Finite Group Databasebeta

← #29779371

Subgroups — #29779371

Order 15616.

780 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21449669C211yesmaximal, characteristic, complemented
2#21447315C211yesmaximal, characteristic, complemented
3#21447223C211yesmaximal, characteristic, complemented
4#21447129C211yesmaximal, characteristic
5#21446955C211yesmaximal, characteristic, complemented
6#21446779C211yesmaximal, characteristic, complemented
7#21446684C211yesmaximal, characteristic
8#21446519C211yesmaximal, characteristic, complemented
9#21446519C211yesmaximal, characteristic, complemented
10#21446515C211yesmaximal, characteristic, complemented
11#21446411C211yesmaximal, characteristic, complemented
12#21446170C211yesmaximal, characteristic
13#21445694C211yesmaximal, characteristic, complemented
14#21445647C211yesmaximal, characteristic, complemented
15C61×#2512C211yesmaximal, characteristic, complemented
16C22×#11758199C2211yescharacteristic
17C2×#14519777C2211yescharacteristic
18C2×#14519755—21no—
19C2×C4×D244C2211yescharacteristic
20C2×#14519710C2211yescharacteristic
21C2×C4⋊#92418C2211yescharacteristic
22C2×#14519698C2211yescharacteristic
23C2×#14519698C2211yescharacteristic
24C2×#14519698C2211yescharacteristic
25C2×#14519697C2211yescharacteristic
26C2×#14519697C2211yescharacteristic
27C2×#14519697C2211yescharacteristic
28C2×#14519688C2211yescharacteristic
29C2×#14519688C2211yescharacteristic
30C2×C4×#92418C2211yescharacteristic
31#16839684—21no—
32#16839675—21no—
33#16839664C2211yescharacteristic
34#16839664C2211yescharacteristic
35#16839660C2211yescharacteristic
36#16839660C2211yescharacteristic
37#16839636—21no—
38#16839524C2211yescharacteristic
39#16839524C2211yescharacteristic
40#16839524C2211yescharacteristic
41#16839524C2211yescharacteristic
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839517C2211yescharacteristic
47#16839517C2211yescharacteristic
48C2×#126×C61—21no—
49C61×#397—21no—
50C61×#396—21no—
51C61×#390C2211yescharacteristic
52C61×#390C2211yescharacteristic
53C61×#390C2211yescharacteristic
54C61×#389C2211yescharacteristic
55C61×#388—21no—
56C61×#384C2211yescharacteristic
57C4×C4⋊C4×C61C2211yescharacteristic
58C4×C4⋊C4×C61C2211yescharacteristic
59C22×Dic122—21no—
60C22×D244C2311yescharacteristic
61C22×C4×D61—21no—
62C2×#11758199—22no—
63C2×#11758199—22no—
64C2×#11758199—41no—
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69#14519777—22no—
70#14519777—41no—
71#14519755—44no—
72C4×D244—22no—
73C4×D244—41no—
74C2×C4⋊Dic61—21no—
75C2×C4⋊Dic61C2311yescharacteristic
76C2×C4⋊Dic61C2311yescharacteristic
77C2×C4⋊Dic61C2311yescharacteristic
78C2×#11758196—21no—
79C2×#11758196—21no—
80C2×#11758198—21no—
81C2×#11758198—21no—
82C2×#11758198—21no—
83C2×#11758198—21no—
84C2×#11758198—21no—
85#14519710—22no—
86C4⋊#92418—22no—
87#14519698—22no—
88#14519698—22no—
89#14519698—41no—
90#14519697—22no—
91#14519697—22no—
92#14519697—22no—
93#14519688—22no—
94#14519688—41no—
95C4×#92418—41no—
96#14519684—21no—
97#14519684—21no—
98C22×D4×C61C2311yescharacteristic
99#126×C61—44no—
100C2×C4⋊C4×C61—21no—
101C2×C4⋊C4×C61—21no—
102C2×C4⋊C4×C61—21no—
103C2×C4⋊C4×C61D411yescharacteristic
104C2×C4⋊C4×C61D411yescharacteristic
105C2×C4⋊C4×C61C2311yescharacteristic
106C2×C4⋊C4×C61C2311yescharacteristic
107C2×C4⋊C4×C61C2311yescharacteristic
108C2×C22⋊C4×C61—21no—
109C2×C22⋊C4×C61—21no—
110C2×C22⋊C4×C61—21no—
111C2×C22⋊C4×C61—21no—
112C2×C22⋊C4×C61—21no—
113C2×C22⋊C4×C61—21no—
114C2×C42×C61—21no—
115C2×C42×C61C2311yescharacteristic
116C2×C42×C61C2311yescharacteristic
117C2×C42×C61C2311yescharacteristic
118#95×C61—21no—
119#95×C61—21no—
120#95×C61D411yescharacteristic
121#95×C61D411yescharacteristic
122C24×C61—21no—
123C23×D61—21no—
124C2×D4×C61—21no—
125C2×D4×C61—21no—
126C2×D4×C61—21no—
127C2×D4×C61—21no—
128C2×D4×C61—21no—
129C2×D4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61—21no—
132C22×C4×C61—21no—
133C22×C4×C61C2×D411yescharacteristic
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2×D411yescharacteristic
139C22×C4×C61C2411yescharacteristic
140C22×Dic61—21no—
141C22×Dic61—21no—
142C22×Dic61—21no—
143C2×D244—21no—
144C2×D244—21no—
145C2×D244—21no—
146C2×D244—21no—
147C2×D244—21no—
148C2×D244#4112yes—
149C2×C4×D61—42no—
150C2×C4×D61—42no—
151C2×C4×D61—81no—
152C2×Dic122—42no—
153C2×Dic122—42no—
154C2×Dic122—81no—
155C4⋊C4×C61—22no—
156C4⋊C4×C61—22no—
157C4⋊C4×C61—21no—
158C4⋊C4×C61—21no—
159C4⋊C4×C61—21no—
160C4⋊C4×C61—21no—
161C4⋊C4×C61—21no—
162C4⋊C4×C61—21no—
163C4⋊C4×C61—42no—
164C4⋊C4×C61—42no—
165C4⋊C4×C61—81no—
166C22⋊C4×C61—42no—
167C22⋊C4×C61—42no—
168C22⋊C4×C61—42no—
169C22⋊C4×C61—42no—
170C22⋊C4×C61—81no—
171C22⋊C4×C61—81no—
172C42×C61—21no—
173C42×C61—21no—
174C42×C61—21no—
175C42×C61—21no—
176C42×C61—21no—
177C42×C61—21no—
178C42×C61—42no—
179#11758199—44no—
180#11758198—42no—
181#11758198—42no—
182#11758198—42no—
183#11758198—42no—
184#11758198—81no—
185C4⋊Dic61—21no—
186C4⋊Dic61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—42no—
191C4⋊Dic61#4112yes—
192#11758196—42no—
193#11758196—42no—
194C2×#92418—21no—
195C2×#92418—21no—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418#4112yes—
205C2×#92418#4112yes—
206C23×C61—41no—
207C23×C61—41no—
208C23×C61—41no—
209C23×C61—41no—
210C23×C61—41no—
211C23×C61—41no—
212C23×C61—41no—
213C23×C61C22×D411yescharacteristic
214C22×D61—22no—
215C22×D61—41no—
216C22×D61—41no—
217C22×D61—41no—
218C22×D61—41no—
219C22×D61—41no—
220C22×D61—41no—
221D4×C61—41no—
222D4×C61—41no—
223D4×C61—41no—
224D4×C61—41no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—21no—
236C2×C4×C61—21no—
237C2×C4×C61—21no—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—21no—
241C2×C4×C61—41no—
242C2×C4×C61—41no—
243C2×C4×C61—41no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61—41no—
247C2×C4×C61—41no—
248C2×C4×C61—41no—
249C2×C4×C61—41no—
250C2×C4×C61AGL(1,ℤ/8)12yes—
251C2×C4×C61AGL(1,ℤ/8)12yes—
252C2×C4×C61C2×#4111yescharacteristic
253C2×C4×C61C2×#4111yescharacteristic
254C2×C4×C61C2×#4111yescharacteristic
255C2×C4×C61C2×#4111yescharacteristic
256C2×C4×C61H(5,𝔽2)11yescharacteristic
257C2×C4×C612−1+411yescharacteristic
258C2×Dic61—22no—
259C2×Dic61—41no—
260C2×Dic61—41no—
261C2×Dic61—41no—
262C2×Dic61—41no—
263C2×Dic61—41no—
264C2×Dic61—41no—
265C2×Dic61—41no—
266C2×Dic61—41no—
267D244—22no—
268D244—22no—
269D244—41no—
270D244—41no—
271C4×D61—84no—
272Dic122—84no—
273#92418—22no—
274#92418—22no—
275#92418—41no—
276#92418—41no—
277#29095—611nomaximal, Sylow
278C22×C61—81no—
279C22×C61—81no—
280C22×C61—81no—
281C22×C61—81no—
282C22×C61—81no—
283C22×C61—81no—
284C22×C61—81no—
285C22×C61#53211yescharacteristic
286C22×C61#54611yescharacteristic
287C22×C61#54811yescharacteristic
288C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
289C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
290C22×C61#57611yescharacteristic
291C22×C61#57811yescharacteristic
292C2×D61—42no—
293C2×D61—42no—
294C2×D61—42no—
295C2×D61—81no—
296C2×D61—81no—
297C2×D61—81no—
298C2×D61—81no—
299C4×C61—22no—
300C4×C61—22no—
301C4×C61—41no—
302C4×C61—41no—
303C4×C61—41no—
304C4×C61—41no—
305C4×C61—81no—
306C4×C61—81no—
307C4×C61—81no—
308C4×C61#52911yescharacteristic
309C4×C61#53911yescharacteristic
310C4×C61#55111yescharacteristic
311C4×C61#55611yescharacteristic
312Dic61—42no—
313Dic61—81no—
314Dic61—81no—
315#2512D6111yescharacteristic, complemented
316#2452—611no—
317#2087—611no—
318#2071—611no—
319#2054—611no—
320#2023—611no—
321#1990—611no—
322#1970—611no—
323#1936—611no—
324#1936—611no—
325#1936—611no—
326#1921—611no—
327#1879—611no—
328#1771—611no—
329#1762—611no—
330C2×C61—161no—
331C2×C61#256011yescharacteristic
332C2×C61#317511yescharacteristic
333C2×C61#318411yescharacteristic
334C2×C61#330811yescharacteristic
335C2×C61#331811yescharacteristic
336C2×C61#336611yescharacteristic
337C2×C61#336711yescharacteristic
338D61—82no—
339C22×D8—611no—
340C2×C4⋊Q8—611no—
341C2×#126—21no—
342C2×C22⋊Q8—1221no—
343C2×C4×D4—611no—
344C2×#107—611no—
345C2×C4⋊C8—611no—
346C2×#102—611no—
347C2×#102—611no—
348C2×#102—611no—
349C2×#102—611no—
350C2×#102—611no—
351C2×#102—611no—
352C2×#97—611no—
353C2×#97—611no—
354C2×C4×C8—611no—
355#397—21no—
356#396—21no—
357#396—1221no—
358#393—1221no—
359#390—611no—
360#390—611no—
361#390C2×D6111yescharacteristic
362#390C2×D6111yescharacteristic
363#390C2×D6111yescharacteristic
364#389—611no—
365#389—611no—
366#389C2×D6111yescharacteristic
367#388—21no—
368#385—1221no—
369#384C2×D6111yescharacteristic
370C4×C4⋊C4C2×D6111yescharacteristic
371C4×C4⋊C4C2×D6111yescharacteristic
372#340—611no—
373#340—611no—
374#340—611no—
375#340—611no—
376#340—611no—
377#340—611no—
378#340—611no—
379#340—611no—
380#336—611no—
381#336—611no—
382C61#2909511yescharacteristic, complemented, Sylow
383C22×Q8—1221no—
384C22×D4—611no—
385C22×D4C22×D6111yescharacteristic
386C23×C4—1221no—
387C2×D8—1222no—
388C2×D8—1222no—
389C2×D8—2441no—
390C22×C8—611no—
391C22×C8—611no—
392C22×C8—611no—
393C22×C8—611no—
394C4⋊Q8—1222no—
395C4⋊Q8—2441no—
396#126—44no—
397C22⋊Q8—2444no—
398C4×D4—1222no—
399C4×D4—2441no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—611no—
404C2×C4⋊C4—611no—
405C2×C4⋊C4—611no—
406C2×C4⋊C4—1221no—
407C2×C4⋊C4—1221no—
408C2×C4⋊C4—1221no—
409C2×C4⋊C4C22⋊D6111yescharacteristic
410C2×C4⋊C4C22⋊D6111yescharacteristic
411C2×C4⋊C4C22×D6111yescharacteristic
412C2×C4⋊C4C22×D6111yescharacteristic
413C2×C4⋊C4C22×D6111yescharacteristic
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—1221no—
421C2×C22⋊C4—1221no—
422C2×C22⋊C4—1221no—
423C2×C22⋊C4—1221no—
424C2×C22⋊C4—1221no—
425C2×C42—21no—
426C2×C42C22×D6111yescharacteristic
427C2×C42C22×D6111yescharacteristic
428C2×C42C22×D6111yescharacteristic
429#107—1222no—
430C4⋊C8—1222no—
431#102—1222no—
432#102—1222no—
433#102—1222no—
434#102—1222no—
435#102—1222no—
436#102—2441no—
437#97—1222no—
438#97—2441no—
439C4×C8—2441no—
440#95—21no—
441#95—21no—
442#95—1221no—
443#95—1221no—
444#95C22⋊D6111yescharacteristic
445#95C22⋊D6111yescharacteristic
446C24—21no—
447C24—1221no—
448C2×Q8—4881no—
449C2×Q8—2442no—
450C2×Q8—2442no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—612no—
458C2×D4—1221no—
459C2×D4—1221no—
460C2×D4—1221no—
461C2×D4—1221no—
462C2×D4—1221no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—1221no—
467C22×C4—1221no—
468C22×C4—1221no—
469C22×C4—4881no—
470C22×C4—2442no—
471C22×C4—2442no—
472C22×C4C2×C22⋊D6111yescharacteristic
473C22×C4C2×C22⋊D6111yescharacteristic
474C22×C4C2×C22⋊D6111yescharacteristic
475C22×C4C2×C22⋊D6111yescharacteristic
476C22×C4C2×C22⋊D6111yescharacteristic
477C22×C4C2×C22⋊D6111yescharacteristic
478C22×C4C23×D6111yescharacteristic
479D8—2444no—
480C2×C8—612no—
481C2×C8—612no—
482C2×C8—1221no—
483C2×C8—1221no—
484C2×C8—1221no—
485C2×C8—1221no—
486C2×C8—1221no—
487C2×C8—1221no—
488C2×C8—1221no—
489C2×C8—1221no—
490C2×C8—1221no—
491C2×C8—1221no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—42no—
501C4⋊C4—42no—
502C4⋊C4—81no—
503C4⋊C4—612no—
504C4⋊C4—1221no—
505C4⋊C4—1221no—
506C4⋊C4—1221no—
507C4⋊C4—1221no—
508C4⋊C4—1221no—
509C4⋊C4—2442no—
510C4⋊C4—2442no—
511C4⋊C4—2442no—
512C22⋊C4—42no—
513C22⋊C4—42no—
514C22⋊C4—42no—
515C22⋊C4—42no—
516C22⋊C4—81no—
517C22⋊C4—81no—
518C22⋊C4—4881no—
519C22⋊C4—2442no—
520C22⋊C4—2442no—
521C22⋊C4—2442no—
522C22⋊C4—2442no—
523C42—21no—
524C42—21no—
525C42—21no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42—42no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23—41no—
535C23—41no—
536C23—41no—
537C23—1222no—
538C23—2441no—
539C23—2441no—
540C23—2441no—
541C23—2441no—
542C23—2441no—
543C23—2441no—
544C23C22×C22⋊D6111yescharacteristic
545Q8—4884no—
546D4—41no—
547D4—41no—
548D4—41no—
549D4—41no—
550D4—1222no—
551D4—1222no—
552D4—2441no—
553D4—2441no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—1222no—
580C2×C4—4884no—
581C2×C4—2441no—
582C2×C4—2441no—
583C2×C4—2441no—
584C2×C4—2441no—
585C2×C4—2441no—
586C2×C4—2441no—
587C2×C4—2441no—
588C2×C4—2441no—
589C2×C4#1451980212yes—
590C2×C4#1451980312yes—
591C2×C4#41×D6111yescharacteristic
592C2×C4#41×D6111yescharacteristic
593C2×C4#41×D6111yescharacteristic
594C2×C4#41×D6111yescharacteristic
595C2×C4#1451982311yescharacteristic
596C2×C4#1451982411yescharacteristic
597C8—1222no—
598C8—1222no—
599C8—2441no—
600C8—2441no—
601C22—81no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22—81no—
608C22—4881no—
609C22—4881no—
610C22—4881no—
611C22—4881no—
612C22—2442no—
613C22—2442no—
614C22—2442no—
615C22#1684030811yescharacteristic
616C22#1684040011yescharacteristic
617C22#1684041911yescharacteristic
618C22C2×#1451980211yescharacteristic
619C22C2×#1451980311yescharacteristic
620C22#1684056511yescharacteristic
621C22#1684057711yescharacteristic
622C4—22no—
623C4—22no—
624C4—41no—
625C4—41no—
626C4—41no—
627C4—41no—
628C4—81no—
629C4—81no—
630C4—81no—
631C4—4881no—
632C4—4881no—
633C4—2442no—
634C4#1684029511yescharacteristic
635C4#1684035311yescharacteristic
636C4#1684043711yescharacteristic
637C4#1684047911yescharacteristic
638C2—161no—
639C2—4882no—
640C2#2145096111yescharacteristic
641C2#2145645211yescharacteristic
642C2#2145655311yescharacteristic
643C2#2145780411yescharacteristic
644C2#2145795411yescharacteristic
645C2#2145852211yescharacteristic
646C2#2145853311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2512C2
socleC23×C61C22×D4
prime radicalC22×#11758199C22
hypercenter#2512D61
hypocenterC61#29095
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2512

Complements

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

NH ≅ G/Ntype
1. #21449669C2semidirect
2. #21447315C2semidirect
3. #21447223C2semidirect
5. #21446955C2semidirect
6. #21446779C2semidirect
8. #21446519C2semidirect
9. #21446519C2semidirect
10. #21446515C2semidirect
11. #21446411C2semidirect
13. #21445694C2semidirect
14. #21445647C2semidirect
15. C61×#2512C2semidirect
315. #2512D61semidirect
382. C61#29095semidirect

Maximal subgroups

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

subgroupindex
#214496692
#214473152
#214472232
#214471292
#214469552
#214467792
#214466842
#214465192
#214465152
#214464112
#214461702
#214456942
#214456472
C61×#25122
#2909561