Finite Group Databasebeta

← #29752831

Subgroups — #29752831

Order 15616.

742 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21448855C211yesmaximal, characteristic
2#21447223C211yesmaximal, characteristic, complemented
3#21447204C211yesmaximal, characteristic, complemented
4#21447001C211yesmaximal, characteristic
5#21447001C211yesmaximal, characteristic
6#21446575C211yesmaximal, characteristic, complemented
7#21446549C211yesmaximal, characteristic, complemented
8#21446427C211yesmaximal, characteristic, complemented
9#21446411C211yesmaximal, characteristic, complemented
10#21446394C211yesmaximal, characteristic, complemented
11#21446079C211yesmaximal, characteristic, complemented
12#21446016C211yesmaximal, characteristic, complemented
13#21445911C211yesmaximal, characteristic, complemented
14C4×#14519697C211yesmaximal, characteristic, complemented
15C61×#2497C211yesmaximal, characteristic, complemented
16C2×#14519751C2211yescharacteristic
17C2×C4×D244C2211yescharacteristic
18C2×#14519736C2211yescharacteristic
19C2×#14519710C2211yescharacteristic
20C2×#14519710C2211yescharacteristic
21C2×#14519710C2211yescharacteristic
22C2×#14519708C2211yescharacteristic
23C2×C4⋊#92418C2211yescharacteristic
24C2×#14519697C2211yescharacteristic
25C2×#14519697C2211yescharacteristic
26C2×#14519697C2211yescharacteristic
27C2×#14519697C2211yescharacteristic
28C2×C22⋊#92418C2211yescharacteristic
29C2×C22⋊#92418C2211yescharacteristic
30C2×C4×#92418C2211yescharacteristic
31#16839664C2211yescharacteristic
32#16839662—21no—
33#16839660C2211yescharacteristic
34#16839651—21no—
35#16839638—21no—
36C4×C4⋊Dic61C2211yescharacteristic
37#16839609—21no—
38#16839524C2211yescharacteristic
39#16839524C2211yescharacteristic
40#16839524C2211yescharacteristic
41#16839524C2211yescharacteristic
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839517C2211yescharacteristic
47#16839517C2211yescharacteristic
48C61×#400—21no—
49C61×#396—21no—
50C61×#389C2211yescharacteristic
51C61×#389C2211yescharacteristic
52C61×#388—21no—
53C61×#387—21no—
54C61×#384C2211yescharacteristic
55C61×#380C2211yescharacteristic
56C61×#380C2211yescharacteristic
57C4×C4⋊C4×C61C2211yescharacteristic
58C4×C22⋊C4×C61C2211yescharacteristic
59C22×D244C2311yescharacteristic
60C22×C22⋊D61—21no—
61C22×C4×D61—21no—
62C22×#92418C2311yescharacteristic
63C22×#92418C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66#14519751—22no—
67#14519751—22no—
68C4×D244—22no—
69C4×D244—41no—
70#14519736—22no—
71#14519736—41no—
72C2×C4⋊Dic61C2311yescharacteristic
73C2×C4⋊Dic61C2311yescharacteristic
74C2×C4⋊Dic61C2311yescharacteristic
75C2×#11758196—21no—
76C2×C22⋊Dic61—21no—
77C2×#11758198—21no—
78C2×#11758198—21no—
79C2×#11758198—21no—
80C2×#11758198—21no—
81C2×C4×Dic61—21no—
82C2×C4×Dic61—21no—
83#14519710—22no—
84#14519710—22no—
85#14519710—41no—
86#14519708—22no—
87C4⋊#92418—22no—
88#14519697—22no—
89#14519697—22no—
90#14519697—22no—
91#14519697—41no—
92C22⋊#92418—22no—
93C22⋊#92418—41no—
94C4×#92418—41no—
95#14519684—21no—
96#14519684—21no—
97C23×C4×C61C2311yescharacteristic
98C2×C4⋊C4×C61—21no—
99C2×C4⋊C4×C61—21no—
100C2×C4⋊C4×C61—21no—
101C2×C4⋊C4×C61—21no—
102C2×C4⋊C4×C61C2311yescharacteristic
103C2×C4⋊C4×C61C2311yescharacteristic
104C2×C4⋊C4×C61C2311yescharacteristic
105C2×C4⋊C4×C61C2311yescharacteristic
106C2×C22⋊C4×C61—21no—
107C2×C22⋊C4×C61—21no—
108C2×C22⋊C4×C61D411yescharacteristic
109C2×C22⋊C4×C61D411yescharacteristic
110C2×C42×C61—21no—
111C2×C42×C61C2311yescharacteristic
112C2×C42×C61C2311yescharacteristic
113#95×C61—21no—
114#95×C61—21no—
115#95×C61—21no—
116#95×C61—21no—
117#95×C61—21no—
118#95×C61D411yescharacteristic
119#95×C61D411yescharacteristic
120C24×C61C2×D411yescharacteristic
121C23×D61—21no—
122C22×C4×C61—21no—
123C22×C4×C61—21no—
124C22×C4×C61—21no—
125C22×C4×C61—21no—
126C22×C4×C61—21no—
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61—21no—
132C22×C4×C61C2×D411yescharacteristic
133C22×C4×C61C2×D411yescharacteristic
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2411yescharacteristic
138C2×C22⋊D61—24no—
139C2×C22⋊D61—81no—
140C2×C22⋊D61—81no—
141C22×Dic61—21no—
142C22×Dic61—21no—
143C22×Dic61—21no—
144C2×D244—21no—
145C2×D244—21no—
146C2×D244—21no—
147C2×D244—21no—
148C2×D244—21no—
149C2×D244#4112yes—
150C2×C4×D61—42no—
151C2×C4×D61—42no—
152C2×C4×D61—81no—
153C4⋊C4×C61—21no—
154C4⋊C4×C61—21no—
155C4⋊C4×C61—21no—
156C4⋊C4×C61—21no—
157C4⋊C4×C61—21no—
158C4⋊C4×C61—21no—
159C4⋊C4×C61—21no—
160C4⋊C4×C61—21no—
161C4⋊C4×C61—42no—
162C4⋊C4×C61—81no—
163C4⋊C4×C61—81no—
164C4⋊C4×C61—81no—
165C22⋊C4×C61—22no—
166C22⋊C4×C61—22no—
167C22⋊C4×C61—81no—
168C22⋊C4×C61—81no—
169C42×C61—21no—
170C42×C61—21no—
171C42×C61—21no—
172C42×C61—21no—
173C42×C61—81no—
174C22⋊Dic61—42no—
175#11758198—24no—
176#11758198—42no—
177#11758198—42no—
178#11758198—81no—
179C4⋊Dic61—21no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61#4112yes—
184C4⋊Dic61#4112yes—
185#11758196—81no—
186C4×Dic61—42no—
187C4×Dic61—81no—
188C2×#92418—21no—
189C2×#92418—21no—
190C2×#92418—21no—
191C2×#92418—21no—
192C2×#92418—21no—
193C2×#92418—21no—
194C2×#92418—21no—
195C2×#92418—21no—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418#4112yes—
200C23×C61—21no—
201C23×C61—21no—
202C23×C61—21no—
203C23×C61—21no—
204C23×C61—21no—
205C23×C61—21no—
206C23×C61—21no—
207C23×C61C22×D411yescharacteristic
208C22×D61—22no—
209C22×D61—41no—
210C22×D61—41no—
211C22×D61—41no—
212C22×D61—41no—
213C22×D61—41no—
214C22×D61—41no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61—41no—
240C2×C4×C61—41no—
241C2×C4×C61—41no—
242C2×C4×C61—41no—
243C2×C4×C61—41no—
244C2×C4×C61#13512yes—
245C2×C4×C61#13712yes—
246C2×C4×C61C2×#4111yescharacteristic
247C2×C4×C61C2×#4111yescharacteristic
248C2×C4×C61C2×#4111yescharacteristic
249C2×C4×C61C2×#4111yescharacteristic
250C2×C4×C61H(5,𝔽2)11yescharacteristic
251C2×C4×C612−1+411yescharacteristic
252C22⋊D61—84no—
253C2×Dic61—22no—
254C2×Dic61—22no—
255C2×Dic61—41no—
256C2×Dic61—41no—
257C2×Dic61—41no—
258C2×Dic61—41no—
259C2×Dic61—41no—
260C2×Dic61—41no—
261C2×Dic61—41no—
262D244—22no—
263D244—22no—
264D244—41no—
265D244—41no—
266C4×D61—84no—
267#92418—22no—
268#92418—41no—
269#92418—41no—
270#92418—41no—
271#27041—611nomaximal, Sylow
272C22×C61—41no—
273C22×C61—41no—
274C22×C61—41no—
275C22×C61—41no—
276C22×C61—41no—
277C22×C61—41no—
278C22×C61—41no—
279C22×C61#52511yescharacteristic
280C22×C61#54611yescharacteristic
281C22×C61#54711yescharacteristic
282C22×C61C2×#13511yescharacteristic
283C22×C61C2×#13711yescharacteristic
284C22×C61#57611yescharacteristic
285C22×C61#57611yescharacteristic
286C2×D61—42no—
287C2×D61—42no—
288C2×D61—42no—
289C2×D61—81no—
290C2×D61—81no—
291C2×D61—81no—
292C2×D61—81no—
293C4×C61—22no—
294C4×C61—22no—
295C4×C61—41no—
296C4×C61—41no—
297C4×C61—41no—
298C4×C61—81no—
299C4×C61—81no—
300C4×C61—81no—
301C4×C61—81no—
302C4×C61#52911yescharacteristic
303C4×C61#53911yescharacteristic
304C4×C61#55311yescharacteristic
305C4×C61#55611yescharacteristic
306Dic61—42no—
307Dic61—42no—
308Dic61—81no—
309#2497D6111yescharacteristic, complemented
310#2363—611no—
311#2071—611no—
312#2067—611no—
313#2033—611no—
314#2033—611no—
315#1947—611no—
316#1942—611no—
317#1923—611no—
318#1921—611no—
319#1919—611no—
320#1864—611no—
321#1854—611no—
322#1825—611no—
323C4×#102—611no—
324C2×C61—81no—
325C2×C61#246611yescharacteristic
326C2×C61#310711yescharacteristic
327C2×C61#312211yescharacteristic
328C2×C61#330511yescharacteristic
329C2×C61#331411yescharacteristic
330C2×C61#333911yescharacteristic
331C2×C61#335711yescharacteristic
332D61—82no—
333C2×#121—611no—
334C2×C4×D4—611no—
335C2×#117—611no—
336C2×#107—611no—
337C2×#107—611no—
338C2×#107—611no—
339C2×#106—611no—
340C2×C4⋊C8—611no—
341C2×#102—611no—
342C2×#102—611no—
343C2×#102—611no—
344C2×#102—611no—
345C2×C22⋊C8—611no—
346C2×C22⋊C8—611no—
347C2×C4×C8—611no—
348#400—21no—
349#396—21no—
350#390—611no—
351#390—1221no—
352#389—611no—
353#389C2×D6111yescharacteristic
354#389C2×D6111yescharacteristic
355#388—21no—
356#388—1221no—
357#387—21no—
358#386—1221no—
359#384C2×D6111yescharacteristic
360#380C2×D6111yescharacteristic
361#380C2×D6111yescharacteristic
362C4×C4⋊C4—611no—
363C4×C4⋊C4C2×D6111yescharacteristic
364C4×C22⋊C4—1221no—
365C4×C22⋊C4C2×D6111yescharacteristic
366#340—611no—
367#340—611no—
368#340—611no—
369#340—611no—
370#340—611no—
371#340—611no—
372#340—611no—
373#340—611no—
374#336—611no—
375#336—611no—
376C61#2704111yescharacteristic, complemented, Sylow
377C22×D4—611no—
378C22×D4—1221no—
379C23×C4—1221no—
380C23×C4C22×D6111yescharacteristic
381C22×C8—611no—
382C22×C8—611no—
383C22×C8—611no—
384C22×C8—611no—
385#121—1222no—
386#121—1222no—
387C4×D4—1222no—
388C4×D4—2441no—
389#117—1222no—
390#117—2441no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—611no—
396C2×C4⋊C4—611no—
397C2×C4⋊C4—611no—
398C2×C4⋊C4—1221no—
399C2×C4⋊C4C22×D6111yescharacteristic
400C2×C4⋊C4C22×D6111yescharacteristic
401C2×C4⋊C4C22×D6111yescharacteristic
402C2×C4⋊C4C22×D6111yescharacteristic
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—1221no—
406C2×C22⋊C4—1221no—
407C2×C22⋊C4—1221no—
408C2×C22⋊C4—1221no—
409C2×C22⋊C4—1221no—
410C2×C22⋊C4C22⋊D6111yescharacteristic
411C2×C22⋊C4C22⋊D6111yescharacteristic
412C2×C42—21no—
413C2×C42—1221no—
414C2×C42—1221no—
415C2×C42C22×D6111yescharacteristic
416C2×C42C22×D6111yescharacteristic
417#107—1222no—
418#107—1222no—
419#107—2441no—
420#106—1222no—
421C4⋊C8—1222no—
422#102—1222no—
423#102—1222no—
424#102—1222no—
425#102—2441no—
426C22⋊C8—1222no—
427C22⋊C8—2441no—
428C4×C8—2441no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—1221no—
435#95—1221no—
436#95C22⋊D6111yescharacteristic
437#95C22⋊D6111yescharacteristic
438C24—1221no—
439C24C2×C22⋊D6111yescharacteristic
440C2×D4—612no—
441C2×D4—1224no—
442C2×D4—1221no—
443C2×D4—1221no—
444C2×D4—1221no—
445C2×D4—1221no—
446C2×D4—1221no—
447C2×D4—4881no—
448C2×D4—4881no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—1221no—
460C22×C4—1221no—
461C22×C4—1221no—
462C22×C4—4881no—
463C22×C4—2442no—
464C22×C4—2442no—
465C22×C4C2×C22⋊D6111yescharacteristic
466C22×C4C2×C22⋊D6111yescharacteristic
467C22×C4C2×C22⋊D6111yescharacteristic
468C22×C4C2×C22⋊D6111yescharacteristic
469C22×C4C2×C22⋊D6111yescharacteristic
470C22×C4C23×D6111yescharacteristic
471C2×C8—612no—
472C2×C8—1221no—
473C2×C8—1221no—
474C2×C8—1221no—
475C2×C8—1221no—
476C2×C8—1221no—
477C2×C8—1221no—
478C2×C8—1221no—
479C2×C8—1221no—
480C2×C8—1221no—
481C2×C8—1221no—
482C2×C8—1221no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—42no—
492C4⋊C4—81no—
493C4⋊C4—81no—
494C4⋊C4—81no—
495C4⋊C4—612no—
496C4⋊C4—612no—
497C4⋊C4—1221no—
498C4⋊C4—1221no—
499C4⋊C4—1221no—
500C4⋊C4—1221no—
501C4⋊C4—4881no—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C22⋊C4—81no—
505C22⋊C4—81no—
506C22⋊C4—1224no—
507C22⋊C4—4881no—
508C22⋊C4—2442no—
509C22⋊C4—2442no—
510C22⋊C4—2442no—
511C42—21no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—81no—
516C42—4881no—
517C42—2442no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—1222no—
526C23—2441no—
527C23—2441no—
528C23—2441no—
529C23—2441no—
530C23—2441no—
531C23—2441no—
532C23C22×C22⋊D6111yescharacteristic
533D4—1222no—
534D4—1222no—
535D4—4884no—
536D4—2441no—
537D4—2441no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—1222no—
568C2×C4—1222no—
569C2×C4—4884no—
570C2×C4—2441no—
571C2×C4—2441no—
572C2×C4—2441no—
573C2×C4—2441no—
574C2×C4—2441no—
575C2×C4—2441no—
576C2×C4—2441no—
577C2×C4#1451979712yes—
578C2×C4#1451980812yes—
579C2×C4#41×D6111yescharacteristic
580C2×C4#41×D6111yescharacteristic
581C2×C4#41×D6111yescharacteristic
582C2×C4#41×D6111yescharacteristic
583C2×C4#1451982311yescharacteristic
584C2×C4#1451982411yescharacteristic
585C8—1222no—
586C8—2441no—
587C8—2441no—
588C8—2441no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—4881no—
597C22—4881no—
598C22—4881no—
599C22—4881no—
600C22—2442no—
601C22—2442no—
602C22—2442no—
603C22#1684026911yescharacteristic
604C22#1684040011yescharacteristic
605C22#1684041111yescharacteristic
606C22C2×#1451979711yescharacteristic
607C22C2×#1451980811yescharacteristic
608C22#1684056511yescharacteristic
609C22#1684056511yescharacteristic
610C4—22no—
611C4—22no—
612C4—41no—
613C4—41no—
614C4—41no—
615C4—81no—
616C4—81no—
617C4—81no—
618C4—81no—
619C4—4881no—
620C4—2442no—
621C4—2442no—
622C4#1684029511yescharacteristic
623C4#1684035311yescharacteristic
624C4#1684046311yescharacteristic
625C4#1684047911yescharacteristic
626C2—81no—
627C2—4882no—
628C2#2144985111yescharacteristic
629C2#2145588411yescharacteristic
630C2#2145605711yescharacteristic
631C2#2145776311yescharacteristic
632C2#2145789411yescharacteristic
633C2#2145821511yescharacteristic
634C2#2145844511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2497C2
socleC23×C61C22×D4
prime radicalC2×#14519751C22
hypercenter#2497D61
hypocenterC61#27041
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2497

Complements

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

NH ≅ G/Ntype
2. #21447223C2semidirect
3. #21447204C2semidirect
6. #21446575C2semidirect
7. #21446549C2semidirect
8. #21446427C2semidirect
9. #21446411C2semidirect
10. #21446394C2semidirect
11. #21446079C2semidirect
12. #21446016C2semidirect
13. #21445911C2semidirect
14. C4×#14519697C2semidirect
15. C61×#2497C2semidirect
309. #2497D61semidirect
376. C61#27041semidirect

Maximal subgroups

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

subgroupindex
#214488552
#214472232
#214472042
#214470012
#214465752
#214465492
#214464272
#214464112
#214463942
#214460792
#214460162
#214459112
C4×#145196972
C61×#24972
#2704161