Finite Group Databasebeta

← #30552762

Subgroups — #30552762

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#21459638C211yesmaximal, characteristic, complemented
2#21459235C211yesmaximal, characteristic
3#21457119C214yesmaximal, complemented
4#21457074C214yesmaximal, complemented
5#21457042C212yesmaximal, complemented
6#21457019C212yesmaximal, complemented
7#21457000C212yesmaximal, complemented
8#21456949C212yesmaximal, complemented
9#21456350C212yesmaximal, complemented
10#21456175C212yesmaximal, complemented
11#21455810C212yesmaximal, complemented
12#21455778C212yesmaximal, complemented
13#21455635C211yesmaximal, characteristic, complemented
14#21455618C211yesmaximal, characteristic, complemented
15#21455609C211yesmaximal, characteristic, complemented
16C2×#16840053C211yesmaximal, characteristic, complemented
17C61×#2925C211yesmaximal, characteristic, complemented
18Q8×Dic122—21no—
19#16840491—21no—
20#16840469—22no—
21#16840469—21no—
22D4×Dic122—22no—
23D4×Dic122—21no—
24#16840390C2211yescharacteristic
25#16840390C2212yes—
26#16840390C2214yescomplemented
27#16840384—21no—
28#16840383C2212yes—
29#16840367C2212yes—
30#16840363—21no—
31#16840345—22no—
32#16840340C2211yescharacteristic
33#16840331C2211yescharacteristic
34#16840326C2211yescharacteristic
35#16840319C2211yescharacteristic
36#16840319C2212yescomplemented
37#16840312C2212yes—
38#16840309—21no—
39C2×#14519777C2211yescharacteristic
40C2×#14519777C2212yescomplemented
41#16840299—21no—
42#16840296C2212yes—
43#16840271—22no—
44#16840245C2212yes—
45C4×#11758222C2211yescharacteristic
46C2×C4×D244C2211yescharacteristic
47#16840171C2214yescomplemented
48#16840171C2214yescomplemented
49#16840164C2214yescomplemented
50#16840160C2214yescomplemented
51#16840127C2214yes—
52#16840122C2214yes—
53#16840117C2214yes—
54#16840109C2214yes—
55#16840104C2214yescomplemented
56#16840093C2214yescomplemented
57#16840087C2214yes—
58#16840087C2214yes—
59#16840087C2214yescomplemented
60#16840081C2214yes—
61#16840081C2214yescomplemented
62#16840076C2214yes—
63#16840070C2212yescomplemented
64#16840063C2214yes—
65#16840063C2212yescomplemented
66#16840058C2212yescomplemented
67#16840058C2211yescharacteristic, complemented
68#16840053C2212yes—
69#16840053C2212yes—
70#16840053C2212yes—
71#16840053C2214yes—
72#16840053C2212yescomplemented
73#16840053C2211yescharacteristic, complemented
74#16840048C2212yescomplemented
75#16840048C2211yescharacteristic, complemented
76#16840043C2212yes—
77#16840043C2212yescomplemented
78#16840043C2211yescharacteristic, complemented
79#16839804C2212yes—
80#16839804C2212yes—
81#16839800C2212yes—
82C2×#14519709C2212yes—
83#16839768C2212yes—
84#16839764C2212yes—
85#16839759C2212yes—
86C2×#14519699C2212yes—
87C4×#41×C61C2211yescharacteristic
88C61×#433C2214yescomplemented
89C61×#432C2212yescomplemented
90C61×#431C2212yescomplemented
91C61×#423C2211yescharacteristic
92C2×C4⋊C8×C61C2211yescharacteristic
93C61×#408C2212yes—
94C61×#405C2212yes—
95C2×#11758222—22no—
96C2×#11758222C2311yescharacteristic
97C22×Dic122—21no—
98C22×Dic122—22no—
99C22×D244C2311yescharacteristic
100C22×C4×D61—21no—
101#14519777—21no—
102#14519777—22no—
103#14519777—21no—
104#14519777—22no—
105#14519777C2311yescharacteristic
106#14519777C2312yes—
107#14519777C2312yes—
108#14519777C2311yescharacteristic
109#14519777C2314yes—
110#14519777C2312yes—
111#14519776—22no—
112#14519776—24no—
113#14519776—21no—
114#14519774C2312yes—
115#14519773—21no—
116#14519772—22no—
117#14519771—22no—
118#14519769C2312yes—
119#14519769C2312yes—
120#14519769C2314yes—
121#14519768—22no—
122#14519768—24no—
123#14519768—21no—
124#14519766—21no—
125#14519765—22no—
126#14519765C2312yes—
127#14519763—22no—
128#14519762—22no—
129#14519762—22no—
130#14519760—22no—
131#14519759—22no—
132#14519756—21no—
133#14519756—22no—
134#14519756—21no—
135#14519756—22no—
136#14519756C2312yes—
137#14519755—22no—
138#14519754—24no—
139#14519754—24no—
140#14519754—24no—
141#14519754—22no—
142#14519753—21no—
143#14519752—21no—
144#14519752—21no—
145#14519751—22no—
146#14519751C2312yes—
147#14519751C2312yes—
148#14519751C2312yes—
149#14519750—22no—
150#14519750—22no—
151#14519749—22no—
152#14519748—21no—
153#14519747—22no—
154#14519745—22no—
155Q8×Dic61—22no—
156C4×Dic122—21no—
157C4×Dic122—22no—
158C4×Dic122—21no—
159C4×Dic122—22no—
160C4×Dic122C2311yescharacteristic
161C4×Dic122C2311yescharacteristic
162C4×D244—21no—
163C4×D244—21no—
164C4×D244—22no—
165C4×D244C2312yes—
166C4×D244C2312yes—
167C4×D244C2311yescharacteristic
168C4×D244C2311yescharacteristic
169D4×Dic61—24no—
170D4×Dic61—22no—
171C4×C22⋊D61—21no—
172C4×C22⋊D61—21no—
173C4×C22⋊D61—22no—
174#14519736C2311yescharacteristic
175#14519736C2312yes—
176#14519736C2314yes—
177#14519734—21no—
178#14519734—22no—
179C2×C4⋊Dic61—21no—
180C2×C4⋊Dic61—22no—
181C2×C4⋊Dic61C2311yescharacteristic
182C2×C4⋊Dic61C2312yes—
183C2×C4⋊Dic61C2314yes—
184C2×#11758198—21no—
185C42×D61—21no—
186#14519711C2314yes—
187#14519711C2312yes—
188#14519711C2314yes—
189#14519711C2312yes—
190#14519709C2314yes—
191#14519709C2312yes—
192#14519709C2314yes—
193#14519709C2314yes—
194#14519709C2314yes—
195#14519709C2312yes—
196#14519702C2312yes—
197#14519702C2312yes—
198#14519702C2314yes—
199#14519699C2314yes—
200#14519699C2314yes—
201#14519699C2312yes—
202#14519699C2312yes—
203#14519699C2314yes—
204#14519699C2314yes—
205#14519699C2314yes—
206C2×#41×C61C2311yescharacteristic
207C2×M16×C61C2312yes—
208C22×C8×C61C2312yes—
209C4×Q8×C61D411yescharacteristic
210C4×Q8×C61D411yescharacteristic
211C4×D4×C61D412yes—
212C4×D4×C61D411yescharacteristic
213C4×D4×C61D412yes—
214C4×D4×C61D411yescharacteristic
215#117×C61C2311yescharacteristic
216#117×C61C2312yes—
217C2×C42×C61C2311yescharacteristic
218C2×C42×C61C2312yes—
219C4⋊C8×C61C2312yes—
220C4⋊C8×C61C2312yes—
221C4⋊C8×C61C2311yescharacteristic
222C4⋊C8×C61C2311yescharacteristic
223C4⋊C8×C61C2312yes—
224C22⋊C8×C61C2314yes—
225C22⋊C8×C61C2314yes—
226#97×C61C2314yes—
227C4×C8×C61C2314yes—
228C23×D61—21no—
229#41×C61—22no—
230#41×C61—22no—
231C2×Q8×C61C2×D411yescharacteristic
232C2×D4×C61C2×D412yes—
233C2×D4×C61C2×D411yescharacteristic
234C22×C4×C61C2×D411yescharacteristic
235C22×C4×C61C2×D412yes—
236C22×C4×C61C2×D411yescharacteristic
237C22×C4×C61C2×D412yes—
238C22×C4×C61C2412yes—
239C22×C4×C61C2411yescharacteristic
240C2×C22⋊D61—21no—
241C2×C22⋊D61—22no—
242C2×C22⋊D61—22no—
243C2×C22⋊D61—22no—
244C22×Dic61—21no—
245C22×Dic61—24no—
246C22×Dic61—22no—
247#11758222—22no—
248#11758222—22no—
249#11758222—84no—
250C2×D244—22no—
251C2×D244—22no—
252C2×D244—21no—
253C2×D244—22no—
254C2×D244—22no—
255C2×D244C2412yes—
256C2×D244C2411yescharacteristic
257C2×C4×D61—22no—
258C2×C4×D61—21no—
259C2×C4×D61—21no—
260C2×C4×D61—22no—
261C2×C4×D61—21no—
262C2×C4×D61—82no—
263C2×Dic122—22no—
264C2×Dic122—21no—
265C2×Dic122—21no—
266C2×Dic122—22no—
267C2×Dic122—24no—
268C2×Dic122—22no—
269C2×Dic122—82no—
270C2×Dic122—84no—
271C2×Dic122C2411yescharacteristic
272M16×C61—24no—
273C2×C8×C61—24no—
274C2×C8×C61C2412yes—
275C2×C8×C61C2414yes—
276C2×C8×C61C2412yes—
277C4⋊C4×C61C2×D411yescharacteristic
278C4⋊C4×C61C2×D411yescharacteristic
279C4⋊C4×C61C2×D412yes—
280C4⋊C4×C61C2×D412yes—
281C22⋊C4×C61C2×D412yes—
282C22⋊C4×C61C2×D412yes—
283C22⋊C4×C61C2×D412yes—
284C42×C61C2×D411yescharacteristic
285C42×C61C2×D412yes—
286C42×C61C2×D411yescharacteristic
287C42×C61C2×D412yes—
288C42×C61C2412yes—
289C42×C61C2411yescharacteristic
290C42×C61C2411yescharacteristic
291C22⋊Dic61—21no—
292C22⋊Dic61—24no—
293C22⋊Dic61—22no—
294C22⋊Dic61—22no—
295#11758198—22no—
296#11758198—22no—
297#11758198—21no—
298#11758198—21no—
299#11758198—22no—
300#11758198—22no—
301#11758198—22no—
302#11758198—22no—
303#11758198—22no—
304C4⋊Dic61—22no—
305C4⋊Dic61—21no—
306C4⋊Dic61—24no—
307C4⋊Dic61—22no—
308C4⋊Dic61—24no—
309C4⋊Dic61—22no—
310C4⋊Dic61—21no—
311C4⋊Dic61—22no—
312C4⋊Dic61—21no—
313C4⋊Dic61C2414yes—
314C4⋊Dic61C2412yes—
315C4⋊Dic61C2412yes—
316C4⋊Dic61C2412yes—
317C4⋊Dic61C2411yescharacteristic
318C4⋊Dic61C2411yescharacteristic
319#11758196—21no—
320#11758196—21no—
321#11758196—22no—
322#11758196—22no—
323#11758196—22no—
324#11758196—24no—
325#11758196—22no—
326#11758196—22no—
327#11758196—24no—
328C4×Dic61—21no—
329C4×Dic61—21no—
330C4×Dic61—21no—
331C4×Dic61—24no—
332C4×Dic61—22no—
333C23×C61C22×D412yes—
334C23×C61C22×D411yescharacteristic
335C22×D61—22no—
336C22×D61—21no—
337C22×D61—42no—
338C22×D61—81no—
339C22×D61—81no—
340Q8×C61—22no—
341D4×C61—24no—
342D4×C61—22no—
343C2×C4×C61—22no—
344C2×C4×C61—24no—
345C2×C4×C61—22no—
346C2×C4×C61—22no—
347C2×C4×C61—41no—
348C2×C4×C61—42no—
349C2×C4×C61C22×D412yes—
350C2×C4×C61C22×D411yescharacteristic
351C2×C4×C61C22×D412yes—
352C2×C4×C61C22×D411yescharacteristic
353C2×C4×C61C22×D412yes—
354C2×C4×C61C22×D411yescharacteristic
355C2×C4×C61C22×D411yescharacteristic
356C2×C4×C61C22×D411yescharacteristic
357C2×C4×C612−1+412yes—
358C2×C4×C612−1+412yes—
359C2×C4×C61C2511yescharacteristic
360C22⋊D61—42no—
361C22⋊D61—82no—
362C22⋊D61—82no—
363C22⋊D61—82no—
364C2×Dic61—22no—
365C2×Dic61—21no—
366C2×Dic61—21no—
367C2×Dic61—21no—
368C2×Dic61—24no—
369C2×Dic61—22no—
370C2×Dic61—22no—
371C2×Dic61—82no—
372C2×Dic61—84no—
373C2×Dic61—81no—
374D244—22no—
375D244—22no—
376D244—21no—
377D244—21no—
378D244—42no—
379D244—82no—
380D244—82no—
381C4×D61—42no—
382C4×D61—44no—
383C4×D61—42no—
384C4×D61—81no—
385C4×D61—82no—
386Dic122—21no—
387Dic122—21no—
388Dic122—44no—
389Dic122—42no—
390Dic122—42no—
391Dic122—82no—
392Dic122—84no—
393Dic122—82no—
394C8×C61—22no—
395C8×C61—22no—
396C8×C61—24no—
397#60892—611nomaximal, Sylow
398C22×C61—21no—
399C22×C61—21no—
400C22×C61—22no—
401C22×C61—22no—
402C22×C61—22no—
403C22×C61#53612yes—
404C22×C61C23×D411yescharacteristic
405C2×D61—41no—
406C2×D61—42no—
407C2×D61—41no—
408C2×D61—42no—
409C2×D61—42no—
410C2×D61—41no—
411C2×D61—84no—
412C4×C61—21no—
413C4×C61—21no—
414C4×C61—22no—
415C4×C61—22no—
416C4×C61—22no—
417C4×C61—21no—
418C4×C61#53612yes—
419C4×C61#57712yes—
420C4×C61C2×2−1+411yescharacteristic
421C4×C61C2×2−1+411yescharacteristic
422Dic61—44no—
423Dic61—42no—
424Dic61—41no—
425Dic61—41no—
426Dic61—42no—
427Dic61—41no—
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#3079—611no—
442#3077—611no—
443#3076—611no—
444C2×#476—611no—
445#2925D6111yescharacteristic, complemented
446C2×C61—22no—
447C2×C61—42no—
448C2×C61C2×#53611yescharacteristic
449C2×C61C2×#57711yescharacteristic
450C2×C61#358511yescharacteristic
451D61—81no—
452D61—82no—
453Q82—1221no—
454#557—1221no—
455#554—1222no—
456#554—1221no—
457D4×Q8—1222no—
458D4×Q8—1221no—
459#544—612no—
460#544—611no—
461#544—614no—
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—611no—
471#533—612no—
472#532—612no—
473#532—1221no—
474C2×C4⋊Q8—611no—
475C2×C4⋊Q8—612no—
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#477—612no—
504#476—611no—
505#476—612no—
506#476—612no—
507#476—612no—
508#476—612no—
509#476—614no—
510#475—611no—
511#475—612no—
512#474—611no—
513#474—612no—
514#474—612no—
515#433C2×D6114yescomplemented
516#432C2×D6112yescomplemented
517#431C2×D6112yescomplemented
518#428—612no—
519#428—612no—
520#427—612no—
521C2×#106—612no—
522#423C2×D6111yescharacteristic
523C2×C4⋊C8C2×D6111yescharacteristic
524#418—612no—
525#417—612no—
526#416—612no—
527C2×#102—612no—
528#408C2×D6112yes—
529#405C2×D6112yes—
530C61#6089211yescharacteristic, complemented, Sylow
531C2×#41—611no—
532C2×#41—1222no—
533C2×#41C22×D6111yescharacteristic
534C22×Q8—1221no—
535C22×Q8—1222no—
536C22×D4—611no—
537C23×C4—1221no—
538C2×M16C22×D6112yes—
539C22×C8C22×D6112yes—
540C4⋊Q8—612no—
541C4⋊Q8—611no—
542C4⋊Q8—612no—
543C4⋊Q8—614no—
544C4⋊Q8—612no—
545C4⋊Q8—611no—
546C4⋊Q8—1221no—
547C4⋊Q8—1222no—
548C4⋊Q8—1224no—
549C4⋊Q8—1221no—
550C4⋊Q8—1222no—
551C4⋊Q8—1221no—
552C4⋊Q8—1222no—
553#127—612no—
554#127—1221no—
555#126—1222no—
556#126—1222no—
557#125—612no—
558#125—612no—
559#125—614no—
560#125—1221no—
561#125—1222no—
562#125—1224no—
563#124—612no—
564#124—1221no—
565#124—1222no—
566#124—1222no—
567#123—1222no—
568#123—1222no—
569#123—1222no—
570#123—1222no—
571C22⋊Q8—612no—
572C22⋊Q8—1221no—
573C22⋊Q8—1221no—
574C22⋊Q8—1222no—
575C22⋊Q8—1221no—
576C22⋊Q8—1222no—
577C22⋊Q8—1222no—
578C22⋊Q8—1222no—
579C22⋊Q8—1224no—
580C22⋊Q8—1224no—
581C22⋊Q8—1224no—
582#121—612no—
583#121—612no—
584#121—612no—
585#121—1222no—
586#121—1221no—
587#121—1222no—
588#121—1221no—
589#121—1221no—
590#121—1222no—
591#121—1222no—
592#120—1222no—
593#120—1222no—
594C4×Q8—611no—
595C4×Q8—611no—
596C4×Q8—1222no—
597C4×Q8—1221no—
598C4×Q8—1222no—
599C4×Q8—1221no—
600C4×Q8—1222no—
601C4×Q8D24411yescharacteristic
602C4×Q8D24411yescharacteristic
603C4×D4—612no—
604C4×D4—612no—
605C4×D4—611no—
606C4×D4—611no—
607C4×D4—1224no—
608C4×D4—1222no—
609C4×D4—1221no—
610C4×D4—1221no—
611C4×D4—1222no—
612C4×D4—1221no—
613C4×D4—1221no—
614C4×D4—1222no—
615C4×D4D24412yes—
616C4×D4D24411yescharacteristic
617C4×D4D24412yes—
618C4×D4D24411yescharacteristic
619#117—611no—
620#117—612no—
621#117—614no—
622#117—1221no—
623#117—1222no—
624#117C22×D6111yescharacteristic
625#117C22×D6112yes—
626C2×C4⋊C4—611no—
627C2×C4⋊C4—612no—
628C2×C4⋊C4—614no—
629C2×C4⋊C4—1221no—
630C2×C4⋊C4—1222no—
631C2×C22⋊C4—1221no—
632C2×C42—1221no—
633C2×C42C22×D6111yescharacteristic
634C2×C42C22×D6112yes—
635#107—612no—
636#107—612no—
637#107—614no—
638#107—614no—
639#106—614no—
640#106—614no—
641#106—612no—
642#106—612no—
643#106—614no—
644#106—614no—
645C4⋊C8C22×D6111yescharacteristic
646C4⋊C8C22×D6111yescharacteristic
647C4⋊C8C22×D6112yes—
648C4⋊C8C22×D6112yes—
649C4⋊C8C22×D6112yes—
650#103—612no—
651#103—612no—
652#103—614no—
653#102—614no—
654#102—614no—
655#102—612no—
656#102—612no—
657#102—614no—
658#102—614no—
659#102—614no—
660C22⋊C8C22×D6114yes—
661C22⋊C8C22×D6114yes—
662#97C22×D6114yes—
663C4×C8C22×D6114yes—
664C24—1221no—
665#41—22no—
666#41—22no—
667#41—1222no—
668#41—1222no—
669#41—4884no—
670C2×Q8—611no—
671C2×Q8—1222no—
672C2×Q8—1222no—
673C2×Q8—1224no—
674C2×Q8—1221no—
675C2×Q8—1221no—
676C2×Q8—1222no—
677C2×Q8—4882no—
678C2×Q8—4884no—
679C2×Q8C2×D24411yescharacteristic
680C2×D4—612no—
681C2×D4—611no—
682C2×D4—1222no—
683C2×D4—1222no—
684C2×D4—1222no—
685C2×D4—1221no—
686C2×D4—1222no—
687C2×D4—1222no—
688C2×D4—1221no—
689C2×D4—1222no—
690C2×D4—1222no—
691C2×D4C2×D24412yes—
692C2×D4C2×D24411yescharacteristic
693C22×C4—1221no—
694C22×C4—1224no—
695C22×C4—1222no—
696C22×C4—1221no—
697C22×C4—1222no—
698C22×C4—1221no—
699C22×C4—1221no—
700C22×C4—1222no—
701C22×C4—4882no—
702C22×C4C2×D24411yescharacteristic
703C22×C4C2×D24412yes—
704C22×C4C2×D24411yescharacteristic
705C22×C4C2×D24412yes—
706C22×C4C23×D6112yes—
707C22×C4C23×D6111yescharacteristic
708M16—24no—
709C2×C8—24no—
710C2×C8C23×D6112yes—
711C2×C8C23×D6114yes—
712C2×C8C23×D6112yes—
713C4⋊C4—614no—
714C4⋊C4—612no—
715C4⋊C4—612no—
716C4⋊C4—612no—
717C4⋊C4—611no—
718C4⋊C4—611no—
719C4⋊C4—1221no—
720C4⋊C4—1224no—
721C4⋊C4—1222no—
722C4⋊C4—1222no—
723C4⋊C4—1221no—
724C4⋊C4—1222no—
725C4⋊C4—1224no—
726C4⋊C4—1221no—
727C4⋊C4—1221no—
728C4⋊C4—1222no—
729C4⋊C4—1222no—
730C4⋊C4—1222no—
731C4⋊C4—1222no—
732C4⋊C4—1224no—
733C4⋊C4—1222no—
734C4⋊C4—1224no—
735C4⋊C4—1222no—
736C4⋊C4—1221no—
737C4⋊C4C2×D24411yescharacteristic
738C4⋊C4C2×D24411yescharacteristic
739C4⋊C4C2×D24412yes—
740C4⋊C4C2×D24412yes—
741C22⋊C4—1221no—
742C22⋊C4—1224no—
743C22⋊C4—1222no—
744C22⋊C4—1222no—
745C22⋊C4—1222no—
746C22⋊C4—1222no—
747C22⋊C4—1221no—
748C22⋊C4—1221no—
749C22⋊C4—1222no—
750C22⋊C4—1222no—
751C22⋊C4—1222no—
752C22⋊C4—1222no—
753C22⋊C4—1222no—
754C22⋊C4C2×D24412yes—
755C22⋊C4C2×D24412yes—
756C22⋊C4C2×D24412yes—
757C42—1221no—
758C42—1221no—
759C42—1221no—
760C42—1224no—
761C42—1222no—
762C42C2×D24411yescharacteristic
763C42C2×D24412yes—
764C42C2×D24411yescharacteristic
765C42C2×D24412yes—
766C42C23×D6112yes—
767C42C23×D6111yescharacteristic
768C42C23×D6111yescharacteristic
769C23—1222no—
770C23—1221no—
771C23—4881no—
772C23—4881no—
773C23—2442no—
774C23C22×D24412yes—
775C23C22×D24411yescharacteristic
776Q8—22no—
777Q8—1221no—
778Q8—1221no—
779Q8—4882no—
780Q8—4884no—
781Q8—4882no—
782Q8—2444no—
783Q8—2442no—
784Q8—2442no—
785D4—24no—
786D4—22no—
787D4—1222no—
788D4—1222no—
789D4—1221no—
790D4—1221no—
791D4—4882no—
792D4—4882no—
793D4—4882no—
794D4—4882no—
795D4—4882no—
796D4—2442no—
797D4—2442no—
798C2×C4—22no—
799C2×C4—24no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—41no—
803C2×C4—42no—
804C2×C4—1222no—
805C2×C4—1221no—
806C2×C4—1221no—
807C2×C4—1221no—
808C2×C4—1224no—
809C2×C4—1222no—
810C2×C4—1222no—
811C2×C4—4881no—
812C2×C4—4882no—
813C2×C4—4881no—
814C2×C4—4882no—
815C2×C4—4884no—
816C2×C4—2444no—
817C2×C4—2442no—
818C2×C4—2442no—
819C2×C4C22×D24412yes—
820C2×C4C22×D24411yescharacteristic
821C2×C4C22×D24411yescharacteristic
822C2×C4C22×D24411yescharacteristic
823C2×C4C22×D24412yes—
824C2×C4C22×D24412yes—
825C2×C4C22×D24411yescharacteristic
826C2×C4C22×D24411yescharacteristic
827C2×C4#1451982412yes—
828C2×C4#1451982412yes—
829C2×C4C24×D6111yescharacteristic
830C8—22no—
831C8—22no—
832C8—24no—
833C22—21no—
834C22—21no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—4884no—
839C22—2442no—
840C22—2441no—
841C22—2441no—
842C22—2442no—
843C22—2441no—
844C22—2442no—
845C22#1684033812yes—
846C22C23×D24411yescharacteristic
847C4—21no—
848C4—22no—
849C4—21no—
850C4—21no—
851C4—22no—
852C4—22no—
853C4—2442no—
854C4—2441no—
855C4—2442no—
856C4—2444no—
857C4—2442no—
858C4—2441no—
859C4—2441no—
860C4#1684033812yes—
861C4#1684057412yes—
862C4C2×#1451982411yescharacteristic
863C4C2×#1451982411yescharacteristic
864C2—22no—
865C2—42no—
866C2—4882no—
867C2—4881no—
868C2C2×#1684033811yescharacteristic
869C2C2×#1684057411yescharacteristic
870C2#2146060011yescharacteristic
subgroupG/H
centerC22C23×D244
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#2925C2
socleC22×C61C23×D4
prime radical#21459235C2
hypercenter#2925D61
hypocenterC61#60892
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×#41 ◁ #2925

Complements

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

NH ≅ G/Ntype
1. #21459638C2semidirect
3. #21457119C2semidirect
4. #21457074C2semidirect
5. #21457042C2semidirect
6. #21457019C2semidirect
7. #21457000C2semidirect
8. #21456949C2semidirect
9. #21456350C2semidirect
10. #21456175C2semidirect
11. #21455810C2semidirect
12. #21455778C2semidirect
13. #21455635C2semidirect
14. #21455618C2semidirect
15. #21455609C2semidirect
16. C2×#16840053C2semidirect
17. C61×#2925C2semidirect
26. #16840390C22semidirect
36. #16840319C22semidirect
40. C2×#14519777C22semidirect
47. #16840171C22semidirect
48. #16840171C22semidirect
49. #16840164C22semidirect
50. #16840160C22semidirect
55. #16840104C22semidirect
56. #16840093C22semidirect
59. #16840087C22semidirect
61. #16840081C22semidirect
63. #16840070C22semidirect
65. #16840063C22semidirect
66. #16840058C22semidirect
67. #16840058C22semidirect
72. #16840053C22semidirect
73. #16840053C22semidirect
74. #16840048C22semidirect
75. #16840048C22semidirect
77. #16840043C22semidirect
78. #16840043C22semidirect
88. C61×#433C22semidirect
89. C61×#432C22semidirect
90. C61×#431C22semidirect
445. #2925D61semidirect
515. #433C2×D61semidirect
516. #432C2×D61semidirect
517. #431C2×D61semidirect
530. C61#60892semidirect

Maximal subgroups

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

subgroupindex
#214596382
#214592352
#214571192
#214570742
#214570422
#214570192
#214570002
#214569492
#214563502
#214561752
#214558102
#214557782
#214556352
#214556182
#214556092
C2×#168400532
C61×#29252
#6089261