Finite Group Databasebeta

← #30548547

Subgroups — #30548547

Order 15616.

2010 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840372C211yesmaximal, characteristic, complemented
2#21459020C211yesmaximal, characteristic
3#21456115C214yesmaximal, complemented
4#21456067C214yesmaximal, complemented
5#21456036C214yesmaximal, complemented
6#21456028C214yesmaximal, complemented
7#21455767C211yesmaximal, characteristic, complemented
8#21455640C212yesmaximal, complemented
9#21455305C212yesmaximal, complemented
10#21455081C211yesmaximal, characteristic
11#21455077C211yesmaximal, characteristic
12#21454637C212yesmaximal, complemented
13#21454634C212yesmaximal, complemented
14#21454454C211yesmaximal, characteristic, complemented
15C61×#3095C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C2×#14519810C2212yes—
18C2×#14519808C2212yes—
19#16840372—22no—
20#16840372—22no—
21#16840372C2214yes—
22#16840372C2214yescomplemented
23C2×#14519775C2211yescharacteristic, complemented
24C2×#14519770—21no—
25C2×#14519770—21no—
26C2×#14519768—21no—
27C2×#14519768C2211yescharacteristic, complemented
28C2×#14519767—21no—
29C2×#14519756C2211yescharacteristic
30#16840243C2212yes—
31#16840243C2212yes—
32#16840242—21no—
33#16840242—21no—
34#16840239C2212yes—
35#16840236C2212yes—
36#16840235—21no—
37#16840235—21no—
38C4×#11758222—22no—
39#16840230C2212yes—
40#16840230C2212yes—
41C2×Q8×Dic61C2211yescharacteristic, complemented
42C2×#14519742C2211yescharacteristic, complemented
43C2×#14519736C2211yescharacteristic
44#117×D61—22no—
45#16840103C2214yes—
46#16840097C2212yescomplemented
47#16840092C2212yescomplemented
48#16840072C2214yescomplemented
49#16840068C2214yescomplemented
50#16840065C2214yescomplemented
51#16840061C2214yescomplemented
52#16839971C2214yescomplemented
53#16839971C2214yescomplemented
54#16839966C2214yescomplemented
55#16839966C2214yescomplemented
56#16839926C2214yes—
57#16839922C2214yes—
58#16839920C2212yes—
59#16839917C2212yes—
60#16839915C2212yes—
61#16839912C2212yes—
62#16839868C2214yescomplemented
63#16839866C2214yescomplemented
64#16839865C2214yescomplemented
65#16839861C2214yescomplemented
66#16839856C2214yescomplemented
67#16839854C2214yescomplemented
68#16839849C2214yescomplemented
69#16839847C2214yescomplemented
70#16839820C2214yes—
71#16839820C2214yescomplemented
72#16839805C2212yescomplemented
73#16839785C2212yescomplemented
74#16839770C2212yescomplemented
75#16839764C2212yes—
76#16839761C2212yes—
77#16839726C2211yescharacteristic
78M16×Dic61C2212yescomplemented
79C2×C22⋊Q8×C61C2211yescharacteristic
80C2×#117×C61C2211yescharacteristic
81C61×#485C2214yes—
82C61×#484C2212yescomplemented
83C61×#483C2212yescomplemented
84C61×#428C2212yescomplemented
85C61×#419C2212yescomplemented
86C61×#407C2211yescharacteristic
87C2×#11758222—21no—
88C2×#11758222—21no—
89C2×#11758222—28no—
90C2×#11758222C2312yes—
91C2×#11758222C2312yes—
92C22×Dic122C2311yescharacteristic
93C22×Dic122C2311yescharacteristic
94C22×D244C2311yescharacteristic
95C22×C22⋊D61—21no—
96C22×C4×D61—21no—
97#14519810—28no—
98#14519808—28no—
99C2×Dic244C2314yes—
100C2×#11758202C2314yes—
101C2×#11758190C2314yes—
102C2×#11758201C2314yes—
103C2×#11758194C2312yes—
104#14519775—22no—
105#14519775C2314yes—
106#14519770—24no—
107#14519770—24no—
108#14519770—24no—
109#14519770—24no—
110#14519768—24no—
111#14519768—24no—
112#14519768—22no—
113#14519768C2314yes—
114#14519767—24no—
115#14519767—24no—
116#14519756—21no—
117#14519756—21no—
118#14519756C2312yes—
119#14519756C2312yes—
120Q8×Dic61—22no—
121Q8×Dic61C2314yes—
122C4×Dic122—22no—
123C4×Dic122—22no—
124#14519742—22no—
125#14519742C2314yes—
126#14519742C2312yes—
127#14519742C2312yes—
128#14519742C2312yes—
129#14519742C2312yes—
130C4×D244—22no—
131C4×D244—22no—
132#14519739C2312yes—
133#14519739C2312yes—
134#14519739C2312yes—
135#14519739C2312yes—
136C4×C22⋊D61—22no—
137C4×C22⋊D61—22no—
138C4×C22⋊D61—22no—
139C4×C22⋊D61—22no—
140#14519737—22no—
141#14519737—22no—
142#14519737—22no—
143#14519737—22no—
144#14519736D412yes—
145#14519736D412yes—
146#14519736C2312yes—
147#14519736C2312yes—
148#14519735—22no—
149#14519735—22no—
150#14519734—22no—
151#14519734—22no—
152#14519733—22no—
153#14519733—22no—
154C2×C4⋊Dic61—21no—
155C2×C4⋊Dic61—21no—
156C2×C4⋊Dic61D411yescharacteristic
157C2×C4⋊Dic61D411yescharacteristic
158C2×C4⋊Dic61C2311yescharacteristic
159C2×#11758196—21no—
160C2×#11758196—21no—
161C2×#11758196—21no—
162C2×#11758196—21no—
163C2×#11758196—21no—
164C4⋊C4×D61—22no—
165C4⋊C4×D61—22no—
166C2×C22⋊Dic61—21no—
167C2×C22⋊Dic61D411yescharacteristic
168C2×C22⋊Dic61D411yescharacteristic
169C22⋊C4×D61—22no—
170C22⋊C4×D61—22no—
171C2×C4×Dic61—21no—
172C2×C4×Dic61—21no—
173C2×C4×Dic61C2311yescharacteristic
174C2×C4×Dic61C2311yescharacteristic
175C42×D61—22no—
176C42×D61—22no—
177#14519710C2314yes—
178#14519708C2314yes—
179#14519706C2314yes—
180#14519706C2314yes—
181#14519702C2314yes—
182#14519700C2314yes—
183#14519700C2314yes—
184#14519700C2314yes—
185#14519699C2314yes—
186#14519697C2314yes—
187C22⋊#92418C2312yes—
188C22⋊#92418C2312yes—
189#14519687C2314yes—
190C8×Dic61C2314yes—
191C22×Q8×C61C2311yescharacteristic
192C23×C4×C61C2311yescharacteristic
193C2×M16×C61C2312yes—
194C22⋊Q8×C61—21no—
195C22⋊Q8×C61—21no—
196C22⋊Q8×C61C2312yes—
197C22⋊Q8×C61C2312yes—
198#117×C61—21no—
199#117×C61—21no—
200#117×C61C2312yes—
201#117×C61C2312yes—
202C2×C4⋊C4×C61—21no—
203C2×C4⋊C4×C61C2311yescharacteristic
204C2×C4⋊C4×C61C2311yescharacteristic
205C2×C4⋊C4×C61C2311yescharacteristic
206C2×C22⋊C4×C61—21no—
207C2×C22⋊C4×C61—21no—
208C2×C42×C61—21no—
209#107×C61C2314yes—
210#106×C61C2314yes—
211#103×C61C2314yes—
212#103×C61C2314yes—
213C22⋊C8×C61C2312yes—
214C22⋊C8×C61C2312yes—
215C24×C61C2×D411yescharacteristic
216C23×D61—21no—
217C2×Q8×C61—21no—
218C2×Q8×C61—24no—
219C2×Q8×C61C2412yes—
220C22×C4×C61—24no—
221C22×C4×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61—21no—
224C22×C4×C61—21no—
225C22×C4×C61C2×D411yescharacteristic
226C22×C4×C61C2×D411yescharacteristic
227C22×C4×C61C2×D411yescharacteristic
228C22×C4×C61C2411yescharacteristic
229C22×C4×C61C2411yescharacteristic
230C22×C4×C61C2411yescharacteristic
231C2×C22⋊D61—28no—
232C2×C22⋊D61—22no—
233C2×C22⋊D61—22no—
234C22×Dic61—21no—
235C22×Dic61—21no—
236C22×Dic61—21no—
237C22×Dic61C2×D411yescharacteristic
238C22×Dic61C2×D411yescharacteristic
239C22×Dic61C2×D411yescharacteristic
240C22×Dic61C2×D411yescharacteristic
241#11758222—28no—
242#11758222—28no—
243#11758222—24no—
244#11758222—24no—
245#11758222—24no—
246#11758222#4118yes—
247C2×D244—21no—
248C2×D244—24no—
249C2×D244C2412yes—
250C2×C4×D61—28no—
251C2×C4×D61—22no—
252C2×C4×D61—22no—
253C2×C4×D61—22no—
254C2×C4×D61—22no—
255C2×C4×D61—22no—
256C2×C4×D61—22no—
257C2×Dic122—21no—
258C2×Dic122—24no—
259C2×Dic122—24no—
260C2×Dic122—21no—
261C2×Dic122C2412yes—
262C2×Dic122C2412yes—
263M16×C61—24no—
264C2×C8×C61C2414yes—
265C4⋊C4×C61—22no—
266C4⋊C4×C61—22no—
267C4⋊C4×C61—21no—
268C4⋊C4×C61—21no—
269C4⋊C4×C61—21no—
270C4⋊C4×C61C2412yes—
271C4⋊C4×C61C2412yes—
272C4⋊C4×C61C2412yes—
273C22⋊C4×C61—22no—
274C22⋊C4×C61—22no—
275C22⋊C4×C61—22no—
276C22⋊C4×C61—22no—
277C42×C61—22no—
278C42×C61—22no—
279C22⋊Dic61—22no—
280C22⋊Dic61—22no—
281C22⋊Dic61C2×D412yes—
282C22⋊Dic61C2×D412yes—
283C22⋊Dic61C2×D412yes—
284C22⋊Dic61C2×D412yes—
285#11758202—28no—
286#11758201—28no—
287#11758198—22no—
288#11758198—22no—
289#11758198—22no—
290#11758198—22no—
291C4⋊Dic61—21no—
292C4⋊Dic61—24no—
293C4⋊Dic61—24no—
294C4⋊Dic61C2×D412yes—
295C4⋊Dic61C2×D412yes—
296C4⋊Dic61C2×D412yes—
297C4⋊Dic61C2×D412yes—
298C4⋊Dic61C2412yes—
299#11758196—22no—
300#11758196—22no—
301#11758196—22no—
302#11758196—22no—
303#11758196—22no—
304#11758196—22no—
305#11758196—24no—
306#11758196—24no—
307#11758196—24no—
308#11758196—24no—
309C4×Dic61—22no—
310C4×Dic61—22no—
311C4×Dic61—22no—
312C4×Dic61—22no—
313C4×Dic61—24no—
314C4×Dic61—24no—
315C4×Dic61C2×D412yes—
316C4×Dic61C2×D412yes—
317C4×Dic61C2412yes—
318C4×Dic61C2412yes—
319#11758194—24no—
320C2×#92418C2414yes—
321Dic244—28no—
322#11758190—28no—
323C23×C61—22no—
324C23×C61—41no—
325C23×C61—41no—
326C23×C61C22×D411yescharacteristic
327C23×C61C22×D411yescharacteristic
328C23×C61C22×D411yescharacteristic
329C22×D61—22no—
330C22×D61—24no—
331C22×D61—81no—
332C22×D61—81no—
333Q8×C61—24no—
334Q8×C61—42no—
335C2×C4×C61—22no—
336C2×C4×C61—22no—
337C2×C4×C61—22no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
340C2×C4×C61—22no—
341C2×C4×C61—22no—
342C2×C4×C61—22no—
343C2×C4×C61—22no—
344C2×C4×C61—42no—
345C2×C4×C61—42no—
346C2×C4×C61—81no—
347C2×C4×C61—81no—
348C2×C4×C61C22×D411yescharacteristic
349C2×C4×C61C22×D411yescharacteristic
350C2×C4×C61C22×D411yescharacteristic
351C2×C4×C61C2×#4114yes—
352C2×C4×C61C2511yescharacteristic
353C22⋊D61—28no—
354C22⋊D61—28no—
355C2×Dic61—24no—
356C2×Dic61—22no—
357C2×Dic61—22no—
358C2×Dic61—22no—
359C2×Dic61—41no—
360C2×Dic61—41no—
361C2×Dic61—41no—
362C2×Dic61—41no—
363C2×Dic61—42no—
364C2×Dic61—42no—
365C2×Dic61C22×D412yes—
366C2×Dic61C22×D412yes—
367C2×Dic61C22×D412yes—
368C2×Dic61C22×D412yes—
369D244—24no—
370D244—22no—
371D244C2×#4114yes—
372C4×D61—28no—
373C4×D61—28no—
374C4×D61—82no—
375C4×D61—82no—
376C4×D61—82no—
377C4×D61—82no—
378Dic122—24no—
379Dic122—22no—
380Dic122—24no—
381Dic122—42no—
382Dic122C2×#4114yes—
383C8×C61—24no—
384#92418—24no—
385#60569—611nomaximal, Sylow
386C22×C61—21no—
387C22×C61—21no—
388C22×C61—21no—
389C22×C61—21no—
390C22×C61—21no—
391C22×C61—21no—
392C22×C61—21no—
393C22×C61—21no—
394C22×C61—82no—
395C22×C61#52512yes—
396C22×C61C23×D411yescharacteristic
397C2×D61—24no—
398C2×D61—42no—
399C2×D61—42no—
400C2×D61—84no—
401C4×C61—21no—
402C4×C61—21no—
403C4×C61—42no—
404C4×C61—42no—
405C4×C61—42no—
406C4×C61—42no—
407C4×C61#52512yes—
408C4×C61C22×#4112yes—
409Dic61—22no—
410Dic61—22no—
411Dic61—22no—
412Dic61—22no—
413Dic61—24no—
414Dic61—42no—
415Dic61—42no—
416C2×#541—611no—
417#3428—611no—
418#3127—614no—
419#3123—614no—
420#3120—614no—
421#3120—614no—
422#3095—611no—
423#3095D6111yescharacteristic, complemented
424#3080—612no—
425#3039—612no—
426#3007—611no—
427#3007—611no—
428C4×#137—612no—
429C4×#137—612no—
430#2921—611no—
431C2×C61—22no—
432C2×C61—41no—
433C2×C61—41no—
434C2×C61C2×#52511yescharacteristic
435C2×C61#358611yescharacteristic
436C2×C61#358611yescharacteristic
437D61—44no—
438C22×#41—611no—
439C2×#137—612no—
440C2×#137—612no—
441#541—614no—
442#541—614no—
443#541—1222no—
444#541—1222no—
445C2×C4⋊Q8—611no—
446C2×#126—1221no—
447C2×#126—1221no—
448C2×#125—611no—
449C2×#125—1221no—
450C2×#125—1221no—
451C2×C22⋊Q8—611no—
452C2×C22⋊Q8C2×D6111yescharacteristic
453#520—612no—
454#520—612no—
455#520—1221no—
456#520—1221no—
457#519—612no—
458#518—612no—
459#518—1221no—
460#518—1221no—
461C4×#41—612no—
462C4×#41—612no—
463C4×#41—1222no—
464C2×C4×Q8—611no—
465C2×C4×Q8—611no—
466C2×#117—611no—
467C2×#117—1222no—
468C2×#117C2×D6111yescharacteristic
469#485—614no—
470#485C2×D6114yes—
471#484—612no—
472#484C2×D6112yescomplemented
473#483—612no—
474#483C2×D6112yescomplemented
475#479—614no—
476#479—614no—
477#478—614no—
478#478—614no—
479#462—614no—
480#462—614no—
481#461—614no—
482#461—614no—
483#452—614no—
484#452—614no—
485#451—612no—
486#451—612no—
487#450—612no—
488#450—612no—
489#441—614no—
490#441—614no—
491#440—614no—
492#440—614no—
493C4×Q16—614no—
494C4×Q16—614no—
495C4×SD16—614no—
496C4×SD16—614no—
497#433—614no—
498#433—614no—
499#428—612no—
500#428C2×D6112yescomplemented
501#423—612no—
502#419—612no—
503#419C2×D6112yescomplemented
504#417—612no—
505#417—612no—
506#407—611no—
507#407C2×D6111yescharacteristic
508C4×M16—612no—
509C61#6056911yescharacteristic, complemented, Sylow
510C2×#41—612no—
511C2×#41—612no—
512C2×#41—1228no—
513C2×#41—1221no—
514C2×#41—1221no—
515C22×Q8—611no—
516C22×Q8—611no—
517C22×Q8C22×D6111yescharacteristic
518C22×D4—611no—
519C22×D4—1221no—
520C23×C4—1221no—
521C23×C4C22×D6111yescharacteristic
522#137—1228no—
523#137—1228no—
524C2×Q16—614no—
525C2×Q16—614no—
526C2×SD16—614no—
527C2×SD16—614no—
528C2×M16—612no—
529C2×M16C22×D6112yes—
530C4⋊Q8—614no—
531C4⋊Q8—1222no—
532#126—1224no—
533#126—1224no—
534#126—1224no—
535#126—1224no—
536#125—614no—
537#125—1222no—
538#125—1224no—
539#125—1224no—
540#125—1224no—
541#125—1224no—
542C22⋊Q8—21no—
543C22⋊Q8—21no—
544C22⋊Q8—612no—
545C22⋊Q8—612no—
546C22⋊Q8—1221no—
547C22⋊Q8—1221no—
548C22⋊Q8C22×D6112yes—
549C22⋊Q8C22×D6112yes—
550C4×Q8—614no—
551C4×Q8—614no—
552C4×Q8—612no—
553C4×Q8—612no—
554C4×Q8—612no—
555C4×Q8—612no—
556C4×Q8—1222no—
557C4×Q8—1222no—
558C4×Q8—1222no—
559C4×Q8—1222no—
560C4×D4—612no—
561C4×D4—612no—
562C4×D4—612no—
563C4×D4—612no—
564C4×D4—1222no—
565C4×D4—1222no—
566C4×D4—1222no—
567C4×D4—1222no—
568C4×D4—1222no—
569C4×D4—1222no—
570C4×D4—1222no—
571C4×D4—1222no—
572C4×D4—1222no—
573C4×D4—1222no—
574#117—21no—
575#117—21no—
576#117—612no—
577#117—612no—
578#117—612no—
579#117—612no—
580#117—1222no—
581#117—1222no—
582#117—1222no—
583#117—1222no—
584#117—1222no—
585#117—1222no—
586#117C22×D6112yes—
587#117C22×D6112yes—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—611no—
590C2×C4⋊C4—611no—
591C2×C4⋊C4—611no—
592C2×C4⋊C4—1222no—
593C2×C4⋊C4—1222no—
594C2×C4⋊C4—1221no—
595C2×C4⋊C4—1221no—
596C2×C4⋊C4—1221no—
597C2×C4⋊C4—1221no—
598C2×C4⋊C4—1221no—
599C2×C4⋊C4—1221no—
600C2×C4⋊C4—1221no—
601C2×C4⋊C4C22×D6111yescharacteristic
602C2×C4⋊C4C22×D6111yescharacteristic
603C2×C4⋊C4C22×D6111yescharacteristic
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—611no—
607C2×C22⋊C4—611no—
608C2×C22⋊C4—1222no—
609C2×C22⋊C4—1222no—
610C2×C22⋊C4—1221no—
611C2×C42—21no—
612C2×C42—611no—
613C2×C42—611no—
614C2×C42—1222no—
615C2×C42—1222no—
616C2×C42—1221no—
617C2×C42—1221no—
618#107—614no—
619#107C22×D6114yes—
620#106—614no—
621#106C22×D6114yes—
622C4⋊C8—614no—
623C4⋊C8—614no—
624#103—614no—
625#103—614no—
626#103—614no—
627#103—614no—
628#103C22×D6114yes—
629#103C22×D6114yes—
630#102—614no—
631#102—614no—
632C22⋊C8—612no—
633C22⋊C8—612no—
634C22⋊C8C22×D6112yes—
635C22⋊C8C22×D6112yes—
636#97—614no—
637C4×C8—614no—
638C24—1221no—
639C24D4×D6111yescharacteristic
640#41—618no—
641#41—1224no—
642#41—1224no—
643#41—1228no—
644#41—1228no—
645#41—1224no—
646C2×Q8—21no—
647C2×Q8—24no—
648C2×Q8—612no—
649C2×Q8—612no—
650C2×Q8—1224no—
651C2×Q8—1221no—
652C2×Q8—1221no—
653C2×Q8—1224no—
654C2×Q8C23×D6112yes—
655C2×D4—612no—
656C2×D4—1224no—
657C2×D4—1228no—
658C2×D4—1222no—
659C2×D4—1222no—
660C2×D4—1221no—
661C22×C4—24no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—611no—
667C22×C4—611no—
668C22×C4—611no—
669C22×C4—611no—
670C22×C4—1222no—
671C22×C4—1222no—
672C22×C4—1222no—
673C22×C4—1222no—
674C22×C4—1228no—
675C22×C4—1221no—
676C22×C4—1222no—
677C22×C4—1222no—
678C22×C4—1221no—
679C22×C4—1221no—
680C22×C4D4×D6111yescharacteristic
681C22×C4D4×D6111yescharacteristic
682C22×C4D4×D6111yescharacteristic
683C22×C4C23×D6111yescharacteristic
684C22×C4C23×D6111yescharacteristic
685C22×C4C23×D6111yescharacteristic
686Q16—1228no—
687Q16—1228no—
688SD16—1228no—
689SD16—1228no—
690M16—24no—
691M16—1224no—
692C2×C8—614no—
693C2×C8C23×D6114yes—
694C4⋊C4—22no—
695C4⋊C4—22no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—612no—
700C4⋊C4—612no—
701C4⋊C4—612no—
702C4⋊C4—612no—
703C4⋊C4—612no—
704C4⋊C4—1222no—
705C4⋊C4—1222no—
706C4⋊C4—1222no—
707C4⋊C4—1222no—
708C4⋊C4—1224no—
709C4⋊C4—1224no—
710C4⋊C4—1224no—
711C4⋊C4—1224no—
712C4⋊C4—1224no—
713C4⋊C4—1224no—
714C4⋊C4—1221no—
715C4⋊C4—1222no—
716C4⋊C4—1222no—
717C4⋊C4C23×D6112yes—
718C4⋊C4C23×D6112yes—
719C4⋊C4C23×D6112yes—
720C22⋊C4—22no—
721C22⋊C4—22no—
722C22⋊C4—22no—
723C22⋊C4—22no—
724C22⋊C4—612no—
725C22⋊C4—612no—
726C22⋊C4—612no—
727C22⋊C4—612no—
728C22⋊C4—1222no—
729C22⋊C4—1222no—
730C22⋊C4—1222no—
731C22⋊C4—1222no—
732C22⋊C4—1222no—
733C22⋊C4—1222no—
734C42—22no—
735C42—22no—
736C42—612no—
737C42—612no—
738C42—612no—
739C42—612no—
740C42—1222no—
741C42—1222no—
742C42—1222no—
743C42—1222no—
744C42—1224no—
745C42—1224no—
746C23—22no—
747C23—41no—
748C23—41no—
749C23—1224no—
750C23—1222no—
751C23—4881no—
752C23—4881no—
753C23C2×D4×D6111yescharacteristic
754C23C2×D4×D6111yescharacteristic
755C23C2×D4×D6111yescharacteristic
756Q8—24no—
757Q8—42no—
758Q8—614no—
759Q8—1224no—
760Q8—1222no—
761Q8—1224no—
762Q8—2442no—
763D4—614no—
764D4—1224no—
765D4—1228no—
766D4—1228no—
767D4—1222no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—81no—
780C2×C4—81no—
781C2×C4—612no—
782C2×C4—612no—
783C2×C4—612no—
784C2×C4—612no—
785C2×C4—1228no—
786C2×C4—1224no—
787C2×C4—1222no—
788C2×C4—1228no—
789C2×C4—1222no—
790C2×C4—1222no—
791C2×C4—4882no—
792C2×C4—4882no—
793C2×C4—4882no—
794C2×C4—4882no—
795C2×C4—2441no—
796C2×C4—2441no—
797C2×C4—2441no—
798C2×C4—2441no—
799C2×C4—2442no—
800C2×C4—2442no—
801C2×C4C2×D4×D6111yescharacteristic
802C2×C4C2×D4×D6111yescharacteristic
803C2×C4C2×D4×D6111yescharacteristic
804C2×C4#41×D6114yes—
805C2×C4C24×D6111yescharacteristic
806C8—24no—
807C8—1224no—
808C22—21no—
809C22—21no—
810C22—21no—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—21no—
815C22—21no—
816C22—82no—
817C22—1224no—
818C22—4884no—
819C22—2442no—
820C22—2442no—
821C22#1684027012yes—
822C22C22×D4×D6111yescharacteristic
823C4—21no—
824C4—21no—
825C4—42no—
826C4—42no—
827C4—42no—
828C4—42no—
829C4—1224no—
830C4—1222no—
831C4—1222no—
832C4—1222no—
833C4—1222no—
834C4—2442no—
835C4—2442no—
836C4#1684027012yes—
837C4C2×#41×D6112yes—
838C2—22no—
839C2—41no—
840C2—41no—
841C2—2444no—
842C2C2×#1684027011yescharacteristic
843C2#2146060211yescharacteristic
844C2#2146060311yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3095C2
socleC22×C61C23×D4
prime radicalC22×#11758222C22
hypercenter#3095D61
hypocenterC61#60569
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3095

Complements

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

NH ≅ G/Ntype
1. C2×#16840372C2semidirect
3. #21456115C2semidirect
4. #21456067C2semidirect
5. #21456036C2semidirect
6. #21456028C2semidirect
7. #21455767C2semidirect
8. #21455640C2semidirect
9. #21455305C2semidirect
12. #21454637C2semidirect
13. #21454634C2semidirect
14. #21454454C2semidirect
15. C61×#3095C2semidirect
22. #16840372C22semidirect
23. C2×#14519775C22semidirect
27. C2×#14519768C22semidirect
41. C2×Q8×Dic61C22semidirect
42. C2×#14519742C22semidirect
46. #16840097C22semidirect
47. #16840092C22semidirect
48. #16840072C22semidirect
49. #16840068C22semidirect
50. #16840065C22semidirect
51. #16840061C22semidirect
52. #16839971C22semidirect
53. #16839971C22semidirect
54. #16839966C22semidirect
55. #16839966C22semidirect
62. #16839868C22semidirect
63. #16839866C22semidirect
64. #16839865C22semidirect
65. #16839861C22semidirect
66. #16839856C22semidirect
67. #16839854C22semidirect
68. #16839849C22semidirect
69. #16839847C22semidirect
71. #16839820C22semidirect
72. #16839805C22semidirect
73. #16839785C22semidirect
74. #16839770C22semidirect
78. M16×Dic61C22semidirect
82. C61×#484C22semidirect
83. C61×#483C22semidirect
84. C61×#428C22semidirect
85. C61×#419C22semidirect
423. #3095D61semidirect
472. #484C2×D61semidirect
474. #483C2×D61semidirect
500. #428C2×D61semidirect
503. #419C2×D61semidirect
509. C61#60569semidirect

Maximal subgroups

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

subgroupindex
C2×#168403722
#214590202
#214561152
#214560672
#214560362
#214560282
#214557672
#214556402
#214553052
#214550812
#214550772
#214546372
#214546342
#214544542
C61×#30952
#6056961