Finite Group Databasebeta

← #30611928

Subgroups — #30611928

Order 15616.

1028 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462739C211yesmaximal, characteristic, complemented
2#21462466C211yesmaximal, characteristic, complemented
3#21461357C211yesmaximal, characteristic, complemented
4#21461356C211yesmaximal, characteristic, complemented
5#21461351C211yesmaximal, characteristic, complemented
6#21461350C211yesmaximal, characteristic, complemented
7#21461339C211yesmaximal, characteristic, complemented
8#21461338C211yesmaximal, characteristic, complemented
9#21461337C211yesmaximal, characteristic, complemented
10#21461331C211yesmaximal, characteristic, complemented
11#21461330C211yesmaximal, characteristic, complemented
12#21461326C211yesmaximal, characteristic, complemented
13#21461321C211yesmaximal, characteristic, complemented
14C2×#16840620C211yesmaximal, characteristic, complemented
15#21459687C211yesmaximal, characteristic
16C2×#14519864—21no—
17#16840814—21no—
18#16840795—21no—
19#16840793—21no—
20#16840791—21no—
21#16840785C2211yescharacteristic, complemented
22#16840782C2211yescharacteristic, complemented
23#16840779C2211yescharacteristic
24#16840769—21no—
25#16840768—21no—
26#16840768—21no—
27#16840767C2211yescharacteristic, complemented
28#16840767C2211yescharacteristic, complemented
29#16840765C2211yescharacteristic
30#16840765C2211yescharacteristic, complemented
31#16840765C2211yescharacteristic, complemented
32C2×#14519844C2211yescharacteristic
33C2×#14519844C2211yescharacteristic
34C2×#14519844C2211yescharacteristic, complemented
35D61⋊(C4⋊C8)C2211yescharacteristic, complemented
36#16840622C2211yescharacteristic, complemented
37#16840622C2211yescharacteristic, complemented
38#16840622C2211yescharacteristic, complemented
39#16840622C2211yescharacteristic, complemented
40#16840621C2211yescharacteristic, complemented
41#16840621C2211yescharacteristic, complemented
42#16840621C2211yescharacteristic, complemented
43#16840621C2211yescharacteristic, complemented
44#16840620C2211yescharacteristic
45#16840620C2211yescharacteristic
46#16840620C2211yescharacteristic
47#16840620C2211yescharacteristic
48#16840620C2211yescharacteristic
49#16840620C2211yescharacteristic
50#16840620C2211yescharacteristic
51#16840620C2211yescharacteristic
52#16840496—21no—
53#16840495C411yescharacteristic
54#16840494C411yescharacteristic
55#16840431C411yescharacteristic
56#16840430—21no—
57#16840430C411yescharacteristic
58#16840408C411yescharacteristic
59#16840406C411yescharacteristic
60#16840403C411yescharacteristic
61#16840402—21no—
62#16840399—21no—
63#16840364—21no—
64#16840362—21no—
65#16840327—21no—
66#16840314C2211yescharacteristic
67#16840311C2211yescharacteristic
68#16840309C2211yescharacteristic
69#16840308C2211yescharacteristic
70#16840307C2211yescharacteristic
71C2×#14519773C2211yescharacteristic
72#16840235—21no—
73C4×#11758224C2211yescharacteristic
74C61×#546C411yescharacteristic
75#14519864—44no—
76C2×#11758213—21no—
77C2×#11758213—21no—
78C2×#11758217—21no—
79C2×#11758217—21no—
80C2×#11758217—21no—
81C2×D61⋊C8—21no—
82C22×#92420—21no—
83C22×#92420—21no—
84C22×#92420—21no—
85#14519844—21no—
86#14519844—21no—
87#14519844—21no—
88#14519844—21no—
89#14519844—21no—
90#14519844C2311yescharacteristic
91#14519844C2311yescharacteristic
92#14519844C2311yescharacteristic
93#14519844C2311yescharacteristic
94#14519844C2311yescharacteristic
95#14519844C2311yescharacteristic
96#14519844C2311yescharacteristic
97#14519844C2311yescharacteristic
98C4⋊#92420—21no—
99C4⋊#92420—21no—
100C4⋊#92420—21no—
101C4⋊#92420—21no—
102#14519834—21no—
103C22⋊#92420—21no—
104C22⋊#92420—21no—
105#14519832—21no—
106#14519832—21no—
107C4×#92420—21no—
108C2×#11758226C2×C411yescharacteristic
109C2×#11758222—21no—
110C2×#11758222C2×C411yescharacteristic
111C2×#11758224—21no—
112C2×#11758224C2×C411yescharacteristic
113C2×#11758224D411yescharacteristic
114C22×D244C2×C411yescharacteristic
115C22×C22⋊D61—21no—
116C22×C22⋊D61—21no—
117#14519776C2311yescharacteristic
118#14519775C2311yescharacteristic
119#14519773—21no—
120#14519773—21no—
121#14519773—21no—
122#14519773—21no—
123#14519773C2×C411yescharacteristic
124#14519773C2×C411yescharacteristic
125#14519773C2311yescharacteristic
126#14519773C2311yescharacteristic
127#14519767—21no—
128#14519766C2×C411yescharacteristic
129#14519765C2×C411yescharacteristic
130#14519764C2×C411yescharacteristic
131#14519763—21no—
132#14519763—21no—
133#14519763—21no—
134#14519763—21no—
135#14519762—21no—
136#14519762—21no—
137#14519761—21no—
138#14519760—21no—
139#14519759—21no—
140#14519759—21no—
141#14519758—21no—
142#14519756C2×C411yescharacteristic
143#14519754—21no—
144#14519752—21no—
145#14519752C2×C411yescharacteristic
146#14519751—21no—
147#14519751C2×C411yescharacteristic
148#14519750—21no—
149#14519750—21no—
150#14519750—21no—
151#14519750—21no—
152#14519750—21no—
153#14519749—21no—
154#14519749—21no—
155#14519749—21no—
156#14519749—21no—
157#14519749—21no—
158#14519748—21no—
159#14519748C2×C411yescharacteristic
160#14519747—21no—
161#14519746—21no—
162#14519745—21no—
163Q8×Dic61C2×C411yescharacteristic
164C4×Dic122C2×C411yescharacteristic
165#14519742—21no—
166#14519742C2×C411yescharacteristic
167#14519742D411yescharacteristic
168C4×D244C2×C411yescharacteristic
169D4×Dic61C2×C411yescharacteristic
170D4×Dic61D411yescharacteristic
171#14519739C2×C411yescharacteristic
172C4×C22⋊D61—21no—
173C4×C22⋊D61—21no—
174C4×C22⋊D61—21no—
175C4×C22⋊D61—21no—
176C4×C22⋊D61—21no—
177C4×C22⋊D61C2×C411yescharacteristic
178C4×C22⋊D61C2×C411yescharacteristic
179#14519737—21no—
180#14519737—21no—
181#14519737—21no—
182#14519737—21no—
183#14519737—21no—
184#14519737D411yescharacteristic
185#14519737D411yescharacteristic
186#14519735D411yescharacteristic
187#14519733—21no—
188#14519733D411yescharacteristic
189#14519733D411yescharacteristic
190C2×C22⋊Dic61—21no—
191C22⋊C4×D61—21no—
192C22⋊C4×D61—21no—
193C2×C4×Dic61C2311yescharacteristic
194C2×C4×Dic61C2311yescharacteristic
195C42×D61C2311yescharacteristic
196C2×#41×C61C2×C411yescharacteristic
197C22×D4×C61C2×C411yescharacteristic
198#124×C61C2×C411yescharacteristic
199#123×C61—21no—
200C22⋊Q8×C61C2×C411yescharacteristic
201#121×C61—21no—
202#121×C61C2×C411yescharacteristic
203#120×C61—21no—
204C4×D4×C61C2×C411yescharacteristic
205C4×D4×C61C2×C411yescharacteristic
206C2×C22⋊C4×C61—21no—
207C24×C61—21no—
208C23×D61—21no—
209#41×C61—81no—
210C2×Q8×C61C22×C411yescharacteristic
211C2×D4×C61—21no—
212C2×D4×C61—21no—
213C2×D4×C61—21no—
214C2×D4×C61—81no—
215C2×D4×C61C22⋊C411yescharacteristic
216C2×D4×C61C22×C411yescharacteristic
217C2×D4×C61C22×C411yescharacteristic
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61C22×C411yescharacteristic
221C22×C4×C61C22×C411yescharacteristic
222C2×C22⋊D61—21no—
223C2×C22⋊D61—21no—
224C2×C22⋊D61—21no—
225C2×C22⋊D61—21no—
226C2×C22⋊D61—21no—
227C2×C22⋊D61—21no—
228C2×C22⋊D61—21no—
229C2×C22⋊D61—21no—
230C2×C22⋊D61—21no—
231C2×C22⋊D61—21no—
232C2×C22⋊D61—21no—
233C2×C22⋊D61—21no—
234C2×C22⋊D61—42no—
235C2×C22⋊D61—42no—
236C2×C22⋊D61—81no—
237C2×C22⋊D61—81no—
238C2×C22⋊D61C22⋊C411yescharacteristic
239C2×C22⋊D61C22⋊C411yescharacteristic
240C22×Dic61—21no—
241C22×Dic61—21no—
242C22×Dic61C2×D411yescharacteristic
243C22×Dic61C2×D411yescharacteristic
244C22×Dic61C2×D411yescharacteristic
245C22×Dic61C2×D411yescharacteristic
246#11758226—81no—
247#11758224—22no—
248#11758224—22no—
249#11758224—81no—
250#11758224—81no—
251#11758224—81no—
252#11758222—81no—
253#11758222—81no—
254#11758222—81no—
255C2×D244—21no—
256C2×D244—21no—
257C2×D244—21no—
258C2×D244—81no—
259C2×D244C22×C411yescharacteristic
260C2×D244C22×C411yescharacteristic
261C2×C4×D61—21no—
262C2×C4×D61—21no—
263C2×C4×D61—21no—
264C2×C4×D61—21no—
265C2×C4×D61C22×C411yescharacteristic
266C2×C4×D61C2×D411yescharacteristic
267C2×C4×D61C2×D411yescharacteristic
268C2×Dic122—21no—
269C2×Dic122C22⋊C411yescharacteristic
270C2×Dic122C22×C411yescharacteristic
271#11758217—42no—
272#11758217—42no—
273#11758217—81no—
274C2×#92420—21no—
275C2×#92420—21no—
276C2×#92420—21no—
277C2×#92420—21no—
278C2×#92420—21no—
279C2×#92420—21no—
280C2×#92420—21no—
281C2×#92420—21no—
282C2×#92420—42no—
283C2×#92420—42no—
284C2×#92420—81no—
285#11758213—42no—
286#11758213—81no—
287D61⋊C8—42no—
288C4⋊C4×C61—21no—
289C4⋊C4×C61C22⋊C411yescharacteristic
290C4⋊C4×C61C22×C411yescharacteristic
291C22⋊C4×C61—21no—
292C22⋊C4×C61—21no—
293C22⋊C4×C61—21no—
294C22⋊C4×C61—21no—
295C22⋊C4×C61—21no—
296C22⋊C4×C61C22⋊C411yescharacteristic
297C22⋊C4×C61C22⋊C411yescharacteristic
298C42×C61C22×C411yescharacteristic
299C22⋊Dic61—21no—
300C22⋊Dic61—21no—
301C22⋊Dic61—21no—
302C22⋊Dic61—21no—
303C22⋊Dic61—21no—
304C22⋊Dic61C22⋊C411yescharacteristic
305C22⋊Dic61C22⋊C411yescharacteristic
306#11758198—21no—
307#11758198—21no—
308#11758198—21no—
309#11758198—21no—
310#11758198—21no—
311#11758198—21no—
312#11758198—21no—
313#11758198—21no—
314#11758198C22⋊C411yescharacteristic
315#11758198C22⋊C411yescharacteristic
316C4⋊Dic61—21no—
317C4⋊Dic61C22⋊C411yescharacteristic
318C4⋊Dic61C22×C411yescharacteristic
319#11758196—21no—
320#11758196—21no—
321#11758196—21no—
322#11758196—21no—
323#11758196—21no—
324#11758196C22⋊C411yescharacteristic
325#11758196C22⋊C411yescharacteristic
326#11758196C22⋊C411yescharacteristic
327#11758196C22⋊C411yescharacteristic
328C4×Dic61—21no—
329C4×Dic61—21no—
330C4×Dic61C22×C411yescharacteristic
331C4×Dic61C22×C411yescharacteristic
332C4×Dic61C2×D411yescharacteristic
333C4×Dic61C2×D411yescharacteristic
334C4×Dic61C2×D411yescharacteristic
335C4×Dic61C2×D411yescharacteristic
336C4×Dic61C2×D411yescharacteristic
337C4×Dic61C2×D411yescharacteristic
338C4×Dic61C2411yescharacteristic
339C23×C61—21no—
340C23×C61—21no—
341C23×C61—42no—
342C23×C61—81no—
343C23×C61—81no—
344C23×C61C2×C22⋊C411yescharacteristic
345C23×C61C2×C22⋊C411yescharacteristic
346C22×D61—21no—
347C22×D61—21no—
348C22×D61—42no—
349C22×D61—81no—
350C22×D61—81no—
351C22×D61C2×C22⋊C411yescharacteristic
352Q8×C61—41no—
353D4×C61—22no—
354D4×C61—41no—
355D4×C61—41no—
356D4×C61—81no—
357D4×C61—81no—
358D4×C61—81no—
359C2×C4×C61—21no—
360C2×C4×C61—21no—
361C2×C4×C61—41no—
362C2×C4×C61—41no—
363C2×C4×C61—81no—
364C2×C4×C61—81no—
365C2×C4×C61C2×C22⋊C411yescharacteristic
366C2×C4×C61C2×C22⋊C411yescharacteristic
367C2×C4×C61C2×C22⋊C411yescharacteristic
368C2×C4×C61C2×C22⋊C411yescharacteristic
369C2×C4×C61C23×C411yescharacteristic
370C22⋊D61—22no—
371C22⋊D61—22no—
372C22⋊D61—41no—
373C22⋊D61—41no—
374C22⋊D61—41no—
375C22⋊D61—41no—
376C22⋊D61—41no—
377C22⋊D61—41no—
378C22⋊D61—41no—
379C22⋊D61—41no—
380C22⋊D61—42no—
381C22⋊D61—42no—
382C22⋊D61—81no—
383C22⋊D61—81no—
384C22⋊D61—81no—
385C22⋊D61—81no—
386C22⋊D61—81no—
387C22⋊D61—81no—
388C2×Dic61—21no—
389C2×Dic61—21no—
390C2×Dic61—21no—
391C2×Dic61—21no—
392C2×Dic61—21no—
393C2×Dic61—21no—
394C2×Dic61—21no—
395C2×Dic61—21no—
396C2×Dic61—81no—
397C2×Dic61—81no—
398C2×Dic61C2×C22⋊C411yescharacteristic
399C2×Dic61C2×C22⋊C411yescharacteristic
400C2×Dic61C2×C22⋊C411yescharacteristic
401C2×Dic61C2×C22⋊C411yescharacteristic
402C2×Dic61C2×C22⋊C411yescharacteristic
403C2×Dic61AGL(1,ℤ/8)12yes—
404C2×Dic61#13712yes—
405C2×Dic61C22×D411yescharacteristic
406C2×Dic61C22×D411yescharacteristic
407D244—41no—
408D244—41no—
409D244—81no—
410D244—81no—
411D244—81no—
412C4×D61—21no—
413C4×D61—21no—
414C4×D61—21no—
415C4×D61—21no—
416C4×D61—41no—
417C4×D61—81no—
418C4×D61—81no—
419C4×D61—81no—
420C4×D61—81no—
421Dic122—22no—
422Dic122—41no—
423Dic122—41no—
424Dic122—41no—
425#92420—41no—
426#92420—41no—
427#92420—41no—
428#92420—41no—
429#92420—41no—
430#92420—41no—
431#92420—41no—
432#92420—41no—
433#17762—611nomaximal, Sylow
434C22×C61—21no—
435C22×C61—21no—
436C22×C61—21no—
437C22×C61—21no—
438C22×C61—21no—
439C22×C61—41no—
440C22×C61—41no—
441C22×C61—41no—
442C22×C61—41no—
443C22×C61—41no—
444C22×C61—41no—
445C22×C61—162no—
446C22×C61#41712yes—
447C22×C61C22×C22⋊C411yescharacteristic
448C2×D61—21no—
449C2×D61—21no—
450C2×D61—21no—
451C2×D61—41no—
452C2×D61—41no—
453C2×D61—41no—
454C2×D61—41no—
455C2×D61—41no—
456C2×D61—41no—
457C2×D61—162no—
458C4×C61—21no—
459C4×C61—21no—
460C4×C61—21no—
461C4×C61—21no—
462C4×C61—21no—
463C4×C61—41no—
464C4×C61—41no—
465Dic61—21no—
466Dic61—21no—
467Dic61—21no—
468Dic61—21no—
469Dic61—41no—
470Dic61—41no—
471Dic61#41712yes—
472Dic61C2×AGL(1,ℤ/8)11yescharacteristic
473Dic61C2×#13711yescharacteristic
474Dic61#57611yescharacteristic
475Dic61#57711yescharacteristic
476#3508—611no—
477#2989—611no—
478#2906—611no—
479#1560—611no—
480#1560—611no—
481#1557—611no—
482#1557—611no—
483#1551—611no—
484#1551—611no—
485#1550—611no—
486#1547—611no—
487#1547—611no—
488#1545—611no—
489#1542—611no—
490C2×#331—611no—
491C2×C61—22no—
492C2×C61—41no—
493C2×C61—81no—
494C2×C61—81no—
495C2×C61#288811yescharacteristic
496C2×C61C2×#41711yescharacteristic
497C2×C61#289711yescharacteristic
498D61—41no—
499D61—81no—
500D61—81no—
501C2×#131—1221no—
502#559—611no—
503#559—611no—
504#559—1221no—
505#550—611no—
506#550—611no—
507#550—1221no—
508#546—611no—
509#546—611no—
510#546—611no—
511#546—1221no—
512#546—1221no—
513#546#692311yescharacteristic
514#540—1221no—
515#540—1221no—
516#535—1221no—
517#533—611no—
518#532—611no—
519#532—611no—
520#532—611no—
521#532—611no—
522C2×#127—611no—
523#518—1221no—
524C4×#41—611no—
525#446—1221no—
526#436—1221no—
527#435—1221no—
528#435—1221no—
529#432—611no—
530#432—611no—
531#431—611no—
532#424—1221no—
533#424—1221no—
534#424—1221no—
535#423—611no—
536#423—611no—
537#423—611no—
538#423—611no—
539#423—611no—
540C2×C4⋊C8—611no—
541C2×C4⋊C8—611no—
542C2×C4⋊C8—611no—
543C2×C4⋊C8—611no—
544#333—611no—
545#333—611no—
546#333—611no—
547#333—611no—
548#332—611no—
549#332—611no—
550#332—611no—
551#332—611no—
552#331—611no—
553#331—611no—
554#331—611no—
555#331—611no—
556#331—611no—
557#331—611no—
558#331—611no—
559#331—611no—
560C61#1776211yescharacteristic, complemented, Sylow
561C2×#41—611no—
562C2×#41—611no—
563C2×#41—611no—
564C2×#41—611no—
565C2×#41—1221no—
566C2×#41—1221no—
567C2×#41C2×#692311yescharacteristic
568C22×D4—611no—
569C22×D4—1221no—
570C22×D4—1221no—
571C22×D4C2×#692311yescharacteristic
572#131—2444no—
573C2×M16—1221no—
574C2×M16—1221no—
575C2×M16—1221no—
576C2×M16—1221no—
577C2×M16—1221no—
578C22×C8—1221no—
579C22×C8—1221no—
580C22×C8—1221no—
581C22×C8—1221no—
582C4⋊Q8—611no—
583C4⋊Q8—611no—
584#127—611no—
585#127—611no—
586#127—611no—
587#127—611no—
588#127—1221no—
589#127—1221no—
590#127—1221no—
591#127—1221no—
592#125—1221no—
593#124—611no—
594#124—611no—
595#124—611no—
596#124—1221no—
597#124—1221no—
598#124—1221no—
599#124—1221no—
600#124C2×#692311yescharacteristic
601#123—21no—
602#123—1221no—
603#123—1221no—
604#123—1221no—
605#123—1221no—
606#123—1221no—
607#123—1221no—
608#123—1221no—
609C22⋊Q8—611no—
610C22⋊Q8—1221no—
611C22⋊Q8C2×#692311yescharacteristic
612#121—21no—
613#121—611no—
614#121—611no—
615#121—611no—
616#121—1221no—
617#121—1221no—
618#121—1221no—
619#121—1221no—
620#121—1221no—
621#121—1221no—
622#121—1221no—
623#121—1221no—
624#121—1221no—
625#121—1221no—
626#121—1221no—
627#121—1221no—
628#121—1221no—
629#121C2×#692311yescharacteristic
630#120—21no—
631#120—1221no—
632#120—1221no—
633#120—1221no—
634C4×Q8—611no—
635C4×Q8—611no—
636C4×Q8—611no—
637C4×Q8—611no—
638C4×Q8—1221no—
639C4×D4—611no—
640C4×D4—611no—
641C4×D4—611no—
642C4×D4—611no—
643C4×D4—611no—
644C4×D4—611no—
645C4×D4—611no—
646C4×D4—611no—
647C4×D4—1221no—
648C4×D4—1221no—
649C4×D4—1221no—
650C4×D4—1221no—
651C4×D4—1221no—
652C4×D4—1221no—
653C4×D4—1221no—
654C4×D4—1221no—
655C4×D4—1221no—
656C4×D4—1221no—
657C4×D4C2×#692311yescharacteristic
658C4×D4C2×#692311yescharacteristic
659#117—611no—
660#117—611no—
661#117—611no—
662#117—1221no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—1221no—
665C2×C22⋊C4—1221no—
666C2×C22⋊C4—1221no—
667C2×C42—611no—
668C2×C42—611no—
669C2×C42—611no—
670C4⋊C8—611no—
671C4⋊C8—611no—
672C4⋊C8—611no—
673C4⋊C8—611no—
674C4⋊C8—611no—
675C4⋊C8—611no—
676C4⋊C8—611no—
677C4⋊C8—611no—
678C4⋊C8—1221no—
679C4⋊C8—1221no—
680C4⋊C8—1221no—
681C4⋊C8—1221no—
682C4⋊C8—1221no—
683C4⋊C8—1221no—
684C4⋊C8—1221no—
685C4⋊C8—1221no—
686C4⋊C8—1221no—
687C22⋊C8—1221no—
688C22⋊C8—1221no—
689C22⋊C8—1221no—
690#97—1221no—
691#97—1221no—
692C4×C8—1221no—
693C24—21no—
694C24—1221no—
695#41—81no—
696#41—1222no—
697#41—1222no—
698#41—4881no—
699#41—4881no—
700#41—4881no—
701#41—4881no—
702#41—4881no—
703#41—4881no—
704#41—4881no—
705C2×Q8—611no—
706C2×Q8—611no—
707C2×Q8—1221no—
708C2×Q8C22×#692311yescharacteristic
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—81no—
713C2×D4—611no—
714C2×D4—611no—
715C2×D4—611no—
716C2×D4—611no—
717C2×D4—1221no—
718C2×D4—1221no—
719C2×D4—1221no—
720C2×D4—1221no—
721C2×D4—1221no—
722C2×D4—1221no—
723C2×D4—1221no—
724C2×D4—1221no—
725C2×D4—1221no—
726C2×D4—1221no—
727C2×D4—1221no—
728C2×D4—1221no—
729C2×D4—1221no—
730C2×D4—1221no—
731C2×D4—1221no—
732C2×D4—4881no—
733C2×D4—4881no—
734C2×D4—4881no—
735C2×D4—2442no—
736C2×D4—2442no—
737C2×D4C22⋊#692311yescharacteristic
738C2×D4C22×#692311yescharacteristic
739C2×D4C22×#692311yescharacteristic
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—611no—
743C22×C4—611no—
744C22×C4—611no—
745C22×C4—611no—
746C22×C4—611no—
747C22×C4—611no—
748C22×C4—611no—
749C22×C4—1221no—
750C22×C4—1221no—
751C22×C4—1221no—
752C22×C4—1221no—
753C22×C4—1221no—
754C22×C4—1221no—
755C22×C4C22×#692311yescharacteristic
756C22×C4C22×#692311yescharacteristic
757M16—4881no—
758M16—4881no—
759M16—2442no—
760M16—2442no—
761M16—2442no—
762C2×C8—1221no—
763C2×C8—1221no—
764C2×C8—1221no—
765C2×C8—1221no—
766C2×C8—1221no—
767C2×C8—1221no—
768C2×C8—1221no—
769C2×C8—1221no—
770C2×C8—4881no—
771C2×C8—2442no—
772C2×C8—2442no—
773C2×C8—2442no—
774C4⋊C4—21no—
775C4⋊C4—611no—
776C4⋊C4—611no—
777C4⋊C4—611no—
778C4⋊C4—611no—
779C4⋊C4—611no—
780C4⋊C4—611no—
781C4⋊C4—1221no—
782C4⋊C4—1221no—
783C4⋊C4—1221no—
784C4⋊C4—1221no—
785C4⋊C4—1221no—
786C4⋊C4—1221no—
787C4⋊C4C22⋊#692311yescharacteristic
788C4⋊C4C22×#692311yescharacteristic
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—611no—
795C22⋊C4—611no—
796C22⋊C4—611no—
797C22⋊C4—611no—
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⋊C4C22⋊#692311yescharacteristic
812C22⋊C4C22⋊#692311yescharacteristic
813C42—611no—
814C42—611no—
815C42—611no—
816C42—611no—
817C42—611no—
818C42—611no—
819C42—611no—
820C42—611no—
821C42—611no—
822C42—1221no—
823C42—1221no—
824C42C22×#692311yescharacteristic
825C23—21no—
826C23—21no—
827C23—42no—
828C23—81no—
829C23—81no—
830C23—611no—
831C23—1221no—
832C23—1221no—
833C23—4881no—
834C23—4881no—
835C23—2442no—
836C23C2×C22⋊#692311yescharacteristic
837C23C2×C22⋊#692311yescharacteristic
838Q8—41no—
839Q8—1222no—
840Q8—2441no—
841Q8—2441no—
842Q8—2441no—
843D4—22no—
844D4—41no—
845D4—41no—
846D4—81no—
847D4—81no—
848D4—81no—
849D4—1222no—
850D4—1222no—
851D4—4881no—
852D4—4881no—
853D4—4881no—
854D4—4881no—
855D4—4881no—
856D4—4881no—
857D4—4881no—
858D4—4881no—
859D4—4881no—
860D4—2441no—
861D4—2441no—
862D4—2441no—
863D4—2441no—
864D4—2441no—
865D4—2441no—
866D4—2441no—
867D4—2441no—
868D4—2441no—
869D4—2441no—
870D4—2442no—
871D4—2442no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—81no—
877C2×C4—81no—
878C2×C4—612no—
879C2×C4—612no—
880C2×C4—611no—
881C2×C4—611no—
882C2×C4—611no—
883C2×C4—611no—
884C2×C4—611no—
885C2×C4—611no—
886C2×C4—611no—
887C2×C4—1221no—
888C2×C4—1221no—
889C2×C4—1221no—
890C2×C4—1221no—
891C2×C4—1221no—
892C2×C4—1221no—
893C2×C4—1221no—
894C2×C4—1221no—
895C2×C4—1221no—
896C2×C4—1221no—
897C2×C4—1221no—
898C2×C4—1221no—
899C2×C4—4881no—
900C2×C4—4881no—
901C2×C4—4881no—
902C2×C4—4881no—
903C2×C4—4881no—
904C2×C4—4881no—
905C2×C4—2441no—
906C2×C4C2×C22⋊#692311yescharacteristic
907C2×C4C2×C22⋊#692311yescharacteristic
908C2×C4C2×C22⋊#692311yescharacteristic
909C2×C4C2×C22⋊#692311yescharacteristic
910C2×C4C23×#692311yescharacteristic
911C8—2441no—
912C8—2441no—
913C8—2441no—
914C8—2441no—
915C8—2441no—
916C8—2441no—
917C8—2441no—
918C8—2441no—
919C22—21no—
920C22—21no—
921C22—21no—
922C22—21no—
923C22—21no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—162no—
931C22—1221no—
932C22—1221no—
933C22—1221no—
934C22—9762no—
935C22—2441no—
936C22—2441no—
937C22—2441no—
938C22—2441no—
939C22—2441no—
940C22—2441no—
941C22#1684075312yes—
942C22C22×C22⋊#692311yescharacteristic
943C4—21no—
944C4—21no—
945C4—21no—
946C4—21no—
947C4—21no—
948C4—41no—
949C4—41no—
950C4—611no—
951C4—611no—
952C4—612no—
953C4—611no—
954C4—611no—
955C4—1221no—
956C4—1221no—
957C4—1221no—
958C4—1221no—
959C4—2441no—
960C4—2441no—
961C2—22no—
962C2—41no—
963C2—81no—
964C2—81no—
965C2—4881no—
966C2—4881no—
967C2—2441no—
968C2#2146242911yescharacteristic
969C2C2×#1684075311yescharacteristic
970C2#2146244011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#546C4
socleC22×C61C22×C22⋊C4
prime radical#21459687C2
cosocleC4×Dic61C24
hypercenter#546#6923
hypocenterC61#17762
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #21462739C2semidirect
2. #21462466C2semidirect
3. #21461357C2semidirect
4. #21461356C2semidirect
5. #21461351C2semidirect
6. #21461350C2semidirect
7. #21461339C2semidirect
8. #21461338C2semidirect
9. #21461337C2semidirect
10. #21461331C2semidirect
11. #21461330C2semidirect
12. #21461326C2semidirect
13. #21461321C2semidirect
14. C2×#16840620C2semidirect
21. #16840785C22semidirect
22. #16840782C22semidirect
27. #16840767C22semidirect
28. #16840767C22semidirect
30. #16840765C22semidirect
31. #16840765C22semidirect
34. C2×#14519844C22semidirect
35. D61⋊(C4⋊C8)C22semidirect
36. #16840622C22semidirect
37. #16840622C22semidirect
38. #16840622C22semidirect
39. #16840622C22semidirect
40. #16840621C22semidirect
41. #16840621C22semidirect
42. #16840621C22semidirect
43. #16840621C22semidirect
560. C61#17762semidirect

Maximal subgroups

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

subgroupindex
#214627392
#214624662
#214613572
#214613562
#214613512
#214613502
#214613392
#214613382
#214613372
#214613312
#214613302
#214613262
#214613212
C2×#168406202
#214596872
#1776261