Finite Group Databasebeta

← #30611402

Subgroups — #30611402

Order 15616.

1010 conjugacy classes of subgroups.

The subgroup lattice has 974 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462671C211yesmaximal, characteristic, complemented
2#21462336C211yesmaximal, characteristic, complemented
3#21461245C211yesmaximal, characteristic, complemented
4#21461244C211yesmaximal, characteristic, complemented
5#21461241C211yesmaximal, characteristic, complemented
6#21461239C211yesmaximal, characteristic, complemented
7#21461235C211yesmaximal, characteristic, complemented
8#21461234C211yesmaximal, characteristic, complemented
9#21461212C211yesmaximal, characteristic, complemented
10#21461208C211yesmaximal, characteristic, complemented
11#21461205C211yesmaximal, characteristic, complemented
12#21461204C211yesmaximal, characteristic, complemented
13#21461195C211yesmaximal, characteristic, complemented
14#21461194C211yesmaximal, characteristic, complemented
15#21459663C211yesmaximal, characteristic
16#16840794—21no—
17#16840793—21no—
18#16840792—21no—
19#16840791—21no—
20#16840785C2211yescharacteristic
21#16840784C2211yescharacteristic
22#16840734C2211yescharacteristic
23#16840733C2211yescharacteristic
24C2×#14519834C2211yescharacteristic
25D61⋊(C22⋊C8)C2211yescharacteristic
26#16840712—21no—
27#16840711—21no—
28#16840710—21no—
29#16840707C2211yescharacteristic
30#16840705C2211yescharacteristic
31#16840704C2211yescharacteristic
32C22⋊C4×#6923—21no—
33C4×C22⋊#6923C2211yescharacteristic
34#16840698C2211yescharacteristic
35C2×(C2×#6923)⋊C4C2211yescharacteristic
36#16840616C2211yescharacteristic
37#16840616C2211yescharacteristic
38#16840616C2211yescharacteristic
39#16840616C2211yescharacteristic
40#16840615C2211yescharacteristic
41#16840615C2211yescharacteristic
42#16840615C2211yescharacteristic
43#16840615C2211yescharacteristic
44#16840613C2211yescharacteristic
45#16840613C2211yescharacteristic
46#16840613C2211yescharacteristic
47#16840613C2211yescharacteristic
48#16840613C2211yescharacteristic
49#16840613C2211yescharacteristic
50#16840613C2211yescharacteristic
51#16840613C2211yescharacteristic
52#16840498—21no—
53#16840495—21no—
54#16840485C411yescharacteristic, complemented
55#16840482C411yescharacteristic, complemented
56#16840476C411yescharacteristic, complemented
57#16840476C411yescharacteristic, complemented
58#16840455—21no—
59#16840455—21no—
60#16840432C411yescharacteristic, complemented
61#16840411C411yescharacteristic, complemented
62#16840411C411yescharacteristic, complemented
63#16840344—21no—
64#16840344—21no—
65#16840325—21no—
66#16840316C2211yescharacteristic
67#16840310C2211yescharacteristic
68#16840272C2211yescharacteristic
69#16840272C2211yescharacteristic
70#16840269C2211yescharacteristic
71#16840269C2211yescharacteristic
72#16840241—21no—
73C4×D4×D61C2211yescharacteristic
74C61×#550C411yescharacteristic, complemented
75C23×#6923—21no—
76C2×#11758213—21no—
77C2×#11758217—21no—
78C2×D61⋊C8—21no—
79C22×#92420—21no—
80C2×C4⋊#6923—21no—
81C2×C22⋊#6923—21no—
82C2×C22⋊#6923—21no—
83C2×C22⋊#6923—21no—
84C2×C4×#6923—21no—
85C2×C4×#6923—21no—
86#14519844—21no—
87C4⋊#92420—21no—
88#14519834—21no—
89#14519834—21no—
90#14519834C2311yescharacteristic
91#14519834C2311yescharacteristic
92#14519834C2311yescharacteristic
93#14519834C2311yescharacteristic
94C22⋊#92420—21no—
95C22⋊#92420—21no—
96#14519832—21no—
97#14519832—21no—
98(C2×#6923)⋊C4—21no—
99(C2×#6923)⋊C4—21no—
100(C2×#6923)⋊C4—21no—
101(C2×#6923)⋊C4—21no—
102(C2×#6923)⋊C4—21no—
103(C2×#6923)⋊C4C2311yescharacteristic
104(C2×#6923)⋊C4C2311yescharacteristic
105(C2×#6923)⋊C4C2311yescharacteristic
106(C2×#6923)⋊C4C2311yescharacteristic
107C2×#11758224—21no—
108C2×#11758224C2×C411yescharacteristic
109C2×#11758224C2×C411yescharacteristic, complemented
110C2×D4×D61D411yescharacteristic
111C22×C4×D61C2311yescharacteristic
112C22×C4×D61C2311yescharacteristic
113#14519777C2×C411yescharacteristic, complemented
114#14519776C2×C411yescharacteristic, complemented
115#14519775C2×C411yescharacteristic, complemented
116#14519773—21no—
117#14519772—21no—
118#14519772—21no—
119#14519770—21no—
120#14519770—21no—
121#14519767—21no—
122#14519765—21no—
123#14519764—21no—
124#14519764—21no—
125#14519764—21no—
126#14519764—21no—
127#14519763—21no—
128#14519763—21no—
129#14519760—21no—
130#14519760—21no—
131#14519759—21no—
132#14519759—21no—
133#14519758—21no—
134#14519758—21no—
135#14519758—21no—
136#14519758—21no—
137#14519757C2311yescharacteristic
138#14519756C2×C411yescharacteristic
139#14519756C2×C411yescharacteristic, complemented
140#14519755—21no—
141#14519753C2×C411yescharacteristic
142#14519753C2×C411yescharacteristic, complemented
143#14519753C2311yescharacteristic
144#14519749—21no—
145#14519749—21no—
146#14519749—21no—
147#14519749—21no—
148#14519749—21no—
149#14519749—21no—
150#14519748—21no—
151#14519748C2×C411yescharacteristic
152#14519748C2×C411yescharacteristic, complemented
153#14519748C2311yescharacteristic
154#14519748C2311yescharacteristic
155#14519745—21no—
156#14519745—21no—
157#14519745—21no—
158#14519745—21no—
159C4×Dic122—21no—
160C4×Dic122—21no—
161C4×Dic122C2×C411yescharacteristic, complemented
162#14519742—21no—
163C4×D244C2×C411yescharacteristic
164D4×Dic61—21no—
165D4×Dic61—21no—
166D4×Dic61—21no—
167D4×Dic61—21no—
168D4×Dic61C2×C411yescharacteristic, complemented
169D4×Dic61C2×C411yescharacteristic, complemented
170D4×Dic61D411yescharacteristic
171#14519739D411yescharacteristic
172C4×C22⋊D61—21no—
173C4×C22⋊D61—21no—
174C4×C22⋊D61—21no—
175C4×C22⋊D61—21no—
176C4×C22⋊D61C2×C411yescharacteristic
177C4×C22⋊D61C2×C411yescharacteristic
178#14519737—21no—
179#14519737—21no—
180#14519737D411yescharacteristic
181#14519737D411yescharacteristic
182#14519736C2×C411yescharacteristic
183#14519736C2×C411yescharacteristic, complemented
184#14519735C2×C411yescharacteristic
185#14519735C2×C411yescharacteristic, complemented
186#14519734—21no—
187#14519733—21no—
188#14519733—21no—
189C2×#11758196—21no—
190C2×#11758196—21no—
191C4⋊C4×D61D411yescharacteristic
192C22⋊C4×D61D411yescharacteristic
193C22⋊C4×D61D411yescharacteristic
194C42×D61C2311yescharacteristic
195C2×#41×C61C2×C411yescharacteristic
196C2×#41×C61C2×C411yescharacteristic, complemented
197#127×C61—21no—
198#127×C61C2×C411yescharacteristic, complemented
199#121×C61—21no—
200#121×C61—21no—
201#121×C61C2×C411yescharacteristic
202#121×C61C2×C411yescharacteristic, complemented
203C4×Q8×C61C2×C411yescharacteristic, complemented
204C4×D4×C61—21no—
205C4×D4×C61C2×C411yescharacteristic
206C23×D61C2×D411yescharacteristic
207C23×D61C2×D411yescharacteristic
208C22×#6923—21no—
209C22×#6923—21no—
210C22×#6923—21no—
211C22×#6923—21no—
212C22×#6923—42no—
213C22×#6923—42no—
214C22×#6923—81no—
215#41×C61—81no—
216#41×C61—81no—
217C2×Q8×C61C22×C411yescharacteristic
218C2×D4×C61—21no—
219C2×D4×C61—21no—
220C2×D4×C61—21no—
221C2×D4×C61—21no—
222C2×D4×C61—21no—
223C2×D4×C61—21no—
224C2×D4×C61C22⋊C411yescharacteristic
225C2×D4×C61C22×C411yescharacteristic
226C2×D4×C61C22×C411yescharacteristic
227C22×C4×C61—21no—
228C22×C4×C61—21no—
229C22×C4×C61C22×C411yescharacteristic
230C22×C4×C61C22×C411yescharacteristic
231C2×C22⋊D61—21no—
232C2×C22⋊D61—21no—
233C2×C22⋊D61—21no—
234C2×C22⋊D61—21no—
235C2×C22⋊D61—21no—
236C2×C22⋊D61—21no—
237C2×C22⋊D61C22⋊C411yescharacteristic
238C2×C22⋊D61C22⋊C411yescharacteristic
239C22×Dic61—21no—
240C22×Dic61—21no—
241C22×Dic61—21no—
242C22×Dic61—21no—
243C22×Dic61C2×D411yescharacteristic
244C22×Dic61C2×D411yescharacteristic
245#11758224—42no—
246#11758224—42no—
247#11758224—81no—
248#11758224—81no—
249D4×D61—41no—
250D4×D61—41no—
251C2×D244C22⋊C411yescharacteristic
252C2×C4×D61—81no—
253C2×C4×D61—81no—
254C2×C4×D61C22×C411yescharacteristic
255C2×C4×D61C22×C411yescharacteristic
256C2×C4×D61C2×D411yescharacteristic
257C2×C4×D61C2×D411yescharacteristic
258C2×C4×D61C2×D411yescharacteristic
259C2×C4×D61C2×D411yescharacteristic
260C2×C4×D61C2×D411yescharacteristic
261C2×C4×D61C2×D411yescharacteristic
262C2×C4×D61C2411yescharacteristic
263C2×Dic122—21no—
264C2×Dic122—21no—
265C2×Dic122C22×C411yescharacteristic
266C22⋊#6923—42no—
267C22⋊#6923—42no—
268C22⋊#6923—81no—
269#11758217—81no—
270C2×#92420—21no—
271C2×#92420—21no—
272C2×#92420—21no—
273C2×#92420—21no—
274C2×#92420—81no—
275C4⋊#6923—81no—
276C4×#6923—42no—
277C4×#6923—81no—
278#11758213—81no—
279D61⋊C8—81no—
280C4⋊C4×C61—21no—
281C4⋊C4×C61C22⋊C411yescharacteristic
282C4⋊C4×C61C22×C411yescharacteristic
283C22⋊C4×C61—21no—
284C22⋊C4×C61—21no—
285C22⋊C4×C61C22⋊C411yescharacteristic
286C22⋊C4×C61C22⋊C411yescharacteristic
287C42×C61—21no—
288C42×C61C22×C411yescharacteristic
289C22⋊Dic61—21no—
290C22⋊Dic61—21no—
291C22⋊Dic61—21no—
292C22⋊Dic61—21no—
293C22⋊Dic61—21no—
294C22⋊Dic61—21no—
295C22⋊Dic61—21no—
296C22⋊Dic61—21no—
297C22⋊Dic61—21no—
298C22⋊Dic61—21no—
299C22⋊Dic61C22⋊C411yescharacteristic
300C22⋊Dic61C22⋊C411yescharacteristic
301#11758198—21no—
302#11758198—21no—
303#11758198—21no—
304#11758198—21no—
305#11758198—21no—
306#11758198—21no—
307#11758198C22⋊C411yescharacteristic
308#11758198C22⋊C411yescharacteristic
309#11758198C22⋊C411yescharacteristic
310#11758198C22⋊C411yescharacteristic
311C4⋊Dic61—21no—
312C4⋊Dic61—21no—
313C4⋊Dic61C22⋊C411yescharacteristic
314C4⋊Dic61C22×C411yescharacteristic
315C4⋊Dic61C22×C411yescharacteristic
316C4⋊Dic61C22×C411yescharacteristic
317#11758196—21no—
318#11758196—21no—
319#11758196—21no—
320#11758196—21no—
321#11758196—21no—
322#11758196—21no—
323#11758196—21no—
324#11758196—21no—
325#11758196—21no—
326#11758196C22⋊C411yescharacteristic
327#11758196C22⋊C411yescharacteristic
328C4×Dic61—21no—
329C4×Dic61—21no—
330C4×Dic61—21no—
331C4×Dic61—21no—
332C4×Dic61—21no—
333C4×Dic61C22×C411yescharacteristic
334C4×Dic61C2×D411yescharacteristic
335C4×Dic61C2×D411yescharacteristic
336C23×C61—21no—
337C23×C61—21no—
338C23×C61C2×C22⋊C411yescharacteristic
339C23×C61C2×C22⋊C411yescharacteristic
340C22×D61—21no—
341C22×D61—21no—
342C22×D61—21no—
343C22×D61—21no—
344C22×D61—41no—
345C22×D61—41no—
346C22×D61—41no—
347C22×D61—41no—
348C22×D61C2×C22⋊C411yescharacteristic
349C22×D61C2×C22⋊C411yescharacteristic
350C22×D61C22×D411yescharacteristic
351C2×#6923—22no—
352C2×#6923—41no—
353C2×#6923—41no—
354C2×#6923—41no—
355C2×#6923—41no—
356C2×#6923—41no—
357C2×#6923—41no—
358C2×#6923—41no—
359C2×#6923—41no—
360C2×#6923—41no—
361C2×#6923—41no—
362C2×#6923—41no—
363C2×#6923—84no—
364Q8×C61—41no—
365D4×C61—41no—
366D4×C61—41no—
367D4×C61—41no—
368D4×C61—42no—
369D4×C61—81no—
370D4×C61—81no—
371D4×C61—81no—
372D4×C61—81no—
373D4×C61—81no—
374C2×C4×C61—21no—
375C2×C4×C61—21no—
376C2×C4×C61—41no—
377C2×C4×C61—41no—
378C2×C4×C61—81no—
379C2×C4×C61—81no—
380C2×C4×C61C2×C22⋊C411yescharacteristic
381C2×C4×C61C2×C22⋊C411yescharacteristic
382C2×C4×C61C2×C22⋊C411yescharacteristic
383C2×C4×C61C2×C22⋊C411yescharacteristic
384C2×C4×C61C23×C411yescharacteristic
385C22⋊D61—41no—
386C22⋊D61—41no—
387C22⋊D61—41no—
388C22⋊D61—41no—
389C22⋊D61—41no—
390C22⋊D61—41no—
391C22⋊D61—81no—
392C22⋊D61—81no—
393C22⋊D61—81no—
394C22⋊D61—81no—
395C2×Dic61—21no—
396C2×Dic61—21no—
397C2×Dic61—21no—
398C2×Dic61—21no—
399C2×Dic61—41no—
400C2×Dic61—41no—
401C2×Dic61—42no—
402C2×Dic61—42no—
403C2×Dic61—81no—
404C2×Dic61—81no—
405C2×Dic61C2×C22⋊C411yescharacteristic
406C2×Dic61C2×C22⋊C411yescharacteristic
407C2×Dic61C2×C22⋊C411yescharacteristic
408C2×Dic61C2×C22⋊C411yescharacteristic
409C2×Dic61C22×D411yescharacteristic
410D244—41no—
411C4×D61—21no—
412C4×D61—21no—
413C4×D61—41no—
414C4×D61—41no—
415C4×D61—41no—
416C4×D61—41no—
417C4×D61—41no—
418C4×D61—41no—
419C4×D61—41no—
420C4×D61—41no—
421Dic122—42no—
422Dic122—41no—
423Dic122—81no—
424#92420—41no—
425#92420—41no—
426#92420—41no—
427#92420—41no—
428#17629—611nomaximal, Sylow
429C22×C61—21no—
430C22×C61—21no—
431C22×C61—21no—
432C22×C61—21no—
433C22×C61—21no—
434C22×C61—21no—
435C22×C61—41no—
436C22×C61—41no—
437C22×C61—41no—
438C22×C61—41no—
439C22×C61—41no—
440C22×C61—41no—
441C22×C61C22×C22⋊C411yescharacteristic
442C2×D61—21no—
443C2×D61—21no—
444C2×D61—21no—
445C2×D61—21no—
446C2×D61—21no—
447C2×D61—21no—
448C2×D61—21no—
449C2×D61—21no—
450C2×D61—42no—
451C2×D61—42no—
452C2×D61—81no—
453C2×D61—81no—
454C2×D61#57511yescharacteristic
455C2×D61#57511yescharacteristic
456#6923—42no—
457#6923—81no—
458#6923—81no—
459#6923—81no—
460C4×C61—21no—
461C4×C61—21no—
462C4×C61—21no—
463C4×C61—21no—
464C4×C61—21no—
465C4×C61—41no—
466C4×C61—41no—
467Dic61—21no—
468Dic61—21no—
469Dic61—21no—
470Dic61—21no—
471Dic61—21no—
472Dic61—41no—
473Dic61—41no—
474Dic61—41no—
475Dic61—41no—
476#3506—611no—
477#2973—611no—
478#2353—611no—
479#1516—611no—
480#1516—611no—
481#1515—611no—
482#1514—611no—
483#1513—611no—
484#1513—611no—
485#1506—611no—
486#1505—611no—
487#1504—611no—
488#1504—611no—
489#1501—611no—
490#1501—611no—
491C2×C61—41no—
492C2×C61—41no—
493C2×C61—81no—
494C2×C61—81no—
495C2×C61#288311yescharacteristic
496C2×C61#289611yescharacteristic
497C2×C61#290111yescharacteristic
498D61—21no—
499D61—21no—
500D61—41no—
501D61—41no—
502#559—1221no—
503#559—1221no—
504#556—611no—
505#556—611no—
506#555—611no—
507#555—611no—
508#553—1221no—
509#553—1221no—
510#550—611no—
511#550#692311yescharacteristic, complemented
512#547—611no—
513#547—611no—
514#538—1221no—
515#538—1221no—
516#535—1221no—
517#533—611no—
518#532—611no—
519#525—611no—
520#525—611no—
521#525—611no—
522#525—611no—
523#520—1221no—
524C2×C4×D4—611no—
525#435—1221no—
526#435—1221no—
527#435—1221no—
528#435—1221no—
529#432—611no—
530#432—611no—
531#407—611no—
532#407—611no—
533C2×C22⋊C8—611no—
534C2×C22⋊C8—611no—
535#388—1221no—
536#387—1221no—
537#386—1221no—
538#383—611no—
539#381—611no—
540#380—611no—
541C4×C22⋊C4—611no—
542C4×C22⋊C4—1221no—
543#376—611no—
544C2×#95—611no—
545#328—611no—
546#328—611no—
547#328—611no—
548#328—611no—
549#328—611no—
550#328—611no—
551#328—611no—
552#328—611no—
553#327—611no—
554#327—611no—
555#327—611no—
556#327—611no—
557#327—611no—
558#327—611no—
559#327—611no—
560#327—611no—
561C61#1762911yescharacteristic, complemented, Sylow
562C2×#41—611no—
563C2×#41—611no—
564C2×#41—1221no—
565C2×#41C2×#692311yescharacteristic
566C2×#41C2×#692311yescharacteristic, complemented
567C22×D4—611no—
568C23×C4—611no—
569C23×C4—611no—
570C23×C4—1221no—
571C2×M16—1221no—
572C2×M16—1221no—
573C22×C8—1221no—
574C22×C8—1221no—
575C4⋊Q8—611no—
576C4⋊Q8—611no—
577C4⋊Q8—611no—
578#127—21no—
579#127—1221no—
580#127C2×#692311yescharacteristic, complemented
581#126—1221no—
582#126—1221no—
583#126—1221no—
584#126—1221no—
585#125—1221no—
586#124—1221no—
587#124—1221no—
588#124—1221no—
589#124—1221no—
590#124—1221no—
591#124—1221no—
592#124—1221no—
593#123—1221no—
594#123—1221no—
595#123—1221no—
596#123—1221no—
597#123—1221no—
598#123—1221no—
599#123—1221no—
600#123—1221no—
601C22⋊Q8—611no—
602C22⋊Q8—611no—
603C22⋊Q8—611no—
604C22⋊Q8—611no—
605C22⋊Q8—611no—
606C22⋊Q8—611no—
607C22⋊Q8—1221no—
608#121—21no—
609#121—21no—
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#121C2×#692311yescharacteristic
622#121C2×#692311yescharacteristic, complemented
623#120—1221no—
624#120—1221no—
625#120—1221no—
626#120—1221no—
627C4×Q8—611no—
628C4×Q8—1221no—
629C4×Q8—1221no—
630C4×Q8—1221no—
631C4×Q8C2×#692311yescharacteristic, complemented
632C4×D4—21no—
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—
650C4×D4—1221no—
651C4×D4—1221no—
652C4×D4C2×#692311yescharacteristic
653#117—611no—
654#117—611no—
655#117—611no—
656#117—611no—
657#117—1221no—
658#117—1221no—
659#117—1221no—
660C2×C4⋊C4—611no—
661C2×C4⋊C4—1221no—
662C2×C4⋊C4—1221no—
663C2×C4⋊C4—1221no—
664C2×C22⋊C4—611no—
665C2×C22⋊C4—611no—
666C2×C22⋊C4—1221no—
667C2×C22⋊C4—1221no—
668C2×C22⋊C4—1221no—
669C2×C42—611no—
670C2×C42—1221no—
671C2×C42—1221no—
672C4⋊C8—1221no—
673C4⋊C8—1221no—
674C22⋊C8—611no—
675C22⋊C8—611no—
676C22⋊C8—611no—
677C22⋊C8—611no—
678C22⋊C8—1221no—
679C22⋊C8—1221no—
680C22⋊C8—1221no—
681C22⋊C8—1221no—
682#97—1221no—
683#97—1221no—
684#95—611no—
685#95—611no—
686#95—611no—
687#95—611no—
688#95—1221no—
689#95—1221no—
690#95—1221no—
691#95—1221no—
692#95—1221no—
693C24—611no—
694C24—611no—
695#41—81no—
696#41—81no—
697#41—4881no—
698#41—4881no—
699#41—2442no—
700#41—2442no—
701C2×Q8—611no—
702C2×Q8—1221no—
703C2×Q8—1221no—
704C2×Q8C22×#692311yescharacteristic
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—611no—
712C2×D4—611no—
713C2×D4—611no—
714C2×D4—1221no—
715C2×D4—1221no—
716C2×D4—1221no—
717C2×D4—1221no—
718C2×D4—1221no—
719C2×D4—1221no—
720C2×D4—2441no—
721C2×D4—2441no—
722C2×D4C22⋊#692311yescharacteristic
723C2×D4C22×#692311yescharacteristic
724C2×D4C22×#692311yescharacteristic
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—611no—
728C22×C4—611no—
729C22×C4—611no—
730C22×C4—611no—
731C22×C4—611no—
732C22×C4—611no—
733C22×C4—611no—
734C22×C4—611no—
735C22×C4—611no—
736C22×C4—611no—
737C22×C4—611no—
738C22×C4—1221no—
739C22×C4—1221no—
740C22×C4—1221no—
741C22×C4—1221no—
742C22×C4—1221no—
743C22×C4—1221no—
744C22×C4—1221no—
745C22×C4—1221no—
746C22×C4—4881no—
747C22×C4—4881no—
748C22×C4—4881no—
749C22×C4—2442no—
750C22×C4—2442no—
751C22×C4C22×#692311yescharacteristic
752C22×C4C22×#692311yescharacteristic
753M16—4881no—
754M16—4881no—
755C2×C8—1221no—
756C2×C8—1221no—
757C2×C8—1221no—
758C2×C8—1221no—
759C2×C8—4881no—
760C2×C8—4881no—
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—4881no—
780C4⋊C4C22⋊#692311yescharacteristic
781C4⋊C4C22×#692311yescharacteristic
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—611no—
785C22⋊C4—611no—
786C22⋊C4—611no—
787C22⋊C4—611no—
788C22⋊C4—611no—
789C22⋊C4—611no—
790C22⋊C4—1221no—
791C22⋊C4—1221no—
792C22⋊C4—1221no—
793C22⋊C4—1221no—
794C22⋊C4—1221no—
795C22⋊C4—1221no—
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—4881no—
807C22⋊C4—2442no—
808C22⋊C4—2442no—
809C22⋊C4C22⋊#692311yescharacteristic
810C22⋊C4C22⋊#692311yescharacteristic
811C42—21no—
812C42—611no—
813C42—611no—
814C42—611no—
815C42—1221no—
816C42—1221no—
817C42—1221no—
818C42—1221no—
819C42—1221no—
820C42—4881no—
821C42—2442no—
822C42C22×#692311yescharacteristic
823C23—21no—
824C23—21no—
825C23—611no—
826C23—611no—
827C23—611no—
828C23—1221no—
829C23—1221no—
830C23—1221no—
831C23—1221no—
832C23—2441no—
833C23—2441no—
834C23—2441no—
835C23—2441no—
836C23C2×C22⋊#692311yescharacteristic
837C23C2×C22⋊#692311yescharacteristic
838Q8—41no—
839Q8—4881no—
840Q8—2441no—
841Q8—2442no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—42no—
846D4—81no—
847D4—81no—
848D4—81no—
849D4—81no—
850D4—81no—
851D4—4881no—
852D4—4881no—
853D4—4881no—
854D4—4881no—
855D4—2441no—
856D4—2441no—
857D4—2441no—
858D4—2441no—
859D4—2441no—
860D4—2441no—
861D4—2441no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—81no—
867C2×C4—81no—
868C2×C4—611no—
869C2×C4—611no—
870C2×C4—611no—
871C2×C4—611no—
872C2×C4—611no—
873C2×C4—1221no—
874C2×C4—1221no—
875C2×C4—1222no—
876C2×C4—1221no—
877C2×C4—1221no—
878C2×C4—1221no—
879C2×C4—1221no—
880C2×C4—4881no—
881C2×C4—4881no—
882C2×C4—4884no—
883C2×C4—2441no—
884C2×C4—2441no—
885C2×C4—2441no—
886C2×C4—2441no—
887C2×C4—2441no—
888C2×C4—2441no—
889C2×C4—2441no—
890C2×C4—2441no—
891C2×C4—2441no—
892C2×C4—2441no—
893C2×C4—2442no—
894C2×C4—2442no—
895C2×C4—2441no—
896C2×C4—2441no—
897C2×C4—2441no—
898C2×C4—2441no—
899C2×C4—2441no—
900C2×C4—2441no—
901C2×C4—2441no—
902C2×C4—2441no—
903C2×C4—2441no—
904C2×C4—2441no—
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—
915C22—21no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—611no—
928C22—611no—
929C22—1221no—
930C22—1221no—
931C22—1221no—
932C22—1221no—
933C22—1221no—
934C22—1221no—
935C22—1221no—
936C22—1221no—
937C22—4881no—
938C22—4881no—
939C22—2442no—
940C22—2442no—
941C22C22×C22⋊#692311yescharacteristic
942C4—21no—
943C4—21no—
944C4—21no—
945C4—21no—
946C4—21no—
947C4—41no—
948C4—41no—
949C4—1221no—
950C4—1221no—
951C4—1221no—
952C4—1221no—
953C4—1221no—
954C4—4881no—
955C4—4881no—
956C4—4881no—
957C4—2442no—
958C4—2441no—
959C4—2441no—
960C4—2441no—
961C4—2441no—
962C2—41no—
963C2—41no—
964C2—81no—
965C2—81no—
966C2—1221no—
967C2—1221no—
968C2—2441no—
969C2—2441no—
970C2#2146241811yescharacteristic
971C2#2146243911yescharacteristic
972C2#2146244911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#550C4
socleC22×C61C22×C22⋊C4
prime radical#21459663C2
cosocleC2×C4×D61C24
hypercenter#550#6923
hypocenterC61#17629
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #550

Complements

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

NH ≅ G/Ntype
1. #21462671C2semidirect
2. #21462336C2semidirect
3. #21461245C2semidirect
4. #21461244C2semidirect
5. #21461241C2semidirect
6. #21461239C2semidirect
7. #21461235C2semidirect
8. #21461234C2semidirect
9. #21461212C2semidirect
10. #21461208C2semidirect
11. #21461205C2semidirect
12. #21461204C2semidirect
13. #21461195C2semidirect
14. #21461194C2semidirect
54. #16840485C4semidirect
55. #16840482C4semidirect
56. #16840476C4semidirect
57. #16840476C4semidirect
60. #16840432C4semidirect
61. #16840411C4semidirect
62. #16840411C4semidirect
74. C61×#550C4semidirect
109. C2×#11758224C2×C4semidirect
113. #14519777C2×C4semidirect
114. #14519776C2×C4semidirect
115. #14519775C2×C4semidirect
139. #14519756C2×C4semidirect
142. #14519753C2×C4semidirect
152. #14519748C2×C4semidirect
161. C4×Dic122C2×C4semidirect
168. D4×Dic61C2×C4semidirect
169. D4×Dic61C2×C4semidirect
183. #14519736C2×C4semidirect
185. #14519735C2×C4semidirect
196. C2×#41×C61C2×C4semidirect
198. #127×C61C2×C4semidirect
202. #121×C61C2×C4semidirect
203. C4×Q8×C61C2×C4semidirect
511. #550#6923semidirect
561. C61#17629semidirect
566. C2×#41C2×#6923semidirect
580. #127C2×#6923semidirect
622. #121C2×#6923semidirect
631. C4×Q8C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214626712
#214623362
#214612452
#214612442
#214612412
#214612392
#214612352
#214612342
#214612122
#214612082
#214612052
#214612042
#214611952
#214611942
#214596632
#1762961