Finite Group Databasebeta

← #29647799

Subgroups — #29647799

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#21448755C211yesmaximal, characteristic, complemented
4#21444395C211yesmaximal, characteristic, complemented
5#21444393C211yesmaximal, characteristic, complemented
6#21444363C211yesmaximal, characteristic, complemented
7#21444362C211yesmaximal, characteristic, complemented
8#21444350C211yesmaximal, characteristic, complemented
9#21444346C211yesmaximal, characteristic, complemented
10#21444337C211yesmaximal, characteristic, complemented
11#21444333C211yesmaximal, characteristic, complemented
12#21444321C211yesmaximal, characteristic, complemented
13#21444304C211yesmaximal, characteristic, complemented
14#21444302C211yesmaximal, characteristic, complemented
15C61×#1504C211yesmaximal, 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#16839654—21no—
48#16839649—21no—
49#16839641—21no—
50#16839629C2211yescharacteristic, complemented
51#16839624C2211yescharacteristic
52#16839622C2211yescharacteristic, complemented
53C4×C22⋊Dic61—21no—
54#16839609C2211yescharacteristic
55#16839607C2211yescharacteristic, 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
70C2×#95×C61C2211yescharacteristic, 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
80C22×C4×D61C2311yescharacteristic
81C2×#11758194—21no—
82C2×#11758189—21no—
83C2×#11758189—21no—
84#14519772—21no—
85#14519771—21no—
86#14519770—21no—
87#14519770—21no—
88#14519770—21no—
89#14519770—21no—
90#14519769—21no—
91#14519768C2×C411yescharacteristic, complemented
92#14519768C2×C411yescharacteristic, complemented
93#14519767—21no—
94#14519766C2×C411yescharacteristic, complemented
95#14519764—21no—
96#14519764C2×C411yescharacteristic, complemented
97#14519763—21no—
98#14519761—21no—
99#14519760—21no—
100#14519760—21no—
101#14519759—21no—
102#14519759—21no—
103#14519759—21no—
104#14519759—21no—
105#14519758—21no—
106#14519758—21no—
107#14519757C2×C411yescharacteristic, complemented
108#14519756—21no—
109#14519756C2×C411yescharacteristic
110#14519756C2311yescharacteristic
111#14519755—21no—
112#14519755—21no—
113#14519754—21no—
114#14519753C2×C411yescharacteristic, complemented
115#14519752C2×C411yescharacteristic, complemented
116#14519751C2×C411yescharacteristic
117#14519751C2311yescharacteristic
118#14519750—21no—
119#14519750—21no—
120#14519750—21no—
121#14519749—21no—
122#14519749—21no—
123#14519748—21no—
124#14519748—21no—
125#14519748—21no—
126#14519748C2×C411yescharacteristic, complemented
127#14519746—21no—
128#14519745—21no—
129#14519745—21no—
130Q8×Dic61C2×C411yescharacteristic, complemented
131#14519742C2×C411yescharacteristic, complemented
132C4×D244—21no—
133D4×Dic61—21no—
134D4×Dic61C2×C411yescharacteristic, complemented
135#14519739—21no—
136#14519739C2×C411yescharacteristic, complemented
137C4×C22⋊D61—21no—
138C4×C22⋊D61—21no—
139C4×C22⋊D61—21no—
140C4×C22⋊D61C2×C411yescharacteristic
141C4×C22⋊D61C2×C411yescharacteristic
142C4×C22⋊D61C2×C411yescharacteristic
143C4×C22⋊D61C2×C411yescharacteristic
144C4×C22⋊D61D411yescharacteristic
145C4×C22⋊D61D411yescharacteristic
146C4×C22⋊D61D411yescharacteristic
147C4×C22⋊D61D411yescharacteristic
148#14519737—21no—
149#14519737—21no—
150#14519736C2×C411yescharacteristic
151#14519735—21no—
152#14519735—21no—
153#14519734—21no—
154#14519733—21no—
155C2×C4⋊Dic61—21no—
156C2×#11758196D411yescharacteristic
157C4⋊C4×D61—21no—
158C4⋊C4×D61C2×C411yescharacteristic, complemented
159C4⋊C4×D61C2×C411yescharacteristic, complemented
160C2×C22⋊Dic61—21no—
161C2×C22⋊Dic61D411yescharacteristic
162C2×#11758198—21no—
163C2×#11758198—21no—
164C2×#11758198—21no—
165C2×#11758198D411yescharacteristic
166C22⋊C4×D61—21no—
167C22⋊C4×D61—21no—
168C22⋊C4×D61—21no—
169C2×C4×Dic61—21no—
170C2×C4×Dic61—21no—
171C2×C4×Dic61C2311yescharacteristic
172#14519706—21no—
173#14519706—21no—
174C22⋊#92418—21no—
175C22⋊#92418C2311yescharacteristic
176C22⋊#92418C2311yescharacteristic
177#14519689—21no—
178#14519689—21no—
179C8×Dic61—21no—
180C8×Dic61—21no—
181#14519684—21no—
182#14519684—21no—
183#14519684—21no—
184#14519684—21no—
185#14519684C2311yescharacteristic
186#14519684C2311yescharacteristic
187C2×#41×C61C2×C411yescharacteristic
188C23×C4×C61—21no—
189C23×C4×C61C2311yescharacteristic
190C2×M16×C61—21no—
191#123×C61—21no—
192C22⋊Q8×C61C2×C411yescharacteristic
193C22⋊Q8×C61C2311yescharacteristic
194#121×C61C2×C411yescharacteristic
195#121×C61C2311yescharacteristic
196#120×C61—21no—
197C4×D4×C61—21no—
198C4×D4×C61—21no—
199#117×C61C2×C411yescharacteristic
200C22⋊C8×C61—21no—
201C22⋊C8×C61C2311yescharacteristic
202C22⋊C8×C61C2311yescharacteristic
203#95×C61—21no—
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—42no—
219C22×C4×C61—42no—
220C22×C4×C61—81no—
221C22×C4×C61—81no—
222C22×C4×C61C22×C411yescharacteristic
223C22×C4×C61C22×C411yescharacteristic
224C22×C4×C61C2×D411yescharacteristic
225C22×C4×C61C2×D411yescharacteristic
226C22×C4×C61C2×D411yescharacteristic
227C22×C4×C61C2411yescharacteristic
228C2×C22⋊D61—21no—
229C2×C22⋊D61—21no—
230C2×C22⋊D61—21no—
231C2×C22⋊D61—21no—
232C2×C22⋊D61—21no—
233C2×C22⋊D61—41no—
234C2×C22⋊D61—41no—
235C2×C22⋊D61C22⋊C411yescharacteristic
236C2×C22⋊D61C22⋊C411yescharacteristic
237C2×C22⋊D61C22⋊C411yescharacteristic
238C2×C22⋊D61C22⋊C411yescharacteristic
239C22×Dic61—21no—
240C22×Dic61—21no—
241C22×Dic61—21no—
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×C61C22×C411yescharacteristic
270C4⋊C4×C61C22×C411yescharacteristic
271C22⋊C4×C61—21no—
272C22⋊C4×C61—21no—
273C22⋊C4×C61—21no—
274C22⋊C4×C61—21no—
275C22⋊C4×C61—21no—
276C42×C61—21no—
277C22⋊Dic61—21no—
278C22⋊Dic61—21no—
279C22⋊Dic61—21no—
280C22⋊Dic61—21no—
281C22⋊Dic61—21no—
282C22⋊Dic61—21no—
283C22⋊Dic61—21no—
284C22⋊Dic61—42no—
285C22⋊Dic61C22⋊C411yescharacteristic
286C22⋊Dic61C22⋊C411yescharacteristic
287C22⋊Dic61C22⋊C411yescharacteristic
288C22⋊Dic61C22⋊C411yescharacteristic
289#11758198—21no—
290#11758198—21no—
291#11758198—21no—
292#11758198—21no—
293#11758198—21no—
294#11758198—21no—
295#11758198—21no—
296#11758198—21no—
297#11758198—42no—
298#11758198—81no—
299#11758198C22⋊C411yescharacteristic
300#11758198C22⋊C411yescharacteristic
301#11758198C22⋊C411yescharacteristic
302#11758198C22⋊C411yescharacteristic
303C4⋊Dic61—21no—
304C4⋊Dic61—21no—
305C4⋊Dic61—21no—
306C4⋊Dic61—21no—
307C4⋊Dic61—81no—
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—22no—
361C2×C4×C61—21no—
362C2×C4×C61—21no—
363C2×C4×C61—21no—
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×C61—84no—
377C2×C4×C61C2×C22⋊C411yescharacteristic
378C2×C4×C61C2×C22⋊C411yescharacteristic
379C2×C4×C61C23×C411yescharacteristic
380C2×C4×C61C22×D411yescharacteristic
381C22⋊D61—41no—
382C22⋊D61—41no—
383C22⋊D61—41no—
384C22⋊D61—41no—
385C22⋊D61—42no—
386C22⋊D61—41no—
387C22⋊D61—41no—
388C22⋊D61—81no—
389C22⋊D61—81no—
390C22⋊D61—81no—
391C2×Dic61—21no—
392C2×Dic61—21no—
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—41no—
404C2×Dic61—81no—
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—42no—
462C4×C61—41no—
463C4×C61—41no—
464C4×C61—41no—
465C4×C61—81no—
466Dic61—21no—
467Dic61—21no—
468Dic61—21no—
469Dic61—21no—
470Dic61—21no—
471Dic61—21no—
472Dic61—41no—
473Dic61—41no—
474Dic61—41no—
475Dic61—81no—
476Dic61—81no—
477#3505—611no—
478#2975—611no—
479#2353—611no—
480#1521—611no—
481#1521—611no—
482#1513—611no—
483#1513—611no—
484#1511—611no—
485#1510—611no—
486#1508—611no—
487#1507—611no—
488#1504—611no—
489#1504D6111yescharacteristic, complemented
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#380—611no—
542C4×C22⋊C4—611no—
543C4×C22⋊C4—1221no—
544#376—611no—
545C2×#95C2×D6111yescharacteristic, complemented
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—21no—
570C23×C4—611no—
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—611no—
657C2×C4⋊C4—611no—
658C2×C4⋊C4—611no—
659C2×C4⋊C4—1221no—
660C2×C4⋊C4—1221no—
661C2×C22⋊C4—611no—
662C2×C22⋊C4—611no—
663C2×C22⋊C4—1221no—
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—21no—
686#95—611no—
687#95—611no—
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—42no—
727C22×C4—42no—
728C22×C4—81no—
729C22×C4—81no—
730C22×C4—611no—
731C22×C4—611no—
732C22×C4—611no—
733C22×C4—611no—
734C22×C4—611no—
735C22×C4—611no—
736C22×C4—611no—
737C22×C4—1221no—
738C22×C4—1221no—
739C22×C4—1221no—
740C22×C4—1221no—
741C22×C4—1221no—
742C22×C4—1221no—
743C22×C4—1221no—
744C22×C4—1221no—
745C22×C4—4881no—
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—611no—
763C4⋊C4—611no—
764C4⋊C4—611no—
765C4⋊C4—611no—
766C4⋊C4—611no—
767C4⋊C4—611no—
768C4⋊C4—1221no—
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—4881no—
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—611no—
789C22⋊C4—611no—
790C22⋊C4—611no—
791C22⋊C4—611no—
792C22⋊C4—611no—
793C22⋊C4—611no—
794C22⋊C4—611no—
795C22⋊C4—611no—
796C22⋊C4—1221no—
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—4881no—
812C22⋊C4—2442no—
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—22no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
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—84no—
879C2×C4—611no—
880C2×C4—611no—
881C2×C4—611no—
882C2×C4—611no—
883C2×C4—611no—
884C2×C4—611no—
885C2×C4—1221no—
886C2×C4—1221no—
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—2441no—
896C2×C4—2441no—
897C2×C4—2441no—
898C2×C4—2441no—
899C2×C4—2442no—
900C2×C4—2441no—
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—42no—
949C4—41no—
950C4—41no—
951C4—41no—
952C4—81no—
953C4—1221no—
954C4—1221no—
955C4—1221no—
956C4—1221no—
957C4—1221no—
958C4—1221no—
959C4—4881no—
960C4—4881no—
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#2145436311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1504C2
socleC22×C61C22×C22⋊C4
prime radical#21459647C2
cosocleC22×C4×C61C24
hypercenter#1504D61
hypocenterC61#17623
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1504

Complements

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

NH ≅ G/Ntype
2. #21454858C2semidirect
3. #21448755C2semidirect
4. #21444395C2semidirect
5. #21444393C2semidirect
6. #21444363C2semidirect
7. #21444362C2semidirect
8. #21444350C2semidirect
9. #21444346C2semidirect
10. #21444337C2semidirect
11. #21444333C2semidirect
12. #21444321C2semidirect
13. #21444304C2semidirect
14. #21444302C2semidirect
15. C61×#1504C2semidirect
17. #16840459C4semidirect
19. #16840456C4semidirect
20. #16840451C4semidirect
21. #16840446C4semidirect
24. #16840422C4semidirect
25. #16840419C4semidirect
26. #16840409C4semidirect
27. #16840400C4semidirect
42. #16839812C22semidirect
43. #16839812C22semidirect
44. #16839726C22semidirect
50. #16839629C22semidirect
52. #16839622C22semidirect
55. #16839607C22semidirect
56. #16839500C22semidirect
57. #16839500C22semidirect
58. #16839499C22semidirect
59. #16839499C22semidirect
60. #16839498C22semidirect
61. #16839498C22semidirect
69. C61×#407C22semidirect
70. C2×#95×C61C22semidirect
71. C61×#328C22semidirect
72. C61×#328C22semidirect
76. C2×Q8×D61C2×C4semidirect
79. C2×D4×D61C2×C4semidirect
91. #14519768C2×C4semidirect
92. #14519768C2×C4semidirect
94. #14519766C2×C4semidirect
96. #14519764C2×C4semidirect
107. #14519757C2×C4semidirect
114. #14519753C2×C4semidirect
115. #14519752C2×C4semidirect
126. #14519748C2×C4semidirect
130. Q8×Dic61C2×C4semidirect
131. #14519742C2×C4semidirect
134. D4×Dic61C2×C4semidirect
136. #14519739C2×C4semidirect
158. C4⋊C4×D61C2×C4semidirect
159. C4⋊C4×D61C2×C4semidirect
489. #1504D61semidirect
535. #407C2×D61semidirect
545. C2×#95C2×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
#214487552
#214443952
#214443932
#214443632
#214443622
#214443502
#214443462
#214443372
#214443332
#214443212
#214443042
#214443022
C61×#15042
#1762361