Finite Group Databasebeta

← #29697357

Subgroups — #29697357

Order 15616.

894 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#21454474C211yesmaximal, characteristic, complemented
2#416×D61C211yesmaximal, characteristic
3#21454267C211yesmaximal, characteristic
4#21446533C211yesmaximal, characteristic, complemented
5#21446527C211yesmaximal, characteristic, complemented
6#21446469C211yesmaximal, characteristic, complemented
7#21446097C211yesmaximal, characteristic, complemented
8#21446091C211yesmaximal, characteristic, complemented
9#21445917C211yesmaximal, characteristic, complemented
10#21445854C211yesmaximal, characteristic, complemented
11#21445761C211yesmaximal, characteristic
12#21445665C211yesmaximal, characteristic, complemented
13#21445660C211yesmaximal, characteristic, complemented
14#21445594C211yesmaximal, characteristic, complemented
15C61×#1929C211yesmaximal, characteristic, complemented
16C2×#41×D61C2211yescharacteristic
17C2×#14519785C2211yescharacteristic
18C2×#14519783C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20#117×D61C2211yescharacteristic
21#16839824—21no—
22#16839821—21no—
23#16839817—21no—
24#16839813—21no—
25C2×#14519713C2211yescharacteristic, complemented
26#16839790C2211yescharacteristic, complemented
27#16839788C2211yescharacteristic, complemented
28C2×#14519705C2211yescharacteristic
29C2×#14519704C2211yescharacteristic
30C2×#14519703C2211yescharacteristic
31#16839759C2211yescharacteristic
32#16839758C2211yescharacteristic
33#16839757C411yescharacteristic, complemented
34#16839757C411yescharacteristic, complemented
35#16839756C2211yescharacteristic
36#16839755C411yescharacteristic, complemented
37#16839755C411yescharacteristic, complemented
38#103×D61C411yescharacteristic, complemented
39#103×D61C411yescharacteristic, complemented
40#102×D61C411yescharacteristic, complemented
41#102×D61C411yescharacteristic, complemented
42#16839729C2211yescharacteristic
43#16839727—21no—
44#16839727—21no—
45#16839725C2211yescharacteristic
46#16839725C2211yescharacteristic
47#16839724—21no—
48C2×#14519689C2211yescharacteristic
49C22⋊C8×D61—21no—
50#16839718C2211yescharacteristic, complemented
51C2×#14519688C2211yescharacteristic, complemented
52C2×#14519687C2211yescharacteristic, complemented
53C4×#11758198C2211yescharacteristic
54#16839526C2211yescharacteristic, complemented
55#16839526C2211yescharacteristic, complemented
56#16839523C2211yescharacteristic, complemented
57#16839522C2211yescharacteristic, complemented
58#16839521C2211yescharacteristic, complemented
59#16839516C2211yescharacteristic, complemented
60C2×#108×C61C2211yescharacteristic, complemented
61C2×#104×C61C2211yescharacteristic
62C61×#416C2211yescharacteristic
63C61×#408C2211yescharacteristic
64C61×#405C2211yescharacteristic, complemented
65C61×#339C2211yescharacteristic, complemented
66C61×#336C2211yescharacteristic, complemented
67C2×#11758226C2×C411yescharacteristic
68C2×#11758222—21no—
69C2×#11758222C2311yescharacteristic
70C2×#11758224—21no—
71C2×#11758224C2×C411yescharacteristic
72#41×D61—22no—
73#41×D61—22no—
74#41×D61—41no—
75#41×D61—41no—
76C2×Q8×D61C2×C411yescharacteristic
77C2×D4×D61—21no—
78C2×D4×D61C2×C411yescharacteristic
79C22×C4×D61—21no—
80C22×C4×D61C2311yescharacteristic
81#14519785—22no—
82#14519785—41no—
83#14519783—22no—
84#14519783—41no—
85C2×#11758194C2311yescharacteristic
86C2×#11758194C2311yescharacteristic
87C2×#11758189—21no—
88C2×#11758189—21no—
89C22×#92418C2311yescharacteristic
90C22×#92418C2311yescharacteristic
91C2×C8×D61—21no—
92C2×C8×D61—21no—
93C2×C8×D61—41no—
94C2×C8×D61—41no—
95C2×C8×D61C2×C411yescharacteristic
96C2×C8×D61C2×C411yescharacteristic
97C2×C8×D61C2×C411yescharacteristic
98C2×C8×D61C2×C411yescharacteristic
99#14519736C2311yescharacteristic
100#14519735C2×C411yescharacteristic
101#14519735C2×C411yescharacteristic
102#14519734—21no—
103#14519733—21no—
104C4⋊C4×D61C2×C411yescharacteristic
105C4⋊C4×D61C2×C411yescharacteristic
106C2×#11758198—21no—
107C22⋊C4×D61—21no—
108C2×C4×Dic61C2311yescharacteristic
109C42×D61—21no—
110#14519713—41no—
111#14519706—21no—
112#14519706—21no—
113#14519706—21no—
114#14519706—21no—
115#14519705—22no—
116#14519704—41no—
117#14519703—22no—
118#14519702C2×C411yescharacteristic
119#14519702C2×C411yescharacteristic
120#14519701C2×C411yescharacteristic
121#14519701C2×C411yescharacteristic
122#14519700C2×C411yescharacteristic
123#14519700C2×C411yescharacteristic
124#14519699C2×C411yescharacteristic
125#14519699C2×C411yescharacteristic
126#14519698C2×C411yescharacteristic
127#14519698C2×C411yescharacteristic
128#14519697C2×C411yescharacteristic
129#14519697C2×C411yescharacteristic
130C22⋊#92418—21no—
131C22⋊#92418—21no—
132#14519689—21no—
133#14519689—21no—
134#14519689—21no—
135#14519689—21no—
136#14519689D411yescharacteristic
137#14519689D411yescharacteristic
138#14519689D411yescharacteristic
139#14519689D411yescharacteristic
140#14519688—21no—
141#14519688—41no—
142#14519687—41no—
143C4×#92418—21no—
144#14519684—21no—
145C2×#41×C61C2311yescharacteristic
146C2×M16×C61C2311yescharacteristic
147C2×M16×C61C2311yescharacteristic
148C22×C8×C61C2311yescharacteristic
149C22×C8×C61C2311yescharacteristic
150#117×C61C2311yescharacteristic
151C2×C42×C61C2311yescharacteristic
152#108×C61—41no—
153#104×C61—41no—
154#103×C61C2×C411yescharacteristic
155#103×C61C2×C411yescharacteristic
156#102×C61C2×C411yescharacteristic
157#102×C61C2×C411yescharacteristic
158C22⋊C8×C61—21no—
159C22⋊C8×C61—21no—
160#97×C61—21no—
161C4×C8×C61—21no—
162C23×D61—21no—
163C23×D61#4111yescharacteristic
164#41×C61—21no—
165#41×C61—21no—
166#41×C61—21no—
167#41×C61—21no—
168C2×Q8×C61C22×C411yescharacteristic
169C2×D4×C61—21no—
170C2×D4×C61C22×C411yescharacteristic
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61C2411yescharacteristic
174C2×C22⋊D61—21no—
175C2×C22⋊D61—21no—
176C2×C22⋊D61—21no—
177C22×Dic61—21no—
178C22×Dic61—21no—
179C22×Dic61#4111yescharacteristic
180#11758226—22no—
181#11758226—41no—
182Q8×D61—22no—
183Q8×D61—41no—
184#11758224—22no—
185#11758224—41no—
186#11758224—42no—
187#11758224—42no—
188D4×D61—22no—
189D4×D61—41no—
190D4×D61—42no—
191D4×D61—42no—
192#11758222—21no—
193#11758222—21no—
194#11758222—42no—
195#11758222—42no—
196#11758222#4112yes—
197#11758222#4112yes—
198C2×D244—21no—
199C2×D244C22×C411yescharacteristic
200C2×C4×D61—21no—
201C2×C4×D61—21no—
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×D61C22×C411yescharacteristic
213C2×C4×D61C2×D411yescharacteristic
214C2×C4×D61C2×D411yescharacteristic
215C2×Dic122—21no—
216C2×Dic122C22×C411yescharacteristic
217M16×C61—21no—
218M16×C61—21no—
219M16×C61—21no—
220M16×C61—21no—
221C2×C8×C61—21no—
222C2×C8×C61—21no—
223C2×C8×C61—21no—
224C2×C8×C61—21no—
225C2×C8×C61—21no—
226C2×C8×C61—21no—
227C2×C8×C61C22×C411yescharacteristic
228C2×C8×C61C22×C411yescharacteristic
229C2×C8×C61C2×D411yescharacteristic
230C2×C8×C61C2×D411yescharacteristic
231C4⋊C4×C61C22×C411yescharacteristic
232C4⋊C4×C61C22×C411yescharacteristic
233C22⋊C4×C61—21no—
234C42×C61—21no—
235C42×C61—21no—
236C42×C61—21no—
237C22⋊Dic61—21no—
238#11758198—21no—
239#11758198—21no—
240#11758198—42no—
241C4⋊Dic61C22×C411yescharacteristic
242C4⋊Dic61C22×C411yescharacteristic
243#11758196—21no—
244#11758196—21no—
245C4×Dic61—21no—
246C4×Dic61—21no—
247C4×Dic61—21no—
248C4×Dic61—21no—
249C4×Dic61—21no—
250#11758194—21no—
251#11758194—21no—
252#11758194—21no—
253#11758194—21no—
254C2×#92418—21no—
255C2×#92418—21no—
256C2×#92418—21no—
257C2×#92418—21no—
258C2×#92418—21no—
259C2×#92418—21no—
260C2×#92418C22×C411yescharacteristic
261C2×#92418C22×C411yescharacteristic
262C2×#92418C2×D411yescharacteristic
263C2×#92418C2×D411yescharacteristic
264#11758189—42no—
265#11758189—42no—
266C8×D61—41no—
267C8×D61—41no—
268C8×D61—41no—
269C8×D61—41no—
270C8×D61—42no—
271C8×D61—42no—
272C23×C61—21no—
273C23×C61C2×#4111yescharacteristic
274C22×D61—21no—
275C22×D61—21no—
276C22×D61—21no—
277C22×D61—22no—
278C22×D61—41no—
279C22×D61—42no—
280C22×D61—42no—
281C22×D61—81no—
282C22×D61C4×D411yescharacteristic
283C22×D61C4×D411yescharacteristic
284Q8×C61—21no—
285Q8×C61—21no—
286D4×C61—21no—
287D4×C61—21no—
288D4×C61—41no—
289D4×C61—41no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61C23×C411yescharacteristic
299C2×C4×C61C22×D411yescharacteristic
300C2×C4×C61C2×#4111yescharacteristic
301C2×C4×C61C2×#4111yescharacteristic
302C2×C4×C61H(5,𝔽2)11yescharacteristic
303C2×C4×C61H(5,𝔽2)11yescharacteristic
304C22⋊D61—22no—
305C22⋊D61—22no—
306C22⋊D61—42no—
307C22⋊D61—42no—
308C2×Dic61—21no—
309C2×Dic61—21no—
310C2×Dic61—21no—
311C2×Dic61—21no—
312C2×Dic61—21no—
313C2×Dic61—42no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61C4×D411yescharacteristic
318C2×Dic61C4×D411yescharacteristic
319D244—21no—
320D244—42no—
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—21no—
331C4×D61—21no—
332C4×D61—42no—
333C4×D61—42no—
334C4×D61—42no—
335C4×D61—81no—
336Dic122—21no—
337Dic122—42no—
338Dic122#11712yes—
339C8×C61—21no—
340C8×C61—21no—
341C8×C61—21no—
342C8×C61—21no—
343C8×C61—41no—
344C8×C61—41no—
345#92418—21no—
346#92418—21no—
347#92418—21no—
348#92418—21no—
349#92418—41no—
350#92418—41no—
351#22586—611nomaximal, Sylow
352C22×C61—21no—
353C22×C61—21no—
354C22×C61—41no—
355C22×C61—41no—
356C22×C61—41no—
357C22×C61C2×C4×D411yescharacteristic
358C22×C61#55111yescharacteristic
359C22×C61#55111yescharacteristic
360C2×D61—21no—
361C2×D61—21no—
362C2×D61—21no—
363C2×D61—22no—
364C2×D61—21no—
365C2×D61—21no—
366C2×D61—42no—
367C2×D61—42no—
368C2×D61—41no—
369C2×D61—41no—
370C2×D61—84no—
371C2×D61#44412yes—
372C4×C61—41no—
373C4×C61—41no—
374C4×C61—41no—
375C4×C61—81no—
376C4×C61C2×#11711yescharacteristic
377C4×C61#51811yescharacteristic
378C4×C61#54611yescharacteristic
379C4×C61#54611yescharacteristic
380Dic61—22no—
381Dic61—21no—
382Dic61—21no—
383Dic61—41no—
384Dic61—41no—
385Dic61—81no—
386#2924—611no—
387C2×#416—611no—
388#2880—611no—
389#1938—611no—
390#1938—611no—
391#1929—611no—
392#1929D6111yescharacteristic, complemented
393#1866—611no—
394#1866—611no—
395#1826—611no—
396#1810—611no—
397#1789—611no—
398#1765—611no—
399#1765—611no—
400#1752—611no—
401C2×C61—21no—
402C2×C61—21no—
403C2×C61—81no—
404C2×C61#234211yescharacteristic
405C2×C61C2×#44411yescharacteristic
406C2×C61#295711yescharacteristic
407D61—22no—
408D61—41no—
409D61—42no—
410C22×#41—611no—
411C2×#131—611no—
412C2×#131—611no—
413C23×C8—611no—
414C2×#117—611no—
415#433—1221no—
416#433—1221no—
417#432—1221no—
418#431—1221no—
419C2×#108—611no—
420C2×#108C2×D6111yescharacteristic, complemented
421#424—611no—
422#424—611no—
423C2×#104—611no—
424C2×#104—611no—
425C2×#104—611no—
426C2×#104C2×D6111yescharacteristic
427#416—611no—
428#416—611no—
429#416—611no—
430#416—611no—
431#416—611no—
432#416—611no—
433#416—611no—
434#416C2×D6111yescharacteristic
435C2×#103—611no—
436C2×#103—611no—
437C2×#102—611no—
438C2×#102—611no—
439#408—611no—
440#408—1221no—
441#408—1221no—
442#408C2×D6111yescharacteristic
443#407—611no—
444#407—611no—
445#407—1221no—
446C2×C22⋊C8—611no—
447C2×C22⋊C8—1221no—
448#405—611no—
449#405C2×D6111yescharacteristic, complemented
450C2×#97—611no—
451C2×#97—611no—
452C4×C22⋊C4—611no—
453#341—611no—
454#341—611no—
455#339—611no—
456#339—611no—
457#339—611no—
458#339C2×D6111yescharacteristic, complemented
459#336—611no—
460#336C2×D6111yescharacteristic, complemented
461C61#2258611yescharacteristic, 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×#41C22×D6111yescharacteristic
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—1221no—
484C2×M16—1221no—
485C2×M16C22×D6111yescharacteristic
486C2×M16C22×D6111yescharacteristic
487C22×C8—611no—
488C22×C8—611no—
489C22×C8—611no—
490C22×C8—611no—
491C22×C8—611no—
492C22×C8—611no—
493C22×C8—1221no—
494C22×C8—1221no—
495C22×C8—2441no—
496C22×C8—2441no—
497C22×C8C22×D6111yescharacteristic
498C22×C8C22×D6111yescharacteristic
499#117—611no—
500#117—611no—
501#117—611no—
502#117—1221no—
503#117—1221no—
504#117C22×D6111yescharacteristic
505C2×C4⋊C4—611no—
506C2×C4⋊C4—611no—
507C2×C22⋊C4—1221no—
508C2×C22⋊C4—1221no—
509C2×C42—611no—
510C2×C42—1221no—
511C2×C42C22×D6111yescharacteristic
512#108—41no—
513#108—2441no—
514C4⋊C8—1221no—
515C4⋊C8—1221no—
516C4⋊C8—1221no—
517C4⋊C8—1221no—
518#104—41no—
519#104—1222no—
520#104—1222no—
521#104—2441no—
522#103—611no—
523#103—611no—
524#103—611no—
525#103—611no—
526#103—611no—
527#103—611no—
528#103C4×D6111yescharacteristic
529#103C4×D6111yescharacteristic
530#102—611no—
531#102—611no—
532#102—611no—
533#102—611no—
534#102—611no—
535#102—611no—
536#102C4×D6111yescharacteristic
537#102C4×D6111yescharacteristic
538C22⋊C8—21no—
539C22⋊C8—21no—
540C22⋊C8—611no—
541C22⋊C8—611no—
542C22⋊C8—611no—
543C22⋊C8—611no—
544C22⋊C8—1221no—
545C22⋊C8—1221no—
546C22⋊C8—1221no—
547C22⋊C8—1221no—
548C22⋊C8—1221no—
549C22⋊C8—1221no—
550#97—21no—
551#97—1221no—
552#97—2441no—
553#97—2441no—
554C4×C8—21no—
555C4×C8—1221no—
556#95—1221no—
557C24—611no—
558C24—1221no—
559#41—21no—
560#41—21no—
561#41—21no—
562#41—21no—
563#41—612no—
564#41—612no—
565#41—1221no—
566#41—1221no—
567#41—1222no—
568#41—1222no—
569#41—2442no—
570#41—2442no—
571#41—2441no—
572#41—2442no—
573#41—2442no—
574#41—2441no—
575C2×Q8—611no—
576C2×Q8—1221no—
577C2×Q8—1222no—
578C2×Q8—2441no—
579C2×Q8C2×C4×D6111yescharacteristic
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×D4C2×C4×D6111yescharacteristic
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×C4C23×D6111yescharacteristic
612M16—21no—
613M16—21no—
614M16—21no—
615M16—21no—
616M16—1221no—
617M16—1221no—
618M16—1221no—
619M16—1221no—
620M16—2442no—
621M16—2442no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
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—2441no—
639C2×C8—2441no—
640C2×C8—2441no—
641C2×C8—2441no—
642C2×C8—2442no—
643C2×C8—2442no—
644C2×C8C2×C4×D6111yescharacteristic
645C2×C8C2×C4×D6111yescharacteristic
646C2×C8D4×D6111yescharacteristic
647C2×C8D4×D6111yescharacteristic
648C4⋊C4—611no—
649C4⋊C4—611no—
650C4⋊C4—1221no—
651C4⋊C4—1221no—
652C4⋊C4C2×C4×D6111yescharacteristic
653C4⋊C4C2×C4×D6111yescharacteristic
654C22⋊C4—21no—
655C22⋊C4—1221no—
656C22⋊C4—1221no—
657C22⋊C4—1221no—
658C22⋊C4—2442no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—1221no—
663C42—1221no—
664C42—1221no—
665C42—1221no—
666C42—1221no—
667C23—21no—
668C23—611no—
669C23—611no—
670C23—1222no—
671C23—1221no—
672C23—1221no—
673C23—1221no—
674C23—4881no—
675C23—2441no—
676C23—2442no—
677C23—2442no—
678C23#41×D6111yescharacteristic
679Q8—21no—
680Q8—21no—
681Q8—612no—
682Q8—1221no—
683Q8—2442no—
684D4—21no—
685D4—21no—
686D4—41no—
687D4—41no—
688D4—612no—
689D4—1222no—
690D4—1222no—
691D4—1221no—
692D4—2442no—
693D4—2442no—
694D4—2442no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—611no—
704C2×C4—611no—
705C2×C4—1221no—
706C2×C4—1221no—
707C2×C4—1221no—
708C2×C4—1221no—
709C2×C4—1221no—
710C2×C4—1221no—
711C2×C4—1221no—
712C2×C4—1222no—
713C2×C4—1221no—
714C2×C4—1221no—
715C2×C4—1222no—
716C2×C4—1221no—
717C2×C4—1221no—
718C2×C4—1221no—
719C2×C4—1221no—
720C2×C4—4881no—
721C2×C4—2442no—
722C2×C4—2442no—
723C2×C4—2442no—
724C2×C4—2442no—
725C2×C4—2441no—
726C2×C4—2441no—
727C2×C4—2441no—
728C2×C4C22×C4×D6111yescharacteristic
729C2×C4C2×D4×D6111yescharacteristic
730C2×C4#41×D6111yescharacteristic
731C2×C4#41×D6111yescharacteristic
732C2×C4#1451982211yescharacteristic
733C2×C4#1451982311yescharacteristic
734C8—21no—
735C8—21no—
736C8—21no—
737C8—21no—
738C8—41no—
739C8—41no—
740C8—1221no—
741C8—1221no—
742C8—1221no—
743C8—1221no—
744C8—2441no—
745C8—2441no—
746C22—21no—
747C22—21no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—612no—
752C22—1221no—
753C22—1221no—
754C22—1221no—
755C22—1221no—
756C22—1221no—
757C22—1222no—
758C22—4884no—
759C22—2442no—
760C22—2442no—
761C22—2441no—
762C22—2441no—
763C22C4×D4×D6111yescharacteristic
764C22#1684043711yescharacteristic
765C22#1684044211yescharacteristic
766C4—41no—
767C4—41no—
768C4—41no—
769C4—81no—
770C4—1221no—
771C4—1221no—
772C4—1222no—
773C4—4881no—
774C4—2441no—
775C4—2441no—
776C4#117×D6111yescharacteristic
777C4#1684023411yescharacteristic
778C4#1684040411yescharacteristic
779C4#1684040911yescharacteristic
780C2—21no—
781C2—21no—
782C2—81no—
783C2—1222no—
784C2—2441no—
785C2—2442no—
786C2#2144866311yescharacteristic
787C2#444×D6111yescharacteristic
788C2#2145473111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1929C2
socleC22×C61C2×C4×D4
prime radicalC2×#41×D61C22
cosocleC22×C4×C61C24
hypercenter#1929D61
hypocenterC61#22586
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1929

Complements

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

NH ≅ G/Ntype
1. #21454474C2semidirect
4. #21446533C2semidirect
5. #21446527C2semidirect
6. #21446469C2semidirect
7. #21446097C2semidirect
8. #21446091C2semidirect
9. #21445917C2semidirect
10. #21445854C2semidirect
12. #21445665C2semidirect
13. #21445660C2semidirect
14. #21445594C2semidirect
15. C61×#1929C2semidirect
25. C2×#14519713C22semidirect
26. #16839790C22semidirect
27. #16839788C22semidirect
33. #16839757C4semidirect
34. #16839757C4semidirect
36. #16839755C4semidirect
37. #16839755C4semidirect
38. #103×D61C4semidirect
39. #103×D61C4semidirect
40. #102×D61C4semidirect
41. #102×D61C4semidirect
50. #16839718C22semidirect
51. C2×#14519688C22semidirect
52. C2×#14519687C22semidirect
54. #16839526C22semidirect
55. #16839526C22semidirect
56. #16839523C22semidirect
57. #16839522C22semidirect
58. #16839521C22semidirect
59. #16839516C22semidirect
60. C2×#108×C61C22semidirect
64. C61×#405C22semidirect
65. C61×#339C22semidirect
66. C61×#336C22semidirect
392. #1929D61semidirect
420. C2×#108C2×D61semidirect
449. #405C2×D61semidirect
458. #339C2×D61semidirect
460. #336C2×D61semidirect
461. C61#22586semidirect

Maximal subgroups

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

subgroupindex
#214544742
#416×D612
#214542672
#214465332
#214465272
#214464692
#214460972
#214460912
#214459172
#214458542
#214457612
#214456652
#214456602
#214455942
C61×#19292
#2258661