Finite Group Databasebeta

← #30611293

Subgroups — #30611293

Order 15616.

1366 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462409C211yesmaximal, characteristic, complemented
2#21462322C211yesmaximal, characteristic, complemented
3#21461255C211yesmaximal, characteristic, complemented
4#21461245C212yesmaximal, complemented
5#21461234C211yesmaximal, characteristic, complemented
6#21461224C212yesmaximal, complemented
7#21461215C211yesmaximal, characteristic, complemented
8#21461205C212yesmaximal, complemented
9#21461194C211yesmaximal, characteristic, complemented
10C2×#16840613C212yesmaximal, complemented
11#21459481C211yesmaximal, characteristic
12C2×#14519864—21no—
13C2×D4×#6923—21no—
14#16840737—21no—
15#16840735—22no—
16#16840734C2212yescomplemented
17#16840733C2211yescharacteristic, complemented
18C2×#14519834C2212yescomplemented
19D61⋊(C22⋊C8)C2211yescharacteristic, complemented
20(C2×#6923)⋊Q8—21no—
21#16840710—22no—
22#16840705C2212yescomplemented
23#16840704C2211yescharacteristic, complemented
24C4×C22⋊#6923C2211yescharacteristic, complemented
25C2×(C2×#6923)⋊C4C2212yescomplemented
26#16840616C2211yescharacteristic, complemented
27#16840616C2211yescharacteristic, complemented
28#16840616C2212yescomplemented
29#16840613C2212yescomplemented
30#16840613C2212yescomplemented
31#16840613C2211yescharacteristic, complemented
32#16840613C2212yescomplemented
33#16840613C2212yescomplemented
34#16840613C2211yescharacteristic, complemented
35#16840613C2212yescomplemented
36C2×#41×D61C2211yescharacteristic
37#16840431—21no—
38#16840419—21no—
39#16840406—21no—
40#16840406—22no—
41D4×C22⋊D61—21no—
42D4×C22⋊D61—22no—
43#16840340C411yescharacteristic, complemented
44#16840340C412yescomplemented
45#16840329C411yescharacteristic, complemented
46#16840329C412yescomplemented
47#16840269C2211yescharacteristic
48#16840269C2212yes—
49C2×#14519748C2211yescharacteristic
50C2×#14519748C2212yes—
51#16840245C411yescharacteristic, complemented
52C2×H(5,𝔽2)×C61C411yescharacteristic, complemented
53C23×#6923—22no—
54#14519864—44no—
55C2×#11758213—21no—
56C2×#11758217—22no—
57C2×D61⋊C8—21no—
58C22×#92420—22no—
59D4×#6923—44no—
60C2×C4⋊#6923—21no—
61C2×C22⋊#6923—22no—
62C2×C22⋊#6923—21no—
63C2×C22⋊#6923—21no—
64C2×C4×#6923—21no—
65#14519834—22no—
66#14519834—22no—
67#14519834C2311yescharacteristic
68#14519834C2311yescharacteristic
69#14519834C2312yes—
70C22⋊#92420—21no—
71C22⋊#92420—21no—
72(C2×#6923)⋊C4—22no—
73(C2×#6923)⋊C4—22no—
74(C2×#6923)⋊C4C2312yes—
75(C2×#6923)⋊C4C2311yescharacteristic
76(C2×#6923)⋊C4C2311yescharacteristic
77C2×#11758226D411yescharacteristic
78C2×#11758222C2×C411yescharacteristic
79C2×#11758222C2×C412yes—
80C2×#11758224D411yescharacteristic
81C2×#11758224D412yes—
82#41×D61—44no—
83C2×Q8×D61D411yescharacteristic
84C22×C22⋊D61—22no—
85C22×C22⋊D61—21no—
86C2×D4×D61D411yescharacteristic
87C2×D4×D61D412yes—
88C22×C4×D61C2311yescharacteristic
89C22×C4×D61C2312yes—
90#14519773—21no—
91#14519773—22no—
92#14519764—21no—
93#14519764—22no—
94#14519758—22no—
95#14519758—21no—
96#14519756—21no—
97#14519756—22no—
98#14519753C2×C411yescharacteristic, complemented
99#14519753C2×C412yescomplemented
100#14519753C2311yescharacteristic
101#14519751—21no—
102#14519751—22no—
103#14519749—22no—
104#14519749—22no—
105#14519749—22no—
106#14519748—21no—
107#14519748—22no—
108#14519748—21no—
109#14519748—22no—
110#14519748C2×C412yescomplemented
111#14519748C2×C412yescomplemented
112#14519748C2×C412yescomplemented
113#14519748C2×C411yescharacteristic, complemented
114#14519748C2×C412yescomplemented
115#14519748C2312yes—
116#14519748C2311yescharacteristic
117#14519746—22no—
118#14519746—22no—
119#14519746—22no—
120#14519745—22no—
121#14519745—21no—
122Q8×Dic61—21no—
123D4×Dic61—22no—
124D4×Dic61—21no—
125C4×C22⋊D61—21no—
126C4×C22⋊D61—22no—
127C4×C22⋊D61—21no—
128C4×C22⋊D61—22no—
129#14519736C2×C411yescharacteristic, complemented
130#14519736C2×C412yescomplemented
131C2×C4⋊Dic61C2×C411yescharacteristic, complemented
132C2×C4⋊Dic61C2×C412yescomplemented
133C2×C22⋊Dic61—22no—
134C2×C22⋊Dic61—21no—
135H(5,𝔽2)×C61—44no—
136C2×#41×C61—21no—
137C2×#41×C61C2×C411yescharacteristic
138C2×#41×C61C2×C412yescomplemented
139C2×#41×C61C2×C411yescharacteristic, complemented
140C22×D4×C61—22no—
141C22×D4×C61—21no—
142C22×D4×C61C2×C412yescomplemented
143C22×D4×C61C2×C411yescharacteristic, complemented
144C24×C61—21no—
145C24×C61—22no—
146C23×D61C2×D412yes—
147C23×D61C2×D411yescharacteristic
148C22×#6923—21no—
149C22×#6923—21no—
150C22×#6923—22no—
151C22×#6923—44no—
152C22×#6923—44no—
153C22×#6923—82no—
154#41×C61—24no—
155#41×C61—44no—
156#41×C61—42no—
157#41×C61—44no—
158C2×Q8×C61C22⋊C411yescharacteristic
159C2×Q8×C61C22×C411yescharacteristic
160C2×D4×C61—21no—
161C2×D4×C61—22no—
162C2×D4×C61—22no—
163C2×D4×C61—21no—
164C2×D4×C61—44no—
165C2×D4×C61—42no—
166C2×D4×C61—48no—
167C2×D4×C61—44no—
168C2×D4×C61C22⋊C412yes—
169C2×D4×C61C22⋊C411yescharacteristic
170C2×D4×C61C22×C411yescharacteristic
171C2×D4×C61C22×C412yes—
172C22×C4×C61—22no—
173C22×C4×C61—21no—
174C22×C4×C61C22×C412yes—
175C22×C4×C61C22×C411yescharacteristic
176C2×C22⋊D61—21no—
177C2×C22⋊D61—22no—
178C2×C22⋊D61—22no—
179C2×C22⋊D61—22no—
180C2×C22⋊D61—22no—
181C2×C22⋊D61—21no—
182C2×C22⋊D61—22no—
183C2×C22⋊D61—82no—
184C2×C22⋊D61—81no—
185C2×C22⋊D61—82no—
186C2×C22⋊D61—81no—
187C2×C22⋊D61C22⋊C412yes—
188C2×C22⋊D61C22⋊C412yes—
189C2×C22⋊D61C22⋊C412yes—
190C22×Dic61—21no—
191C22×Dic61—22no—
192C22×Dic61C2×D412yes—
193C22×Dic61C2×D411yescharacteristic
194#11758226—42no—
195Q8×D61—42no—
196#11758224—24no—
197#11758224—44no—
198D4×D61—24no—
199D4×D61—44no—
200#11758222—42no—
201#11758222—44no—
202C2×D244C22⋊C411yescharacteristic
203C2×D244C22⋊C412yes—
204C2×C4×D61—42no—
205C2×C4×D61—44no—
206C2×C4×D61C22×C411yescharacteristic
207C2×C4×D61C22×C412yes—
208C2×C4×D61C2×D411yescharacteristic
209C2×C4×D61C2×D411yescharacteristic
210C2×C4×D61C2×D412yes—
211C2×C4×D61C2×D412yes—
212C2×C4×D61C2411yescharacteristic
213C2×Dic122C22⋊C411yescharacteristic
214C2×Dic122C22⋊C412yes—
215C22⋊#6923—42no—
216C22⋊#6923—44no—
217C22⋊#6923—81no—
218#11758217—44no—
219C2×#92420—21no—
220C2×#92420—22no—
221C2×#92420—21no—
222C2×#92420—44no—
223C4⋊#6923—42no—
224C4×#6923—42no—
225#11758213—42no—
226D61⋊C8—42no—
227C22⋊Dic61—21no—
228C22⋊Dic61—22no—
229C22⋊Dic61—22no—
230C22⋊Dic61—22no—
231C22⋊Dic61—22no—
232C22⋊Dic61—22no—
233C22⋊Dic61—21no—
234C22⋊Dic61—21no—
235C22⋊Dic61—22no—
236#11758198—21no—
237#11758198—22no—
238#11758198—21no—
239C4⋊Dic61—22no—
240C4⋊Dic61—21no—
241C4⋊Dic61C22×C412yes—
242C4⋊Dic61C22×C411yescharacteristic
243C4⋊Dic61C22×C411yescharacteristic
244#11758196—22no—
245#11758196—21no—
246#11758196—21no—
247C4×Dic61—22no—
248C4×Dic61—21no—
249C23×C61—22no—
250C23×C61—21no—
251C23×C61—42no—
252C23×C61—44no—
253C23×C61—82no—
254C23×C61—81no—
255C23×C61—82no—
256C23×C61—81no—
257C23×C61C2×C22⋊C411yescharacteristic
258C23×C61C2×C22⋊C412yes—
259C22×D61—24no—
260C22×D61—22no—
261C22×D61—22no—
262C22×D61—21no—
263C22×D61—21no—
264C22×D61—42no—
265C22×D61—41no—
266C22×D61—41no—
267C22×D61C2×C22⋊C411yescharacteristic
268C22×D61C2×C22⋊C412yes—
269C22×D61C22×D411yescharacteristic
270C2×#6923—22no—
271C2×#6923—41no—
272C2×#6923—41no—
273C2×#6923—41no—
274C2×#6923—42no—
275C2×#6923—41no—
276C2×#6923—42no—
277C2×#6923—42no—
278C2×#6923—41no—
279C2×#6923—88no—
280Q8×C61—22no—
281Q8×C61—41no—
282D4×C61—24no—
283D4×C61—41no—
284D4×C61—42no—
285D4×C61—44no—
286D4×C61—42no—
287D4×C61—44no—
288D4×C61—42no—
289D4×C61#9914yes—
290C2×C4×C61—24no—
291C2×C4×C61—22no—
292C2×C4×C61—21no—
293C2×C4×C61—44no—
294C2×C4×C61—42no—
295C2×C4×C61C2×C22⋊C412yes—
296C2×C4×C61C2×C22⋊C411yescharacteristic
297C2×C4×C61C23×C411yescharacteristic
298C22⋊D61—24no—
299C22⋊D61—24no—
300C22⋊D61—42no—
301C22⋊D61—41no—
302C22⋊D61—42no—
303C22⋊D61—41no—
304C22⋊D61—42no—
305C22⋊D61—82no—
306C22⋊D61—81no—
307C22⋊D61—82no—
308C22⋊D61—82no—
309C22⋊D61—82no—
310C2×Dic61—24no—
311C2×Dic61—21no—
312C2×Dic61—22no—
313C2×Dic61—21no—
314C2×Dic61—41no—
315C2×Dic61—82no—
316C2×Dic61—81no—
317C2×Dic61C2×C22⋊C412yes—
318C2×Dic61C2×C22⋊C411yescharacteristic
319C2×Dic61C22×D411yescharacteristic
320D244—22no—
321D244—42no—
322C4×D61—22no—
323C4×D61—22no—
324C4×D61—41no—
325C4×D61—42no—
326C4×D61—41no—
327C4×D61—42no—
328C4×D61—42no—
329Dic122—22no—
330Dic122—42no—
331#92420—41no—
332#92420—41no—
333#92420—42no—
334#17603—611nomaximal, Sylow
335C22×C61—22no—
336C22×C61—22no—
337C22×C61—21no—
338C22×C61—21no—
339C22×C61—21no—
340C22×C61—42no—
341C22×C61—41no—
342C22×C61—41no—
343C22×C61—42no—
344C22×C61—41no—
345C22×C61—42no—
346C22×C61—164no—
347C22×C61—162no—
348C22×C61C2×#9914yes—
349C22×C61C22×C22⋊C411yescharacteristic
350C2×D61—21no—
351C2×D61—21no—
352C2×D61—21no—
353C2×D61—22no—
354C2×D61—22no—
355C2×D61—21no—
356C2×D61—22no—
357C2×D61—21no—
358C2×D61—44no—
359C2×D61—44no—
360C2×D61—81no—
361C2×D61—81no—
362C2×D61#57611yescharacteristic
363C2×D61#57711yescharacteristic
364#6923—42no—
365#6923—81no—
366#6923—82no—
367C4×C61—22no—
368C4×C61—21no—
369C4×C61—41no—
370C4×C61C2×#9912yes—
371Dic61—21no—
372Dic61—22no—
373Dic61—21no—
374Dic61—41no—
375Dic61—42no—
376Dic61—41no—
377#3488—611no—
378#2880—611no—
379#2339—611no—
380#1519—611no—
381#1516—612no—
382#1513—611no—
383#1510—612no—
384#1507—611no—
385#1504—612no—
386#1501—611no—
387C2×#327—612no—
388C2×C61—24no—
389C2×C61—41no—
390C2×C61—81no—
391C2×C61—82no—
392C2×C61C22×#9911yescharacteristic
393C2×C61#289711yescharacteristic
394C2×C61#290111yescharacteristic
395D61—21no—
396D61—21no—
397D61—42no—
398D61—41no—
399C2×H(5,𝔽2)#692311yescharacteristic, complemented
400C22×#41—611no—
401C2×#131—1221no—
402#550—1221no—
403#548—1221no—
404#546—1221no—
405#546—1222no—
406D42—1221no—
407D42—1222no—
408#537—612no—
409#537—611no—
410#535—611no—
411#535—612no—
412#525—611no—
413#525—612no—
414C2×#121—612no—
415C2×#121—611no—
416#520—611no—
417C2×C4×D4—1221no—
418#408—1222no—
419#408—1221no—
420#407—611no—
421#407—612no—
422C2×C22⋊C8—611no—
423C2×C22⋊C8—612no—
424#391—1221no—
425#386—1222no—
426#381—612no—
427#380—611no—
428C4×C22⋊C4—611no—
429C2×#95—612no—
430#328—611no—
431#328—611no—
432#328—612no—
433#327—611no—
434#327—612no—
435#327—612no—
436#327—612no—
437#327—611no—
438#327—612no—
439#327—612no—
440C61#1760311yescharacteristic, complemented, Sylow
441H(5,𝔽2)—44no—
442C2×#41—21no—
443C2×#41—611no—
444C2×#41—611no—
445C2×#41—612no—
446C2×#41—612no—
447C2×#41—611no—
448C2×#41—2444no—
449C2×#41C2×#692311yescharacteristic
450C2×#41C2×#692312yescomplemented
451C2×#41C2×#692311yescharacteristic, complemented
452C22×Q8—611no—
453C22×D4—22no—
454C22×D4—21no—
455C22×D4—611no—
456C22×D4—612no—
457C22×D4—1222no—
458C22×D4—1221no—
459C22×D4C2×#692312yescomplemented
460C22×D4C2×#692311yescharacteristic, complemented
461C23×C4—612no—
462C23×C4—611no—
463C23×C4—1222no—
464#131—2444no—
465C2×M16—1222no—
466C2×M16—1221no—
467C22×C8—1222no—
468C22×C8—1221no—
469#127—1221no—
470#127—1222no—
471#124—1221no—
472#124—1222no—
473#123—1222no—
474#123—1221no—
475C22⋊Q8—611no—
476C22⋊Q8—611no—
477C22⋊Q8—612no—
478C22⋊Q8—1221no—
479C22⋊Q8—1222no—
480#121—611no—
481#121—612no—
482#121—612no—
483#121—612no—
484#121—612no—
485#121—611no—
486#121—612no—
487#121—1221no—
488#121—1222no—
489#121—1221no—
490#121—1222no—
491#121—1221no—
492#121—1222no—
493#121—1222no—
494#121—1222no—
495#121—1222no—
496#120—1222no—
497#120—1221no—
498#120—1222no—
499#120—1222no—
500#120—1222no—
501C4×Q8—1221no—
502C4×D4—1221no—
503C4×D4—1222no—
504C4×D4—1221no—
505C4×D4—1222no—
506C4×D4—1222no—
507C4×D4—1221no—
508C4×D4—2444no—
509#117—611no—
510#117—612no—
511C2×C4⋊C4—612no—
512C2×C4⋊C4—611no—
513C2×C4⋊C4—1221no—
514C2×C22⋊C4—1222no—
515C2×C22⋊C4—1221no—
516C2×C22⋊C4—1221no—
517C2×C22⋊C4—1222no—
518C2×C22⋊C4—1221no—
519C2×C42—1221no—
520C22⋊C8—611no—
521C22⋊C8—611no—
522C22⋊C8—612no—
523C22⋊C8—1221no—
524C22⋊C8—1221no—
525C22⋊C8—1222no—
526C22⋊C8—1222no—
527#95—611no—
528#95—612no—
529#95—611no—
530#95—1222no—
531#95—1222no—
532C24—21no—
533C24—22no—
534C24—612no—
535C24—611no—
536#41—24no—
537#41—44no—
538#41—42no—
539#41—44no—
540#41—1224no—
541#41—2444no—
542#41—2442no—
543#41—2444no—
544#41—2442no—
545C2×Q8—611no—
546C2×Q8—612no—
547C2×Q8—2442no—
548C2×Q8C22⋊#692311yescharacteristic
549C2×Q8C22×#692311yescharacteristic
550C2×D4—21no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—21no—
554C2×D4—44no—
555C2×D4—42no—
556C2×D4—48no—
557C2×D4—44no—
558C2×D4—612no—
559C2×D4—612no—
560C2×D4—612no—
561C2×D4—611no—
562C2×D4—612no—
563C2×D4—1224no—
564C2×D4—1221no—
565C2×D4—1222no—
566C2×D4—1222no—
567C2×D4—1222no—
568C2×D4—1222no—
569C2×D4—1221no—
570C2×D4—1222no—
571C2×D4—4881no—
572C2×D4—4881no—
573C2×D4—4882no—
574C2×D4—4882no—
575C2×D4—2444no—
576C2×D4C22⋊#692312yes—
577C2×D4C22⋊#692311yescharacteristic
578C2×D4C22×#692311yescharacteristic
579C2×D4C22×#692312yes—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—612no—
583C22×C4—611no—
584C22×C4—611no—
585C22×C4—611no—
586C22×C4—612no—
587C22×C4—612no—
588C22×C4—611no—
589C22×C4—612no—
590C22×C4—611no—
591C22×C4—1221no—
592C22×C4—1222no—
593C22×C4—1221no—
594C22×C4—1221no—
595C22×C4—1222no—
596C22×C4—4882no—
597C22×C4—2442no—
598C22×C4—2444no—
599C22×C4—2444no—
600C22×C4—2444no—
601C22×C4C22×#692312yes—
602C22×C4C22×#692311yescharacteristic
603M16—2442no—
604M16—2444no—
605C2×C8—1221no—
606C2×C8—1221no—
607C2×C8—1222no—
608C2×C8—2442no—
609C2×C8—2444no—
610C4⋊C4—611no—
611C4⋊C4—612no—
612C4⋊C4—611no—
613C4⋊C4—1221no—
614C4⋊C4—1221no—
615C4⋊C4—1222no—
616C4⋊C4—1222no—
617C4⋊C4—1221no—
618C4⋊C4—2442no—
619C22⋊C4—1221no—
620C22⋊C4—1221no—
621C22⋊C4—1222no—
622C22⋊C4—1221no—
623C22⋊C4—1222no—
624C22⋊C4—1222no—
625C22⋊C4—1222no—
626C22⋊C4—1222no—
627C22⋊C4—1221no—
628C22⋊C4—1222no—
629C22⋊C4—1221no—
630C22⋊C4—1222no—
631C22⋊C4—4881no—
632C22⋊C4—2442no—
633C22⋊C4—2444no—
634C42—1222no—
635C42—1221no—
636C42—2442no—
637C23—22no—
638C23—21no—
639C23—42no—
640C23—44no—
641C23—82no—
642C23—81no—
643C23—82no—
644C23—81no—
645C23—611no—
646C23—611no—
647C23—612no—
648C23—1221no—
649C23—1221no—
650C23—1222no—
651C23—1222no—
652C23—1224no—
653C23—2441no—
654C23—2441no—
655C23—2442no—
656C23C2×C22⋊#692311yescharacteristic
657C23C2×C22⋊#692312yes—
658Q8—22no—
659Q8—41no—
660Q8—1222no—
661Q8—2442no—
662D4—24no—
663D4—41no—
664D4—42no—
665D4—44no—
666D4—42no—
667D4—44no—
668D4—42no—
669D4—1224no—
670D4—1224no—
671D4—1222no—
672D4—4881no—
673D4—4882no—
674D4—4882no—
675D4—4882no—
676D4—4882no—
677D4—2442no—
678D4—2442no—
679D4—2442no—
680D4—2441no—
681D4—2442no—
682D4—2441no—
683D4#1451983514yes—
684C2×C4—24no—
685C2×C4—22no—
686C2×C4—21no—
687C2×C4—44no—
688C2×C4—42no—
689C2×C4—611no—
690C2×C4—612no—
691C2×C4—611no—
692C2×C4—1224no—
693C2×C4—1222no—
694C2×C4—1222no—
695C2×C4—1222no—
696C2×C4—1221no—
697C2×C4—1222no—
698C2×C4—1221no—
699C2×C4—4888no—
700C2×C4—4882no—
701C2×C4—4881no—
702C2×C4—2441no—
703C2×C4—2442no—
704C2×C4—2441no—
705C2×C4—2442no—
706C2×C4—2442no—
707C2×C4—2441no—
708C2×C4—2442no—
709C2×C4—2441no—
710C2×C4—2441no—
711C2×C4—2442no—
712C2×C4—2441no—
713C2×C4—2442no—
714C2×C4—2441no—
715C2×C4—2441no—
716C2×C4C2×C22⋊#692312yes—
717C2×C4C2×C22⋊#692311yescharacteristic
718C2×C4C23×#692311yescharacteristic
719C8—2441no—
720C8—2441no—
721C8—2442no—
722C22—22no—
723C22—22no—
724C22—21no—
725C22—21no—
726C22—21no—
727C22—42no—
728C22—41no—
729C22—41no—
730C22—42no—
731C22—41no—
732C22—42no—
733C22—164no—
734C22—162no—
735C22—611no—
736C22—611no—
737C22—1221no—
738C22—1221no—
739C22—1221no—
740C22—1222no—
741C22—1221no—
742C22—1222no—
743C22—1221no—
744C22—1222no—
745C22—4881no—
746C22—4881no—
747C22—2444no—
748C22—2444no—
749C22C2×#1451983514yes—
750C22C22×C22⋊#692311yescharacteristic
751C4—21no—
752C4—22no—
753C4—41no—
754C4—1221no—
755C4—1221no—
756C4—1222no—
757C4—4882no—
758C4—4881no—
759C4—2442no—
760C4—2441no—
761C4—2442no—
762C4—2441no—
763C4C2×#1451983512yes—
764C2—24no—
765C2—41no—
766C2—81no—
767C2—82no—
768C2—1221no—
769C2—1221no—
770C2—2441no—
771C2—2442no—
772C2C22×#1451983511yescharacteristic
773C2#2146244011yescharacteristic
774C2#2146244911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×H(5,𝔽2)×C61C4
socleC22×C61C22×C22⋊C4
prime radical#21459481C2
cosocleC2×C4×D61C24
hypercenterC2×H(5,𝔽2)#6923
hypocenterC61#17603
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #21462409C2semidirect
2. #21462322C2semidirect
3. #21461255C2semidirect
4. #21461245C2semidirect
5. #21461234C2semidirect
6. #21461224C2semidirect
7. #21461215C2semidirect
8. #21461205C2semidirect
9. #21461194C2semidirect
10. C2×#16840613C2semidirect
16. #16840734C22semidirect
17. #16840733C22semidirect
18. C2×#14519834C22semidirect
19. D61⋊(C22⋊C8)C22semidirect
22. #16840705C22semidirect
23. #16840704C22semidirect
24. C4×C22⋊#6923C22semidirect
25. C2×(C2×#6923)⋊C4C22semidirect
26. #16840616C22semidirect
27. #16840616C22semidirect
28. #16840616C22semidirect
29. #16840613C22semidirect
30. #16840613C22semidirect
31. #16840613C22semidirect
32. #16840613C22semidirect
33. #16840613C22semidirect
34. #16840613C22semidirect
35. #16840613C22semidirect
43. #16840340C4semidirect
44. #16840340C4semidirect
45. #16840329C4semidirect
46. #16840329C4semidirect
51. #16840245C4semidirect
52. C2×H(5,𝔽2)×C61C4semidirect
98. #14519753C2×C4semidirect
99. #14519753C2×C4semidirect
110. #14519748C2×C4semidirect
111. #14519748C2×C4semidirect
112. #14519748C2×C4semidirect
113. #14519748C2×C4semidirect
114. #14519748C2×C4semidirect
129. #14519736C2×C4semidirect
130. #14519736C2×C4semidirect
131. C2×C4⋊Dic61C2×C4semidirect
132. C2×C4⋊Dic61C2×C4semidirect
138. C2×#41×C61C2×C4semidirect
139. C2×#41×C61C2×C4semidirect
142. C22×D4×C61C2×C4semidirect
143. C22×D4×C61C2×C4semidirect
399. C2×H(5,𝔽2)#6923semidirect
440. C61#17603semidirect
450. C2×#41C2×#6923semidirect
451. C2×#41C2×#6923semidirect
459. C22×D4C2×#6923semidirect
460. C22×D4C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214624092
#214623222
#214612552
#214612452
#214612342
#214612242
#214612152
#214612052
#214611942
C2×#168406132
#214594812
#1760361