Finite Group Databasebeta

← C2×#21457712 #30556426

Subgroups — C2×#21457712 #30556426

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×#16840454C211yesmaximal, characteristic, complemented
2C2×#16840418C211yesmaximal, characteristic
3#21457712C2116yesmaximal, direct product factor
4C2×#16840115C211yesmaximal, characteristic, complemented
5C2×#16840106C211yesmaximal, characteristic, complemented
6C2×#16840073C211yesmaximal, characteristic, complemented
7C2×#16840072C211yesmaximal, characteristic, complemented
8C2×#16840002C211yesmaximal, characteristic, complemented
9C2×#16839982C211yesmaximal, characteristic, complemented
10C2×#16839921C211yesmaximal, characteristic, complemented
11C2×#16839917C211yesmaximal, characteristic, complemented
12C2×#16839854C211yesmaximal, characteristic, complemented
13C2×C8×C22⋊D61C211yesmaximal, characteristic, complemented
14C2×#16839755C211yesmaximal, characteristic, complemented
15C22×#14519702C211yesmaximal, characteristic, complemented
16C2×C61×#465C211yesmaximal, characteristic, complemented
17C22×#11758224C2211yescharacteristic
18C23×Dic122C2211yescharacteristic
19C22×#11758202C2211yescharacteristic
20C22×#11758202C2211yescharacteristic
21C22×C8×D61C2211yescharacteristic
22#16840454—24no—
23#16840454C2218yescomplemented
24#16840418—24no—
25#16840418C2218yes—
26C2×#14519772—21no—
27C2×#14519768—21no—
28C2×#14519768C2211yescharacteristic
29C2×#14519764C2211yescharacteristic
30C2×#14519763—21no—
31C2×#14519761—21no—
32C2×#14519757C2211yescharacteristic
33C2×#14519754—21no—
34C2×#14519753C2211yescharacteristic
35C2×#14519749—21no—
36C2×Q8×Dic61C2211yescharacteristic
37C2×#14519742C2211yescharacteristic
38C2×D4×Dic61—21no—
39C2×C4×C22⋊D61C2211yescharacteristic
40C2×#14519735C2211yescharacteristic
41C2×#14519733—21no—
42C22×C4⋊Dic61C2211yescharacteristic
43#16840115C2218yescomplemented
44#16840106C2218yescomplemented
45#16840073C2218yescomplemented
46#16840072C2218yescomplemented
47#16840002C2218yescomplemented
48#16839982C2218yescomplemented
49#16839921C2218yescomplemented
50#16839917C2218yescomplemented
51#16839854C2218yescomplemented
52C8×C22⋊D61C2218yescomplemented
53C2×#14519710C2211yescharacteristic
54C2×#14519710C2211yescharacteristic
55C2×#14519706C2211yescharacteristic
56#16839755C2218yescomplemented
57C2×#14519702C2211yescharacteristic
58C2×#14519702C2211yescharacteristic
59C2×#14519702C2211yescharacteristic
60C2×#14519702C2211yescharacteristic
61C2×#14519702C2218yescomplemented
62C2×#14519700C2211yescharacteristic
63C2×#14519700C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65C2×#14519698C2211yescharacteristic
66C2×C22⋊#92418C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C22×SD16×C61C2211yescharacteristic
70C23×C8×C61C2211yescharacteristic
71C2×C22⋊Q8×C61C2211yescharacteristic
72C2×#121×C61C2211yescharacteristic
73C61×#465C2218yescomplemented
74C2×#106×C61C2211yescharacteristic
75C2×#103×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C2×#11758224—22no—
78C2×#11758224—24no—
79C2×#11758224—42no—
80C2×#11758224C2314yes—
81C22×Dic122—24no—
82C22×Dic122—21no—
83C22×Dic122—22no—
84C22×Dic122—42no—
85C22×Dic122C2311yescharacteristic
86C22×Dic122C2314yes—
87C22×Dic122C2311yescharacteristic
88C22×C22⋊D61—21no—
89C22×C22⋊D61D411yescharacteristic
90C23×Dic61—21no—
91C23×Dic61—21no—
92C23×Dic61—21no—
93C22×C4×D61C2311yescharacteristic
94C2×#11758202—24no—
95C2×#11758202—42no—
96C2×#11758202C2314yes—
97C2×#11758202C2314yes—
98C22×#92418C2311yescharacteristic
99C22×#92418C2311yescharacteristic
100C2×C8×D61—42no—
101C2×C8×D61C2314yes—
102#14519772—28no—
103#14519768—28no—
104#14519768—22no—
105#14519768C2314yes—
106#14519764—22no—
107#14519764C2314yes—
108#14519763—28no—
109#14519761—28no—
110#14519757—22no—
111#14519757C2314yes—
112#14519754—28no—
113#14519753—22no—
114#14519753C2314yes—
115#14519749—28no—
116Q8×Dic61—22no—
117Q8×Dic61C2314yes—
118#14519742—22no—
119#14519742C2314yes—
120D4×Dic61—28no—
121C4×C22⋊D61D414yes—
122C4×C22⋊D61C2314yes—
123#14519735—22no—
124#14519735C2314yes—
125#14519733—28no—
126C2×C4⋊Dic61—22no—
127C2×C4⋊Dic61—21no—
128C2×C4⋊Dic61—21no—
129C2×C4⋊Dic61—21no—
130C2×C4⋊Dic61—21no—
131C2×C4⋊Dic61C2314yes—
132C2×C4⋊Dic61C2311yescharacteristic
133C2×C4⋊Dic61C2311yescharacteristic
134C2×#11758196—21no—
135C2×#11758196—21no—
136C2×#11758196—21no—
137C2×#11758196D411yescharacteristic
138C2×C22⋊Dic61—21no—
139C2×C22⋊Dic61—21no—
140C2×C22⋊Dic61D411yescharacteristic
141C2×#11758198—21no—
142C2×#11758198—21no—
143C2×#11758198—21no—
144C2×#11758198D411yescharacteristic
145C2×C4×Dic61—21no—
146C2×C4×Dic61—21no—
147C2×C4×Dic61—21no—
148C2×C4×Dic61C2311yescharacteristic
149#14519710C2314yes—
150#14519710C2314yes—
151#14519706C2314yes—
152#14519702C2314yes—
153#14519702C2314yes—
154#14519702C2314yes—
155#14519702C2314yes—
156#14519700C2314yes—
157#14519700C2314yes—
158#14519698C2314yes—
159#14519698C2314yes—
160C22⋊#92418C2314yes—
161#14519689C2314yes—
162C8×Dic61C2314yes—
163C22×Q8×C61C2311yescharacteristic
164C22×D4×C61—21no—
165C22×D4×C61C2311yescharacteristic
166C23×C4×C61C2311yescharacteristic
167C2×SD16×C61—42no—
168C2×SD16×C61C2314yes—
169C22×C8×C61—42no—
170C22×C8×C61C2311yescharacteristic
171C22×C8×C61C2311yescharacteristic
172C22×C8×C61C2314yes—
173C22⋊Q8×C61—22no—
174C22⋊Q8×C61C2314yes—
175#121×C61—22no—
176#121×C61C2314yes—
177C2×C4⋊C4×C61—21no—
178C2×C4⋊C4×C61C2311yescharacteristic
179C2×C4⋊C4×C61C2311yescharacteristic
180C2×C22⋊C4×C61—21no—
181C2×C22⋊C4×C61—21no—
182#106×C61C2314yes—
183#103×C61C2314yes—
184#102×C61C2314yes—
185C24×C61—21no—
186C24×C61C2×D411yescharacteristic
187C23×D61C2×D411yescharacteristic
188C2×Q8×C61—21no—
189C2×Q8×C61—22no—
190C2×Q8×C61—22no—
191C2×Q8×C61C2412yes—
192C2×D4×C61—24no—
193C2×D4×C61—21no—
194C2×D4×C61—22no—
195C2×D4×C61—22no—
196C2×D4×C61—44no—
197C2×D4×C61C2412yes—
198C22×C4×C61—22no—
199C22×C4×C61—22no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61C2×D411yescharacteristic
204C22×C4×C61C2×D412yes—
205C22×C4×C61C2412yes—
206C22×C4×C61C2411yescharacteristic
207C2×C22⋊D61—24no—
208C2×C22⋊D61—24no—
209C2×C22⋊D61—44no—
210C2×C22⋊D61C2×D414yes—
211C22×Dic61—21no—
212C22×Dic61—21no—
213C22×Dic61—24no—
214C22×Dic61—21no—
215C22×Dic61—21no—
216C22×Dic61—24no—
217C22×Dic61—24no—
218C22×Dic61—44no—
219C22×Dic61—44no—
220C22×Dic61—44no—
221C22×Dic61C2×D411yescharacteristic
222C22×Dic61C2×D411yescharacteristic
223C22×Dic61C2×D411yescharacteristic
224#11758224—28no—
225#11758224—44no—
226#11758224—48no—
227C2×C4×D61—22no—
228C2×C4×D61—22no—
229C2×C4×D61C2×D412yes—
230C2×C4×D61C2412yes—
231C2×Dic122—21no—
232C2×Dic122—22no—
233C2×Dic122—22no—
234C2×Dic122—22no—
235C2×Dic122—28no—
236C2×Dic122—24no—
237C2×Dic122—21no—
238C2×Dic122—44no—
239C2×Dic122—48no—
240C2×Dic122—44no—
241C2×Dic122#4114yes—
242C2×Dic122C2412yes—
243C2×Dic122C2412yes—
244SD16×C61—44no—
245C2×C8×C61—22no—
246C2×C8×C61—22no—
247C2×C8×C61—44no—
248C2×C8×C61C2412yes—
249C2×C8×C61C2412yes—
250C4⋊C4×C61—24no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61C2412yes—
254C4⋊C4×C61C2412yes—
255C22⋊C4×C61—24no—
256C22⋊C4×C61—24no—
257C22⋊Dic61—24no—
258C22⋊Dic61—24no—
259C22⋊Dic61C2×D414yes—
260#11758202—28no—
261#11758202—44no—
262#11758198—24no—
263#11758198—24no—
264#11758198—24no—
265#11758198C2×D414yes—
266C4⋊Dic61—21no—
267C4⋊Dic61—21no—
268C4⋊Dic61—24no—
269C4⋊Dic61—24no—
270C4⋊Dic61—24no—
271C4⋊Dic61—24no—
272C4⋊Dic61C2412yes—
273C4⋊Dic61C2412yes—
274#11758196—24no—
275#11758196—24no—
276#11758196—24no—
277#11758196C2×D414yes—
278C4×Dic61—24no—
279C4×Dic61—24no—
280C4×Dic61—24no—
281C4×Dic61C2×D412yes—
282C4×Dic61C2412yes—
283C2×#92418—22no—
284C2×#92418—22no—
285C2×#92418C2412yes—
286C2×#92418C2412yes—
287C8×D61—44no—
288C23×C61—22no—
289C23×C61—22no—
290C23×C61—22no—
291C23×C61—42no—
292C23×C61—42no—
293C23×C61—42no—
294C23×C61#13514yes—
295C23×C61C22×D412yes—
296C23×C61C22×D411yescharacteristic
297C22×D61—22no—
298C22×D61—22no—
299C22×D61—22no—
300C22×D61C22×D412yes—
301Q8×C61—22no—
302Q8×C61—22no—
303Q8×C61—42no—
304D4×C61—22no—
305D4×C61—22no—
306D4×C61—48no—
307D4×C61—42no—
308C2×C4×C61—22no—
309C2×C4×C61—24no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—22no—
315C2×C4×C61—42no—
316C2×C4×C61—42no—
317C2×C4×C61—42no—
318C2×C4×C61C22×D412yes—
319C2×C4×C61C22×D411yescharacteristic
320C2×C4×C61C2×#4112yes—
321C2×C4×C61H(5,𝔽2)12yes—
322C2×C4×C61C2511yescharacteristic
323C22⋊D61—28no—
324C22⋊D61—48no—
325C2×Dic61—24no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—48no—
334C2×Dic61—48no—
335C2×Dic61—42no—
336C2×Dic61—48no—
337C2×Dic61—42no—
338C2×Dic61—42no—
339C2×Dic61C22×D412yes—
340C2×Dic61C22×D412yes—
341C2×Dic61C22×D412yes—
342C4×D61—24no—
343C4×D61—22no—
344C4×D61—22no—
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—22no—
358C22×C61—28no—
359C22×C61—22no—
360C22×C61—42no—
361C22×C61—42no—
362C22×C61—42no—
363C22×C61—84no—
364C22×C61#54612yes—
365C22×C61C2×#13514yes—
366C22×C61C2×#13512yes—
367C22×C61#57812yes—
368C22×C61C23×D411yescharacteristic
369C2×D61—22no—
370C2×D61—22no—
371C2×D61—22no—
372C2×D61—44no—
373C4×C61—22no—
374C4×C61—42no—
375C4×C61—42no—
376C4×C61—42no—
377C4×C61#54612yes—
378C4×C61C22×#4111yescharacteristic
379C4×C61C2×H(5,𝔽2)11yescharacteristic
380Dic61—24no—
381Dic61—22no—
382Dic61—22no—
383Dic61—22no—
384Dic61—42no—
385Dic61—42no—
386Dic61—42no—
387C2×#552—611no—
388C2×#548—611no—
389#3300—6116no—
390C2×#488—611no—
391C2×#485—611no—
392C2×#480—611no—
393C2×#479—611no—
394C2×#467—611no—
395C2×#465D6111yescharacteristic, complemented
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—24no—
404C2×C61—82no—
405C2×C61#330014yescomplemented
406C2×C61C2×#54611yescharacteristic
407C2×C61C22×#13511yescharacteristic
408C2×C61C2×#57811yescharacteristic
409D61—42no—
410C22×#41—611no—
411C23×Q8—611no—
412C22×Q16—611no—
413C22×Q16—611no—
414C22×SD16C2×D6111yescharacteristic
415C23×C8—611no—
416C23×C8C2×D6111yescharacteristic
417#552—618no—
418#552—1224no—
419#548—618no—
420#548—1224no—
421C2×#126—1221no—
422C2×#125—611no—
423C2×#125—1221no—
424C2×#124—611no—
425C2×#124—1221no—
426C2×#123—1221no—
427C2×C22⋊Q8—611no—
428C2×C22⋊Q8—611no—
429C2×C22⋊Q8—1221no—
430C2×C22⋊Q8C2×D6111yescharacteristic
431C2×#121—1221no—
432C2×#121C2×D6111yescharacteristic
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#488—618no—
441#485—618no—
442#480—618no—
443#479—618no—
444#467—618no—
445#465C2×D6118yescomplemented
446#464—618no—
447#452—618no—
448#451—618no—
449C4×Q16—618no—
450C8×D4—618no—
451C2×#107—611no—
452C2×#107—611no—
453C2×#106C2×D6111yescharacteristic
454C2×C4⋊C8—611no—
455#416—618no—
456C2×#103—611no—
457C2×#103—611no—
458C2×#103—611no—
459C2×#103—611no—
460C2×#103—618no—
461C2×#103—611no—
462C2×#103—611no—
463C2×#103C2×D6111yescharacteristic
464C2×#102—611no—
465C2×#102—611no—
466C2×#102C2×D6111yescharacteristic
467C2×C22⋊C8—611no—
468C2×C22⋊C8—611no—
469C2×C4×C8—611no—
470C61C2×#330011yescharacteristic, complemented, Sylow
471C2×#41—614no—
472C2×#41—1222no—
473C2×#41—1224no—
474C2×#41—2442no—
475C22×Q8—611no—
476C22×Q8—611no—
477C22×Q8—614no—
478C22×Q8—1224no—
479C22×Q8—1221no—
480C22×Q8—1222no—
481C22×Q8—2442no—
482C22×Q8C22×D6111yescharacteristic
483C22×D4—21no—
484C22×D4—611no—
485C22×D4—1221no—
486C22×D4C22×D6111yescharacteristic
487C23×C4—611no—
488C23×C4—1221no—
489C23×C4—1221no—
490C23×C4—1221no—
491C23×C4C22×D6111yescharacteristic
492C2×Q16—614no—
493C2×Q16—614no—
494C2×Q16—1224no—
495C2×Q16—2442no—
496C2×SD16—42no—
497C2×SD16C22×D6114yes—
498C22×C8—42no—
499C22×C8—611no—
500C22×C8—611no—
501C22×C8—614no—
502C22×C8—2442no—
503C22×C8C22×D6111yescharacteristic
504C22×C8C22×D6111yescharacteristic
505C22×C8C22×D6114yes—
506#126—1228no—
507#125—614no—
508#125—1222no—
509#125—1228no—
510#124—614no—
511#124—1222no—
512#124—1228no—
513#123—1228no—
514C22⋊Q8—22no—
515C22⋊Q8—614no—
516C22⋊Q8—614no—
517C22⋊Q8—1228no—
518C22⋊Q8—1222no—
519C22⋊Q8—1222no—
520C22⋊Q8C22×D6114yes—
521#121—22no—
522#121—1228no—
523#121C22×D6114yes—
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—611no—
536C2×C4⋊C4—611no—
537C2×C4⋊C4—611no—
538C2×C4⋊C4—614no—
539C2×C4⋊C4—1221no—
540C2×C4⋊C4—1221no—
541C2×C4⋊C4—1221no—
542C2×C4⋊C4—1221no—
543C2×C4⋊C4—1221no—
544C2×C4⋊C4—1221no—
545C2×C4⋊C4—1221no—
546C2×C4⋊C4—1222no—
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—611no—
559C2×C42—1221no—
560C2×C42—1221no—
561C2×C42—1221no—
562#107—614no—
563#107—614no—
564#106C22×D6114yes—
565C4⋊C8—614no—
566#103—614no—
567#103—614no—
568#103—614no—
569#103—614no—
570#103—614no—
571#103—614no—
572#103C22×D6114yes—
573#102—614no—
574#102—614no—
575#102C22×D6114yes—
576C22⋊C8—614no—
577C22⋊C8—614no—
578C4×C8—614no—
579C24—21no—
580C24—611no—
581C24D4×D6111yescharacteristic
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—1228no—
592C2×Q8—1221no—
593C2×Q8—1224no—
594C2×Q8—1221no—
595C2×Q8—1222no—
596C2×Q8—1222no—
597C2×Q8—1222no—
598C2×Q8—2444no—
599C2×Q8—2444no—
600C2×Q8—2448no—
601C2×Q8C23×D6112yes—
602C2×D4—24no—
603C2×D4—21no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—44no—
607C2×D4—614no—
608C2×D4—1224no—
609C2×D4—1224no—
610C2×D4—2444no—
611C2×D4C23×D6112yes—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—611no—
618C22×C4—611no—
619C22×C4—611no—
620C22×C4—612no—
621C22×C4—612no—
622C22×C4—1224no—
623C22×C4—1221no—
624C22×C4—1222no—
625C22×C4—1222no—
626C22×C4—1224no—
627C22×C4—1224no—
628C22×C4—1221no—
629C22×C4—1221no—
630C22×C4—1221no—
631C22×C4—2444no—
632C22×C4—2444no—
633C22×C4—2444no—
634C22×C4D4×D6112yes—
635C22×C4D4×D6111yescharacteristic
636C22×C4C23×D6112yes—
637C22×C4C23×D6111yescharacteristic
638Q16—1228no—
639Q16—2444no—
640SD16—44no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—44no—
644C2×C8—612no—
645C2×C8—612no—
646C2×C8—1222no—
647C2×C8—1222no—
648C2×C8—2444no—
649C2×C8C23×D6112yes—
650C2×C8C23×D6112yes—
651C4⋊C4—24no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—614no—
655C4⋊C4—612no—
656C4⋊C4—612no—
657C4⋊C4—1224no—
658C4⋊C4—1224no—
659C4⋊C4—1224no—
660C4⋊C4—1224no—
661C4⋊C4—1224no—
662C4⋊C4—1224no—
663C4⋊C4—1221no—
664C4⋊C4—1221no—
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—612no—
678C42—612no—
679C42—1224no—
680C42—1224no—
681C42—1224no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—612no—
689C23—1222no—
690C23—1222no—
691C23—1222no—
692C23#1451979814yes—
693C23C2×D4×D6112yes—
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—48no—
708D4—42no—
709D4—1228no—
710D4—2448no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—612no—
722C2×C4—612no—
723C2×C4—612no—
724C2×C4—1222no—
725C2×C4—1222no—
726C2×C4—1222no—
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—2448no—
736C2×C4—2448no—
737C2×C4—2448no—
738C2×C4—2442no—
739C2×C4—2442no—
740C2×C4—2442no—
741C2×C4C2×D4×D6112yes—
742C2×C4C2×D4×D6111yescharacteristic
743C2×C4#41×D6112yes—
744C2×C4#1451982212yes—
745C2×C4C24×D6111yescharacteristic
746C8—22no—
747C8—22no—
748C8—1222no—
749C8—1222no—
750C22—28no—
751C22—22no—
752C22—22no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—84no—
757C22—1222no—
758C22—1222no—
759C22—1222no—
760C22—2444no—
761C22#1684040112yes—
762C22C2×#1451979814yes—
763C22C2×#1451979812yes—
764C22#1684057612yes—
765C22C22×D4×D6111yescharacteristic
766C4—22no—
767C4—42no—
768C4—42no—
769C4—42no—
770C4—1222no—
771C4—1224no—
772C4—1222no—
773C4—1222no—
774C4—2442no—
775C4—2442no—
776C4—2442no—
777C4#1684040112yes—
778C4C2×#41×D6111yescharacteristic
779C4C2×#1451982211yescharacteristic
780C2—24no—
781C2—82no—
782C2—2442no—
783C2#2145771214yesdirect product factor
784C2C2×#1684040111yescharacteristic
785C2C22×#1451979811yescharacteristic
786C2C2×#1684057611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#465C2
socleC23×C61C22×D4
prime radicalC2×#16840418C2
hypercenterC2×#465D61
hypocenterC61C2×#3300
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×#16840454C2semidirect
3. #21457712C2direct (N × H)
4. C2×#16840115C2semidirect
5. C2×#16840106C2semidirect
6. C2×#16840073C2semidirect
7. C2×#16840072C2semidirect
8. C2×#16840002C2semidirect
9. C2×#16839982C2semidirect
10. C2×#16839921C2semidirect
11. C2×#16839917C2semidirect
12. C2×#16839854C2semidirect
13. C2×C8×C22⋊D61C2semidirect
14. C2×#16839755C2semidirect
15. C22×#14519702C2semidirect
16. C2×C61×#465C2semidirect
23. #16840454C22semidirect
43. #16840115C22semidirect
44. #16840106C22semidirect
45. #16840073C22semidirect
46. #16840072C22semidirect
47. #16840002C22semidirect
48. #16839982C22semidirect
49. #16839921C22semidirect
50. #16839917C22semidirect
51. #16839854C22semidirect
52. C8×C22⋊D61C22semidirect
56. #16839755C22semidirect
61. C2×#14519702C22semidirect
73. C61×#465C22semidirect
395. C2×#465D61semidirect
405. C2×C61#3300semidirect
445. #465C2×D61semidirect
470. C61C2×#3300semidirect
783. C2#21457712direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404542
C2×#168404182
#214577122
C2×#168401152
C2×#168401062
C2×#168400732
C2×#168400722
C2×#168400022
C2×#168399822
C2×#168399212
C2×#168399172
C2×#168398542
C2×C8×C22⋊D612
C2×#168397552
C22×#145197022
C2×C61×#4652
C2×#330061