Finite Group Databasebeta

← #30548451

Subgroups — #30548451

Order 15616.

2148 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840314C211yesmaximal, characteristic, complemented
2C2×#41×Dic61C211yesmaximal, characteristic
3#21455974C214yesmaximal, complemented
4#21455944C212yesmaximal, complemented
5#21455913C212yesmaximal, complemented
6#21455883C214yesmaximal, complemented
7#21455853C212yesmaximal, complemented
8#21455822C212yesmaximal, complemented
9#21455768C211yesmaximal, characteristic, complemented
10#21455763C211yesmaximal, characteristic, complemented
11#21455630C212yesmaximal, complemented
12#21455304C212yesmaximal, complemented
13#21455079C211yesmaximal, characteristic
14#21454643C212yesmaximal, complemented
15#137×Dic61C212yesmaximal, complemented
16#21454448C211yesmaximal, characteristic, complemented
17C61×#3007C211yesmaximal, characteristic
18C2×#14519807C2212yes—
19#16840314—21no—
20#16840314—21no—
21#16840314—21no—
22#16840314—21no—
23#16840314C2212yes—
24#16840314C2212yes—
25#16840314C2212yescomplemented
26#16840314C2212yescomplemented
27C2×#14519776C2211yescharacteristic, complemented
28C2×#14519775C2211yescharacteristic, complemented
29C2×#14519767—21no—
30C2×#14519756C2211yescharacteristic
31C2×#14519754—21no—
32#41×Dic61—21no—
33#41×Dic61—21no—
34#41×Dic61—21no—
35#41×Dic61—21no—
36#41×Dic61C2212yes—
37#41×Dic61C2212yes—
38#41×Dic61C2212yes—
39#41×Dic61C2212yes—
40C2×Q8×Dic61C2211yescharacteristic
41C2×Q8×Dic61C2211yescharacteristic
42C2×Q8×Dic61C2211yescharacteristic, complemented
43C2×#14519742—21no—
44C2×#14519742C2211yescharacteristic, complemented
45C2×D4×Dic61—21no—
46C2×D4×Dic61—21no—
47C2×D4×Dic61C2211yescharacteristic
48C2×D4×Dic61C2211yescharacteristic
49C2×#14519736—21no—
50C2×#14519736C2211yescharacteristic
51C2×#14519733—21no—
52C22×C4×Dic61—21no—
53C22×C4×Dic61C2211yescharacteristic
54#16840104C2214yescomplemented
55#16840100C2214yescomplemented
56#16840098C2212yes—
57#16840095C2212yes—
58#16840093C2212yes—
59#16840090C2212yes—
60#16840055C2214yescomplemented
61#16840050C2214yescomplemented
62#16840045C2214yescomplemented
63#16840040C2214yescomplemented
64#16839970C2214yescomplemented
65#16839970C2214yescomplemented
66#16839965C2214yescomplemented
67#16839965C2214yescomplemented
68#16839924C2214yes—
69#16839918C2212yes—
70#16839913C2212yes—
71#16839869C2214yescomplemented
72#16839866C2214yescomplemented
73#16839863C2214yescomplemented
74#16839859C2214yescomplemented
75Q16×Dic61C2214yescomplemented
76#16839854C2214yescomplemented
77#16839853C2214yescomplemented
78SD16×Dic61C2214yescomplemented
79#16839816C2212yes—
80#16839816C2212yescomplemented
81#16839812C2212yes—
82#16839812C2212yescomplemented
83#16839804C2212yescomplemented
84#16839802C2212yescomplemented
85#16839785C2212yescomplemented
86#16839772C2212yescomplemented
87#16839771C2212yescomplemented
88#16839763C2212yes—
89#16839726C2211yescharacteristic
90M16×Dic61C2212yescomplemented
91C22×#41×C61C2211yescharacteristic
92C2×#137×C61C2212yes—
93C2×C22⋊Q8×C61C2211yescharacteristic
94C61×#452C2214yes—
95C61×#451C2212yes—
96C61×#450C2212yes—
97C61×#417C2212yes—
98C61×#407C2211yescharacteristic
99C22×Dic122—21no—
100C22×Dic122C2311yescharacteristic
101C23×Dic61—21no—
102C23×Dic61—21no—
103C23×Dic61D411yescharacteristic
104C23×Dic61D411yescharacteristic
105#14519807—28no—
106C2×#11758202C2314yes—
107C2×#11758200C2314yes—
108C2×#11758194C2312yes—
109#14519776—21no—
110#14519776—21no—
111#14519776C2312yes—
112#14519776C2312yes—
113#14519775—21no—
114#14519775—21no—
115#14519775C2312yes—
116#14519775C2312yes—
117#14519767—22no—
118#14519767—22no—
119#14519767—22no—
120#14519767—22no—
121#14519756—21no—
122#14519756—21no—
123#14519756C2312yes—
124#14519756C2312yes—
125#14519754—22no—
126#14519754—22no—
127#14519754—22no—
128#14519754—22no—
129Q8×Dic61—21no—
130Q8×Dic61—21no—
131Q8×Dic61—21no—
132Q8×Dic61—21no—
133Q8×Dic61—21no—
134Q8×Dic61—21no—
135Q8×Dic61C2312yes—
136Q8×Dic61C2312yes—
137Q8×Dic61C2312yes—
138Q8×Dic61C2312yes—
139Q8×Dic61C2312yes—
140Q8×Dic61C2312yes—
141#14519742—22no—
142#14519742—22no—
143#14519742—22no—
144#14519742—22no—
145#14519742—21no—
146#14519742—21no—
147#14519742C2312yes—
148#14519742C2312yes—
149D4×Dic61—22no—
150D4×Dic61—22no—
151D4×Dic61—22no—
152D4×Dic61—22no—
153D4×Dic61—22no—
154D4×Dic61—22no—
155D4×Dic61—22no—
156D4×Dic61—22no—
157D4×Dic61—21no—
158D4×Dic61—21no—
159D4×Dic61—21no—
160D4×Dic61—21no—
161D4×Dic61C2312yes—
162D4×Dic61C2312yes—
163D4×Dic61C2312yes—
164D4×Dic61C2312yes—
165#14519736—21no—
166#14519736—21no—
167#14519736—22no—
168#14519736—22no—
169#14519736—22no—
170#14519736—22no—
171#14519736C2312yes—
172#14519736C2312yes—
173#14519733—22no—
174#14519733—22no—
175#14519733—22no—
176#14519733—22no—
177C2×C4⋊Dic61—21no—
178C2×C4⋊Dic61—21no—
179C2×C4⋊Dic61—21no—
180C2×C4⋊Dic61C2311yescharacteristic
181C2×C4⋊Dic61C2311yescharacteristic
182C2×C4⋊Dic61C2311yescharacteristic
183C2×#11758196—21no—
184C2×#11758196—21no—
185C2×#11758196—21no—
186C2×#11758196—21no—
187C2×#11758196—21no—
188C2×C22⋊Dic61—21no—
189C2×C22⋊Dic61—21no—
190C2×C22⋊Dic61—21no—
191C2×C22⋊Dic61—21no—
192C2×C4×Dic61—21no—
193C2×C4×Dic61—21no—
194C2×C4×Dic61—21no—
195C2×C4×Dic61—21no—
196C2×C4×Dic61—21no—
197C2×C4×Dic61—22no—
198C2×C4×Dic61—22no—
199C2×C4×Dic61—22no—
200C2×C4×Dic61—22no—
201C2×C4×Dic61D411yescharacteristic
202C2×C4×Dic61D411yescharacteristic
203C2×C4×Dic61D411yescharacteristic
204C2×C4×Dic61D411yescharacteristic
205C2×C4×Dic61D411yescharacteristic
206C2×C4×Dic61D411yescharacteristic
207C2×C4×Dic61C2311yescharacteristic
208C2×C4×Dic61C2311yescharacteristic
209C2×C4×Dic61C2311yescharacteristic
210C2×C4×Dic61C2311yescharacteristic
211C2×C4×Dic61C2311yescharacteristic
212C2×C4×Dic61C2311yescharacteristic
213#14519711C2314yes—
214#14519710C2314yes—
215#14519709C2314yes—
216#14519708C2314yes—
217#14519706C2314yes—
218#14519706C2314yes—
219#14519702C2314yes—
220#14519702C2314yes—
221#14519701C2314yes—
222#14519701C2314yes—
223#14519701C2314yes—
224#14519698C2314yes—
225C22⋊#92418C2312yes—
226C22⋊#92418C2312yes—
227#14519687C2314yes—
228C8×Dic61C2314yes—
229C2×#41×C61—28no—
230C2×#41×C61—21no—
231C2×#41×C61—21no—
232C2×#41×C61C2312yes—
233C2×#41×C61C2312yes—
234C22×Q8×C61C2311yescharacteristic
235C22×Q8×C61C2311yescharacteristic
236C22×D4×C61—21no—
237C22×D4×C61C2311yescharacteristic
238C23×C4×C61—21no—
239C23×C4×C61C2311yescharacteristic
240#137×C61—28no—
241C2×Q16×C61C2314yes—
242C2×SD16×C61C2314yes—
243C2×M16×C61C2312yes—
244C22⋊Q8×C61—21no—
245C22⋊Q8×C61—21no—
246C22⋊Q8×C61C2312yes—
247C22⋊Q8×C61C2312yes—
248C2×C4⋊C4×C61—21no—
249C2×C4⋊C4×C61C2311yescharacteristic
250C2×C22⋊C4×C61—21no—
251#103×C61C2314yes—
252#102×C61C2314yes—
253C22⋊C8×C61C2312yes—
254C22⋊C8×C61C2312yes—
255C24×C61—21no—
256C24×C61C2×D411yescharacteristic
257#41×C61—28no—
258#41×C61—28no—
259#41×C61—24no—
260#41×C61—24no—
261#41×C61—24no—
262#41×C61#4118yes—
263C2×Q8×C61—24no—
264C2×Q8×C61—21no—
265C2×Q8×C61—21no—
266C2×Q8×C61—24no—
267C2×Q8×C61C2412yes—
268C2×Q8×C61C2412yes—
269C2×D4×C61—28no—
270C2×D4×C61—22no—
271C2×D4×C61—22no—
272C2×D4×C61—24no—
273C2×D4×C61—21no—
274C2×D4×C61C2412yes—
275C22×C4×C61—28no—
276C22×C4×C61—21no—
277C22×C4×C61—22no—
278C22×C4×C61—22no—
279C22×C4×C61—24no—
280C22×C4×C61—21no—
281C22×C4×C61—21no—
282C22×C4×C61C2×D411yescharacteristic
283C22×C4×C61C2×D411yescharacteristic
284C22×C4×C61C2×D411yescharacteristic
285C22×C4×C61C2411yescharacteristic
286C22×C4×C61C2411yescharacteristic
287C22×C4×C61C2411yescharacteristic
288C22×Dic61—24no—
289C22×Dic61—21no—
290C22×Dic61—21no—
291C22×Dic61—21no—
292C22×Dic61—21no—
293C22×Dic61—22no—
294C22×Dic61—22no—
295C22×Dic61—22no—
296C22×Dic61—22no—
297C22×Dic61—42no—
298C22×Dic61—44no—
299C22×Dic61—44no—
300C22×Dic61C2×D411yescharacteristic
301C22×Dic61C2×D411yescharacteristic
302C22×Dic61C2×D411yescharacteristic
303C22×Dic61C2×D411yescharacteristic
304C22×Dic61C2×D411yescharacteristic
305C22×Dic61C2×D411yescharacteristic
306C22×Dic61C2×D411yescharacteristic
307C22×Dic61C2×D411yescharacteristic
308C22×Dic61C2×D411yescharacteristic
309C22×Dic61C2×D411yescharacteristic
310C22×Dic61C2×D411yescharacteristic
311C22×Dic61C2×D411yescharacteristic
312C2×Dic122—24no—
313C2×Dic122—21no—
314C2×Dic122—22no—
315C2×Dic122—22no—
316C2×Dic122—44no—
317C2×Dic122C2412yes—
318Q16×C61—28no—
319SD16×C61—28no—
320M16×C61—24no—
321C2×C8×C61C2414yes—
322C4⋊C4×C61—22no—
323C4⋊C4×C61—22no—
324C4⋊C4×C61—21no—
325C4⋊C4×C61C2412yes—
326C22⋊C4×C61—22no—
327C22⋊C4×C61—22no—
328C22⋊Dic61—22no—
329C22⋊Dic61—22no—
330C22⋊Dic61—22no—
331C22⋊Dic61—22no—
332C22⋊Dic61—22no—
333C22⋊Dic61—22no—
334C22⋊Dic61—22no—
335C22⋊Dic61—22no—
336#11758202—28no—
337#11758200—28no—
338C4⋊Dic61—21no—
339C4⋊Dic61—21no—
340C4⋊Dic61—21no—
341C4⋊Dic61—22no—
342C4⋊Dic61—22no—
343C4⋊Dic61—22no—
344C4⋊Dic61—22no—
345C4⋊Dic61—22no—
346C4⋊Dic61—22no—
347C4⋊Dic61C2412yes—
348C4⋊Dic61C2412yes—
349C4⋊Dic61C2412yes—
350#11758196—22no—
351#11758196—22no—
352#11758196—22no—
353#11758196—22no—
354#11758196—22no—
355#11758196—22no—
356#11758196—22no—
357#11758196—22no—
358#11758196—22no—
359#11758196—22no—
360C4×Dic61—22no—
361C4×Dic61—22no—
362C4×Dic61—22no—
363C4×Dic61—22no—
364C4×Dic61—22no—
365C4×Dic61—22no—
366C4×Dic61—22no—
367C4×Dic61—22no—
368C4×Dic61—22no—
369C4×Dic61—22no—
370C4×Dic61C2×D411yescharacteristic
371C4×Dic61C2×D411yescharacteristic
372C4×Dic61C2×D411yescharacteristic
373C4×Dic61C2×D411yescharacteristic
374C4×Dic61C2×D411yescharacteristic
375C4×Dic61C2×D411yescharacteristic
376C4×Dic61C2×D411yescharacteristic
377C4×Dic61C2×D411yescharacteristic
378C4×Dic61C2×D411yescharacteristic
379C4×Dic61C2×D411yescharacteristic
380C4×Dic61C2×D411yescharacteristic
381C4×Dic61C2×D411yescharacteristic
382C4×Dic61C2411yescharacteristic
383C4×Dic61C2411yescharacteristic
384C4×Dic61C2411yescharacteristic
385C4×Dic61C2411yescharacteristic
386#11758194—24no—
387C2×#92418C2414yes—
388C23×C61—24no—
389C23×C61—22no—
390C23×C61—22no—
391C23×C61—22no—
392C23×C61—41no—
393C23×C61—42no—
394C23×C61—42no—
395C23×C61C22×D411yescharacteristic
396C23×C61C22×D411yescharacteristic
397C23×C61C22×D411yescharacteristic
398Q8×C61—24no—
399Q8×C61—22no—
400Q8×C61—24no—
401Q8×C61—42no—
402Q8×C61C2×#4114yes—
403D4×C61—28no—
404D4×C61—24no—
405D4×C61—28no—
406D4×C61—22no—
407D4×C61C2×#4114yes—
408C2×C4×C61—24no—
409C2×C4×C61—28no—
410C2×C4×C61—22no—
411C2×C4×C61—22no—
412C2×C4×C61—22no—
413C2×C4×C61—28no—
414C2×C4×C61—22no—
415C2×C4×C61—22no—
416C2×C4×C61—22no—
417C2×C4×C61—22no—
418C2×C4×C61—22no—
419C2×C4×C61—42no—
420C2×C4×C61—42no—
421C2×C4×C61C22×D411yescharacteristic
422C2×C4×C61C22×D411yescharacteristic
423C2×C4×C61C22×D411yescharacteristic
424C2×C4×C61C2×#4114yes—
425C2×C4×C61C2511yescharacteristic
426C2×Dic61—22no—
427C2×Dic61—22no—
428C2×Dic61—22no—
429C2×Dic61—22no—
430C2×Dic61—22no—
431C2×Dic61—22no—
432C2×Dic61—22no—
433C2×Dic61—22no—
434C2×Dic61—22no—
435C2×Dic61—22no—
436C2×Dic61—22no—
437C2×Dic61—22no—
438C2×Dic61—41no—
439C2×Dic61—41no—
440C2×Dic61—41no—
441C2×Dic61—44no—
442C2×Dic61—42no—
443C2×Dic61—42no—
444C2×Dic61—42no—
445C2×Dic61—42no—
446C2×Dic61—44no—
447C2×Dic61—44no—
448C2×Dic61—44no—
449C2×Dic61#13714yescomplemented
450C2×Dic61C22×D411yescharacteristic
451C2×Dic61C22×D411yescharacteristic
452C2×Dic61C22×D411yescharacteristic
453C2×Dic61C22×D411yescharacteristic
454C2×Dic61C22×D411yescharacteristic
455C2×Dic61C22×D411yescharacteristic
456C2×Dic61C22×D411yescharacteristic
457C2×Dic61C22×D411yescharacteristic
458Dic122—24no—
459Dic122—44no—
460Dic122—42no—
461Dic122—44no—
462C8×C61—24no—
463#92418—24no—
464#60562—611nomaximal, Sylow
465C22×C61—21no—
466C22×C61—21no—
467C22×C61—21no—
468C22×C61—21no—
469C22×C61—21no—
470C22×C61—24no—
471C22×C61—21no—
472C22×C61—21no—
473C22×C61—44no—
474C22×C61—48no—
475C22×C61—42no—
476C22×C61—42no—
477C22×C61#52512yes—
478C22×C61C2×#13712yes—
479C22×C61C23×D411yescharacteristic
480C4×C61—21no—
481C4×C61—24no—
482C4×C61—21no—
483C4×C61—42no—
484C4×C61—42no—
485C4×C61#52512yes—
486C4×C61C22×#4112yes—
487Dic61—21no—
488Dic61—21no—
489Dic61—21no—
490Dic61—21no—
491Dic61—21no—
492Dic61—42no—
493Dic61—42no—
494Dic61—42no—
495Dic61—42no—
496Dic61C2×#13712yes—
497Dic61C2×#13712yes—
498Dic61#57512yes—
499C2×#533—611no—
500C2×C4×#41—611no—
501#3116—614no—
502#3113—612no—
503#3110—612no—
504#3107—614no—
505#3104—612no—
506#3101—612no—
507#3095—611no—
508#3095—611no—
509#3079—612no—
510#3039—612no—
511#3007—611no—
512#3007D6111yescharacteristic
513C4×#137—612no—
514C4×#137—612no—
515#2920—611no—
516C2×C61—22no—
517C2×C61—22no—
518C2×C61—41no—
519C2×C61—44no—
520C2×C61C2×#52511yescharacteristic
521C2×C61C22×#13711yescharacteristic
522C2×C61C2×#57511yescharacteristic
523C22×#41C2×D6111yescharacteristic
524C2×#137—612no—
525C2×#137C2×D6112yes—
526#533—612no—
527#533—612no—
528#533—612no—
529#533—612no—
530#533—1221no—
531#533—1221no—
532#533—1221no—
533#533—1221no—
534C2×C4⋊Q8—611no—
535C2×C4⋊Q8—611no—
536C2×#125—1221no—
537C2×C22⋊Q8—611no—
538C2×C22⋊Q8—1221no—
539C2×C22⋊Q8C2×D6111yescharacteristic
540C4×#41—612no—
541C4×#41—612no—
542C4×#41—612no—
543C4×#41—612no—
544C4×#41—1221no—
545C4×#41—1221no—
546C4×#41—1221no—
547C4×#41—1221no—
548C2×C4×Q8—611no—
549C2×C4×Q8—611no—
550C2×C4×Q8—611no—
551C2×C4×Q8—611no—
552C2×C4×Q8—1221no—
553C2×C4×D4—611no—
554C2×C4×D4—611no—
555C2×C4×D4—1221no—
556C2×C4×D4—1221no—
557C2×#117—611no—
558C2×#117—1221no—
559C2×#117—1221no—
560C22×C42—611no—
561C22×C42—1221no—
562#485—614no—
563#485—614no—
564#484—612no—
565#484—612no—
566#483—612no—
567#483—612no—
568#477—614no—
569#476—614no—
570#475—614no—
571#474—614no—
572#462—614no—
573#462—614no—
574#461—614no—
575#461—614no—
576#452—614no—
577#452C2×D6114yes—
578#451—612no—
579#451C2×D6112yes—
580#450—612no—
581#450C2×D6112yes—
582#441—614no—
583#441—614no—
584#440—614no—
585#440—614no—
586C4×Q16—614no—
587C4×Q16—614no—
588C4×SD16—614no—
589C4×SD16—614no—
590#432—612no—
591#432—612no—
592#431—612no—
593#431—612no—
594#428—612no—
595#428—612no—
596#423—612no—
597#419—612no—
598#419—612no—
599#417—612no—
600#417C2×D6112yes—
601#407—611no—
602#407C2×D6111yescharacteristic
603C4×M16—612no—
604C61#6056211yescharacteristic, complemented, Sylow
605C2×#41—28no—
606C2×#41—21no—
607C2×#41—21no—
608C2×#41C22×D6112yes—
609C2×#41C22×D6112yes—
610C22×Q8—611no—
611C22×Q8—1221no—
612C22×Q8C22×D6111yescharacteristic
613C22×Q8C22×D6111yescharacteristic
614C22×D4—21no—
615C22×D4C22×D6111yescharacteristic
616C23×C4—21no—
617C23×C4—611no—
618C23×C4—611no—
619C23×C4—1221no—
620C23×C4—1221no—
621C23×C4C22×D6111yescharacteristic
622#137—28no—
623#137—1228no—
624C2×Q16—614no—
625C2×Q16C22×D6114yes—
626C2×SD16—614no—
627C2×SD16C22×D6114yes—
628C2×M16—612no—
629C2×M16C22×D6112yes—
630C4⋊Q8—612no—
631C4⋊Q8—612no—
632C4⋊Q8—612no—
633C4⋊Q8—612no—
634C4⋊Q8—1221no—
635C4⋊Q8—1221no—
636C4⋊Q8—1221no—
637C4⋊Q8—1221no—
638#125—1222no—
639#125—1222no—
640#125—1222no—
641#125—1222no—
642C22⋊Q8—21no—
643C22⋊Q8—21no—
644C22⋊Q8—612no—
645C22⋊Q8—612no—
646C22⋊Q8—1222no—
647C22⋊Q8—1222no—
648C22⋊Q8—1222no—
649C22⋊Q8—1222no—
650C22⋊Q8—1221no—
651C22⋊Q8—1221no—
652C22⋊Q8C22×D6112yes—
653C22⋊Q8C22×D6112yes—
654C4×Q8—612no—
655C4×Q8—612no—
656C4×Q8—612no—
657C4×Q8—612no—
658C4×Q8—612no—
659C4×Q8—612no—
660C4×Q8—612no—
661C4×Q8—612no—
662C4×Q8—1221no—
663C4×Q8—1221no—
664C4×Q8—1222no—
665C4×Q8—1222no—
666C4×Q8—1222no—
667C4×Q8—1222no—
668C4×Q8—1221no—
669C4×Q8—1221no—
670C4×Q8—1221no—
671C4×Q8—1221no—
672C4×Q8—1221no—
673C4×Q8—1221no—
674C4×D4—612no—
675C4×D4—612no—
676C4×D4—612no—
677C4×D4—612no—
678C4×D4—1221no—
679C4×D4—1221no—
680C4×D4—1221no—
681C4×D4—1221no—
682C4×D4—1222no—
683C4×D4—1222no—
684C4×D4—1222no—
685C4×D4—1222no—
686C4×D4—1222no—
687C4×D4—1222no—
688C4×D4—1222no—
689C4×D4—1222no—
690#117—612no—
691#117—612no—
692#117—1222no—
693#117—1222no—
694#117—1222no—
695#117—1222no—
696#117—1222no—
697#117—1222no—
698#117—1222no—
699#117—1222no—
700#117—1221no—
701#117—1221no—
702C2×C4⋊C4—21no—
703C2×C4⋊C4—611no—
704C2×C4⋊C4—611no—
705C2×C4⋊C4—611no—
706C2×C4⋊C4—1221no—
707C2×C4⋊C4—1221no—
708C2×C4⋊C4—1221no—
709C2×C4⋊C4—1221no—
710C2×C4⋊C4—1221no—
711C2×C4⋊C4—1221no—
712C2×C4⋊C4—1221no—
713C2×C4⋊C4—1221no—
714C2×C4⋊C4C22×D6111yescharacteristic
715C2×C22⋊C4—21no—
716C2×C22⋊C4—1221no—
717C2×C22⋊C4—1221no—
718C2×C22⋊C4—1221no—
719C2×C22⋊C4—1221no—
720C2×C42—611no—
721C2×C42—611no—
722C2×C42—611no—
723C2×C42—611no—
724C2×C42—611no—
725C2×C42—611no—
726C2×C42—611no—
727C2×C42—611no—
728C2×C42—611no—
729C2×C42—611no—
730C2×C42—611no—
731C2×C42—611no—
732C2×C42—1222no—
733C2×C42—1222no—
734C2×C42—1222no—
735C2×C42—1222no—
736C2×C42—1221no—
737C2×C42—1221no—
738C2×C42—1221no—
739C2×C42—1221no—
740C2×C42—1221no—
741#107—614no—
742#107—614no—
743#106—614no—
744#106—614no—
745C4⋊C8—614no—
746C4⋊C8—614no—
747#103—614no—
748#103—614no—
749#103—614no—
750#103—614no—
751#103—614no—
752#103C22×D6114yes—
753#102—614no—
754#102C22×D6114yes—
755C22⋊C8—612no—
756C22⋊C8—612no—
757C22⋊C8C22×D6112yes—
758C22⋊C8C22×D6112yes—
759#97—614no—
760C4×C8—614no—
761C24—21no—
762C24D4×D6111yescharacteristic
763#41—28no—
764#41—28no—
765#41—24no—
766#41—24no—
767#41—24no—
768#41#1175822418yes—
769C2×Q8—24no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—24no—
773C2×Q8—612no—
774C2×Q8—1222no—
775C2×Q8—1222no—
776C2×Q8—1221no—
777C2×Q8—1224no—
778C2×Q8—2444no—
779C2×Q8C23×D6112yes—
780C2×Q8C23×D6112yes—
781C2×D4—28no—
782C2×D4—22no—
783C2×D4—22no—
784C2×D4—24no—
785C2×D4—21no—
786C2×D4C23×D6112yes—
787C22×C4—28no—
788C22×C4—21no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—24no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—611no—
795C22×C4—611no—
796C22×C4—611no—
797C22×C4—611no—
798C22×C4—611no—
799C22×C4—611no—
800C22×C4—611no—
801C22×C4—611no—
802C22×C4—611no—
803C22×C4—611no—
804C22×C4—611no—
805C22×C4—611no—
806C22×C4—1224no—
807C22×C4—1222no—
808C22×C4—1222no—
809C22×C4—1222no—
810C22×C4—1222no—
811C22×C4—1221no—
812C22×C4—1221no—
813C22×C4—1221no—
814C22×C4—1221no—
815C22×C4—2444no—
816C22×C4—2442no—
817C22×C4—2444no—
818C22×C4D4×D6111yescharacteristic
819C22×C4D4×D6111yescharacteristic
820C22×C4D4×D6111yescharacteristic
821C22×C4C23×D6111yescharacteristic
822C22×C4C23×D6111yescharacteristic
823C22×C4C23×D6111yescharacteristic
824Q16—28no—
825Q16—1228no—
826SD16—28no—
827SD16—1228no—
828M16—24no—
829M16—1224no—
830C2×C8—614no—
831C2×C8C23×D6114yes—
832C4⋊C4—22no—
833C4⋊C4—22no—
834C4⋊C4—21no—
835C4⋊C4—612no—
836C4⋊C4—612no—
837C4⋊C4—612no—
838C4⋊C4—1222no—
839C4⋊C4—1222no—
840C4⋊C4—1222no—
841C4⋊C4—1222no—
842C4⋊C4—1222no—
843C4⋊C4—1222no—
844C4⋊C4—1222no—
845C4⋊C4—1222no—
846C4⋊C4—1222no—
847C4⋊C4—1222no—
848C4⋊C4—1222no—
849C4⋊C4—1222no—
850C4⋊C4—1222no—
851C4⋊C4—1222no—
852C4⋊C4—1221no—
853C4⋊C4—1221no—
854C4⋊C4—1221no—
855C4⋊C4—1222no—
856C4⋊C4—1222no—
857C4⋊C4C23×D6112yes—
858C22⋊C4—22no—
859C22⋊C4—22no—
860C22⋊C4—1222no—
861C22⋊C4—1222no—
862C22⋊C4—1222no—
863C22⋊C4—1222no—
864C22⋊C4—1222no—
865C22⋊C4—1222no—
866C22⋊C4—1222no—
867C22⋊C4—1222no—
868C42—611no—
869C42—611no—
870C42—611no—
871C42—611no—
872C42—611no—
873C42—611no—
874C42—611no—
875C42—611no—
876C42—611no—
877C42—611no—
878C42—611no—
879C42—611no—
880C42—611no—
881C42—611no—
882C42—611no—
883C42—611no—
884C42—1222no—
885C42—1222no—
886C42—1222no—
887C42—1222no—
888C42—1222no—
889C42—1222no—
890C42—1222no—
891C42—1222no—
892C42—1222no—
893C42—1222no—
894C23—24no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—41no—
899C23—42no—
900C23—42no—
901C23C2×D4×D6111yescharacteristic
902C23C2×D4×D6111yescharacteristic
903C23C2×D4×D6111yescharacteristic
904Q8—24no—
905Q8—22no—
906Q8—24no—
907Q8—42no—
908Q8—1224no—
909Q8—2444no—
910Q8—2444no—
911Q8—2442no—
912Q8C2×#1175822414yes—
913D4—28no—
914D4—24no—
915D4—28no—
916D4—22no—
917D4C2×#1175822414yes—
918C2×C4—24no—
919C2×C4—28no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—28no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—614no—
932C2×C4—611no—
933C2×C4—611no—
934C2×C4—611no—
935C2×C4—611no—
936C2×C4—611no—
937C2×C4—611no—
938C2×C4—611no—
939C2×C4—611no—
940C2×C4—1222no—
941C2×C4—1222no—
942C2×C4—1222no—
943C2×C4—1222no—
944C2×C4—1222no—
945C2×C4—1222no—
946C2×C4—1222no—
947C2×C4—1222no—
948C2×C4—1222no—
949C2×C4—1222no—
950C2×C4—1222no—
951C2×C4—1222no—
952C2×C4—2444no—
953C2×C4—2444no—
954C2×C4—2444no—
955C2×C4—2441no—
956C2×C4—2441no—
957C2×C4—2441no—
958C2×C4—2444no—
959C2×C4—2442no—
960C2×C4—2442no—
961C2×C4—2442no—
962C2×C4—2442no—
963C2×C4C2×D4×D6111yescharacteristic
964C2×C4C2×D4×D6111yescharacteristic
965C2×C4C2×D4×D6111yescharacteristic
966C2×C4C2×#1175822414yes—
967C2×C4C24×D6111yescharacteristic
968C8—24no—
969C8—1224no—
970C22—21no—
971C22—21no—
972C22—21no—
973C22—21no—
974C22—21no—
975C22—21no—
976C22—21no—
977C22—24no—
978C22—44no—
979C22—48no—
980C22—42no—
981C22—42no—
982C22#1684026812yes—
983C22#137×D6112yes—
984C22C22×D4×D6111yescharacteristic
985C4—21no—
986C4—24no—
987C4—21no—
988C4—42no—
989C4—42no—
990C4—612no—
991C4—612no—
992C4—612no—
993C4—1221no—
994C4—1221no—
995C4—1221no—
996C4—1221no—
997C4—1221no—
998C4—2442no—
999C4—2442no—
1000C4—2442no—
1001C4—2442no—
1002C4#1684026812yes—
1003C4C22×#1175822412yes—
1004C2—22no—
1005C2—22no—
1006C2—41no—
1007C2—44no—
1008C2C2×#1684026811yescharacteristic
1009C2C2×#137×D6111yescharacteristic
1010C2#575×D6111yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3007C2
socleC22×C61C23×D4
prime radicalC22×#41×C61C22
hypercenter#3007D61
hypocenterC61#60562
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3007

Complements

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

NH ≅ G/Ntype
1. C2×#16840314C2semidirect
3. #21455974C2semidirect
4. #21455944C2semidirect
5. #21455913C2semidirect
6. #21455883C2semidirect
7. #21455853C2semidirect
8. #21455822C2semidirect
9. #21455768C2semidirect
10. #21455763C2semidirect
11. #21455630C2semidirect
12. #21455304C2semidirect
14. #21454643C2semidirect
15. #137×Dic61C2semidirect
16. #21454448C2semidirect
25. #16840314C22semidirect
26. #16840314C22semidirect
27. C2×#14519776C22semidirect
28. C2×#14519775C22semidirect
42. C2×Q8×Dic61C22semidirect
44. C2×#14519742C22semidirect
54. #16840104C22semidirect
55. #16840100C22semidirect
60. #16840055C22semidirect
61. #16840050C22semidirect
62. #16840045C22semidirect
63. #16840040C22semidirect
64. #16839970C22semidirect
65. #16839970C22semidirect
66. #16839965C22semidirect
67. #16839965C22semidirect
71. #16839869C22semidirect
72. #16839866C22semidirect
73. #16839863C22semidirect
74. #16839859C22semidirect
75. Q16×Dic61C22semidirect
76. #16839854C22semidirect
77. #16839853C22semidirect
78. SD16×Dic61C22semidirect
80. #16839816C22semidirect
82. #16839812C22semidirect
83. #16839804C22semidirect
84. #16839802C22semidirect
85. #16839785C22semidirect
86. #16839772C22semidirect
87. #16839771C22semidirect
90. M16×Dic61C22semidirect
449. C2×Dic61#137semidirect
604. C61#60562semidirect

Maximal subgroups

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

subgroupindex
C2×#168403142
C2×#41×Dic612
#214559742
#214559442
#214559132
#214558832
#214558532
#214558222
#214557682
#214557632
#214556302
#214553042
#214550792
#214546432
#137×Dic612
#214544482
C61×#30072
#6056261