Finite Group Databasebeta

← #29752801

Subgroups — #29752801

Order 15616.

762 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21448855C211yesmaximal, characteristic
2#21447223C211yesmaximal, characteristic, complemented
3#21447190C211yesmaximal, characteristic, complemented
4#21447008C211yesmaximal, characteristic
5#21447008C211yesmaximal, characteristic
6#21446580C211yesmaximal, characteristic, complemented
7#21446544C211yesmaximal, characteristic, complemented
8#21446427C211yesmaximal, characteristic, complemented
9#21446408C211yesmaximal, characteristic, complemented
10#21446404C211yesmaximal, characteristic, complemented
11#21446065C211yesmaximal, characteristic, complemented
12#21446016C211yesmaximal, characteristic, complemented
13#21445911C211yesmaximal, characteristic, complemented
14C4×#14519697C211yesmaximal, characteristic, complemented
15C61×#2496C211yesmaximal, characteristic, complemented
16C2×#14519751C2211yescharacteristic
17C2×C4×D244C2211yescharacteristic
18C2×#14519736C2211yescharacteristic
19C2×#14519710C2211yescharacteristic
20C2×#14519708C2211yescharacteristic
21C2×#14519708C2211yescharacteristic
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
48C2×#126×C61—21no—
49C61×#400—21no—
50C61×#397—21no—
51C61×#389C2211yescharacteristic
52C61×#389C2211yescharacteristic
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#14519708—22no—
85#14519708—22no—
86#14519708—41no—
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
98#126×C61—44no—
99C2×C4⋊C4×C61—21no—
100C2×C4⋊C4×C61—21no—
101C2×C4⋊C4×C61—21no—
102C2×C4⋊C4×C61—21no—
103C2×C4⋊C4×C61C2311yescharacteristic
104C2×C4⋊C4×C61C2311yescharacteristic
105C2×C4⋊C4×C61C2311yescharacteristic
106C2×C4⋊C4×C61C2311yescharacteristic
107C2×C22⋊C4×C61—21no—
108C2×C22⋊C4×C61—21no—
109C2×C22⋊C4×C61D411yescharacteristic
110C2×C22⋊C4×C61D411yescharacteristic
111C2×C42×C61—21no—
112C2×C42×C61C2311yescharacteristic
113C2×C42×C61C2311yescharacteristic
114#95×C61—21no—
115#95×C61—21no—
116#95×C61—21no—
117#95×C61—21no—
118#95×C61—21no—
119#95×C61D411yescharacteristic
120#95×C61D411yescharacteristic
121C24×C61C2×D411yescharacteristic
122C23×D61—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×C61—21no—
133C22×C4×C61C2×D411yescharacteristic
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2411yescharacteristic
139C2×C22⋊D61—24no—
140C2×C22⋊D61—81no—
141C2×C22⋊D61—81no—
142C22×Dic61—21no—
143C22×Dic61—21no—
144C22×Dic61—21no—
145C2×D244—21no—
146C2×D244—21no—
147C2×D244—21no—
148C2×D244—21no—
149C2×D244—21no—
150C2×D244#4112yes—
151C2×C4×D61—42no—
152C2×C4×D61—42no—
153C2×C4×D61—81no—
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—21no—
162C4⋊C4×C61—42no—
163C4⋊C4×C61—42no—
164C4⋊C4×C61—42no—
165C4⋊C4×C61—42no—
166C22⋊C4×C61—22no—
167C22⋊C4×C61—22no—
168C22⋊C4×C61—42no—
169C22⋊C4×C61—42no—
170C42×C61—21no—
171C42×C61—21no—
172C42×C61—21no—
173C42×C61—21no—
174C42×C61—42no—
175C22⋊Dic61—42no—
176#11758198—24no—
177#11758198—42no—
178#11758198—42no—
179#11758198—81no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61#4112yes—
185C4⋊Dic61#4112yes—
186#11758196—81no—
187C4×Dic61—42no—
188C4×Dic61—81no—
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—21no—
200C2×#92418#4112yes—
201C23×C61—21no—
202C23×C61—21no—
203C23×C61—21no—
204C23×C61—21no—
205C23×C61—21no—
206C23×C61—21no—
207C23×C61—21no—
208C23×C61C22×D411yescharacteristic
209C22×D61—22no—
210C22×D61—41no—
211C22×D61—41no—
212C22×D61—41no—
213C22×D61—41no—
214C22×D61—41no—
215C22×D61—41no—
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—21no—
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—41no—
245C2×C4×C61#13512yes—
246C2×C4×C61AGL(1,ℤ/8)12yes—
247C2×C4×C61C2×#4111yescharacteristic
248C2×C4×C61C2×#4111yescharacteristic
249C2×C4×C61C2×#4111yescharacteristic
250C2×C4×C61C2×#4111yescharacteristic
251C2×C4×C61H(5,𝔽2)11yescharacteristic
252C2×C4×C612−1+411yescharacteristic
253C22⋊D61—84no—
254C2×Dic61—22no—
255C2×Dic61—22no—
256C2×Dic61—41no—
257C2×Dic61—41no—
258C2×Dic61—41no—
259C2×Dic61—41no—
260C2×Dic61—41no—
261C2×Dic61—41no—
262C2×Dic61—41no—
263D244—22no—
264D244—22no—
265D244—41no—
266D244—41no—
267C4×D61—84no—
268#92418—22no—
269#92418—41no—
270#92418—41no—
271#92418—41no—
272#27039—611nomaximal, Sylow
273C22×C61—41no—
274C22×C61—41no—
275C22×C61—41no—
276C22×C61—41no—
277C22×C61—41no—
278C22×C61—41no—
279C22×C61—41no—
280C22×C61#52511yescharacteristic
281C22×C61#54611yescharacteristic
282C22×C61#54711yescharacteristic
283C22×C61C2×#13511yescharacteristic
284C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
285C22×C61#57711yescharacteristic
286C22×C61#57711yescharacteristic
287C2×D61—42no—
288C2×D61—42no—
289C2×D61—42no—
290C2×D61—81no—
291C2×D61—81no—
292C2×D61—81no—
293C2×D61—81no—
294C4×C61—22no—
295C4×C61—22no—
296C4×C61—41no—
297C4×C61—41no—
298C4×C61—41no—
299C4×C61—81no—
300C4×C61—81no—
301C4×C61—81no—
302C4×C61—81no—
303C4×C61#52911yescharacteristic
304C4×C61#53911yescharacteristic
305C4×C61#55311yescharacteristic
306C4×C61#55611yescharacteristic
307Dic61—42no—
308Dic61—42no—
309Dic61—81no—
310#2496D6111yescharacteristic, complemented
311#2363—611no—
312#2071—611no—
313#2065—611no—
314#2034—611no—
315#2034—611no—
316#1948—611no—
317#1941—611no—
318#1923—611no—
319#1921—611no—
320#1920—611no—
321#1862—611no—
322#1854—611no—
323#1825—611no—
324C4×#102—611no—
325C2×C61—81no—
326C2×C61#246611yescharacteristic
327C2×C61#310611yescharacteristic
328C2×C61#312311yescharacteristic
329C2×C61#330411yescharacteristic
330C2×C61#330611yescharacteristic
331C2×C61#333711yescharacteristic
332C2×C61#335411yescharacteristic
333D61—82no—
334C2×#126—21no—
335C2×#121—611no—
336C2×C4×D4—611no—
337C2×#117—611no—
338C2×#107—611no—
339C2×#106—611no—
340C2×#106—611no—
341C2×#106—611no—
342C2×C4⋊C8—611no—
343C2×#102—611no—
344C2×#102—611no—
345C2×#102—611no—
346C2×#102—611no—
347C2×C22⋊C8—611no—
348C2×C22⋊C8—611no—
349C2×C4×C8—611no—
350#400—21no—
351#397—21no—
352#390—611no—
353#390—1221no—
354#389—611no—
355#389C2×D6111yescharacteristic
356#389C2×D6111yescharacteristic
357#388—1221no—
358#387—21no—
359#386—1221no—
360#384C2×D6111yescharacteristic
361#380C2×D6111yescharacteristic
362#380C2×D6111yescharacteristic
363C4×C4⋊C4—611no—
364C4×C4⋊C4C2×D6111yescharacteristic
365C4×C22⋊C4—1221no—
366C4×C22⋊C4C2×D6111yescharacteristic
367#340—611no—
368#340—611no—
369#340—611no—
370#340—611no—
371#340—611no—
372#340—611no—
373#340—611no—
374#340—611no—
375#336—611no—
376#336—611no—
377C61#2703911yescharacteristic, complemented, Sylow
378C22×D4—611no—
379C22×D4—1221no—
380C23×C4—1221no—
381C23×C4C22×D6111yescharacteristic
382C22×C8—611no—
383C22×C8—611no—
384C22×C8—611no—
385C22×C8—611no—
386#126—44no—
387#121—1222no—
388#121—1222no—
389C4×D4—1222no—
390C4×D4—2441no—
391#117—1222no—
392#117—2441no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—611no—
398C2×C4⋊C4—611no—
399C2×C4⋊C4—611no—
400C2×C4⋊C4—1221no—
401C2×C4⋊C4C22×D6111yescharacteristic
402C2×C4⋊C4C22×D6111yescharacteristic
403C2×C4⋊C4C22×D6111yescharacteristic
404C2×C4⋊C4C22×D6111yescharacteristic
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—1221no—
408C2×C22⋊C4—1221no—
409C2×C22⋊C4—1221no—
410C2×C22⋊C4—1221no—
411C2×C22⋊C4—1221no—
412C2×C22⋊C4C22⋊D6111yescharacteristic
413C2×C22⋊C4C22⋊D6111yescharacteristic
414C2×C42—21no—
415C2×C42—1221no—
416C2×C42—1221no—
417C2×C42C22×D6111yescharacteristic
418C2×C42C22×D6111yescharacteristic
419#107—1222no—
420#106—1222no—
421#106—1222no—
422#106—2441no—
423C4⋊C8—1222no—
424#102—1222no—
425#102—1222no—
426#102—1222no—
427#102—2441no—
428C22⋊C8—1222no—
429C22⋊C8—2441no—
430C4×C8—2441no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—1221no—
437#95—1221no—
438#95C22⋊D6111yescharacteristic
439#95C22⋊D6111yescharacteristic
440C24—1221no—
441C24C2×C22⋊D6111yescharacteristic
442C2×D4—612no—
443C2×D4—1224no—
444C2×D4—1221no—
445C2×D4—1221no—
446C2×D4—1221no—
447C2×D4—1221no—
448C2×D4—1221no—
449C2×D4—4881no—
450C2×D4—4881no—
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—21no—
460C22×C4—21no—
461C22×C4—1221no—
462C22×C4—1221no—
463C22×C4—1221no—
464C22×C4—4881no—
465C22×C4—2442no—
466C22×C4—2442no—
467C22×C4C2×C22⋊D6111yescharacteristic
468C22×C4C2×C22⋊D6111yescharacteristic
469C22×C4C2×C22⋊D6111yescharacteristic
470C22×C4C2×C22⋊D6111yescharacteristic
471C22×C4C2×C22⋊D6111yescharacteristic
472C22×C4C23×D6111yescharacteristic
473C2×C8—612no—
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—
483C2×C8—1221no—
484C2×C8—1221no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—42no—
494C4⋊C4—42no—
495C4⋊C4—42no—
496C4⋊C4—42no—
497C4⋊C4—612no—
498C4⋊C4—612no—
499C4⋊C4—1221no—
500C4⋊C4—1221no—
501C4⋊C4—1221no—
502C4⋊C4—1221no—
503C4⋊C4—4881no—
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—42no—
507C22⋊C4—42no—
508C22⋊C4—1224no—
509C22⋊C4—4881no—
510C22⋊C4—2442no—
511C22⋊C4—2442no—
512C22⋊C4—2442no—
513C42—21no—
514C42—21no—
515C42—21no—
516C42—21no—
517C42—42no—
518C42—4881no—
519C42—2442no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—21no—
527C23—1222no—
528C23—2441no—
529C23—2441no—
530C23—2441no—
531C23—2441no—
532C23—2441no—
533C23—2441no—
534C23C22×C22⋊D6111yescharacteristic
535D4—1222no—
536D4—1222no—
537D4—4884no—
538D4—2441no—
539D4—2441no—
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—21no—
552C2×C4—21no—
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—41no—
568C2×C4—41no—
569C2×C4—1222no—
570C2×C4—1222no—
571C2×C4—4884no—
572C2×C4—2441no—
573C2×C4—2441no—
574C2×C4—2441no—
575C2×C4—2441no—
576C2×C4—2441no—
577C2×C4—2441no—
578C2×C4—2441no—
579C2×C4#1451979712yes—
580C2×C4#1451980312yes—
581C2×C4#41×D6111yescharacteristic
582C2×C4#41×D6111yescharacteristic
583C2×C4#41×D6111yescharacteristic
584C2×C4#41×D6111yescharacteristic
585C2×C4#1451982311yescharacteristic
586C2×C4#1451982411yescharacteristic
587C8—1222no—
588C8—2441no—
589C8—2441no—
590C8—2441no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—4881no—
599C22—4881no—
600C22—4881no—
601C22—4881no—
602C22—2442no—
603C22—2442no—
604C22—2442no—
605C22#1684026911yescharacteristic
606C22#1684040011yescharacteristic
607C22#1684041111yescharacteristic
608C22C2×#1451979711yescharacteristic
609C22C2×#1451980311yescharacteristic
610C22#1684057011yescharacteristic
611C22#1684057011yescharacteristic
612C4—22no—
613C4—22no—
614C4—41no—
615C4—41no—
616C4—41no—
617C4—81no—
618C4—81no—
619C4—81no—
620C4—81no—
621C4—4881no—
622C4—2442no—
623C4—2442no—
624C4#1684029511yescharacteristic
625C4#1684035311yescharacteristic
626C4#1684046311yescharacteristic
627C4#1684047911yescharacteristic
628C2—81no—
629C2—4882no—
630C2#2144985111yescharacteristic
631C2#2145587311yescharacteristic
632C2#2145606611yescharacteristic
633C2#2145775211yescharacteristic
634C2#2145777411yescharacteristic
635C2#2145819811yescharacteristic
636C2#2145841411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2496C2
socleC23×C61C22×D4
prime radicalC2×#14519751C22
hypercenter#2496D61
hypocenterC61#27039
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2496

Complements

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

NH ≅ G/Ntype
2. #21447223C2semidirect
3. #21447190C2semidirect
6. #21446580C2semidirect
7. #21446544C2semidirect
8. #21446427C2semidirect
9. #21446408C2semidirect
10. #21446404C2semidirect
11. #21446065C2semidirect
12. #21446016C2semidirect
13. #21445911C2semidirect
14. C4×#14519697C2semidirect
15. C61×#2496C2semidirect
310. #2496D61semidirect
377. C61#27039semidirect

Maximal subgroups

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

subgroupindex
#214488552
#214472232
#214471902
#214470082
#214465802
#214465442
#214464272
#214464082
#214464042
#214460652
#214460162
#214459112
C4×#145196972
C61×#24962
#2703961