Finite Group Databasebeta

← #30619806

Subgroups — #30619806

Order 15616.

822 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461941C211yesmaximal, characteristic
2#21461916C211yesmaximal, characteristic, complemented
3#21461891C211yesmaximal, characteristic, complemented
4#21461891C211yesmaximal, characteristic, complemented
5#21461891C211yesmaximal, characteristic, complemented
6#21461890C211yesmaximal, characteristic, complemented
7#21461873C211yesmaximal, characteristic, complemented
8#21461872C211yesmaximal, characteristic, complemented
9#21461795C211yesmaximal, characteristic
10#21461764C211yesmaximal, characteristic, complemented
11#21461674C211yesmaximal, characteristic, complemented
12#21461611C211yesmaximal, characteristic, complemented
13#21461553C211yesmaximal, characteristic, complemented
14C4×#14519834C211yesmaximal, characteristic, complemented
15#21448340C211yesmaximal, characteristic
16C22×D61⋊C8C2211yescharacteristic
17C2×#14519844C2211yescharacteristic
18C2×C4⋊#92420C2211yescharacteristic
19C2×C4⋊#92420C2211yescharacteristic
20C2×C4⋊#92420C2211yescharacteristic
21C2×C4⋊#92420C2211yescharacteristic
22C2×#14519834C2211yescharacteristic
23C2×#14519834C2211yescharacteristic
24C2×#14519834C2211yescharacteristic
25C2×#14519834C2211yescharacteristic
26C2×#14519834C2211yescharacteristic
27C2×#14519834C2211yescharacteristic
28C2×#14519834C2211yescharacteristic
29C2×C4×#92420C2211yescharacteristic
30C2×C4×#92420C2211yescharacteristic
31C2×C4×#92420C2211yescharacteristic
32C2×C4×#92420C2211yescharacteristic
33C2×C4×#92420C2211yescharacteristic
34#16840628C2211yescharacteristic
35#16840628C2211yescharacteristic
36#16840628C2211yescharacteristic
37#16840628C2211yescharacteristic
38#16840628C2211yescharacteristic
39#16840628C2211yescharacteristic
40#16840628C2211yescharacteristic
41#16840628C2211yescharacteristic
42#16840628C2211yescharacteristic
43#16840628C2211yescharacteristic
44C2×#14519762C411yescharacteristic
45C2×#14519739C2211yescharacteristic
46C2×C42×D61C2211yescharacteristic
47#16839654C411yescharacteristic
48#16839653C411yescharacteristic
49#16839643C411yescharacteristic
50#16839640C411yescharacteristic
51#16839636C411yescharacteristic
52#16839624C411yescharacteristic
53C4⋊C4×Dic61C2211yescharacteristic
54#16839613C2211yescharacteristic
55#16839609C2211yescharacteristic
56#16839609C2211yescharacteristic
57#16839609C2211yescharacteristic
58C61×#387C411yescharacteristic
59C2×D61⋊C8—22no—
60C2×D61⋊C8—41no—
61C2×D61⋊C8—41no—
62C22×#92420C2311yescharacteristic
63C22×#92420C2311yescharacteristic
64C22×#92420C2311yescharacteristic
65C22×#92420C2311yescharacteristic
66C22×#92420C2311yescharacteristic
67C22×#92420C2311yescharacteristic
68C22×#92420C2311yescharacteristic
69C22×#92420C2311yescharacteristic
70#14519844—22no—
71C4⋊#92420—41no—
72C4⋊#92420—41no—
73C4⋊#92420—41no—
74C4⋊#92420—41no—
75#14519834—22no—
76#14519834—22no—
77#14519834—22no—
78#14519834—41no—
79#14519834—41no—
80#14519834—41no—
81#14519834—41no—
82C4×#92420—22no—
83C4×#92420—41no—
84C4×#92420—41no—
85C4×#92420—41no—
86C4×#92420—41no—
87C22×D244C2×C411yescharacteristic
88C22×C4×D61C2×C411yescharacteristic
89C22×C4×D61C2×C411yescharacteristic
90C22×C4×D61C2311yescharacteristic
91C22×C4×D61C2311yescharacteristic
92#14519762C818yescomplemented
93#14519739—41no—
94#14519739—41no—
95C2×C4⋊Dic61C2×C411yescharacteristic
96C2×#11758196C2×C411yescharacteristic
97C2×#11758196C2×C411yescharacteristic
98C2×#11758198C2×C411yescharacteristic
99C2×#11758198C2×C411yescharacteristic
100C2×#11758198C2×C411yescharacteristic
101C2×#11758198C2×C411yescharacteristic
102C2×#11758198C2×C411yescharacteristic
103C2×#11758198C2×C411yescharacteristic
104C2×#11758198C2×C411yescharacteristic
105C2×#11758198C2×C411yescharacteristic
106C2×C4×Dic61C2×C411yescharacteristic
107C2×C4×Dic61C2311yescharacteristic
108C2×C4×Dic61C2311yescharacteristic
109C2×C4×Dic61C2311yescharacteristic
110C2×C4×Dic61C2311yescharacteristic
111C2×C4×Dic61C2311yescharacteristic
112C42×D61—41no—
113C42×D61—41no—
114#14519684C2×C411yescharacteristic
115#14519684C2×C411yescharacteristic
116#14519684C2×C411yescharacteristic
117#14519684C2×C411yescharacteristic
118#14519684C2×C411yescharacteristic
119#14519684C2×C411yescharacteristic
120C2×C4⋊C4×C61C2×C411yescharacteristic
121C2×C4⋊C4×C61C2×C411yescharacteristic
122C2×C42×C61C2×C411yescharacteristic
123#95×C61C2×C411yescharacteristic
124#95×C61C2×C411yescharacteristic
125#95×C61C2×C411yescharacteristic
126#95×C61C2×C411yescharacteristic
127C23×D61C22×C411yescharacteristic
128C23×D61C22×C411yescharacteristic
129C22×C4×C61C22×C411yescharacteristic
130C22×C4×C61C22×C411yescharacteristic
131C22×C4×C61C22×C411yescharacteristic
132C22×C4×C61C22×C411yescharacteristic
133C22×C4×C61C22×C411yescharacteristic
134C22×C4×C61C22×C411yescharacteristic
135C22×C4×C61C22×C411yescharacteristic
136C22×Dic61C22×C411yescharacteristic
137C22×Dic61C22×C411yescharacteristic
138C22×Dic61C22×C411yescharacteristic
139C22×Dic61C22×C411yescharacteristic
140C22×Dic61C22×C411yescharacteristic
141C22×Dic61C2411yescharacteristic
142C2×D244—41no—
143C2×D244—41no—
144C2×D244C2×C814yes—
145C2×C4×D61—22no—
146C2×C4×D61—21no—
147C2×C4×D61—21no—
148C2×C4×D61—21no—
149C2×C4×D61—21no—
150C2×C4×D61—21no—
151C2×C4×D61—21no—
152C2×C4×D61—21no—
153C2×C4×D61—21no—
154C2×C4×D61—21no—
155C2×C4×D61—21no—
156C2×C4×D61—21no—
157C2×C4×D61—21no—
158C2×C4×D61—41no—
159C2×C4×D61—41no—
160C2×C4×D61—41no—
161C2×C4×D61—41no—
162C2×C4×D61C2×C814yescomplemented
163C2×#92420—21no—
164C2×#92420—21no—
165C2×#92420—21no—
166C2×#92420—21no—
167C2×#92420—21no—
168C2×#92420—21no—
169C2×#92420—21no—
170C2×#92420—21no—
171C2×#92420—21no—
172C2×#92420—21no—
173C2×#92420—21no—
174C2×#92420—21no—
175C2×#92420—21no—
176C2×#92420—21no—
177C2×#92420—21no—
178C2×#92420—21no—
179C2×#92420—21no—
180C2×#92420—21no—
181C2×#92420—21no—
182C2×#92420—21no—
183C2×#92420—21no—
184C2×#92420—21no—
185C2×#92420#4112yes—
186C2×#92420#4112yes—
187D61⋊C8—44no—
188C4⋊C4×C61—41no—
189C4⋊C4×C61C2×C814yescomplemented
190C42×C61—41no—
191#11758198—22no—
192#11758198—41no—
193#11758198—41no—
194#11758198—41no—
195#11758198—41no—
196#11758198C2×C814yes—
197#11758198C2×C814yes—
198#11758198C2×C814yescomplemented
199C4⋊Dic61—41no—
200#11758196—22no—
201#11758196C2×C814yescomplemented
202C4×Dic61—21no—
203C4×Dic61—21no—
204C4×Dic61—21no—
205C4×Dic61—21no—
206C4×Dic61—21no—
207C4×Dic61—21no—
208C4×Dic61—21no—
209C4×Dic61—21no—
210C4×Dic61—21no—
211C4×Dic61—21no—
212C4×Dic61—41no—
213C23×C61C23×C411yescharacteristic
214C22×D61—21no—
215C22×D61—21no—
216C22×D61—21no—
217C22×D61—21no—
218C22×D61—21no—
219C22×D61—21no—
220C22×D61—21no—
221C22×D61—21no—
222C22×D61—21no—
223C22×D61—21no—
224C22×D61—21no—
225C22×D61—21no—
226C22×D61C22×C812yes—
227C22×D61C22×C812yes—
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—21no—
242C2×C4×C61—21no—
243C2×C4×C61—21no—
244C2×C4×C61—21no—
245C2×C4×C61C22×C812yes—
246C2×C4×C61C22×C812yes—
247C2×C4×C61C22×C812yes—
248C2×C4×C61#13112yes—
249C2×Dic61—21no—
250C2×Dic61—21no—
251C2×Dic61—21no—
252C2×Dic61—21no—
253C2×Dic61—21no—
254C2×Dic61—21no—
255C2×Dic61—21no—
256C2×Dic61—21no—
257C2×Dic61—21no—
258C2×Dic61—21no—
259C2×Dic61—21no—
260C2×Dic61—21no—
261C2×Dic61—21no—
262C2×Dic61C22×C812yes—
263C2×Dic61C22×C812yes—
264C2×Dic61C2×#4111yescharacteristic
265C2×Dic61C2×#4111yescharacteristic
266C2×Dic61H(5,𝔽2)11yescharacteristic
267C2×Dic61H(5,𝔽2)11yescharacteristic
268C2×Dic61H(5,𝔽2)11yescharacteristic
269C2×Dic612−1+411yescharacteristic
270D244—44no—
271C4×D61—44no—
272C4×D61—44no—
273C4×D61—41no—
274C4×D61—41no—
275C4×D61—41no—
276C4×D61—41no—
277C4×D61—41no—
278C4×D61—41no—
279C4×D61—41no—
280C4×D61—41no—
281#92420—22no—
282#92420—22no—
283#92420—41no—
284#92420—41no—
285#92420—41no—
286#92420—41no—
287#92420—41no—
288#92420—41no—
289#22357—611nomaximal, Sylow
290C22×C61C4×#4111yescharacteristic
291C22×C61#51811yescharacteristic
292C22×C61#52011yescharacteristic
293C22×C61C23×C811yescharacteristic
294C22×C61C2×#13111yescharacteristic
295C22×C61#56811yescharacteristic
296C22×C61#56811yescharacteristic
297C2×D61—22no—
298C2×D61—22no—
299C2×D61—22no—
300C2×D61—22no—
301C2×D61—22no—
302C2×D61—22no—
303C2×D61—41no—
304C2×D61—41no—
305C2×D61—41no—
306C2×D61—41no—
307C2×D61—41no—
308C2×D61—41no—
309C2×D61—41no—
310C2×D61—41no—
311C4×C61—22no—
312C4×C61—22no—
313C4×C61—22no—
314C4×C61—22no—
315C4×C61—41no—
316C4×C61—41no—
317C4×C61—41no—
318Dic61—22no—
319Dic61—22no—
320Dic61—41no—
321Dic61—41no—
322Dic61—41no—
323Dic61#53811yescharacteristic
324Dic61#53911yescharacteristic
325Dic61#54011yescharacteristic
326Dic61#54211yescharacteristic
327C4×#123—611no—
328#1954—611no—
329#1939—611no—
330#1923—611no—
331#1923—611no—
332#1923—611no—
333#1923—611no—
334#1916—611no—
335#1916—611no—
336#1869—611no—
337#1850—611no—
338#1797—611no—
339C8×C4⋊C4—611no—
340C8×C22⋊C4—611no—
341C4×C22⋊C8—611no—
342C2×C61#233511yescharacteristic
343C2×C61C8×#4111yescharacteristic
344C2×C61#296711yescharacteristic
345C2×C61#297211yescharacteristic
346C2×C61#297611yescharacteristic
347C2×C61#298811yescharacteristic
348C2×C61#299311yescharacteristic
349D61—42no—
350D61—42no—
351C23×C8—611no—
352C2×#123—611no—
353C2×C4×D4—611no—
354C22×C42—611no—
355C2×C4⋊C8—611no—
356C2×C4⋊C8—611no—
357C2×C4⋊C8—611no—
358C2×C4⋊C8—611no—
359C2×C4⋊C8—611no—
360C2×C22⋊C8—611no—
361C2×C22⋊C8—611no—
362C2×C22⋊C8—611no—
363C2×C22⋊C8—611no—
364C2×C22⋊C8—611no—
365C2×C22⋊C8—611no—
366C2×C22⋊C8—611no—
367C2×C4×C8—611no—
368C2×C4×C8—611no—
369C2×C4×C8—611no—
370C2×C4×C8—611no—
371C2×C4×C8—611no—
372#388—611no—
373#388—611no—
374#387—611no—
375#387#692311yescharacteristic
376#386—611no—
377#385—611no—
378#381—611no—
379C4×C4⋊C4—611no—
380C4×C4⋊C4—611no—
381C4×C22⋊C4—611no—
382C4×C22⋊C4—611no—
383C4×C22⋊C4—611no—
384#336—611no—
385#336—611no—
386#336—611no—
387#336—611no—
388#336—611no—
389#336—611no—
390#336—611no—
391#336—611no—
392#336—611no—
393#336—611no—
394C61#2235711yescharacteristic, complemented, Sylow
395C22×D4—611no—
396C23×C4—611no—
397C23×C4—611no—
398C23×C4—611no—
399C23×C4—611no—
400C22×C8—611no—
401C22×C8—611no—
402C22×C8—611no—
403C22×C8—611no—
404C22×C8—611no—
405C22×C8—611no—
406C22×C8—611no—
407C22×C8—611no—
408C22×C8—1222no—
409C22×C8—2441no—
410C22×C8—2441no—
411#123—618no—
412C4×D4—2441no—
413C4×D4—2441no—
414C2×C4⋊C4—611no—
415C2×C4⋊C4—611no—
416C2×C4⋊C4—611no—
417C2×C4⋊C4C2×#692311yescharacteristic
418C2×C4⋊C4C2×#692311yescharacteristic
419C2×C22⋊C4—611no—
420C2×C22⋊C4—611no—
421C2×C22⋊C4—611no—
422C2×C22⋊C4—611no—
423C2×C22⋊C4—611no—
424C2×C22⋊C4—611no—
425C2×C22⋊C4—611no—
426C2×C22⋊C4—611no—
427C2×C42—611no—
428C2×C42—611no—
429C2×C42—611no—
430C2×C42—611no—
431C2×C42—611no—
432C2×C42—611no—
433C2×C42—2441no—
434C2×C42—2441no—
435C2×C42C2×#692311yescharacteristic
436C4⋊C8—1222no—
437C4⋊C8—2441no—
438C4⋊C8—2441no—
439C4⋊C8—2441no—
440C4⋊C8—2441no—
441C22⋊C8—1222no—
442C22⋊C8—1222no—
443C22⋊C8—1222no—
444C22⋊C8—2441no—
445C22⋊C8—2441no—
446C22⋊C8—2441no—
447C22⋊C8—2441no—
448C4×C8—1222no—
449C4×C8—2441no—
450C4×C8—2441no—
451C4×C8—2441no—
452C4×C8—2441no—
453#95—611no—
454#95—611no—
455#95—611no—
456#95—611no—
457#95—611no—
458#95—611no—
459#95C2×#692311yescharacteristic
460#95C2×#692311yescharacteristic
461#95C2×#692311yescharacteristic
462#95C2×#692311yescharacteristic
463C24—611no—
464C24—611no—
465C2×D4—614no—
466C2×D4—2441no—
467C2×D4—2441no—
468C22×C4—611no—
469C22×C4—611no—
470C22×C4—611no—
471C22×C4—614no—
472C22×C4—611no—
473C22×C4—611no—
474C22×C4—611no—
475C22×C4—1221no—
476C22×C4—1221no—
477C22×C4—1221no—
478C22×C4—1221no—
479C22×C4—1221no—
480C22×C4—1221no—
481C22×C4—1221no—
482C22×C4—1221no—
483C22×C4—1221no—
484C22×C4—1221no—
485C22×C4—1221no—
486C22×C4—1221no—
487C22×C4—1222no—
488C22×C4—2441no—
489C22×C4—2441no—
490C22×C4—2441no—
491C22×C4—2441no—
492C22×C4C22×#692311yescharacteristic
493C22×C4C22×#692311yescharacteristic
494C22×C4C22×#692311yescharacteristic
495C22×C4C22×#692311yescharacteristic
496C22×C4C22×#692311yescharacteristic
497C22×C4C22×#692311yescharacteristic
498C22×C4C22×#692311yescharacteristic
499C2×C8—612no—
500C2×C8—612no—
501C2×C8—1221no—
502C2×C8—1221no—
503C2×C8—1221no—
504C2×C8—1221no—
505C2×C8—1221no—
506C2×C8—1221no—
507C2×C8—1221no—
508C2×C8—1221no—
509C2×C8—1221no—
510C2×C8—1221no—
511C2×C8—1221no—
512C2×C8—1221no—
513C2×C8—1221no—
514C2×C8—1221no—
515C2×C8—1221no—
516C2×C8—1221no—
517C2×C8—1221no—
518C2×C8—1221no—
519C2×C8—1221no—
520C2×C8—1221no—
521C2×C8—1221no—
522C2×C8—1221no—
523C2×C8—2444no—
524C4⋊C4—41no—
525C4⋊C4—614no—
526C4⋊C4—1222no—
527C4⋊C4—2441no—
528C4⋊C4D61⋊C814yescomplemented
529C22⋊C4—614no—
530C22⋊C4—614no—
531C22⋊C4—614no—
532C22⋊C4—1222no—
533C22⋊C4—2441no—
534C22⋊C4—2441no—
535C22⋊C4—2441no—
536C22⋊C4—2441no—
537C42—41no—
538C42—1221no—
539C42—1221no—
540C42—1221no—
541C42—1221no—
542C42—1221no—
543C42—1221no—
544C42—1221no—
545C42—1221no—
546C42—1221no—
547C42—1221no—
548C42—2441no—
549C23—612no—
550C23—612no—
551C23—1221no—
552C23—1221no—
553C23—1221no—
554C23—1221no—
555C23—1221no—
556C23—1221no—
557C23—1221no—
558C23—1221no—
559C23—1221no—
560C23—1221no—
561C23—1221no—
562C23—1221no—
563C23C23×#692311yescharacteristic
564D4—2444no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—611no—
583C2×C4—611no—
584C2×C4—611no—
585C2×C4—611no—
586C2×C4—611no—
587C2×C4—611no—
588C2×C4—612no—
589C2×C4—612no—
590C2×C4—1221no—
591C2×C4—1221no—
592C2×C4—1221no—
593C2×C4—1221no—
594C2×C4—1221no—
595C2×C4—1221no—
596C2×C4—1221no—
597C2×C4—1221no—
598C2×C4—1221no—
599C2×C4—1221no—
600C2×C4—1221no—
601C2×C4—1221no—
602C2×C4—1221no—
603C2×C4—2444no—
604C2×C4—2444no—
605C2×C4—2441no—
606C2×C4—2441no—
607C2×C4—2441no—
608C2×C4—2441no—
609C2×C4—2441no—
610C2×C4—2441no—
611C2×C4—2441no—
612C2×C4—2441no—
613C2×C4C2×D61⋊C812yes—
614C2×C4C2×D61⋊C812yes—
615C2×C4C2×D61⋊C812yes—
616C2×C4#1451986512yes—
617C8—1222no—
618C8—1222no—
619C8—2441no—
620C8—2441no—
621C8—2441no—
622C8—2441no—
623C8—2441no—
624C8—2441no—
625C22—1222no—
626C22—1222no—
627C22—1222no—
628C22—1222no—
629C22—1222no—
630C22—1222no—
631C22—2441no—
632C22—2441no—
633C22—2441no—
634C22—2441no—
635C22—2441no—
636C22—2441no—
637C22—2441no—
638C22—2441no—
639C22#41×#692311yescharacteristic
640C22#1684082911yescharacteristic
641C22#1684083111yescharacteristic
642C22C22×D61⋊C811yescharacteristic
643C22C2×#1451986511yescharacteristic
644C22#1684084111yescharacteristic
645C22#1684084111yescharacteristic
646C4—22no—
647C4—22no—
648C4—22no—
649C4—22no—
650C4—41no—
651C4—41no—
652C4—41no—
653C4—611no—
654C4—611no—
655C4—611no—
656C4—611no—
657C4—1222no—
658C4—1222no—
659C4—2441no—
660C4—2441no—
661C4—2441no—
662C2—2442no—
663C2—2442no—
664C2#2146231811yescharacteristic
665C2#2146262511yescharacteristic
666C2#2146264211yescharacteristic
667C2#2146266711yescharacteristic
668C2#2146268911yescharacteristic
669C2#2146273611yescharacteristic
670C2#2146276511yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutatorC22×C61C23×C8
FittingC61×#387C4
socleC23×C61C23×C4
prime radicalC22×D244C2×C4
cosocleC22×Dic61C24
hypercenter#387#6923
hypocenterC61#22357
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. #21461916C2semidirect
3. #21461891C2semidirect
4. #21461891C2semidirect
5. #21461891C2semidirect
6. #21461890C2semidirect
7. #21461873C2semidirect
8. #21461872C2semidirect
10. #21461764C2semidirect
11. #21461674C2semidirect
12. #21461611C2semidirect
13. #21461553C2semidirect
14. C4×#14519834C2semidirect
92. #14519762C8semidirect
162. C2×C4×D61C2×C8semidirect
189. C4⋊C4×C61C2×C8semidirect
198. #11758198C2×C8semidirect
201. #11758196C2×C8semidirect
394. C61#22357semidirect
528. C4⋊C4D61⋊C8semidirect

Maximal subgroups

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

subgroupindex
#214619412
#214619162
#214618912
#214618902
#214618732
#214618722
#214617952
#214617642
#214616742
#214616112
#214615532
C4×#145198342
#214483402
#2235761