Finite Group Databasebeta

← C2×#21461778 #30615497

Subgroups — C2×#21461778 #30615497

Order 15616.

1566 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840831C211yesmaximal, characteristic
2C2×#16840773C211yesmaximal, characteristic, complemented
3C2×#16840753C211yesmaximal, characteristic
4C2×#16840708C211yesmaximal, characteristic, complemented
5#21461778C218yesmaximal, direct product factor
6C2×#16840641C211yesmaximal, characteristic, complemented
7C2×#16840633C211yesmaximal, characteristic, complemented
8C2×#104×D61C211yesmaximal, characteristic
9C2×D61⋊M16C2211yescharacteristic
10#16840831—22no—
11#16840831—22no—
12#16840831—22no—
13#16840831C2214yes—
14C2×Q8×#6923—21no—
15C2×D4×#6923—22no—
16C2×D4×#6923—21no—
17C2×#14519856—21no—
18C2×#14519856C2211yescharacteristic
19C22×C4⋊#6923—21no—
20C22×C4⋊#6923—22no—
21C22×C4⋊#6923C2211yescharacteristic
22C22×C4⋊#6923C2211yescharacteristic
23#16840773—22no—
24#16840773C2214yescomplemented
25C2×#14519846—21no—
26C2×#14519845—21no—
27#16840753—22no—
28#16840753C2214yes—
29C2×#14519840—21no—
30C2×#14519839—21no—
31#16840708—22no—
32#16840708C2214yescomplemented
33#16840641C2214yescomplemented
34#16840633C2214yescomplemented
35C2×#41×D61C2211yescharacteristic
36C2×M16×D61C2211yescharacteristic
37C2×C42×D61C2211yescharacteristic
38C2×#14519705C411yescharacteristic, complemented
39C2×#14519704C411yescharacteristic, complemented
40C2×#14519703C411yescharacteristic, complemented
41#104×D61C414yescomplemented
42#104×D61C2214yes—
43C2×#104×C61C411yescharacteristic, complemented
44C23×#6923—22no—
45C23×#6923—21no—
46C23×#6923D412yes—
47C2×#11758213—21no—
48D61⋊M16—21no—
49D61⋊M16—21no—
50D61⋊M16—21no—
51D61⋊M16C2312yes—
52C2×#11758217—21no—
53C2×D61⋊C8—21no—
54Q8×#6923—24no—
55Q8×#6923—24no—
56D4×#6923—28no—
57D4×#6923—24no—
58D4×#6923—28no—
59D4×#6923—24no—
60#14519856—24no—
61#14519856—21no—
62#14519856—21no—
63#14519856—24no—
64#14519856D412yes—
65#14519856C2312yes—
66C2×C4⋊#6923—22no—
67C2×C4⋊#6923—24no—
68C2×C4⋊#6923—21no—
69C2×C4⋊#6923—21no—
70C2×C4⋊#6923—21no—
71C2×C4⋊#6923—21no—
72C2×C4⋊#6923—24no—
73C2×C4⋊#6923—21no—
74C2×C4⋊#6923—21no—
75C2×C4⋊#6923—21no—
76C2×C4⋊#6923—21no—
77C2×C4⋊#6923—28no—
78C2×C4⋊#6923—21no—
79C2×C4⋊#6923—48no—
80C2×C4⋊#6923D412yes—
81C2×C4⋊#6923D411yescharacteristic
82C2×C4⋊#6923D411yescharacteristic
83C2×C4⋊#6923C2312yes—
84C2×C4⋊#6923C2312yes—
85C2×C22⋊#6923—22no—
86C2×C22⋊#6923—21no—
87C2×C4×#6923—22no—
88C2×C4×#6923—21no—
89#14519846—24no—
90#14519845—24no—
91#14519840—24no—
92#14519839—24no—
93C2×#11758226Q811yescharacteristic
94C2×#11758222—21no—
95C2×#11758222C2×C411yescharacteristic
96C2×#11758224—21no—
97C2×#11758224Q811yescharacteristic
98#41×D61—21no—
99#41×D61—21no—
100#41×D61—21no—
101#41×D61—21no—
102#41×D61C2×C412yes—
103#41×D61D412yes—
104#41×D61Q812yes—
105#41×D61C2312yes—
106C2×Q8×D61D411yescharacteristic
107C2×D4×D61—21no—
108C2×D4×D61D411yescharacteristic
109C22×C4×D61—21no—
110C22×C4×D61—21no—
111C22×C4×D61C2311yescharacteristic
112C2×#11758194C2×C411yescharacteristic, complemented
113C2×#11758189—21no—
114M16×D61—21no—
115M16×D61—21no—
116M16×D61C2×C412yescomplemented
117M16×D61C2312yes—
118C2×C8×D61—21no—
119C2×C4×Dic61—21no—
120C2×C4×Dic61C2×C411yescharacteristic, complemented
121C42×D61—21no—
122C42×D61—21no—
123C42×D61C2×C412yescomplemented
124C42×D61C2312yes—
125#14519705C2×C414yescomplemented
126#14519704C2×C414yescomplemented
127#14519703C2×C414yescomplemented
128C2×#41×C61C2×C411yescharacteristic
129C2×M16×C61C2×C411yescharacteristic, complemented
130C2×C42×C61C2×C411yescharacteristic, complemented
131#104×C61C2×C414yescomplemented
132C23×D61—21no—
133C23×D61C2×D411yescharacteristic
134C22×#6923—21no—
135C22×#6923—22no—
136C22×#6923—21no—
137C22×#6923—28no—
138C22×#6923—22no—
139C22×#6923—22no—
140C22×#6923—44no—
141C22×#6923—44no—
142C22×#6923—41no—
143C22×#6923—41no—
144C22×#6923—84no—
145C22×#6923C2×D414yes—
146#41×C61—21no—
147#41×C61—21no—
148#41×C61C4⋊C412yescomplemented
149#41×C61C22×C412yes—
150C2×Q8×C61C4⋊C411yescharacteristic, complemented
151C2×D4×C61—21no—
152C2×D4×C61C4⋊C411yescharacteristic, complemented
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61C22×C411yescharacteristic
156C2×C22⋊D61—21no—
157C2×C22⋊D61—21no—
158C2×C22⋊D61—21no—
159C22×Dic61—21no—
160C22×Dic61—21no—
161C22×Dic61#4111yescharacteristic
162#11758226—21no—
163#11758226—21no—
164#11758226C4⋊C412yescomplemented
165#11758226C2×Q812yes—
166Q8×D61—21no—
167Q8×D61—21no—
168Q8×D61C4⋊C412yescomplemented
169Q8×D61C2×D412yes—
170#11758224—22no—
171#11758224—22no—
172#11758224—22no—
173#11758224—22no—
174#11758224—21no—
175#11758224—21no—
176#11758224C4⋊C412yescomplemented
177#11758224C2×Q812yes—
178D4×D61—22no—
179D4×D61—22no—
180D4×D61—22no—
181D4×D61—22no—
182D4×D61—21no—
183D4×D61—21no—
184D4×D61C4⋊C412yescomplemented
185D4×D61C2×D412yes—
186#11758222—21no—
187#11758222—21no—
188#11758222—22no—
189#11758222—22no—
190#11758222—22no—
191#11758222—22no—
192#11758222C4⋊C412yescomplemented
193#11758222C22×C412yes—
194C2×D244—21no—
195C2×D244C4⋊C411yescharacteristic, complemented
196C2×C4×D61—24no—
197C2×C4×D61—24no—
198C2×C4×D61—22no—
199C2×C4×D61—21no—
200C2×C4×D61—22no—
201C2×C4×D61—21no—
202C2×C4×D61—21no—
203C2×C4×D61—22no—
204C2×C4×D61—22no—
205C2×C4×D61—22no—
206C2×C4×D61—22no—
207C2×C4×D61C22×C411yescharacteristic
208C2×C4×D61C2×D411yescharacteristic
209C2×C4×D61C2×D411yescharacteristic
210C2×C4×D61C2×D411yescharacteristic
211C2×C4×D61C2×D411yescharacteristic
212C2×C4×D61C2×D411yescharacteristic
213C2×C4×D61C2×Q811yescharacteristic
214C2×C4×D61C2×Q811yescharacteristic
215C2×C4×D61#4111yescharacteristic
216C2×C4×D61#4111yescharacteristic
217C2×C4×D61#4111yescharacteristic
218C2×C4×D61C2411yescharacteristic
219C2×Dic122—21no—
220C2×Dic122C4⋊C411yescharacteristic, complemented
221C22⋊#6923—28no—
222C22⋊#6923—22no—
223C22⋊#6923—22no—
224#11758217—22no—
225#11758217—41no—
226C2×#92420—41no—
227C4⋊#6923—28no—
228C4⋊#6923—22no—
229C4⋊#6923—21no—
230C4⋊#6923—22no—
231C4⋊#6923—21no—
232C4⋊#6923—22no—
233C4⋊#6923—22no—
234C4⋊#6923—22no—
235C4⋊#6923—22no—
236C4⋊#6923—416no—
237C4⋊#6923—41no—
238C4⋊#6923—41no—
239C4⋊#6923C2×D412yes—
240C4⋊#6923C2×D412yes—
241C4×#6923—28no—
242C4×#6923—22no—
243C4×#6923—22no—
244#11758213—22no—
245#11758213—41no—
246D61⋊C8—22no—
247D61⋊C8—41no—
248M16×C61—21no—
249M16×C61C22×C412yescomplemented
250C2×C8×C61—21no—
251C42×C61—21no—
252C42×C61C22×C412yescomplemented
253C4×Dic61—21no—
254C4×Dic61—22no—
255C4×Dic61—22no—
256C4×Dic61C22×C412yescomplemented
257#11758194—21no—
258#11758194C22×C412yescomplemented
259C2×#92418—21no—
260#11758189—22no—
261#11758189—22no—
262C8×D61—22no—
263C8×D61—22no—
264C23×C61—21no—
265C23×C61C4×D411yescharacteristic
266C22×D61—22no—
267C22×D61—22no—
268C22×D61—21no—
269C22×D61—22no—
270C22×D61—22no—
271C22×D61—42no—
272C22×D61—42no—
273C22×D61C4×D411yescharacteristic
274C22×D61#12011yescharacteristic
275C22×D61#12011yescharacteristic
276C22×D61C22⋊Q811yescharacteristic
277C22×D61C22⋊Q811yescharacteristic
278C22×D61C22×D411yescharacteristic
279C2×#6923—22no—
280C2×#6923—24no—
281C2×#6923—22no—
282C2×#6923—44no—
283C2×#6923—42no—
284C2×#6923—42no—
285C2×#6923—44no—
286C2×#6923—44no—
287C2×#6923—42no—
288C2×#6923—82no—
289C2×#6923—88no—
290C2×#6923—82no—
291C2×#6923—82no—
292Q8×C61—21no—
293Q8×C61C2×C4⋊C412yescomplemented
294D4×C61—22no—
295D4×C61—22no—
296D4×C61—21no—
297D4×C61C2×C4⋊C412yescomplemented
298C2×C4×C61—24no—
299C2×C4×C61—22no—
300C2×C4×C61—21no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61C2×C4⋊C411yescharacteristic
304C2×C4×C61C2×C4⋊C411yescharacteristic
305C2×C4×C61C4×D411yescharacteristic
306C2×C4×C61C4×D411yescharacteristic
307C2×C4×C61C4×D411yescharacteristic
308C2×C4×C61C23×C411yescharacteristic
309C22⋊D61—22no—
310C22⋊D61—22no—
311C22⋊D61—22no—
312C22⋊D61—22no—
313C22⋊D61—22no—
314C22⋊D61—22no—
315C2×Dic61—24no—
316C2×Dic61—22no—
317C2×Dic61—21no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61C4×D411yescharacteristic
321C2×Dic61C22⋊Q811yescharacteristic
322C2×Dic61C22⋊Q811yescharacteristic
323C2×Dic61#12311yescharacteristic
324C2×Dic61#12311yescharacteristic
325C2×Dic61C2×#4111yescharacteristic
326D244—22no—
327D244—22no—
328D244—21no—
329D244C2×C4⋊C412yescomplemented
330C4×D61—24no—
331C4×D61—28no—
332C4×D61—24no—
333C4×D61—22no—
334C4×D61—22no—
335C4×D61—22no—
336C4×D61—22no—
337C4×D61—22no—
338C4×D61—22no—
339C4×D61C2×C4⋊C411yescharacteristic
340C4×D61C2×C4⋊C411yescharacteristic
341C4×D61C4×D411yescharacteristic
342C4×D61C4×D411yescharacteristic
343C4×D61#12011yescharacteristic
344C4×D61#12011yescharacteristic
345C4×D61C22⋊Q811yescharacteristic
346C4×D61C22⋊Q811yescharacteristic
347C4×D61C22⋊Q811yescharacteristic
348C4×D61C22⋊Q811yescharacteristic
349C4×D61#12311yescharacteristic
350C4×D61#12311yescharacteristic
351C4×D61C22×D411yescharacteristic
352C4×D61C22×D411yescharacteristic
353C4×D61C22×Q811yescharacteristic
354C4×D61C2×#4111yescharacteristic
355Dic122—21no—
356Dic122—22no—
357Dic122—22no—
358Dic122C2×C4⋊C412yescomplemented
359#92420—42no—
360C8×C61—22no—
361#92418—22no—
362C2×#1859—611nomaximal, Sylow
363C22×C61—22no—
364C22×C61—22no—
365C22×C61—42no—
366C22×C61#38511yescharacteristic
367C22×C61#38511yescharacteristic
368C22×C61C2×C4×D411yescharacteristic
369C2×D61—22no—
370C2×D61—22no—
371C2×D61—22no—
372C2×D61—21no—
373C2×D61—21no—
374C2×D61—21no—
375C2×D61—21no—
376C2×D61—22no—
377C2×D61—42no—
378C2×D61—44no—
379C2×D61—42no—
380C2×D61—42no—
381C2×D61#38511yescharacteristic
382C2×D61#38511yescharacteristic
383C2×D61#45312yes—
384C2×D61#45612yes—
385C2×D61C2×#12011yescharacteristic
386C2×D61C2×C22⋊Q811yescharacteristic
387#6923—44no—
388#6923—42no—
389#6923—42no—
390#6923—82no—
391C4×C61—24no—
392C4×C61—22no—
393C4×C61#38511yescharacteristic
394C4×C61#38511yescharacteristic
395C4×C61C22×C4⋊C411yescharacteristic
396C4×C61C2×C4×D411yescharacteristic
397Dic61—24no—
398Dic61—22no—
399Dic61#38511yescharacteristic
400Dic61#38511yescharacteristic
401Dic61C2×C22⋊Q811yescharacteristic
402Dic61C2×#12311yescharacteristic
403C2×#520—611no—
404C2×#428—611no—
405C22×#104—611no—
406C2×#417—611no—
407C2×#384—611no—
408#1859—618no—
409C2×#343—611no—
410C2×#339—611no—
411C2×C61—21no—
412C2×C61—21no—
413C2×C61—42no—
414C2×C61#185912yescomplemented
415C2×C61C2×#38511yescharacteristic
416D61—21no—
417D61—21no—
418D61—42no—
419D61#185912yescomplemented
420D61C2×#45311yescharacteristic
421D61C2×#45611yescharacteristic
422C22×#41—611no—
423C22×M16—611no—
424C22×M16—611no—
425#520—614no—
426#520—1222no—
427#520—1222no—
428#520—1222no—
429C2×C4×Q8—1221no—
430C2×C4×D4—1222no—
431C2×C4×D4—1221no—
432C2×#117—611no—
433C2×#117—1221no—
434C22×C4⋊C4—611no—
435C22×C4⋊C4—611no—
436C22×C4⋊C4—1221no—
437C22×C4⋊C4—1222no—
438C22×C42—611no—
439#428—614no—
440#428—1222no—
441C2×#107—1221no—
442C2×#106—1221no—
443C2×#104—611no—
444C2×#104—611no—
445C2×#104—611no—
446C2×#104—614no—
447C2×#104—614no—
448C2×#104#692311yescharacteristic, complemented
449#417—614no—
450#417—1222no—
451C2×#103—1221no—
452C2×#102—1221no—
453#384—614no—
454#384—1222no—
455#343—614no—
456#339—614no—
457C61C2×#185911yescharacteristic, complemented, Sylow
458C2×#41—612no—
459C2×#41—612no—
460C2×#41—612no—
461C2×#41—612no—
462C2×#41—611no—
463C2×#41—611no—
464C2×#41—611no—
465C2×#41—1221no—
466C2×#41—1221no—
467C2×#41—1221no—
468C2×#41—1221no—
469C2×#41—1221no—
470C2×#41—1221no—
471C2×#41C2×#692311yescharacteristic
472C22×Q8—611no—
473C22×D4—611no—
474C22×D4—1221no—
475C23×C4—611no—
476C23×C4—612no—
477C23×C4—1221no—
478C23×C4—1221no—
479C23×C4—1222no—
480C23×C4—1221no—
481C2×M16—611no—
482C2×M16—612no—
483C2×M16—612no—
484C2×M16—612no—
485C2×M16—1221no—
486C2×M16—1221no—
487C2×M16—1221no—
488C2×M16—1221no—
489C2×M16—1221no—
490C2×M16—1221no—
491C2×M16—1221no—
492C2×M16—1221no—
493C2×M16C2×#692311yescharacteristic, complemented
494C22×C8—1221no—
495C22×C8—1221no—
496C4×Q8—1224no—
497C4×Q8—1224no—
498C4×D4—1228no—
499C4×D4—1224no—
500C4×D4—1224no—
501C4×D4—1228no—
502#117—612no—
503#117—612no—
504#117—1224no—
505#117—1221no—
506#117—1221no—
507#117—1224no—
508C2×C4⋊C4—611no—
509C2×C4⋊C4—611no—
510C2×C4⋊C4—612no—
511C2×C4⋊C4—612no—
512C2×C4⋊C4—612no—
513C2×C4⋊C4—1224no—
514C2×C4⋊C4—1221no—
515C2×C4⋊C4—1221no—
516C2×C4⋊C4—1221no—
517C2×C4⋊C4—1221no—
518C2×C4⋊C4—1222no—
519C2×C4⋊C4—1224no—
520C2×C4⋊C4—1221no—
521C2×C4⋊C4—1221no—
522C2×C4⋊C4—1221no—
523C2×C4⋊C4—1221no—
524C2×C4⋊C4—1221no—
525C2×C4⋊C4—1228no—
526C2×C4⋊C4—2448no—
527C2×C22⋊C4—1221no—
528C2×C22⋊C4—1222no—
529C2×C42—611no—
530C2×C42—612no—
531C2×C42—612no—
532C2×C42—1221no—
533C2×C42—1221no—
534C2×C42—1221no—
535C2×C42—1221no—
536C2×C42—1222no—
537C2×C42C2×#692311yescharacteristic, complemented
538#107—1224no—
539#106—1224no—
540#104—614no—
541#104—614no—
542#104—614no—
543#104C2×#692314yescomplemented
544#103—1224no—
545#102—1224no—
546C24—611no—
547C24—1221no—
548#41—21no—
549#41—21no—
550#41—612no—
551#41—612no—
552#41—612no—
553#41—612no—
554#41—612no—
555#41—612no—
556#41—1222no—
557#41—1222no—
558#41—1222no—
559#41—1222no—
560#41—1222no—
561#41—1222no—
562#41—1222no—
563#41—1222no—
564#41—1221no—
565#41—1221no—
566#41—1221no—
567#41—1221no—
568#41—1221no—
569#41—1221no—
570#41C4⋊#692312yescomplemented
571#41C22×#692312yes—
572C2×Q8—612no—
573C2×Q8—612no—
574C2×Q8—611no—
575C2×Q8—1221no—
576C2×Q8—1221no—
577C2×Q8—1221no—
578C2×Q8C4⋊#692311yescharacteristic, complemented
579C2×D4—21no—
580C2×D4—612no—
581C2×D4—612no—
582C2×D4—611no—
583C2×D4—1221no—
584C2×D4—1221no—
585C2×D4—1221no—
586C2×D4—1221no—
587C2×D4—1222no—
588C2×D4—1222no—
589C2×D4—1222no—
590C2×D4—1222no—
591C2×D4—1221no—
592C2×D4—1221no—
593C2×D4C4⋊#692311yescharacteristic, complemented
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—611no—
597C22×C4—611no—
598C22×C4—611no—
599C22×C4—611no—
600C22×C4—611no—
601C22×C4—611no—
602C22×C4—611no—
603C22×C4—611no—
604C22×C4—611no—
605C22×C4—611no—
606C22×C4—611no—
607C22×C4—611no—
608C22×C4—611no—
609C22×C4—614no—
610C22×C4—1222no—
611C22×C4—1222no—
612C22×C4—1221no—
613C22×C4—1222no—
614C22×C4—1222no—
615C22×C4—1222no—
616C22×C4—1222no—
617C22×C4—1221no—
618C22×C4—1224no—
619C22×C4—1224no—
620C22×C4—1221no—
621C22×C4—1221no—
622C22×C4—1221no—
623C22×C4—1222no—
624C22×C4—1228no—
625C22×C4—1221no—
626C22×C4—1221no—
627C22×C4—1222no—
628C22×C4—1222no—
629C22×C4—4884no—
630C22×C4—2441no—
631C22×C4—2441no—
632C22×C4—2444no—
633C22×C4—2444no—
634C22×C4C22×#692311yescharacteristic
635M16—21no—
636M16—612no—
637M16—1222no—
638M16—1222no—
639M16—1221no—
640M16—1222no—
641M16—1222no—
642M16—2441no—
643M16—2441no—
644M16C22×#692312yescomplemented
645C2×C8—21no—
646C2×C8—1222no—
647C2×C8—1222no—
648C2×C8—1221no—
649C2×C8—1222no—
650C2×C8—2441no—
651C2×C8—2441no—
652C4⋊C4—612no—
653C4⋊C4—612no—
654C4⋊C4—1221no—
655C4⋊C4—1222no—
656C4⋊C4—1222no—
657C4⋊C4—1222no—
658C4⋊C4—1222no—
659C4⋊C4—1221no—
660C4⋊C4—1222no—
661C4⋊C4—1222no—
662C4⋊C4—1228no—
663C4⋊C4—2441no—
664C4⋊C4—2441no—
665C4⋊C4—24416no—
666C22⋊C4—1222no—
667C22⋊C4—1222no—
668C22⋊C4—1228no—
669C42—21no—
670C42—612no—
671C42—1222no—
672C42—1222no—
673C42—1222no—
674C42—1222no—
675C42—1228no—
676C42—1221no—
677C42C22×#692312yescomplemented
678C23—21no—
679C23—611no—
680C23—611no—
681C23—611no—
682C23—611no—
683C23—611no—
684C23—611no—
685C23—1222no—
686C23—1222no—
687C23—1222no—
688C23—1222no—
689C23—1221no—
690C23—2442no—
691C23—2442no—
692C23D4×#692311yescharacteristic
693Q8—21no—
694Q8—612no—
695Q8—1222no—
696Q8—1222no—
697Q8—1221no—
698Q8C2×C4⋊#692312yescomplemented
699D4—22no—
700D4—22no—
701D4—21no—
702D4—612no—
703D4—1222no—
704D4—1222no—
705D4—1222no—
706D4—1222no—
707D4—1222no—
708D4—1222no—
709D4—1222no—
710D4—1222no—
711D4—1221no—
712D4C2×C4⋊#692312yescomplemented
713C2×C4—24no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—611no—
719C2×C4—611no—
720C2×C4—611no—
721C2×C4—611no—
722C2×C4—611no—
723C2×C4—611no—
724C2×C4—611no—
725C2×C4—611no—
726C2×C4—611no—
727C2×C4—611no—
728C2×C4—611no—
729C2×C4—611no—
730C2×C4—611no—
731C2×C4—611no—
732C2×C4—611no—
733C2×C4—611no—
734C2×C4—611no—
735C2×C4—611no—
736C2×C4—611no—
737C2×C4—611no—
738C2×C4—611no—
739C2×C4—611no—
740C2×C4—1222no—
741C2×C4—1222no—
742C2×C4—1222no—
743C2×C4—1222no—
744C2×C4—1224no—
745C2×C4—1224no—
746C2×C4—1228no—
747C2×C4—1222no—
748C2×C4—1222no—
749C2×C4—1224no—
750C2×C4—1221no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—1222no—
754C2×C4—1222no—
755C2×C4—1222no—
756C2×C4—1224no—
757C2×C4—4882no—
758C2×C4—4882no—
759C2×C4—4882no—
760C2×C4—4888no—
761C2×C4—2442no—
762C2×C4—2444no—
763C2×C4—2442no—
764C2×C4—2442no—
765C2×C4—2444no—
766C2×C4—2444no—
767C2×C4C2×C4⋊#692311yescharacteristic
768C2×C4C2×C4⋊#692311yescharacteristic
769C2×C4D4×#692311yescharacteristic
770C2×C4D4×#692311yescharacteristic
771C2×C4D4×#692311yescharacteristic
772C2×C4C23×#692311yescharacteristic
773C8—22no—
774C8—1222no—
775C8—2442no—
776C22—22no—
777C22—22no—
778C22—42no—
779C22—612no—
780C22—612no—
781C22—611no—
782C22—611no—
783C22—611no—
784C22—611no—
785C22—1221no—
786C22—1221no—
787C22—1222no—
788C22—1221no—
789C22—1221no—
790C22—1222no—
791C22—1222no—
792C22—1222no—
793C22—2442no—
794C22—2442no—
795C22—2444no—
796C22—2442no—
797C22#1684070911yescharacteristic
798C22#1684070911yescharacteristic
799C22C2×D4×#692311yescharacteristic
800C4—24no—
801C4—22no—
802C4—611no—
803C4—611no—
804C4—611no—
805C4—611no—
806C4—1224no—
807C4—1222no—
808C4—4882no—
809C4—2442no—
810C4—2444no—
811C4—2442no—
812C4#1684070911yescharacteristic
813C4#1684070911yescharacteristic
814C4C22×C4⋊#692311yescharacteristic
815C4C2×D4×#692311yescharacteristic
816C2—21no—
817C2—21no—
818C2—42no—
819C2—611no—
820C2—611no—
821C2—612no—
822C2—1221no—
823C2—1221no—
824C2—2442no—
825C2#2146177812yesdirect product factor
826C2C2×#1684070911yescharacteristic
subgroupG/H
centerC22#16840709
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×#104×C61C4
socleC22×C61#385
prime radicalC2×#41×D61C22
cosocleC2×C4×D61C24
hypercenterC2×#104#6923
hypocenterC61C2×#1859
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C2×#16840773C2semidirect
4. C2×#16840708C2semidirect
5. #21461778C2direct (N × H)
6. C2×#16840641C2semidirect
7. C2×#16840633C2semidirect
24. #16840773C22semidirect
32. #16840708C22semidirect
33. #16840641C22semidirect
34. #16840633C22semidirect
38. C2×#14519705C4semidirect
39. C2×#14519704C4semidirect
40. C2×#14519703C4semidirect
41. #104×D61C4semidirect
43. C2×#104×C61C4semidirect
112. C2×#11758194C2×C4semidirect
116. M16×D61C2×C4semidirect
120. C2×C4×Dic61C2×C4semidirect
123. C42×D61C2×C4semidirect
125. #14519705C2×C4semidirect
126. #14519704C2×C4semidirect
127. #14519703C2×C4semidirect
129. C2×M16×C61C2×C4semidirect
130. C2×C42×C61C2×C4semidirect
131. #104×C61C2×C4semidirect
148. #41×C61C4⋊C4semidirect
150. C2×Q8×C61C4⋊C4semidirect
152. C2×D4×C61C4⋊C4semidirect
164. #11758226C4⋊C4semidirect
168. Q8×D61C4⋊C4semidirect
176. #11758224C4⋊C4semidirect
184. D4×D61C4⋊C4semidirect
192. #11758222C4⋊C4semidirect
195. C2×D244C4⋊C4semidirect
220. C2×Dic122C4⋊C4semidirect
249. M16×C61C22×C4semidirect
252. C42×C61C22×C4semidirect
256. C4×Dic61C22×C4semidirect
258. #11758194C22×C4semidirect
293. Q8×C61C2×C4⋊C4semidirect
297. D4×C61C2×C4⋊C4semidirect
329. D244C2×C4⋊C4semidirect
358. Dic122C2×C4⋊C4semidirect
414. C2×C61#1859semidirect
419. D61#1859semidirect
448. C2×#104#6923semidirect
457. C61C2×#1859semidirect
493. C2×M16C2×#6923semidirect
537. C2×C42C2×#6923semidirect
543. #104C2×#6923semidirect
570. #41C4⋊#6923semidirect
578. C2×Q8C4⋊#6923semidirect
593. C2×D4C4⋊#6923semidirect
644. M16C22×#6923semidirect
677. C42C22×#6923semidirect
698. Q8C2×C4⋊#6923semidirect
712. D4C2×C4⋊#6923semidirect
825. C2#21461778direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168408312
C2×#168407732
C2×#168407532
C2×#168407082
#214617782
C2×#168406412
C2×#168406332
C2×#104×D612
C2×#185961