Finite Group Databasebeta

← #29700867

Subgroups — #29700867

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#21454651C211yesmaximal, characteristic, complemented
3#21454342C211yesmaximal, characteristic, complemented
4#21454341C211yesmaximal, characteristic, complemented
5#21446623C211yesmaximal, characteristic, complemented
6#21446481C211yesmaximal, characteristic, complemented
7#21446480C211yesmaximal, characteristic, complemented
8#21446330C211yesmaximal, characteristic, complemented
9#21446329C211yesmaximal, characteristic, complemented
10#21446217C211yesmaximal, characteristic, complemented
11#21446045C211yesmaximal, characteristic, complemented
12#21446042C211yesmaximal, characteristic, complemented
13#21445659C211yesmaximal, characteristic, complemented
14#21445658C211yesmaximal, characteristic, complemented
15C61×#2946C211yesmaximal, characteristic, complemented
16C2×#14519823C2211yescharacteristic
17C2×#14519803C2211yescharacteristic
18C2×#14519784C2211yescharacteristic
19C2×#14519783C2211yescharacteristic
20C2×#14519773C2211yescharacteristic
21#16840242C2211yescharacteristic
22#16839928C418yescomplemented
23#16839872—21no—
24#16839862—21no—
25C4×#11758200—21no—
26C4×#11758199—21no—
27#16839805C2211yescharacteristic, complemented
28C2×#14519704C2211yescharacteristic
29C2×#14519703C2211yescharacteristic
30#16839766—21no—
31#16839766C2211yescharacteristic
32#16839766C2211yescharacteristic
33#16839765—21no—
34#16839763C2211yescharacteristic
35#16839762—21no—
36#16839761—21no—
37#16839761C2211yescharacteristic
38#16839757—21no—
39#16839756—21no—
40#16839756C2211yescharacteristic
41C2×#14519699C2211yescharacteristic
42C2×#14519698C2211yescharacteristic, complemented
43C2×#14519697—21no—
44C2×#14519697C2211yescharacteristic
45#102×D61—21no—
46C2×#14519694C2211yescharacteristic, complemented
47C2×#14519693C2211yescharacteristic
48#16839718C2211yescharacteristic, complemented
49C2×C8×Dic61C2211yescharacteristic, complemented
50#16839631C2211yescharacteristic, complemented
51#16839531C2211yescharacteristic, complemented
52#16839530C2211yescharacteristic, complemented
53#16839527C2211yescharacteristic, complemented
54#16839526C2211yescharacteristic, complemented
55#16839521C2211yescharacteristic, complemented
56#16839521C2211yescharacteristic, complemented
57C2×AGL(1,ℤ/8)×C61C2211yescharacteristic
58C61×#520C2211yescharacteristic
59C61×#518C2211yescharacteristic, complemented
60C61×#442—21no—
61C61×#440—21no—
62C4×SD16×C61—21no—
63C4×D8×C61—21no—
64C61×#428C2211yescharacteristic, complemented
65C61×#416C2211yescharacteristic
66C2×#102×C61C2211yescharacteristic, complemented
67C61×#405C2211yescharacteristic, 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#14519784—22no—
85#14519784—41no—
86#14519783—22no—
87#14519783—41no—
88C2×#11758194—21no—
89C2×#11758194C2311yescharacteristic
90C2×#11758194C2311yescharacteristic
91C2×#11758194C2311yescharacteristic
92C2×#11758189—21no—
93C22×#92418—21no—
94C22×#92418C2311yescharacteristic
95C2×C8×D61—21no—
96#14519773—41no—
97#14519773C2×C414yescomplemented
98C4×Dic122—21no—
99C4×D244—21no—
100#14519737—41no—
101#14519735—21no—
102C2×C4⋊Dic61C2311yescharacteristic
103C2×#11758196—41no—
104C4⋊C4×D61—21no—
105C2×C4×Dic61C2311yescharacteristic
106#14519710—21no—
107#14519708—21no—
108#14519704C2×C414yescomplemented
109#14519703C2×C414yescomplemented
110#14519701—21no—
111#14519700—21no—
112#14519700D411yescharacteristic, complemented
113#14519700D411yescharacteristic, complemented
114#14519699—21no—
115#14519699—21no—
116#14519698—21no—
117#14519698—21no—
118#14519698—21no—
119#14519697—21no—
120#14519697—21no—
121#14519697—21no—
122#14519697—21no—
123#14519697—21no—
124#14519697—21no—
125#14519697—21no—
126#14519697D411yescharacteristic, complemented
127#14519697D411yescharacteristic, complemented
128#14519694—41no—
129#14519693C2×C414yescomplemented
130#14519688—21no—
131C4×#92418—21no—
132C8×Dic61—41no—
133C2×#41×C61C2311yescharacteristic
134C22×D4×C61C2311yescharacteristic
135AGL(1,ℤ/8)×C61—22no—
136AGL(1,ℤ/8)×C61C2×C414yescomplemented
137C2×SD16×C61—21no—
138C2×D8×C61—21no—
139C2×M16×C61C2311yescharacteristic
140C22×C8×C61C2311yescharacteristic
141C4×Q8×C61—21no—
142C4×D4×C61—21no—
143C4×D4×C61—21no—
144C4×D4×C61—21no—
145C4×D4×C61—21no—
146C4×D4×C61—21no—
147C4×D4×C61—41no—
148#117×C61—21no—
149#117×C61C2311yescharacteristic
150#117×C61C2311yescharacteristic
151C2×C4⋊C4×C61—21no—
152C2×C4⋊C4×C61C2311yescharacteristic
153C2×C22⋊C4×C61—41no—
154#107×C61—21no—
155#106×C61—21no—
156#103×C61D411yescharacteristic, complemented
157#103×C61D411yescharacteristic, complemented
158#102×C61—21no—
159#102×C61—21no—
160#102×C61D411yescharacteristic, complemented
161#102×C61D411yescharacteristic, complemented
162#97×C61—21no—
163C4×C8×C61—21no—
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×C61—41no—
183C22×C4×C61—41no—
184C22×C4×C61—41no—
185C22×C4×C61C2411yescharacteristic
186C2×C22⋊D61—21no—
187C2×C22⋊D61—41no—
188C2×C22⋊D61—44no—
189C2×C22⋊D61—82no—
190C2×C22⋊D61—82no—
191C22×Dic61—21no—
192C22×Dic61—21no—
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×C61C22×C412yes—
223C2×C8×C61—21no—
224C2×C8×C61—21no—
225C2×C8×C61—21no—
226C2×C8×C61C2×D411yescharacteristic
227C2×C8×C61C2×D411yescharacteristic
228C4⋊C4×C61—21no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61—41no—
231C4⋊C4×C61C2×D411yescharacteristic
232C4⋊C4×C61C2×D411yescharacteristic
233C4⋊C4×C61C2×D411yescharacteristic
234C4⋊C4×C61C2×D411yescharacteristic
235C22⋊C4×C61—21no—
236C22⋊C4×C61—21no—
237C22⋊C4×C61—41no—
238C22⋊C4×C61—41no—
239C22⋊C4×C61—41no—
240C42×C61—21no—
241C42×C61—21no—
242C42×C61—41no—
243#11758200—24no—
244#11758199—24no—
245#11758198—41no—
246C4⋊Dic61—21no—
247C4⋊Dic61—21no—
248#11758196—41no—
249#11758196—82no—
250C4×Dic61—21no—
251C4×Dic61—41no—
252C4×Dic61C22×C412yes—
253#11758194—21no—
254#11758194—21no—
255#11758194—21no—
256#11758194—21no—
257#11758194—21no—
258#11758194—42no—
259#11758194C22×C412yes—
260C2×#92418—21no—
261C2×#92418—21no—
262C2×#92418—21no—
263C2×#92418—21no—
264C2×#92418—21no—
265C2×#92418—42no—
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—21no—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—41no—
304C2×C4×C61—81no—
305C2×C4×C61—161no—
306C2×C4×C61—161no—
307C2×C4×C61—161no—
308C2×C4×C61C23×C411yescharacteristic
309C2×C4×C61C22×D411yescharacteristic
310C2×C4×C61C22×D411yescharacteristic
311C2×C4×C61C2×#4111yescharacteristic
312C2×C4×C61C2×#4111yescharacteristic
313C2×C4×C61H(5,𝔽2)11yescharacteristic
314C22⋊D61—22no—
315C22⋊D61—22no—
316C22⋊D61—44no—
317C22⋊D61—88no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—22no—
321C2×Dic61—21no—
322C2×Dic61—41no—
323C2×Dic61—81no—
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—
340#92418—22no—
341#92418—21no—
342#92418—21no—
343#92418—41no—
344#92418—41no—
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—41no—
370C4×C61—41no—
371C4×C61—41no—
372C4×C61—41no—
373C4×C61—81no—
374C4×C61C2×C4×D411yescharacteristic
375C4×C61C2×C4×D411yescharacteristic
376C4×C61#54611yescharacteristic
377C4×C61#54611yescharacteristic
378Dic61—24no—
379Dic61—22no—
380Dic61—81no—
381C2×#453—611no—
382#2946—611no—
383#2946D6111yescharacteristic, complemented
384#2897—611no—
385#2897—611no—
386#1957—611no—
387#1931—611no—
388#1931—611no—
389#1907—611no—
390#1907—611no—
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×#131—611no—
410C2×#127—611no—
411#520—611no—
412#520C2×D6111yescharacteristic
413#518C2×D6111yescharacteristic, complemented
414#453—618no—
415#442—21no—
416#442—1221no—
417#440—21no—
418#440—1221no—
419C4×SD16—21no—
420C4×SD16—1221no—
421C4×D8—21no—
422C4×D8—1221no—
423#428—611no—
424#428C2×D6111yescharacteristic, complemented
425C2×#104—611no—
426C2×#104—611no—
427#418—611no—
428#418—611no—
429#418—1221no—
430#418—1221no—
431#417—611no—
432#417—611no—
433#417—1221no—
434#417—1221no—
435#416—611no—
436#416—1221no—
437#416—1221no—
438#416C2×D6111yescharacteristic
439C2×#102—611no—
440C2×#102—611no—
441C2×#102—611no—
442C2×#102—1221no—
443C2×#102—1221no—
444C2×#102C2×D6111yescharacteristic, complemented
445C2×#100—611no—
446C2×#100—611no—
447#405—611no—
448#405C2×D6111yescharacteristic, complemented
449C2×C4×C8—611no—
450#384—611no—
451#343—611no—
452#343—611no—
453#341—611no—
454#341—611no—
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—1222no—
481#131—1222no—
482#131—2441no—
483#131—2441no—
484C2×M16—611no—
485C2×M16—611no—
486C2×M16—611no—
487C2×M16—1221no—
488C2×M16—1221no—
489C2×M16C22×D6111yescharacteristic
490C22×C8—611no—
491C22×C8—1221no—
492C22×C8—1221no—
493C22×C8C22×D6111yescharacteristic
494#127—614no—
495#127—2441no—
496C4×Q8—21no—
497C4×Q8—1221no—
498C4×D4—21no—
499C4×D4—21no—
500C4×D4—21no—
501C4×D4—21no—
502C4×D4—21no—
503C4×D4—41no—
504C4×D4—1221no—
505C4×D4—2441no—
506#117—21no—
507#117—1221no—
508#117C22×D6111yescharacteristic
509#117C22×D6111yescharacteristic
510C2×C4⋊C4—21no—
511C2×C4⋊C4—611no—
512C2×C4⋊C4—1221no—
513C2×C4⋊C4—2441no—
514C2×C4⋊C4C22×D6111yescharacteristic
515C2×C22⋊C4—41no—
516C2×C42—611no—
517#107—21no—
518#107—1221no—
519#106—21no—
520#106—1221no—
521#104—614no—
522#104—614no—
523#103—611no—
524#103—611no—
525#103—1221no—
526#103—1221no—
527#103C22⋊D6111yescharacteristic, complemented
528#103C22⋊D6111yescharacteristic, complemented
529#102—21no—
530#102—21no—
531#102—611no—
532#102—611no—
533#102—1221no—
534#102—1221no—
535#102—1221no—
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#102C22⋊D6111yescharacteristic, complemented
546#102C22⋊D6111yescharacteristic, complemented
547#100—614no—
548#100—2441no—
549#97—21no—
550#97—1221no—
551C4×C8—21no—
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#1175822212yes—
569C2×Q8—611no—
570C2×Q8C2×C22⋊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×D4C2×C22⋊D6111yescharacteristic
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—1221no—
604C22×C4—1221no—
605C22×C4—1221no—
606C22×C4—2441no—
607C22×C4—2441no—
608C22×C4C23×D6111yescharacteristic
609SD16—24no—
610SD16—1224no—
611D8—24no—
612D8—1224no—
613M16—21no—
614M16—612no—
615M16—1221no—
616M16—1221no—
617M16—1221no—
618M16—1221no—
619M16—1221no—
620M16—2442no—
621M16—2442no—
622M16C2×C4×D6112yes—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—611no—
627C2×C8—611no—
628C2×C8—1221no—
629C2×C8—1221no—
630C2×C8—1221no—
631C2×C8—1221no—
632C2×C8—1221no—
633C2×C8—2442no—
634C2×C8—2442no—
635C2×C8C2×C22⋊D6111yescharacteristic
636C2×C8C2×C22⋊D6111yescharacteristic
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—41no—
640C4⋊C4—1221no—
641C4⋊C4—1221no—
642C4⋊C4—4882no—
643C4⋊C4—2441no—
644C4⋊C4D4×D6111yescharacteristic
645C4⋊C4D4×D6111yescharacteristic
646C4⋊C4C2×C22⋊D6111yescharacteristic
647C4⋊C4C2×C22⋊D6111yescharacteristic
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—41no—
651C22⋊C4—41no—
652C22⋊C4—41no—
653C22⋊C4—2441no—
654C42—21no—
655C42—21no—
656C42—41no—
657C42—612no—
658C42—1221no—
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#1451982211yescharacteristic
676Q8—21no—
677Q8—612no—
678Q8—1221no—
679Q8C4×C22⋊D6112yes—
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—
698D4C4×C22⋊D6112yes—
699C2×C4—21no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—41no—
707C2×C4—81no—
708C2×C4—161no—
709C2×C4—161no—
710C2×C4—161no—
711C2×C4—1222no—
712C2×C4—1222no—
713C2×C4—1222no—
714C2×C4—1221no—
715C2×C4—1222no—
716C2×C4—1222no—
717C2×C4—9761no—
718C2×C4—4881no—
719C2×C4—2444no—
720C2×C4—2441no—
721C2×C4C22×C4×D6111yescharacteristic
722C2×C4C2×D4×D6111yescharacteristic
723C2×C4C22×C22⋊D6111yescharacteristic
724C2×C4#41×D6111yescharacteristic
725C2×C4C2×#1175822211yescharacteristic
726C2×C4#1451982311yescharacteristic
727C8—22no—
728C8—21no—
729C8—21no—
730C8—1222no—
731C8—1221no—
732C8—1221no—
733C8—2441no—
734C8—2441no—
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
755C22D4×C22⋊D6111yescharacteristic
756C22#1684044111yescharacteristic
757C4—22no—
758C4—41no—
759C4—41no—
760C4—41no—
761C4—41no—
762C4—81no—
763C4—1224no—
764C4—1222no—
765C4—4881no—
766C4C4×D4×D6111yescharacteristic
767C4C2×C4×C22⋊D6111yescharacteristic
768C4#1684040011yescharacteristic
769C4#1684040811yescharacteristic
770C2—21no—
771C2—21no—
772C2—42no—
773C2—82no—
774C2—4882no—
775C2—2442no—
776C2#2144879611yescharacteristic
777C2#2145761011yescharacteristic
778C2#2145761611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2946C2
socleC22×C61D42
prime radicalC2×#16839928C2
cosocleC22×C4×C61C24
hypercenter#2946D61
hypocenterC61#22897
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2946

Complements

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

NH ≅ G/Ntype
2. #21454651C2semidirect
3. #21454342C2semidirect
4. #21454341C2semidirect
5. #21446623C2semidirect
6. #21446481C2semidirect
7. #21446480C2semidirect
8. #21446330C2semidirect
9. #21446329C2semidirect
10. #21446217C2semidirect
11. #21446045C2semidirect
12. #21446042C2semidirect
13. #21445659C2semidirect
14. #21445658C2semidirect
15. C61×#2946C2semidirect
22. #16839928C4semidirect
27. #16839805C22semidirect
42. C2×#14519698C22semidirect
46. C2×#14519694C22semidirect
48. #16839718C22semidirect
49. C2×C8×Dic61C22semidirect
50. #16839631C22semidirect
51. #16839531C22semidirect
52. #16839530C22semidirect
53. #16839527C22semidirect
54. #16839526C22semidirect
55. #16839521C22semidirect
56. #16839521C22semidirect
59. C61×#518C22semidirect
64. C61×#428C22semidirect
66. C2×#102×C61C22semidirect
67. C61×#405C22semidirect
71. #14519823C2×C4semidirect
81. #14519803C2×C4semidirect
97. #14519773C2×C4semidirect
108. #14519704C2×C4semidirect
109. #14519703C2×C4semidirect
112. #14519700D4semidirect
113. #14519700D4semidirect
126. #14519697D4semidirect
127. #14519697D4semidirect
129. #14519693C2×C4semidirect
136. AGL(1,ℤ/8)×C61C2×C4semidirect
156. #103×C61D4semidirect
157. #103×C61D4semidirect
160. #102×C61D4semidirect
161. #102×C61D4semidirect
383. #2946D61semidirect
413. #518C2×D61semidirect
424. #428C2×D61semidirect
444. C2×#102C2×D61semidirect
448. #405C2×D61semidirect
457. C61#22897semidirect
475. AGL(1,ℤ/8)C4×D61semidirect
527. #103C22⋊D61semidirect
528. #103C22⋊D61semidirect
545. #102C22⋊D61semidirect
546. #102C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168399282
#214546512
#214543422
#214543412
#214466232
#214464812
#214464802
#214463302
#214463292
#214462172
#214460452
#214460422
#214456592
#214456582
C61×#29462
#2289761