Finite Group Databasebeta

← #29700870

Subgroups — #29700870

Order 15616.

1074 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839928C211yesmaximal, characteristic
2#21454652C211yesmaximal, characteristic, complemented
3#21454645C211yesmaximal, characteristic, complemented
4#21454346C211yesmaximal, characteristic, complemented
5#21454343C211yesmaximal, characteristic, complemented
6#21446623C211yesmaximal, characteristic, complemented
7#21446482C211yesmaximal, characteristic, complemented
8#21446479C211yesmaximal, characteristic, complemented
9#21446324C211yesmaximal, characteristic, complemented
10#21446215C211yesmaximal, characteristic, complemented
11#21446048C211yesmaximal, characteristic, complemented
12#21446043C211yesmaximal, characteristic, complemented
13#21445655C211yesmaximal, characteristic, complemented
14#21445654C211yesmaximal, characteristic, complemented
15C61×#1907C211yesmaximal, characteristic, complemented
16C2×#14519823C2211yescharacteristic
17C2×#14519803C2211yescharacteristic
18C2×#14519785C2211yescharacteristic
19C2×#14519773C2211yescharacteristic
20#16840245C2211yescharacteristic
21#16840243C2211yescharacteristic
22#16840237C2211yescharacteristic, complemented
23#16839928C418yescomplemented
24#16839874—21no—
25#16839871—21no—
26#16839863—21no—
27#16839859—21no—
28#16839853—21no—
29SD16×Dic61—21no—
30D8×Dic61—21no—
31#16839842—21no—
32#16839804C2211yescharacteristic, complemented
33#16839802C2211yescharacteristic, complemented
34C2×#14519704C2211yescharacteristic
35C2×#14519703C2211yescharacteristic
36#16839768—21no—
37#16839768C2211yescharacteristic
38#16839768C2211yescharacteristic
39#16839765—21no—
40#16839764—21no—
41#16839764C2211yescharacteristic
42#16839762—21no—
43#16839759—21no—
44#16839759C2211yescharacteristic
45#16839758C2211yescharacteristic
46#16839757—21no—
47C2×#14519699—21no—
48C2×#14519699C2211yescharacteristic
49C2×#14519698C2211yescharacteristic, complemented
50C2×#14519697C2211yescharacteristic
51#102×D61—21no—
52C2×#14519693C2211yescharacteristic
53#16839720C2211yescharacteristic, complemented
54#16839717C2211yescharacteristic, complemented
55C2×C8×Dic61C2211yescharacteristic, complemented
56#16839631C2211yescharacteristic, complemented
57#16839530C2211yescharacteristic, complemented
58#16839526C2211yescharacteristic, complemented
59#16839523C2211yescharacteristic, complemented
60#16839523C2211yescharacteristic, complemented
61C2×AGL(1,ℤ/8)×C61C2211yescharacteristic
62C2×#131×C61C2211yescharacteristic
63C61×#417C2211yescharacteristic
64C2×#102×C61C2211yescharacteristic, complemented
65C2×#100×C61C2211yescharacteristic, complemented
66C61×#343C2211yescharacteristic, complemented
67C61×#341C2211yescharacteristic, complemented
68#14519823—22no—
69#14519823—22no—
70#14519823—41no—
71#14519823C2×C414yescomplemented
72C2×#11758226—21no—
73C2×#11758222—21no—
74C2×#11758222C2311yescharacteristic
75C22×D244—21no—
76C22×D244C2311yescharacteristic
77C22×C22⋊D61—41no—
78C2×D4×D61—21no—
79C2×D4×D61—41no—
80#14519803—22no—
81#14519803C2×C414yescomplemented
82C2×#11758200—21no—
83C2×#11758199—21no—
84#14519785—22no—
85#14519785—41no—
86C2×#11758194C2311yescharacteristic
87C2×#11758189—21no—
88C22×#92418C2311yescharacteristic
89C2×C8×D61—21no—
90#14519773—41no—
91#14519773C2×C414yescomplemented
92Q8×Dic61—21no—
93#14519742—21no—
94D4×Dic61—21no—
95D4×Dic61—21no—
96D4×Dic61—21no—
97D4×Dic61—21no—
98D4×Dic61—21no—
99D4×Dic61—41no—
100#14519739—21no—
101C4×C22⋊D61—41no—
102#14519736—21no—
103#14519736C2311yescharacteristic
104#14519736C2311yescharacteristic
105#14519735—21no—
106C2×C4⋊Dic61—21no—
107C2×C4⋊Dic61C2311yescharacteristic
108C2×#11758196—41no—
109C4⋊C4×D61—21no—
110C2×C22⋊Dic61—41no—
111C2×C4×Dic61C2311yescharacteristic
112#14519711—21no—
113#14519710—21no—
114#14519709—21no—
115#14519708—21no—
116#14519704C2×C414yescomplemented
117#14519703C2×C414yescomplemented
118#14519702—21no—
119#14519702D411yescharacteristic, complemented
120#14519702D411yescharacteristic, complemented
121#14519701D411yescharacteristic, complemented
122#14519701D411yescharacteristic, complemented
123#14519699—21no—
124#14519699—21no—
125#14519699—21no—
126#14519699—21no—
127#14519699—21no—
128#14519699—21no—
129#14519699—21no—
130#14519699D411yescharacteristic, complemented
131#14519699D411yescharacteristic, complemented
132#14519698—21no—
133#14519698—21no—
134#14519698D411yescharacteristic, complemented
135#14519698D411yescharacteristic, complemented
136#14519697—21no—
137#14519697—21no—
138#14519693C2×C414yescomplemented
139#14519687—21no—
140#14519687—21no—
141C8×Dic61—21no—
142C8×Dic61—21no—
143C8×Dic61—41no—
144C2×#41×C61C2311yescharacteristic
145C22×D4×C61C2311yescharacteristic
146AGL(1,ℤ/8)×C61—22no—
147AGL(1,ℤ/8)×C61C2×C414yescomplemented
148C2×SD16×C61—21no—
149C2×D8×C61—21no—
150#131×C61—22no—
151#131×C61—41no—
152C2×M16×C61—21no—
153C2×M16×C61C2311yescharacteristic
154C2×M16×C61C2311yescharacteristic
155C2×M16×C61C2311yescharacteristic
156C22×C8×C61—21no—
157C22×C8×C61C2311yescharacteristic
158C2×C4⋊C4×C61C2311yescharacteristic
159#103×C61—21no—
160#102×C61—21no—
161#102×C61—21no—
162#102×C61—21no—
163#100×C61—41no—
164C24×C61—21no—
165C23×D61—21no—
166C23×D61—41no—
167#41×C61—21no—
168#41×C61—21no—
169#41×C61C22×C412yes—
170#41×C61#4112yes—
171C2×Q8×C61C2×D411yescharacteristic
172C2×D4×C61—21no—
173C2×D4×C61—21no—
174C2×D4×C61—21no—
175C2×D4×C61—21no—
176C2×D4×C61—21no—
177C2×D4×C61—21no—
178C2×D4×C61C22×C412yes—
179C2×D4×C61C2×D411yescharacteristic
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61C2411yescharacteristic
183C2×C22⋊D61—21no—
184C2×C22⋊D61—41no—
185C2×C22⋊D61—44no—
186C2×C22⋊D61—82no—
187C2×C22⋊D61—82no—
188C22×Dic61—21no—
189C22×Dic61—21no—
190C22×Dic61—41no—
191C22×Dic61—41no—
192C22×Dic61—41no—
193#11758226—24no—
194#11758226—42no—
195D4×D61—24no—
196D4×D61—42no—
197D4×D61—44no—
198D4×D61—44no—
199#11758222—21no—
200#11758222—21no—
201#11758222—24no—
202#11758222—42no—
203#11758222C22×C412yes—
204#11758222#4112yes—
205C2×D244—21no—
206C2×D244—21no—
207C2×D244—21no—
208C2×D244—21no—
209C2×D244—24no—
210C2×D244—21no—
211C2×D244—42no—
212C2×D244—41no—
213C2×D244C22×C412yes—
214C2×D244C2×D411yescharacteristic
215C2×C4×D61—21no—
216C2×C4×D61—41no—
217C2×C4×D61—41no—
218C2×Dic122C2×D411yescharacteristic
219SD16×C61—24no—
220D8×C61—24no—
221M16×C61—21no—
222M16×C61—21no—
223M16×C61—21no—
224M16×C61—21no—
225M16×C61—21no—
226M16×C61—42no—
227M16×C61C22×C412yes—
228C2×C8×C61—21no—
229C2×C8×C61—21no—
230C2×C8×C61—21no—
231C2×C8×C61—21no—
232C2×C8×C61—21no—
233C2×C8×C61—42no—
234C2×C8×C61C2×D411yescharacteristic
235C2×C8×C61C2×D411yescharacteristic
236C4⋊C4×C61—21no—
237C4⋊C4×C61—21no—
238C22⋊Dic61—21no—
239C22⋊Dic61—21no—
240C22⋊Dic61—41no—
241C22⋊Dic61—41no—
242C22⋊Dic61—41no—
243#11758200—24no—
244#11758199—24no—
245#11758198—41no—
246C4⋊Dic61—21no—
247C4⋊Dic61—21no—
248C4⋊Dic61—41no—
249C4⋊Dic61C2×D411yescharacteristic
250C4⋊Dic61C2×D411yescharacteristic
251C4⋊Dic61C2×D411yescharacteristic
252C4⋊Dic61C2×D411yescharacteristic
253#11758196—41no—
254#11758196—82no—
255C4×Dic61—21no—
256C4×Dic61—21no—
257C4×Dic61—21no—
258C4×Dic61—41no—
259C4×Dic61—41no—
260C4×Dic61C22×C412yes—
261#11758194—21no—
262#11758194C22×C412yes—
263C2×#92418—21no—
264C2×#92418—21no—
265C2×#92418—21no—
266C2×#92418C2×D411yescharacteristic
267C2×#92418C2×D411yescharacteristic
268#11758189—42no—
269C8×D61—42no—
270C23×C61—21no—
271C23×C61—22no—
272C23×C61—41no—
273C23×C61—41no—
274C23×C61—81no—
275C23×C61—81no—
276C23×C61H(5,𝔽2)11yescharacteristic
277C22×D61—21no—
278C22×D61—22no—
279C22×D61—44no—
280C22×D61—41no—
281C22×D61—41no—
282C22×D61—81no—
283C22×D61—81no—
284C22×D61—161no—
285C22×D61—161no—
286Q8×C61—21no—
287Q8×C61C4×D412yes—
288D4×C61—22no—
289D4×C61—22no—
290D4×C61—22no—
291D4×C61—22no—
292D4×C61—21no—
293D4×C61—41no—
294D4×C61—41no—
295D4×C61C4×D412yes—
296C2×C4×C61—21no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—41no—
300C2×C4×C61—81no—
301C2×C4×C61C23×C411yescharacteristic
302C2×C4×C61C22×D411yescharacteristic
303C2×C4×C61C22×D411yescharacteristic
304C2×C4×C61C2×#4111yescharacteristic
305C2×C4×C61C2×#4111yescharacteristic
306C2×C4×C61H(5,𝔽2)11yescharacteristic
307C22⋊D61—22no—
308C22⋊D61—22no—
309C22⋊D61—44no—
310C22⋊D61—88no—
311C2×Dic61—22no—
312C2×Dic61—22no—
313C2×Dic61—22no—
314C2×Dic61—21no—
315C2×Dic61—21no—
316C2×Dic61—21no—
317C2×Dic61—21no—
318C2×Dic61—21no—
319C2×Dic61—41no—
320C2×Dic61—81no—
321C2×Dic61—161no—
322C2×Dic61—161no—
323C2×Dic61—161no—
324D244—22no—
325D244—22no—
326D244—21no—
327D244—44no—
328D244—41no—
329D244—41no—
330D244C4×D412yes—
331C4×D61—22no—
332C4×D61—22no—
333C4×D61—44no—
334C4×D61—161no—
335Dic122—21no—
336Dic122C4×D412yes—
337C8×C61—22no—
338C8×C61—21no—
339C8×C61—21no—
340C8×C61—41no—
341C8×C61—41no—
342#92418—22no—
343#92418—21no—
344#92418—21no—
345#22897—611nomaximal, Sylow
346C22×C61—21no—
347C22×C61—21no—
348C22×C61—22no—
349C22×C61—41no—
350C22×C61—41no—
351C22×C61—42no—
352C22×C61—82no—
353C22×C61—81no—
354C22×C61—81no—
355C22×C61—161no—
356C22×C61#51811yescharacteristic
357C22×C61D4211yescharacteristic
358C22×C61#55111yescharacteristic
359C2×D61—22no—
360C2×D61—41no—
361C2×D61—41no—
362C2×D61—42no—
363C2×D61—81no—
364C2×D61—81no—
365C2×D61—82no—
366C2×D61—164no—
367C2×D61—161no—
368C4×C61—22no—
369C4×C61—81no—
370C4×C61C2×C4×D411yescharacteristic
371C4×C61C2×C4×D411yescharacteristic
372C4×C61#54611yescharacteristic
373C4×C61#54611yescharacteristic
374Dic61—24no—
375Dic61—22no—
376Dic61—41no—
377Dic61—41no—
378Dic61—41no—
379Dic61—41no—
380Dic61—81no—
381C2×#453—611no—
382#2946—611no—
383#2946—611no—
384#2897—611no—
385#2897—611no—
386#1957—611no—
387#1931—611no—
388#1931—611no—
389#1907—611no—
390#1907D6111yescharacteristic, complemented
391#1887—611no—
392#1859—611no—
393#1859—611no—
394#1764—611no—
395#1764—611no—
396C2×C61—21no—
397C2×C61—21no—
398C2×C61—42no—
399C2×C61—82no—
400C2×C61#235811yescharacteristic
401C2×C61#329111yescharacteristic
402C2×C61#329211yescharacteristic
403D61—42no—
404D61—82no—
405C2×H(5,𝔽2)—611no—
406C2×AGL(1,ℤ/8)—611no—
407C2×AGL(1,ℤ/8)C2×D6111yescharacteristic
408C2×#131—611no—
409C2×#131C2×D6111yescharacteristic
410C2×#127—611no—
411#520—611no—
412#520—611no—
413#518—611no—
414#453—618no—
415#442—1221no—
416#442—1221no—
417#440—1221no—
418#440—1221no—
419C4×SD16—1221no—
420C4×SD16—1221no—
421C4×D8—1221no—
422C4×D8—1221no—
423#428—611no—
424#428—611no—
425C2×#104—611no—
426C2×#104—611no—
427#418—611no—
428#418—611no—
429#418—1221no—
430#418—1221no—
431#417—611no—
432#417—1221no—
433#417—1221no—
434#417C2×D6111yescharacteristic
435#416—611no—
436#416—611no—
437#416—1221no—
438#416—1221no—
439C2×#102—611no—
440C2×#102—611no—
441C2×#102—611no—
442C2×#102—1221no—
443C2×#102—1221no—
444C2×#102C2×D6111yescharacteristic, complemented
445C2×#100—611no—
446C2×#100C2×D6111yescharacteristic, complemented
447#405—611no—
448#405—611no—
449C2×C4×C8—611no—
450#384—611no—
451#343—611no—
452#343C2×D6111yescharacteristic, complemented
453#341—611no—
454#341C2×D6111yescharacteristic, complemented
455#339—611no—
456#339—611no—
457C61#2289711yescharacteristic, complemented, Sylow
458H(5,𝔽2)—614no—
459H(5,𝔽2)—1222no—
460H(5,𝔽2)—1222no—
461H(5,𝔽2)—2441no—
462C2×#41—611no—
463C2×#41—1221no—
464C2×#41—1221no—
465C2×#41C22×D6111yescharacteristic
466C22×D4—611no—
467C22×D4—1221no—
468C22×D4—1221no—
469C22×D4—2441no—
470C22×D4—2441no—
471C22×D4C22×D6111yescharacteristic
472AGL(1,ℤ/8)—22no—
473AGL(1,ℤ/8)—614no—
474AGL(1,ℤ/8)—1222no—
475AGL(1,ℤ/8)C4×D6114yescomplemented
476C2×SD16—21no—
477C2×SD16—1221no—
478C2×D8—21no—
479C2×D8—1221no—
480#131—22no—
481#131—41no—
482#131—1222no—
483#131—2441no—
484C2×M16—21no—
485C2×M16—611no—
486C2×M16—1221no—
487C2×M16C22×D6111yescharacteristic
488C2×M16C22×D6111yescharacteristic
489C2×M16C22×D6111yescharacteristic
490C22×C8—21no—
491C22×C8—611no—
492C22×C8—1221no—
493C22×C8C22×D6111yescharacteristic
494#127—614no—
495#127—2441no—
496C4×Q8—1221no—
497C4×Q8—1221no—
498C4×D4—1221no—
499C4×D4—1221no—
500C4×D4—1221no—
501C4×D4—1221no—
502C4×D4—1221no—
503C4×D4—1221no—
504C4×D4—2441no—
505C4×D4—2441no—
506#117—611no—
507#117—611no—
508#117—1221no—
509#117—1221no—
510C2×C4⋊C4—611no—
511C2×C4⋊C4—1221no—
512C2×C4⋊C4—1221no—
513C2×C4⋊C4—2441no—
514C2×C4⋊C4C22×D6111yescharacteristic
515C2×C22⋊C4—2441no—
516C2×C42—611no—
517#107—1221no—
518#107—1221no—
519#106—1221no—
520#106—1221no—
521#104—614no—
522#104—614no—
523#103—21no—
524#103—611no—
525#103—611no—
526#103—611no—
527#103—611no—
528#103—1221no—
529#102—21no—
530#102—21no—
531#102—21no—
532#102—611no—
533#102—611no—
534#102—611no—
535#102—611no—
536#102—1221no—
537#102—1221no—
538#102—1221no—
539#102—1221no—
540#102—1221no—
541#102—1221no—
542#102—1221no—
543#102—1221no—
544#102—1221no—
545#102—1221no—
546#102—1221no—
547#100—41no—
548#100—614no—
549#97—1221no—
550#97—1221no—
551C4×C8—1221no—
552C4×C8—1221no—
553C4×C8—2441no—
554C24—21no—
555C24—1221no—
556C24—2441no—
557#41—21no—
558#41—21no—
559#41—612no—
560#41—612no—
561#41—1224no—
562#41—1221no—
563#41—1221no—
564#41—1224no—
565#41—2442no—
566#41—2442no—
567#41C2×C4×D6112yes—
568#41#1175822412yes—
569C2×Q8—611no—
570C2×Q8D4×D6111yescharacteristic
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—612no—
578C2×D4—611no—
579C2×D4—1224no—
580C2×D4—1221no—
581C2×D4—1224no—
582C2×D4—1221no—
583C2×D4—1221no—
584C2×D4—1221no—
585C2×D4—1221no—
586C2×D4—1221no—
587C2×D4—4882no—
588C2×D4—4882no—
589C2×D4—2442no—
590C2×D4—2441no—
591C2×D4—2442no—
592C2×D4—2444no—
593C2×D4—2441no—
594C2×D4—2444no—
595C2×D4—2444no—
596C2×D4C2×C4×D6112yes—
597C2×D4D4×D6111yescharacteristic
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—1221no—
601C22×C4—1221no—
602C22×C4—1221no—
603C22×C4—2441no—
604C22×C4—2441no—
605C22×C4—2441no—
606C22×C4—2441no—
607C22×C4—2441no—
608C22×C4C23×D6111yescharacteristic
609SD16—24no—
610SD16—1224no—
611D8—24no—
612D8—1224no—
613M16—21no—
614M16—21no—
615M16—21no—
616M16—21no—
617M16—21no—
618M16—42no—
619M16—612no—
620M16—1221no—
621M16—2442no—
622M16C2×C4×D6112yes—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—42no—
629C2×C8—611no—
630C2×C8—611no—
631C2×C8—1221no—
632C2×C8—1221no—
633C2×C8—1221no—
634C2×C8—2442no—
635C2×C8D4×D6111yescharacteristic
636C2×C8D4×D6111yescharacteristic
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—611no—
640C4⋊C4—611no—
641C4⋊C4—611no—
642C4⋊C4—611no—
643C4⋊C4—1221no—
644C4⋊C4—1221no—
645C4⋊C4—4882no—
646C4⋊C4—2441no—
647C4⋊C4—2441no—
648C22⋊C4—1221no—
649C22⋊C4—1221no—
650C22⋊C4—2441no—
651C22⋊C4—2441no—
652C22⋊C4—2441no—
653C22⋊C4—2441no—
654C42—612no—
655C42—1221no—
656C42—1221no—
657C42—1221no—
658C42—2441no—
659C42—2441no—
660C23—21no—
661C23—22no—
662C23—41no—
663C23—41no—
664C23—81no—
665C23—81no—
666C23—1221no—
667C23—1222no—
668C23—9761no—
669C23—9761no—
670C23—4881no—
671C23—4881no—
672C23—2444no—
673C23—2441no—
674C23—2441no—
675C23#1451982311yescharacteristic
676Q8—21no—
677Q8—612no—
678Q8—1221no—
679Q8#1451973712yes—
680D4—22no—
681D4—22no—
682D4—22no—
683D4—22no—
684D4—21no—
685D4—41no—
686D4—41no—
687D4—612no—
688D4—1222no—
689D4—1222no—
690D4—1222no—
691D4—1222no—
692D4—1221no—
693D4—4888no—
694D4—2444no—
695D4—2444no—
696D4—2441no—
697D4—2441no—
698D4#1451973712yes—
699C2×C4—21no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—41no—
703C2×C4—81no—
704C2×C4—1222no—
705C2×C4—1222no—
706C2×C4—1222no—
707C2×C4—1221no—
708C2×C4—1222no—
709C2×C4—1222no—
710C2×C4—1221no—
711C2×C4—1221no—
712C2×C4—1221no—
713C2×C4—1221no—
714C2×C4—9761no—
715C2×C4—9761no—
716C2×C4—9761no—
717C2×C4—9761no—
718C2×C4—4881no—
719C2×C4—2444no—
720C2×C4—2441no—
721C2×C4C22×C4×D6111yescharacteristic
722C2×C4C2×D4×D6111yescharacteristic
723C2×C4C2×D4×D6111yescharacteristic
724C2×C4#41×D6111yescharacteristic
725C2×C4C2×#1175822411yescharacteristic
726C2×C4#1451982211yescharacteristic
727C8—22no—
728C8—21no—
729C8—21no—
730C8—41no—
731C8—41no—
732C8—1222no—
733C8—1221no—
734C8—1221no—
735C22—21no—
736C22—21no—
737C22—22no—
738C22—41no—
739C22—41no—
740C22—42no—
741C22—82no—
742C22—81no—
743C22—81no—
744C22—161no—
745C22—1222no—
746C22—9761no—
747C22—9764no—
748C22—4882no—
749C22—4881no—
750C22—4881no—
751C22—2442no—
752C22—2441no—
753C22—2441no—
754C22#1684023411yescharacteristic
755C22#1684039611yescharacteristic
756C22#1684043511yescharacteristic
757C4—22no—
758C4—81no—
759C4—1224no—
760C4—1222no—
761C4—4881no—
762C4—2441no—
763C4—2441no—
764C4—2441no—
765C4—2441no—
766C4C4×D4×D6111yescharacteristic
767C4C2×#1451973711yescharacteristic
768C4#1684039911yescharacteristic
769C4#1684040111yescharacteristic
770C2—21no—
771C2—21no—
772C2—42no—
773C2—82no—
774C2—4882no—
775C2—2442no—
776C2#2144879911yescharacteristic
777C2#2145761111yescharacteristic
778C2#2145761711yescharacteristic
subgroupG/H
centerC22#16840396
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1907C2
socleC22×C61D42
prime radicalC2×#16839928C2
cosocleC22×C4×C61C24
hypercenter#1907D61
hypocenterC61#22897
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1907

Complements

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

NH ≅ G/Ntype
2. #21454652C2semidirect
3. #21454645C2semidirect
4. #21454346C2semidirect
5. #21454343C2semidirect
6. #21446623C2semidirect
7. #21446482C2semidirect
8. #21446479C2semidirect
9. #21446324C2semidirect
10. #21446215C2semidirect
11. #21446048C2semidirect
12. #21446043C2semidirect
13. #21445655C2semidirect
14. #21445654C2semidirect
15. C61×#1907C2semidirect
22. #16840237C22semidirect
23. #16839928C4semidirect
32. #16839804C22semidirect
33. #16839802C22semidirect
49. C2×#14519698C22semidirect
53. #16839720C22semidirect
54. #16839717C22semidirect
55. C2×C8×Dic61C22semidirect
56. #16839631C22semidirect
57. #16839530C22semidirect
58. #16839526C22semidirect
59. #16839523C22semidirect
60. #16839523C22semidirect
64. C2×#102×C61C22semidirect
65. C2×#100×C61C22semidirect
66. C61×#343C22semidirect
67. C61×#341C22semidirect
71. #14519823C2×C4semidirect
81. #14519803C2×C4semidirect
91. #14519773C2×C4semidirect
116. #14519704C2×C4semidirect
117. #14519703C2×C4semidirect
119. #14519702D4semidirect
120. #14519702D4semidirect
121. #14519701D4semidirect
122. #14519701D4semidirect
130. #14519699D4semidirect
131. #14519699D4semidirect
134. #14519698D4semidirect
135. #14519698D4semidirect
138. #14519693C2×C4semidirect
147. AGL(1,ℤ/8)×C61C2×C4semidirect
390. #1907D61semidirect
444. C2×#102C2×D61semidirect
446. C2×#100C2×D61semidirect
452. #343C2×D61semidirect
454. #341C2×D61semidirect
457. C61#22897semidirect
475. AGL(1,ℤ/8)C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168399282
#214546522
#214546452
#214543462
#214543432
#214466232
#214464822
#214464792
#214463242
#214462152
#214460482
#214460432
#214456552
#214456542
C61×#19072
#2289761