Finite Group Databasebeta

← #30611403

Subgroups — #30611403

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#21461247C211yesmaximal, characteristic, complemented
4#21461244C211yesmaximal, characteristic, complemented
5#21461242C211yesmaximal, characteristic, complemented
6#21461238C211yesmaximal, characteristic, complemented
7#21461236C211yesmaximal, characteristic, complemented
8#21461235C211yesmaximal, characteristic, complemented
9#21461211C211yesmaximal, characteristic, complemented
10#21461209C211yesmaximal, characteristic, complemented
11#21461207C211yesmaximal, characteristic, complemented
12#21461204C211yesmaximal, characteristic, complemented
13#21461196C211yesmaximal, characteristic, complemented
14#21461195C211yesmaximal, characteristic, complemented
15#21459661C211yesmaximal, 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#16840615C2211yescharacteristic
37#16840615C2211yescharacteristic
38#16840615C2211yescharacteristic
39#16840615C2211yescharacteristic
40#16840615C2211yescharacteristic
41#16840615C2211yescharacteristic
42#16840615C2211yescharacteristic
43#16840615C2211yescharacteristic
44#16840614C2211yescharacteristic
45#16840614C2211yescharacteristic
46#16840614C2211yescharacteristic
47#16840614C2211yescharacteristic
48#16840613C2211yescharacteristic
49#16840613C2211yescharacteristic
50#16840613C2211yescharacteristic
51#16840613C2211yescharacteristic
52#16840494—21no—
53#16840494—21no—
54#16840480C411yescharacteristic, complemented
55#16840480C411yescharacteristic, complemented
56#16840478C411yescharacteristic, complemented
57#16840464—21no—
58#16840456—21no—
59#16840430C411yescharacteristic, complemented
60#16840430C411yescharacteristic, complemented
61#16840417C411yescharacteristic, complemented
62#16840416C411yescharacteristic, complemented
63#16840346—21no—
64#16840346—21no—
65#16840328—21no—
66#16840317C2211yescharacteristic
67#16840309C2211yescharacteristic
68#16840274C2211yescharacteristic
69#16840274C2211yescharacteristic
70#16840272C2211yescharacteristic
71#16840272C2211yescharacteristic
72#16840242—21no—
73C4×D4×D61C2211yescharacteristic
74C61×#555C411yescharacteristic, 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×#11758222—21no—
108C2×#11758222C2×C411yescharacteristic
109C2×#11758222C2×C411yescharacteristic, complemented
110C2×#11758224C2×C411yescharacteristic
111C2×#11758224C2×C411yescharacteristic, complemented
112C2×D4×D61D411yescharacteristic
113C22×C4×D61C2311yescharacteristic
114C22×C4×D61C2311yescharacteristic
115#14519777C2×C411yescharacteristic, complemented
116#14519776C2×C411yescharacteristic, complemented
117#14519773—21no—
118#14519773—21no—
119#14519773C2×C411yescharacteristic, complemented
120#14519771—21no—
121#14519771—21no—
122#14519770—21no—
123#14519770—21no—
124#14519768—21no—
125#14519766—21no—
126#14519766—21no—
127#14519763—21no—
128#14519763—21no—
129#14519763—21no—
130#14519761—21no—
131#14519761—21no—
132#14519761—21no—
133#14519761—21no—
134#14519759—21no—
135#14519759—21no—
136#14519759—21no—
137#14519759—21no—
138#14519757C2×C411yescharacteristic
139#14519757C2×C411yescharacteristic, complemented
140#14519757C2311yescharacteristic
141#14519757C2311yescharacteristic
142#14519756C2×C411yescharacteristic
143#14519756C2×C411yescharacteristic, complemented
144#14519753—21no—
145#14519752—21no—
146#14519752C2×C411yescharacteristic
147#14519752C2×C411yescharacteristic, complemented
148#14519752C2311yescharacteristic
149#14519751—21no—
150#14519750—21no—
151#14519750—21no—
152#14519750—21no—
153#14519749—21no—
154#14519749—21no—
155#14519748—21no—
156#14519748C2311yescharacteristic
157#14519747—21no—
158#14519747—21no—
159#14519745—21no—
160#14519745—21no—
161Q8×Dic61—21no—
162C4×Dic122—21no—
163C4×Dic122—21no—
164#14519742C2×C411yescharacteristic, complemented
165#14519742C2×C411yescharacteristic, complemented
166C4×D244—21no—
167C4×D244—21no—
168C4×D244—21no—
169C4×D244—21no—
170C4×D244C2×C411yescharacteristic
171C4×D244C2×C411yescharacteristic, complemented
172D4×Dic61—21no—
173D4×Dic61—21no—
174D4×Dic61D411yescharacteristic
175#14519739D411yescharacteristic
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#14519737D411yescharacteristic
184#14519737D411yescharacteristic
185#14519735—21no—
186#14519735—21no—
187#14519735C2×C411yescharacteristic
188#14519735C2×C411yescharacteristic, complemented
189C2×C4⋊Dic61—21no—
190C4⋊C4×D61—21no—
191C4⋊C4×D61D411yescharacteristic
192C22⋊C4×D61D411yescharacteristic
193C22⋊C4×D61D411yescharacteristic
194C42×D61C2311yescharacteristic
195C4⋊Q8×C61C2×C411yescharacteristic, complemented
196#124×C61—21no—
197#124×C61—21no—
198#121×C61—21no—
199#121×C61C2×C411yescharacteristic
200#121×C61C2×C411yescharacteristic, complemented
201C4×D4×C61C2×C411yescharacteristic
202C4×D4×C61C2×C411yescharacteristic, complemented
203#117×C61—21no—
204#117×C61C2×C411yescharacteristic
205#117×C61C2×C411yescharacteristic, complemented
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—
215C2×Q8×C61—21no—
216C2×D4×C61—21no—
217C2×D4×C61—21no—
218C2×D4×C61C22⋊C411yescharacteristic
219C2×D4×C61C22×C411yescharacteristic
220C22×C4×C61—21no—
221C22×C4×C61C22×C411yescharacteristic
222C22×C4×C61C22×C411yescharacteristic
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⋊D61C22⋊C411yescharacteristic
231C2×C22⋊D61C22⋊C411yescharacteristic
232C22×Dic61—21no—
233C22×Dic61—21no—
234C22×Dic61C2×D411yescharacteristic
235C22×Dic61C2×D411yescharacteristic
236#11758224—81no—
237#11758224—81no—
238D4×D61—41no—
239D4×D61—41no—
240#11758222—42no—
241#11758222—42no—
242#11758222—81no—
243#11758222—81no—
244C2×D244—21no—
245C2×D244—21no—
246C2×D244—21no—
247C2×D244C22⋊C411yescharacteristic
248C2×D244C22×C411yescharacteristic
249C2×C4×D61—21no—
250C2×C4×D61—21no—
251C2×C4×D61—21no—
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×Dic122C22×C411yescharacteristic
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
283C4⋊C4×C61C22×C411yescharacteristic
284C4⋊C4×C61C22×C411yescharacteristic
285C22⋊C4×C61—21no—
286C22⋊C4×C61—21no—
287C22⋊C4×C61—21no—
288C22⋊C4×C61—21no—
289C22⋊C4×C61—21no—
290C22⋊C4×C61C22⋊C411yescharacteristic
291C22⋊C4×C61C22⋊C411yescharacteristic
292C42×C61—21no—
293C42×C61—21no—
294C42×C61C22×C411yescharacteristic
295C22⋊Dic61—21no—
296C22⋊Dic61—21no—
297C22⋊Dic61—21no—
298C22⋊Dic61C22⋊C411yescharacteristic
299C22⋊Dic61C22⋊C411yescharacteristic
300#11758198—21no—
301#11758198—21no—
302#11758198—21no—
303#11758198—21no—
304#11758198—21no—
305#11758198—21no—
306#11758198—21no—
307#11758198—21no—
308#11758198—21no—
309#11758198—21no—
310#11758198C22⋊C411yescharacteristic
311#11758198C22⋊C411yescharacteristic
312#11758198C22⋊C411yescharacteristic
313#11758198C22⋊C411yescharacteristic
314C4⋊Dic61—21no—
315C4⋊Dic61—21no—
316C4⋊Dic61—21no—
317C4⋊Dic61—21no—
318C4⋊Dic61—21no—
319C4⋊Dic61—21no—
320C4⋊Dic61C22⋊C411yescharacteristic
321C4⋊Dic61C22×C411yescharacteristic
322#11758196—21no—
323#11758196—21no—
324#11758196—21no—
325#11758196—21no—
326#11758196—21no—
327#11758196C22⋊C411yescharacteristic
328#11758196C22⋊C411yescharacteristic
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×C61C2×C22⋊C411yescharacteristic
338C23×C61C2×C22⋊C411yescharacteristic
339C22×D61—21no—
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—81no—
365D4×C61—41no—
366D4×C61—41no—
367D4×C61—81no—
368D4×C61—81no—
369C2×C4×C61—21no—
370C2×C4×C61—21no—
371C2×C4×C61—21no—
372C2×C4×C61—41no—
373C2×C4×C61—41no—
374C2×C4×C61—42no—
375C2×C4×C61C2×C22⋊C411yescharacteristic
376C2×C4×C61C2×C22⋊C411yescharacteristic
377C2×C4×C61C2×C22⋊C411yescharacteristic
378C2×C4×C61C2×C22⋊C411yescharacteristic
379C2×C4×C61C23×C411yescharacteristic
380C22⋊D61—41no—
381C22⋊D61—41no—
382C22⋊D61—42no—
383C22⋊D61—41no—
384C22⋊D61—41no—
385C22⋊D61—81no—
386C22⋊D61—81no—
387C22⋊D61—81no—
388C22⋊D61—81no—
389C22⋊D61—81no—
390C2×Dic61—21no—
391C2×Dic61—21no—
392C2×Dic61—21no—
393C2×Dic61—41no—
394C2×Dic61—41no—
395C2×Dic61—81no—
396C2×Dic61—81no—
397C2×Dic61C2×C22⋊C411yescharacteristic
398C2×Dic61C2×C22⋊C411yescharacteristic
399C2×Dic61C2×C22⋊C411yescharacteristic
400C2×Dic61C2×C22⋊C411yescharacteristic
401C2×Dic61C22×D411yescharacteristic
402D244—41no—
403D244—41no—
404D244—41no—
405D244—41no—
406D244—81no—
407D244—81no—
408C4×D61—21no—
409C4×D61—21no—
410C4×D61—41no—
411C4×D61—41no—
412C4×D61—41no—
413C4×D61—41no—
414C4×D61—41no—
415C4×D61—41no—
416C4×D61—41no—
417C4×D61—41no—
418C4×D61—42no—
419C4×D61—81no—
420C4×D61—81no—
421Dic122—42no—
422Dic122—41no—
423Dic122—41no—
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×C61C22×C22⋊C411yescharacteristic
439C2×D61—21no—
440C2×D61—21no—
441C2×D61—21no—
442C2×D61—21no—
443C2×D61—21no—
444C2×D61—21no—
445C2×D61—21no—
446C2×D61—21no—
447C2×D61—42no—
448C2×D61—42no—
449C2×D61—41no—
450C2×D61—41no—
451C2×D61—41no—
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—
467C4×C61—41no—
468Dic61—21no—
469Dic61—21no—
470Dic61—21no—
471Dic61—21no—
472Dic61—21no—
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#288311yescharacteristic
495C2×C61#289611yescharacteristic
496C2×C61#290111yescharacteristic
497D61—21no—
498D61—21no—
499D61—41no—
500D61—41no—
501D61—81no—
502#559—1221no—
503#559—1221no—
504#556—611no—
505#556—611no—
506#555—611no—
507#555#692311yescharacteristic, complemented
508#553—1221no—
509#553—1221no—
510#550—611no—
511#550—611no—
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—611no—
565C2×#41—611no—
566C2×#41—1221no—
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⋊Q8C2×#692311yescharacteristic, complemented
578#127—611no—
579#127—1221no—
580#127—1221no—
581#126—1221no—
582#126—1221no—
583#126—1221no—
584#126—1221no—
585#125—1221no—
586#124—21no—
587#124—21no—
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—611no—
610#121—611no—
611#121—611no—
612#121—611no—
613#121—1221no—
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—611no—
629C4×Q8—1221no—
630C4×Q8—1221no—
631C4×Q8—1221no—
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—1221no—
641C4×D4—1221no—
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×D4C2×#692311yescharacteristic
652C4×D4C2×#692311yescharacteristic, complemented
653#117—21no—
654#117—611no—
655#117—611no—
656#117—1221no—
657#117—1221no—
658#117C2×#692311yescharacteristic
659#117C2×#692311yescharacteristic, complemented
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—4881no—
696#41—4881no—
697#41—4881no—
698#41—4881no—
699#41—2442no—
700#41—2442no—
701C2×Q8—21no—
702C2×Q8—611no—
703C2×Q8—611no—
704C2×Q8—1221no—
705C2×D4—21no—
706C2×D4—21no—
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—1221no—
718C2×D4—1221no—
719C2×D4—1221no—
720C2×D4—1221no—
721C2×D4—2441no—
722C2×D4—2441no—
723C2×D4C22⋊#692311yescharacteristic
724C2×D4C22×#692311yescharacteristic
725C22×C4—21no—
726C22×C4—611no—
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—1221no—
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—1221no—
767C4⋊C4—1221no—
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—4881no—
778C4⋊C4C22⋊#692311yescharacteristic
779C4⋊C4C22×#692311yescharacteristic
780C4⋊C4C22×#692311yescharacteristic
781C4⋊C4C22×#692311yescharacteristic
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—611no—
788C22⋊C4—611no—
789C22⋊C4—611no—
790C22⋊C4—611no—
791C22⋊C4—611no—
792C22⋊C4—611no—
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—21no—
813C42—611no—
814C42—611no—
815C42—611no—
816C42—1221no—
817C42—1221no—
818C42—1221no—
819C42—1221no—
820C42—4881no—
821C42—2442no—
822C42C22×#692311yescharacteristic
823C23—21no—
824C23—611no—
825C23—611no—
826C23—611no—
827C23—1221no—
828C23—1221no—
829C23—1221no—
830C23—1221no—
831C23—1221no—
832C23—2441no—
833C23—2441no—
834C23—2441no—
835C23—2441no—
836C23C2×C22⋊#692311yescharacteristic
837C23C2×C22⋊#692311yescharacteristic
838Q8—81no—
839Q8—2441no—
840Q8—2441no—
841Q8—2442no—
842D4—41no—
843D4—41no—
844D4—81no—
845D4—81no—
846D4—4881no—
847D4—4881no—
848D4—4881no—
849D4—4881no—
850D4—4881no—
851D4—4881no—
852D4—4881no—
853D4—2441no—
854D4—2441no—
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—42no—
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—4881no—
880C2×C4—4881no—
881C2×C4—4881no—
882C2×C4—4881no—
883C2×C4—4884no—
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—2442no—
893C2×C4—2441no—
894C2×C4—2441no—
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—611no—
925C22—611no—
926C22—1221no—
927C22—1221no—
928C22—1221no—
929C22—1221no—
930C22—1221no—
931C22—1221no—
932C22—1221no—
933C22—1221no—
934C22—4881no—
935C22—4881no—
936C22—2442no—
937C22—2442no—
938C22—2441no—
939C22—2441no—
940C22—2441no—
941C22C22×C22⋊#692311yescharacteristic
942C4—21no—
943C4—21no—
944C4—21no—
945C4—21no—
946C4—21no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—1221no—
951C4—1221no—
952C4—1221no—
953C4—1221no—
954C4—1221no—
955C4—4881no—
956C4—4881no—
957C4—4881no—
958C4—2442no—
959C4—2441no—
960C4—2441no—
961C4—2441no—
962C2—41no—
963C2—41no—
964C2—81no—
965C2—1221no—
966C2—1221no—
967C2—4881no—
968C2—2441no—
969C2—2441no—
970C2#2146241911yescharacteristic
971C2#2146243911yescharacteristic
972C2#2146244911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#555C4
socleC22×C61C22×C22⋊C4
prime radical#21459661C2
cosocleC2×C4×D61C24
hypercenter#555#6923
hypocenterC61#17629
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #555

Complements

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

NH ≅ G/Ntype
1. #21462671C2semidirect
2. #21462336C2semidirect
3. #21461247C2semidirect
4. #21461244C2semidirect
5. #21461242C2semidirect
6. #21461238C2semidirect
7. #21461236C2semidirect
8. #21461235C2semidirect
9. #21461211C2semidirect
10. #21461209C2semidirect
11. #21461207C2semidirect
12. #21461204C2semidirect
13. #21461196C2semidirect
14. #21461195C2semidirect
54. #16840480C4semidirect
55. #16840480C4semidirect
56. #16840478C4semidirect
59. #16840430C4semidirect
60. #16840430C4semidirect
61. #16840417C4semidirect
62. #16840416C4semidirect
74. C61×#555C4semidirect
109. C2×#11758222C2×C4semidirect
111. C2×#11758224C2×C4semidirect
115. #14519777C2×C4semidirect
116. #14519776C2×C4semidirect
119. #14519773C2×C4semidirect
139. #14519757C2×C4semidirect
143. #14519756C2×C4semidirect
147. #14519752C2×C4semidirect
164. #14519742C2×C4semidirect
165. #14519742C2×C4semidirect
171. C4×D244C2×C4semidirect
188. #14519735C2×C4semidirect
195. C4⋊Q8×C61C2×C4semidirect
200. #121×C61C2×C4semidirect
202. C4×D4×C61C2×C4semidirect
205. #117×C61C2×C4semidirect
507. #555#6923semidirect
561. C61#17629semidirect
577. C4⋊Q8C2×#6923semidirect
622. #121C2×#6923semidirect
652. C4×D4C2×#6923semidirect
659. #117C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214626712
#214623362
#214612472
#214612442
#214612422
#214612382
#214612362
#214612352
#214612112
#214612092
#214612072
#214612042
#214611962
#214611952
#214596612
#1762961