Finite Group Databasebeta

← #29647805

Subgroups — #29647805

Order 15616.

1014 conjugacy classes of subgroups.

The subgroup lattice has 976 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459647C211yesmaximal, characteristic
2#21454858C211yesmaximal, characteristic, complemented
3#21448761C211yesmaximal, characteristic, complemented
4#21444395C211yesmaximal, characteristic, complemented
5#21444393C211yesmaximal, characteristic, complemented
6#21444360C211yesmaximal, characteristic, complemented
7#21444350C211yesmaximal, characteristic, complemented
8#21444346C211yesmaximal, characteristic, complemented
9#21444337C211yesmaximal, characteristic, complemented
10#21444333C211yesmaximal, characteristic, complemented
11#21444324C211yesmaximal, characteristic, complemented
12#21444323C211yesmaximal, characteristic, complemented
13#21444304C211yesmaximal, characteristic, complemented
14#21444302C211yesmaximal, characteristic, complemented
15C61×#1513C211yesmaximal, characteristic, complemented
16#16840462—21no—
17#16840459C411yescharacteristic, complemented
18#16840457—21no—
19#16840456C411yescharacteristic, complemented
20#16840451C411yescharacteristic, complemented
21#16840446C411yescharacteristic, complemented
22#16840441—21no—
23#16840440—21no—
24#16840422C411yescharacteristic, complemented
25#16840419C411yescharacteristic, complemented
26#16840409C411yescharacteristic, complemented
27#16840400C411yescharacteristic, complemented
28#16840354—21no—
29#16840347—21no—
30#16840322—21no—
31#16840298C2211yescharacteristic
32#16840293C2211yescharacteristic
33#16840273C2211yescharacteristic
34C22⋊Q8×D61C2211yescharacteristic
35#121×D61C2211yescharacteristic
36#16840234—21no—
37C2×C4×C22⋊D61C2211yescharacteristic
38#16839838—21no—
39#16839838—21no—
40#16839837—21no—
41#16839837—21no—
42#16839812C2211yescharacteristic, complemented
43#16839812C2211yescharacteristic, complemented
44#16839726C2211yescharacteristic, complemented
45#16839724C2211yescharacteristic
46#16839724C2211yescharacteristic
47#16839652—21no—
48#16839643—21no—
49#16839639—21no—
50#16839629C2211yescharacteristic, complemented
51#16839624C2211yescharacteristic
52C22⋊C4×Dic61—21no—
53#16839609C2211yescharacteristic
54#16839607C2211yescharacteristic, complemented
55C2×#14519684C2211yescharacteristic, complemented
56#16839500C2211yescharacteristic, complemented
57#16839500C2211yescharacteristic, complemented
58#16839499C2211yescharacteristic, complemented
59#16839499C2211yescharacteristic, complemented
60#16839498C2211yescharacteristic, complemented
61#16839498C2211yescharacteristic, complemented
62#16839497C2211yescharacteristic
63#16839497C2211yescharacteristic
64#16839496C2211yescharacteristic
65#16839496C2211yescharacteristic
66#16839495C2211yescharacteristic
67#16839495C2211yescharacteristic
68C61×#525C2211yescharacteristic
69C61×#407C2211yescharacteristic, complemented
70C61×#380C2211yescharacteristic, complemented
71C61×#328C2211yescharacteristic, complemented
72C61×#328C2211yescharacteristic, complemented
73C61×#327C2211yescharacteristic
74C61×#327C2211yescharacteristic
75C2×#11758222C2×C411yescharacteristic
76C2×Q8×D61C2×C411yescharacteristic, complemented
77C22×C22⋊D61D411yescharacteristic
78C2×D4×D61—21no—
79C2×D4×D61C2×C411yescharacteristic, complemented
80C23×Dic61—21no—
81C22×C4×D61C2311yescharacteristic
82C2×#11758194—21no—
83C2×#11758189—21no—
84C2×#11758189—21no—
85#14519772—21no—
86#14519771—21no—
87#14519770—21no—
88#14519770—21no—
89#14519770—21no—
90#14519770—21no—
91#14519769—21no—
92#14519768C2×C411yescharacteristic, complemented
93#14519768C2×C411yescharacteristic, complemented
94#14519767—21no—
95#14519766C2×C411yescharacteristic, complemented
96#14519764—21no—
97#14519764C2×C411yescharacteristic, complemented
98#14519763—21no—
99#14519761—21no—
100#14519760—21no—
101#14519760—21no—
102#14519759—21no—
103#14519759—21no—
104#14519759—21no—
105#14519759—21no—
106#14519758—21no—
107#14519758—21no—
108#14519757C2×C411yescharacteristic, complemented
109#14519756—21no—
110#14519756C2×C411yescharacteristic
111#14519756C2311yescharacteristic
112#14519755—21no—
113#14519755—21no—
114#14519754—21no—
115#14519753C2×C411yescharacteristic, complemented
116#14519752C2×C411yescharacteristic, complemented
117#14519751C2×C411yescharacteristic
118#14519751C2311yescharacteristic
119#14519750—21no—
120#14519750—21no—
121#14519750—21no—
122#14519749—21no—
123#14519749—21no—
124#14519748—21no—
125#14519748—21no—
126#14519748—21no—
127#14519748C2×C411yescharacteristic, complemented
128#14519746—21no—
129#14519745—21no—
130#14519745—21no—
131Q8×Dic61C2×C411yescharacteristic, complemented
132#14519742C2×C411yescharacteristic, complemented
133C4×D244—21no—
134D4×Dic61—21no—
135D4×Dic61C2×C411yescharacteristic, complemented
136#14519739—21no—
137#14519739C2×C411yescharacteristic, complemented
138C4×C22⋊D61—21no—
139C4×C22⋊D61—21no—
140C4×C22⋊D61—21no—
141C4×C22⋊D61C2×C411yescharacteristic
142C4×C22⋊D61C2×C411yescharacteristic
143C4×C22⋊D61C2×C411yescharacteristic
144C4×C22⋊D61C2×C411yescharacteristic
145C4×C22⋊D61D411yescharacteristic
146C4×C22⋊D61D411yescharacteristic
147C4×C22⋊D61D411yescharacteristic
148C4×C22⋊D61D411yescharacteristic
149#14519737—21no—
150#14519737—21no—
151#14519736C2×C411yescharacteristic
152#14519735—21no—
153#14519735—21no—
154#14519734—21no—
155#14519733—21no—
156C2×#11758196D411yescharacteristic
157C4⋊C4×D61—21no—
158C4⋊C4×D61C2×C411yescharacteristic, complemented
159C4⋊C4×D61C2×C411yescharacteristic, complemented
160C2×C22⋊Dic61D411yescharacteristic
161C2×#11758198—21no—
162C2×#11758198—21no—
163C2×#11758198—21no—
164C2×#11758198D411yescharacteristic
165C22⋊C4×D61—21no—
166C22⋊C4×D61—21no—
167C22⋊C4×D61—21no—
168C2×C4×Dic61—21no—
169C2×C4×Dic61—21no—
170C2×C4×Dic61C2311yescharacteristic
171#14519706—21no—
172#14519706—21no—
173C22⋊#92418—21no—
174C22⋊#92418C2311yescharacteristic
175C22⋊#92418C2311yescharacteristic
176#14519689—21no—
177#14519689—21no—
178C8×Dic61—21no—
179C8×Dic61—21no—
180#14519684—21no—
181#14519684—21no—
182#14519684—21no—
183#14519684—21no—
184#14519684—21no—
185#14519684C2311yescharacteristic
186#14519684C2311yescharacteristic
187C2×#41×C61C2×C411yescharacteristic
188C23×C4×C61C2311yescharacteristic
189C2×M16×C61—21no—
190#123×C61—21no—
191C22⋊Q8×C61C2×C411yescharacteristic
192C22⋊Q8×C61C2311yescharacteristic
193#121×C61C2×C411yescharacteristic
194#121×C61C2311yescharacteristic
195#120×C61—21no—
196C4×D4×C61—21no—
197C4×D4×C61—21no—
198#117×C61C2×C411yescharacteristic
199C2×C4⋊C4×C61—21no—
200C2×C22⋊C4×C61—21no—
201C22⋊C8×C61—21no—
202C22⋊C8×C61C2311yescharacteristic
203C22⋊C8×C61C2311yescharacteristic
204#95×C61C2311yescharacteristic
205#95×C61C2311yescharacteristic
206C24×C61C2×D411yescharacteristic
207C23×D61—21no—
208C23×D61C2×D411yescharacteristic
209#41×C61—81no—
210C2×Q8×C61C22×C411yescharacteristic
211C2×D4×C61—21no—
212C2×D4×C61—21no—
213C2×D4×C61—21no—
214C2×D4×C61C22×C411yescharacteristic
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—81no—
219C22×C4×C61C22×C411yescharacteristic
220C22×C4×C61C22×C411yescharacteristic
221C22×C4×C61C2×D411yescharacteristic
222C22×C4×C61C2×D411yescharacteristic
223C22×C4×C61C2×D411yescharacteristic
224C22×C4×C61C2411yescharacteristic
225C2×C22⋊D61—21no—
226C2×C22⋊D61—21no—
227C2×C22⋊D61—21no—
228C2×C22⋊D61—21no—
229C2×C22⋊D61—21no—
230C2×C22⋊D61—41no—
231C2×C22⋊D61—41no—
232C2×C22⋊D61C22⋊C411yescharacteristic
233C2×C22⋊D61C22⋊C411yescharacteristic
234C2×C22⋊D61C22⋊C411yescharacteristic
235C2×C22⋊D61C22⋊C411yescharacteristic
236C22×Dic61—21no—
237C22×Dic61—21no—
238C22×Dic61—21no—
239C22×Dic61—42no—
240C22×Dic61—42no—
241C22×Dic61—81no—
242C22×Dic61C2×D411yescharacteristic
243C22×Dic61C2×D411yescharacteristic
244C22×Dic61C2×D411yescharacteristic
245Q8×D61—81no—
246D4×D61—42no—
247D4×D61—42no—
248D4×D61—81no—
249#11758222—81no—
250C2×D244—21no—
251C2×D244C22×C411yescharacteristic
252C2×C4×D61—21no—
253C2×C4×D61—21no—
254C2×C4×D61—21no—
255C2×C4×D61—21no—
256C2×C4×D61—21no—
257C2×C4×D61—81no—
258C2×C4×D61C22×C411yescharacteristic
259C2×C4×D61C22×C411yescharacteristic
260C2×C4×D61C2×D411yescharacteristic
261C2×C4×D61C2×D411yescharacteristic
262C2×Dic122—21no—
263C2×Dic122C22×C411yescharacteristic
264M16×C61—81no—
265C2×C8×C61—21no—
266C2×C8×C61—21no—
267C4⋊C4×C61—21no—
268C4⋊C4×C61—21no—
269C4⋊C4×C61—81no—
270C4⋊C4×C61C22×C411yescharacteristic
271C4⋊C4×C61C22×C411yescharacteristic
272C22⋊C4×C61—21no—
273C22⋊C4×C61—21no—
274C22⋊C4×C61—21no—
275C22⋊C4×C61—21no—
276C22⋊C4×C61—21no—
277C22⋊C4×C61—42no—
278C42×C61—21no—
279C22⋊Dic61—21no—
280C22⋊Dic61—21no—
281C22⋊Dic61—21no—
282C22⋊Dic61—21no—
283C22⋊Dic61—21no—
284C22⋊Dic61—21no—
285C22⋊Dic61—21no—
286C22⋊Dic61C22⋊C411yescharacteristic
287C22⋊Dic61C22⋊C411yescharacteristic
288C22⋊Dic61C22⋊C411yescharacteristic
289C22⋊Dic61C22⋊C411yescharacteristic
290#11758198—21no—
291#11758198—21no—
292#11758198—21no—
293#11758198—21no—
294#11758198—21no—
295#11758198—21no—
296#11758198—21no—
297#11758198—21no—
298#11758198—42no—
299#11758198—81no—
300#11758198C22⋊C411yescharacteristic
301#11758198C22⋊C411yescharacteristic
302#11758198C22⋊C411yescharacteristic
303#11758198C22⋊C411yescharacteristic
304C4⋊Dic61—21no—
305C4⋊Dic61—21no—
306C4⋊Dic61—21no—
307C4⋊Dic61—21no—
308C4⋊Dic61C22×C411yescharacteristic
309C4⋊Dic61C22×C411yescharacteristic
310#11758196—21no—
311#11758196—21no—
312#11758196—21no—
313#11758196—21no—
314#11758196—21no—
315#11758196—21no—
316#11758196—21no—
317#11758196—21no—
318#11758196C22⋊C411yescharacteristic
319#11758196C22⋊C411yescharacteristic
320#11758196C22⋊C411yescharacteristic
321#11758196C22⋊C411yescharacteristic
322C4×Dic61—21no—
323C4×Dic61—21no—
324C4×Dic61—21no—
325C4×Dic61—42no—
326C4×Dic61—81no—
327C4×Dic61C22×C411yescharacteristic
328C4×Dic61C22×C411yescharacteristic
329C4×Dic61C2×D411yescharacteristic
330C4×Dic61C2×D411yescharacteristic
331#11758194—81no—
332C2×#92418—21no—
333C2×#92418—21no—
334#11758189—81no—
335#11758189—81no—
336C23×C61—21no—
337C23×C61—21no—
338C23×C61—21no—
339C23×C61—41no—
340C23×C61—41no—
341C23×C61C2×C22⋊C411yescharacteristic
342C23×C61C2×C22⋊C411yescharacteristic
343C23×C61C22×D411yescharacteristic
344C22×D61—21no—
345C22×D61—21no—
346C22×D61—21no—
347C22×D61—41no—
348C22×D61—41no—
349C22×D61—42no—
350C22×D61—81no—
351C22×D61—81no—
352C22×D61C2×C22⋊C411yescharacteristic
353C22×D61C2×C22⋊C411yescharacteristic
354Q8×C61—41no—
355D4×C61—41no—
356D4×C61—41no—
357D4×C61—41no—
358D4×C61—81no—
359D4×C61—81no—
360C2×C4×C61—21no—
361C2×C4×C61—21no—
362C2×C4×C61—21no—
363C2×C4×C61—41no—
364C2×C4×C61—41no—
365C2×C4×C61—41no—
366C2×C4×C61—41no—
367C2×C4×C61—41no—
368C2×C4×C61—41no—
369C2×C4×C61—41no—
370C2×C4×C61—41no—
371C2×C4×C61—41no—
372C2×C4×C61—41no—
373C2×C4×C61—41no—
374C2×C4×C61—41no—
375C2×C4×C61—81no—
376C2×C4×C61C2×C22⋊C411yescharacteristic
377C2×C4×C61C2×C22⋊C411yescharacteristic
378C2×C4×C61C23×C411yescharacteristic
379C2×C4×C61C22×D411yescharacteristic
380C22⋊D61—41no—
381C22⋊D61—41no—
382C22⋊D61—41no—
383C22⋊D61—41no—
384C22⋊D61—42no—
385C22⋊D61—41no—
386C22⋊D61—41no—
387C22⋊D61—81no—
388C22⋊D61—81no—
389C22⋊D61—81no—
390C2×Dic61—21no—
391C2×Dic61—21no—
392C2×Dic61—22no—
393C2×Dic61—21no—
394C2×Dic61—21no—
395C2×Dic61—21no—
396C2×Dic61—41no—
397C2×Dic61—41no—
398C2×Dic61—41no—
399C2×Dic61—41no—
400C2×Dic61—41no—
401C2×Dic61—41no—
402C2×Dic61—41no—
403C2×Dic61—81no—
404C2×Dic61—84no—
405C2×Dic61C2×C22⋊C411yescharacteristic
406C2×Dic61C2×C22⋊C411yescharacteristic
407C2×Dic61C2×C22⋊C411yescharacteristic
408C2×Dic61C2×C22⋊C411yescharacteristic
409C2×Dic61C2×C22⋊C411yescharacteristic
410C2×Dic61C2×C22⋊C411yescharacteristic
411D244—41no—
412D244—42no—
413C4×D61—41no—
414C4×D61—41no—
415C4×D61—41no—
416C4×D61—41no—
417C4×D61—42no—
418C4×D61—81no—
419C4×D61—81no—
420C4×D61—81no—
421C4×D61—81no—
422Dic122—41no—
423Dic122—81no—
424C8×C61—41no—
425C8×C61—41no—
426#92418—41no—
427#92418—41no—
428#17623—611nomaximal, Sylow
429C22×C61—21no—
430C22×C61—21no—
431C22×C61—21no—
432C22×C61—21no—
433C22×C61—21no—
434C22×C61—21no—
435C22×C61—21no—
436C22×C61—21no—
437C22×C61—42no—
438C22×C61—42no—
439C22×C61—41no—
440C22×C61—41no—
441C22×C61—41no—
442C22×C61C22×C22⋊C411yescharacteristic
443C22×C61#57511yescharacteristic
444C22×C61#57511yescharacteristic
445C2×D61—21no—
446C2×D61—21no—
447C2×D61—21no—
448C2×D61—21no—
449C2×D61—21no—
450C2×D61—21no—
451C2×D61—41no—
452C2×D61—41no—
453C2×D61—41no—
454C2×D61—81no—
455C2×D61—81no—
456C2×D61—162no—
457C4×C61—21no—
458C4×C61—21no—
459C4×C61—21no—
460C4×C61—21no—
461C4×C61—41no—
462C4×C61—41no—
463C4×C61—41no—
464C4×C61—81no—
465C4×C61—81no—
466Dic61—21no—
467Dic61—21no—
468Dic61—21no—
469Dic61—21no—
470Dic61—21no—
471Dic61—21no—
472Dic61—42no—
473Dic61—41no—
474Dic61—41no—
475Dic61—41no—
476Dic61—81no—
477#3505—611no—
478#2975—611no—
479#2353—611no—
480#1521—611no—
481#1521—611no—
482#1513—611no—
483#1513D6111yescharacteristic, complemented
484#1511—611no—
485#1510—611no—
486#1508—611no—
487#1507—611no—
488#1504—611no—
489#1504—611no—
490#1500—611no—
491#1500—611no—
492C2×C61—21no—
493C2×C61—21no—
494C2×C61—41no—
495C2×C61—41no—
496C2×C61—81no—
497C2×C61#288311yescharacteristic
498C2×C61#289611yescharacteristic
499C2×C61#290111yescharacteristic
500D61—41no—
501D61—41no—
502D61—81no—
503#553—611no—
504#553—611no—
505#553—1221no—
506#553—1221no—
507#552—611no—
508#552—611no—
509#551—1221no—
510#551—1221no—
511#548—611no—
512#548—611no—
513#546—611no—
514#546—611no—
515#539—1221no—
516#538—1221no—
517#534—1221no—
518#529—611no—
519#529—611no—
520#525—611no—
521#525C2×D6111yescharacteristic
522C2×C22⋊Q8—611no—
523C2×#121—611no—
524#518—1221no—
525C2×C4×D4—611no—
526#436—1221no—
527#436—1221no—
528#436—1221no—
529#436—1221no—
530#431—611no—
531#431—611no—
532#407—611no—
533#407—611no—
534#407—611no—
535#407C2×D6111yescharacteristic, complemented
536#388—1221no—
537#387—1221no—
538#386—1221no—
539#383—611no—
540#381—611no—
541#380C2×D6111yescharacteristic, complemented
542C4×C22⋊C4—611no—
543C4×C22⋊C4—1221no—
544#376—611no—
545C2×#95—611no—
546#328—611no—
547#328—611no—
548#328—611no—
549#328—611no—
550#328—611no—
551#328—611no—
552#328C2×D6111yescharacteristic, complemented
553#328C2×D6111yescharacteristic, complemented
554#327—611no—
555#327—611no—
556#327—611no—
557#327—611no—
558#327—611no—
559#327—611no—
560#327C2×D6111yescharacteristic
561#327C2×D6111yescharacteristic
562C61#1762311yescharacteristic, complemented, Sylow
563C2×#41—611no—
564C2×#41C4×D6111yescharacteristic
565C22×Q8—611no—
566C22×D4—611no—
567C22×D4—611no—
568C22×D4—1221no—
569C23×C4—611no—
570C23×C4—1221no—
571C23×C4C22×D6111yescharacteristic
572C2×M16—21no—
573C2×M16—1221no—
574C2×M16—1221no—
575C2×M16—1221no—
576#126—1221no—
577#126—1221no—
578#126—1221no—
579#126—1221no—
580#126—1221no—
581#126—1221no—
582#125—611no—
583#125—611no—
584#125—1221no—
585#125—1221no—
586#124—611no—
587#124—611no—
588#124—1221no—
589#124—1221no—
590#123—21no—
591#123—1221no—
592#123—1221no—
593#123—1221no—
594#123—1221no—
595#123—1221no—
596#123—1221no—
597#123—1221no—
598#123—1221no—
599#123—1221no—
600C22⋊Q8—611no—
601C22⋊Q8—611no—
602C22⋊Q8—611no—
603C22⋊Q8—611no—
604C22⋊Q8—1221no—
605C22⋊Q8—1221no—
606C22⋊Q8—1221no—
607C22⋊Q8—1221no—
608C22⋊Q8C4×D6111yescharacteristic
609C22⋊Q8C22×D6111yescharacteristic
610#121—611no—
611#121—611no—
612#121—611no—
613#121—611no—
614#121—1221no—
615#121—1221no—
616#121—1221no—
617#121—1221no—
618#121—1221no—
619#121—1221no—
620#121—1221no—
621#121—1221no—
622#121C4×D6111yescharacteristic
623#121C22×D6111yescharacteristic
624#120—21no—
625#120—1221no—
626#120—1221no—
627#120—1221no—
628C4×Q8—611no—
629C4×Q8—611no—
630C4×D4—21no—
631C4×D4—21no—
632C4×D4—611no—
633C4×D4—611no—
634C4×D4—611no—
635C4×D4—611no—
636C4×D4—611no—
637C4×D4—611no—
638C4×D4—611no—
639C4×D4—611no—
640C4×D4—611no—
641C4×D4—611no—
642C4×D4—1221no—
643C4×D4—1221no—
644C4×D4—1221no—
645C4×D4—1221no—
646C4×D4—1221no—
647C4×D4—1221no—
648C4×D4—1221no—
649C4×D4—1221no—
650#117—611no—
651#117—1221no—
652#117—1221no—
653#117—1221no—
654#117—1221no—
655#117C4×D6111yescharacteristic
656C2×C4⋊C4—21no—
657C2×C4⋊C4—611no—
658C2×C4⋊C4—611no—
659C2×C4⋊C4—611no—
660C2×C4⋊C4—1221no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—611no—
663C2×C22⋊C4—611no—
664C2×C22⋊C4—1221no—
665C2×C22⋊C4—1221no—
666C2×C22⋊C4—1221no—
667C2×C22⋊C4—1221no—
668C2×C22⋊C4—1221no—
669C2×C22⋊C4—1221no—
670C2×C42—611no—
671C2×C42—1221no—
672C2×C42—1221no—
673C4⋊C8—1221no—
674C4⋊C8—1221no—
675C22⋊C8—21no—
676C22⋊C8—611no—
677C22⋊C8—611no—
678C22⋊C8—1221no—
679C22⋊C8—1221no—
680C22⋊C8—1221no—
681C22⋊C8C22×D6111yescharacteristic
682C22⋊C8C22×D6111yescharacteristic
683C4×C8—1221no—
684C4×C8—1221no—
685#95—611no—
686#95—611no—
687#95—1221no—
688#95—1221no—
689#95—1221no—
690#95—1221no—
691#95—1221no—
692#95C22×D6111yescharacteristic
693#95C22×D6111yescharacteristic
694C24—611no—
695C24—1221no—
696C24D4×D6111yescharacteristic
697#41—81no—
698#41—4881no—
699C2×Q8—611no—
700C2×Q8—1221no—
701C2×Q8—4881no—
702C2×Q8C2×C4×D6111yescharacteristic
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—611no—
707C2×D4—611no—
708C2×D4—611no—
709C2×D4—611no—
710C2×D4—611no—
711C2×D4—1221no—
712C2×D4—1221no—
713C2×D4—1221no—
714C2×D4—1221no—
715C2×D4—1221no—
716C2×D4—1221no—
717C2×D4—4881no—
718C2×D4—2441no—
719C2×D4—2441no—
720C2×D4—2442no—
721C2×D4—2442no—
722C2×D4C2×C4×D6111yescharacteristic
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—81no—
727C22×C4—611no—
728C22×C4—611no—
729C22×C4—611no—
730C22×C4—611no—
731C22×C4—611no—
732C22×C4—611no—
733C22×C4—611no—
734C22×C4—1221no—
735C22×C4—1221no—
736C22×C4—1221no—
737C22×C4—1221no—
738C22×C4—1221no—
739C22×C4—1221no—
740C22×C4—1221no—
741C22×C4—1221no—
742C22×C4—4881no—
743C22×C4—4881no—
744C22×C4—2442no—
745C22×C4—2442no—
746C22×C4C2×C4×D6111yescharacteristic
747C22×C4C2×C4×D6111yescharacteristic
748C22×C4D4×D6111yescharacteristic
749C22×C4D4×D6111yescharacteristic
750C22×C4D4×D6111yescharacteristic
751C22×C4C23×D6111yescharacteristic
752M16—81no—
753M16—4881no—
754M16—4881no—
755M16—4881no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—1221no—
759C2×C8—1221no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—81no—
763C4⋊C4—611no—
764C4⋊C4—611no—
765C4⋊C4—611no—
766C4⋊C4—611no—
767C4⋊C4—611no—
768C4⋊C4—611no—
769C4⋊C4—1221no—
770C4⋊C4—1221no—
771C4⋊C4—1221no—
772C4⋊C4—1221no—
773C4⋊C4—1221no—
774C4⋊C4—1221no—
775C4⋊C4—1221no—
776C4⋊C4—1221no—
777C4⋊C4—1221no—
778C4⋊C4—1221no—
779C4⋊C4—1221no—
780C4⋊C4—1221no—
781C4⋊C4C2×C4×D6111yescharacteristic
782C4⋊C4C2×C4×D6111yescharacteristic
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—42no—
789C22⋊C4—611no—
790C22⋊C4—611no—
791C22⋊C4—611no—
792C22⋊C4—611no—
793C22⋊C4—611no—
794C22⋊C4—611no—
795C22⋊C4—611no—
796C22⋊C4—611no—
797C22⋊C4—1221no—
798C22⋊C4—1221no—
799C22⋊C4—1221no—
800C22⋊C4—1221no—
801C22⋊C4—1221no—
802C22⋊C4—1221no—
803C22⋊C4—1221no—
804C22⋊C4—1221no—
805C22⋊C4—1221no—
806C22⋊C4—1221no—
807C22⋊C4—1221no—
808C22⋊C4—1221no—
809C22⋊C4—1221no—
810C22⋊C4—1221no—
811C22⋊C4—1221no—
812C22⋊C4—4881no—
813C22⋊C4—2442no—
814C42—21no—
815C42—611no—
816C42—611no—
817C42—611no—
818C42—611no—
819C42—1221no—
820C42—1221no—
821C42—1221no—
822C42—4881no—
823C42—2442no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—41no—
828C23—41no—
829C23—611no—
830C23—611no—
831C23—1221no—
832C23—1221no—
833C23—1221no—
834C23—4881no—
835C23—4881no—
836C23—2441no—
837C23—2441no—
838C23—2442no—
839C23C22⋊C4×D6111yescharacteristic
840C23C22⋊C4×D6111yescharacteristic
841C23C2×D4×D6111yescharacteristic
842Q8—41no—
843Q8—4881no—
844Q8—2441no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—81no—
849D4—81no—
850D4—4881no—
851D4—4881no—
852D4—4881no—
853D4—2441no—
854D4—2442no—
855D4—2441no—
856D4—2441no—
857D4—2441no—
858D4—2441no—
859D4—2442no—
860D4—2441no—
861D4—2441no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—81no—
878C2×C4—611no—
879C2×C4—611no—
880C2×C4—611no—
881C2×C4—611no—
882C2×C4—611no—
883C2×C4—611no—
884C2×C4—1221no—
885C2×C4—1221no—
886C2×C4—1222no—
887C2×C4—1221no—
888C2×C4—1221no—
889C2×C4—1221no—
890C2×C4—4881no—
891C2×C4—4881no—
892C2×C4—4881no—
893C2×C4—4881no—
894C2×C4—4881no—
895C2×C4—4884no—
896C2×C4—2441no—
897C2×C4—2441no—
898C2×C4—2441no—
899C2×C4—2441no—
900C2×C4—2442no—
901C2×C4—2441no—
902C2×C4—2441no—
903C2×C4—2441no—
904C2×C4—2441no—
905C2×C4—2441no—
906C2×C4—2441no—
907C2×C4—2441no—
908C2×C4C22⋊C4×D6111yescharacteristic
909C2×C4C22⋊C4×D6111yescharacteristic
910C2×C4C22×C4×D6111yescharacteristic
911C2×C4C2×D4×D6111yescharacteristic
912C8—41no—
913C8—41no—
914C8—2441no—
915C8—2441no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—21no—
922C22—21no—
923C22—21no—
924C22—42no—
925C22—42no—
926C22—41no—
927C22—41no—
928C22—41no—
929C22—1221no—
930C22—1221no—
931C22—1221no—
932C22—1221no—
933C22—1221no—
934C22—1221no—
935C22—9762no—
936C22—4881no—
937C22—4881no—
938C22—2441no—
939C22—2441no—
940C22—2441no—
941C22C2×C22⋊C4×D6111yescharacteristic
942C22#1684055811yescharacteristic
943C22#1684056111yescharacteristic
944C4—21no—
945C4—21no—
946C4—21no—
947C4—21no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—81no—
952C4—81no—
953C4—1221no—
954C4—1221no—
955C4—1221no—
956C4—1221no—
957C4—1221no—
958C4—1221no—
959C4—4881no—
960C4—2442no—
961C4—2441no—
962C4—2441no—
963C4—2441no—
964C2—21no—
965C2—21no—
966C2—41no—
967C2—41no—
968C2—81no—
969C2—4881no—
970C2—2441no—
971C2—2441no—
972C2#2145427711yescharacteristic
973C2#2145433511yescharacteristic
974C2#2145436511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1513C2
socleC22×C61C22×C22⋊C4
prime radical#21459647C2
cosocleC22×C4×C61C24
hypercenter#1513D61
hypocenterC61#17623
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1513

Complements

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

NH ≅ G/Ntype
2. #21454858C2semidirect
3. #21448761C2semidirect
4. #21444395C2semidirect
5. #21444393C2semidirect
6. #21444360C2semidirect
7. #21444350C2semidirect
8. #21444346C2semidirect
9. #21444337C2semidirect
10. #21444333C2semidirect
11. #21444324C2semidirect
12. #21444323C2semidirect
13. #21444304C2semidirect
14. #21444302C2semidirect
15. C61×#1513C2semidirect
17. #16840459C4semidirect
19. #16840456C4semidirect
20. #16840451C4semidirect
21. #16840446C4semidirect
24. #16840422C4semidirect
25. #16840419C4semidirect
26. #16840409C4semidirect
27. #16840400C4semidirect
42. #16839812C22semidirect
43. #16839812C22semidirect
44. #16839726C22semidirect
50. #16839629C22semidirect
54. #16839607C22semidirect
55. C2×#14519684C22semidirect
56. #16839500C22semidirect
57. #16839500C22semidirect
58. #16839499C22semidirect
59. #16839499C22semidirect
60. #16839498C22semidirect
61. #16839498C22semidirect
69. C61×#407C22semidirect
70. C61×#380C22semidirect
71. C61×#328C22semidirect
72. C61×#328C22semidirect
76. C2×Q8×D61C2×C4semidirect
79. C2×D4×D61C2×C4semidirect
92. #14519768C2×C4semidirect
93. #14519768C2×C4semidirect
95. #14519766C2×C4semidirect
97. #14519764C2×C4semidirect
108. #14519757C2×C4semidirect
115. #14519753C2×C4semidirect
116. #14519752C2×C4semidirect
127. #14519748C2×C4semidirect
131. Q8×Dic61C2×C4semidirect
132. #14519742C2×C4semidirect
135. D4×Dic61C2×C4semidirect
137. #14519739C2×C4semidirect
158. C4⋊C4×D61C2×C4semidirect
159. C4⋊C4×D61C2×C4semidirect
483. #1513D61semidirect
535. #407C2×D61semidirect
541. #380C2×D61semidirect
552. #328C2×D61semidirect
553. #328C2×D61semidirect
562. C61#17623semidirect

Maximal subgroups

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

subgroupindex
#214596472
#214548582
#214487612
#214443952
#214443932
#214443602
#214443502
#214443462
#214443372
#214443332
#214443242
#214443232
#214443042
#214443022
C61×#15132
#1762361