Finite Group Databasebeta

← #30611253

Subgroups — #30611253

Order 15616.

1060 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462676C211yesmaximal, characteristic, complemented
2#21462301C211yesmaximal, characteristic, complemented
3#21461261C211yesmaximal, characteristic, complemented
4#21461255C211yesmaximal, characteristic, complemented
5#21461248C211yesmaximal, characteristic, complemented
6#21461244C211yesmaximal, characteristic, complemented
7#21461239C211yesmaximal, characteristic, complemented
8#21461235C211yesmaximal, characteristic, complemented
9#21461230C211yesmaximal, characteristic, complemented
10#21461224C211yesmaximal, characteristic, complemented
11#21461215C211yesmaximal, characteristic, complemented
12#21461204C211yesmaximal, characteristic, complemented
13#21461195C211yesmaximal, characteristic, complemented
14C2×#16840613C211yesmaximal, characteristic, complemented
15#21459842C211yesmaximal, characteristic
16#16840795—21no—
17#16840793—21no—
18#16840792—21no—
19#16840789—21no—
20#16840785C2211yescharacteristic, complemented
21#16840780C2211yescharacteristic, complemented
22#16840734C2211yescharacteristic, complemented
23#16840733C2211yescharacteristic, complemented
24C2×#14519834C2211yescharacteristic, complemented
25D61⋊(C22⋊C8)C2211yescharacteristic, complemented
26#16840712—21no—
27#16840711—21no—
28#16840710—21no—
29#16840709—21no—
30#16840707C2211yescharacteristic, complemented
31#16840706C2211yescharacteristic, complemented
32#16840705C2211yescharacteristic, complemented
33#16840704C2211yescharacteristic, complemented
34C4×C22⋊#6923C2211yescharacteristic, complemented
35C2×(C2×#6923)⋊C4C2211yescharacteristic, complemented
36#16840615C2211yescharacteristic, complemented
37#16840615C2211yescharacteristic, complemented
38#16840615C2211yescharacteristic, complemented
39#16840615C2211yescharacteristic, complemented
40#16840613C2211yescharacteristic
41#16840613C2211yescharacteristic
42#16840613C2211yescharacteristic
43#16840613C2211yescharacteristic
44#16840613C2211yescharacteristic, complemented
45#16840613C2211yescharacteristic, complemented
46#16840613C2211yescharacteristic, complemented
47#16840613C2211yescharacteristic, complemented
48#16840613C2211yescharacteristic, complemented
49#16840613C2211yescharacteristic, complemented
50#16840613C2211yescharacteristic, complemented
51#16840613C2211yescharacteristic, complemented
52#16840477C411yescharacteristic, complemented
53#16840469C411yescharacteristic, complemented
54#16840464C411yescharacteristic, complemented
55#16840464C411yescharacteristic, complemented
56#16840459—21no—
57#16840432C411yescharacteristic, complemented
58#16840406C411yescharacteristic, complemented
59#16840406C411yescharacteristic, complemented
60#16840399—21no—
61#16840399—21no—
62D4×C22⋊D61—21no—
63#16840365—21no—
64#16840347—21no—
65#16840347—21no—
66#16840310C2211yescharacteristic
67#16840294C2211yescharacteristic
68#16840272C2211yescharacteristic
69#16840272C2211yescharacteristic
70C2×#14519748C2211yescharacteristic
71C2×#14519748C2211yescharacteristic
72#16840237—21no—
73C4×D4×D61C2211yescharacteristic
74D42×C61C411yescharacteristic, complemented
75C23×#6923—21no—
76C2×#11758213—21no—
77C2×#11758217—21no—
78C2×D61⋊C8—21no—
79C22×#92420—21no—
80C2×C4⋊#6923—21no—
81C2×C4⋊#6923—21no—
82C2×C22⋊#6923—21no—
83C2×C22⋊#6923—21no—
84C2×C22⋊#6923—21no—
85C2×C4×#6923—21no—
86#14519844—21no—
87#14519844—21no—
88#14519834—21no—
89#14519834—21no—
90#14519834C2311yescharacteristic
91#14519834C2311yescharacteristic
92#14519834C2311yescharacteristic
93#14519834C2311yescharacteristic
94C22⋊#92420—21no—
95C22⋊#92420—21no—
96#14519832—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×#11758224—21no—
108C2×#11758224C2×C411yescharacteristic
109C2×#11758224C2×C411yescharacteristic, complemented
110C22×C22⋊D61—21no—
111C22×C22⋊D61—21no—
112C2×D4×D61D411yescharacteristic
113C22×C4×D61C2311yescharacteristic
114C22×C4×D61C2311yescharacteristic
115#14519777C2×C411yescharacteristic, complemented
116#14519773—21no—
117#14519770—21no—
118#14519770—21no—
119#14519770—21no—
120#14519768—21no—
121#14519768C2×C411yescharacteristic, complemented
122#14519764—21no—
123#14519764C2×C411yescharacteristic, complemented
124#14519763—21no—
125#14519763—21no—
126#14519761—21no—
127#14519761—21no—
128#14519759—21no—
129#14519759—21no—
130#14519759—21no—
131#14519758—21no—
132#14519758—21no—
133#14519757C2311yescharacteristic
134#14519756C2×C411yescharacteristic
135#14519756C2×C411yescharacteristic, complemented
136#14519754—21no—
137#14519754—21no—
138#14519751—21no—
139#14519749—21no—
140#14519749—21no—
141#14519749—21no—
142#14519749—21no—
143#14519749—21no—
144#14519749—21no—
145#14519748—21no—
146#14519748—21no—
147#14519748—21no—
148#14519748—21no—
149#14519748—21no—
150#14519748C2×C411yescharacteristic
151#14519748C2×C411yescharacteristic
152#14519748C2×C411yescharacteristic, complemented
153#14519748C2×C411yescharacteristic, complemented
154#14519748C2311yescharacteristic
155#14519748C2311yescharacteristic
156#14519748C2311yescharacteristic
157#14519746—21no—
158#14519746—21no—
159#14519745—21no—
160#14519745—21no—
161C4×Dic122C2×C411yescharacteristic, complemented
162C4×D244C2×C411yescharacteristic
163D4×Dic61—21no—
164D4×Dic61—21no—
165D4×Dic61—21no—
166D4×Dic61—21no—
167D4×Dic61—21no—
168D4×Dic61—21no—
169D4×Dic61—21no—
170D4×Dic61C2×C411yescharacteristic, complemented
171D4×Dic61C2×C411yescharacteristic, complemented
172D4×Dic61D411yescharacteristic
173#14519739D411yescharacteristic
174C4×C22⋊D61—21no—
175C4×C22⋊D61C2×C411yescharacteristic
176C4×C22⋊D61C2×C411yescharacteristic
177#14519737—21no—
178#14519737—21no—
179#14519737D411yescharacteristic
180#14519737D411yescharacteristic
181#14519736—21no—
182#14519736—21no—
183#14519735C2×C411yescharacteristic
184#14519735C2×C411yescharacteristic, complemented
185C2×C4⋊Dic61C2×C411yescharacteristic
186C2×C4⋊Dic61C2×C411yescharacteristic, complemented
187C4⋊C4×D61D411yescharacteristic
188C2×C22⋊Dic61—21no—
189C2×C22⋊Dic61—21no—
190C2×C22⋊Dic61—21no—
191C2×C22⋊Dic61—21no—
192C22⋊C4×D61D411yescharacteristic
193C22⋊C4×D61D411yescharacteristic
194C42×D61C2311yescharacteristic
195C22×D4×C61—21no—
196C22×D4×C61C2×C411yescharacteristic
197C22×D4×C61C2×C411yescharacteristic, complemented
198#127×C61C2×C411yescharacteristic, complemented
199#121×C61—21no—
200#121×C61C2×C411yescharacteristic
201#121×C61C2×C411yescharacteristic, complemented
202#120×C61—21no—
203#120×C61—21no—
204C4×D4×C61C2×C411yescharacteristic
205C4×D4×C61C2×C411yescharacteristic, complemented
206C24×C61—21no—
207C24×C61—21no—
208C23×D61C2×D411yescharacteristic
209C23×D61C2×D411yescharacteristic
210C22×#6923—21no—
211C22×#6923—21no—
212C22×#6923—21no—
213C22×#6923—21no—
214C22×#6923—42no—
215C22×#6923—81no—
216C22×#6923—81no—
217C2×D4×C61—21no—
218C2×D4×C61—21no—
219C2×D4×C61—21no—
220C2×D4×C61—21no—
221C2×D4×C61—21no—
222C2×D4×C61—21no—
223C2×D4×C61—44no—
224C2×D4×C61—81no—
225C2×D4×C61—81no—
226C2×D4×C61C22⋊C411yescharacteristic
227C2×D4×C61C22×C411yescharacteristic
228C2×D4×C61C22×C411yescharacteristic
229C2×D4×C61C22×C411yescharacteristic
230C22×C4×C61—21no—
231C22×C4×C61C22×C411yescharacteristic
232C22×C4×C61C22×C411yescharacteristic
233C2×C22⋊D61—21no—
234C2×C22⋊D61—21no—
235C2×C22⋊D61—21no—
236C2×C22⋊D61—21no—
237C2×C22⋊D61—21no—
238C2×C22⋊D61—21no—
239C2×C22⋊D61—21no—
240C2×C22⋊D61—21no—
241C2×C22⋊D61—21no—
242C2×C22⋊D61—81no—
243C2×C22⋊D61—81no—
244C2×C22⋊D61—81no—
245C2×C22⋊D61—81no—
246C2×C22⋊D61C22⋊C411yescharacteristic
247C2×C22⋊D61C22⋊C411yescharacteristic
248C22×Dic61—21no—
249C22×Dic61—21no—
250C22×Dic61—21no—
251C22×Dic61—21no—
252C22×Dic61—21no—
253C22×Dic61—21no—
254C22×Dic61C2×D411yescharacteristic
255C22×Dic61C2×D411yescharacteristic
256#11758224—81no—
257#11758224—81no—
258#11758224—81no—
259#11758224—81no—
260D4×D61—42no—
261C2×D244C22⋊C411yescharacteristic
262C2×C4×D61—81no—
263C2×C4×D61—81no—
264C2×C4×D61C22×C411yescharacteristic
265C2×C4×D61C22×C411yescharacteristic
266C2×C4×D61C2×D411yescharacteristic
267C2×C4×D61C2×D411yescharacteristic
268C2×C4×D61C2×D411yescharacteristic
269C2×C4×D61C2×D411yescharacteristic
270C2×C4×D61C2×D411yescharacteristic
271C2×C4×D61C2×D411yescharacteristic
272C2×C4×D61C2411yescharacteristic
273C2×Dic122—21no—
274C2×Dic122C22×C411yescharacteristic
275C22⋊#6923—42no—
276C22⋊#6923—81no—
277C22⋊#6923—81no—
278#11758217—81no—
279C2×#92420—21no—
280C2×#92420—21no—
281C2×#92420—21no—
282C2×#92420—21no—
283C2×#92420—81no—
284C4⋊#6923—81no—
285C4⋊#6923—81no—
286C4×#6923—81no—
287#11758213—81no—
288D61⋊C8—81no—
289C4⋊C4×C61C22⋊C411yescharacteristic
290C4⋊C4×C61C22×C411yescharacteristic
291C22⋊C4×C61—21no—
292C22⋊C4×C61—21no—
293C22⋊C4×C61—21no—
294C22⋊C4×C61C22⋊C411yescharacteristic
295C22⋊C4×C61C22⋊C411yescharacteristic
296C42×C61C22×C411yescharacteristic
297C22⋊Dic61—21no—
298C22⋊Dic61—21no—
299C22⋊Dic61—21no—
300C22⋊Dic61—21no—
301C22⋊Dic61—21no—
302C22⋊Dic61—21no—
303C22⋊Dic61—21no—
304C22⋊Dic61—21no—
305C22⋊Dic61—21no—
306C22⋊Dic61—21no—
307C22⋊Dic61—21no—
308C22⋊Dic61—21no—
309C22⋊Dic61—21no—
310C22⋊Dic61C22⋊C411yescharacteristic
311C22⋊Dic61C22⋊C411yescharacteristic
312#11758198—21no—
313#11758198—21no—
314#11758198—21no—
315#11758198C22⋊C411yescharacteristic
316#11758198C22⋊C411yescharacteristic
317#11758198C22⋊C411yescharacteristic
318#11758198C22⋊C411yescharacteristic
319C4⋊Dic61—21no—
320C4⋊Dic61—21no—
321C4⋊Dic61—21no—
322C4⋊Dic61—21no—
323C4⋊Dic61—21no—
324C4⋊Dic61C22⋊C411yescharacteristic
325C4⋊Dic61C22×C411yescharacteristic
326C4⋊Dic61C22×C411yescharacteristic
327C4⋊Dic61C22×C411yescharacteristic
328#11758196—21no—
329#11758196—21no—
330#11758196—21no—
331#11758196—21no—
332#11758196C22⋊C411yescharacteristic
333#11758196C22⋊C411yescharacteristic
334C4×Dic61—21no—
335C4×Dic61—21no—
336C4×Dic61—21no—
337C4×Dic61C22×C411yescharacteristic
338C4×Dic61C2×D411yescharacteristic
339C4×Dic61C2×D411yescharacteristic
340C23×C61—21no—
341C23×C61—21no—
342C23×C61—21no—
343C23×C61—42no—
344C23×C61—42no—
345C23×C61—81no—
346C23×C61—81no—
347C23×C61—81no—
348C23×C61—81no—
349C23×C61C2×C22⋊C411yescharacteristic
350C23×C61C2×C22⋊C411yescharacteristic
351C22×D61—22no—
352C22×D61—21no—
353C22×D61—21no—
354C22×D61—21no—
355C22×D61—21no—
356C22×D61—41no—
357C22×D61—41no—
358C22×D61—41no—
359C22×D61C2×C22⋊C411yescharacteristic
360C22×D61C2×C22⋊C411yescharacteristic
361C22×D61C22×D411yescharacteristic
362C2×#6923—41no—
363C2×#6923—41no—
364C2×#6923—41no—
365C2×#6923—41no—
366C2×#6923—41no—
367C2×#6923—41no—
368C2×#6923—41no—
369C2×#6923—41no—
370C2×#6923—41no—
371C2×#6923—41no—
372C2×#6923—41no—
373C2×#6923—41no—
374C2×#6923—84no—
375D4×C61—22no—
376D4×C61—41no—
377D4×C61—41no—
378D4×C61—41no—
379D4×C61—42no—
380D4×C61—42no—
381D4×C61—42no—
382D4×C61—81no—
383D4×C61—81no—
384D4×C61—81no—
385C2×C4×C61—21no—
386C2×C4×C61—41no—
387C2×C4×C61—41no—
388C2×C4×C61—42no—
389C2×C4×C61C2×C22⋊C411yescharacteristic
390C2×C4×C61C2×C22⋊C411yescharacteristic
391C2×C4×C61C2×C22⋊C411yescharacteristic
392C2×C4×C61C2×C22⋊C411yescharacteristic
393C2×C4×C61C23×C411yescharacteristic
394C22⋊D61—22no—
395C22⋊D61—41no—
396C22⋊D61—41no—
397C22⋊D61—41no—
398C22⋊D61—41no—
399C22⋊D61—41no—
400C22⋊D61—41no—
401C22⋊D61—41no—
402C22⋊D61—81no—
403C22⋊D61—81no—
404C22⋊D61—81no—
405C22⋊D61—81no—
406C22⋊D61—81no—
407C22⋊D61—81no—
408C2×Dic61—21no—
409C2×Dic61—21no—
410C2×Dic61—21no—
411C2×Dic61—21no—
412C2×Dic61—41no—
413C2×Dic61—41no—
414C2×Dic61—81no—
415C2×Dic61—81no—
416C2×Dic61—81no—
417C2×Dic61—81no—
418C2×Dic61—81no—
419C2×Dic61—81no—
420C2×Dic61C2×C22⋊C411yescharacteristic
421C2×Dic61C2×C22⋊C411yescharacteristic
422C2×Dic61C2×C22⋊C411yescharacteristic
423C2×Dic61C2×C22⋊C411yescharacteristic
424C2×Dic61C22×D411yescharacteristic
425D244—41no—
426C4×D61—21no—
427C4×D61—21no—
428C4×D61—41no—
429C4×D61—41no—
430C4×D61—41no—
431C4×D61—41no—
432C4×D61—41no—
433C4×D61—41no—
434C4×D61—41no—
435C4×D61—41no—
436Dic122—41no—
437Dic122—81no—
438#92420—41no—
439#92420—41no—
440#92420—41no—
441#92420—41no—
442#17597—611nomaximal, Sylow
443C22×C61—21no—
444C22×C61—21no—
445C22×C61—21no—
446C22×C61—21no—
447C22×C61—21no—
448C22×C61—41no—
449C22×C61—41no—
450C22×C61—41no—
451C22×C61—41no—
452C22×C61—41no—
453C22×C61—41no—
454C22×C61—41no—
455C22×C61—41no—
456C22×C61—41no—
457C22×C61—162no—
458C22×C61—162no—
459C22×C61#42112yes—
460C22×C61C22×C22⋊C411yescharacteristic
461C2×D61—21no—
462C2×D61—21no—
463C2×D61—21no—
464C2×D61—21no—
465C2×D61—21no—
466C2×D61—21no—
467C2×D61—21no—
468C2×D61—21no—
469C2×D61—42no—
470C2×D61—42no—
471C2×D61—81no—
472C2×D61—81no—
473C2×D61#57611yescharacteristic
474C2×D61#57711yescharacteristic
475#6923—81no—
476#6923—81no—
477#6923—81no—
478#6923—81no—
479C4×C61—21no—
480C4×C61—21no—
481C4×C61—21no—
482C4×C61—21no—
483C4×C61—21no—
484C4×C61—41no—
485Dic61—21no—
486Dic61—21no—
487Dic61—21no—
488Dic61—21no—
489Dic61—21no—
490Dic61—41no—
491Dic61—41no—
492Dic61—41no—
493Dic61—41no—
494#3519—611no—
495#2974—611no—
496#2318—611no—
497#1521—611no—
498#1519—611no—
499#1517—611no—
500#1516—611no—
501#1514—611no—
502#1513—611no—
503#1512—611no—
504#1510—611no—
505#1507—611no—
506#1504—611no—
507#1501—611no—
508C2×#327—611no—
509C2×C61—22no—
510C2×C61—41no—
511C2×C61—81no—
512C2×C61—81no—
513C2×C61—81no—
514C2×C61#288311yescharacteristic
515C2×C61#289711yescharacteristic
516C2×C61C2×#42111yescharacteristic
517D61—21no—
518D61—21no—
519D61—41no—
520D61—41no—
521#555—611no—
522#554—611no—
523#553—611no—
524#553—611no—
525#553—1221no—
526#550—611no—
527#546—611no—
528#546—611no—
529#546—1221no—
530#546—1221no—
531D42—1221no—
532D42#692311yescharacteristic, complemented
533#540—1221no—
534#538—1221no—
535#538—1221no—
536#532—611no—
537#529—611no—
538#525—611no—
539#525—611no—
540C2×#121—611no—
541C2×#121—611no—
542#518—1221no—
543C2×C4×D4—611no—
544#436—1221no—
545#435—1221no—
546#435—1221no—
547C8×D4—1221no—
548#432—611no—
549#431—611no—
550#407—611no—
551#407—611no—
552C2×C22⋊C8—611no—
553C2×C22⋊C8—611no—
554#388—1221no—
555#387—1221no—
556#386—1221no—
557#385—1221no—
558#383—611no—
559#382—611no—
560#381—611no—
561#380—611no—
562C4×C22⋊C4—611no—
563C2×#95—611no—
564#328—611no—
565#328—611no—
566#328—611no—
567#328—611no—
568#327—611no—
569#327—611no—
570#327—611no—
571#327—611no—
572#327—611no—
573#327—611no—
574#327—611no—
575#327—611no—
576#327—611no—
577#327—611no—
578#327—611no—
579#327—611no—
580C61#1759711yescharacteristic, complemented, Sylow
581C2×#41—611no—
582C2×#41—611no—
583C2×#41—1221no—
584C22×D4—21no—
585C22×D4—611no—
586C22×D4—1221no—
587C22×D4—1221no—
588C22×D4C2×#692311yescharacteristic
589C22×D4C2×#692311yescharacteristic, complemented
590C23×C4—611no—
591C23×C4—611no—
592C23×C4—1221no—
593C2×M16—1221no—
594C2×M16—1221no—
595C22×C8—1221no—
596C22×C8—1221no—
597C4⋊Q8—611no—
598#127—1221no—
599#127C2×#692311yescharacteristic, complemented
600#126—1221no—
601#126—1221no—
602#126—1221no—
603#125—611no—
604#125—1221no—
605#124—611no—
606#124—1221no—
607#124—1221no—
608#124—1221no—
609#123—1221no—
610#123—1221no—
611#123—1221no—
612#123—1221no—
613#123—1221no—
614#123—1221no—
615#123—1221no—
616C22⋊Q8—611no—
617C22⋊Q8—611no—
618C22⋊Q8—611no—
619C22⋊Q8—1221no—
620C22⋊Q8—1221no—
621#121—21no—
622#121—611no—
623#121—611no—
624#121—611no—
625#121—611no—
626#121—611no—
627#121—611no—
628#121—611no—
629#121—1221no—
630#121—1221no—
631#121—1221no—
632#121—1221no—
633#121—1221no—
634#121—1221no—
635#121—1221no—
636#121—1221no—
637#121—1221no—
638#121—1221no—
639#121—1221no—
640#121—1221no—
641#121C2×#692311yescharacteristic
642#121C2×#692311yescharacteristic, complemented
643#120—21no—
644#120—21no—
645#120—1221no—
646#120—1221no—
647#120—1221no—
648#120—1221no—
649C4×Q8—611no—
650C4×D4—611no—
651C4×D4—611no—
652C4×D4—611no—
653C4×D4—611no—
654C4×D4—611no—
655C4×D4—611no—
656C4×D4—611no—
657C4×D4—611no—
658C4×D4—611no—
659C4×D4—1221no—
660C4×D4—1221no—
661C4×D4—1221no—
662C4×D4—1221no—
663C4×D4—1221no—
664C4×D4—1221no—
665C4×D4—1221no—
666C4×D4—1221no—
667C4×D4—1221no—
668C4×D4—1221no—
669C4×D4C2×#692311yescharacteristic
670C4×D4C2×#692311yescharacteristic, complemented
671#117—611no—
672#117—611no—
673#117—1221no—
674#117—1221no—
675C2×C4⋊C4—611no—
676C2×C4⋊C4—611no—
677C2×C4⋊C4—611no—
678C2×C4⋊C4—1221no—
679C2×C4⋊C4—1221no—
680C2×C22⋊C4—611no—
681C2×C22⋊C4—611no—
682C2×C22⋊C4—1221no—
683C2×C22⋊C4—1221no—
684C2×C22⋊C4—1221no—
685C2×C22⋊C4—1221no—
686C2×C22⋊C4—1221no—
687C2×C22⋊C4—1221no—
688C2×C22⋊C4—1221no—
689C2×C42—611no—
690C2×C42—1221no—
691C4⋊C8—1221no—
692C4⋊C8—1221no—
693C22⋊C8—611no—
694C22⋊C8—611no—
695C22⋊C8—611no—
696C22⋊C8—611no—
697C22⋊C8—1221no—
698C22⋊C8—1221no—
699C22⋊C8—1221no—
700C22⋊C8—1221no—
701#97—1221no—
702C4×C8—1221no—
703#95—611no—
704#95—611no—
705#95—611no—
706#95—611no—
707#95—1221no—
708#95—1221no—
709#95—1221no—
710#95—1221no—
711#95—1221no—
712C24—21no—
713C24—21no—
714C24—611no—
715C24—611no—
716#41—4881no—
717#41—4881no—
718#41—4881no—
719#41—4881no—
720C2×Q8—611no—
721C2×Q8—1221no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—44no—
729C2×D4—81no—
730C2×D4—81no—
731C2×D4—611no—
732C2×D4—611no—
733C2×D4—611no—
734C2×D4—1221no—
735C2×D4—1221no—
736C2×D4—1221no—
737C2×D4—1221no—
738C2×D4—1221no—
739C2×D4—1221no—
740C2×D4—1221no—
741C2×D4—1221no—
742C2×D4—1221no—
743C2×D4—4881no—
744C2×D4—4881no—
745C2×D4—4881no—
746C2×D4—4881no—
747C2×D4—2442no—
748C2×D4C22⋊#692311yescharacteristic
749C2×D4C22×#692311yescharacteristic
750C2×D4C22×#692311yescharacteristic
751C2×D4C22×#692311yescharacteristic
752C22×C4—21no—
753C22×C4—611no—
754C22×C4—611no—
755C22×C4—611no—
756C22×C4—611no—
757C22×C4—611no—
758C22×C4—611no—
759C22×C4—611no—
760C22×C4—611no—
761C22×C4—611no—
762C22×C4—611no—
763C22×C4—611no—
764C22×C4—1221no—
765C22×C4—1221no—
766C22×C4—1221no—
767C22×C4—1221no—
768C22×C4—1221no—
769C22×C4—1221no—
770C22×C4—1221no—
771C22×C4—1221no—
772C22×C4—1221no—
773C22×C4—1221no—
774C22×C4—4881no—
775C22×C4—4881no—
776C22×C4—4881no—
777C22×C4—4881no—
778C22×C4—2442no—
779C22×C4C22×#692311yescharacteristic
780C22×C4C22×#692311yescharacteristic
781M16—4881no—
782M16—4881no—
783C2×C8—1221no—
784C2×C8—1221no—
785C2×C8—1221no—
786C2×C8—1221no—
787C2×C8—4881no—
788C2×C8—4881no—
789C4⋊C4—611no—
790C4⋊C4—611no—
791C4⋊C4—611no—
792C4⋊C4—611no—
793C4⋊C4—611no—
794C4⋊C4—611no—
795C4⋊C4—1221no—
796C4⋊C4—1221no—
797C4⋊C4—1221no—
798C4⋊C4—1221no—
799C4⋊C4—1221no—
800C4⋊C4—1221no—
801C4⋊C4—1221no—
802C4⋊C4—1221no—
803C4⋊C4—1221no—
804C4⋊C4—4881no—
805C4⋊C4—4881no—
806C4⋊C4C22⋊#692311yescharacteristic
807C4⋊C4C22×#692311yescharacteristic
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—611no—
812C22⋊C4—611no—
813C22⋊C4—611no—
814C22⋊C4—611no—
815C22⋊C4—611no—
816C22⋊C4—611no—
817C22⋊C4—1221no—
818C22⋊C4—1221no—
819C22⋊C4—1221no—
820C22⋊C4—1221no—
821C22⋊C4—1221no—
822C22⋊C4—1221no—
823C22⋊C4—1221no—
824C22⋊C4—1221no—
825C22⋊C4—1221no—
826C22⋊C4—1221no—
827C22⋊C4—1221no—
828C22⋊C4—1221no—
829C22⋊C4—1221no—
830C22⋊C4—1221no—
831C22⋊C4—1221no—
832C22⋊C4—1221no—
833C22⋊C4—4881no—
834C22⋊C4—4881no—
835C22⋊C4—2442no—
836C22⋊C4C22⋊#692311yescharacteristic
837C22⋊C4C22⋊#692311yescharacteristic
838C42—611no—
839C42—611no—
840C42—611no—
841C42—1221no—
842C42—1221no—
843C42—1221no—
844C42—4881no—
845C42C22×#692311yescharacteristic
846C23—21no—
847C23—21no—
848C23—21no—
849C23—42no—
850C23—42no—
851C23—81no—
852C23—81no—
853C23—81no—
854C23—81no—
855C23—611no—
856C23—611no—
857C23—611no—
858C23—1221no—
859C23—1221no—
860C23—1221no—
861C23—1221no—
862C23—1222no—
863C23—2441no—
864C23—2441no—
865C23—2441no—
866C23C2×C22⋊#692311yescharacteristic
867C23C2×C22⋊#692311yescharacteristic
868Q8—4881no—
869Q8—2441no—
870D4—22no—
871D4—41no—
872D4—41no—
873D4—41no—
874D4—42no—
875D4—42no—
876D4—42no—
877D4—81no—
878D4—81no—
879D4—81no—
880D4—1222no—
881D4—4881no—
882D4—4881no—
883D4—4881no—
884D4—4881no—
885D4—4881no—
886D4—4881no—
887D4—2441no—
888D4—2441no—
889D4—2441no—
890D4—2441no—
891D4—2441no—
892D4—2441no—
893D4—2441no—
894D4—2441no—
895C2×C4—21no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—42no—
899C2×C4—611no—
900C2×C4—611no—
901C2×C4—611no—
902C2×C4—611no—
903C2×C4—611no—
904C2×C4—1221no—
905C2×C4—1221no—
906C2×C4—1221no—
907C2×C4—1221no—
908C2×C4—1221no—
909C2×C4—1221no—
910C2×C4—4881no—
911C2×C4—4881no—
912C2×C4—4881no—
913C2×C4—4881no—
914C2×C4—4884no—
915C2×C4—4881no—
916C2×C4—4881no—
917C2×C4—2441no—
918C2×C4—2441no—
919C2×C4—2441no—
920C2×C4—2441no—
921C2×C4—2441no—
922C2×C4—2441no—
923C2×C4—2441no—
924C2×C4—2441no—
925C2×C4—2441no—
926C2×C4—2441no—
927C2×C4—2441no—
928C2×C4—2441no—
929C2×C4—2441no—
930C2×C4—2441no—
931C2×C4—2441no—
932C2×C4—2441no—
933C2×C4—2441no—
934C2×C4—2441no—
935C2×C4—2441no—
936C2×C4—2441no—
937C2×C4—2441no—
938C2×C4—2441no—
939C2×C4C2×C22⋊#692311yescharacteristic
940C2×C4C2×C22⋊#692311yescharacteristic
941C2×C4C2×C22⋊#692311yescharacteristic
942C2×C4C2×C22⋊#692311yescharacteristic
943C2×C4C23×#692311yescharacteristic
944C8—2441no—
945C8—2441no—
946C8—2441no—
947C8—2441no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—41no—
954C22—41no—
955C22—41no—
956C22—41no—
957C22—41no—
958C22—41no—
959C22—41no—
960C22—41no—
961C22—41no—
962C22—162no—
963C22—162no—
964C22—611no—
965C22—611no—
966C22—1221no—
967C22—1221no—
968C22—1221no—
969C22—1221no—
970C22—1221no—
971C22—1221no—
972C22—1221no—
973C22—1221no—
974C22—4881no—
975C22—4881no—
976C22—2442no—
977C22—2442no—
978C22#1684076012yes—
979C22C22×C22⋊#692311yescharacteristic
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—21no—
985C4—41no—
986C4—1221no—
987C4—1221no—
988C4—1221no—
989C4—1221no—
990C4—1221no—
991C4—4881no—
992C4—4881no—
993C4—4881no—
994C4—4881no—
995C4—2441no—
996C4—2441no—
997C4—2441no—
998C4—2441no—
999C2—22no—
1000C2—41no—
1001C2—81no—
1002C2—81no—
1003C2—81no—
1004C2—1221no—
1005C2—1221no—
1006C2—2441no—
1007C2—2441no—
1008C2#2146241811yescharacteristic
1009C2#2146244011yescharacteristic
1010C2C2×#1684076011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingD42×C61C4
socleC22×C61C22×C22⋊C4
prime radical#21459842C2
cosocleC2×C4×D61C24
hypercenterD42#6923
hypocenterC61#17597
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. #21462676C2semidirect
2. #21462301C2semidirect
3. #21461261C2semidirect
4. #21461255C2semidirect
5. #21461248C2semidirect
6. #21461244C2semidirect
7. #21461239C2semidirect
8. #21461235C2semidirect
9. #21461230C2semidirect
10. #21461224C2semidirect
11. #21461215C2semidirect
12. #21461204C2semidirect
13. #21461195C2semidirect
14. C2×#16840613C2semidirect
20. #16840785C22semidirect
21. #16840780C22semidirect
22. #16840734C22semidirect
23. #16840733C22semidirect
24. C2×#14519834C22semidirect
25. D61⋊(C22⋊C8)C22semidirect
30. #16840707C22semidirect
31. #16840706C22semidirect
32. #16840705C22semidirect
33. #16840704C22semidirect
34. C4×C22⋊#6923C22semidirect
35. C2×(C2×#6923)⋊C4C22semidirect
36. #16840615C22semidirect
37. #16840615C22semidirect
38. #16840615C22semidirect
39. #16840615C22semidirect
44. #16840613C22semidirect
45. #16840613C22semidirect
46. #16840613C22semidirect
47. #16840613C22semidirect
48. #16840613C22semidirect
49. #16840613C22semidirect
50. #16840613C22semidirect
51. #16840613C22semidirect
52. #16840477C4semidirect
53. #16840469C4semidirect
54. #16840464C4semidirect
55. #16840464C4semidirect
57. #16840432C4semidirect
58. #16840406C4semidirect
59. #16840406C4semidirect
74. D42×C61C4semidirect
109. C2×#11758224C2×C4semidirect
115. #14519777C2×C4semidirect
121. #14519768C2×C4semidirect
123. #14519764C2×C4semidirect
135. #14519756C2×C4semidirect
152. #14519748C2×C4semidirect
153. #14519748C2×C4semidirect
161. C4×Dic122C2×C4semidirect
170. D4×Dic61C2×C4semidirect
171. D4×Dic61C2×C4semidirect
184. #14519735C2×C4semidirect
186. C2×C4⋊Dic61C2×C4semidirect
197. C22×D4×C61C2×C4semidirect
198. #127×C61C2×C4semidirect
201. #121×C61C2×C4semidirect
205. C4×D4×C61C2×C4semidirect
532. D42#6923semidirect
580. C61#17597semidirect
589. C22×D4C2×#6923semidirect
599. #127C2×#6923semidirect
642. #121C2×#6923semidirect
670. C4×D4C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214626762
#214623012
#214612612
#214612552
#214612482
#214612442
#214612392
#214612352
#214612302
#214612242
#214612152
#214612042
#214611952
C2×#168406132
#214598422
#1759761