Finite Group Databasebeta

← #30617907

Subgroups — #30617907

Order 15616.

970 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#433C211yesmaximal, characteristic
2#21462297C211yesmaximal, characteristic
3#21462003C211yesmaximal, characteristic, complemented
4#21462002C211yesmaximal, characteristic, complemented
5#21462001C211yesmaximal, characteristic, complemented
6#21462000C211yesmaximal, characteristic, complemented
7#21461999C211yesmaximal, characteristic, complemented
8#21461999C211yesmaximal, characteristic, complemented
9#21461998C211yesmaximal, characteristic, complemented
10#21461997C211yesmaximal, characteristic, complemented
11#21461724C211yesmaximal, characteristic
12#21461724C211yesmaximal, characteristic
13#21461723C211yesmaximal, characteristic
14#21461722C211yesmaximal, characteristic
15#544×D61C211yesmaximal, characteristic
16#16840787—21no—
17#16840787—21no—
18#16840786—21no—
19#16840786—21no—
20D61⋊(C4⋊C8)C2211yescharacteristic
21D61⋊(C4⋊C8)C2211yescharacteristic
22D61⋊(C22⋊C8)C2211yescharacteristic
23D61⋊(C22⋊C8)C2211yescharacteristic
24#16840721C2211yescharacteristic
25C4×D61⋊C8C2211yescharacteristic
26#16840712—21no—
27#16840712—21no—
28#16840711—21no—
29#16840711—21no—
30#16840708C2211yescharacteristic
31#16840706C2211yescharacteristic
32#16840704C2211yescharacteristic
33#16840704C2211yescharacteristic
34C4×C4⋊#6923C2211yescharacteristic
35C4×C4⋊#6923C2211yescharacteristic
36#16840635C2211yescharacteristic
37#16840635C2211yescharacteristic
38#16840635C2211yescharacteristic
39#16840635C2211yescharacteristic
40#16840635C2211yescharacteristic
41#16840635C2211yescharacteristic
42#16840635C2211yescharacteristic
43#16840635C2211yescharacteristic
44#16840635C2211yescharacteristic
45#16840635C2211yescharacteristic
46#16840635C2211yescharacteristic
47#16840635C2211yescharacteristic
48#16840635C2211yescharacteristic
49#16840635C2211yescharacteristic
50#16840635C2211yescharacteristic
51#16840635C2211yescharacteristic
52#16840393C411yescharacteristic, complemented
53#16840392—21no—
54#16840392C411yescharacteristic, complemented
55#16840392C411yescharacteristic, complemented
56#16840391—21no—
57#16840391—21no—
58#16840390C411yescharacteristic, complemented
59#16840390C411yescharacteristic, complemented
60#16840389—21no—
61#16840389C411yescharacteristic, complemented
62#16840389C411yescharacteristic, complemented
63C4⋊Q8×D61—21no—
64C4⋊Q8×D61C2211yescharacteristic
65C4⋊Q8×D61C2211yescharacteristic
66#125×D61—21no—
67#125×D61C2211yescharacteristic
68#125×D61C2211yescharacteristic
69C22⋊Q8×D61—21no—
70C22⋊Q8×D61—21no—
71#117×D61C2211yescharacteristic
72#117×D61C2211yescharacteristic
73C2×C4⋊C4×D61C2211yescharacteristic
74C61×#544C411yescharacteristic, complemented
75C2×D61⋊C8C2311yescharacteristic
76C2×D61⋊C8C2311yescharacteristic
77C2×D61⋊C8C2311yescharacteristic
78C2×D61⋊C8C2311yescharacteristic
79C2×C4⋊#6923—21no—
80C2×C4⋊#6923—21no—
81C2×C4⋊#6923C2311yescharacteristic
82C2×C4⋊#6923C2311yescharacteristic
83C2×C4⋊#6923C2311yescharacteristic
84C2×C4⋊#6923C2311yescharacteristic
85C2×C22⋊#6923—21no—
86C2×C22⋊#6923—21no—
87C2×C4×#6923—21no—
88C2×C4×#6923—21no—
89#14519844—21no—
90#14519844—21no—
91C4⋊#92420—21no—
92C4⋊#92420—21no—
93#14519834—21no—
94#14519834—21no—
95C22⋊#92420—21no—
96C22⋊#92420—21no—
97#14519832—21no—
98#14519832—21no—
99C4×#92420—21no—
100C4×#92420—21no—
101(C2×#6923)⋊C4—21no—
102(C2×#6923)⋊C4—21no—
103(C2×#6923)⋊C4—21no—
104(C2×#6923)⋊C4—21no—
105(C2×#6923)⋊C4—21no—
106(C2×#6923)⋊C4—21no—
107C2×Q8×D61—21no—
108C2×Q8×D61—21no—
109C22×C4×D61—21no—
110C22×C4×D61C2311yescharacteristic
111#14519777—21no—
112#14519777C2×C411yescharacteristic
113#14519777C2×C411yescharacteristic
114#14519776—21no—
115#14519776—21no—
116#14519776—21no—
117#14519776—21no—
118#14519776—21no—
119#14519776—21no—
120#14519776C2×C411yescharacteristic
121#14519776C2×C411yescharacteristic
122#14519776C2×C411yescharacteristic
123#14519776C2×C411yescharacteristic
124#14519775—21no—
125#14519775—21no—
126#14519775—21no—
127#14519775—21no—
128#14519769—21no—
129#14519769C2×C411yescharacteristic
130#14519769C2×C411yescharacteristic
131#14519768—21no—
132#14519768—21no—
133#14519768C2×C411yescharacteristic
134#14519768C2×C411yescharacteristic
135#14519768C2×C411yescharacteristic
136#14519768C2×C411yescharacteristic
137#14519767—21no—
138#14519767—21no—
139#14519767—21no—
140#14519767—21no—
141#14519767—21no—
142#14519767—21no—
143#14519767—21no—
144#14519767—21no—
145#14519757—21no—
146#14519757—21no—
147#14519756—21no—
148#14519756—21no—
149#14519755—21no—
150#14519755—21no—
151#14519755—21no—
152#14519755—21no—
153#14519754—21no—
154#14519754—21no—
155#14519754—21no—
156#14519754—21no—
157#14519753—21no—
158#14519753—21no—
159#14519736C2×C411yescharacteristic
160#14519736C2×C411yescharacteristic
161#14519735C2×C411yescharacteristic
162#14519735C2×C411yescharacteristic
163#14519735D411yescharacteristic
164#14519735D411yescharacteristic
165#14519734—21no—
166#14519734C2×C411yescharacteristic
167#14519734C2×C411yescharacteristic
168#14519733—21no—
169#14519733D411yescharacteristic
170#14519733D411yescharacteristic
171C2×C4⋊Dic61C2×C411yescharacteristic
172C2×#11758196—21no—
173C4⋊C4×D61—21no—
174C4⋊C4×D61—21no—
175C4⋊C4×D61—21no—
176C4⋊C4×D61—21no—
177C4⋊C4×D61—21no—
178C4⋊C4×D61—21no—
179C4⋊C4×D61—21no—
180C4⋊C4×D61—21no—
181C4⋊C4×D61C2×C411yescharacteristic
182C4⋊C4×D61C2×C411yescharacteristic
183C4⋊C4×D61D411yescharacteristic
184C4⋊C4×D61D411yescharacteristic
185C4⋊C4×D61C2311yescharacteristic
186C4⋊C4×D61C2311yescharacteristic
187C4⋊C4×D61C2311yescharacteristic
188C4⋊C4×D61C2311yescharacteristic
189C22⋊C4×D61—21no—
190C22⋊C4×D61D411yescharacteristic
191C22⋊C4×D61D411yescharacteristic
192C42×D61—21no—
193C42×D61C2311yescharacteristic
194C42×D61C2311yescharacteristic
195C4⋊Q8×C61—21no—
196C4⋊Q8×C61C2×C411yescharacteristic
197C4⋊Q8×C61C2×C411yescharacteristic
198#125×C61—21no—
199#125×C61C2×C411yescharacteristic
200#125×C61C2×C411yescharacteristic
201C22⋊Q8×C61—21no—
202C22⋊Q8×C61—21no—
203#117×C61C2×C411yescharacteristic
204#117×C61C2×C411yescharacteristic
205C2×C4⋊C4×C61C2×C411yescharacteristic
206C23×D61C2×D411yescharacteristic
207C22×#6923—21no—
208C22×#6923—21no—
209C22×#6923—21no—
210C22×#6923—21no—
211C2×Q8×C61—21no—
212C2×Q8×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61C22×C411yescharacteristic
215C22×Dic61—21no—
216C22×Dic61C2×D411yescharacteristic
217Q8×D61—81no—
218Q8×D61—81no—
219Q8×D61—81no—
220Q8×D61—81no—
221C2×C4×D61—21no—
222C2×C4×D61—21no—
223C2×C4×D61—21no—
224C2×C4×D61—21no—
225C2×C4×D61—21no—
226C2×C4×D61—21no—
227C2×C4×D61—21no—
228C2×C4×D61—21no—
229C2×C4×D61—21no—
230C2×C4×D61—21no—
231C2×C4×D61—81no—
232C2×C4×D61—81no—
233C2×C4×D61C22×C411yescharacteristic
234C2×C4×D61C2×D411yescharacteristic
235C2×C4×D61C2×D411yescharacteristic
236C2×C4×D61C2×D411yescharacteristic
237C2×C4×D61C2×D411yescharacteristic
238C2×C4×D61C2×D411yescharacteristic
239C2×C4×D61C2×D411yescharacteristic
240C2×C4×D61C2411yescharacteristic
241C2×Dic122—21no—
242C2×Dic122—21no—
243C2×Dic122—21no—
244C2×Dic122—21no—
245C2×Dic122—21no—
246C2×Dic122—21no—
247C22⋊#6923—81no—
248C22⋊#6923—81no—
249C2×#92420—21no—
250C2×#92420—21no—
251C2×#92420—21no—
252C2×#92420—21no—
253C4⋊#6923—21no—
254C4⋊#6923—21no—
255C4⋊#6923—21no—
256C4⋊#6923—21no—
257C4⋊#6923—21no—
258C4⋊#6923—21no—
259C4⋊#6923—21no—
260C4⋊#6923—21no—
261C4⋊#6923—81no—
262C4⋊#6923—81no—
263C4×#6923—81no—
264C4×#6923—81no—
265D61⋊C8—21no—
266D61⋊C8—21no—
267D61⋊C8—21no—
268D61⋊C8—21no—
269D61⋊C8—21no—
270D61⋊C8—21no—
271D61⋊C8—21no—
272D61⋊C8—21no—
273C4⋊C4×C61—21no—
274C4⋊C4×C61—21no—
275C4⋊C4×C61—21no—
276C4⋊C4×C61—21no—
277C4⋊C4×C61—21no—
278C4⋊C4×C61—21no—
279C4⋊C4×C61—21no—
280C4⋊C4×C61C22⋊C411yescharacteristic
281C4⋊C4×C61C22⋊C411yescharacteristic
282C4⋊C4×C61C22×C411yescharacteristic
283C4⋊C4×C61C22×C411yescharacteristic
284C4⋊C4×C61C22×C411yescharacteristic
285C4⋊C4×C61C22×C411yescharacteristic
286C22⋊C4×C61—21no—
287C22⋊C4×C61C22⋊C411yescharacteristic
288C22⋊C4×C61C22⋊C411yescharacteristic
289C42×C61—21no—
290C42×C61C22×C411yescharacteristic
291C42×C61C22×C411yescharacteristic
292C22⋊Dic61—21no—
293C22⋊Dic61C22⋊C411yescharacteristic
294C22⋊Dic61C22⋊C411yescharacteristic
295#11758198—21no—
296#11758198—21no—
297#11758198C22⋊C411yescharacteristic
298#11758198C22⋊C411yescharacteristic
299#11758198C22⋊C411yescharacteristic
300#11758198C22⋊C411yescharacteristic
301C4⋊Dic61—21no—
302C4⋊Dic61—21no—
303C4⋊Dic61—21no—
304C4⋊Dic61—21no—
305C4⋊Dic61—21no—
306C4⋊Dic61—21no—
307C4⋊Dic61—21no—
308C4⋊Dic61C22⋊C411yescharacteristic
309C4⋊Dic61C22⋊C411yescharacteristic
310C4⋊Dic61C22×C411yescharacteristic
311C4⋊Dic61C22×C411yescharacteristic
312C4⋊Dic61C22×C411yescharacteristic
313C4⋊Dic61C22×C411yescharacteristic
314#11758196—21no—
315#11758196—21no—
316#11758196—21no—
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#11758196—21no—
327#11758196—21no—
328#11758196—21no—
329#11758196—21no—
330#11758196—21no—
331#11758196—21no—
332#11758196C22⋊C411yescharacteristic
333#11758196C22⋊C411yescharacteristic
334#11758196C22⋊C411yescharacteristic
335#11758196C22⋊C411yescharacteristic
336C4×Dic61—21no—
337C4×Dic61—21no—
338C4×Dic61—21no—
339C4×Dic61C22×C411yescharacteristic
340C4×Dic61C22×C411yescharacteristic
341C4×Dic61C2×D411yescharacteristic
342C4×Dic61C2×D411yescharacteristic
343C4×Dic61C2×D411yescharacteristic
344C4×Dic61C2×D411yescharacteristic
345C23×C61C2×C22⋊C411yescharacteristic
346C22×D61—21no—
347C22×D61—21no—
348C22×D61—21no—
349C22×D61—21no—
350C22×D61—21no—
351C22×D61—21no—
352C22×D61C2×C22⋊C411yescharacteristic
353C22×D61C22×D411yescharacteristic
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—41no—
364C2×#6923—41no—
365C2×#6923—41no—
366Q8×C61—81no—
367Q8×C61—81no—
368C2×C4×C61—21no—
369C2×C4×C61—21no—
370C2×C4×C61—21no—
371C2×C4×C61—21no—
372C2×C4×C61—21no—
373C2×C4×C61—21no—
374C2×C4×C61—81no—
375C2×C4×C61C2×C22⋊C411yescharacteristic
376C2×C4×C61C2×C22⋊C411yescharacteristic
377C2×C4×C61C2×C22⋊C411yescharacteristic
378C2×C4×C61C2×C22⋊C411yescharacteristic
379C2×C4×C61C2×C22⋊C411yescharacteristic
380C2×C4×C61C23×C411yescharacteristic
381C2×Dic61—21no—
382C2×Dic61—21no—
383C2×Dic61—21no—
384C2×Dic61—21no—
385C2×Dic61—21no—
386C2×Dic61—21no—
387C2×Dic61—81no—
388C2×Dic61C2×C22⋊C411yescharacteristic
389C2×Dic61C2×C22⋊C411yescharacteristic
390C2×Dic61C2×C22⋊C411yescharacteristic
391C2×Dic61C2×C22⋊C411yescharacteristic
392C2×Dic61C2×C22⋊C411yescharacteristic
393C2×Dic61C22×D411yescharacteristic
394C4×D61—21no—
395C4×D61—21no—
396C4×D61—21no—
397C4×D61—21no—
398C4×D61—21no—
399C4×D61—21no—
400C4×D61—21no—
401C4×D61—21no—
402C4×D61—21no—
403C4×D61—21no—
404C4×D61—21no—
405C4×D61—21no—
406C4×D61—21no—
407C4×D61—21no—
408C4×D61—41no—
409C4×D61—41no—
410C4×D61—41no—
411C4×D61—41no—
412C4×D61—41no—
413C4×D61—41no—
414C4×D61—41no—
415C4×D61—41no—
416C4×D61—81no—
417C4×D61—81no—
418C4×D612−1+411yescharacteristic
419C4×D612−1+411yescharacteristic
420C4×D612−1+411yescharacteristic
421C4×D612−1+411yescharacteristic
422Dic122—81no—
423Dic122—81no—
424Dic122—81no—
425Dic122—81no—
426Dic122—81no—
427Dic122—81no—
428#92420—41no—
429#92420—41no—
430#92420—41no—
431#92420—41no—
432#21843—611nomaximal, Sylow
433C22×C61—21no—
434C22×C61—21no—
435C22×C61—21no—
436C22×C61C22×C22⋊C411yescharacteristic
437C2×D61—21no—
438C2×D61—21no—
439C2×D61—21no—
440C2×D61—41no—
441C2×D61—41no—
442C2×D61—41no—
443C2×D61—41no—
444C2×D61#53611yescharacteristic
445C2×D61#53611yescharacteristic
446C2×D61#57611yescharacteristic
447C2×D61#57711yescharacteristic
448C2×D61#57711yescharacteristic
449C2×D61#57811yescharacteristic
450#6923—81no—
451#6923—81no—
452#6923—81no—
453#6923—81no—
454C4×C61—21no—
455C4×C61—21no—
456C4×C61—21no—
457C4×C61—21no—
458C4×C61—21no—
459C4×C61—41no—
460C4×C61—41no—
461C4×C61—41no—
462C4×C61—41no—
463C4×C61#51911yescharacteristic
464C4×C61#51911yescharacteristic
465Dic61—21no—
466Dic61—21no—
467Dic61—21no—
468Dic61—21no—
469Dic61—21no—
470Dic61—41no—
471Dic61—41no—
472Dic61—41no—
473Dic61—41no—
474Dic61#53611yescharacteristic
475Dic61#53611yescharacteristic
476C2×#544—611no—
477C2×#433—611no—
478#2314—611no—
479#1993—611no—
480#1992—611no—
481#1991—611no—
482#1990—611no—
483#1989—611no—
484#1989—611no—
485#1988—611no—
486#1987—611no—
487#1825—611no—
488#1825—611no—
489#1824—611no—
490#1823—611no—
491C2×C61—41no—
492C2×C61#231011yescharacteristic
493C2×C61#289711yescharacteristic
494C2×C61#289811yescharacteristic
495D61—41no—
496D61#324111yescharacteristic
497D61#324211yescharacteristic
498D61#324311yescharacteristic
499D61#324411yescharacteristic
500#544—611no—
501#544—611no—
502#544—611no—
503#544—611no—
504#544—611no—
505#544—611no—
506#544—611no—
507#544—1221no—
508#544—1221no—
509#544—1221no—
510#544—1221no—
511#544#692311yescharacteristic, complemented
512C2×C4⋊Q8—611no—
513C2×C4⋊Q8—611no—
514C2×C4⋊Q8—1221no—
515C2×#125—611no—
516C2×#125—611no—
517C2×#125—1221no—
518C2×C22⋊Q8—1221no—
519C2×C22⋊Q8—1221no—
520C2×#117—611no—
521C2×#117—611no—
522C22×C4⋊C4—611no—
523#433—1221no—
524#433—1221no—
525#433—1221no—
526#433—1221no—
527C2×C4⋊C8—611no—
528C2×C4⋊C8—611no—
529C2×C22⋊C8—611no—
530C2×C22⋊C8—611no—
531C2×#97—611no—
532C2×C4×C8—611no—
533#388—1221no—
534#388—1221no—
535#387—1221no—
536#387—1221no—
537#384—611no—
538#382—611no—
539#380—611no—
540#380—611no—
541C4×C4⋊C4—611no—
542C4×C4⋊C4—611no—
543#340—611no—
544#340—611no—
545#340—611no—
546#340—611no—
547#340—611no—
548#340—611no—
549#340—611no—
550#340—611no—
551#340—611no—
552#340—611no—
553#340—611no—
554#340—611no—
555#340—611no—
556#340—611no—
557#340—611no—
558#340—611no—
559C61#2184311yescharacteristic, complemented, Sylow
560C22×Q8—1221no—
561C22×Q8—1221no—
562C23×C4—611no—
563C23×C4—1221no—
564C22×C8—611no—
565C22×C8—611no—
566C22×C8—611no—
567C22×C8—611no—
568C4⋊Q8—21no—
569C4⋊Q8—611no—
570C4⋊Q8—611no—
571C4⋊Q8—611no—
572C4⋊Q8—611no—
573C4⋊Q8—611no—
574C4⋊Q8—611no—
575C4⋊Q8—1221no—
576C4⋊Q8—1221no—
577C4⋊Q8—1221no—
578C4⋊Q8—1221no—
579C4⋊Q8—1221no—
580C4⋊Q8—1221no—
581C4⋊Q8—1221no—
582C4⋊Q8—1221no—
583C4⋊Q8—1221no—
584C4⋊Q8—1221no—
585C4⋊Q8—1221no—
586C4⋊Q8C2×#692311yescharacteristic
587C4⋊Q8C2×#692311yescharacteristic
588#125—21no—
589#125—611no—
590#125—611no—
591#125—611no—
592#125—611no—
593#125—611no—
594#125—611no—
595#125—1221no—
596#125—1221no—
597#125—1221no—
598#125—1221no—
599#125—1221no—
600#125—1221no—
601#125—1221no—
602#125—1221no—
603#125—1221no—
604#125—1221no—
605#125—1221no—
606#125C2×#692311yescharacteristic
607#125C2×#692311yescharacteristic
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—1221no—
611C22⋊Q8—1221no—
612C22⋊Q8—1221no—
613C22⋊Q8—1221no—
614C22⋊Q8—1221no—
615C22⋊Q8—1221no—
616C22⋊Q8—1221no—
617C22⋊Q8—1221no—
618C22⋊Q8—1221no—
619C22⋊Q8—1221no—
620C22⋊Q8—1221no—
621C22⋊Q8—1221no—
622C22⋊Q8—1221no—
623C22⋊Q8—1221no—
624#117—611no—
625#117—611no—
626#117—611no—
627#117—611no—
628#117—611no—
629#117—611no—
630#117—611no—
631#117—611no—
632#117—611no—
633#117—611no—
634#117—1221no—
635#117—1221no—
636#117C2×#692311yescharacteristic
637#117C2×#692311yescharacteristic
638C2×C4⋊C4—611no—
639C2×C4⋊C4—611no—
640C2×C4⋊C4—611no—
641C2×C4⋊C4—611no—
642C2×C4⋊C4—611no—
643C2×C4⋊C4—611no—
644C2×C4⋊C4—611no—
645C2×C4⋊C4—611no—
646C2×C4⋊C4—611no—
647C2×C4⋊C4—611no—
648C2×C4⋊C4—611no—
649C2×C4⋊C4—611no—
650C2×C4⋊C4—611no—
651C2×C4⋊C4—1221no—
652C2×C4⋊C4—1221no—
653C2×C4⋊C4—1221no—
654C2×C4⋊C4—1221no—
655C2×C4⋊C4—1221no—
656C2×C4⋊C4—1221no—
657C2×C4⋊C4—1221no—
658C2×C4⋊C4—1221no—
659C2×C4⋊C4—1221no—
660C2×C4⋊C4—1221no—
661C2×C4⋊C4—1221no—
662C2×C4⋊C4C2×#692311yescharacteristic
663C2×C22⋊C4—611no—
664C2×C22⋊C4—611no—
665C2×C22⋊C4—1221no—
666C2×C22⋊C4—1221no—
667C2×C22⋊C4—1221no—
668C2×C42—611no—
669C2×C42—611no—
670C2×C42—1221no—
671C2×C42—1221no—
672C2×C42—1221no—
673C4⋊C8—1221no—
674C4⋊C8—1221no—
675C4⋊C8—1221no—
676C4⋊C8—1221no—
677C22⋊C8—1221no—
678C22⋊C8—1221no—
679C22⋊C8—1221no—
680C22⋊C8—1221no—
681#97—1221no—
682#97—1221no—
683C4×C8—1221no—
684C4×C8—1221no—
685#95—1221no—
686#95—1221no—
687#95—1221no—
688#95—1221no—
689#95—1221no—
690#95—1221no—
691C24—611no—
692C2×Q8—21no—
693C2×Q8—21no—
694C2×Q8—1221no—
695C2×Q8—1221no—
696C2×Q8—1221no—
697C2×Q8—1221no—
698C2×Q8—1221no—
699C2×Q8—1221no—
700C2×Q8—4881no—
701C2×Q8—4881no—
702C2×Q8—4881no—
703C2×Q8—4881no—
704C22×C4—21no—
705C22×C4—611no—
706C22×C4—611no—
707C22×C4—611no—
708C22×C4—611no—
709C22×C4—611no—
710C22×C4—611no—
711C22×C4—611no—
712C22×C4—611no—
713C22×C4—611no—
714C22×C4—1221no—
715C22×C4—1221no—
716C22×C4—1221no—
717C22×C4—1221no—
718C22×C4—1221no—
719C22×C4—1221no—
720C22×C4—1221no—
721C22×C4—1221no—
722C22×C4—1221no—
723C22×C4—1221no—
724C22×C4—1221no—
725C22×C4—1221no—
726C22×C4—1221no—
727C22×C4—1221no—
728C22×C4—1221no—
729C22×C4—4881no—
730C22×C4—4881no—
731C22×C4C22×#692311yescharacteristic
732C2×C8—1221no—
733C2×C8—1221no—
734C2×C8—1221no—
735C2×C8—1221no—
736C2×C8—1221no—
737C2×C8—1221no—
738C2×C8—1221no—
739C2×C8—1221no—
740C2×C8—1221no—
741C2×C8—1221no—
742C2×C8—1221no—
743C2×C8—1221no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—611no—
752C4⋊C4—611no—
753C4⋊C4—611no—
754C4⋊C4—611no—
755C4⋊C4—611no—
756C4⋊C4—611no—
757C4⋊C4—611no—
758C4⋊C4—611no—
759C4⋊C4—611no—
760C4⋊C4—611no—
761C4⋊C4—1221no—
762C4⋊C4—1221no—
763C4⋊C4—1221no—
764C4⋊C4—1221no—
765C4⋊C4—1221no—
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—1221no—
778C4⋊C4—1221no—
779C4⋊C4—1221no—
780C4⋊C4—1221no—
781C4⋊C4—1221no—
782C4⋊C4—1221no—
783C4⋊C4—1221no—
784C4⋊C4—1221no—
785C4⋊C4—1221no—
786C4⋊C4—1221no—
787C4⋊C4—1221no—
788C4⋊C4—1221no—
789C4⋊C4—1221no—
790C4⋊C4—1221no—
791C4⋊C4—1221no—
792C4⋊C4—1221no—
793C4⋊C4—1221no—
794C4⋊C4—4881no—
795C4⋊C4—4881no—
796C4⋊C4C22⋊#692311yescharacteristic
797C4⋊C4C22⋊#692311yescharacteristic
798C4⋊C4C22×#692311yescharacteristic
799C4⋊C4C22×#692311yescharacteristic
800C4⋊C4C22×#692311yescharacteristic
801C4⋊C4C22×#692311yescharacteristic
802C22⋊C4—21no—
803C22⋊C4—611no—
804C22⋊C4—611no—
805C22⋊C4—611no—
806C22⋊C4—611no—
807C22⋊C4—611no—
808C22⋊C4—611no—
809C22⋊C4—1221no—
810C22⋊C4—1221no—
811C22⋊C4—1221no—
812C22⋊C4—4881no—
813C22⋊C4—4881no—
814C22⋊C4C22⋊#692311yescharacteristic
815C22⋊C4C22⋊#692311yescharacteristic
816C42—21no—
817C42—611no—
818C42—611no—
819C42—611no—
820C42—611no—
821C42—611no—
822C42—611no—
823C42—1221no—
824C42—1221no—
825C42—1221no—
826C42—4881no—
827C42—4881no—
828C42C22×#692311yescharacteristic
829C42C22×#692311yescharacteristic
830C23—611no—
831C23—611no—
832C23—1221no—
833C23—1221no—
834C23—1221no—
835C23—1221no—
836C23—1221no—
837C23—1221no—
838C23C2×C22⋊#692311yescharacteristic
839Q8—81no—
840Q8—81no—
841Q8—4881no—
842Q8—4881no—
843Q8—4881no—
844Q8—4881no—
845Q8—4881no—
846Q8—4881no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—81no—
854C2×C4—611no—
855C2×C4—611no—
856C2×C4—611no—
857C2×C4—611no—
858C2×C4—611no—
859C2×C4—611no—
860C2×C4—611no—
861C2×C4—611no—
862C2×C4—611no—
863C2×C4—611no—
864C2×C4—1221no—
865C2×C4—1221no—
866C2×C4—1221no—
867C2×C4—1221no—
868C2×C4—1221no—
869C2×C4—1221no—
870C2×C4—1221no—
871C2×C4—1221no—
872C2×C4—1221no—
873C2×C4—1221no—
874C2×C4—1221no—
875C2×C4—1221no—
876C2×C4—1221no—
877C2×C4—1221no—
878C2×C4—1221no—
879C2×C4—1221no—
880C2×C4—1221no—
881C2×C4—1221no—
882C2×C4—1221no—
883C2×C4—1221no—
884C2×C4—4881no—
885C2×C4—4881no—
886C2×C4—4881no—
887C2×C4—2441no—
888C2×C4—2441no—
889C2×C4—2441no—
890C2×C4—2441no—
891C2×C4—2441no—
892C2×C4—2441no—
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×C4—2441no—
907C2×C4C2×C22⋊#692311yescharacteristic
908C2×C4C2×C22⋊#692311yescharacteristic
909C2×C4C2×C22⋊#692311yescharacteristic
910C2×C4C2×C22⋊#692311yescharacteristic
911C2×C4C2×C22⋊#692311yescharacteristic
912C2×C4C23×#692311yescharacteristic
913C8—2441no—
914C8—2441no—
915C8—2441no—
916C8—2441no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—611no—
921C22—611no—
922C22—611no—
923C22—611no—
924C22—611no—
925C22—611no—
926C22—1221no—
927C22—1221no—
928C22—1221no—
929C22—2441no—
930C22—2441no—
931C22—2441no—
932C22—2441no—
933C22C22×C22⋊#692311yescharacteristic
934C4—21no—
935C4—21no—
936C4—21no—
937C4—21no—
938C4—21no—
939C4—41no—
940C4—41no—
941C4—41no—
942C4—41no—
943C4—611no—
944C4—611no—
945C4—1221no—
946C4—1221no—
947C4—1221no—
948C4—1221no—
949C4—1221no—
950C4—4881no—
951C4—4881no—
952C4—4881no—
953C4—4881no—
954C4—2441no—
955C4—2441no—
956C4—2441no—
957C4—2441no—
958C4#1684083011yescharacteristic
959C4#1684083011yescharacteristic
960C2—41no—
961C2—611no—
962C2—611no—
963C2—611no—
964C2—611no—
965C2—2441no—
966C2#2146229311yescharacteristic
967C2#2146244011yescharacteristic
968C2#2146244111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#544C4
socleC22×C61C22×C22⋊C4
prime radicalC23×D61C2×D4
cosocleC2×C4×D61C24
hypercenter#544#6923
hypocenterC61#21843
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #544

Complements

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

NH ≅ G/Ntype
3. #21462003C2semidirect
4. #21462002C2semidirect
5. #21462001C2semidirect
6. #21462000C2semidirect
7. #21461999C2semidirect
8. #21461999C2semidirect
9. #21461998C2semidirect
10. #21461997C2semidirect
52. #16840393C4semidirect
54. #16840392C4semidirect
55. #16840392C4semidirect
58. #16840390C4semidirect
59. #16840390C4semidirect
61. #16840389C4semidirect
62. #16840389C4semidirect
74. C61×#544C4semidirect
511. #544#6923semidirect
559. C61#21843semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4332
#214622972
#214620032
#214620022
#214620012
#214620002
#214619992
#214619982
#214619972
#214617242
#214617232
#214617222
#544×D612
#2184361