Finite Group Databasebeta

← #30552764

Subgroups — #30552764

Order 15616.

1736 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459635C211yesmaximal, characteristic, complemented
2#21459235C211yesmaximal, characteristic
3#21457122C214yesmaximal, complemented
4#21457079C214yesmaximal, complemented
5#21457044C212yesmaximal, complemented
6#21457015C212yesmaximal, complemented
7#21457003C212yesmaximal, complemented
8#21456946C212yesmaximal, complemented
9#21456349C212yesmaximal, complemented
10#21456176C212yesmaximal, complemented
11#21455807C212yesmaximal, complemented
12#21455779C212yesmaximal, complemented
13#21455618C211yesmaximal, characteristic, complemented
14#21455607C211yesmaximal, characteristic, complemented
15C2×#16840049C211yesmaximal, characteristic, complemented
16#21454487C211yesmaximal, characteristic, complemented
17C61×#3079C211yesmaximal, characteristic, complemented
18#16840492—21no—
19#16840487—21no—
20#16840473—21no—
21#16840467—22no—
22#16840427—21no—
23Q8×C22⋊D61—22no—
24#16840393C2212yes—
25#16840390C2211yescharacteristic
26#16840389C2214yescomplemented
27#16840384C2212yes—
28#16840383—21no—
29#16840367—21no—
30#16840363C2212yes—
31#16840345—22no—
32#16840340C2211yescharacteristic
33#16840331C2211yescharacteristic
34#16840326C2211yescharacteristic
35#16840319C2211yescharacteristic
36#16840317C2212yescomplemented
37#16840312—21no—
38#16840309C2212yes—
39C4⋊Q8×D61C2212yescomplemented
40#16840299C2212yes—
41#16840296—21no—
42#16840271—22no—
43#16840243C2212yes—
44C4×#11758222C2211yescharacteristic
45C2×C4×D244C2211yescharacteristic
46#16840170C2214yescomplemented
47#16840169C2214yescomplemented
48#16840163C2214yescomplemented
49#16840159C2214yescomplemented
50#16840125C2214yes—
51#16840123C2214yes—
52#16840118C2214yes—
53#16840107C2214yes—
54#16840102C2214yescomplemented
55#16840091C2214yescomplemented
56#16840089C2214yes—
57#16840088C2214yes—
58#16840084C2214yescomplemented
59#16840082C2214yes—
60#16840079C2214yescomplemented
61#16840077C2214yes—
62#16840069C2212yescomplemented
63#16840063C2214yes—
64#16840062C2212yescomplemented
65#16840057C2211yescharacteristic, complemented
66#16840053C2212yes—
67#16840052C2211yescharacteristic, complemented
68#16840049C2212yes—
69#16840049C2212yes—
70#16840049C2214yes—
71#16840047C2211yescharacteristic, complemented
72#16840043C2212yes—
73#16840042C2211yescharacteristic, complemented
74#16839822C2214yescomplemented
75#16839818C2212yescomplemented
76#16839814C2212yescomplemented
77#16839804C2212yes—
78#16839798C2212yes—
79C2×#14519708C2212yes—
80C2×C4⋊#92418C2211yescharacteristic
81#16839768C2212yes—
82#16839758C2212yes—
83C2×#14519697C2212yes—
84#16839730C2212yes—
85#16839720C2212yes—
86C2×C4⋊Q8×C61C2211yescharacteristic
87C4×#41×C61C2211yescharacteristic
88C61×#477C2212yescomplemented
89C61×#476C2212yescomplemented
90C61×#475C2212yescomplemented
91C61×#474C2212yescomplemented
92C61×#428C2212yes—
93C61×#423C2211yescharacteristic
94C61×#417C2212yes—
95C2×#11758222—22no—
96C2×#11758222C2311yescharacteristic
97C2×Q8×D61—22no—
98C22×D244C2311yescharacteristic
99C22×C4×D61—21no—
100C22×#92418C2312yes—
101#14519777—21no—
102#14519777C2311yescharacteristic
103#14519777C2311yescharacteristic
104#14519776—22no—
105#14519776—22no—
106#14519776C2314yes—
107#14519776C2312yes—
108#14519775—24no—
109#14519775—22no—
110#14519774—21no—
111#14519773C2312yes—
112#14519772—22no—
113#14519771—22no—
114#14519769—21no—
115#14519769C2312yes—
116#14519768—22no—
117#14519768C2312yes—
118#14519768C2314yes—
119#14519767—24no—
120#14519766C2312yes—
121#14519765—21no—
122#14519765—22no—
123#14519763—22no—
124#14519762—22no—
125#14519762—22no—
126#14519760—22no—
127#14519759—22no—
128#14519757—22no—
129#14519756—21no—
130#14519756—21no—
131#14519756—21no—
132#14519756—24no—
133#14519755—24no—
134#14519755—22no—
135#14519754—22no—
136#14519753—22no—
137#14519753—24no—
138#14519753C2312yes—
139#14519752C2312yes—
140#14519752C2312yes—
141#14519751—21no—
142#14519751—22no—
143#14519751—21no—
144#14519751—21no—
145#14519750—22no—
146#14519750—22no—
147#14519749—22no—
148#14519748C2312yes—
149#14519747—22no—
150#14519745—22no—
151Q8×Dic61—22no—
152C4×Dic122—21no—
153C4×Dic122—21no—
154C4×Dic122D411yescharacteristic
155C4×Dic122D411yescharacteristic
156#14519742—22no—
157#14519742—22no—
158C4×D244—22no—
159C4×D244—21no—
160C4×D244—21no—
161C4×D244D411yescharacteristic
162C4×D244D411yescharacteristic
163C4×D244C2312yes—
164C4×D244C2312yes—
165#14519739—22no—
166C4×C22⋊D61—24no—
167C4×C22⋊D61—22no—
168C4×C22⋊D61D412yes—
169C4×C22⋊D61D412yes—
170#14519736C2312yes—
171#14519736C2311yescharacteristic
172#14519735C2314yes—
173#14519734—22no—
174#14519734C2312yes—
175C2×C4⋊Dic61C2311yescharacteristic
176C4⋊C4×D61—22no—
177C4⋊C4×D61C2314yes—
178C2×#11758198—21no—
179C42×D61C2312yes—
180#14519711C2314yes—
181#14519710C2312yes—
182#14519710C2312yes—
183#14519709C2314yes—
184#14519708C2312yes—
185#14519708C2314yes—
186#14519708C2314yes—
187#14519708C2312yes—
188C4⋊#92418C2311yescharacteristic
189C4⋊#92418C2311yescharacteristic
190C4⋊#92418C2312yes—
191#14519701C2312yes—
192#14519701C2312yes—
193#14519699C2314yes—
194#14519699C2314yes—
195#14519698C2312yes—
196#14519698C2312yes—
197#14519697C2314yes—
198#14519697C2314yes—
199#14519689C2314yes—
200#14519689C2314yes—
201#14519687C2314yes—
202C8×Dic61C2314yes—
203C2×#41×C61C2311yescharacteristic
204C22×Q8×C61—21no—
205C2×M16×C61C2312yes—
206C4⋊Q8×C61—21no—
207C4⋊Q8×C61—21no—
208C4⋊Q8×C61C2312yes—
209C4⋊Q8×C61C2312yes—
210C4×Q8×C61C2311yescharacteristic
211C4×Q8×C61C2311yescharacteristic
212C4×D4×C61—21no—
213C4×D4×C61—21no—
214C4×D4×C61C2311yescharacteristic
215C4×D4×C61C2311yescharacteristic
216#117×C61—21no—
217#117×C61C2311yescharacteristic
218C2×C4⋊C4×C61—21no—
219C2×C4⋊C4×C61C2312yes—
220C2×C42×C61—21no—
221C2×C42×C61C2311yescharacteristic
222#107×C61C2314yes—
223#106×C61C2314yes—
224C4⋊C8×C61C2312yes—
225C4⋊C8×C61C2312yes—
226#103×C61C2314yes—
227#102×C61C2314yes—
228C23×D61—21no—
229#41×C61—22no—
230#41×C61—22no—
231C2×Q8×C61—22no—
232C2×Q8×C61—22no—
233C2×Q8×C61—82no—
234C2×Q8×C61C2411yescharacteristic
235C2×D4×C61—21no—
236C2×D4×C61C2411yescharacteristic
237C22×C4×C61—22no—
238C22×C4×C61—21no—
239C22×C4×C61—21no—
240C22×C4×C61—21no—
241C22×C4×C61C2×D411yescharacteristic
242C22×C4×C61C2×D411yescharacteristic
243C22×C4×C61C2411yescharacteristic
244C2×C22⋊D61—22no—
245C2×C22⋊D61—22no—
246C2×C22⋊D61—22no—
247C2×C22⋊D61C2×D412yes—
248C22×Dic61—21no—
249Q8×D61—84no—
250#11758222—22no—
251#11758222—22no—
252#11758222—84no—
253C2×D244—22no—
254C2×D244—22no—
255C2×D244—21no—
256C2×D244—22no—
257C2×D244—22no—
258C2×D244C2×D411yescharacteristic
259C2×D244C2412yes—
260C2×C4×D61—22no—
261C2×C4×D61—24no—
262C2×C4×D61—22no—
263C2×C4×D61—82no—
264C2×C4×D61C2×D412yes—
265C2×C4×D61C2×D412yes—
266C2×C4×D61C2412yes—
267C2×Dic122—21no—
268C2×Dic122—21no—
269C2×Dic122—24no—
270C2×Dic122—22no—
271C2×Dic122C2×D411yescharacteristic
272M16×C61—24no—
273C2×C8×C61C2414yes—
274C4⋊C4×C61—22no—
275C4⋊C4×C61—22no—
276C4⋊C4×C61—22no—
277C4⋊C4×C61—21no—
278C4⋊C4×C61—21no—
279C4⋊C4×C61C2414yes—
280C4⋊C4×C61C2411yescharacteristic
281C4⋊C4×C61C2411yescharacteristic
282C22⋊C4×C61—21no—
283C22⋊C4×C61—21no—
284C22⋊C4×C61—21no—
285C42×C61—21no—
286C42×C61—21no—
287C42×C61—21no—
288C42×C61C2×D411yescharacteristic
289C42×C61C2×D411yescharacteristic
290C42×C61C2411yescharacteristic
291C42×C61C2411yescharacteristic
292C22⋊Dic61—22no—
293C22⋊Dic61—22no—
294C22⋊Dic61C2×D412yes—
295#11758198—24no—
296#11758198—22no—
297#11758198—22no—
298#11758198—22no—
299#11758198—22no—
300#11758198—22no—
301#11758198—22no—
302#11758198—22no—
303#11758198C2×D412yes—
304#11758198C2×D412yes—
305C4⋊Dic61—21no—
306C4⋊Dic61—21no—
307C4⋊Dic61—21no—
308C4⋊Dic61—22no—
309C4⋊Dic61—24no—
310C4⋊Dic61C2×D411yescharacteristic
311C4⋊Dic61C2×D411yescharacteristic
312C4⋊Dic61C2412yes—
313C4⋊Dic61C2412yes—
314C4⋊Dic61C2412yes—
315#11758196—22no—
316#11758196—22no—
317#11758196—24no—
318#11758196—24no—
319#11758196—22no—
320#11758196—22no—
321#11758196—22no—
322#11758196—24no—
323#11758196C2×D412yes—
324#11758196C2×D412yes—
325C4×Dic61—22no—
326C4×Dic61—24no—
327C4×Dic61C2×D412yes—
328C4×Dic61C2×D412yes—
329C4×Dic61C2412yes—
330C2×#92418—24no—
331C2×#92418C2412yes—
332C2×#92418C2412yes—
333C23×C61—21no—
334C23×C61C22×D411yescharacteristic
335C22×D61—22no—
336C22×D61—42no—
337C22×D61—81no—
338C22×D61—81no—
339C22×D61C22×D412yes—
340Q8×C61—21no—
341Q8×C61—21no—
342Q8×C61—44no—
343Q8×C61—82no—
344D4×C61—21no—
345D4×C61—21no—
346D4×C61—42no—
347C2×C4×C61—22no—
348C2×C4×C61—24no—
349C2×C4×C61—21no—
350C2×C4×C61—21no—
351C2×C4×C61—21no—
352C2×C4×C61—41no—
353C2×C4×C61—42no—
354C2×C4×C61—42no—
355C2×C4×C61—81no—
356C2×C4×C61—82no—
357C2×C4×C61C22×D411yescharacteristic
358C2×C4×C61C22×D411yescharacteristic
359C2×C4×C61C22×D411yescharacteristic
360C2×C4×C61C22×D411yescharacteristic
361C2×C4×C61C22×D411yescharacteristic
362C2×C4×C612−1+412yes—
363C2×C4×C612−1+412yes—
364C2×C4×C61C2511yescharacteristic
365C22⋊D61—24no—
366C22⋊D61—82no—
367C22⋊D61—82no—
368C22⋊D61—82no—
369C2×Dic61—22no—
370C2×Dic61—22no—
371C2×Dic61—22no—
372C2×Dic61—81no—
373C2×Dic61C22×D412yes—
374C2×Dic61C22×D412yes—
375C2×Dic61C22×D412yes—
376D244—22no—
377D244—22no—
378D244—22no—
379D244—42no—
380D244—82no—
381D244—82no—
382C4×D61—24no—
383C4×D61—22no—
384C4×D61—22no—
385C4×D61—42no—
386C4×D61—44no—
387C4×D61—82no—
388C4×D61—84no—
389Dic122—22no—
390Dic122—42no—
391Dic122—42no—
392Dic122—82no—
393Dic122—84no—
394C8×C61—24no—
395#92418—22no—
396#92418—22no—
397#60892—611nomaximal, Sylow
398C22×C61—21no—
399C22×C61—21no—
400C22×C61—41no—
401C22×C61—41no—
402C22×C61—41no—
403C22×C61#53612yes—
404C22×C61C23×D411yescharacteristic
405C2×D61—22no—
406C2×D61—22no—
407C2×D61—22no—
408C2×D61—42no—
409C2×D61—42no—
410C2×D61—42no—
411C2×D61—84no—
412C4×C61—21no—
413C4×C61—21no—
414C4×C61—21no—
415C4×C61—44no—
416C4×C61—41no—
417C4×C61—41no—
418C4×C61—41no—
419C4×C61#53612yes—
420C4×C61#57712yes—
421C4×C61C2×2−1+411yescharacteristic
422C4×C61C2×2−1+411yescharacteristic
423Dic61—22no—
424Dic61—22no—
425Dic61—22no—
426Dic61—42no—
427Dic61—42no—
428Dic61—42no—
429#3503—611no—
430#3460—611no—
431#3244—614no—
432#3241—614no—
433#3238—612no—
434#3235—612no—
435#3233—612no—
436#3227—612no—
437#3163—612no—
438#3136—612no—
439#3099—612no—
440#3096—612no—
441#3079D6111yescharacteristic, complemented
442#3077—611no—
443#3076—611no—
444C2×#476—611no—
445#2925—611no—
446C2×C61—22no—
447C2×C61—81no—
448C2×C61C2×#53611yescharacteristic
449C2×C61C2×#57711yescharacteristic
450C2×C61#358511yescharacteristic
451D61—42no—
452D61—82no—
453Q82—1221no—
454#557—1221no—
455#554—1222no—
456#554—1221no—
457D4×Q8—1221no—
458D4×Q8—1222no—
459#544—614no—
460#544—611no—
461#544—612no—
462#542—612no—
463#542—1221no—
464#540—612no—
465#540—1221no—
466#538—1222no—
467#537—611no—
468#535—611no—
469#535—611no—
470#533—612no—
471#533—611no—
472#532—612no—
473#532—1221no—
474C2×C4⋊Q8—612no—
475C2×C4⋊Q8C2×D6111yescharacteristic
476#529—612no—
477#529—1221no—
478#525—1222no—
479#520—612no—
480C4×#41—611no—
481C4×#41C2×D6111yescharacteristic
482C2×C4×D4—611no—
483#501—614no—
484#501—614no—
485#499—614no—
486#498—614no—
487#490—614no—
488#489—614no—
489#488—614no—
490#486—614no—
491#485—614no—
492#483—614no—
493#482—614no—
494#482—614no—
495#482—614no—
496#481—614no—
497#481—614no—
498#480—614no—
499#479—612no—
500#478—612no—
501#478—614no—
502#477—611no—
503#477C2×D6112yescomplemented
504#476—612no—
505#476—612no—
506#476—614no—
507#476—611no—
508#476—612no—
509#476C2×D6112yescomplemented
510#475—611no—
511#475C2×D6112yescomplemented
512#474—611no—
513#474—612no—
514#474C2×D6112yescomplemented
515#433—614no—
516#432—612no—
517#431—612no—
518#428—612no—
519#428C2×D6112yes—
520#427—612no—
521C2×#106—612no—
522#423C2×D6111yescharacteristic
523C2×C4⋊C8—611no—
524#418—612no—
525#417C2×D6112yes—
526#416—612no—
527C2×#102—612no—
528#408—612no—
529#405—612no—
530C61#6089211yescharacteristic, complemented, Sylow
531C2×#41—611no—
532C2×#41—1222no—
533C2×#41C22×D6111yescharacteristic
534C22×Q8—21no—
535C22×Q8—1222no—
536C22×D4—611no—
537C23×C4—1221no—
538C2×M16C22×D6112yes—
539C22×C8—612no—
540C4⋊Q8—21no—
541C4⋊Q8—21no—
542C4⋊Q8—614no—
543C4⋊Q8—612no—
544C4⋊Q8—611no—
545C4⋊Q8—611no—
546C4⋊Q8—1221no—
547C4⋊Q8—1222no—
548C4⋊Q8—1222no—
549C4⋊Q8—1222no—
550C4⋊Q8—1224no—
551C4⋊Q8C22×D6112yes—
552C4⋊Q8C22×D6112yes—
553#127—612no—
554#127—1221no—
555#126—1222no—
556#126—1222no—
557#125—612no—
558#125—614no—
559#125—612no—
560#125—1221no—
561#125—1224no—
562#125—1222no—
563#124—612no—
564#124—1222no—
565#124—1221no—
566#124—1222no—
567#123—1222no—
568#123—1222no—
569#123—1222no—
570#123—1222no—
571C22⋊Q8—612no—
572C22⋊Q8—1222no—
573C22⋊Q8—1224no—
574C22⋊Q8—1224no—
575C22⋊Q8—1224no—
576C22⋊Q8—1222no—
577C22⋊Q8—1222no—
578C22⋊Q8—1221no—
579C22⋊Q8—1222no—
580C22⋊Q8—1221no—
581C22⋊Q8—1221no—
582#121—612no—
583#121—612no—
584#121—612no—
585#121—1222no—
586#121—1222no—
587#121—1222no—
588#121—1221no—
589#121—1221no—
590#121—1221no—
591#121—1222no—
592#120—1222no—
593#120—1222no—
594C4×Q8—611no—
595C4×Q8—611no—
596C4×Q8—1222no—
597C4×Q8—1222no—
598C4×Q8—1222no—
599C4×Q8—1221no—
600C4×Q8—1221no—
601C4×Q8C22×D6111yescharacteristic
602C4×Q8C22×D6111yescharacteristic
603C4×D4—21no—
604C4×D4—21no—
605C4×D4—612no—
606C4×D4—612no—
607C4×D4—611no—
608C4×D4—611no—
609C4×D4—612no—
610C4×D4—612no—
611C4×D4—1222no—
612C4×D4—1222no—
613C4×D4—1222no—
614C4×D4—1224no—
615C4×D4—1221no—
616C4×D4—1221no—
617C4×D4C22×D6111yescharacteristic
618C4×D4C22×D6111yescharacteristic
619#117—21no—
620#117—611no—
621#117—612no—
622#117—612no—
623#117—614no—
624#117—1222no—
625#117C22×D6111yescharacteristic
626C2×C4⋊C4—21no—
627C2×C4⋊C4—611no—
628C2×C4⋊C4—614no—
629C2×C4⋊C4—1222no—
630C2×C4⋊C4C22×D6112yes—
631C2×C22⋊C4—1221no—
632C2×C42—21no—
633C2×C42—612no—
634C2×C42C22×D6111yescharacteristic
635#107—614no—
636#107—612no—
637#107—612no—
638#107C22×D6114yes—
639#106—614no—
640#106—614no—
641#106—614no—
642#106—612no—
643#106—612no—
644#106C22×D6114yes—
645C4⋊C8—611no—
646C4⋊C8—611no—
647C4⋊C8—612no—
648C4⋊C8C22×D6112yes—
649C4⋊C8C22×D6112yes—
650#103—612no—
651#103—612no—
652#103C22×D6114yes—
653#102—612no—
654#102—612no—
655#102—614no—
656#102—614no—
657#102—614no—
658#102—614no—
659#102C22×D6114yes—
660C22⋊C8—614no—
661C22⋊C8—614no—
662#97—614no—
663C4×C8—614no—
664C24—1221no—
665#41—22no—
666#41—22no—
667#41—1222no—
668#41—1222no—
669#41—4884no—
670C2×Q8—22no—
671C2×Q8—22no—
672C2×Q8—82no—
673C2×Q8—611no—
674C2×Q8—1222no—
675C2×Q8—1224no—
676C2×Q8—1221no—
677C2×Q8—1221no—
678C2×Q8—4884no—
679C2×Q8C23×D6111yescharacteristic
680C2×D4—21no—
681C2×D4—612no—
682C2×D4—611no—
683C2×D4—612no—
684C2×D4—1222no—
685C2×D4—1222no—
686C2×D4—1222no—
687C2×D4—1222no—
688C2×D4—1222no—
689C2×D4—1221no—
690C2×D4—1222no—
691C2×D4—1222no—
692C2×D4C23×D6111yescharacteristic
693C22×C4—22no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—612no—
698C22×C4—612no—
699C22×C4—612no—
700C22×C4—1224no—
701C22×C4—1221no—
702C22×C4—1222no—
703C22×C4—1222no—
704C22×C4—4882no—
705C22×C4D4×D6111yescharacteristic
706C22×C4D4×D6111yescharacteristic
707C22×C4C23×D6111yescharacteristic
708M16—24no—
709C2×C8—612no—
710C2×C8—612no—
711C2×C8—1224no—
712C2×C8C23×D6114yes—
713C4⋊C4—22no—
714C4⋊C4—22no—
715C4⋊C4—22no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—612no—
719C4⋊C4—612no—
720C4⋊C4—611no—
721C4⋊C4—611no—
722C4⋊C4—612no—
723C4⋊C4—612no—
724C4⋊C4—612no—
725C4⋊C4—1224no—
726C4⋊C4—1224no—
727C4⋊C4—1222no—
728C4⋊C4—1222no—
729C4⋊C4—1222no—
730C4⋊C4—1224no—
731C4⋊C4—1222no—
732C4⋊C4—1224no—
733C4⋊C4—1221no—
734C4⋊C4—1221no—
735C4⋊C4—1222no—
736C4⋊C4—1222no—
737C4⋊C4—1221no—
738C4⋊C4C23×D6114yes—
739C4⋊C4C23×D6111yescharacteristic
740C4⋊C4C23×D6111yescharacteristic
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—612no—
745C22⋊C4—612no—
746C22⋊C4—612no—
747C22⋊C4—1222no—
748C22⋊C4—1222no—
749C22⋊C4—1222no—
750C22⋊C4—1222no—
751C22⋊C4—1224no—
752C22⋊C4—1222no—
753C22⋊C4—1222no—
754C22⋊C4—1222no—
755C22⋊C4—1222no—
756C22⋊C4—1222no—
757C42—21no—
758C42—21no—
759C42—21no—
760C42—612no—
761C42—612no—
762C42—612no—
763C42—1224no—
764C42—1222no—
765C42D4×D6111yescharacteristic
766C42D4×D6111yescharacteristic
767C42C23×D6111yescharacteristic
768C42C23×D6111yescharacteristic
769C23—21no—
770C23—612no—
771C23—1222no—
772C23—4881no—
773C23—4881no—
774C23—2442no—
775C23C2×D4×D6111yescharacteristic
776Q8—21no—
777Q8—21no—
778Q8—44no—
779Q8—82no—
780Q8—1222no—
781Q8—4884no—
782Q8—4882no—
783Q8—2442no—
784Q8—2442no—
785D4—21no—
786D4—21no—
787D4—42no—
788D4—1224no—
789D4—1222no—
790D4—1222no—
791D4—1222no—
792D4—4882no—
793D4—4882no—
794D4—4882no—
795D4—4882no—
796D4—4882no—
797D4—2442no—
798C2×C4—22no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—24no—
803C2×C4—41no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—81no—
807C2×C4—82no—
808C2×C4—612no—
809C2×C4—612no—
810C2×C4—612no—
811C2×C4—1224no—
812C2×C4—1222no—
813C2×C4—1222no—
814C2×C4—1222no—
815C2×C4—1222no—
816C2×C4—1222no—
817C2×C4—4882no—
818C2×C4—4884no—
819C2×C4—4881no—
820C2×C4—2442no—
821C2×C4—2444no—
822C2×C4C2×D4×D6111yescharacteristic
823C2×C4C2×D4×D6111yescharacteristic
824C2×C4C2×D4×D6111yescharacteristic
825C2×C4C2×D4×D6111yescharacteristic
826C2×C4C2×D4×D6111yescharacteristic
827C2×C4#1451982412yes—
828C2×C4#1451982512yes—
829C2×C4C24×D6111yescharacteristic
830C8—24no—
831C8—1222no—
832C8—1222no—
833C22—21no—
834C22—21no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—1222no—
839C22—1222no—
840C22—1222no—
841C22—4884no—
842C22—2442no—
843C22—2442no—
844C22—2442no—
845C22#1684033512yes—
846C22C22×D4×D6111yescharacteristic
847C4—21no—
848C4—21no—
849C4—21no—
850C4—41no—
851C4—44no—
852C4—41no—
853C4—41no—
854C4—1222no—
855C4—1222no—
856C4—1222no—
857C4—2442no—
858C4—2442no—
859C4—2442no—
860C4#1684033512yes—
861C4#1684057112yes—
862C4C2×#1451982411yescharacteristic
863C4C2×#1451982511yescharacteristic
864C2—22no—
865C2—81no—
866C2—4882no—
867C2—2442no—
868C2C2×#1684033511yescharacteristic
869C2C2×#1684057111yescharacteristic
870C2#2146059511yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3079C2
socleC22×C61C23×D4
prime radical#21459235C2
hypercenter#3079D61
hypocenterC61#60892
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3079

Complements

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

NH ≅ G/Ntype
1. #21459635C2semidirect
3. #21457122C2semidirect
4. #21457079C2semidirect
5. #21457044C2semidirect
6. #21457015C2semidirect
7. #21457003C2semidirect
8. #21456946C2semidirect
9. #21456349C2semidirect
10. #21456176C2semidirect
11. #21455807C2semidirect
12. #21455779C2semidirect
13. #21455618C2semidirect
14. #21455607C2semidirect
15. C2×#16840049C2semidirect
16. #21454487C2semidirect
17. C61×#3079C2semidirect
26. #16840389C22semidirect
36. #16840317C22semidirect
39. C4⋊Q8×D61C22semidirect
46. #16840170C22semidirect
47. #16840169C22semidirect
48. #16840163C22semidirect
49. #16840159C22semidirect
54. #16840102C22semidirect
55. #16840091C22semidirect
58. #16840084C22semidirect
60. #16840079C22semidirect
62. #16840069C22semidirect
64. #16840062C22semidirect
65. #16840057C22semidirect
67. #16840052C22semidirect
71. #16840047C22semidirect
73. #16840042C22semidirect
74. #16839822C22semidirect
75. #16839818C22semidirect
76. #16839814C22semidirect
88. C61×#477C22semidirect
89. C61×#476C22semidirect
90. C61×#475C22semidirect
91. C61×#474C22semidirect
441. #3079D61semidirect
503. #477C2×D61semidirect
509. #476C2×D61semidirect
511. #475C2×D61semidirect
514. #474C2×D61semidirect
530. C61#60892semidirect

Maximal subgroups

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

subgroupindex
#214596352
#214592352
#214571222
#214570792
#214570442
#214570152
#214570032
#214569462
#214563492
#214561762
#214558072
#214557792
#214556182
#214556072
C2×#168400492
#214544872
C61×#30792
#6089261