Finite Group Databasebeta

← #30611360

Subgroups — #30611360

Order 15616.

1038 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#21462667C211yesmaximal, characteristic, complemented
2#21462336C211yesmaximal, characteristic, complemented
3#21461263C211yesmaximal, characteristic, complemented
4#21461260C211yesmaximal, characteristic, complemented
5#21461259C211yesmaximal, characteristic, complemented
6#21461254C211yesmaximal, characteristic, complemented
7#21461246C211yesmaximal, characteristic, complemented
8#21461245C211yesmaximal, characteristic, complemented
9#21461197C211yesmaximal, characteristic, complemented
10#21461194C211yesmaximal, characteristic, complemented
11#21461192C211yesmaximal, characteristic, complemented
12#21461191C211yesmaximal, characteristic, complemented
13C2×#16840616C211yesmaximal, characteristic, complemented
14D61⋊#327C211yesmaximal, characteristic, complemented
15#21459655C211yesmaximal, characteristic
16#16840790—21no—
17#16840789—21no—
18#16840789—21no—
19D4×#92420—21no—
20#16840781C2211yescharacteristic, complemented
21#16840780C2211yescharacteristic, complemented
22C2×#14519834C2211yescharacteristic
23C2×#14519834C2211yescharacteristic, complemented
24D61⋊(C22⋊C8)C2211yescharacteristic
25D61⋊(C22⋊C8)C2211yescharacteristic, complemented
26#16840712—21no—
27#16840711—21no—
28#16840710—21no—
29#16840707C2211yescharacteristic, complemented
30#16840705C2211yescharacteristic, complemented
31#16840704C2211yescharacteristic
32C22⋊C4×#6923—21no—
33C4×C22⋊#6923C2211yescharacteristic, complemented
34#16840698C2211yescharacteristic, complemented
35C2×(C2×#6923)⋊C4C2211yescharacteristic
36#16840616C2211yescharacteristic, complemented
37#16840616C2211yescharacteristic, complemented
38#16840616C2211yescharacteristic, complemented
39#16840616C2211yescharacteristic, complemented
40#16840616C2211yescharacteristic, complemented
41#16840616C2211yescharacteristic, complemented
42#16840616C2211yescharacteristic, complemented
43#16840616C2211yescharacteristic, complemented
44#16840614C2211yescharacteristic
45#16840614C2211yescharacteristic
46#16840614C2211yescharacteristic
47#16840614C2211yescharacteristic
48#16840613C2211yescharacteristic
49#16840613C2211yescharacteristic
50#16840613C2211yescharacteristic
51#16840613C2211yescharacteristic
52#16840464C411yescharacteristic, complemented
53#16840461—21no—
54#16840458C411yescharacteristic, complemented
55#16840455—21no—
56#16840453C411yescharacteristic, complemented
57#16840446C411yescharacteristic, complemented
58#16840442—21no—
59#16840439—21no—
60#16840423C411yescharacteristic, complemented
61#16840405C411yescharacteristic, complemented
62#16840400C411yescharacteristic, complemented
63#16840358—21no—
64#16840346—21no—
65#16840320—21no—
66#16840299C2211yescharacteristic
67#16840291C2211yescharacteristic
68#16840275C2211yescharacteristic
69#16840269C2211yescharacteristic
70C2×#14519753C2211yescharacteristic
71#121×D61C2211yescharacteristic
72#16840234—21no—
73C4×D4×D61C2211yescharacteristic
74C61×#548C411yescharacteristic, complemented
75C23×#6923—21no—
76C2×D61⋊C8—21no—
77C2×D61⋊C8—21no—
78C22×#92420—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—
96C4×#92420—21no—
97C4×#92420—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×#11758226C2×C411yescharacteristic, complemented
108C2×D4×D61—21no—
109C2×D4×D61C2×C411yescharacteristic
110C2×D4×D61D411yescharacteristic
111C22×C4×D61C2311yescharacteristic
112C22×C4×D61C2311yescharacteristic
113#14519772—21no—
114#14519772—21no—
115#14519771—21no—
116#14519770—21no—
117#14519770—21no—
118#14519770—21no—
119#14519769C2×C411yescharacteristic, complemented
120#14519768C2×C411yescharacteristic, complemented
121#14519767—21no—
122#14519767—21no—
123#14519766—21no—
124#14519766C2×C411yescharacteristic, complemented
125#14519762—21no—
126#14519762—21no—
127#14519762—21no—
128#14519761—21no—
129#14519760—21no—
130#14519759—21no—
131#14519759—21no—
132#14519759—21no—
133#14519759—21no—
134#14519758—21no—
135#14519753—21no—
136#14519753—21no—
137#14519753—21no—
138#14519753C2×C411yescharacteristic
139#14519753C2×C411yescharacteristic
140#14519753C2×C411yescharacteristic, complemented
141#14519753C2311yescharacteristic
142#14519753C2311yescharacteristic
143#14519752C2311yescharacteristic
144#14519751—21no—
145#14519751C2×C411yescharacteristic
146#14519751C2×C411yescharacteristic, complemented
147#14519750—21no—
148#14519750—21no—
149#14519749—21no—
150#14519749—21no—
151#14519749—21no—
152#14519749—21no—
153#14519748C2×C411yescharacteristic, complemented
154#14519748C2311yescharacteristic
155#14519747—21no—
156#14519747—21no—
157#14519745—21no—
158#14519745—21no—
159Q8×Dic61C2×C411yescharacteristic, complemented
160C4×D244—21no—
161C4×D244C2×C411yescharacteristic
162C4×D244C2×C411yescharacteristic, complemented
163D4×Dic61—21no—
164D4×Dic61C2×C411yescharacteristic, complemented
165D4×Dic61D411yescharacteristic
166#14519739—21no—
167#14519739D411yescharacteristic
168C4×C22⋊D61—21no—
169C4×C22⋊D61—21no—
170C4×C22⋊D61—21no—
171C4×C22⋊D61C2×C411yescharacteristic
172C4×C22⋊D61C2×C411yescharacteristic
173#14519737—21no—
174#14519737—21no—
175#14519737—21no—
176#14519737D411yescharacteristic
177#14519737D411yescharacteristic
178#14519736C2×C411yescharacteristic, complemented
179#14519735—21no—
180#14519735C2×C411yescharacteristic, complemented
181#14519734—21no—
182#14519734—21no—
183#14519733—21no—
184C2×C4⋊Dic61C2×C411yescharacteristic
185C2×#11758196—21no—
186C4⋊C4×D61C2×C411yescharacteristic
187C4⋊C4×D61D411yescharacteristic
188C2×#11758198—21no—
189C2×#11758198—21no—
190C22⋊C4×D61—21no—
191C22⋊C4×D61—21no—
192C22⋊C4×D61D411yescharacteristic
193C22⋊C4×D61D411yescharacteristic
194C42×D61C2311yescharacteristic
195C2×#41×C61C2×C411yescharacteristic, complemented
196C22×Q8×C61C2×C411yescharacteristic
197#124×C61—21no—
198#124×C61C2×C411yescharacteristic, complemented
199C22⋊Q8×C61—21no—
200C22⋊Q8×C61C2×C411yescharacteristic, complemented
201#121×C61—21no—
202#121×C61C2×C411yescharacteristic
203C4×Q8×C61C2×C411yescharacteristic, complemented
204C4×D4×C61—21no—
205C4×D4×C61C2×C411yescharacteristic
206C23×D61—21no—
207C23×D61C2×D411yescharacteristic
208C23×D61C2×D411yescharacteristic
209C22×#6923—21no—
210C22×#6923—21no—
211C22×#6923—21no—
212C22×#6923—21no—
213C22×#6923—42no—
214C22×#6923—42no—
215C22×#6923—81no—
216#41×C61—81no—
217C2×Q8×C61—21no—
218C2×Q8×C61—81no—
219C2×Q8×C61C22×C411yescharacteristic
220C2×Q8×C61C22×C411yescharacteristic
221C2×D4×C61—21no—
222C2×D4×C61—21no—
223C2×D4×C61C22⋊C411yescharacteristic
224C2×D4×C61C22×C411yescharacteristic
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61C22×C411yescharacteristic
228C22×C4×C61C22×C411yescharacteristic
229C2×C22⋊D61—21no—
230C2×C22⋊D61—21no—
231C2×C22⋊D61—21no—
232C2×C22⋊D61—21no—
233C2×C22⋊D61—21no—
234C2×C22⋊D61C22⋊C411yescharacteristic
235C2×C22⋊D61C22⋊C411yescharacteristic
236C22×Dic61—21no—
237C22×Dic61—21no—
238C22×Dic61C2×D411yescharacteristic
239C22×Dic61C2×D411yescharacteristic
240#11758226—81no—
241D4×D61—22no—
242D4×D61—22no—
243D4×D61—42no—
244D4×D61—42no—
245D4×D61—81no—
246C2×D244—21no—
247C2×D244—21no—
248C2×D244C22⋊C411yescharacteristic
249C2×D244C22×C411yescharacteristic
250C2×C4×D61—21no—
251C2×C4×D61—21no—
252C2×C4×D61—21no—
253C2×C4×D61—81no—
254C2×C4×D61—81no—
255C2×C4×D61C22×C411yescharacteristic
256C2×C4×D61C22×C411yescharacteristic
257C2×C4×D61C2×D411yescharacteristic
258C2×C4×D61C2×D411yescharacteristic
259C2×C4×D61C2×D411yescharacteristic
260C2×C4×D61C2×D411yescharacteristic
261C2×C4×D61C2×D411yescharacteristic
262C2×C4×D61C2×D411yescharacteristic
263C2×C4×D61C2411yescharacteristic
264C22⋊#6923—42no—
265C22⋊#6923—42no—
266C22⋊#6923—81no—
267C2×#92420—21no—
268C2×#92420—21no—
269C2×#92420—21no—
270C2×#92420—21no—
271C2×#92420—81no—
272C2×#92420—81no—
273C4⋊#6923—81no—
274C4×#6923—42no—
275C4×#6923—81no—
276D61⋊C8—81no—
277D61⋊C8—81no—
278C4⋊C4×C61—21no—
279C4⋊C4×C61—21no—
280C4⋊C4×C61C22⋊C411yescharacteristic
281C4⋊C4×C61C22×C411yescharacteristic
282C22⋊C4×C61—21no—
283C22⋊C4×C61—21no—
284C22⋊C4×C61—21no—
285C22⋊C4×C61—21no—
286C22⋊C4×C61C22⋊C411yescharacteristic
287C22⋊C4×C61C22⋊C411yescharacteristic
288C42×C61—21no—
289C42×C61C22×C411yescharacteristic
290C22⋊Dic61—21no—
291C22⋊Dic61—21no—
292C22⋊Dic61—21no—
293C22⋊Dic61—21no—
294C22⋊Dic61C22⋊C411yescharacteristic
295C22⋊Dic61C22⋊C411yescharacteristic
296#11758198—21no—
297#11758198—21no—
298#11758198—21no—
299#11758198—21no—
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#11758198C22⋊C411yescharacteristic
309#11758198C22⋊C411yescharacteristic
310#11758198C22⋊C411yescharacteristic
311#11758198C22⋊C411yescharacteristic
312C4⋊Dic61—21no—
313C4⋊Dic61—21no—
314C4⋊Dic61—21no—
315C4⋊Dic61C22⋊C411yescharacteristic
316C4⋊Dic61C22×C411yescharacteristic
317C4⋊Dic61C22×C411yescharacteristic
318C4⋊Dic61C22×C411yescharacteristic
319#11758196—21no—
320#11758196—21no—
321#11758196—21no—
322#11758196—21no—
323#11758196—21no—
324#11758196—21no—
325#11758196—21no—
326#11758196—21no—
327#11758196—21no—
328#11758196C22⋊C411yescharacteristic
329#11758196C22⋊C411yescharacteristic
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—41no—
343C22×D61—41no—
344C22×D61—41no—
345C22×D61—41no—
346C22×D61—42no—
347C22×D61—81no—
348C22×D61—81no—
349C22×D61C2×C22⋊C411yescharacteristic
350C22×D61C2×C22⋊C411yescharacteristic
351C22×D61#13512yes—
352C22×D61#13512yes—
353C22×D61C22×D411yescharacteristic
354C2×#6923—22no—
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—41no—
364C2×#6923—41no—
365C2×#6923—41no—
366C2×#6923—84no—
367Q8×C61—41no—
368Q8×C61—41no—
369Q8×C61—81no—
370D4×C61—22no—
371D4×C61—41no—
372D4×C61—42no—
373D4×C61—81no—
374C2×C4×C61—21no—
375C2×C4×C61—21no—
376C2×C4×C61—21no—
377C2×C4×C61—41no—
378C2×C4×C61—41no—
379C2×C4×C61—81no—
380C2×C4×C61—81no—
381C2×C4×C61C2×C22⋊C411yescharacteristic
382C2×C4×C61C2×C22⋊C411yescharacteristic
383C2×C4×C61C2×C22⋊C411yescharacteristic
384C2×C4×C61C2×C22⋊C411yescharacteristic
385C2×C4×C61C23×C411yescharacteristic
386C22⋊D61—22no—
387C22⋊D61—22no—
388C22⋊D61—42no—
389C22⋊D61—41no—
390C22⋊D61—41no—
391C22⋊D61—81no—
392C22⋊D61—81no—
393C22⋊D61—81no—
394C2×Dic61—21no—
395C2×Dic61—21no—
396C2×Dic61—21no—
397C2×Dic61—41no—
398C2×Dic61—41no—
399C2×Dic61—81no—
400C2×Dic61—81no—
401C2×Dic61C2×C22⋊C411yescharacteristic
402C2×Dic61C2×C22⋊C411yescharacteristic
403C2×Dic61C2×C22⋊C411yescharacteristic
404C2×Dic61C2×C22⋊C411yescharacteristic
405C2×Dic61C22×D411yescharacteristic
406D244—22no—
407D244—41no—
408D244—41no—
409D244—41no—
410D244—81no—
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—
421C4×D61—42no—
422C4×D61—81no—
423C4×D61—81no—
424#92420—41no—
425#92420—41no—
426#92420—41no—
427#92420—41no—
428#17615—611nomaximal, Sylow
429C22×C61—21no—
430C22×C61—21no—
431C22×C61—21no—
432C22×C61—21no—
433C22×C61—21no—
434C22×C61—41no—
435C22×C61—41no—
436C22×C61—41no—
437C22×C61#41612yes—
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—42no—
447C2×D61—42no—
448C2×D61—41no—
449C2×D61—41no—
450C2×D61—41no—
451C2×D61—81no—
452C2×D61—81no—
453C2×D61—162no—
454C2×D61#41612yes—
455C2×D61C2×#13511yescharacteristic
456C2×D61C2×#13511yescharacteristic
457#6923—42no—
458#6923—81no—
459#6923—81no—
460#6923—81no—
461C4×C61—21no—
462C4×C61—21no—
463C4×C61—21no—
464C4×C61—21no—
465C4×C61—21no—
466C4×C61—41no—
467C4×C61—41no—
468C4×C61—41no—
469Dic61—21no—
470Dic61—21no—
471Dic61—21no—
472Dic61—21no—
473Dic61—21no—
474Dic61—41no—
475Dic61—41no—
476Dic61—41no—
477#3505—611no—
478#2972—611no—
479#2353—611no—
480#1521—611no—
481#1521—611no—
482#1520—611no—
483#1519—611no—
484#1516—611no—
485#1516—611no—
486#1501—611no—
487#1501—611no—
488#1500—611no—
489#1500—611no—
490C2×#328—611no—
491C2×#327—611no—
492C2×C61—22no—
493C2×C61—41no—
494C2×C61—81no—
495C2×C61#288311yescharacteristic
496C2×C61C2×#41611yescharacteristic
497C2×C61#290111yescharacteristic
498D61—21no—
499D61—21no—
500D61—22no—
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#692311yescharacteristic, complemented
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#525—611no—
522C2×C22⋊Q8—611no—
523C2×#121—611no—
524#518—1221no—
525C2×C4×D4—611no—
526C8×D4—1221no—
527C8×D4—1221no—
528C8×D4—1221no—
529C8×D4—1221no—
530#431—611no—
531#431—611no—
532C2×C22⋊C8—611no—
533C2×C22⋊C8—611no—
534C2×C22⋊C8—611no—
535C2×C22⋊C8—611no—
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×#95—611no—
546#328—611no—
547#328—611no—
548#328—611no—
549#328—611no—
550#328—611no—
551#328—611no—
552#328—611no—
553#328—611no—
554#327—611no—
555#327—611no—
556#327—611no—
557#327—611no—
558#327—611no—
559#327—611no—
560#327—611no—
561#327—611no—
562C61#1761511yescharacteristic, complemented, Sylow
563C2×#41—611no—
564C2×#41C2×#692311yescharacteristic, complemented
565C22×Q8C2×#692311yescharacteristic
566C22×D4—611no—
567C22×D4—611no—
568C22×D4—1221no—
569C23×C4—611no—
570C23×C4—611no—
571C23×C4—1221no—
572C22×C8—1221no—
573C22×C8—1221no—
574C22×C8—1221no—
575C22×C8—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—21no—
587#124—611no—
588#124—1221no—
589#124C2×#692311yescharacteristic, complemented
590#123—1221no—
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—21no—
601C22⋊Q8—611no—
602C22⋊Q8—611no—
603C22⋊Q8—611no—
604C22⋊Q8—611no—
605C22⋊Q8—611no—
606C22⋊Q8—1221no—
607C22⋊Q8—1221no—
608C22⋊Q8—1221no—
609C22⋊Q8C2×#692311yescharacteristic, complemented
610#121—21no—
611#121—611no—
612#121—611no—
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#121C2×#692311yescharacteristic
624#120—1221no—
625#120—1221no—
626#120—1221no—
627#120—1221no—
628C4×Q8—611no—
629C4×Q8C2×#692311yescharacteristic, complemented
630C4×D4—21no—
631C4×D4—611no—
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×D4C2×#692311yescharacteristic
650#117—611no—
651#117—611no—
652#117—1221no—
653#117—1221no—
654#117—1221no—
655#117—1221no—
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—611no—
676C22⋊C8—611no—
677C22⋊C8—611no—
678C22⋊C8—611no—
679C22⋊C8—1221no—
680C22⋊C8—1221no—
681C22⋊C8—1221no—
682C22⋊C8—1221no—
683C4×C8—1221no—
684C4×C8—1221no—
685#95—611no—
686#95—611no—
687#95—611no—
688#95—611no—
689#95—1221no—
690#95—1221no—
691#95—1221no—
692#95—1221no—
693#95—1221no—
694C24—611no—
695C24—611no—
696C24—1221no—
697#41—81no—
698#41—4881no—
699C2×Q8—21no—
700C2×Q8—81no—
701C2×Q8C22×#692311yescharacteristic
702C2×Q8C22×#692311yescharacteristic
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—611no—
706C2×D4—611no—
707C2×D4—611no—
708C2×D4—611no—
709C2×D4—1221no—
710C2×D4—1221no—
711C2×D4—1221no—
712C2×D4—1222no—
713C2×D4—1222no—
714C2×D4—1221no—
715C2×D4—1221no—
716C2×D4—1221no—
717C2×D4—1221no—
718C2×D4—4881no—
719C2×D4—2442no—
720C2×D4—2442no—
721C2×D4C22⋊#692311yescharacteristic
722C2×D4C22×#692311yescharacteristic
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—611no—
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—1221no—
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×C4—4881no—
747C22×C4—4881no—
748C22×C4—2442no—
749C22×C4—2442no—
750C22×C4C22×#692311yescharacteristic
751C22×C4C22×#692311yescharacteristic
752C2×C8—1221no—
753C2×C8—1221no—
754C2×C8—1221no—
755C2×C8—1221no—
756C2×C8—4881no—
757C2×C8—4881no—
758C2×C8—4881no—
759C2×C8—4881no—
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⋊C4C22⋊#692311yescharacteristic
782C4⋊C4C22×#692311yescharacteristic
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—1221no—
807C22⋊C4—1221no—
808C22⋊C4—1221no—
809C22⋊C4—4881no—
810C22⋊C4—2442no—
811C22⋊C4—2442no—
812C22⋊C4C22⋊#692311yescharacteristic
813C22⋊C4C22⋊#692311yescharacteristic
814C42—21no—
815C42—611no—
816C42—611no—
817C42—611no—
818C42—1221no—
819C42—1221no—
820C42—1221no—
821C42—4881no—
822C42—2442no—
823C42C22×#692311yescharacteristic
824C23—21no—
825C23—611no—
826C23—611no—
827C23—612no—
828C23—612no—
829C23—611no—
830C23—1221no—
831C23—1221no—
832C23—1221no—
833C23—4881no—
834C23—4881no—
835C23—2441no—
836C23—2441no—
837C23—2441no—
838C23—2441no—
839C23—2442no—
840C23C2×C22⋊#692311yescharacteristic
841C23C2×C22⋊#692311yescharacteristic
842Q8—41no—
843Q8—41no—
844Q8—81no—
845D4—22no—
846D4—41no—
847D4—42no—
848D4—81no—
849D4—1222no—
850D4—1222no—
851D4—1222no—
852D4—4881no—
853D4—4881no—
854D4—4881no—
855D4—4881no—
856D4—2441no—
857D4—2441no—
858D4—2441no—
859D4—2441no—
860D4—2441no—
861D4—2442no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—81no—
868C2×C4—81no—
869C2×C4—611no—
870C2×C4—611no—
871C2×C4—611no—
872C2×C4—611no—
873C2×C4—611no—
874C2×C4—1221no—
875C2×C4—1221no—
876C2×C4—1222no—
877C2×C4—1221no—
878C2×C4—1221no—
879C2×C4—1221no—
880C2×C4—4881no—
881C2×C4—4881no—
882C2×C4—4881no—
883C2×C4—4884no—
884C2×C4—4881no—
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—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×C4—2441no—
907C2×C4C2×C22⋊#692311yescharacteristic
908C2×C4C2×C22⋊#692311yescharacteristic
909C2×C4C2×C22⋊#692311yescharacteristic
910C2×C4C2×C22⋊#692311yescharacteristic
911C2×C4C23×#692311yescharacteristic
912C8—2441no—
913C8—2441no—
914C8—2441no—
915C8—2441no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—611no—
925C22—611no—
926C22—612no—
927C22—1221no—
928C22—1221no—
929C22—1221no—
930C22—1221no—
931C22—1221no—
932C22—1221no—
933C22—1221no—
934C22—9762no—
935C22—4881no—
936C22—4881no—
937C22—2442no—
938C22—2442no—
939C22—2441no—
940C22—2441no—
941C22—2441no—
942C22#1684075212yes—
943C22C22×C22⋊#692311yescharacteristic
944C4—21no—
945C4—21no—
946C4—21no—
947C4—21no—
948C4—21no—
949C4—41no—
950C4—41no—
951C4—41no—
952C4—1221no—
953C4—1221no—
954C4—1221no—
955C4—1221no—
956C4—1221no—
957C4—4881no—
958C4—4881no—
959C4—4881no—
960C4—2442no—
961C4—2441no—
962C4—2441no—
963C4—2441no—
964C2—22no—
965C2—41no—
966C2—81no—
967C2—1221no—
968C2—1221no—
969C2—1222no—
970C2—4881no—
971C2—2441no—
972C2#2146241811yescharacteristic
973C2C2×#1684075211yescharacteristic
974C2#2146245011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#548C4
socleC22×C61C22×C22⋊C4
prime radical#21459655C2
cosocleC2×C4×D61C24
hypercenter#548#6923
hypocenterC61#17615
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #21462667C2semidirect
2. #21462336C2semidirect
3. #21461263C2semidirect
4. #21461260C2semidirect
5. #21461259C2semidirect
6. #21461254C2semidirect
7. #21461246C2semidirect
8. #21461245C2semidirect
9. #21461197C2semidirect
10. #21461194C2semidirect
11. #21461192C2semidirect
12. #21461191C2semidirect
13. C2×#16840616C2semidirect
14. D61⋊#327C2semidirect
20. #16840781C22semidirect
21. #16840780C22semidirect
23. C2×#14519834C22semidirect
25. D61⋊(C22⋊C8)C22semidirect
29. #16840707C22semidirect
30. #16840705C22semidirect
33. C4×C22⋊#6923C22semidirect
34. #16840698C22semidirect
36. #16840616C22semidirect
37. #16840616C22semidirect
38. #16840616C22semidirect
39. #16840616C22semidirect
40. #16840616C22semidirect
41. #16840616C22semidirect
42. #16840616C22semidirect
43. #16840616C22semidirect
52. #16840464C4semidirect
54. #16840458C4semidirect
56. #16840453C4semidirect
57. #16840446C4semidirect
60. #16840423C4semidirect
61. #16840405C4semidirect
62. #16840400C4semidirect
74. C61×#548C4semidirect
107. C2×#11758226C2×C4semidirect
119. #14519769C2×C4semidirect
120. #14519768C2×C4semidirect
124. #14519766C2×C4semidirect
140. #14519753C2×C4semidirect
146. #14519751C2×C4semidirect
153. #14519748C2×C4semidirect
159. Q8×Dic61C2×C4semidirect
162. C4×D244C2×C4semidirect
164. D4×Dic61C2×C4semidirect
178. #14519736C2×C4semidirect
180. #14519735C2×C4semidirect
195. C2×#41×C61C2×C4semidirect
198. #124×C61C2×C4semidirect
200. C22⋊Q8×C61C2×C4semidirect
203. C4×Q8×C61C2×C4semidirect
512. #548#6923semidirect
562. C61#17615semidirect
564. C2×#41C2×#6923semidirect
589. #124C2×#6923semidirect
609. C22⋊Q8C2×#6923semidirect
629. C4×Q8C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214626672
#214623362
#214612632
#214612602
#214612592
#214612542
#214612462
#214612452
#214611972
#214611942
#214611922
#214611912
C2×#168406162
D61⋊#3272
#214596552
#1761561