Finite Group Databasebeta

← #30620640

Subgroups — #30620640

Order 15616.

888 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462509C211yesmaximal, characteristic, complemented
2#21462410C211yesmaximal, characteristic
3#21461915C211yesmaximal, characteristic, complemented
4#21461913C211yesmaximal, characteristic, complemented
5#21461901C211yesmaximal, characteristic, complemented
6#21461900C211yesmaximal, characteristic, complemented
7#21461789C211yesmaximal, characteristic, complemented
8#21461787C211yesmaximal, characteristic, complemented
9#21461726C211yesmaximal, characteristic, complemented
10#21461700C211yesmaximal, characteristic, complemented
11#21461661C211yesmaximal, characteristic
12#21461600C211yesmaximal, characteristic, complemented
13#21461596C211yesmaximal, characteristic, complemented
14#21461559C211yesmaximal, characteristic, complemented
15#21454335C211yesmaximal, characteristic
16C2×#14519865C2211yescharacteristic
17C2×#14519865C2211yescharacteristic
18#16840787—21no—
19#16840787—21no—
20#16840782—21no—
21#16840778—21no—
22C2×#14519848C2211yescharacteristic, complemented
23C2×#14519847C2211yescharacteristic, complemented
24#16840769C2211yescharacteristic, complemented
25#16840769C2211yescharacteristic, complemented
26C2×#14519842C2211yescharacteristic
27C2×#14519842C2211yescharacteristic
28C2×#14519841C2211yescharacteristic
29C2×#14519841C2211yescharacteristic
30#16840736—21no—
31#16840736—21no—
32#16840736C2211yescharacteristic
33#16840736C2211yescharacteristic
34#16840733—21no—
35#16840733C2211yescharacteristic
36#16840733C2211yescharacteristic
37D61⋊(C22⋊C8)—21no—
38D61⋊(C22⋊C8)C2211yescharacteristic
39#16840727C2211yescharacteristic, complemented
40#16840727C2211yescharacteristic, complemented
41C2×#14519831C2211yescharacteristic, complemented
42C2×C8×#6923C2211yescharacteristic, complemented
43C4×C22⋊#6923C2211yescharacteristic
44#16840638C2211yescharacteristic, complemented
45#16840638C2211yescharacteristic, complemented
46#16840632C2211yescharacteristic, complemented
47#16840632C2211yescharacteristic, complemented
48#16840632C2211yescharacteristic, complemented
49#16840632C2211yescharacteristic, complemented
50(C2×#6923)⋊C8C2211yescharacteristic, complemented
51(C2×#6923)⋊C8C2211yescharacteristic, complemented
52C2×#41×D61C2211yescharacteristic
53C2×M16×D61C2211yescharacteristic
54C2×#14519735C2211yescharacteristic
55#16839769C411yescharacteristic, complemented
56#16839769C411yescharacteristic, complemented
57#16839765C411yescharacteristic, complemented
58#16839765C411yescharacteristic, complemented
59#16839764C411yescharacteristic, complemented
60#16839763C411yescharacteristic, complemented
61#16839761C411yescharacteristic, complemented
62#16839757C2211yescharacteristic
63#16839757C2211yescharacteristic
64#16839755C2211yescharacteristic
65#16839755C2211yescharacteristic
66C61×#417C411yescharacteristic, complemented
67#14519865—22no—
68#14519865—22no—
69#14519865—41no—
70#14519865—41no—
71C2×#11758213—21no—
72C2×#11758213—21no—
73C2×#11758213C2311yescharacteristic
74C2×#11758213C2311yescharacteristic
75C2×#11758213C2311yescharacteristic
76C2×#11758213C2311yescharacteristic
77C2×D61⋊C8—21no—
78C2×D61⋊C8—21no—
79C2×D61⋊C8C2311yescharacteristic
80C2×D61⋊C8C2311yescharacteristic
81C2×C22⋊#6923—21no—
82C2×C4×#6923C2311yescharacteristic
83C2×C4×#6923C2311yescharacteristic
84#14519848—41no—
85#14519847—41no—
86#14519844—21no—
87#14519844—21no—
88C4⋊#92420—21no—
89C4⋊#92420—21no—
90#14519842—22no—
91#14519842—22no—
92#14519841—41no—
93#14519841—41no—
94#14519834—21no—
95#14519834—21no—
96#14519834D411yescharacteristic
97#14519834D411yescharacteristic
98C22⋊#92420—21no—
99C22⋊#92420—21no—
100C22⋊#92420—21no—
101C22⋊#92420—21no—
102C22⋊#92420—21no—
103C22⋊#92420—21no—
104C22⋊#92420D411yescharacteristic
105C22⋊#92420D411yescharacteristic
106#14519832—21no—
107#14519832—21no—
108#14519831—41no—
109C4×#92420—21no—
110C4×#92420—21no—
111C8×#6923—41no—
112(C2×#6923)⋊C4—21no—
113C2×#11758226C2311yescharacteristic
114C2×#11758222—21no—
115C2×#11758222C2×C411yescharacteristic
116C2×#11758224—21no—
117C2×#11758224C2311yescharacteristic
118#41×D61—22no—
119#41×D61—22no—
120#41×D61—41no—
121#41×D61—41no—
122C2×Q8×D61C2×C411yescharacteristic
123C2×D4×D61—21no—
124C2×D4×D61C2×C411yescharacteristic
125C22×C4×D61—21no—
126C22×C4×D61C2311yescharacteristic
127C2×#11758194C2×C411yescharacteristic
128C2×#11758189C2×C411yescharacteristic
129C2×#11758189C2×C411yescharacteristic
130M16×D61—41no—
131M16×D61—41no—
132C2×C8×D61C2311yescharacteristic
133C2×C8×D61C2311yescharacteristic
134#14519735—21no—
135#14519735—21no—
136#14519735C2×C411yescharacteristic
137#14519735C2×C411yescharacteristic
138#14519735C2311yescharacteristic
139#14519735C2311yescharacteristic
140C2×C4⋊Dic61C2×C411yescharacteristic
141C2×#11758198—21no—
142C2×C4×Dic61—21no—
143#14519702C2×C411yescharacteristic
144#14519702C2×C411yescharacteristic
145#14519701C2×C411yescharacteristic
146#14519701C2×C411yescharacteristic
147#14519700C2×C411yescharacteristic
148#14519700C2×C411yescharacteristic
149#14519699C2×C411yescharacteristic
150#14519699C2×C411yescharacteristic
151#14519698C2×C411yescharacteristic
152#14519698C2×C411yescharacteristic
153#14519697C2×C411yescharacteristic
154#14519697C2×C411yescharacteristic
155C2×#41×C61C2×C411yescharacteristic
156C2×M16×C61C2×C411yescharacteristic
157C2×C4⋊C4×C61C2×C411yescharacteristic
158#103×C61C2×C411yescharacteristic
159#103×C61C2×C411yescharacteristic
160#102×C61C2×C411yescharacteristic
161#102×C61C2×C411yescharacteristic
162C23×D61—21no—
163C23×D61#4111yescharacteristic
164C22×#6923—21no—
165C22×#6923—21no—
166#41×C61—22no—
167#41×C61—41no—
168C2×Q8×C61C22×C411yescharacteristic
169C2×D4×C61—21no—
170C2×D4×C61C22×C411yescharacteristic
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61C22×C411yescharacteristic
174C2×C22⋊D61—21no—
175C2×C22⋊D61—21no—
176C2×C22⋊D61—21no—
177C22×Dic61—21no—
178C22×Dic61—21no—
179C22×Dic61C2×D411yescharacteristic
180#11758226—21no—
181#11758226—21no—
182#11758226#4112yes—
183#11758226#4112yes—
184Q8×D61—22no—
185Q8×D61—41no—
186#11758224—21no—
187#11758224—21no—
188#11758224—21no—
189#11758224—21no—
190#11758224—42no—
191#11758224—42no—
192D4×D61—22no—
193D4×D61—41no—
194D4×D61—42no—
195D4×D61—42no—
196#11758222—22no—
197#11758222—41no—
198#11758222—42no—
199#11758222—42no—
200C2×D244—21no—
201C2×D244C22×C411yescharacteristic
202C2×C4×D61—21no—
203C2×C4×D61—21no—
204C2×C4×D61—21no—
205C2×C4×D61—21no—
206C2×C4×D61—21no—
207C2×C4×D61—21no—
208C2×C4×D61—21no—
209C2×C4×D61—42no—
210C2×C4×D61—42no—
211C2×C4×D61C22×C411yescharacteristic
212C2×C4×D61C2×D411yescharacteristic
213C2×C4×D61#4111yescharacteristic
214C2×C4×D61C2411yescharacteristic
215C2×Dic122—21no—
216C2×Dic122C22×C411yescharacteristic
217C22⋊#6923—42no—
218C2×#92420—21no—
219C2×#92420—21no—
220C2×#92420—21no—
221C2×#92420—21no—
222C2×#92420C2×D411yescharacteristic
223C2×#92420C2×D411yescharacteristic
224C2×#92420C2×D411yescharacteristic
225C2×#92420C2×D411yescharacteristic
226C4×#6923—21no—
227C4×#6923—21no—
228C4×#6923—21no—
229C4×#6923—21no—
230#11758213—21no—
231#11758213—21no—
232#11758213—21no—
233#11758213—21no—
234#11758213—21no—
235#11758213—21no—
236#11758213—21no—
237#11758213—21no—
238#11758213—42no—
239#11758213—42no—
240D61⋊C8—21no—
241D61⋊C8—21no—
242D61⋊C8—21no—
243D61⋊C8—21no—
244D61⋊C8—42no—
245D61⋊C8—42no—
246M16×C61—41no—
247C2×C8×C61C22×C411yescharacteristic
248C2×C8×C61C22×C411yescharacteristic
249C4⋊C4×C61—21no—
250C4⋊C4×C61C22×C411yescharacteristic
251C4⋊C4×C61C22×C411yescharacteristic
252#11758198—21no—
253#11758198—21no—
254#11758198—21no—
255#11758198—21no—
256C4⋊Dic61—21no—
257C4⋊Dic61C22×C411yescharacteristic
258C4⋊Dic61C22×C411yescharacteristic
259C4×Dic61—21no—
260C4×Dic61—21no—
261C4×Dic61—21no—
262C4×Dic61—21no—
263#11758194—41no—
264C2×#92418C22×C411yescharacteristic
265C2×#92418C22×C411yescharacteristic
266#11758189—41no—
267#11758189—41no—
268C8×D61—21no—
269C8×D61—21no—
270C8×D61—21no—
271C8×D61—21no—
272C23×C61—21no—
273C23×C61C4×D411yescharacteristic
274C22×D61—21no—
275C22×D61—21no—
276C22×D61—21no—
277C22×D61—41no—
278C22×D61—41no—
279C22×D61—42no—
280C22×D61—42no—
281C22×D61—81no—
282C22×D61C4×D411yescharacteristic
283C22×D61C2×#4111yescharacteristic
284C2×#6923—22no—
285C2×#6923—41no—
286C2×#6923—41no—
287C2×#6923—41no—
288C2×#6923—41no—
289C2×#6923—41no—
290Q8×C61—21no—
291Q8×C61#11712yes—
292D4×C61—21no—
293D4×C61—21no—
294D4×C61—42no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—42no—
301C2×C4×C61—42no—
302C2×C4×C61C4×D411yescharacteristic
303C2×C4×C61C23×C411yescharacteristic
304C22⋊D61—42no—
305C22⋊D61—42no—
306C22⋊D61—41no—
307C22⋊D61—41no—
308C2×Dic61—21no—
309C2×Dic61—21no—
310C2×Dic61—21no—
311C2×Dic61—21no—
312C2×Dic61—21no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—81no—
316C2×Dic61C4×D411yescharacteristic
317C2×Dic61C22×D411yescharacteristic
318D244—22no—
319D244—22no—
320D244—21no—
321D244#11712yes—
322C4×D61—21no—
323C4×D61—21no—
324C4×D61—21no—
325C4×D61—21no—
326C4×D61—22no—
327C4×D61—22no—
328C4×D61—21no—
329C4×D61—21no—
330C4×D61—42no—
331C4×D61—42no—
332C4×D61C2×#4111yescharacteristic
333C4×D61C2×#4111yescharacteristic
334C4×D61H(5,𝔽2)11yescharacteristic
335C4×D61H(5,𝔽2)11yescharacteristic
336Dic122—21no—
337Dic122—21no—
338Dic122—42no—
339#92420—21no—
340#92420—21no—
341#92420—21no—
342#92420—21no—
343#92420—41no—
344#92420—41no—
345#92420—41no—
346#92420—41no—
347C8×C61—21no—
348C8×C61—21no—
349#92418—21no—
350#92418—21no—
351#22588—611nomaximal, Sylow
352C22×C61—21no—
353C22×C61—21no—
354C22×C61—21no—
355C22×C61—41no—
356C22×C61—41no—
357C22×C61—41no—
358C22×C61C2×C4×D411yescharacteristic
359C2×D61—21no—
360C2×D61—21no—
361C2×D61—21no—
362C2×D61—22no—
363C2×D61—21no—
364C2×D61—21no—
365C2×D61—41no—
366C2×D61—41no—
367C2×D61—81no—
368C2×D61—81no—
369C2×D61—84no—
370C2×D61#55111yescharacteristic
371C2×D61#55111yescharacteristic
372#6923—42no—
373#6923—81no—
374C4×C61—22no—
375C4×C61—21no—
376C4×C61—41no—
377C4×C61—41no—
378C4×C61C2×#11711yescharacteristic
379C4×C61#51811yescharacteristic
380Dic61—21no—
381Dic61—41no—
382Dic61—41no—
383Dic61—41no—
384Dic61#54611yescharacteristic
385Dic61#54611yescharacteristic
386#2924—611no—
387#2896—611no—
388#2880—611no—
389#1938—611no—
390#1937—611no—
391#1929—611no—
392#1929—611no—
393#1866—611no—
394#1866—611no—
395#1826—611no—
396#1811—611no—
397#1789—611no—
398#1765—611no—
399#1764—611no—
400#1753—611no—
401C2×C61—41no—
402C2×C61—81no—
403C2×C61#234211yescharacteristic
404C2×C61#295511yescharacteristic
405C2×C61#295611yescharacteristic
406D61—21no—
407D61—21no—
408D61—41no—
409D61—42no—
410C22×#41—611no—
411C2×#131—611no—
412C2×#131—611no—
413C22×M16—611no—
414C2×#117—611no—
415#433—1221no—
416#433—1221no—
417#432—1221no—
418#431—1221no—
419C2×#108—611no—
420C2×#108—611no—
421#424—611no—
422#424—611no—
423C2×#104—611no—
424C2×#104—611no—
425C2×#104—611no—
426C2×#104—611no—
427#419—611no—
428#419—611no—
429#418—611no—
430#418—611no—
431#417—611no—
432#417—611no—
433#417—611no—
434#417#692311yescharacteristic, complemented
435#416—611no—
436#416—611no—
437#416—611no—
438#416—611no—
439#408—611no—
440#408—611no—
441#408—1221no—
442#408—1221no—
443#407—611no—
444#407—611no—
445#407—1221no—
446C2×C22⋊C8—611no—
447C2×C22⋊C8—1221no—
448#405—611no—
449#405—611no—
450C2×#97—611no—
451C2×C4×C8—611no—
452C4×C22⋊C4—611no—
453#341—611no—
454#341—611no—
455#339—611no—
456#339—611no—
457#339—611no—
458#339—611no—
459#336—611no—
460#336—611no—
461C61#2258811yescharacteristic, complemented, Sylow
462C2×#41—611no—
463C2×#41—611no—
464C2×#41—611no—
465C2×#41—1221no—
466C2×#41—1221no—
467C2×#41—1222no—
468C2×#41—1222no—
469C2×#41—2441no—
470C2×#41—2441no—
471C2×#41C2×#692311yescharacteristic
472C22×Q8—611no—
473C22×D4—611no—
474C22×D4—1221no—
475C23×C4—611no—
476C23×C4—1221no—
477#131—1222no—
478#131—1222no—
479#131—2441no—
480#131—2441no—
481C2×M16—611no—
482C2×M16—611no—
483C2×M16—611no—
484C2×M16—611no—
485C2×M16—611no—
486C2×M16—611no—
487C2×M16—611no—
488C2×M16—1221no—
489C2×M16—1221no—
490C2×M16—2441no—
491C2×M16—2441no—
492C2×M16C2×#692311yescharacteristic
493C22×C8—611no—
494C22×C8—611no—
495C22×C8—611no—
496C22×C8—611no—
497C22×C8—1221no—
498C22×C8—1221no—
499#117—611no—
500#117—611no—
501#117—611no—
502#117—611no—
503#117—1221no—
504#117—1221no—
505C2×C4⋊C4—611no—
506C2×C4⋊C4C2×#692311yescharacteristic
507C2×C22⋊C4—1221no—
508C2×C22⋊C4—1221no—
509C2×C42—611no—
510C2×C42—611no—
511C2×C42—1221no—
512#108—2441no—
513#108—2441no—
514C4⋊C8—1221no—
515C4⋊C8—1221no—
516C4⋊C8—1221no—
517C4⋊C8—1221no—
518#104—1222no—
519#104—1222no—
520#104—2441no—
521#104—2441no—
522#103—611no—
523#103—611no—
524#103—611no—
525#103—611no—
526#103—611no—
527#103—611no—
528#103C2×#692311yescharacteristic
529#103C2×#692311yescharacteristic
530#102—611no—
531#102—611no—
532#102—611no—
533#102—611no—
534#102—611no—
535#102—611no—
536#102C2×#692311yescharacteristic
537#102C2×#692311yescharacteristic
538C22⋊C8—611no—
539C22⋊C8—611no—
540C22⋊C8—611no—
541C22⋊C8—611no—
542C22⋊C8—1221no—
543C22⋊C8—1221no—
544C22⋊C8—1221no—
545C22⋊C8—1221no—
546C22⋊C8—1221no—
547C22⋊C8—1221no—
548C22⋊C8—1221no—
549C22⋊C8—1221no—
550#97—1221no—
551#97—1221no—
552#97—2441no—
553C4×C8—1221no—
554C4×C8—1221no—
555C4×C8—2441no—
556#95—1221no—
557C24—611no—
558C24—1221no—
559#41—22no—
560#41—41no—
561#41—612no—
562#41—612no—
563#41—1222no—
564#41—1221no—
565#41—1221no—
566#41—1221no—
567#41—1221no—
568#41—1221no—
569#41—1221no—
570#41—2441no—
571#41—2442no—
572#41—2442no—
573#41—2442no—
574#41—2442no—
575C2×Q8—611no—
576C2×Q8—1221no—
577C2×Q8—1222no—
578C2×Q8—2441no—
579C2×Q8C22×#692311yescharacteristic
580C2×D4—21no—
581C2×D4—611no—
582C2×D4—1221no—
583C2×D4—1221no—
584C2×D4—1222no—
585C2×D4—1221no—
586C2×D4—1221no—
587C2×D4—2441no—
588C2×D4—2442no—
589C2×D4—2442no—
590C2×D4C22×#692311yescharacteristic
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—611no—
594C22×C4—611no—
595C22×C4—611no—
596C22×C4—611no—
597C22×C4—611no—
598C22×C4—1221no—
599C22×C4—1221no—
600C22×C4—1221no—
601C22×C4—1221no—
602C22×C4—1221no—
603C22×C4—1221no—
604C22×C4—1221no—
605C22×C4—1221no—
606C22×C4—1221no—
607C22×C4—1221no—
608C22×C4—1221no—
609C22×C4—2442no—
610C22×C4—2442no—
611C22×C4C22×#692311yescharacteristic
612M16—41no—
613M16—1221no—
614M16—1221no—
615M16—1221no—
616M16—1221no—
617M16—1221no—
618M16—1221no—
619M16—1221no—
620M16—1221no—
621M16—2441no—
622M16—2441no—
623M16—2441no—
624M16—2442no—
625M16—2442no—
626C2×C8—611no—
627C2×C8—611no—
628C2×C8—611no—
629C2×C8—611no—
630C2×C8—611no—
631C2×C8—611no—
632C2×C8—1221no—
633C2×C8—1221no—
634C2×C8—1221no—
635C2×C8—1221no—
636C2×C8—1221no—
637C2×C8—1221no—
638C2×C8—1221no—
639C2×C8—1221no—
640C2×C8—1221no—
641C2×C8—1221no—
642C2×C8—1221no—
643C2×C8—1221no—
644C2×C8—2442no—
645C2×C8—2442no—
646C2×C8C22×#692311yescharacteristic
647C2×C8C22×#692311yescharacteristic
648C4⋊C4—21no—
649C4⋊C4—611no—
650C4⋊C4—611no—
651C4⋊C4—1221no—
652C4⋊C4C22×#692311yescharacteristic
653C4⋊C4C22×#692311yescharacteristic
654C22⋊C4—1221no—
655C22⋊C4—1221no—
656C22⋊C4—1221no—
657C22⋊C4—1221no—
658C22⋊C4—2442no—
659C42—1221no—
660C42—1221no—
661C42—1221no—
662C42—1221no—
663C42—1221no—
664C42—1221no—
665C42—1221no—
666C42—1221no—
667C23—21no—
668C23—611no—
669C23—611no—
670C23—1221no—
671C23—1221no—
672C23—1221no—
673C23—4881no—
674C23—2441no—
675C23—2441no—
676C23—2442no—
677C23—2442no—
678C23D4×#692311yescharacteristic
679Q8—21no—
680Q8—1221no—
681Q8—1221no—
682Q8—2442no—
683Q8#1451985612yes—
684D4—21no—
685D4—21no—
686D4—42no—
687D4—612no—
688D4—1222no—
689D4—1222no—
690D4—1221no—
691D4—2442no—
692D4—2442no—
693D4—2441no—
694D4—2441no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—611no—
703C2×C4—611no—
704C2×C4—611no—
705C2×C4—611no—
706C2×C4—611no—
707C2×C4—611no—
708C2×C4—1222no—
709C2×C4—1222no—
710C2×C4—1221no—
711C2×C4—1221no—
712C2×C4—1221no—
713C2×C4—1221no—
714C2×C4—1221no—
715C2×C4—1221no—
716C2×C4—1221no—
717C2×C4—1221no—
718C2×C4—1222no—
719C2×C4—1221no—
720C2×C4—1221no—
721C2×C4—1221no—
722C2×C4—4881no—
723C2×C4—2442no—
724C2×C4—2442no—
725C2×C4—2441no—
726C2×C4—2441no—
727C2×C4—2441no—
728C2×C4—2441no—
729C2×C4—2441no—
730C2×C4—2441no—
731C2×C4—2441no—
732C2×C4D4×#692311yescharacteristic
733C2×C4C23×#692311yescharacteristic
734C8—21no—
735C8—21no—
736C8—1221no—
737C8—1221no—
738C8—1221no—
739C8—1221no—
740C8—1221no—
741C8—1221no—
742C8—2441no—
743C8—2441no—
744C8—2441no—
745C8—2441no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—611no—
753C22—611no—
754C22—1221no—
755C22—1221no—
756C22—1221no—
757C22—1222no—
758C22—1221no—
759C22—1221no—
760C22—4881no—
761C22—4881no—
762C22—4884no—
763C22—2441no—
764C22—2441no—
765C22C2×D4×#692311yescharacteristic
766C4—21no—
767C4—22no—
768C4—41no—
769C4—41no—
770C4—611no—
771C4—611no—
772C4—1221no—
773C4—4881no—
774C4—2442no—
775C4—2441no—
776C4—2441no—
777C4—2441no—
778C4C2×#1451985611yescharacteristic
779C4#1684082911yescharacteristic
780C2—41no—
781C2—81no—
782C2—1221no—
783C2—1221no—
784C2—2441no—
785C2—2442no—
786C2#2146232511yescharacteristic
787C2#2146259111yescharacteristic
788C2#2146259411yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#417C4
socleC22×C61C2×C4×D4
prime radicalC2×#41×D61C22
cosocleC2×C4×D61C24
hypercenter#417#6923
hypocenterC61#22588
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #21462509C2semidirect
3. #21461915C2semidirect
4. #21461913C2semidirect
5. #21461901C2semidirect
6. #21461900C2semidirect
7. #21461789C2semidirect
8. #21461787C2semidirect
9. #21461726C2semidirect
10. #21461700C2semidirect
12. #21461600C2semidirect
13. #21461596C2semidirect
14. #21461559C2semidirect
22. C2×#14519848C22semidirect
23. C2×#14519847C22semidirect
24. #16840769C22semidirect
25. #16840769C22semidirect
39. #16840727C22semidirect
40. #16840727C22semidirect
41. C2×#14519831C22semidirect
42. C2×C8×#6923C22semidirect
44. #16840638C22semidirect
45. #16840638C22semidirect
46. #16840632C22semidirect
47. #16840632C22semidirect
48. #16840632C22semidirect
49. #16840632C22semidirect
50. (C2×#6923)⋊C8C22semidirect
51. (C2×#6923)⋊C8C22semidirect
55. #16839769C4semidirect
56. #16839769C4semidirect
57. #16839765C4semidirect
58. #16839765C4semidirect
59. #16839764C4semidirect
60. #16839763C4semidirect
61. #16839761C4semidirect
66. C61×#417C4semidirect
434. #417#6923semidirect
461. C61#22588semidirect

Maximal subgroups

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

subgroupindex
#214625092
#214624102
#214619152
#214619132
#214619012
#214619002
#214617892
#214617872
#214617262
#214617002
#214616612
#214616002
#214615962
#214615592
#214543352
#2258861