Finite Group Databasebeta

← #30549057

Subgroups — #30549057

Order 15616.

1990 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459706C211yesmaximal, characteristic, complemented
2C4×#14519824C211yesmaximal, characteristic
3#21456121C214yesmaximal, complemented
4#21456038C214yesmaximal, complemented
5#21455983C212yesmaximal, complemented
6#21455951C212yesmaximal, complemented
7#21455892C212yesmaximal, complemented
8#21455860C212yesmaximal, complemented
9#21455791C212yesmaximal, complemented
10#21455620C211yesmaximal, characteristic, complemented
11#21455306C211yesmaximal, characteristic, complemented
12C2×#16839973C211yesmaximal, characteristic, complemented
13#21455117C212yesmaximal
14#21454686C212yesmaximal, complemented
15#21454665C212yesmaximal, complemented
16#21454484C211yesmaximal, characteristic, complemented
17C61×#3076C211yesmaximal, characteristic, complemented
18C2×#14519824C2211yescharacteristic
19C2×#14519807C2212yes—
20C22×Dic244C2212yes—
21#16840491—21no—
22#16840491—21no—
23#16840485—21no—
24#16840485—21no—
25#16840454—22no—
26#16840454—22no—
27#16840375C2214yes—
28#16840338C2212yes—
29#16840317C2212yes—
30#16840317C2212yes—
31C2×#14519777C2211yescharacteristic
32#16840245C2211yescharacteristic
33#16840242—21no—
34#16840242C2211yescharacteristic
35#16840241—22no—
36#16840241C2212yes—
37#16840239—21no—
38#16840239C2212yes—
39#16840239C2211yescharacteristic
40#16840238C2212yes—
41C4×#11758222—21no—
42C4×#11758222C2211yescharacteristic
43C4×#11758224—22no—
44C4×#11758224C2212yes—
45C2×C4×Dic122—21no—
46C2×C4×Dic122C2211yescharacteristic
47C4×Q8×D61C2212yes—
48#16840106C2214yes—
49#16840105C2214yes—
50#16840099C2214yes—
51#16840094C2214yes—
52#16840066C2214yes—
53#16840054C2212yes—
54#16840044C2212yes—
55#16839973C2212yes—
56#16839973C2212yes—
57#16839973C2214yes—
58#16839972C2212yes—
59#16839972C2212yes—
60#16839967C2212yes—
61#16839967C2212yes—
62#16839925C2214yes—
63#16839925C2214yes—
64#16839919C2214yes—
65#16839919C2214yes—
66#16839868C2214yes—
67#16839868C2214yes—
68#16839866C2214yes—
69#16839859C2214yes—
70#16839856C2214yes—
71#16839856C2214yes—
72#16839854C2214yes—
73#16839853C2214yes—
74#16839822C2214yes—
75#16839818C2212yes—
76#16839814C2212yes—
77#16839805C2212yes—
78#16839786C2211yescharacteristic
79#16839770C2212yes—
80#16839770C2212yes—
81C2×#14519702C2212yes—
82#16839728C2212yes—
83#16839717C2212yes—
84C61×#533C2211yescharacteristic
85C4×#41×C61C2211yescharacteristic
86C61×#479C2212yes—
87C61×#478C2212yes—
88C61×#477C2211yescharacteristic
89C61×#476C2211yescharacteristic
90C61×#475C2211yescharacteristic
91C61×#474C2211yescharacteristic
92C61×#427C2212yes—
93C2×C4⋊C8×C61C2211yescharacteristic
94C61×#416C2212yes—
95#14519824—24no—
96#14519824—24no—
97C2×#11758222—21no—
98C2×#11758222C2311yescharacteristic
99C2×#11758224—22no—
100C2×#11758224C2312yes—
101C22×Dic122—21no—
102C22×Dic122C2312yes—
103C22×Dic122C2311yescharacteristic
104C2×Q8×D61C2312yes—
105#14519807—28no—
106C2×Dic244—28no—
107C2×Dic244C2314yes—
108C2×Dic244C2314yes—
109C2×#11758202C2314yes—
110C2×#11758200C2314yes—
111C2×#11758194C2312yes—
112#14519777—22no—
113#14519777—21no—
114#14519777—21no—
115#14519777C2312yes—
116#14519777C2312yes—
117#14519772—24no—
118#14519772—24no—
119#14519768—24no—
120#14519768—24no—
121#14519768—22no—
122#14519768—22no—
123#14519765—22no—
124#14519761—24no—
125#14519757C2314yes—
126#14519757C2314yes—
127#14519753—22no—
128#14519753—22no—
129Q8×Dic61—22no—
130Q8×Dic61—22no—
131Q8×Dic61C2312yes—
132C4×Dic122—21no—
133C4×Dic122—21no—
134C4×Dic122—21no—
135C4×Dic122—21no—
136C4×Dic122—22no—
137C4×Dic122—22no—
138C4×Dic122—21no—
139C4×Dic122—22no—
140C4×Dic122—22no—
141C4×Dic122D411yescharacteristic
142C4×Dic122D411yescharacteristic
143C4×Dic122C2312yes—
144C4×Dic122C2312yes—
145#14519742—22no—
146#14519742—22no—
147#14519742C2312yes—
148#14519742C2312yes—
149#14519742C2314yes—
150#14519742C2314yes—
151C4×D244—21no—
152C4×D244D411yescharacteristic
153C4×D244D411yescharacteristic
154D4×Dic61—22no—
155D4×Dic61C2312yes—
156C4×C22⋊D61—22no—
157C4×C22⋊D61—22no—
158C4×C22⋊D61D412yes—
159C4×C22⋊D61D412yes—
160#14519737—22no—
161#14519737—22no—
162#14519737—22no—
163#14519736—21no—
164#14519736C2311yescharacteristic
165#14519735—22no—
166#14519735—22no—
167#14519735—22no—
168#14519735C2312yes—
169#14519734—22no—
170#14519734C2312yes—
171#14519733—24no—
172#14519733—22no—
173#14519733—22no—
174#14519733—22no—
175C2×C4⋊Dic61—21no—
176C2×C4⋊Dic61—21no—
177C2×C4⋊Dic61—21no—
178C2×C4⋊Dic61C2311yescharacteristic
179C2×#11758196—21no—
180C2×#11758196—22no—
181C4⋊C4×D61—22no—
182C4⋊C4×D61C2312yes—
183C2×C4×Dic61—21no—
184C2×C4×Dic61—22no—
185C42×D61—22no—
186C42×D61C2312yes—
187#14519710C2314yes—
188#14519708C2314yes—
189C4⋊#92418C2312yes—
190C4⋊#92418C2312yes—
191#14519702C2314yes—
192#14519702C2314yes—
193#14519700C2314yes—
194#14519700C2314yes—
195#14519700C2314yes—
196#14519700C2314yes—
197#14519689C2314yes—
198#14519689C2314yes—
199#14519687C2314yes—
200C8×Dic61C2314yes—
201C2×#41×C61C2311yescharacteristic
202C22×C8×C61C2312yes—
203C4⋊Q8×C61C2311yescharacteristic
204C4⋊Q8×C61C2311yescharacteristic
205#125×C61C2312yes—
206C22⋊Q8×C61—21no—
207C22⋊Q8×C61—21no—
208C4×Q8×C61—21no—
209C4×Q8×C61—21no—
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×C61C2312yes—
218#117×C61C2311yescharacteristic
219C2×C42×C61—21no—
220C2×C42×C61C2311yescharacteristic
221#107×C61C2312yes—
222#107×C61C2312yes—
223#106×C61C2312yes—
224#106×C61C2312yes—
225C4⋊C8×C61C2311yescharacteristic
226C4⋊C8×C61C2311yescharacteristic
227C4⋊C8×C61C2312yes—
228#103×C61C2312yes—
229#103×C61C2312yes—
230#102×C61C2312yes—
231#102×C61C2312yes—
232#41×C61—22no—
233#41×C61#4114yes—
234C2×Q8×C61—21no—
235C2×Q8×C61—21no—
236C2×Q8×C61C2411yescharacteristic
237C2×D4×C61—21no—
238C2×D4×C61C2411yescharacteristic
239C22×C4×C61—21no—
240C22×C4×C61—21no—
241C22×C4×C61—21no—
242C22×C4×C61C2×D411yescharacteristic
243C22×C4×C61C2×D411yescharacteristic
244C22×C4×C61C2411yescharacteristic
245C2×C22⋊D61—22no—
246C2×C22⋊D61C2×D412yes—
247C22×Dic61—21no—
248C22×Dic61—22no—
249C22×Dic61—22no—
250C22×Dic61—21no—
251C22×Dic61—22no—
252Q8×D61—24no—
253Q8×D61—24no—
254#11758224—216no—
255#11758224—24no—
256#11758224—24no—
257#11758222—28no—
258#11758222—22no—
259#11758222—22no—
260C2×D244C2×D411yescharacteristic
261C2×C4×D61—22no—
262C2×C4×D61—22no—
263C2×C4×D61C2×D412yes—
264C2×C4×D61C2×D412yes—
265C2×C4×D61C2412yes—
266C2×Dic122—28no—
267C2×Dic122—21no—
268C2×Dic122—22no—
269C2×Dic122—22no—
270C2×Dic122—24no—
271C2×Dic122—24no—
272C2×Dic122—22no—
273C2×Dic122C2×D411yescharacteristic
274C2×Dic122#4114yes—
275C2×Dic122C2414yes—
276C2×Dic122C2412yes—
277C2×C8×C61—24no—
278C2×C8×C61C2412yes—
279C2×C8×C61C2412yes—
280C4⋊C4×C61—21no—
281C4⋊C4×C61—21no—
282C4⋊C4×C61—22no—
283C4⋊C4×C61—22no—
284C4⋊C4×C61—21no—
285C4⋊C4×C61—21no—
286C4⋊C4×C61C2412yes—
287C4⋊C4×C61C2412yes—
288C4⋊C4×C61C2411yescharacteristic
289C4⋊C4×C61C2411yescharacteristic
290C22⋊C4×C61—21no—
291C22⋊C4×C61—22no—
292C22⋊C4×C61—21no—
293C22⋊C4×C61—21no—
294C42×C61—21no—
295C42×C61—21no—
296C42×C61—21no—
297C42×C61—22no—
298C42×C61C2×D411yescharacteristic
299C42×C61C2×D411yescharacteristic
300C42×C61C2411yescharacteristic
301C42×C61C2411yescharacteristic
302C22⋊Dic61—22no—
303C22⋊Dic61C2×D412yes—
304#11758202—28no—
305#11758200—28no—
306#11758198—22no—
307#11758198—24no—
308#11758198—24no—
309#11758198C2×D412yes—
310#11758198C2×D412yes—
311C4⋊Dic61—21no—
312C4⋊Dic61—22no—
313C4⋊Dic61—22no—
314C4⋊Dic61—22no—
315C4⋊Dic61—22no—
316C4⋊Dic61—22no—
317C4⋊Dic61—24no—
318C4⋊Dic61—24no—
319C4⋊Dic61C2×D411yescharacteristic
320C4⋊Dic61C2×D411yescharacteristic
321C4⋊Dic61C2412yes—
322#11758196—22no—
323#11758196—22no—
324#11758196—22no—
325#11758196—22no—
326#11758196—22no—
327#11758196—24no—
328#11758196—24no—
329#11758196C2×D412yes—
330#11758196C2×D412yes—
331C4×Dic61—22no—
332C4×Dic61—22no—
333C4×Dic61—22no—
334C4×Dic61—22no—
335C4×Dic61—22no—
336C4×Dic61—22no—
337C4×Dic61—24no—
338C4×Dic61—24no—
339C4×Dic61C2×D412yes—
340C4×Dic61C2×D412yes—
341C4×Dic61C2412yes—
342#11758194—24no—
343C2×#92418C2414yes—
344Dic244—28no—
345Dic244—28no—
346C23×C61—21no—
347C23×C61C22×D411yescharacteristic
348C22×D61C22×D412yes—
349Q8×C61—21no—
350Q8×C61—42no—
351Q8×C61—42no—
352Q8×C61C2×#4112yes—
353D4×C61—24no—
354D4×C61—21no—
355D4×C61C2×#4112yes—
356C2×C4×C61—21no—
357C2×C4×C61—24no—
358C2×C4×C61—22no—
359C2×C4×C61—21no—
360C2×C4×C61—21no—
361C2×C4×C61—22no—
362C2×C4×C61—22no—
363C2×C4×C61—41no—
364C2×C4×C61—42no—
365C2×C4×C61—81no—
366C2×C4×C61C22×D411yescharacteristic
367C2×C4×C61C22×D411yescharacteristic
368C2×C4×C61C22×D411yescharacteristic
369C2×C4×C61C22×D411yescharacteristic
370C2×C4×C61C22×D411yescharacteristic
371C2×C4×C61C2×#4112yes—
372C2×C4×C61C2×#4112yes—
373C2×C4×C61C2511yescharacteristic
374C22⋊D61—28no—
375C22⋊D61—24no—
376C2×Dic61—28no—
377C2×Dic61—24no—
378C2×Dic61—22no—
379C2×Dic61—22no—
380C2×Dic61—24no—
381C2×Dic61—44no—
382C2×Dic61—82no—
383C2×Dic61—81no—
384C2×Dic61C22×D412yes—
385C2×Dic61C22×D412yes—
386C2×Dic61C22×D412yes—
387D244—22no—
388C4×D61—28no—
389C4×D61—24no—
390C4×D61—22no—
391C4×D61—22no—
392C4×D61—42no—
393C4×D61—82no—
394Dic122—28no—
395Dic122—22no—
396Dic122—24no—
397Dic122—22no—
398Dic122—24no—
399Dic122—24no—
400Dic122—44no—
401Dic122C2×#4114yes—
402C8×C61—22no—
403C8×C61—22no—
404#92418—24no—
405#60594—611nomaximal, Sylow
406C22×C61—21no—
407C22×C61—21no—
408C22×C61—22no—
409C22×C61—41no—
410C22×C61—41no—
411C22×C61#52512yes—
412C22×C61C23×D411yescharacteristic
413C2×D61—22no—
414C2×D61—22no—
415C2×D61—22no—
416C4×C61—21no—
417C4×C61—21no—
418C4×C61—22no—
419C4×C61—21no—
420C4×C61—41no—
421C4×C61—42no—
422C4×C61—41no—
423C4×C61—42no—
424C4×C61#52512yes—
425C4×C61#57812yes—
426C4×C61C22×#4111yescharacteristic
427C4×C61C22×#4111yescharacteristic
428Dic61—22no—
429Dic61—22no—
430Dic61—24no—
431Dic61—22no—
432Dic61—42no—
433Dic61—44no—
434#3509—611no—
435C4×2−1+4—611no—
436#3127—614no—
437#3120—614no—
438#3116—612no—
439#3113—612no—
440#3107—612no—
441#3104—612no—
442#3097—612no—
443#3078—611no—
444#3076D6111yescharacteristic, complemented
445#3039—611no—
446C2×#462—611no—
447#3011—612no—
448#2950—612no—
449#2947—612no—
450#2925—611no—
451C2×C61—22no—
452C2×C61—42no—
453C2×C61C2×#52511yescharacteristic
454C2×C61C2×#57811yescharacteristic
455C2×C61#358611yescharacteristic
456D61—42no—
457C2×2−1+4—611no—
458C2×#137—612no—
459C22×Q16—612no—
460#557—1221no—
461#557—1221no—
462#556—1221no—
463#556—1221no—
464#552—1222no—
465#552—1222no—
466#541—614no—
467#536—612no—
468#533—612no—
469#533—612no—
470#533C2×D6111yescharacteristic
471C2×C4⋊Q8—611no—
472#520—611no—
473#520—611no—
474#520—612no—
475#520—1221no—
476#520—1222no—
477#519—612no—
478#519—611no—
479#519—612no—
480#519—1221no—
481C4×#41—611no—
482C4×#41—612no—
483C4×#41—1221no—
484C4×#41—1222no—
485C4×#41C2×D6111yescharacteristic
486C2×C4×Q8—612no—
487C2×C4×Q8—611no—
488C2×C4×Q8—1221no—
489#485—614no—
490#485—614no—
491#484—614no—
492#483—614no—
493#479—614no—
494#479C2×D6112yes—
495#478C2×D6112yes—
496#477—612no—
497#477C2×D6111yescharacteristic
498#476C2×D6111yescharacteristic
499#475—612no—
500#475C2×D6111yescharacteristic
501#474C2×D6111yescharacteristic
502#462—612no—
503#462—612no—
504#462—612no—
505#462—612no—
506#462—614no—
507#461—612no—
508#461—612no—
509#452—614no—
510#452—614no—
511#451—614no—
512#451—614no—
513#441—614no—
514#441—614no—
515#441—614no—
516#440—614no—
517C4×Q16—614no—
518C4×Q16—614no—
519C4×Q16—614no—
520C4×SD16—614no—
521#433—614no—
522#432—612no—
523#431—612no—
524#428—612no—
525#427C2×D6112yes—
526#423—611no—
527C2×C4⋊C8C2×D6111yescharacteristic
528#419—612no—
529#419—612no—
530#416C2×D6112yes—
531C2×#103—612no—
532#408—612no—
533#405—612no—
534C61#6059411yescharacteristic, complemented, Sylow
5352−1+4—1224no—
5362−1+4—1224no—
537C2×#41—611no—
538C2×#41—612no—
539C2×#41—1221no—
540C2×#41—1222no—
541C2×#41C22×D6111yescharacteristic
542C22×Q8—612no—
543C22×Q8—611no—
544C22×Q8—612no—
545C22×Q8—1221no—
546#137—1228no—
547C2×Q16—614no—
548C2×Q16—614no—
549C2×Q16—614no—
550C2×Q16—1228no—
551C2×SD16—614no—
552C2×M16—612no—
553C22×C8C22×D6112yes—
554C4⋊Q8—612no—
555C4⋊Q8—612no—
556C4⋊Q8—1222no—
557C4⋊Q8—1221no—
558C4⋊Q8—1221no—
559C4⋊Q8C22×D6111yescharacteristic
560C4⋊Q8C22×D6111yescharacteristic
561#126—1224no—
562#126—1224no—
563#125—1222no—
564#125—1222no—
565#125—1224no—
566#125—1224no—
567#125C22×D6112yes—
568#124—1222no—
569#123—1224no—
570C22⋊Q8—21no—
571C22⋊Q8—21no—
572C22⋊Q8—614no—
573C22⋊Q8—614no—
574C22⋊Q8—1222no—
575C22⋊Q8—1222no—
576C4×Q8—21no—
577C4×Q8—21no—
578C4×Q8—611no—
579C4×Q8—611no—
580C4×Q8—612no—
581C4×Q8—612no—
582C4×Q8—612no—
583C4×Q8—614no—
584C4×Q8—614no—
585C4×Q8—612no—
586C4×Q8—612no—
587C4×Q8—1222no—
588C4×Q8—1221no—
589C4×Q8—1222no—
590C4×Q8—1221no—
591C4×Q8—1222no—
592C4×Q8—1222no—
593C4×Q8—1221no—
594C4×Q8—1222no—
595C4×Q8—1222no—
596C4×Q8—1222no—
597C4×Q8—1222no—
598C4×Q8—1221no—
599C4×Q8—1221no—
600C4×Q8C22×D6111yescharacteristic
601C4×Q8C22×D6111yescharacteristic
602C4×D4—21no—
603C4×D4—21no—
604C4×D4—612no—
605C4×D4—612no—
606C4×D4—612no—
607C4×D4—611no—
608C4×D4—611no—
609C4×D4—1221no—
610C4×D4—1222no—
611C4×D4—1222no—
612C4×D4—1222no—
613C4×D4—1222no—
614C4×D4—1222no—
615C4×D4—1222no—
616C4×D4C22×D6111yescharacteristic
617C4×D4C22×D6111yescharacteristic
618#117—21no—
619#117—611no—
620#117—612no—
621#117—612no—
622#117—1222no—
623#117—1222no—
624#117—1222no—
625#117—1224no—
626#117—1222no—
627#117—1222no—
628#117—1222no—
629#117—1222no—
630#117—1221no—
631#117C22×D6111yescharacteristic
632#117C22×D6112yes—
633C2×C4⋊C4—611no—
634C2×C4⋊C4—612no—
635C2×C4⋊C4—1222no—
636C2×C4⋊C4—1222no—
637C2×C4⋊C4—1221no—
638C2×C4⋊C4—1221no—
639C2×C4⋊C4—1221no—
640C2×C4⋊C4—1221no—
641C2×C42—21no—
642C2×C42—612no—
643C2×C42—1222no—
644C2×C42—1222no—
645C2×C42—1221no—
646C2×C42C22×D6111yescharacteristic
647#107—614no—
648#107C22×D6112yes—
649#107C22×D6112yes—
650#106—614no—
651#106C22×D6112yes—
652#106C22×D6112yes—
653C4⋊C8—612no—
654C4⋊C8—612no—
655C4⋊C8C22×D6111yescharacteristic
656C4⋊C8C22×D6111yescharacteristic
657C4⋊C8C22×D6112yes—
658#103—614no—
659#103—614no—
660#103—614no—
661#103—614no—
662#103—614no—
663#103—614no—
664#103C22×D6112yes—
665#103C22×D6112yes—
666#102C22×D6112yes—
667#102C22×D6112yes—
668C22⋊C8—614no—
669C22⋊C8—614no—
670#97—614no—
671C4×C8—614no—
672#41—22no—
673#41—1228no—
674#41—1224no—
675#41—12216no—
676#41—1224no—
677#41—1222no—
678#41—1222no—
679#41#1175822614yes—
680C2×Q8—21no—
681C2×Q8—21no—
682C2×Q8—611no—
683C2×Q8—614no—
684C2×Q8—612no—
685C2×Q8—614no—
686C2×Q8—1222no—
687C2×Q8—1228no—
688C2×Q8—1224no—
689C2×Q8—1224no—
690C2×Q8—1221no—
691C2×Q8—1222no—
692C2×Q8—1222no—
693C2×Q8—1224no—
694C2×Q8—1224no—
695C2×Q8C23×D6111yescharacteristic
696C2×D4—21no—
697C2×D4—612no—
698C2×D4—611no—
699C2×D4—1222no—
700C2×D4C23×D6111yescharacteristic
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—612no—
705C22×C4—612no—
706C22×C4—612no—
707C22×C4—1222no—
708C22×C4—1222no—
709C22×C4—1222no—
710C22×C4—1222no—
711C22×C4—1221no—
712C22×C4—1221no—
713C22×C4—1222no—
714C22×C4D4×D6111yescharacteristic
715C22×C4D4×D6111yescharacteristic
716C22×C4C23×D6111yescharacteristic
717Q16—1228no—
718Q16—1228no—
719Q16—1228no—
720SD16—1228no—
721M16—1224no—
722C2×C8—24no—
723C2×C8—614no—
724C2×C8C23×D6112yes—
725C2×C8C23×D6112yes—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—22no—
731C4⋊C4—22no—
732C4⋊C4—612no—
733C4⋊C4—611no—
734C4⋊C4—612no—
735C4⋊C4—611no—
736C4⋊C4—612no—
737C4⋊C4—1222no—
738C4⋊C4—1222no—
739C4⋊C4—1222no—
740C4⋊C4—1222no—
741C4⋊C4—1224no—
742C4⋊C4—1224no—
743C4⋊C4—1224no—
744C4⋊C4—1224no—
745C4⋊C4—1221no—
746C4⋊C4—1222no—
747C4⋊C4—1222no—
748C4⋊C4—1222no—
749C4⋊C4—1222no—
750C4⋊C4—1222no—
751C4⋊C4—1222no—
752C4⋊C4C23×D6112yes—
753C4⋊C4C23×D6112yes—
754C4⋊C4C23×D6111yescharacteristic
755C4⋊C4C23×D6111yescharacteristic
756C22⋊C4—21no—
757C22⋊C4—22no—
758C22⋊C4—21no—
759C22⋊C4—21no—
760C22⋊C4—612no—
761C22⋊C4—612no—
762C22⋊C4—612no—
763C22⋊C4—1222no—
764C22⋊C4—1224no—
765C22⋊C4—1224no—
766C22⋊C4—1222no—
767C42—21no—
768C42—21no—
769C42—21no—
770C42—22no—
771C42—612no—
772C42—612no—
773C42—612no—
774C42—1222no—
775C42—1222no—
776C42—1222no—
777C42—1222no—
778C42—1224no—
779C42—1224no—
780C42—1222no—
781C42—1222no—
782C42D4×D6111yescharacteristic
783C42D4×D6111yescharacteristic
784C42C23×D6111yescharacteristic
785C42C23×D6111yescharacteristic
786C23—21no—
787C23—612no—
788C23C2×D4×D6111yescharacteristic
789Q8—21no—
790Q8—42no—
791Q8—42no—
792Q8—614no—
793Q8—1228no—
794Q8—1222no—
795Q8—1224no—
796Q8—1222no—
797Q8—1224no—
798Q8—1224no—
799Q8—2444no—
800Q8C2×#1175822612yes—
801D4—24no—
802D4—21no—
803D4—1228no—
804D4—1224no—
805D4—1222no—
806D4C2×#1175822612yes—
807C2×C4—21no—
808C2×C4—24no—
809C2×C4—22no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—41no—
815C2×C4—42no—
816C2×C4—81no—
817C2×C4—612no—
818C2×C4—612no—
819C2×C4—612no—
820C2×C4—1228no—
821C2×C4—1228no—
822C2×C4—1224no—
823C2×C4—1222no—
824C2×C4—1224no—
825C2×C4—1222no—
826C2×C4—1222no—
827C2×C4—1222no—
828C2×C4—1224no—
829C2×C4—4882no—
830C2×C4—4882no—
831C2×C4—4881no—
832C2×C4—2442no—
833C2×C4—2444no—
834C2×C4C2×D4×D6111yescharacteristic
835C2×C4C2×D4×D6111yescharacteristic
836C2×C4C2×D4×D6111yescharacteristic
837C2×C4C2×D4×D6111yescharacteristic
838C2×C4C2×D4×D6111yescharacteristic
839C2×C4#41×D6112yes—
840C2×C4C2×#1175822612yes—
841C2×C4C24×D6111yescharacteristic
842C8—22no—
843C8—22no—
844C8—1224no—
845C22—21no—
846C22—21no—
847C22—22no—
848C22—41no—
849C22—41no—
850C22—1222no—
851C22—1222no—
852C22—1222no—
853C22#1684027512yes—
854C22C22×D4×D6111yescharacteristic
855C4—21no—
856C4—22no—
857C4—21no—
858C4—21no—
859C4—41no—
860C4—42no—
861C4—41no—
862C4—42no—
863C4—1222no—
864C4—1222no—
865C4—1224no—
866C4—1222no—
867C4—2444no—
868C4—2442no—
869C4#1684027512yes—
870C4#1684057612yes—
871C4C2×#41×D6111yescharacteristic
872C4C22×#1175822611yescharacteristic
873C2—22no—
874C2—42no—
875C2—2442no—
876C2C2×#1684027511yescharacteristic
877C2C2×#1684057611yescharacteristic
878C2#2146060311yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3076C2
socleC22×C61C23×D4
prime radicalC2×#14519824C22
hypercenter#3076D61
hypocenterC61#60594
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3076

Complements

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

NH ≅ G/Ntype
1. #21459706C2semidirect
3. #21456121C2semidirect
4. #21456038C2semidirect
5. #21455983C2semidirect
6. #21455951C2semidirect
7. #21455892C2semidirect
8. #21455860C2semidirect
9. #21455791C2semidirect
10. #21455620C2semidirect
11. #21455306C2semidirect
12. C2×#16839973C2semidirect
14. #21454686C2semidirect
15. #21454665C2semidirect
16. #21454484C2semidirect
17. C61×#3076C2semidirect
444. #3076D61semidirect
534. C61#60594semidirect

Maximal subgroups

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

subgroupindex
#214597062
C4×#145198242
#214561212
#214560382
#214559832
#214559512
#214558922
#214558602
#214557912
#214556202
#214553062
C2×#168399732
#214551172
#214546862
#214546652
#214544842
C61×#30762
#6059461