Finite Group Databasebeta

← #30620069

Subgroups — #30620069

Order 15616.

738 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461992C211yesmaximal, characteristic, complemented
2#21461991C211yesmaximal, characteristic, complemented
3#21461895C211yesmaximal, characteristic, complemented
4#21461894C211yesmaximal, characteristic, complemented
5#21461891C211yesmaximal, characteristic, complemented
6#21461890C211yesmaximal, characteristic, complemented
7#21461795C211yesmaximal, characteristic
8#21461795C211yesmaximal, characteristic
9#21461764C211yesmaximal, characteristic, complemented
10#21461764C211yesmaximal, characteristic, complemented
11#21461748C211yesmaximal, characteristic, complemented
12#21461607C211yesmaximal, characteristic, complemented
13#21461557C211yesmaximal, characteristic, complemented
14#21461557C211yesmaximal, characteristic, complemented
15#21449108C211yesmaximal, characteristic
16C22×D61⋊C8C2211yescharacteristic
17C22×D61⋊C8C2211yescharacteristic
18C2×#14519844C2211yescharacteristic
19C2×#14519844C2211yescharacteristic
20C2×C4⋊#92420C2211yescharacteristic
21C2×C4⋊#92420C2211yescharacteristic
22C2×#14519834C2211yescharacteristic
23C2×#14519834C2211yescharacteristic
24C2×#14519834C2211yescharacteristic
25C2×#14519834C2211yescharacteristic
26C2×#14519834C2211yescharacteristic
27C2×#14519834C2211yescharacteristic
28C2×#14519832C2211yescharacteristic
29C2×#14519832C2211yescharacteristic
30C2×#14519832C2211yescharacteristic
31C2×C4×#92420C2211yescharacteristic
32#16840628C2211yescharacteristic
33#16840628C2211yescharacteristic
34#16840628C2211yescharacteristic
35#16840628C2211yescharacteristic
36#16840628C2211yescharacteristic
37#16840628C2211yescharacteristic
38#16840628C2211yescharacteristic
39#16840628C2211yescharacteristic
40#16840628C2211yescharacteristic
41#16840628C2211yescharacteristic
42#16840628C2211yescharacteristic
43#16840628C2211yescharacteristic
44C2×#14519742C2211yescharacteristic
45C2×#14519739C2211yescharacteristic
46#16839700C411yescharacteristic
47#16839691C411yescharacteristic
48#16839691C411yescharacteristic
49#16839680C411yescharacteristic
50#16839679C411yescharacteristic
51#16839675C411yescharacteristic
52#16839675C411yescharacteristic
53#16839609C2211yescharacteristic
54#16839609C2211yescharacteristic
55#16839609C2211yescharacteristic
56#16839609C2211yescharacteristic
57#16839607C2211yescharacteristic
58C61×#400C411yescharacteristic
59C2×D61⋊C8—22no—
60C2×D61⋊C8—22no—
61C2×D61⋊C8—41no—
62C2×D61⋊C8—41no—
63C2×D61⋊C8—41no—
64C2×D61⋊C8—41no—
65C22×#92420C2311yescharacteristic
66C22×#92420C2311yescharacteristic
67C22×#92420C2311yescharacteristic
68C22×#92420C2311yescharacteristic
69C22×#92420C2311yescharacteristic
70C22×#92420C2311yescharacteristic
71C22×#92420C2311yescharacteristic
72C22×#92420C2311yescharacteristic
73#14519844—22no—
74#14519844—41no—
75C4⋊#92420—22no—
76C4⋊#92420—41no—
77#14519834—22no—
78#14519834—22no—
79#14519834—41no—
80#14519834—41no—
81#14519834—41no—
82#14519834—41no—
83#14519832—41no—
84#14519832—41no—
85#14519832—41no—
86C4×#92420—41no—
87C22×Dic122C2×C411yescharacteristic
88C22×D244C2×C411yescharacteristic
89C22×C4×D61C2311yescharacteristic
90C22×C4×D61C2311yescharacteristic
91#14519742—41no—
92#14519742—41no—
93#14519739—41no—
94#14519739—41no—
95C2×#11758196C2×C411yescharacteristic
96C2×#11758196C2×C411yescharacteristic
97C2×#11758198C2×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×#11758198C2×C411yescharacteristic
107C2×C4×Dic61C2311yescharacteristic
108C2×C4×Dic61C2311yescharacteristic
109C2×C4×Dic61C2311yescharacteristic
110C2×C4×Dic61C2311yescharacteristic
111C2×C4×Dic61C2311yescharacteristic
112#14519684C2×C411yescharacteristic
113#14519684C2×C411yescharacteristic
114#14519684C2×C411yescharacteristic
115#14519684C2×C411yescharacteristic
116#14519684C2×C411yescharacteristic
117#14519684C2×C411yescharacteristic
118#14519684C2×C411yescharacteristic
119C2×C4⋊C4×C61C2×C411yescharacteristic
120C2×C4⋊C4×C61C2×C411yescharacteristic
121#95×C61C2×C411yescharacteristic
122#95×C61C2×C411yescharacteristic
123#95×C61C2×C411yescharacteristic
124#95×C61C2×C411yescharacteristic
125#95×C61C2×C411yescharacteristic
126C23×D61C22×C411yescharacteristic
127C23×D61C22×C411yescharacteristic
128C22×C4×C61C22×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×Dic61C22×C411yescharacteristic
136C22×Dic61C22×C411yescharacteristic
137C22×Dic61C22×C411yescharacteristic
138C22×Dic61C22×C411yescharacteristic
139C22×Dic61C22×C411yescharacteristic
140C22×Dic61C2411yescharacteristic
141C2×D244—22no—
142C2×D244—22no—
143C2×D244—41no—
144C2×C4×D61—21no—
145C2×C4×D61—21no—
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×Dic122—41no—
157C2×Dic122—41no—
158C2×Dic122—41no—
159C2×#92420—21no—
160C2×#92420—21no—
161C2×#92420—21no—
162C2×#92420—21no—
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#4112yes—
182C2×#92420#4112yes—
183D61⋊C8—44no—
184D61⋊C8—44no—
185C4⋊C4×C61—41no—
186C4⋊C4×C61—41no—
187#11758198—22no—
188#11758198—22no—
189#11758198—22no—
190#11758198—22no—
191#11758198—41no—
192#11758198—41no—
193#11758198—41no—
194#11758198—41no—
195#11758198—41no—
196#11758198—41no—
197#11758196—41no—
198#11758196—41no—
199C4×Dic61—21no—
200C4×Dic61—21no—
201C4×Dic61—21no—
202C4×Dic61—21no—
203C4×Dic61—21no—
204C4×Dic61—21no—
205C4×Dic61—21no—
206C4×Dic61—21no—
207C4×Dic61—21no—
208C4×Dic61—21no—
209C23×C61C23×C411yescharacteristic
210C22×D61—21no—
211C22×D61—21no—
212C22×D61—21no—
213C22×D61—21no—
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#13112yes—
223C22×D61#13112yes—
224C2×C4×C61—21no—
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—21no—
242C2×C4×C61—21no—
243C2×C4×C61—21no—
244C2×C4×C61—21no—
245C2×Dic61—21no—
246C2×Dic61—21no—
247C2×Dic61—21no—
248C2×Dic61—21no—
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×Dic61C2×#4111yescharacteristic
261C2×Dic61C2×#4111yescharacteristic
262C2×Dic61H(5,𝔽2)11yescharacteristic
263C2×Dic61H(5,𝔽2)11yescharacteristic
264C2×Dic61H(5,𝔽2)11yescharacteristic
265C2×Dic612−1+411yescharacteristic
266D244—44no—
267C4×D61—41no—
268C4×D61—41no—
269C4×D61—41no—
270C4×D61—41no—
271C4×D61—41no—
272C4×D61—41no—
273C4×D61—41no—
274C4×D61—41no—
275Dic122—44no—
276#92420—22no—
277#92420—22no—
278#92420—41no—
279#92420—41no—
280#92420—41no—
281#92420—41no—
282#92420—41no—
283#92420—41no—
284#22396—611nomaximal, Sylow
285C22×C61C4×#4111yescharacteristic
286C22×C61#51811yescharacteristic
287C22×C61#52011yescharacteristic
288C22×C61C2×#13111yescharacteristic
289C22×C61C2×#13111yescharacteristic
290C22×C61#56811yescharacteristic
291C22×C61#56811yescharacteristic
292C2×D61—22no—
293C2×D61—22no—
294C2×D61—22no—
295C2×D61—22no—
296C2×D61—22no—
297C2×D61—22no—
298C2×D61—41no—
299C2×D61—41no—
300C2×D61—41no—
301C2×D61—41no—
302C2×D61—41no—
303C2×D61—41no—
304C2×D61—41no—
305C2×D61—41no—
306C4×C61—41no—
307C4×C61—41no—
308C4×C61—41no—
309C4×C61—41no—
310C4×C61—41no—
311C4×C61—41no—
312C4×C61—41no—
313Dic61—41no—
314Dic61—41no—
315Dic61—41no—
316Dic61—41no—
317Dic61—41no—
318Dic61#53811yescharacteristic
319Dic61#53811yescharacteristic
320Dic61#54211yescharacteristic
321Dic61#54211yescharacteristic
322#2398—611no—
323#1985—611no—
324#1985—611no—
325#1924—611no—
326#1924—611no—
327#1923—611no—
328#1923—611no—
329#1869—611no—
330#1869—611no—
331#1850—611no—
332#1850—611no—
333#1840—611no—
334#1768—611no—
335#1752—611no—
336#1752—611no—
337C2×C61#233711yescharacteristic
338C2×C61#296811yescharacteristic
339C2×C61#296811yescharacteristic
340C2×C61#297711yescharacteristic
341C2×C61#297811yescharacteristic
342C2×C61#299211yescharacteristic
343C2×C61#299211yescharacteristic
344D61—42no—
345D61—42no—
346C23×C8—611no—
347C23×C8—611no—
348C2×C4×Q8—611no—
349C2×C4×D4—611no—
350C2×C4⋊C8—611no—
351C2×C4⋊C8—611no—
352C2×C4⋊C8—611no—
353C2×C4⋊C8—611no—
354C2×C22⋊C8—611no—
355C2×C22⋊C8—611no—
356C2×C22⋊C8—611no—
357C2×C22⋊C8—611no—
358C2×C22⋊C8—611no—
359C2×C22⋊C8—611no—
360C2×#97—611no—
361C2×#97—611no—
362C2×#97—611no—
363C2×C4×C8—611no—
364#400—611no—
365#400#692311yescharacteristic
366#397—611no—
367#397—611no—
368#394—611no—
369#394—611no—
370#393—611no—
371#393—611no—
372C4×C22⋊C4—611no—
373C4×C22⋊C4—611no—
374C4×C22⋊C4—611no—
375C4×C22⋊C4—611no—
376#376—611no—
377#336—611no—
378#336—611no—
379#336—611no—
380#336—611no—
381#336—611no—
382#336—611no—
383#336—611no—
384#336—611no—
385#336—611no—
386#336—611no—
387#336—611no—
388#336—611no—
389C61#2239611yescharacteristic, complemented, Sylow
390C22×Q8—611no—
391C22×D4—611no—
392C23×C4—611no—
393C23×C4—611no—
394C22×C8—611no—
395C22×C8—611no—
396C22×C8—611no—
397C22×C8—611no—
398C22×C8—611no—
399C22×C8—611no—
400C22×C8—611no—
401C22×C8—611no—
402C22×C8—1222no—
403C22×C8—1222no—
404C22×C8—2441no—
405C22×C8—2441no—
406C22×C8—2441no—
407C22×C8—2441no—
408C4×Q8—2441no—
409C4×Q8—2441no—
410C4×D4—2441no—
411C4×D4—2441no—
412C2×C4⋊C4—611no—
413C2×C4⋊C4—611no—
414C2×C4⋊C4C2×#692311yescharacteristic
415C2×C4⋊C4C2×#692311yescharacteristic
416C2×C22⋊C4—611no—
417C2×C22⋊C4—611no—
418C2×C22⋊C4—611no—
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×C42—611no—
427C2×C42—611no—
428C2×C42—611no—
429C2×C42—611no—
430C2×C42—611no—
431C4⋊C8—1222no—
432C4⋊C8—1222no—
433C4⋊C8—2441no—
434C4⋊C8—2441no—
435C22⋊C8—1222no—
436C22⋊C8—1222no—
437C22⋊C8—2441no—
438C22⋊C8—2441no—
439C22⋊C8—2441no—
440C22⋊C8—2441no—
441#97—2441no—
442#97—2441no—
443#97—2441no—
444C4×C8—2441no—
445#95—611no—
446#95—611no—
447#95—611no—
448#95—611no—
449#95—611no—
450#95—611no—
451#95—611no—
452#95C2×#692311yescharacteristic
453#95C2×#692311yescharacteristic
454#95C2×#692311yescharacteristic
455#95C2×#692311yescharacteristic
456#95C2×#692311yescharacteristic
457C24—611no—
458C24—611no—
459C2×Q8—2441no—
460C2×Q8—2441no—
461C2×Q8—2441no—
462C2×D4—1222no—
463C2×D4—1222no—
464C2×D4—2441no—
465C22×C4—611no—
466C22×C4—611no—
467C22×C4—611no—
468C22×C4—611no—
469C22×C4—611no—
470C22×C4—611no—
471C22×C4—1221no—
472C22×C4—1221no—
473C22×C4—1221no—
474C22×C4—1221no—
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×C4C22×#692311yescharacteristic
484C22×C4C22×#692311yescharacteristic
485C22×C4C22×#692311yescharacteristic
486C22×C4C22×#692311yescharacteristic
487C22×C4C22×#692311yescharacteristic
488C22×C4C22×#692311yescharacteristic
489C22×C4C22×#692311yescharacteristic
490C2×C8—612no—
491C2×C8—612no—
492C2×C8—1221no—
493C2×C8—1221no—
494C2×C8—1221no—
495C2×C8—1221no—
496C2×C8—1221no—
497C2×C8—1221no—
498C2×C8—1221no—
499C2×C8—1221no—
500C2×C8—1221no—
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—2444no—
515C2×C8—2444no—
516C4⋊C4—41no—
517C4⋊C4—41no—
518C4⋊C4—2441no—
519C4⋊C4—2441no—
520C22⋊C4—1222no—
521C22⋊C4—1222no—
522C22⋊C4—1222no—
523C22⋊C4—1222no—
524C22⋊C4—2441no—
525C22⋊C4—2441no—
526C22⋊C4—2441no—
527C22⋊C4—2441no—
528C22⋊C4—2441no—
529C22⋊C4—2441no—
530C42—1221no—
531C42—1221no—
532C42—1221no—
533C42—1221no—
534C42—1221no—
535C42—1221no—
536C42—1221no—
537C42—1221no—
538C42—1221no—
539C42—1221no—
540C23—612no—
541C23—612no—
542C23—1221no—
543C23—1221no—
544C23—1221no—
545C23—1221no—
546C23—1221no—
547C23—1221no—
548C23—1221no—
549C23—1221no—
550C23—1221no—
551C23—1221no—
552C23—1221no—
553C23—1221no—
554C23C23×#692311yescharacteristic
555Q8—2444no—
556D4—2444no—
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—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—611no—
579C2×C4—611no—
580C2×C4—611no—
581C2×C4—611no—
582C2×C4—611no—
583C2×C4—611no—
584C2×C4—1221no—
585C2×C4—1221no—
586C2×C4—1221no—
587C2×C4—1221no—
588C2×C4—1221no—
589C2×C4—1221no—
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—2441no—
600C2×C4—2441no—
601C2×C4—2441no—
602C2×C4—2441no—
603C2×C4—2441no—
604C2×C4—2441no—
605C2×C4—2441no—
606C2×C4—2441no—
607C8—1222no—
608C8—1222no—
609C8—2441no—
610C8—2441no—
611C8—2441no—
612C8—2441no—
613C8—2441no—
614C8—2441no—
615C22—1222no—
616C22—1222no—
617C22—1222no—
618C22—1222no—
619C22—1222no—
620C22—1222no—
621C22—2441no—
622C22—2441no—
623C22—2441no—
624C22—2441no—
625C22—2441no—
626C22—2441no—
627C22—2441no—
628C22—2441no—
629C22#41×#692311yescharacteristic
630C22#1684082911yescharacteristic
631C22#1684083111yescharacteristic
632C22D61⋊#13111yescharacteristic
633C22D61⋊#13111yescharacteristic
634C22#1684084111yescharacteristic
635C22#1684084211yescharacteristic
636C4—41no—
637C4—41no—
638C4—41no—
639C4—41no—
640C4—41no—
641C4—41no—
642C4—41no—
643C4—611no—
644C4—611no—
645C4—611no—
646C4—611no—
647C4—2441no—
648C4—2441no—
649C4—2441no—
650C4—2441no—
651C4—2441no—
652C2—2442no—
653C2—2442no—
654C2#2146232011yescharacteristic
655C2#2146264811yescharacteristic
656C2#2146264911yescharacteristic
657C2#2146269311yescharacteristic
658C2#2146269811yescharacteristic
659C2#2146275711yescharacteristic
660C2#2146275911yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#400C4
prime radicalC22×D244C2×C4
cosocleC22×Dic61C24
hypercenter#400#6923
hypocenterC61#22396
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. #21461992C2semidirect
2. #21461991C2semidirect
3. #21461895C2semidirect
4. #21461894C2semidirect
5. #21461891C2semidirect
6. #21461890C2semidirect
9. #21461764C2semidirect
10. #21461764C2semidirect
11. #21461748C2semidirect
12. #21461607C2semidirect
13. #21461557C2semidirect
14. #21461557C2semidirect
389. C61#22396semidirect

Maximal subgroups

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

subgroupindex
#214619922
#214619912
#214618952
#214618942
#214618912
#214618902
#214617952
#214617642
#214617482
#214616072
#214615572
#214491082
#2239661