
769C4—42no—
770C4—42no—
771C4—614no—
772C4—1222no—
773C4—1222no—
774C4—1224no—
775C4—2442no—
776C4—2442no—
777C4#1684027112yes—
778C4C2×#41×D6111yescharacteristic
779C4C22×#1175822211yescharacteristic
780C2—82no—
781C2—1224no—
782C2—4882no—
783C2#2145593914yesdirect product factor
784C2C2×#1684027111yescharacteristic
785C2C2×AGL(1,ℤ/8)×D6111yescharacteristic
786C2C2×#137×D6111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#440C2
socleC23×C61C22×D4
prime radicalC2×#16840309C2
hypercenterC2×#440D61
hypocenterC61C2×#3112
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
2. C2×C4×Q8×D61C2semidirect
3. #21455939C2direct (N × H)
4. C2×#16840077C2semidirect
5. C2×#16840074C2semidirect
6. C2×#16840056C2semidirect
7. C2×#16840055C2semidirect
8. C2×#16839961C2semidirect
9. C2×#16839960C2semidirect
10. C2×#16839902C2semidirect
11. C2×#16839899C2semidirect
12. C2×#16839864C2semidirect
13. C2×#16839862C2semidirect
14. C2×#16839860C2semidirect
15. C2×#16839817C2semidirect
16. C2×C61×#440C2semidirect
36. C4×Q8×D61C22semidirect
43. #16840077C22semidirect
44. #16840074C22semidirect
45. #16840056C22semidirect
46. #16840055C22semidirect
47. #16839961C22semidirect
48. #16839960C22semidirect
49. #16839902C22semidirect
50. #16839899C22semidirect
51. #16839864C22semidirect
52. #16839862C22semidirect
53. #16839860C22semidirect
54. #16839817C22semidirect
72. C61×#440C22semidirect
188. C2×Q8×C61#41semidirect
244. C2×Dic122#41semidirect
301. Q8×C61C2×#41semidirect
351. Dic122C2×#41semidirect
401. C2×#440D61semidirect
404. C2×C61#3112semidirect
450. #440C2×D61semidirect
470. C61C2×#3112semidirect
594. C2×Q8#11758222semidirect
700. Q8C2×#11758222semidirect
783. C2#21455939direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403092
C2×C4×Q8×D612
#214559392
C2×#168400772
C2×#168400742
C2×#168400562
C2×#168400552
C2×#168399612
C2×#168399602
C2×#168399022
C2×#168398992
C2×#168398642
C2×#168398622
C2×#168398602
C2×#168398172
C2×C61×#4402
C2×#311261