Finite Group Databasebeta

← C2×#21457710 #30556424

Subgroups — C2×#21457710 #30556424

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×#16840423C211yesmaximal, characteristic
3#21457710C2116yesmaximal, direct product factor
4C2×#16840118C211yesmaximal, characteristic, complemented
5C2×#16840102C211yesmaximal, characteristic, complemented
6C2×#16840076C211yesmaximal, characteristic, complemented
7C2×#16840071C211yesmaximal, characteristic, complemented
8C2×#16840000C211yesmaximal, characteristic, complemented
9C2×#16839993C211yesmaximal, characteristic, complemented
10C2×#16839986C211yesmaximal, characteristic, complemented
11C2×#16839923C211yesmaximal, characteristic, complemented
12C2×Q16×Dic61C211yesmaximal, characteristic, complemented
13C2×#16839825C211yesmaximal, characteristic, complemented
14C2×#16839757C211yesmaximal, characteristic, complemented
15C22×#14519701C211yesmaximal, characteristic, complemented
16C2×C61×#451C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C22×#11758201C2211yescharacteristic
19C23×#92418C2211yescharacteristic
20C22×C8×D61C2211yescharacteristic
21#16840454—24no—
22#16840454C2218yescomplemented
23#16840423—24no—
24#16840423C2218yes—
25C2×#14519772—21no—
26C2×#14519768—21no—
27C2×#14519768C2211yescharacteristic
28C2×#14519766—21no—
29C2×#14519766C2211yescharacteristic
30C2×#14519761—21no—
31C2×#14519753—21no—
32C2×#14519753C2211yescharacteristic
33C2×#14519753C2211yescharacteristic
34C2×#14519751—21no—
35C2×#14519751C2211yescharacteristic
36C2×Q8×Dic61C2211yescharacteristic
37C2×Q8×Dic61C2211yescharacteristic
38C2×C4×C22⋊D61—21no—
39C2×C4×C22⋊D61C2211yescharacteristic
40C2×#14519735C2211yescharacteristic
41C2×#14519733—21no—
42C22×C4⋊Dic61C2211yescharacteristic
43#16840118C2218yescomplemented
44#16840102C2218yescomplemented
45#16840076C2218yescomplemented
46#16840071C2218yescomplemented
47#16840000C2218yescomplemented
48#16839993C2218yescomplemented
49#16839986C2218yescomplemented
50#16839923C2218yescomplemented
51Q16×Dic61C2218yescomplemented
52#16839825C2218yescomplemented
53C2×#14519711C2211yescharacteristic
54C2×#14519711C2211yescharacteristic
55C2×#14519708C2211yescharacteristic
56C2×#14519706C2211yescharacteristic
57#16839757C2218yescomplemented
58C2×#14519701C2211yescharacteristic
59C2×#14519701C2211yescharacteristic
60C2×#14519701C2211yescharacteristic
61C2×#14519701C2211yescharacteristic
62C2×#14519701C2211yescharacteristic
63C2×#14519701C2218yescomplemented
64C2×#14519699C2211yescharacteristic
65C2×#14519699C2211yescharacteristic
66C2×#14519697C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C23×Q8×C61C2211yescharacteristic
70C22×Q16×C61C2211yescharacteristic
71C22×Q16×C61C2211yescharacteristic
72C2×C22⋊Q8×C61C2211yescharacteristic
73C61×#451C2218yescomplemented
74C2×#103×C61C2211yescharacteristic
75C2×#103×C61C2211yescharacteristic
76C2×C22⋊C8×C61C2211yescharacteristic
77C2×#11758226—22no—
78C2×#11758226—24no—
79C2×#11758226—42no—
80C2×#11758226C2314yes—
81C22×D244—21no—
82C22×D244C2311yescharacteristic
83C22×C22⋊D61—21no—
84C22×C22⋊D61D411yescharacteristic
85C23×Dic61—21no—
86C22×C4×D61—21no—
87C22×C4×D61C2311yescharacteristic
88C2×#11758201—42no—
89C2×#11758201C2314yes—
90C22×#92418—42no—
91C22×#92418C2311yescharacteristic
92C22×#92418C2311yescharacteristic
93C22×#92418C2314yes—
94C2×C8×D61—42no—
95C2×C8×D61C2314yes—
96#14519772—28no—
97#14519768—28no—
98#14519768—22no—
99#14519768C2314yes—
100#14519766—28no—
101#14519766—22no—
102#14519766C2314yes—
103#14519761—28no—
104#14519753—22no—
105#14519753—22no—
106#14519753—28no—
107#14519753C2314yes—
108#14519753C2314yes—
109#14519751—22no—
110#14519751—28no—
111#14519751C2314yes—
112Q8×Dic61—22no—
113Q8×Dic61—22no—
114Q8×Dic61C2314yes—
115Q8×Dic61C2314yes—
116C4×C22⋊D61—28no—
117C4×C22⋊D61D414yes—
118C4×C22⋊D61C2314yes—
119#14519735—22no—
120#14519735C2314yes—
121#14519733—28no—
122C2×C4⋊Dic61—22no—
123C2×C4⋊Dic61—21no—
124C2×C4⋊Dic61—21no—
125C2×C4⋊Dic61—21no—
126C2×C4⋊Dic61—21no—
127C2×C4⋊Dic61C2314yes—
128C2×C4⋊Dic61C2311yescharacteristic
129C2×C4⋊Dic61C2311yescharacteristic
130C2×C4⋊Dic61C2311yescharacteristic
131C2×#11758196—21no—
132C2×#11758196—21no—
133C2×#11758196—21no—
134C2×#11758196D411yescharacteristic
135C2×C22⋊Dic61D411yescharacteristic
136C2×#11758198—21no—
137C2×#11758198—21no—
138C2×#11758198—21no—
139C2×#11758198—21no—
140C2×#11758198—21no—
141C2×#11758198—21no—
142C2×#11758198D411yescharacteristic
143C2×C4×Dic61—21no—
144C2×C4×Dic61—21no—
145C2×C4×Dic61—21no—
146C2×C4×Dic61C2311yescharacteristic
147#14519711C2314yes—
148#14519711C2314yes—
149#14519708C2314yes—
150#14519706C2314yes—
151#14519701C2314yes—
152#14519701C2314yes—
153#14519701C2314yes—
154#14519701C2314yes—
155#14519701C2314yes—
156#14519699C2314yes—
157#14519699C2314yes—
158#14519697C2314yes—
159#14519689C2314yes—
160C8×Dic61C2314yes—
161C22×Q8×C61—21no—
162C22×Q8×C61—22no—
163C22×Q8×C61—24no—
164C22×Q8×C61—42no—
165C22×Q8×C61C2311yescharacteristic
166C22×Q8×C61C2311yescharacteristic
167C22×Q8×C61C2314yes—
168C22×Q8×C61C2311yescharacteristic
169C23×C4×C61—21no—
170C23×C4×C61C2311yescharacteristic
171C2×Q16×C61—24no—
172C2×Q16×C61—42no—
173C2×Q16×C61C2314yes—
174C2×Q16×C61C2314yes—
175C22×C8×C61C2311yescharacteristic
176C22×C8×C61C2311yescharacteristic
177C22⋊Q8×C61—22no—
178C22⋊Q8×C61C2314yes—
179C2×C4⋊C4×C61—21no—
180C2×C4⋊C4×C61C2311yescharacteristic
181C2×C22⋊C4×C61—21no—
182#103×C61C2314yes—
183#103×C61C2314yes—
184C22⋊C8×C61C2314yes—
185C24×C61C2×D411yescharacteristic
186C23×D61—21no—
187C23×D61C2×D411yescharacteristic
188C2×Q8×C61—21no—
189C2×Q8×C61—21no—
190C2×Q8×C61—24no—
191C2×Q8×C61—21no—
192C2×Q8×C61—22no—
193C2×Q8×C61—28no—
194C2×Q8×C61—22no—
195C2×Q8×C61—22no—
196C2×Q8×C61—22no—
197C2×Q8×C61—22no—
198C2×Q8×C61—44no—
199C2×Q8×C61—44no—
200C2×Q8×C61—48no—
201C2×Q8×C61#4114yes—
202C2×Q8×C61C2412yes—
203C2×Q8×C61C2412yes—
204C2×Q8×C61C2412yes—
205C22×C4×C61—21no—
206C22×C4×C61—22no—
207C22×C4×C61—22no—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61—24no—
212C22×C4×C61—44no—
213C22×C4×C61C2×D411yescharacteristic
214C22×C4×C61C2×D412yes—
215C22×C4×C61C2412yes—
216C22×C4×C61C2411yescharacteristic
217C2×C22⋊D61—24no—
218C2×C22⋊D61—24no—
219C2×C22⋊D61—44no—
220C2×C22⋊D61C2×D414yes—
221C22×Dic61—21no—
222C22×Dic61—21no—
223C22×Dic61—24no—
224C22×Dic61—21no—
225C22×Dic61—44no—
226C22×Dic61C2×D411yescharacteristic
227C22×Dic61C2×D411yescharacteristic
228C22×Dic61C2×D411yescharacteristic
229#11758226—28no—
230#11758226—44no—
231#11758226—48no—
232C2×D244—22no—
233C2×D244—22no—
234C2×D244—24no—
235C2×D244—21no—
236C2×D244—44no—
237C2×D244C2412yes—
238C2×C4×D61—22no—
239C2×C4×D61—22no—
240C2×C4×D61—24no—
241C2×C4×D61—44no—
242C2×C4×D61C2×D412yes—
243C2×C4×D61C2412yes—
244Q16×C61—28no—
245Q16×C61—44no—
246C2×C8×C61—22no—
247C2×C8×C61—22no—
248C2×C8×C61C2412yes—
249C2×C8×C61C2412yes—
250C4⋊C4×C61—24no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61C2412yes—
253C22⋊C4×C61—24no—
254C22⋊Dic61C2×D414yes—
255#11758201—44no—
256#11758198—24no—
257#11758198—24no—
258#11758198—24no—
259#11758198—24no—
260#11758198—24no—
261#11758198—24no—
262#11758198C2×D414yes—
263C4⋊Dic61—21no—
264C4⋊Dic61—21no—
265C4⋊Dic61—24no—
266C4⋊Dic61—21no—
267C4⋊Dic61—24no—
268C4⋊Dic61—24no—
269C4⋊Dic61—24no—
270C4⋊Dic61C2412yes—
271C4⋊Dic61C2412yes—
272C4⋊Dic61C2412yes—
273#11758196—24no—
274#11758196—24no—
275#11758196—24no—
276#11758196C2×D414yes—
277C4×Dic61—24no—
278C4×Dic61—24no—
279C4×Dic61—24no—
280C4×Dic61C2×D412yes—
281C4×Dic61C2412yes—
282C2×#92418—22no—
283C2×#92418—22no—
284C2×#92418—44no—
285C2×#92418C2412yes—
286C2×#92418C2412yes—
287C8×D61—44no—
288C23×C61—22no—
289C23×C61—22no—
290C23×C61#13514yes—
291C23×C61C22×D412yes—
292C23×C61C22×D411yescharacteristic
293C22×D61—22no—
294C22×D61—22no—
295C22×D61—22no—
296C22×D61—22no—
297C22×D61—42no—
298C22×D61—42no—
299C22×D61—42no—
300C22×D61C22×D412yes—
301Q8×C61—24no—
302Q8×C61—22no—
303Q8×C61—22no—
304Q8×C61—22no—
305Q8×C61—22no—
306Q8×C61—22no—
307Q8×C61—48no—
308Q8×C61—42no—
309Q8×C61—42no—
310Q8×C61C2×#4114yes—
311C2×C4×C61—24no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—24no—
315C2×C4×C61—22no—
316C2×C4×C61—22no—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61—22no—
320C2×C4×C61—48no—
321C2×C4×C61—42no—
322C2×C4×C61—42no—
323C2×C4×C61—42no—
324C2×C4×C61C22×D412yes—
325C2×C4×C61C22×D411yescharacteristic
326C2×C4×C61C2×#4112yes—
327C2×C4×C61H(5,𝔽2)12yes—
328C2×C4×C61C2511yescharacteristic
329C22⋊D61—28no—
330C22⋊D61—48no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—22no—
337C2×Dic61—48no—
338C2×Dic61—42no—
339C2×Dic61—42no—
340C2×Dic61—42no—
341C2×Dic61C22×D412yes—
342C2×Dic61C22×D412yes—
343C2×Dic61C22×D412yes—
344D244—22no—
345D244—22no—
346D244—48no—
347D244—42no—
348C4×D61—24no—
349C4×D61—22no—
350C4×D61—22no—
351C4×D61—48no—
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#54612yes—
361C22×C61C2×#13514yes—
362C22×C61C2×#13512yes—
363C22×C61#57812yes—
364C22×C61C23×D411yescharacteristic
365C2×D61—22no—
366C2×D61—22no—
367C2×D61—22no—
368C2×D61—44no—
369C2×D61—42no—
370C2×D61—42no—
371C2×D61—42no—
372C2×D61—84no—
373C4×C61—24no—
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—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×#465—611no—
396C2×#464—611no—
397C2×#452—611no—
398C2×#451D6111yescharacteristic, complemented
399C2×C4×Q16—611no—
400C2×C8×D4—611no—
401C2×#416—611no—
402C22×#103—611no—
403C2×C61—24no—
404C2×C61#330014yescomplemented
405C2×C61C2×#54611yescharacteristic
406C2×C61C22×#13511yescharacteristic
407C2×C61C2×#57811yescharacteristic
408D61—42no—
409D61—82no—
410C22×#41—611no—
411C23×Q8C2×D6111yescharacteristic
412C22×Q16C2×D6111yescharacteristic
413C22×Q16C2×D6111yescharacteristic
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—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—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#488—618no—
441#485—618no—
442#480—618no—
443#479—618no—
444#467—618no—
445#465—618no—
446#464—618no—
447#452—618no—
448#451C2×D6118yescomplemented
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×#102—611no—
466C2×#102—611no—
467C2×C22⋊C8—611no—
468C2×C22⋊C8C2×D6111yescharacteristic
469C2×C4×C8—611no—
470C61C2×#330011yescharacteristic, complemented, Sylow
471C2×#41—614no—
472C2×#41—1222no—
473C2×#41—1224no—
474C2×#41—2442no—
475C22×Q8—21no—
476C22×Q8—22no—
477C22×Q8—24no—
478C22×Q8—42no—
479C22×Q8C22×D6111yescharacteristic
480C22×Q8C22×D6111yescharacteristic
481C22×Q8C22×D6114yes—
482C22×Q8C22×D6111yescharacteristic
483C22×D4—611no—
484C22×D4—611no—
485C22×D4—1221no—
486C22×D4—1221no—
487C23×C4—21no—
488C23×C4—611no—
489C23×C4—1221no—
490C23×C4—1221no—
491C23×C4C22×D6111yescharacteristic
492C2×Q16—24no—
493C2×Q16—42no—
494C2×Q16C22×D6114yes—
495C2×Q16C22×D6114yes—
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—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—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—611no—
536C2×C4⋊C4—611no—
537C2×C4⋊C4—611no—
538C2×C4⋊C4—614no—
539C2×C4⋊C4—611no—
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—1221no—
547C2×C4⋊C4—1222no—
548C2×C4⋊C4C22×D6111yescharacteristic
549C2×C22⋊C4—21no—
550C2×C22⋊C4—611no—
551C2×C22⋊C4—611no—
552C2×C22⋊C4—1221no—
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#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#102—614no—
575#102—614no—
576C22⋊C8—614no—
577C22⋊C8C22×D6114yes—
578C4×C8—614no—
579C24—611no—
580C24—1221no—
581C24D4×D6111yescharacteristic
582#41—1228no—
583#41—2444no—
584#41—2448no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—24no—
588C2×Q8—21no—
589C2×Q8—22no—
590C2×Q8—28no—
591C2×Q8—22no—
592C2×Q8—22no—
593C2×Q8—22no—
594C2×Q8—22no—
595C2×Q8—44no—
596C2×Q8—44no—
597C2×Q8—48no—
598C2×Q8#1175822414yes—
599C2×Q8C23×D6112yes—
600C2×Q8C23×D6112yes—
601C2×Q8C23×D6112yes—
602C2×D4—614no—
603C2×D4—612no—
604C2×D4—1224no—
605C2×D4—1224no—
606C2×D4—1224no—
607C2×D4—1221no—
608C2×D4—1222no—
609C2×D4—1222no—
610C2×D4—2444no—
611C2×D4—2444no—
612C22×C4—21no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—24no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—44no—
620C22×C4—611no—
621C22×C4—611no—
622C22×C4—611no—
623C22×C4—612no—
624C22×C4—612no—
625C22×C4—1224no—
626C22×C4—1222no—
627C22×C4—1222no—
628C22×C4—1224no—
629C22×C4—1221no—
630C22×C4—1221no—
631C22×C4—1221no—
632C22×C4—2444no—
633C22×C4—2444no—
634C22×C4D4×D6112yes—
635C22×C4D4×D6111yescharacteristic
636C22×C4C23×D6112yes—
637C22×C4C23×D6111yescharacteristic
638Q16—28no—
639Q16—44no—
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—21no—
653C4⋊C4—614no—
654C4⋊C4—612no—
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⋊C4—1221no—
667C4⋊C4C23×D6112yes—
668C22⋊C4—24no—
669C22⋊C4—614no—
670C22⋊C4—614no—
671C22⋊C4—1224no—
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—612no—
685C23—1222no—
686C23—1222no—
687C23—1222no—
688C23—1222no—
689C23—2442no—
690C23—2442no—
691C23—2442no—
692C23#1451980014yes—
693C23C2×D4×D6112yes—
694C23C2×D4×D6111yescharacteristic
695Q8—22no—
696Q8—24no—
697Q8—22no—
698Q8—22no—
699Q8—22no—
700Q8—22no—
701Q8—48no—
702Q8—42no—
703Q8—42no—
704Q8C2×#1175822414yes—
705D4—1228no—
706D4—1222no—
707D4—1222no—
708D4—2448no—
709D4—2448no—
710D4—2442no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—48no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—612no—
725C2×C4—612no—
726C2×C4—612no—
727C2×C4—1222no—
728C2×C4—1222no—
729C2×C4—1222no—
730C2×C4—1222no—
731C2×C4—1222no—
732C2×C4—1224no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—2448no—
737C2×C4—2448no—
738C2×C4—2442no—
739C2×C4—2442no—
740C2×C4—2442no—
741C2×C4C2×D4×D6112yes—
742C2×C4C2×D4×D6111yescharacteristic
743C2×C4C2×#1175822412yes—
744C2×C4#1451982212yes—
745C2×C4C24×D6111yescharacteristic
746C8—22no—
747C8—22no—
748C8—1222no—
749C8—1222no—
750C22—28no—
751C22—22no—
752C22—22no—
753C22—1222no—
754C22—1222no—
755C22—1222no—
756C22—4884no—
757C22—2442no—
758C22—2442no—
759C22—2442no—
760C22—2444no—
761C22#1684039912yes—
762C22C2×#1451980014yes—
763C22C2×#1451980012yes—
764C22#1684057812yes—
765C22C22×D4×D6111yescharacteristic
766C4—22no—
767C4—24no—
768C4—42no—
769C4—42no—
770C4—42no—
771C4—1222no—
772C4—1222no—
773C4—1222no—
774C4—2442no—
775C4—2442no—
776C4—2442no—
777C4#1684039912yes—
778C4C22×#1175822411yescharacteristic
779C4C2×#1451982211yescharacteristic
780C2—24no—
781C2—4882no—
782C2—2442no—
783C2#2145771014yesdirect product factor
784C2C2×#1684039911yescharacteristic
785C2C22×#1451980011yescharacteristic
786C2C2×#1684057811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#451C2
socleC23×C61C22×D4
prime radicalC2×#16840423C2
hypercenterC2×#451D61
hypocenterC61C2×#3300
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
1. C2×#16840454C2semidirect
3. #21457710C2direct (N × H)
4. C2×#16840118C2semidirect
5. C2×#16840102C2semidirect
6. C2×#16840076C2semidirect
7. C2×#16840071C2semidirect
8. C2×#16840000C2semidirect
9. C2×#16839993C2semidirect
10. C2×#16839986C2semidirect
11. C2×#16839923C2semidirect
12. C2×Q16×Dic61C2semidirect
13. C2×#16839825C2semidirect
14. C2×#16839757C2semidirect
15. C22×#14519701C2semidirect
16. C2×C61×#451C2semidirect
22. #16840454C22semidirect
43. #16840118C22semidirect
44. #16840102C22semidirect
45. #16840076C22semidirect
46. #16840071C22semidirect
47. #16840000C22semidirect
48. #16839993C22semidirect
49. #16839986C22semidirect
50. #16839923C22semidirect
51. Q16×Dic61C22semidirect
52. #16839825C22semidirect
57. #16839757C22semidirect
63. C2×#14519701C22semidirect
73. C61×#451C22semidirect
398. C2×#451D61semidirect
404. C2×C61#3300semidirect
448. #451C2×D61semidirect
470. C61C2×#3300semidirect
783. C2#21457710direct (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×#168404232
#214577102
C2×#168401182
C2×#168401022
C2×#168400762
C2×#168400712
C2×#168400002
C2×#168399932
C2×#168399862
C2×#168399232
C2×Q16×Dic612
C2×#168398252
C2×#168397572
C22×#145197012
C2×C61×#4512
C2×#330061