Finite Group Databasebeta

← #30547560

Subgroups — #30547560

Order 15616.

2130 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840318C211yesmaximal, characteristic, complemented
2C4×#41×D61C211yesmaximal, characteristic
3#21455642C211yesmaximal, characteristic, complemented
4#21455641C211yesmaximal, characteristic, complemented
5#21455637C211yesmaximal, characteristic, complemented
6#21455632C212yesmaximal, complemented
7#21455630C212yesmaximal, complemented
8#21455622C214yesmaximal, complemented
9#21455614C214yesmaximal, complemented
10#21455606C214yesmaximal, complemented
11#21455604C214yesmaximal, complemented
12#21454406C212yesmaximal, complemented
13#423×D61C211yesmaximal, characteristic, complemented
14#21454335C212yesmaximal
15C61×#3080C211yesmaximal, characteristic, complemented
16C2×#41×D61C2211yescharacteristic
17C2×M16×D61C2212yes—
18#16840318—21no—
19#16840318—21no—
20#16840318—21no—
21#16840318—21no—
22#16840318C2214yes—
23#16840318C2214yescomplemented
24C2×#14519776C2212yescomplemented
25C2×#14519769C2211yescharacteristic, complemented
26C2×#14519755—22no—
27#41×Dic61C2211yescharacteristic
28C4×#11758226C2212yes—
29C4×#11758222—21no—
30C4×#11758222C2211yescharacteristic
31#16840230—21no—
32#16840230C2211yescharacteristic
33C4×#11758224—22no—
34C4×#11758224C2212yes—
35C2×#14519742—22no—
36C4×Q8×D61C2212yes—
37C4×D4×D61—22no—
38C4×D4×D61C2212yes—
39C2×#14519735C2212yes—
40#117×D61—21no—
41#117×D61C2211yescharacteristic
42C2×C42×D61—21no—
43C2×C42×D61C2211yescharacteristic
44#16840070C2214yescomplemented
45#16840069C2214yescomplemented
46#16840066C2214yescomplemented
47#16840063C2214yescomplemented
48#16840062C2214yescomplemented
49#16840059C2214yescomplemented
50#16840056C2214yescomplemented
51#16840055C2214yescomplemented
52#16840051C2214yescomplemented
53#16840050C2214yescomplemented
54#16840046C2214yescomplemented
55#16840045C2214yescomplemented
56#16840041C2214yescomplemented
57#16840040C2214yescomplemented
58#16839805C2212yescomplemented
59#16839804C2212yescomplemented
60#16839803C2214yes—
61#16839802C2212yescomplemented
62#16839801C2214yes—
63#16839799C2214yescomplemented
64#16839797C2214yescomplemented
65#16839786C2211yescharacteristic, complemented
66#16839785C2212yescomplemented
67#16839784C2214yes—
68C4⋊C8×D61C2214yescomplemented
69#16839769C2214yes—
70#16839765C2214yes—
71#16839764C2212yes—
72#16839763C2212yes—
73#16839761C2212yes—
74#16839757C2214yes—
75#16839755C2214yes—
76C2×#125×C61C2211yescharacteristic, complemented
77C4×#41×C61C2211yescharacteristic
78C61×#479C2214yescomplemented
79C61×#478C2214yescomplemented
80C61×#428C2212yescomplemented
81C61×#423C2211yescharacteristic, complemented
82C61×#417C2212yes—
83C2×#11758226C2311yescharacteristic
84C2×#11758222—21no—
85C2×#11758222C2311yescharacteristic
86C2×#11758224—21no—
87C2×#11758224C2311yescharacteristic
88#41×D61—24no—
89#41×D61Q818yescomplemented
90C22×Dic122—22no—
91C2×Q8×D61C2311yescharacteristic
92C2×D4×D61—21no—
93C2×D4×D61C2311yescharacteristic
94C22×C4×D61—21no—
95C22×C4×D61—22no—
96C22×C4×D61D412yes—
97C22×C4×D61C2311yescharacteristic
98C2×#11758194C2312yes—
99C2×#11758189C2314yes—
100M16×D61—28no—
101C2×C8×D61C2314yes—
102#14519776—22no—
103#14519776—22no—
104#14519776C2314yes—
105#14519776C2314yes—
106#14519769—21no—
107#14519769—21no—
108#14519769C2314yes—
109#14519755—24no—
110#14519755—24no—
111#14519755—24no—
112#14519755—24no—
113Q8×Dic61C2312yes—
114C4×Dic122—22no—
115C4×Dic122C2312yes—
116#14519742—22no—
117#14519742—24no—
118#14519742—24no—
119#14519742—24no—
120#14519742—24no—
121#14519742C2312yes—
122C4×D244—22no—
123C4×D244C2312yes—
124D4×Dic61—22no—
125D4×Dic61C2312yes—
126#14519739—22no—
127#14519739C2312yes—
128C4×C22⋊D61—22no—
129C4×C22⋊D61—22no—
130C4×C22⋊D61—22no—
131#14519737—22no—
132#14519737—22no—
133#14519737—22no—
134#14519736—21no—
135#14519736C2311yescharacteristic
136#14519735—22no—
137#14519735—22no—
138#14519735—22no—
139#14519735C2312yes—
140#14519735C2314yes—
141#14519735C2314yes—
142#14519734—21no—
143#14519734—21no—
144#14519734—21no—
145#14519733—21no—
146#14519733—22no—
147C2×C4⋊Dic61C2312yes—
148C2×#11758196—22no—
149C2×#11758196—22no—
150C4⋊C4×D61—22no—
151C4⋊C4×D61C2312yes—
152C2×#11758198—22no—
153C22⋊C4×D61—21no—
154C22⋊C4×D61—22no—
155C2×C4×Dic61—22no—
156C2×C4×Dic61—22no—
157C2×C4×Dic61—21no—
158C2×C4×Dic61D412yes—
159C2×C4×Dic61C2311yescharacteristic
160C42×D61—21no—
161C42×D61—22no—
162C42×D61—21no—
163C42×D61—22no—
164C42×D61—21no—
165C42×D61D411yescharacteristic
166C42×D61D411yescharacteristic
167C42×D61D411yescharacteristic
168C42×D61D411yescharacteristic
169C42×D61C2312yes—
170C42×D61C2312yes—
171#14519711C2314yes—
172#14519710C2314yes—
173#14519710C2314yes—
174#14519709C2314yes—
175#14519708C2314yes—
176#14519708C2314yes—
177C4⋊#92418C2314yes—
178#14519706C2314yes—
179#14519706C2314yes—
180#14519702C2314yes—
181#14519701C2314yes—
182#14519700C2314yes—
183#14519699C2314yes—
184#14519698C2314yes—
185#14519697C2314yes—
186C2×#41×C61C2311yescharacteristic
187C2×M16×C61C2312yes—
188#125×C61—21no—
189#125×C61—21no—
190#125×C61C2314yes—
191C4×Q8×C61C2312yes—
192C4×D4×C61—22no—
193C4×D4×C61C2312yes—
194#117×C61—21no—
195#117×C61C2311yescharacteristic
196C2×C4⋊C4×C61—22no—
197C2×C4⋊C4×C61C2312yes—
198C2×C42×C61—21no—
199C2×C42×C61C2311yescharacteristic
200#107×C61C2314yes—
201#106×C61C2314yes—
202C4⋊C8×C61C2314yes—
203#103×C61C2314yes—
204#102×C61C2314yes—
205C23×D61—21no—
206C23×D61C2×D411yescharacteristic
207#41×C61—22no—
208#41×C61C2×Q814yes—
209C2×Q8×C61C2411yescharacteristic
210C2×D4×C61—21no—
211C2×D4×C61C2411yescharacteristic
212C22×C4×C61—21no—
213C22×C4×C61—22no—
214C22×C4×C61—22no—
215C22×C4×C61C2×D412yes—
216C22×C4×C61C2411yescharacteristic
217C2×C22⋊D61—21no—
218C2×C22⋊D61—21no—
219C2×C22⋊D61—21no—
220C22×Dic61—21no—
221C22×Dic61—22no—
222C22×Dic61—22no—
223C22×Dic61C2×D412yes—
224C22×Dic61C2×D411yescharacteristic
225#11758226—22no—
226#11758226C2×Q814yescomplemented
227Q8×D61—22no—
228Q8×D61C2×Q814yescomplemented
229#11758224—28no—
230#11758224—22no—
231#11758224C2×Q814yescomplemented
232D4×D61—28no—
233D4×D61—22no—
234D4×D61C2×Q814yescomplemented
235#11758222—22no—
236#11758222—28no—
237#11758222C2×Q814yes—
238C2×D244—21no—
239C2×D244C2411yescharacteristic
240C2×C4×D61—21no—
241C2×C4×D61—21no—
242C2×C4×D61—21no—
243C2×C4×D61—28no—
244C2×C4×D61—22no—
245C2×C4×D61—22no—
246C2×C4×D61—22no—
247C2×C4×D61—44no—
248C2×C4×D61—48no—
249C2×C4×D61C2×D412yes—
250C2×C4×D61C2×D412yes—
251C2×C4×D61C2×D412yes—
252C2×C4×D61C2×D412yes—
253C2×C4×D61C2×D411yescharacteristic
254C2×C4×D61C2×D411yescharacteristic
255C2×C4×D61C2×Q814yes—
256C2×C4×D61#4114yes—
257C2×C4×D61C2411yescharacteristic
258C2×C4×D61C2411yescharacteristic
259C2×Dic122—21no—
260C2×Dic122—24no—
261C2×Dic122—24no—
262C2×Dic122—48no—
263C2×Dic122C2411yescharacteristic
264M16×C61—24no—
265C2×C8×C61C2414yes—
266C4⋊C4×C61—24no—
267C4⋊C4×C61—24no—
268C4⋊C4×C61—22no—
269C4⋊C4×C61—22no—
270C4⋊C4×C61C2414yes—
271C4⋊C4×C61C2412yes—
272C22⋊C4×C61—21no—
273C22⋊C4×C61—22no—
274C42×C61—21no—
275C42×C61—22no—
276C42×C61C2×D411yescharacteristic
277C42×C61C2×D411yescharacteristic
278C42×C61C2412yes—
279C22⋊Dic61—21no—
280C22⋊Dic61—22no—
281#11758198—22no—
282#11758198—24no—
283#11758198—24no—
284#11758198—22no—
285#11758198—22no—
286C4⋊Dic61—22no—
287C4⋊Dic61—22no—
288C4⋊Dic61C2414yes—
289C4⋊Dic61C2412yes—
290#11758196—22no—
291#11758196—24no—
292#11758196—24no—
293#11758196—22no—
294#11758196—22no—
295#11758196—24no—
296#11758196—24no—
297C4×Dic61—21no—
298C4×Dic61—22no—
299C4×Dic61—22no—
300C4×Dic61—22no—
301C4×Dic61—22no—
302C4×Dic61—24no—
303C4×Dic61—24no—
304C4×Dic61C2×D411yescharacteristic
305C4×Dic61C2×D412yes—
306C4×Dic61C2×D411yescharacteristic
307C4×Dic61C2×D412yes—
308C4×Dic61C2×D412yes—
309C4×Dic61C2×D412yes—
310C4×Dic61C2412yes—
311#11758194—24no—
312C2×#92418C2414yes—
313#11758189—28no—
314C8×D61—28no—
315C23×C61—21no—
316C23×C61C22×D411yescharacteristic
317C22×D61—21no—
318C22×D61—24no—
319C22×D61—42no—
320C22×D61—44no—
321C22×D61C22⋊Q814yes—
322C22×D61C22×D411yescharacteristic
323C22×D61C22×D411yescharacteristic
324Q8×C61—21no—
325Q8×C61C22×Q812yes—
326D4×C61—24no—
327D4×C61—21no—
328D4×C61C22×Q812yes—
329C2×C4×C61—21no—
330C2×C4×C61—24no—
331C2×C4×C61—22no—
332C2×C4×C61—24no—
333C2×C4×C61—42no—
334C2×C4×C61—44no—
335C2×C4×C61—44no—
336C2×C4×C61C22×D412yes—
337C2×C4×C61C22×D412yes—
338C2×C4×C61C22×D411yescharacteristic
339C2×C4×C61C22×Q812yes—
340C2×C4×C61C2×#4112yes—
341C2×C4×C61C2511yescharacteristic
342C22⋊D61—24no—
343C22⋊D61—24no—
344C22⋊D61—24no—
345C2×Dic61—21no—
346C2×Dic61—24no—
347C2×Dic61—24no—
348C2×Dic61—22no—
349C2×Dic61—24no—
350C2×Dic61—44no—
351C2×Dic61—44no—
352C2×Dic61C22⋊Q814yes—
353C2×Dic61C22×D412yes—
354C2×Dic61C22×D411yescharacteristic
355C2×Dic61C22×D411yescharacteristic
356C2×Dic61C22×D412yes—
357D244—24no—
358D244—21no—
359D244C22×Q812yes—
360C4×D61—24no—
361C4×D61—24no—
362C4×D61—24no—
363C4×D61—24no—
364C4×D61—24no—
365C4×D61—42no—
366C4×D61—42no—
367C4×D61—44no—
368C4×D61—44no—
369C4×D61—44no—
370C4×D61C22⋊Q814yes—
371C4×D61C22⋊Q814yes—
372C4×D61C22×Q812yes—
373C4×D61C22×Q812yes—
374C4×D61C2×#4112yes—
375C4×D61C2×#4112yes—
376Dic122—21no—
377Dic122—24no—
378Dic122—48no—
379Dic122—48no—
380Dic122C22×Q812yes—
381C8×C61—24no—
382#92418—24no—
383#60484—611nomaximal, Sylow
384C22×C61—22no—
385C22×C61—22no—
386C22×C61—42no—
387C22×C61C2×C22⋊Q812yes—
388C22×C61C23×D411yescharacteristic
389C2×D61—22no—
390C2×D61—22no—
391C2×D61—22no—
392C2×D61—44no—
393C2×D61—48no—
394C2×D61—42no—
395C2×D61C2×C22⋊Q812yes—
396C2×D61C2×C22⋊Q812yes—
397C4×C61—22no—
398C4×C61—22no—
399C4×C61—22no—
400C4×C61—44no—
401C4×C61—42no—
402C4×C61C2×C22⋊Q812yes—
403C4×C61C23×Q811yescharacteristic
404C4×C61C22×#4111yescharacteristic
405Dic61—22no—
406Dic61—22no—
407Dic61—44no—
408Dic61—42no—
409Dic61C2×C22⋊Q812yes—
410Dic61C2×C22⋊Q812yes—
411Dic61#57514yes—
412C2×#533—611no—
413C2×C4×#41—611no—
414#3080—611no—
415#3080—611no—
416#3080—611no—
417#3080D6111yescharacteristic, complemented
418#3079—612no—
419#3079—612no—
420#3078—614no—
421#3077—614no—
422#3076—614no—
423#3076—614no—
424#2911—612no—
425C2×#423—611no—
426#2896—612no—
427C2×C61—22no—
428C2×C61—42no—
429C2×C61C22×C22⋊Q811yescharacteristic
430C2×C61C2×#57512yes—
431D61—22no—
432D61—22no—
433D61—42no—
434C22×#41—611no—
435C22×M16—612no—
436#533—614no—
437#533—614no—
438#533—1221no—
439#533—1221no—
440#533—1221no—
441#533—1221no—
442C2×C4⋊Q8—612no—
443C2×#125—611no—
444C2×#125C2×D6111yescharacteristic, complemented
445C2×C22⋊Q8—1222no—
446C4×#41—611no—
447C4×#41—612no—
448C4×#41—612no—
449C4×#41—611no—
450C4×#41—611no—
451C4×#41—1221no—
452C4×#41—1221no—
453C4×#41—1222no—
454C4×#41C2×D6111yescharacteristic
455C2×C4×Q8—612no—
456C2×C4×Q8—1222no—
457C2×C4×D4—612no—
458C2×C4×D4—1222no—
459C2×#117—611no—
460C2×#117—612no—
461C2×#117—1221no—
462C22×C42—611no—
463C22×C42—1221no—
464#479—614no—
465#479—614no—
466#479—614no—
467#479C2×D6114yescomplemented
468#478—614no—
469#478—614no—
470#478—614no—
471#478C2×D6114yescomplemented
472#477—614no—
473#477—614no—
474#476—614no—
475#476—614no—
476#475—614no—
477#475—614no—
478#474—614no—
479#474—614no—
480#428—612no—
481#428—612no—
482#428—612no—
483#428—614no—
484#428—614no—
485#428C2×D6112yescomplemented
486#427—614no—
487#427—614no—
488#423—612no—
489#423—611no—
490#423—614no—
491#423C2×D6111yescharacteristic, complemented
492C2×C4⋊C8—614no—
493#419—614no—
494#418—614no—
495#417—612no—
496#417—612no—
497#417—612no—
498#417C2×D6112yes—
499#416—614no—
500#416—614no—
501C61#6048411yescharacteristic, complemented, Sylow
502C2×#41—618no—
503C2×#41—611no—
504C2×#41—611no—
505C2×#41—611no—
506C2×#41—1221no—
507C2×#41—1221no—
508C2×#41—1224no—
509C2×#41C22×D6111yescharacteristic
510C22×Q8—611no—
511C22×Q8—1222no—
512C22×D4—611no—
513C22×D4—1221no—
514C23×C4—611no—
515C23×C4—612no—
516C23×C4—1221no—
517C23×C4—1222no—
518C2×M16—612no—
519C2×M16—614no—
520C2×M16—1228no—
521C2×M16C22×D6112yes—
522C22×C8—614no—
523C4⋊Q8—614no—
524C4⋊Q8—614no—
525C4⋊Q8—1222no—
526C4⋊Q8—1222no—
527#125—21no—
528#125—21no—
529#125—614no—
530#125—1221no—
531#125—1221no—
532#125C22×D6114yes—
533C22⋊Q8—1224no—
534C22⋊Q8—1224no—
535C22⋊Q8—1224no—
536C22⋊Q8—1224no—
537C4×Q8—612no—
538C4×Q8—612no—
539C4×Q8—612no—
540C4×Q8—1222no—
541C4×Q8—1222no—
542C4×Q8—1224no—
543C4×Q8—1224no—
544C4×Q8—1224no—
545C4×Q8—1224no—
546C4×Q8C22×D6112yes—
547C4×D4—22no—
548C4×D4—612no—
549C4×D4—612no—
550C4×D4—612no—
551C4×D4—1222no—
552C4×D4—1222no—
553C4×D4—1222no—
554C4×D4—1222no—
555C4×D4—1222no—
556C4×D4—1222no—
557C4×D4—1222no—
558C4×D4—1222no—
559C4×D4—1222no—
560C4×D4C22×D6112yes—
561#117—21no—
562#117—611no—
563#117—612no—
564#117—614no—
565#117—614no—
566#117—1221no—
567#117—1221no—
568#117—1222no—
569#117—1222no—
570#117—1221no—
571#117—1221no—
572#117—1222no—
573#117—1222no—
574#117—1221no—
575#117C22×D6111yescharacteristic
576C2×C4⋊C4—22no—
577C2×C4⋊C4—612no—
578C2×C4⋊C4—612no—
579C2×C4⋊C4—1222no—
580C2×C4⋊C4—1222no—
581C2×C4⋊C4—1222no—
582C2×C4⋊C4C22×D6112yes—
583C2×C22⋊C4—1222no—
584C2×C22⋊C4—1221no—
585C2×C22⋊C4—1222no—
586C2×C42—21no—
587C2×C42—612no—
588C2×C42—611no—
589C2×C42—611no—
590C2×C42—611no—
591C2×C42—611no—
592C2×C42—611no—
593C2×C42—612no—
594C2×C42—612no—
595C2×C42—1221no—
596C2×C42—1222no—
597C2×C42—1221no—
598C2×C42—1222no—
599C2×C42—1222no—
600C2×C42—1221no—
601C2×C42—1222no—
602C2×C42—1221no—
603C2×C42C22×D6111yescharacteristic
604#107—614no—
605#107—614no—
606#107—614no—
607#107C22×D6114yes—
608#106—614no—
609#106—614no—
610#106—614no—
611#106C22×D6114yes—
612C4⋊C8—614no—
613C4⋊C8—614no—
614C4⋊C8—614no—
615C4⋊C8C22×D6114yes—
616#103—614no—
617#103—614no—
618#103—614no—
619#103C22×D6114yes—
620#102—614no—
621#102—614no—
622#102—614no—
623#102C22×D6114yes—
624C24—611no—
625C24—1221no—
626#41—22no—
627#41—614no—
628#41—614no—
629#41—614no—
630#41—1228no—
631#41—1228no—
632#41—1222no—
633#41—1222no—
634#41—1222no—
635#41Q8×D6114yes—
636C2×Q8—614no—
637C2×Q8—611no—
638C2×Q8—1221no—
639C2×Q8—1224no—
640C2×Q8—1224no—
641C2×Q8—1222no—
642C2×Q8—2448no—
643C2×Q8C23×D6111yescharacteristic
644C2×D4—21no—
645C2×D4—614no—
646C2×D4—611no—
647C2×D4—1221no—
648C2×D4—1222no—
649C2×D4—1221no—
650C2×D4—1228no—
651C2×D4—1221no—
652C2×D4—1221no—
653C2×D4C23×D6111yescharacteristic
654C22×C4—21no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—611no—
658C22×C4—611no—
659C22×C4—611no—
660C22×C4—614no—
661C22×C4—614no—
662C22×C4—611no—
663C22×C4—611no—
664C22×C4—612no—
665C22×C4—612no—
666C22×C4—612no—
667C22×C4—612no—
668C22×C4—612no—
669C22×C4—1221no—
670C22×C4—1228no—
671C22×C4—1222no—
672C22×C4—1221no—
673C22×C4—1222no—
674C22×C4—1221no—
675C22×C4—1222no—
676C22×C4—1221no—
677C22×C4—1222no—
678C22×C4—1222no—
679C22×C4—2444no—
680C22×C4—2448no—
681C22×C4D4×D6112yes—
682C22×C4C23×D6111yescharacteristic
683M16—24no—
684M16—1228no—
685M16—1224no—
686C2×C8—614no—
687C2×C8—1228no—
688C2×C8C23×D6114yes—
689C4⋊C4—24no—
690C4⋊C4—24no—
691C4⋊C4—22no—
692C4⋊C4—22no—
693C4⋊C4—614no—
694C4⋊C4—612no—
695C4⋊C4—1222no—
696C4⋊C4—1222no—
697C4⋊C4—1224no—
698C4⋊C4—1224no—
699C4⋊C4—1222no—
700C4⋊C4—1222no—
701C4⋊C4—1222no—
702C4⋊C4—1224no—
703C4⋊C4—1224no—
704C4⋊C4C23×D6114yes—
705C4⋊C4C23×D6112yes—
706C22⋊C4—21no—
707C22⋊C4—22no—
708C22⋊C4—1222no—
709C22⋊C4—1222no—
710C22⋊C4—1224no—
711C22⋊C4—1224no—
712C22⋊C4—1222no—
713C22⋊C4—1221no—
714C22⋊C4—1222no—
715C42—21no—
716C42—22no—
717C42—612no—
718C42—611no—
719C42—612no—
720C42—611no—
721C42—612no—
722C42—612no—
723C42—612no—
724C42—1222no—
725C42—1222no—
726C42—1222no—
727C42—1224no—
728C42—1224no—
729C42—1221no—
730C42—1222no—
731C42D4×D6111yescharacteristic
732C42D4×D6111yescharacteristic
733C42C23×D6112yes—
734C23—21no—
735C23—611no—
736C23—611no—
737C23—614no—
738C23—1224no—
739C23—1221no—
740C23—2442no—
741C23—2444no—
742C23C2×D4×D6111yescharacteristic
743Q8—21no—
744Q8—612no—
745Q8—1224no—
746Q8—1221no—
747Q8—2448no—
748Q8—2448no—
749Q8C2×Q8×D6112yes—
750D4—24no—
751D4—21no—
752D4—612no—
753D4—1224no—
754D4—1224no—
755D4—1224no—
756D4—1224no—
757D4—1221no—
758D4C2×Q8×D6112yes—
759C2×C4—21no—
760C2×C4—24no—
761C2×C4—22no—
762C2×C4—24no—
763C2×C4—42no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—614no—
767C2×C4—611no—
768C2×C4—611no—
769C2×C4—612no—
770C2×C4—614no—
771C2×C4—614no—
772C2×C4—612no—
773C2×C4—612no—
774C2×C4—612no—
775C2×C4—612no—
776C2×C4—612no—
777C2×C4—1224no—
778C2×C4—1224no—
779C2×C4—1224no—
780C2×C4—1224no—
781C2×C4—1224no—
782C2×C4—1224no—
783C2×C4—1221no—
784C2×C4—1224no—
785C2×C4—1222no—
786C2×C4—1224no—
787C2×C4—2442no—
788C2×C4—2442no—
789C2×C4—2444no—
790C2×C4—2444no—
791C2×C4—2444no—
792C2×C4—2444no—
793C2×C4—2444no—
794C2×C4C2×D4×D6112yes—
795C2×C4C2×D4×D6112yes—
796C2×C4C2×D4×D6111yescharacteristic
797C2×C4C2×Q8×D6112yes—
798C2×C4#41×D6112yes—
799C2×C4C24×D6111yescharacteristic
800C8—24no—
801C8—1224no—
802C22—22no—
803C22—22no—
804C22—42no—
805C22—612no—
806C22—612no—
807C22—1222no—
808C22—1222no—
809C22—1222no—
810C22—2444no—
811C22—2448no—
812C22—2442no—
813C22C22⋊Q8×D6112yes—
814C22C22×D4×D6111yescharacteristic
815C4—22no—
816C4—22no—
817C4—22no—
818C4—42no—
819C4—44no—
820C4—614no—
821C4—612no—
822C4—612no—
823C4—1222no—
824C4—1222no—
825C4—2442no—
826C4—2444no—
827C4C22⋊Q8×D6112yes—
828C4C22×Q8×D6111yescharacteristic
829C4C2×#41×D6111yescharacteristic
830C2—22no—
831C2—42no—
832C2—1222no—
833C2—1222no—
834C2—2442no—
835C2C2×C22⋊Q8×D6111yescharacteristic
836C2#575×D6112yes—
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3080C2
socleC22×C61C23×D4
prime radicalC2×#41×D61C22
hypercenter#3080D61
hypocenterC61#60484
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3080

Complements

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

NH ≅ G/Ntype
1. C2×#16840318C2semidirect
3. #21455642C2semidirect
4. #21455641C2semidirect
5. #21455637C2semidirect
6. #21455632C2semidirect
7. #21455630C2semidirect
8. #21455622C2semidirect
9. #21455614C2semidirect
10. #21455606C2semidirect
11. #21455604C2semidirect
12. #21454406C2semidirect
13. #423×D61C2semidirect
15. C61×#3080C2semidirect
23. #16840318C22semidirect
24. C2×#14519776C22semidirect
25. C2×#14519769C22semidirect
44. #16840070C22semidirect
45. #16840069C22semidirect
46. #16840066C22semidirect
47. #16840063C22semidirect
48. #16840062C22semidirect
49. #16840059C22semidirect
50. #16840056C22semidirect
51. #16840055C22semidirect
52. #16840051C22semidirect
53. #16840050C22semidirect
54. #16840046C22semidirect
55. #16840045C22semidirect
56. #16840041C22semidirect
57. #16840040C22semidirect
58. #16839805C22semidirect
59. #16839804C22semidirect
61. #16839802C22semidirect
63. #16839799C22semidirect
64. #16839797C22semidirect
65. #16839786C22semidirect
66. #16839785C22semidirect
68. C4⋊C8×D61C22semidirect
76. C2×#125×C61C22semidirect
78. C61×#479C22semidirect
79. C61×#478C22semidirect
80. C61×#428C22semidirect
81. C61×#423C22semidirect
89. #41×D61Q8semidirect
226. #11758226C2×Q8semidirect
228. Q8×D61C2×Q8semidirect
231. #11758224C2×Q8semidirect
234. D4×D61C2×Q8semidirect
417. #3080D61semidirect
444. C2×#125C2×D61semidirect
467. #479C2×D61semidirect
471. #478C2×D61semidirect
485. #428C2×D61semidirect
491. #423C2×D61semidirect
501. C61#60484semidirect

Maximal subgroups

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

subgroupindex
C2×#168403182
C4×#41×D612
#214556422
#214556412
#214556372
#214556322
#214556302
#214556222
#214556142
#214556062
#214556042
#214544062
#423×D612
#214543352
C61×#30802
#6048461