Finite Group Databasebeta

← #30548550

Subgroups — #30548550

Order 15616.

2010 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840373C211yesmaximal, characteristic, complemented
2#21459018C211yesmaximal, characteristic
3#21456117C214yesmaximal, complemented
4#21456069C214yesmaximal, complemented
5#21456032C214yesmaximal, complemented
6#21456030C214yesmaximal, complemented
7#21455765C212yesmaximal, complemented
8#21455642C211yesmaximal, characteristic, complemented
9#21455641C211yesmaximal, characteristic, complemented
10#21455302C211yesmaximal, characteristic, complemented
11#21455075C212yesmaximal
12#137×Dic61C212yesmaximal, complemented
13#21454634C212yesmaximal, complemented
14#21454456C211yesmaximal, characteristic, complemented
15C61×#3039C211yesmaximal, characteristic, complemented
16C2×#41×D61C2211yescharacteristic
17C2×#14519808C2212yes—
18#16840373—21no—
19#16840373—21no—
20#16840373—21no—
21#16840373—21no—
22#16840373C2214yes—
23#16840373C2214yescomplemented
24C2×#14519772—22no—
25C2×#14519769C2211yescharacteristic, complemented
26C2×#14519767—22no—
27C2×#14519753C2212yes—
28#16840244C2212yes—
29#16840241—22no—
30#16840241C2212yes—
31#16840238C2212yes—
32#16840234—22no—
33#16840234C2212yes—
34#41×Dic61C2211yescharacteristic
35C4×#11758222—21no—
36C4×#11758222C2211yescharacteristic
37#16840230—21no—
38#16840230C2211yescharacteristic
39C2×Q8×Dic61C2212yescomplemented
40C2×#14519734—21no—
41C2×#14519734C2211yescharacteristic
42#117×D61—21no—
43#117×D61C2211yescharacteristic
44#16840102C2214yes—
45#16840101C2214yes—
46#16840096C2214yescomplemented
47#16840091C2214yescomplemented
48#16840070C2214yescomplemented
49#16840069C2214yescomplemented
50#16840063C2214yescomplemented
51#16840062C2214yescomplemented
52#16839969C2214yescomplemented
53#16839964C2214yescomplemented
54#16839923C2214yes—
55#16839921C2214yes—
56#16839916C2214yes—
57#16839911C2214yes—
58#16839869C2214yescomplemented
59#16839866C2214yescomplemented
60#16839865C2214yescomplemented
61#16839863C2214yescomplemented
62Q16×Dic61C2214yescomplemented
63#16839854C2214yescomplemented
64SD16×Dic61C2214yescomplemented
65#16839847C2214yescomplemented
66#16839822C2214yes—
67#16839822C2214yescomplemented
68#16839805C2212yescomplemented
69#16839804C2212yescomplemented
70#16839786C2211yescharacteristic, complemented
71#16839771C2212yescomplemented
72#16839764C2212yes—
73#16839763C2212yes—
74#16839725C2212yes—
75M16×Dic61C2212yescomplemented
76C2×#137×C61C2212yes—
77C2×C4⋊Q8×C61C2211yescharacteristic, complemented
78C4×#41×C61C2211yescharacteristic
79C61×#462C2214yescomplemented
80C61×#461C2214yescomplemented
81C61×#423C2211yescharacteristic, complemented
82C61×#419C2212yescomplemented
83C2×#11758226C2311yescharacteristic
84C2×#11758222—21no—
85C2×#11758222C2311yescharacteristic
86C2×#11758224—21no—
87C2×#11758224C2311yescharacteristic
88#41×D61—24no—
89#41×D61—24no—
90C2×Q8×D61C2311yescharacteristic
91C2×D4×D61—21no—
92C2×D4×D61C2311yescharacteristic
93C22×C4×D61—21no—
94C22×C4×D61C2311yescharacteristic
95#14519808—28no—
96C2×#11758202C2314yes—
97C2×#11758201C2314yes—
98C2×#11758194C2312yes—
99#14519772—24no—
100#14519772—24no—
101#14519772—24no—
102#14519772—24no—
103#14519769—21no—
104#14519769—21no—
105#14519769C2314yes—
106#14519767—24no—
107#14519767—24no—
108#14519767—24no—
109#14519767—24no—
110#14519753—22no—
111#14519753—22no—
112#14519753C2314yes—
113#14519753C2314yes—
114Q8×Dic61—22no—
115Q8×Dic61—22no—
116Q8×Dic61C2314yes—
117Q8×Dic61C2314yes—
118Q8×Dic61C2312yes—
119C4×Dic122—22no—
120C4×Dic122C2312yes—
121#14519742—22no—
122#14519742C2312yes—
123C4×D244—22no—
124C4×D244C2312yes—
125D4×Dic61—22no—
126D4×Dic61C2312yes—
127#14519739—22no—
128#14519739C2312yes—
129C4×C22⋊D61—22no—
130C4×C22⋊D61—22no—
131C4×C22⋊D61—22no—
132#14519737—22no—
133#14519737—22no—
134#14519737—22no—
135#14519736—21no—
136#14519736C2311yescharacteristic
137#14519735—22no—
138#14519735C2312yes—
139#14519734—21no—
140#14519734—21no—
141#14519734—22no—
142#14519734—22no—
143#14519734—21no—
144#14519734D411yescharacteristic
145#14519734D411yescharacteristic
146#14519734D411yescharacteristic
147#14519734D411yescharacteristic
148#14519734C2312yes—
149#14519734C2312yes—
150#14519733—21no—
151#14519733—22no—
152C2×C4⋊Dic61—22no—
153C2×C4⋊Dic61C2312yes—
154C2×#11758196—22no—
155C2×#11758196—22no—
156C2×#11758196—22no—
157C2×#11758196D412yes—
158C4⋊C4×D61—22no—
159C4⋊C4×D61C2312yes—
160C2×#11758198—22no—
161C2×#11758198—22no—
162C2×#11758198D412yes—
163C22⋊C4×D61—21no—
164C22⋊C4×D61—22no—
165C2×C4×Dic61—22no—
166C2×C4×Dic61—21no—
167C2×C4×Dic61C2311yescharacteristic
168C42×D61—21no—
169C42×D61—21no—
170C42×D61—21no—
171#14519711C2314yes—
172#14519710C2314yes—
173#14519709C2314yes—
174#14519708C2314yes—
175C4⋊#92418C2314yes—
176#14519702C2314yes—
177#14519701C2314yes—
178#14519701C2314yes—
179#14519701C2314yes—
180#14519699C2314yes—
181#14519698C2314yes—
182#14519689C2314yes—
183#14519689C2314yes—
184#14519687C2314yes—
185C8×Dic61C2314yes—
186C2×#41×C61C2311yescharacteristic
187C22×Q8×C61C2312yes—
188#137×C61—28no—
189C2×Q16×C61C2314yes—
190C2×SD16×C61C2314yes—
191C2×M16×C61C2312yes—
192C4⋊Q8×C61—21no—
193C4⋊Q8×C61—21no—
194C4⋊Q8×C61C2314yes—
195C4×Q8×C61C2312yes—
196C4×D4×C61—22no—
197C4×D4×C61C2312yes—
198#117×C61—21no—
199#117×C61C2311yescharacteristic
200C2×C4⋊C4×C61—22no—
201C2×C42×C61—21no—
202C2×C42×C61C2311yescharacteristic
203C4⋊C8×C61C2314yes—
204#103×C61C2314yes—
205#103×C61C2314yes—
206C23×D61—21no—
207C23×D61C2×D411yescharacteristic
208#41×C61—22no—
209#41×C61#4114yes—
210C2×Q8×C61—22no—
211C2×Q8×C61—24no—
212C2×Q8×C61—24no—
213C2×Q8×C61C2414yes—
214C2×Q8×C61C2411yescharacteristic
215C2×D4×C61—21no—
216C2×D4×C61C2411yescharacteristic
217C22×C4×C61—21no—
218C22×C4×C61—22no—
219C22×C4×C61—22no—
220C22×C4×C61C2×D412yes—
221C22×C4×C61C2411yescharacteristic
222C2×C22⋊D61—21no—
223C2×C22⋊D61—21no—
224C2×C22⋊D61—21no—
225C22×Dic61—21no—
226C22×Dic61—22no—
227C22×Dic61—22no—
228C22×Dic61C2×D411yescharacteristic
229C22×Dic61C2×D412yes—
230#11758226—22no—
231#11758226—22no—
232Q8×D61—22no—
233Q8×D61—22no—
234#11758224—28no—
235#11758224—22no—
236#11758224—22no—
237D4×D61—28no—
238D4×D61—22no—
239D4×D61—22no—
240#11758222—28no—
241#11758222—22no—
242#11758222#4114yes—
243C2×D244—21no—
244C2×D244C2411yescharacteristic
245C2×C4×D61—28no—
246C2×C4×D61—21no—
247C2×C4×D61—21no—
248C2×C4×D61—22no—
249C2×C4×D61—22no—
250C2×C4×D61—21no—
251C2×C4×D61—22no—
252C2×C4×D61—22no—
253C2×C4×D61—22no—
254C2×C4×D61C2×D411yescharacteristic
255C2×C4×D61C2×D411yescharacteristic
256C2×C4×D61C2411yescharacteristic
257C2×C4×D61C2411yescharacteristic
258C2×Dic122—21no—
259C2×Dic122C2411yescharacteristic
260Q16×C61—28no—
261SD16×C61—28no—
262M16×C61—24no—
263C2×C8×C61C2414yes—
264C4⋊C4×C61—24no—
265C4⋊C4×C61—24no—
266C4⋊C4×C61—22no—
267C4⋊C4×C61C2412yes—
268C22⋊C4×C61—21no—
269C22⋊C4×C61—22no—
270C42×C61—21no—
271C42×C61—22no—
272C42×C61C2×D411yescharacteristic
273C42×C61C2×D411yescharacteristic
274C42×C61C2412yes—
275C22⋊Dic61—21no—
276C22⋊Dic61—22no—
277#11758202—28no—
278#11758201—28no—
279#11758198—22no—
280#11758198—24no—
281#11758198—24no—
282#11758198—22no—
283#11758198—22no—
284#11758198C2×D412yes—
285#11758198C2×D412yes—
286#11758198C2×D412yes—
287#11758198C2×D412yes—
288C4⋊Dic61—22no—
289C4⋊Dic61—22no—
290C4⋊Dic61—24no—
291C4⋊Dic61—24no—
292C4⋊Dic61C2414yes—
293C4⋊Dic61C2412yes—
294#11758196—22no—
295#11758196—24no—
296#11758196—24no—
297#11758196—22no—
298#11758196—22no—
299#11758196—24no—
300#11758196—24no—
301#11758196C2×D412yes—
302#11758196C2×D412yes—
303#11758196C2×D412yes—
304#11758196C2×D412yes—
305C4×Dic61—21no—
306C4×Dic61—22no—
307C4×Dic61—22no—
308C4×Dic61—22no—
309C4×Dic61—22no—
310C4×Dic61—24no—
311C4×Dic61—24no—
312C4×Dic61C2×D411yescharacteristic
313C4×Dic61C2×D411yescharacteristic
314C4×Dic61C2412yes—
315#11758194—24no—
316C2×#92418C2414yes—
317C23×C61—21no—
318C23×C61C22×D411yescharacteristic
319C22×D61—21no—
320C22×D61—24no—
321C22×D61—22no—
322C22×D61—42no—
323C22×D61—82no—
324C22×D61C22×D411yescharacteristic
325C22×D61C22×D411yescharacteristic
326Q8×C61—21no—
327Q8×C61—24no—
328Q8×C61—24no—
329Q8×C61—44no—
330Q8×C61C2×#4112yes—
331D4×C61—24no—
332D4×C61—21no—
333D4×C61C2×#4112yes—
334C2×C4×C61—21no—
335C2×C4×C61—24no—
336C2×C4×C61—24no—
337C2×C4×C61—22no—
338C2×C4×C61—42no—
339C2×C4×C61—44no—
340C2×C4×C61—82no—
341C2×C4×C61C22×D412yes—
342C2×C4×C61C22×D412yes—
343C2×C4×C61C22×D411yescharacteristic
344C2×C4×C61C2×#4112yes—
345C2×C4×C61C2×#4112yes—
346C2×C4×C61C2511yescharacteristic
347C22⋊D61—24no—
348C22⋊D61—24no—
349C22⋊D61—24no—
350C2×Dic61—24no—
351C2×Dic61—22no—
352C2×Dic61—21no—
353C2×Dic61—22no—
354C2×Dic61—24no—
355C2×Dic61—42no—
356C2×Dic61—44no—
357C2×Dic61—82no—
358C2×Dic61C22×D412yes—
359C2×Dic61C22×D412yes—
360C2×Dic61C22×D411yescharacteristic
361C2×Dic61C22×D411yescharacteristic
362D244—24no—
363D244—21no—
364D244C2×#4112yes—
365C4×D61—24no—
366C4×D61—24no—
367C4×D61—22no—
368C4×D61—24no—
369C4×D61—22no—
370C4×D61—21no—
371C4×D61—21no—
372C4×D61—21no—
373C4×D61—21no—
374C4×D61—82no—
375C4×D61—82no—
376C4×D61—82no—
377Dic122—24no—
378Dic122—21no—
379Dic122C2×#4112yes—
380C8×C61—24no—
381#92418—24no—
382#60569—611nomaximal, Sylow
383C22×C61—22no—
384C22×C61—22no—
385C22×C61—42no—
386C22×C61#52512yes—
387C22×C61C23×D411yescharacteristic
388C2×D61—22no—
389C2×D61—22no—
390C2×D61—21no—
391C2×D61—21no—
392C2×D61—22no—
393C2×D61—42no—
394C2×D61—82no—
395C2×D61—84no—
396C4×C61—22no—
397C4×C61—22no—
398C4×C61—22no—
399C4×C61—42no—
400C4×C61—44no—
401C4×C61#52512yes—
402C4×C61C22×#4111yescharacteristic
403C4×C61C22×#4111yescharacteristic
404Dic61—22no—
405Dic61—22no—
406Dic61—21no—
407Dic61—22no—
408Dic61—21no—
409Dic61—42no—
410Dic61—44no—
411C2×#541—611no—
412#3428—611no—
413#3127—614no—
414#3123—614no—
415#3120—614no—
416#3120—614no—
417#3095—612no—
418#3080—611no—
419#3080—611no—
420#3039—611no—
421#3039D6111yescharacteristic, complemented
422#3007—612no—
423C4×#137—612no—
424C4×#137—612no—
425#2921—611no—
426C2×C61—22no—
427C2×C61—42no—
428C2×C61C2×#52511yescharacteristic
429C2×C61#358612yes—
430D61—41no—
431D61—41no—
432D61—42no—
433C22×#41—611no—
434C2×#137—612no—
435C2×#137C2×D6112yes—
436#541—614no—
437#541—614no—
438#541—1221no—
439#541—1221no—
440#541—1221no—
441#541—1221no—
442C2×C4⋊Q8C2×D6111yescharacteristic, complemented
443C2×#126—1222no—
444C2×#125—611no—
445C2×#125—1222no—
446C2×C22⋊Q8—612no—
447#520—612no—
448#520—612no—
449#520—1222no—
450#519—612no—
451#518—612no—
452#518—1222no—
453C4×#41—611no—
454C4×#41—611no—
455C4×#41—611no—
456C4×#41—1221no—
457C4×#41—1221no—
458C4×#41C2×D6111yescharacteristic
459C2×C4×Q8—612no—
460C2×#117—611no—
461C2×#117—611no—
462C2×#117—1221no—
463C2×#117—1221no—
464#485—614no—
465#485—614no—
466#484—614no—
467#483—614no—
468#479—614no—
469#479—614no—
470#478—614no—
471#478—614no—
472#462—614no—
473#462C2×D6114yescomplemented
474#461—614no—
475#461C2×D6114yescomplemented
476#452—614no—
477#452—614no—
478#451—614no—
479#450—614no—
480#441—614no—
481#441—614no—
482#440—614no—
483#440—614no—
484C4×Q16—614no—
485C4×Q16—614no—
486C4×SD16—614no—
487C4×SD16—614no—
488#433—614no—
489#433—614no—
490#428—612no—
491#428—612no—
492#423—611no—
493#423C2×D6111yescharacteristic, complemented
494#419—612no—
495#419C2×D6112yescomplemented
496#417—612no—
497#417—612no—
498#407—612no—
499C4×M16—612no—
500C61#6056911yescharacteristic, complemented, Sylow
501C2×#41—611no—
502C2×#41—611no—
503C2×#41—611no—
504C2×#41—1221no—
505C2×#41—1221no—
506C2×#41—1224no—
507C2×#41—1224no—
508C2×#41C22×D6111yescharacteristic
509C22×Q8—611no—
510C22×Q8C22×D6112yes—
511C22×D4—611no—
512C22×D4—1221no—
513C23×C4—611no—
514C23×C4—1221no—
515#137—28no—
516#137—1228no—
517C2×Q16—614no—
518C2×Q16C22×D6114yes—
519C2×SD16—614no—
520C2×SD16C22×D6114yes—
521C2×M16—612no—
522C2×M16C22×D6112yes—
523C4⋊Q8—21no—
524C4⋊Q8—21no—
525C4⋊Q8C22×D6114yes—
526#126—1224no—
527#126—1224no—
528#126—1224no—
529#126—1224no—
530#125—614no—
531#125—1224no—
532#125—1224no—
533#125—1224no—
534#125—1224no—
535#125—1221no—
536#125—1221no—
537C22⋊Q8—614no—
538C22⋊Q8—614no—
539C22⋊Q8—1222no—
540C22⋊Q8—1222no—
541C4×Q8—614no—
542C4×Q8—614no—
543C4×Q8—612no—
544C4×Q8—612no—
545C4×Q8—612no—
546C4×Q8—1222no—
547C4×Q8—1222no—
548C4×Q8—1222no—
549C4×Q8—1222no—
550C4×Q8C22×D6112yes—
551C4×D4—22no—
552C4×D4—612no—
553C4×D4—612no—
554C4×D4—612no—
555C4×D4—1222no—
556C4×D4—1222no—
557C4×D4—1222no—
558C4×D4—1222no—
559C4×D4—1222no—
560C4×D4—1222no—
561C4×D4—1222no—
562C4×D4—1222no—
563C4×D4—1222no—
564C4×D4C22×D6112yes—
565#117—21no—
566#117—611no—
567#117—611no—
568#117—611no—
569#117—611no—
570#117—612no—
571#117—612no—
572#117—611no—
573#117—612no—
574#117—1221no—
575#117—1222no—
576#117—1222no—
577#117—1221no—
578#117—1221no—
579#117—1222no—
580#117—1221no—
581#117—1222no—
582#117—1221no—
583#117C22×D6111yescharacteristic
584C2×C4⋊C4—22no—
585C2×C4⋊C4—612no—
586C2×C4⋊C4—612no—
587C2×C4⋊C4—612no—
588C2×C4⋊C4—1222no—
589C2×C4⋊C4—1222no—
590C2×C4⋊C4—1222no—
591C2×C4⋊C4—1222no—
592C2×C4⋊C4—1222no—
593C2×C22⋊C4—612no—
594C2×C22⋊C4—1222no—
595C2×C22⋊C4—1221no—
596C2×C22⋊C4—1222no—
597C2×C22⋊C4—1222no—
598C2×C42—21no—
599C2×C42—611no—
600C2×C42—1221no—
601C2×C42—1221no—
602C2×C42—1221no—
603C2×C42—1222no—
604C2×C42—1221no—
605C2×C42C22×D6111yescharacteristic
606#107—614no—
607#107—614no—
608#106—614no—
609#106—614no—
610C4⋊C8—614no—
611C4⋊C8C22×D6114yes—
612#103—614no—
613#103—614no—
614#103—614no—
615#103—614no—
616#103C22×D6114yes—
617#103C22×D6114yes—
618#102—614no—
619#102—614no—
620C22⋊C8—614no—
621C22⋊C8—614no—
622#97—614no—
623C4×C8—614no—
624C24—611no—
625C24—1221no—
626#41—22no—
627#41—614no—
628#41—1228no—
629#41—1222no—
630#41—1228no—
631#41—1222no—
632#41—1222no—
633#41—1222no—
634#41—1222no—
635#41#1175822414yes—
636C2×Q8—22no—
637C2×Q8—24no—
638C2×Q8—24no—
639C2×Q8—611no—
640C2×Q8—1221no—
641C2×Q8—1222no—
642C2×Q8—1222no—
643C2×Q8C23×D6114yes—
644C2×Q8C23×D6111yescharacteristic
645C2×D4—21no—
646C2×D4—611no—
647C2×D4—1221no—
648C2×D4—1221no—
649C2×D4—1222no—
650C2×D4—1228no—
651C2×D4—1221no—
652C2×D4—1221no—
653C2×D4—1222no—
654C2×D4C23×D6111yescharacteristic
655C22×C4—21no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—611no—
659C22×C4—612no—
660C22×C4—611no—
661C22×C4—611no—
662C22×C4—611no—
663C22×C4—611no—
664C22×C4—1221no—
665C22×C4—1222no—
666C22×C4—1221no—
667C22×C4—1228no—
668C22×C4—1222no—
669C22×C4—1221no—
670C22×C4—1222no—
671C22×C4—1221no—
672C22×C4—1222no—
673C22×C4—1222no—
674C22×C4—1222no—
675C22×C4—1222no—
676C22×C4D4×D6112yes—
677C22×C4C23×D6111yescharacteristic
678Q16—28no—
679Q16—1228no—
680SD16—28no—
681SD16—1228no—
682M16—24no—
683M16—1224no—
684C2×C8—614no—
685C2×C8C23×D6114yes—
686C4⋊C4—24no—
687C4⋊C4—24no—
688C4⋊C4—22no—
689C4⋊C4—612no—
690C4⋊C4—612no—
691C4⋊C4—612no—
692C4⋊C4—612no—
693C4⋊C4—614no—
694C4⋊C4—612no—
695C4⋊C4—1222no—
696C4⋊C4—1222no—
697C4⋊C4—1224no—
698C4⋊C4—1224no—
699C4⋊C4—1222no—
700C4⋊C4—1224no—
701C4⋊C4—1224no—
702C4⋊C4—1222no—
703C4⋊C4—1222no—
704C4⋊C4—1224no—
705C4⋊C4—1224no—
706C4⋊C4C23×D6112yes—
707C22⋊C4—21no—
708C22⋊C4—22no—
709C22⋊C4—612no—
710C22⋊C4—612no—
711C22⋊C4—612no—
712C22⋊C4—612no—
713C22⋊C4—1222no—
714C22⋊C4—1222no—
715C22⋊C4—1224no—
716C22⋊C4—1224no—
717C22⋊C4—1222no—
718C22⋊C4—1221no—
719C22⋊C4—1222no—
720C42—21no—
721C42—22no—
722C42—611no—
723C42—611no—
724C42—612no—
725C42—1222no—
726C42—1222no—
727C42—1222no—
728C42—1224no—
729C42—1224no—
730C42—1221no—
731C42—1222no—
732C42D4×D6111yescharacteristic
733C42D4×D6111yescharacteristic
734C42C23×D6112yes—
735C23—21no—
736C23—611no—
737C23—611no—
738C23—1224no—
739C23—1222no—
740C23—1221no—
741C23—4882no—
742C23—2442no—
743C23C2×D4×D6111yescharacteristic
744Q8—21no—
745Q8—24no—
746Q8—24no—
747Q8—44no—
748Q8—612no—
749Q8—1224no—
750Q8—1221no—
751Q8C2×#1175822412yes—
752D4—24no—
753D4—21no—
754D4—612no—
755D4—1224no—
756D4—1224no—
757D4—1224no—
758D4—1224no—
759D4—1221no—
760D4C2×#1175822412yes—
761C2×C4—21no—
762C2×C4—24no—
763C2×C4—22no—
764C2×C4—24no—
765C2×C4—42no—
766C2×C4—44no—
767C2×C4—82no—
768C2×C4—612no—
769C2×C4—612no—
770C2×C4—611no—
771C2×C4—611no—
772C2×C4—1224no—
773C2×C4—1224no—
774C2×C4—1224no—
775C2×C4—1222no—
776C2×C4—1221no—
777C2×C4—1222no—
778C2×C4—1222no—
779C2×C4—1224no—
780C2×C4—1221no—
781C2×C4—1221no—
782C2×C4—1221no—
783C2×C4—1221no—
784C2×C4—1222no—
785C2×C4—1224no—
786C2×C4—4882no—
787C2×C4—4882no—
788C2×C4—4882no—
789C2×C4—4882no—
790C2×C4—2442no—
791C2×C4—2444no—
792C2×C4C2×D4×D6112yes—
793C2×C4C2×D4×D6112yes—
794C2×C4C2×D4×D6111yescharacteristic
795C2×C4#41×D6112yes—
796C2×C4C2×#1175822412yes—
797C2×C4C24×D6111yescharacteristic
798C8—24no—
799C8—1224no—
800C22—22no—
801C22—22no—
802C22—42no—
803C22—1221no—
804C22—1222no—
805C22—1221no—
806C22—1222no—
807C22—1222no—
808C22—4882no—
809C22—4884no—
810C22—2442no—
811C22#1684027212yes—
812C22C22×D4×D6111yescharacteristic
813C4—22no—
814C4—22no—
815C4—22no—
816C4—44no—
817C4—42no—
818C4—1221no—
819C4—1221no—
820C4—1222no—
821C4—1222no—
822C4—1222no—
823C4—2442no—
824C4—2444no—
825C4#1684027212yes—
826C4C2×#41×D6111yescharacteristic
827C4C22×#1175822411yescharacteristic
828C2—22no—
829C2—42no—
830C2—2441no—
831C2—2441no—
832C2—2442no—
833C2C2×#1684027211yescharacteristic
834C2#2146060212yes—
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3039C2
socleC22×C61C23×D4
prime radicalC2×#41×D61C22
hypercenter#3039D61
hypocenterC61#60569
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3039

Complements

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

NH ≅ G/Ntype
1. C2×#16840373C2semidirect
3. #21456117C2semidirect
4. #21456069C2semidirect
5. #21456032C2semidirect
6. #21456030C2semidirect
7. #21455765C2semidirect
8. #21455642C2semidirect
9. #21455641C2semidirect
10. #21455302C2semidirect
12. #137×Dic61C2semidirect
13. #21454634C2semidirect
14. #21454456C2semidirect
15. C61×#3039C2semidirect
23. #16840373C22semidirect
25. C2×#14519769C22semidirect
39. C2×Q8×Dic61C22semidirect
46. #16840096C22semidirect
47. #16840091C22semidirect
48. #16840070C22semidirect
49. #16840069C22semidirect
50. #16840063C22semidirect
51. #16840062C22semidirect
52. #16839969C22semidirect
53. #16839964C22semidirect
58. #16839869C22semidirect
59. #16839866C22semidirect
60. #16839865C22semidirect
61. #16839863C22semidirect
62. Q16×Dic61C22semidirect
63. #16839854C22semidirect
64. SD16×Dic61C22semidirect
65. #16839847C22semidirect
67. #16839822C22semidirect
68. #16839805C22semidirect
69. #16839804C22semidirect
70. #16839786C22semidirect
71. #16839771C22semidirect
75. M16×Dic61C22semidirect
77. C2×C4⋊Q8×C61C22semidirect
79. C61×#462C22semidirect
80. C61×#461C22semidirect
81. C61×#423C22semidirect
82. C61×#419C22semidirect
421. #3039D61semidirect
442. C2×C4⋊Q8C2×D61semidirect
473. #462C2×D61semidirect
475. #461C2×D61semidirect
493. #423C2×D61semidirect
495. #419C2×D61semidirect
500. C61#60569semidirect

Maximal subgroups

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

subgroupindex
C2×#168403732
#214590182
#214561172
#214560692
#214560322
#214560302
#214557652
#214556422
#214556412
#214553022
#214550752
#137×Dic612
#214546342
#214544562
C61×#30392
#6056961