Finite Group Databasebeta

← #29686479

Subgroups — #29686479

Order 15616.

902 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455274C211yesmaximal, characteristic
2C2×#16839882C211yesmaximal, characteristic, complemented
3C2×#16839877C211yesmaximal, characteristic, complemented
4#21454538C211yesmaximal, characteristic, complemented
5#21446738C211yesmaximal, characteristic, complemented
6#21446594C211yesmaximal, characteristic, complemented
7#21446467C211yesmaximal, characteristic, complemented
8#21446467C211yesmaximal, characteristic, complemented
9#21446146C211yesmaximal, characteristic, complemented
10#21446146C211yesmaximal, characteristic, complemented
11#21445839C211yesmaximal, characteristic, complemented
12#21445691C211yesmaximal, characteristic, complemented
13#21445665C211yesmaximal, characteristic, complemented
14#21445658C211yesmaximal, characteristic, complemented
15C61×#2875C211yesmaximal, characteristic, complemented
16C2×#14519797C2211yescharacteristic
17C2×#14519797C2211yescharacteristic
18C2×#14519783C2211yescharacteristic
19C2×#14519783C2211yescharacteristic
20#16840312C2211yescharacteristic
21#16839984C411yescharacteristic, complemented
22#16839984C411yescharacteristic, complemented
23#16839977C411yescharacteristic, complemented
24#16839977C411yescharacteristic, complemented
25#16839972C411yescharacteristic, complemented
26#16839967C411yescharacteristic, complemented
27#16839962C411yescharacteristic, complemented
28#16839957C411yescharacteristic, complemented
29#16839882—24no—
30#16839877—24no—
31#16839835—21no—
32#16839835—21no—
33#16839835—21no—
34#16839835—21no—
35C2×#14519712C2211yescharacteristic
36C2×#14519712C2211yescharacteristic
37#16839786C2211yescharacteristic
38C2×C4⋊#92418C2211yescharacteristic
39C2×#14519704C2211yescharacteristic
40C2×#14519704C2211yescharacteristic
41C2×#14519703C2211yescharacteristic
42C2×#14519703C2211yescharacteristic
43C2×#14519703C2211yescharacteristic
44C2×#14519703C2211yescharacteristic
45#16839756C2211yescharacteristic
46#16839756C2211yescharacteristic
47#16839728C2211yescharacteristic
48#16839728C2211yescharacteristic
49C2×#14519687C2211yescharacteristic
50C2×C8×Dic61C2211yescharacteristic
51C4×C4⋊Dic61C2211yescharacteristic
52#16839526C2211yescharacteristic
53#16839526C2211yescharacteristic
54#16839521C2211yescharacteristic
55#16839521C2211yescharacteristic
56#16839516C2211yescharacteristic
57#16839516C2211yescharacteristic
58C2×#131×C61C2211yescharacteristic
59C2×#131×C61C2211yescharacteristic
60C4×#41×C61C2211yescharacteristic
61C61×#405—21no—
62C61×#405—21no—
63C61×#405C2211yescharacteristic
64C61×#405C2211yescharacteristic
65C4×M16×C61—21no—
66C4×M16×C61C2211yescharacteristic
67C2×#97×C61—21no—
68C2×#97×C61C2211yescharacteristic
69C2×#11758222C2311yescharacteristic
70C2×#11758222C2311yescharacteristic
71#14519797—22no—
72#14519797—22no—
73#14519797—22no—
74#14519797—22no—
75C2×#11758202C2×C411yescharacteristic
76C2×#11758202C2×C411yescharacteristic
77C2×#11758200C2×C411yescharacteristic
78C2×#11758200C2×C411yescharacteristic
79C2×#11758201C2×C411yescharacteristic
80C2×#11758201C2×C411yescharacteristic
81C2×#11758199C2×C411yescharacteristic
82C2×#11758199C2×C411yescharacteristic
83#14519783—22no—
84#14519783—22no—
85#14519783—22no—
86#14519783—22no—
87C2×#11758194C2311yescharacteristic
88C2×#11758194C2311yescharacteristic
89C2×#11758189—21no—
90C2×#11758189—21no—
91C22×#92418C2311yescharacteristic
92C22×#92418C2311yescharacteristic
93C2×C8×D61—21no—
94C2×C8×D61—21no—
95#14519777C2×C411yescharacteristic
96#14519774C2×C411yescharacteristic
97#14519765C2×C411yescharacteristic
98#14519765C2×C411yescharacteristic
99#14519751—21no—
100#14519751—21no—
101C4×D244—21no—
102C4×D244—21no—
103C2×C4⋊Dic61—21no—
104C2×C4×Dic61C2311yescharacteristic
105C2×C4×Dic61C2311yescharacteristic
106#14519712—22no—
107#14519712—22no—
108C4⋊#92418—21no—
109C4⋊#92418—21no—
110C4⋊#92418C2×C411yescharacteristic
111C4⋊#92418C2×C411yescharacteristic
112C4⋊#92418C2×C411yescharacteristic
113C4⋊#92418C2×C411yescharacteristic
114#14519704—22no—
115#14519704—22no—
116#14519703—22no—
117#14519703—22no—
118#14519703—22no—
119#14519703—22no—
120#14519700C2×C411yescharacteristic
121#14519700C2×C411yescharacteristic
122#14519700C2×C411yescharacteristic
123#14519700C2×C411yescharacteristic
124#14519697C2×C411yescharacteristic
125#14519697C2×C411yescharacteristic
126#14519697C2×C411yescharacteristic
127#14519697C2×C411yescharacteristic
128#14519689—21no—
129#14519689—21no—
130#14519689—21no—
131#14519689—21no—
132#14519687—22no—
133C8×Dic61—22no—
134#14519684—21no—
135C2×#41×C61C2311yescharacteristic
136#131×C61—22no—
137#131×C61—22no—
138#131×C61—22no—
139#131×C61D414yescomplemented
140C2×M16×C61—21no—
141C2×M16×C61—21no—
142C2×M16×C61C2311yescharacteristic
143C2×M16×C61C2311yescharacteristic
144C22×C8×C61—21no—
145C22×C8×C61—21no—
146C22×C8×C61C2311yescharacteristic
147C22×C8×C61C2311yescharacteristic
148C4×Q8×C61C2×C411yescharacteristic
149C4×Q8×C61C2×C411yescharacteristic
150C4×D4×C61—21no—
151C4×D4×C61—21no—
152C4×D4×C61C2×C411yescharacteristic
153C4×D4×C61C2×C411yescharacteristic
154#117×C61—21no—
155#117×C61C2311yescharacteristic
156C2×C42×C61—21no—
157C2×C42×C61C2311yescharacteristic
158#97×C61—21no—
159#97×C61—21no—
160#97×C61—21no—
161#97×C61D411yescharacteristic
162#97×C61D411yescharacteristic
163#97×C61D411yescharacteristic
164#97×C61D411yescharacteristic
165C4×C8×C61—21no—
166C4×C8×C61—21no—
167C4×C8×C61—21no—
168#41×C61—21no—
169#41×C61—21no—
170#41×C61C2×D412yes—
171#41×C61#4112yes—
172C2×Q8×C61C22×C411yescharacteristic
173C2×D4×C61—21no—
174C2×D4×C61C22×C411yescharacteristic
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61#4111yescharacteristic
179C22×C4×C61#4111yescharacteristic
180C22×C4×C61C2411yescharacteristic
181C2×C22⋊D61—21no—
182C2×C22⋊D61—21no—
183C22×Dic61—21no—
184C22×Dic61—21no—
185#11758222—21no—
186#11758222—21no—
187#11758222—21no—
188#11758222—21no—
189#11758222—21no—
190#11758222—21no—
191#11758222—21no—
192#11758222—21no—
193C2×D244—21no—
194C2×D244—21no—
195C2×D244C22×C411yescharacteristic
196C2×D244C22×C411yescharacteristic
197C2×C4×D61—21no—
198C2×C4×D61—21no—
199C2×Dic122C22×C411yescharacteristic
200C2×Dic122C22×C411yescharacteristic
201M16×C61—24no—
202M16×C61—21no—
203M16×C61—21no—
204M16×C61—24no—
205M16×C61C2×D412yes—
206M16×C61#4112yes—
207C2×C8×C61—24no—
208C2×C8×C61—21no—
209C2×C8×C61—21no—
210C2×C8×C61—21no—
211C2×C8×C61—21no—
212C2×C8×C61—24no—
213C2×C8×C61C2×D411yescharacteristic
214C2×C8×C61C2×D411yescharacteristic
215C2×C8×C61C2×D412yes—
216C2×C8×C61C2×D411yescharacteristic
217C2×C8×C61C2×D411yescharacteristic
218C2×C8×C61#4112yes—
219C4⋊C4×C61—21no—
220C4⋊C4×C61—21no—
221C4⋊C4×C61C22×C411yescharacteristic
222C4⋊C4×C61C22×C411yescharacteristic
223C22⋊C4×C61—21no—
224C22⋊C4×C61—21no—
225C22⋊C4×C61—21no—
226C42×C61—21no—
227C42×C61—21no—
228C42×C61—21no—
229C42×C61C22×C411yescharacteristic
230C42×C61C22×C411yescharacteristic
231C42×C61C2×D411yescharacteristic
232C42×C61C2×D411yescharacteristic
233#11758202—22no—
234#11758202—22no—
235#11758201—22no—
236#11758201—22no—
237#11758200—22no—
238#11758200—22no—
239#11758199—22no—
240#11758199—22no—
241#11758198—21no—
242#11758198—21no—
243#11758198—21no—
244#11758198—21no—
245C4⋊Dic61—21no—
246C4⋊Dic61—21no—
247C4⋊Dic61—42no—
248C4×Dic61—21no—
249C4×Dic61—21no—
250C4×Dic61—21no—
251C4×Dic61—21no—
252#11758194—21no—
253#11758194—21no—
254#11758194—21no—
255#11758194—21no—
256C2×#92418—21no—
257C2×#92418—21no—
258C2×#92418—21no—
259C2×#92418—21no—
260C2×#92418—21no—
261C2×#92418—21no—
262C2×#92418C22×C411yescharacteristic
263C2×#92418C22×C411yescharacteristic
264C2×#92418C22×C411yescharacteristic
265C2×#92418C22×C411yescharacteristic
266#11758189—42no—
267#11758189—42no—
268C8×D61—42no—
269C8×D61—42no—
270C23×C61—21no—
271C23×C61C2×#4111yescharacteristic
272C22×D61—21no—
273C22×D61—21no—
274Q8×C61—21no—
275Q8×C61C4×D412yes—
276D4×C61—22no—
277D4×C61—22no—
278D4×C61—21no—
279D4×C61C4×D412yes—
280C2×C4×C61—21no—
281C2×C4×C61—22no—
282C2×C4×C61—22no—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
285C2×C4×C61—41no—
286C2×C4×C61—41no—
287C2×C4×C61—81no—
288C2×C4×C61—81no—
289C2×C4×C61C4×D411yescharacteristic
290C2×C4×C61C4×D411yescharacteristic
291C2×C4×C61C4×D411yescharacteristic
292C2×C4×C61C4×D411yescharacteristic
293C2×C4×C61C23×C411yescharacteristic
294C2×C4×C61C22×D411yescharacteristic
295C2×C4×C61C22×D411yescharacteristic
296C2×C4×C61C2×#4111yescharacteristic
297C2×C4×C61C2×#4111yescharacteristic
298C2×C4×C61C2×#4111yescharacteristic
299C22⋊D61—41no—
300C22⋊D61—41no—
301C22⋊D61—41no—
302C22⋊D61—41no—
303C2×Dic61—22no—
304C2×Dic61—21no—
305C2×Dic61—21no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311D244—21no—
312D244—21no—
313D244—21no—
314D244—21no—
315D244—81no—
316D244—81no—
317C4×D61—41no—
318C4×D61—41no—
319C4×D61—41no—
320C4×D61—41no—
321Dic122—21no—
322Dic122—21no—
323Dic122—21no—
324Dic122—21no—
325C8×C61—22no—
326C8×C61—21no—
327C8×C61—22no—
328C8×C61—21no—
329C8×C61#12112yes—
330C8×C61#12112yes—
331#92418—21no—
332#92418—21no—
333#92418—21no—
334#92418—21no—
335#92418—41no—
336#92418—41no—
337#21519—611nomaximal, Sylow
338C22×C61—21no—
339C22×C61—21no—
340C22×C61—22no—
341C22×C61—41no—
342C22×C61—41no—
343C22×C61C2×C4×D411yescharacteristic
344C22×C61#52911yescharacteristic
345C22×C61#53211yescharacteristic
346C2×D61—41no—
347C2×D61—41no—
348C2×D61—41no—
349C2×D61—41no—
350C2×D61—41no—
351C2×D61—41no—
352C4×C61—21no—
353C4×C61—21no—
354C4×C61—21no—
355C4×C61—21no—
356C4×C61—22no—
357C4×C61—41no—
358C4×C61—41no—
359C4×C61C2×C4×D411yescharacteristic
360C4×C61C4×#4111yescharacteristic
361C4×C61C2×#12111yescharacteristic
362C4×C61#52511yescharacteristic
363Dic61—42no—
364Dic61—41no—
365Dic61—41no—
366Dic61—81no—
367#3035—611no—
368C2×#444—611no—
369C2×#443—611no—
370#2932—611no—
371#2875D6111yescharacteristic, complemented
372#1980—611no—
373#1950—611no—
374#1929—611no—
375#1929—611no—
376#1876—611no—
377#1876—611no—
378#1806—611no—
379#1771—611no—
380#1765—611no—
381#1764—611no—
382C2×C61—21no—
383C2×C61—21no—
384C2×C61—42no—
385C2×C61C4×#12111yescharacteristic
386C2×C61#295611yescharacteristic
387C2×C61#295711yescharacteristic
388D61—81no—
389D61—81no—
390C2×#135—611no—
391C2×#135—611no—
392C2×#131—611no—
393C2×#131—611no—
394C2×#131C2×D6111yescharacteristic
395C2×#131C2×D6111yescharacteristic
396#532—611no—
397C4×#41C2×D6111yescharacteristic
398#464—611no—
399#464—611no—
400#463—611no—
401#463—611no—
402#462—611no—
403#461—611no—
404#460—611no—
405#459—611no—
406#444—1224no—
407#443—1224no—
408#435—1221no—
409#435—1221no—
410#435—1221no—
411#435—1221no—
412C2×#108—611no—
413C2×#108—611no—
414#423—611no—
415C2×C4⋊C8—611no—
416C2×#104—611no—
417C2×#104—611no—
418C2×#104—611no—
419C2×#104—611no—
420C2×#104—611no—
421C2×#104—611no—
422#416—611no—
423#416—611no—
424#408—611no—
425#408—611no—
426#405—21no—
427#405—21no—
428#405C2×D6111yescharacteristic
429#405C2×D6111yescharacteristic
430C4×M16—21no—
431C4×M16C2×D6111yescharacteristic
432C2×#97—21no—
433C2×#97—611no—
434C2×#97C2×D6111yescharacteristic
435C2×C4×C8—611no—
436C4×C4⋊C4—611no—
437#341—611no—
438#341—611no—
439#339—611no—
440#339—611no—
441#336—611no—
442#336—611no—
443C61#2151911yescharacteristic, complemented, Sylow
444C2×#41—611no—
445C2×#41—611no—
446C2×#41C22×D6111yescharacteristic
447#135—1222no—
448#135—1222no—
449#135—1222no—
450#135—1222no—
451C2×Q16—611no—
452C2×Q16—611no—
453C2×SD16—611no—
454C2×SD16—611no—
455C2×SD16—611no—
456C2×SD16—611no—
457C2×D8—611no—
458C2×D8—611no—
459#131—22no—
460#131—22no—
461#131—22no—
462#131—1222no—
463#131—1222no—
464#131—1222no—
465#131—1222no—
466#131D24414yescomplemented
467C2×M16—21no—
468C2×M16—21no—
469C2×M16—611no—
470C2×M16—611no—
471C2×M16—1221no—
472C2×M16—1221no—
473C2×M16C22×D6111yescharacteristic
474C2×M16C22×D6111yescharacteristic
475C22×C8—21no—
476C22×C8—21no—
477C22×C8—611no—
478C22×C8—611no—
479C22×C8—1221no—
480C22×C8—1221no—
481C22×C8C22×D6111yescharacteristic
482C22×C8C22×D6111yescharacteristic
483C4⋊Q8—611no—
484#127—611no—
485#124—611no—
486#124—611no—
487#121—1221no—
488#121—1221no—
489C4×Q8C4×D6111yescharacteristic
490C4×Q8C4×D6111yescharacteristic
491C4×D4—21no—
492C4×D4—21no—
493C4×D4—1221no—
494C4×D4—1221no—
495C4×D4C4×D6111yescharacteristic
496C4×D4C4×D6111yescharacteristic
497#117—21no—
498#117C22×D6111yescharacteristic
499C2×C4⋊C4—1221no—
500C2×C42—21no—
501C2×C42—611no—
502C2×C42—611no—
503C2×C42C22×D6111yescharacteristic
504#108—1222no—
505#108—1222no—
506C4⋊C8—611no—
507C4⋊C8—611no—
508C4⋊C8—611no—
509C4⋊C8—611no—
510C4⋊C8—1221no—
511C4⋊C8—1221no—
512#104—1222no—
513#104—1222no—
514#104—1222no—
515#104—1222no—
516#104—1222no—
517#104—1222no—
518#103—611no—
519#103—611no—
520#103—611no—
521#103—611no—
522#102—611no—
523#102—611no—
524#102—611no—
525#102—611no—
526C22⋊C8—1221no—
527C22⋊C8—1221no—
528C22⋊C8—1221no—
529C22⋊C8—1221no—
530#97—21no—
531#97—21no—
532#97—21no—
533#97—1222no—
534#97C22⋊D6111yescharacteristic
535#97C22⋊D6111yescharacteristic
536#97C22⋊D6111yescharacteristic
537#97C22⋊D6111yescharacteristic
538C4×C8—21no—
539C4×C8—21no—
540C4×C8—21no—
541C4×C8—1222no—
542#95—1221no—
543#41—21no—
544#41—21no—
545#41—1221no—
546#41—1221no—
547#41—1221no—
548#41—1221no—
549#41—1221no—
550#41—1221no—
551#41—1221no—
552#41—1221no—
553#41C2×D24412yes—
554#41#1175822212yes—
555C2×Q8—611no—
556C2×Q8—611no—
557C2×Q8C2×C4×D6111yescharacteristic
558C2×D4—21no—
559C2×D4—611no—
560C2×D4—611no—
561C2×D4—1221no—
562C2×D4—1221no—
563C2×D4—1221no—
564C2×D4—1221no—
565C2×D4C2×C4×D6111yescharacteristic
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—1221no—
570C22×C4—1221no—
571C22×C4—1221no—
572C22×C4—1221no—
573C22×C4#1175822211yescharacteristic
574C22×C4#1175822211yescharacteristic
575C22×C4C23×D6111yescharacteristic
576Q16—1222no—
577Q16—1222no—
578SD16—1222no—
579SD16—1222no—
580SD16—1222no—
581SD16—1222no—
582D8—1222no—
583D8—1222no—
584M16—24no—
585M16—21no—
586M16—21no—
587M16—24no—
588M16—1221no—
589M16—1221no—
590M16—1221no—
591M16—1221no—
592M16—2442no—
593M16—2442no—
594M16C2×D24412yes—
595M16#1175822212yes—
596C2×C8—24no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—24no—
602C2×C8—611no—
603C2×C8—611no—
604C2×C8—611no—
605C2×C8—611no—
606C2×C8—1221no—
607C2×C8—1221no—
608C2×C8—1221no—
609C2×C8—1221no—
610C2×C8—1221no—
611C2×C8—1221no—
612C2×C8—2442no—
613C2×C8—2442no—
614C2×C8C2×D24412yes—
615C2×C8#1175822212yes—
616C2×C8C2×C22⋊D6111yescharacteristic
617C2×C8C2×C22⋊D6111yescharacteristic
618C2×C8C2×C22⋊D6111yescharacteristic
619C2×C8C2×C22⋊D6111yescharacteristic
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—1221no—
623C4⋊C4—1221no—
624C4⋊C4—2442no—
625C4⋊C4C2×C4×D6111yescharacteristic
626C4⋊C4C2×C4×D6111yescharacteristic
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—1221no—
631C22⋊C4—1221no—
632C22⋊C4—1221no—
633C22⋊C4—1221no—
634C42—21no—
635C42—21no—
636C42—21no—
637C42—1221no—
638C42—1221no—
639C42—1221no—
640C42—1221no—
641C42C2×C4×D6111yescharacteristic
642C42C2×C4×D6111yescharacteristic
643C42C2×C22⋊D6111yescharacteristic
644C42C2×C22⋊D6111yescharacteristic
645C23—21no—
646C23—1221no—
647C23—1221no—
648C23C2×#1175822211yescharacteristic
649Q8—21no—
650Q8—1221no—
651Q8—1221no—
652Q8—1221no—
653Q8—1221no—
654Q8C4×D24412yes—
655D4—22no—
656D4—22no—
657D4—21no—
658D4—1221no—
659D4—1221no—
660D4—1221no—
661D4—1221no—
662D4—4881no—
663D4—4881no—
664D4—2441no—
665D4—2441no—
666D4—2441no—
667D4—2441no—
668D4C4×D24412yes—
669C2×C4—21no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—81no—
677C2×C4—81no—
678C2×C4—1222no—
679C2×C4—1221no—
680C2×C4—1221no—
681C2×C4—2441no—
682C2×C4—2441no—
683C2×C4—2441no—
684C2×C4—2441no—
685C2×C4—2441no—
686C2×C4—2441no—
687C2×C4—2441no—
688C2×C4—2441no—
689C2×C4—2441no—
690C2×C4C4×C22⋊D6111yescharacteristic
691C2×C4C4×C22⋊D6111yescharacteristic
692C2×C4C4×C22⋊D6111yescharacteristic
693C2×C4C4×C22⋊D6111yescharacteristic
694C2×C4C22×C4×D6111yescharacteristic
695C2×C4C22×C22⋊D6111yescharacteristic
696C2×C4C22×D24411yescharacteristic
697C2×C4C2×#1175822211yescharacteristic
698C2×C4C2×#1175822211yescharacteristic
699C2×C4C2×#1175822211yescharacteristic
700C8—22no—
701C8—21no—
702C8—22no—
703C8—21no—
704C8—1221no—
705C8—1221no—
706C8—1221no—
707C8—1221no—
708C8—2441no—
709C8—2441no—
710C8#1451975112yes—
711C8#1451975112yes—
712C22—21no—
713C22—21no—
714C22—22no—
715C22—41no—
716C22—41no—
717C22—2441no—
718C22—2441no—
719C22—2441no—
720C22—2441no—
721C22—2441no—
722C22—2441no—
723C22C2×C4×C22⋊D6111yescharacteristic
724C22#1684029611yescharacteristic
725C22#1684031211yescharacteristic
726C4—21no—
727C4—21no—
728C4—22no—
729C4—21no—
730C4—21no—
731C4—41no—
732C4—41no—
733C4—4881no—
734C4—2442no—
735C4—2441no—
736C4—2441no—
737C4C2×C4×D24411yescharacteristic
738C4C4×#1175822211yescharacteristic
739C4C2×#1451975111yescharacteristic
740C4#1684027311yescharacteristic
741C2—21no—
742C2—21no—
743C2—42no—
744C2—4881no—
745C2—4881no—
746C2C4×#1451975111yescharacteristic
747C2#2145472611yescharacteristic
748C2#2145473411yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2875C2
socleC22×C61C2×C4×D4
prime radical#21455274C2
cosocleC22×C4×C61C24
hypercenter#2875D61
hypocenterC61#21519
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×#97 ◁ #2875

Complements

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

NH ≅ G/Ntype
2. C2×#16839882C2semidirect
3. C2×#16839877C2semidirect
4. #21454538C2semidirect
5. #21446738C2semidirect
6. #21446594C2semidirect
7. #21446467C2semidirect
8. #21446467C2semidirect
9. #21446146C2semidirect
10. #21446146C2semidirect
11. #21445839C2semidirect
12. #21445691C2semidirect
13. #21445665C2semidirect
14. #21445658C2semidirect
15. C61×#2875C2semidirect
21. #16839984C4semidirect
22. #16839984C4semidirect
23. #16839977C4semidirect
24. #16839977C4semidirect
25. #16839972C4semidirect
26. #16839967C4semidirect
27. #16839962C4semidirect
28. #16839957C4semidirect
139. #131×C61D4semidirect
371. #2875D61semidirect
443. C61#21519semidirect
466. #131D244semidirect

Maximal subgroups

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

subgroupindex
#214552742
C2×#168398822
C2×#168398772
#214545382
#214467382
#214465942
#214464672
#214461462
#214458392
#214456912
#214456652
#214456582
C61×#28752
#2151961