Finite Group Databasebeta

← #30564948

Subgroups — #30564948

Order 15616.

2178 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459660C211yesmaximal, characteristic, complemented
2C2×#16840430C211yesmaximal, characteristic, complemented
3#21457940C214yesmaximal, complemented
4#21457828C214yesmaximal, complemented
5#21457407C214yesmaximal, complemented
6#21457366C214yesmaximal, complemented
7#21456840C212yesmaximal, complemented
8#21456616C211yesmaximal, characteristic, complemented
9#21456589C212yesmaximal, complemented
10#21455993C212yesmaximal, complemented
11#21455077C211yesmaximal, characteristic, complemented
12#21455073C211yesmaximal, characteristic, complemented
13#21455038C212yesmaximal, complemented
14#21454846C211yesmaximal, characteristic, complemented
15C61×#3193C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×#11758224C2211yescharacteristic, complemented
18C2×#14519808C2212yescomplemented
19C2×#14519805C2212yescomplemented
20C2×#14519798C2214yescomplemented
21#16840460—22no—
22#16840460C2212yescomplemented
23#16840454C2212yescomplemented
24#16840439—22no—
25#16840430—22no—
26#16840430—22no—
27#16840430C2214yes—
28#16840430C2214yescomplemented
29#16840423C2212yescomplemented
30#16840403C2212yescomplemented
31#16840361—21no—
32#16840352—21no—
33#16840324—21no—
34C2×#14519773—21no—
35C2×#14519773C2211yescharacteristic, complemented
36#16840298C2212yes—
37#16840275C2212yes—
38C2×#14519752C2211yescharacteristic, complemented
39C2×#14519751C2211yescharacteristic
40C2×#14519750—21no—
41C2×#14519749—21no—
42#16840235—21no—
43C2×#14519742C2211yescharacteristic, complemented
44C2×C4×C22⋊D61C2211yescharacteristic
45C2×#14519737—21no—
46#16840148C2214yescomplemented
47#16840125C2214yescomplemented
48#16840089C2214yescomplemented
49#16840080C2212yes—
50#16840078C2212yescomplemented
51#16840068C2214yescomplemented
52#16840013C2214yescomplemented
53#16839999C2214yescomplemented
54#16839994C2214yescomplemented
55#16839987C2214yescomplemented
56#16839960C2214yescomplemented
57#16839956C2214yescomplemented
58#16839922C2214yescomplemented
59#16839921C2214yescomplemented
60#16839917C2212yescomplemented
61#16839912C2212yescomplemented
62#16839910C2214yescomplemented
63#16839909C2214yescomplemented
64#16839908C2214yescomplemented
65#16839903C2212yes—
66#16839898C2212yes—
67#16839896C2212yes—
68#16839895C2212yescomplemented
69#16839866C2214yescomplemented
70#16839861C2214yescomplemented
71#16839836C2214yescomplemented
72#16839831C2214yescomplemented
73#16839816C2212yescomplemented
74#16839764C2212yescomplemented
75#16839761C2212yescomplemented
76#16839755C2214yescomplemented
77#16839726C2211yescharacteristic
78C22⋊C8×D61C2212yescomplemented
79C2×C22⋊Q8×C61C2211yescharacteristic
80C2×#121×C61C2211yescharacteristic
81C61×#484C2212yescomplemented
82C61×#480C2212yescomplemented
83C61×#468C2214yescomplemented
84C61×#450C2212yescomplemented
85C61×#448C2212yescomplemented
86C61×#407C2211yescharacteristic
87C2×#11758226C2312yes—
88C2×#11758222—21no—
89C2×#11758222—21no—
90C2×#11758222—44no—
91C2×#11758222C2312yes—
92C2×#11758222C2312yes—
93C2×#11758224—22no—
94C2×#11758224—44no—
95C2×#11758224C2314yes—
96C22×Dic122C2311yescharacteristic
97C22×D244—21no—
98C22×D244C2311yescharacteristic
99C22×D244C2311yescharacteristic
100C22×C22⋊D61—21no—
101C22×C22⋊D61—21no—
102C22×C22⋊D61—21no—
103C22×C22⋊D61—21no—
104C22×C22⋊D61—21no—
105C22×C22⋊D61D411yescharacteristic
106C23×Dic61—21no—
107C22×C4×D61—21no—
108C22×C4×D61C2311yescharacteristic
109#14519808—44no—
110#14519805—44no—
111#14519798—48no—
112C2×#11758202C2314yes—
113C2×#11758190C2314yes—
114C2×#11758201C2314yes—
115C2×D488C2314yes—
116C2×#11758199C2314yes—
117C2×#11758194C2312yes—
118C2×C8×D61C2314yes—
119#14519773—24no—
120#14519773—24no—
121#14519773—22no—
122#14519773C2314yes—
123#14519772—22no—
124#14519772—22no—
125#14519772—22no—
126#14519768—22no—
127#14519768C2312yes—
128#14519766—22no—
129#14519766C2312yes—
130#14519762—22no—
131#14519762—22no—
132#14519762—22no—
133#14519761—22no—
134#14519761—22no—
135#14519753—22no—
136#14519753C2312yes—
137#14519752—22no—
138#14519752—22no—
139#14519752C2312yes—
140#14519752C2314yes—
141#14519751—21no—
142#14519751—21no—
143#14519751—22no—
144#14519751—22no—
145#14519751C2312yes—
146#14519751C2312yes—
147#14519750—24no—
148#14519750—24no—
149#14519749—24no—
150#14519749—24no—
151#14519747—22no—
152#14519747—22no—
153Q8×Dic61C2312yes—
154#14519742—22no—
155#14519742C2314yes—
156#14519739—22no—
157#14519739C2312yes—
158C4×C22⋊D61—22no—
159C4×C22⋊D61—22no—
160C4×C22⋊D61D412yes—
161C4×C22⋊D61D412yes—
162C4×C22⋊D61C2312yes—
163C4×C22⋊D61C2312yes—
164#14519737—22no—
165#14519737—22no—
166#14519737—24no—
167#14519737—24no—
168#14519735—22no—
169#14519735C2312yes—
170#14519733—22no—
171C2×C4⋊Dic61C2311yescharacteristic
172C2×#11758196—21no—
173C2×#11758196D411yescharacteristic
174C2×C22⋊Dic61D411yescharacteristic
175C2×#11758198—21no—
176C2×#11758198—21no—
177C2×#11758198D411yescharacteristic
178C22⋊C4×D61—22no—
179C2×C4×Dic61—21no—
180C2×C4×Dic61C2311yescharacteristic
181#14519708C2314yes—
182#14519706C2314yes—
183#14519702C2314yes—
184#14519700C2314yes—
185#14519699C2314yes—
186#14519698C2314yes—
187#14519697C2314yes—
188#14519697C2314yes—
189C22⋊#92418C2312yes—
190C22⋊#92418C2312yes—
191#14519689C2314yes—
192#14519687C2314yes—
193C22×Q8×C61C2311yescharacteristic
194C22×D4×C61—21no—
195C22×D4×C61C2311yescharacteristic
196C23×C4×C61C2311yescharacteristic
197C2×SD16×C61C2314yes—
198C2×M16×C61C2312yes—
199C22⋊Q8×C61—21no—
200C22⋊Q8×C61—21no—
201C22⋊Q8×C61C2312yes—
202C22⋊Q8×C61C2312yes—
203#121×C61—21no—
204#121×C61—21no—
205#121×C61C2312yes—
206#121×C61C2312yes—
207C2×C4⋊C4×C61—21no—
208C2×C4⋊C4×C61C2311yescharacteristic
209C2×C4⋊C4×C61C2311yescharacteristic
210C2×C22⋊C4×C61—21no—
211C2×C22⋊C4×C61—21no—
212#107×C61C2314yes—
213#103×C61C2314yes—
214#102×C61C2314yes—
215C22⋊C8×C61C2312yes—
216C22⋊C8×C61C2312yes—
217C24×C61—21no—
218C24×C61C2×D411yescharacteristic
219C23×D61—21no—
220C23×D61—21no—
221C23×D61C2×D411yescharacteristic
222C2×Q8×C61—21no—
223C2×Q8×C61—42no—
224C2×Q8×C61C2412yes—
225C2×D4×C61—22no—
226C2×D4×C61—22no—
227C2×D4×C61—21no—
228C2×D4×C61—42no—
229C2×D4×C61—82no—
230C2×D4×C61C2412yes—
231C22×C4×C61—21no—
232C22×C4×C61—21no—
233C22×C4×C61—21no—
234C22×C4×C61—42no—
235C22×C4×C61C2×D411yescharacteristic
236C22×C4×C61C2×D411yescharacteristic
237C22×C4×C61C2×D411yescharacteristic
238C22×C4×C61C2411yescharacteristic
239C22×C4×C61C2411yescharacteristic
240C22×C4×C61C2411yescharacteristic
241C2×C22⋊D61—22no—
242C2×C22⋊D61—22no—
243C2×C22⋊D61—22no—
244C2×C22⋊D61—22no—
245C2×C22⋊D61—24no—
246C2×C22⋊D61—24no—
247C2×C22⋊D61—24no—
248C2×C22⋊D61—42no—
249C2×C22⋊D61—44no—
250C2×C22⋊D61—44no—
251C2×C22⋊D61—44no—
252C2×C22⋊D61—44no—
253C2×C22⋊D61—82no—
254C2×C22⋊D61C2×D412yes—
255C2×C22⋊D61C2×D412yes—
256C22×Dic61—21no—
257C22×Dic61—21no—
258C22×Dic61—24no—
259C22×Dic61—44no—
260C22×Dic61C2×D411yescharacteristic
261C22×Dic61C2×D411yescharacteristic
262C22×Dic61C2×D411yescharacteristic
263#11758226—44no—
264#11758224—28no—
265#11758224—44no—
266#11758224—48no—
267#11758222—24no—
268#11758222—24no—
269#11758222—42no—
270#11758222—42no—
271#11758222—44no—
272#11758222—44no—
273C2×D244—21no—
274C2×D244—24no—
275C2×D244—22no—
276C2×D244—22no—
277C2×D244—21no—
278C2×D244—42no—
279C2×D244—42no—
280C2×D244—82no—
281C2×D244C2412yes—
282C2×D244C2412yes—
283C2×C4×D61—22no—
284C2×C4×D61—22no—
285C2×C4×D61—22no—
286C2×C4×D61—22no—
287C2×C4×D61—42no—
288C2×C4×D61—44no—
289C2×C4×D61C2×D412yes—
290C2×C4×D61C2412yes—
291C2×Dic122—21no—
292C2×Dic122—24no—
293C2×Dic122C2412yes—
294SD16×C61—44no—
295M16×C61—42no—
296C2×C8×C61C2414yes—
297C4⋊C4×C61—22no—
298C4⋊C4×C61—22no—
299C4⋊C4×C61—21no—
300C4⋊C4×C61—21no—
301C4⋊C4×C61C2412yes—
302C4⋊C4×C61C2412yes—
303C22⋊C4×C61—22no—
304C22⋊C4×C61—22no—
305C22⋊C4×C61—22no—
306C22⋊C4×C61—22no—
307C22⋊Dic61C2×D412yes—
308C22⋊Dic61C2×D412yes—
309#11758202—28no—
310#11758201—44no—
311#11758199—44no—
312#11758198—22no—
313#11758198—22no—
314#11758198—22no—
315#11758198—22no—
316#11758198—22no—
317#11758198—22no—
318#11758198—24no—
319#11758198—22no—
320#11758198—22no—
321#11758198C2×D412yes—
322#11758198C2×D412yes—
323C4⋊Dic61—21no—
324C4⋊Dic61—22no—
325C4⋊Dic61—22no—
326C4⋊Dic61C2412yes—
327#11758196—24no—
328#11758196—22no—
329#11758196—22no—
330#11758196C2×D412yes—
331#11758196C2×D412yes—
332C4×Dic61—24no—
333C4×Dic61—22no—
334C4×Dic61—22no—
335C4×Dic61C2×D412yes—
336C4×Dic61C2412yes—
337#11758194—42no—
338C2×#92418C2414yes—
339D488—44no—
340#11758190—28no—
341C8×D61—44no—
342C23×C61—22no—
343C23×C61—22no—
344C23×C61—41no—
345C23×C61—41no—
346C23×C61—42no—
347C23×C61—42no—
348C23×C61—42no—
349C23×C61C22×D411yescharacteristic
350C23×C61C22×D411yescharacteristic
351C23×C61C22×D411yescharacteristic
352C22×D61—22no—
353C22×D61—22no—
354C22×D61—22no—
355C22×D61—41no—
356C22×D61—41no—
357C22×D61—42no—
358C22×D61—42no—
359C22×D61—42no—
360C22×D61—42no—
361C22×D61—81no—
362C22×D61—81no—
363C22×D61C22×D412yes—
364Q8×C61—24no—
365Q8×C61—81no—
366D4×C61—24no—
367D4×C61—42no—
368D4×C61—82no—
369D4×C61—82no—
370C2×C4×C61—22no—
371C2×C4×C61—22no—
372C2×C4×C61—22no—
373C2×C4×C61—22no—
374C2×C4×C61—22no—
375C2×C4×C61—22no—
376C2×C4×C61—41no—
377C2×C4×C61—41no—
378C2×C4×C61—41no—
379C2×C4×C61—42no—
380C2×C4×C61—81no—
381C2×C4×C61—81no—
382C2×C4×C61C22×D411yescharacteristic
383C2×C4×C61C22×D411yescharacteristic
384C2×C4×C61C22×D411yescharacteristic
385C2×C4×C61C2511yescharacteristic
386C22⋊D61—42no—
387C22⋊D61—42no—
388C22⋊D61—48no—
389C22⋊D61—44no—
390C22⋊D61—44no—
391C22⋊D61—48no—
392C22⋊D61—44no—
393C22⋊D61—44no—
394C22⋊D61—84no—
395C2×Dic61—24no—
396C2×Dic61—22no—
397C2×Dic61—22no—
398C2×Dic61—22no—
399C2×Dic61—41no—
400C2×Dic61—41no—
401C2×Dic61—48no—
402C2×Dic61—42no—
403C2×Dic61C22×D412yes—
404C2×Dic61C22×D412yes—
405C2×Dic61C22×D412yes—
406D244—24no—
407D244—22no—
408D244—22no—
409D244—42no—
410D244—81no—
411D244—82no—
412D244—84no—
413D244—82no—
414C4×D61—24no—
415C4×D61—42no—
416C4×D61—44no—
417C4×D61—44no—
418C4×D61—82no—
419C4×D61—82no—
420Dic122—24no—
421Dic122—22no—
422Dic122H(5,𝔽2)14yes—
423C8×C61—24no—
424#92418—24no—
425#61577—611nomaximal, Sylow
426C22×C61—21no—
427C22×C61—21no—
428C22×C61—21no—
429C22×C61—21no—
430C22×C61—21no—
431C22×C61—21no—
432C22×C61—21no—
433C22×C61—21no—
434C22×C61—42no—
435C22×C61—42no—
436C22×C61—42no—
437C22×C61—82no—
438C22×C61—84no—
439C22×C61#57512yes—
440C22×C61C23×D411yescharacteristic
441C2×D61—22no—
442C2×D61—22no—
443C2×D61—22no—
444C2×D61—42no—
445C2×D61—42no—
446C2×D61—42no—
447C2×D61—42no—
448C2×D61—42no—
449C2×D61—42no—
450C2×D61—82no—
451C2×D61—84no—
452C2×D61—162no—
453C4×C61—21no—
454C4×C61—21no—
455C4×C61—21no—
456C4×C61—42no—
457C4×C61—42no—
458C4×C61—42no—
459C4×C61C2×H(5,𝔽2)12yes—
460Dic61—22no—
461Dic61—24no—
462Dic61—22no—
463Dic61—22no—
464Dic61—42no—
465#3505—611no—
466C2×#550—611no—
467#3317—614no—
468#3309—614no—
469#3271—614no—
470#3268—614no—
471#3217—612no—
472#3193D6111yescharacteristic, complemented
473#3192—611no—
474#3188—612no—
475#3117—612no—
476#3007—611no—
477#3006—611no—
478#3002—612no—
479#2973—611no—
480C2×C61—22no—
481C2×C61—41no—
482C2×C61—41no—
483C2×C61—82no—
484C2×C61#348411yescharacteristic
485C2×C61C2×#57511yescharacteristic
486C2×C61#358511yescharacteristic
487D61—42no—
488D61—82no—
489D61—82no—
490C22×#41—611no—
491C22×#41—611no—
492C2×#137—612no—
493C2×AGL(1,ℤ/8)—612no—
494C2×#135—614no—
495#553—612no—
496#553—1222no—
497#552—612no—
498#551—1222no—
499#550—614no—
500#550—614no—
501#550—1222no—
502#550—1222no—
503#548—612no—
504#546—612no—
505#539—1221no—
506#538—1221no—
507#534—1221no—
508C2×#127—611no—
509C2×#127—1221no—
510#529—612no—
511#525—612no—
512C2×C22⋊Q8C2×D6111yescharacteristic
513C2×#121—611no—
514C2×#121—611no—
515C2×#121—1221no—
516C2×#121—1221no—
517C2×#121C2×D6111yescharacteristic
518#518—1221no—
519C2×C4×Q8—611no—
520C2×C4×D4—611no—
521C2×C4×D4—1221no—
522#496—614no—
523#490—614no—
524#484C2×D6112yescomplemented
525#482—614no—
526#481—612no—
527#481—612no—
528#480C2×D6112yescomplemented
529#479—614no—
530#469—614no—
531#468C2×D6114yescomplemented
532#466—614no—
533#465—614no—
534#464—614no—
535#460—614no—
536#459—614no—
537#452—614no—
538#452—614no—
539#451—612no—
540#450—612no—
541#450C2×D6112yescomplemented
542#449—614no—
543#449—614no—
544#449—614no—
545#448—612no—
546#448C2×D6112yescomplemented
547#447—612no—
548#447—612no—
549#447—612no—
550#441—614no—
551#440—614no—
552#435—614no—
553#435—614no—
554#432—612no—
555#417—612no—
556#417—612no—
557#416—614no—
558#407—611no—
559#407C2×D6111yescharacteristic
560C2×C22⋊C8—612no—
561C61#6157711yescharacteristic, complemented, Sylow
562C2×#41—612no—
563C2×#41—614no—
564C2×#41—612no—
565C2×#41—612no—
566C2×#41—1222no—
567C2×#41—1221no—
568C2×#41—1221no—
569C2×#41—2444no—
570C2×#41—2444no—
571C22×Q8—611no—
572C22×Q8C22×D6111yescharacteristic
573C22×D4—21no—
574C22×D4—611no—
575C22×D4—611no—
576C22×D4—611no—
577C22×D4—1221no—
578C22×D4—1221no—
579C22×D4—1221no—
580C22×D4—1221no—
581C22×D4—1221no—
582C22×D4—1221no—
583C22×D4C22×D6111yescharacteristic
584C23×C4—611no—
585C23×C4—1221no—
586C23×C4—1221no—
587C23×C4C22×D6111yescharacteristic
588#137—2444no—
589AGL(1,ℤ/8)—2444no—
590#135—2448no—
591C2×Q16—614no—
592C2×SD16—614no—
593C2×SD16—614no—
594C2×SD16C22×D6114yes—
595C2×D8—614no—
596C2×D8—614no—
597C2×M16—612no—
598C2×M16C22×D6112yes—
599C22×C8—614no—
600#127—614no—
601#127—1222no—
602#127—1224no—
603#127—1224no—
604#126—1222no—
605#126—1222no—
606#126—1222no—
607#125—612no—
608#125—1222no—
609#124—612no—
610#124—1222no—
611#123—1222no—
612#123—1222no—
613#123—1222no—
614#123—1222no—
615#123—1222no—
616C22⋊Q8—21no—
617C22⋊Q8—21no—
618C22⋊Q8—612no—
619C22⋊Q8—1222no—
620C22⋊Q8C22×D6112yes—
621C22⋊Q8C22×D6112yes—
622#121—21no—
623#121—21no—
624#121—612no—
625#121—612no—
626#121—614no—
627#121—612no—
628#121—1224no—
629#121—1224no—
630#121—1222no—
631#121—1224no—
632#121—1224no—
633#121—1222no—
634#121—1222no—
635#121—1222no—
636#121—1221no—
637#121—1221no—
638#121C22×D6112yes—
639#121C22×D6112yes—
640#120—1222no—
641#120—1222no—
642C4×Q8—612no—
643C4×Q8—614no—
644C4×Q8—1222no—
645C4×D4—612no—
646C4×D4—612no—
647C4×D4—612no—
648C4×D4—612no—
649C4×D4—612no—
650C4×D4—1224no—
651C4×D4—1224no—
652C4×D4—1222no—
653C4×D4—1222no—
654C4×D4—1222no—
655C4×D4—1222no—
656C4×D4—1222no—
657#117—612no—
658#117—1222no—
659#117—1222no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—611no—
662C2×C4⋊C4—611no—
663C2×C4⋊C4—1221no—
664C2×C4⋊C4C22×D6111yescharacteristic
665C2×C4⋊C4C22×D6111yescharacteristic
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—611no—
669C2×C22⋊C4—611no—
670C2×C22⋊C4—1222no—
671C2×C22⋊C4—1221no—
672C2×C22⋊C4—1221no—
673C2×C42—611no—
674C2×C42—1221no—
675#107C22×D6114yes—
676#106—614no—
677C4⋊C8—614no—
678#103—614no—
679#103—614no—
680#103C22×D6114yes—
681#102—614no—
682#102—614no—
683#102—614no—
684#102—614no—
685#102C22×D6114yes—
686C22⋊C8—612no—
687C22⋊C8—612no—
688C22⋊C8—614no—
689C22⋊C8C22×D6112yes—
690C22⋊C8C22×D6112yes—
691#97—614no—
692C24—21no—
693C24—611no—
694C24—1221no—
695C24—1221no—
696C24D4×D6111yescharacteristic
697#41—1224no—
698#41—1224no—
699#41—1228no—
700#41—2442no—
701#41—2442no—
702#41—2444no—
703#41—2444no—
704#41—2444no—
705#41—2444no—
706#41—2448no—
707C2×Q8—21no—
708C2×Q8—42no—
709C2×Q8—612no—
710C2×Q8—1224no—
711C2×Q8—1221no—
712C2×Q8C23×D6112yes—
713C2×D4—22no—
714C2×D4—22no—
715C2×D4—21no—
716C2×D4—42no—
717C2×D4—82no—
718C2×D4—612no—
719C2×D4—612no—
720C2×D4—612no—
721C2×D4—612no—
722C2×D4—1222no—
723C2×D4—1222no—
724C2×D4—1224no—
725C2×D4—1224no—
726C2×D4—1224no—
727C2×D4—1224no—
728C2×D4—1222no—
729C2×D4—1222no—
730C2×D4—1222no—
731C2×D4—1222no—
732C2×D4—1221no—
733C2×D4—1221no—
734C2×D4—4882no—
735C2×D4—4882no—
736C2×D4—2442no—
737C2×D4—2442no—
738C2×D4—2442no—
739C2×D4—2444no—
740C2×D4—2444no—
741C2×D4—2444no—
742C2×D4—2444no—
743C2×D4C23×D6112yes—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—42no—
748C22×C4—611no—
749C22×C4—611no—
750C22×C4—611no—
751C22×C4—612no—
752C22×C4—612no—
753C22×C4—1222no—
754C22×C4—1222no—
755C22×C4—1224no—
756C22×C4—1221no—
757C22×C4—1221no—
758C22×C4—1222no—
759C22×C4—1222no—
760C22×C4—2442no—
761C22×C4—2444no—
762C22×C4—2444no—
763C22×C4D4×D6111yescharacteristic
764C22×C4D4×D6111yescharacteristic
765C22×C4D4×D6111yescharacteristic
766C22×C4C23×D6111yescharacteristic
767C22×C4C23×D6111yescharacteristic
768C22×C4C23×D6111yescharacteristic
769Q16—1228no—
770SD16—44no—
771SD16—1228no—
772SD16—2444no—
773D8—2444no—
774D8—2444no—
775M16—42no—
776M16—2442no—
777C2×C8—614no—
778C2×C8—2444no—
779C2×C8C23×D6114yes—
780C4⋊C4—22no—
781C4⋊C4—22no—
782C4⋊C4—21no—
783C4⋊C4—21no—
784C4⋊C4—612no—
785C4⋊C4—612no—
786C4⋊C4—612no—
787C4⋊C4—1224no—
788C4⋊C4—1222no—
789C4⋊C4—1222no—
790C4⋊C4—1222no—
791C4⋊C4—1222no—
792C4⋊C4—1221no—
793C4⋊C4C23×D6112yes—
794C4⋊C4C23×D6112yes—
795C22⋊C4—22no—
796C22⋊C4—22no—
797C22⋊C4—22no—
798C22⋊C4—22no—
799C22⋊C4—612no—
800C22⋊C4—612no—
801C22⋊C4—612no—
802C22⋊C4—612no—
803C22⋊C4—1224no—
804C22⋊C4—1222no—
805C22⋊C4—1222no—
806C22⋊C4—1222no—
807C22⋊C4—1222no—
808C22⋊C4—1222no—
809C22⋊C4—1222no—
810C22⋊C4—1222no—
811C22⋊C4—1222no—
812C42—612no—
813C42—612no—
814C42—1224no—
815C42—1222no—
816C42—1222no—
817C23—22no—
818C23—22no—
819C23—41no—
820C23—41no—
821C23—42no—
822C23—42no—
823C23—42no—
824C23—612no—
825C23—1222no—
826C23—1222no—
827C23—1222no—
828C23—4881no—
829C23—4881no—
830C23—2441no—
831C23—2441no—
832C23—2442no—
833C23—2442no—
834C23—2442no—
835C23—2442no—
836C23C2×D4×D6111yescharacteristic
837C23C2×D4×D6111yescharacteristic
838C23C2×D4×D6111yescharacteristic
839Q8—24no—
840Q8—81no—
841Q8—614no—
842Q8—1224no—
843Q8—1222no—
844D4—24no—
845D4—42no—
846D4—82no—
847D4—82no—
848D4—1224no—
849D4—1222no—
850D4—1222no—
851D4—4881no—
852D4—4882no—
853D4—4884no—
854D4—4882no—
855D4—4884no—
856D4—2442no—
857D4—2442no—
858D4—2442no—
859D4—2444no—
860D4—2444no—
861D4—2448no—
862D4—2448no—
863D4—2444no—
864D4—2444no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—42no—
875C2×C4—81no—
876C2×C4—81no—
877C2×C4—612no—
878C2×C4—612no—
879C2×C4—612no—
880C2×C4—1224no—
881C2×C4—1222no—
882C2×C4—1222no—
883C2×C4—1224no—
884C2×C4—1222no—
885C2×C4—4882no—
886C2×C4—4882no—
887C2×C4—2442no—
888C2×C4—2444no—
889C2×C4—2444no—
890C2×C4—2441no—
891C2×C4—2441no—
892C2×C4—2448no—
893C2×C4—2442no—
894C2×C4C2×D4×D6111yescharacteristic
895C2×C4C2×D4×D6111yescharacteristic
896C2×C4C2×D4×D6111yescharacteristic
897C2×C4C24×D6111yescharacteristic
898C8—24no—
899C8—1224no—
900C22—21no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—21no—
905C22—21no—
906C22—21no—
907C22—21no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—82no—
912C22—84no—
913C22—1222no—
914C22—1222no—
915C22—1222no—
916C22—9762no—
917C22—4884no—
918C22—4882no—
919C22—2442no—
920C22—2442no—
921C22—2442no—
922C22—2442no—
923C22—2442no—
924C22—2442no—
925C22#1684056112yes—
926C22C22×D4×D6111yescharacteristic
927C4—21no—
928C4—21no—
929C4—21no—
930C4—42no—
931C4—42no—
932C4—42no—
933C4—1222no—
934C4—1222no—
935C4—1222no—
936C4—1224no—
937C4—2442no—
938C4H(5,𝔽2)×D6112yes—
939C2—22no—
940C2—41no—
941C2—41no—
942C2—82no—
943C2—4882no—
944C2—4882no—
945C2—2442no—
946C2#2145945111yescharacteristic
947C2C2×#1684056111yescharacteristic
948C2#2146059511yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3193C2
socleC22×C61C23×D4
hypercenter#3193D61
hypocenterC61#61577
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3193

Complements

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

NH ≅ G/Ntype
1. #21459660C2semidirect
2. C2×#16840430C2semidirect
3. #21457940C2semidirect
4. #21457828C2semidirect
5. #21457407C2semidirect
6. #21457366C2semidirect
7. #21456840C2semidirect
8. #21456616C2semidirect
9. #21456589C2semidirect
10. #21455993C2semidirect
11. #21455077C2semidirect
12. #21455073C2semidirect
13. #21455038C2semidirect
14. #21454846C2semidirect
15. C61×#3193C2semidirect
17. C22×#11758224C22semidirect
18. C2×#14519808C22semidirect
19. C2×#14519805C22semidirect
20. C2×#14519798C22semidirect
22. #16840460C22semidirect
23. #16840454C22semidirect
28. #16840430C22semidirect
29. #16840423C22semidirect
30. #16840403C22semidirect
35. C2×#14519773C22semidirect
38. C2×#14519752C22semidirect
43. C2×#14519742C22semidirect
46. #16840148C22semidirect
47. #16840125C22semidirect
48. #16840089C22semidirect
50. #16840078C22semidirect
51. #16840068C22semidirect
52. #16840013C22semidirect
53. #16839999C22semidirect
54. #16839994C22semidirect
55. #16839987C22semidirect
56. #16839960C22semidirect
57. #16839956C22semidirect
58. #16839922C22semidirect
59. #16839921C22semidirect
60. #16839917C22semidirect
61. #16839912C22semidirect
62. #16839910C22semidirect
63. #16839909C22semidirect
64. #16839908C22semidirect
68. #16839895C22semidirect
69. #16839866C22semidirect
70. #16839861C22semidirect
71. #16839836C22semidirect
72. #16839831C22semidirect
73. #16839816C22semidirect
74. #16839764C22semidirect
75. #16839761C22semidirect
76. #16839755C22semidirect
78. C22⋊C8×D61C22semidirect
81. C61×#484C22semidirect
82. C61×#480C22semidirect
83. C61×#468C22semidirect
84. C61×#450C22semidirect
85. C61×#448C22semidirect
472. #3193D61semidirect
524. #484C2×D61semidirect
528. #480C2×D61semidirect
531. #468C2×D61semidirect
541. #450C2×D61semidirect
546. #448C2×D61semidirect
561. C61#61577semidirect

Maximal subgroups

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

subgroupindex
#214596602
C2×#168404302
#214579402
#214578282
#214574072
#214573662
#214568402
#214566162
#214565892
#214559932
#214550772
#214550732
#214550382
#214548462
C61×#31932
#6157761