Finite Group Databasebeta

← #30608768

Subgroups — #30608768

Order 15616.

1630 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840712C212yesmaximal
2#21461000C211yesmaximal, characteristic
3#21461000C211yesmaximal, characteristic
4#21460999C212yesmaximal, complemented
5#21460998C212yesmaximal, complemented
6#21460996C212yesmaximal, complemented
7#21460994C212yesmaximal, complemented
8#21460993C212yesmaximal
9#385×D61C211yesmaximal, characteristic
10C22×C4⋊#6923C2212yes—
11C22×C22⋊#6923C2212yes—
12C22×C22⋊#6923C2212yes—
13C22×C4×#6923C2211yescharacteristic
14C22×C4×#6923C2211yescharacteristic
15C22×C4×#6923C2212yes—
16#16840712C4116yescomplemented
17C2×(C2×#6923)⋊C4C2212yes—
18C2×(C2×#6923)⋊C4C2212yes—
19C2×(C2×#6923)⋊C4C2212yes—
20C2×(C2×#6923)⋊C4C2212yes—
21C2×(C2×#6923)⋊C4C2211yescharacteristic
22C2×(C2×#6923)⋊C4C2212yes—
23C2×(C2×#6923)⋊C4C2211yescharacteristic
24C2×(C2×#6923)⋊C4C2212yes—
25C2×(C2×#6923)⋊C4C2212yes—
26C2×(C2×#6923)⋊C4C2212yes—
27C23×C4×D61C2211yescharacteristic
28C2×C4⋊C4×D61C2212yes—
29C2×C22⋊C4×D61C2211yescharacteristic
30C2×C22⋊C4×D61C2211yescharacteristic
31#16839637C411yescharacteristic, complemented
32#16839636C412yescomplemented
33#16839635C411yescharacteristic, complemented
34#16839634C411yescharacteristic, complemented
35#16839633C412yescomplemented
36#95×D61C2212yes—
37C61×#385C411yescharacteristic, complemented
38C23×#6923C2312yes—
39C23×#6923C2312yes—
40C23×#6923C2312yes—
41C23×#6923C2312yes—
42C2×C4⋊#6923—42no—
43C2×C4⋊#6923—42no—
44C2×C4⋊#6923C2×C418yescomplemented
45C2×C22⋊#6923—42no—
46C2×C22⋊#6923—42no—
47C2×C22⋊#6923—42no—
48C2×C22⋊#6923—42no—
49C2×C22⋊#6923C2×C418yes—
50C2×C22⋊#6923C2×C418yes—
51C2×C4×#6923—42no—
52C2×C4×#6923—42no—
53C2×C4×#6923—42no—
54C2×C4×#6923—41no—
55C2×C4×#6923—41no—
56C2×C4×#6923—42no—
57C2×C4×#6923C2×C418yescomplemented
58(C2×#6923)⋊C4—42no—
59(C2×#6923)⋊C4—42no—
60(C2×#6923)⋊C4—42no—
61(C2×#6923)⋊C4—42no—
62(C2×#6923)⋊C4—42no—
63(C2×#6923)⋊C4—41no—
64(C2×#6923)⋊C4—41no—
65(C2×#6923)⋊C4—42no—
66(C2×#6923)⋊C4C2×C418yescomplemented
67(C2×#6923)⋊C4C2×C418yescomplemented
68C24×D61C2311yescharacteristic
69C23×Dic61C2×C411yescharacteristic
70C22×C4×D61—41no—
71C22×C4×D61—41no—
72C22×C4×D61—42no—
73C22×C4×D61—42no—
74C22×C4×D61C2×C412yes—
75C22×C4×D61C2311yescharacteristic
76C22×C4×D61C2311yescharacteristic
77C22×C4×D61C2312yes—
78C22×C4×D61C2312yes—
79C2×C4⋊Dic61C2×C412yes—
80C2×#11758196C2×C412yes—
81C2×#11758196C2×C412yes—
82C4⋊C4×D61—42no—
83C4⋊C4×D61—42no—
84C2×C22⋊Dic61C2×C411yescharacteristic
85C2×C22⋊Dic61C2×C411yescharacteristic
86C2×#11758198C2×C411yescharacteristic
87C2×#11758198C2×C411yescharacteristic
88C2×#11758198C2×C412yes—
89C22⋊C4×D61—41no—
90C22⋊C4×D61—41no—
91C22⋊C4×D61C2×C418yes—
92#14519684C2×C412yes—
93#14519684C2×C412yes—
94#14519684C2×C412yes—
95C23×C4×C61C2×C411yescharacteristic
96C2×C4⋊C4×C61C2×C412yes—
97C2×C22⋊C4×C61C2×C411yescharacteristic
98C2×C22⋊C4×C61C2×C411yescharacteristic
99#95×C61C2×C412yes—
100C24×C61C22×C411yescharacteristic
101C23×D61—22no—
102C23×D61—22no—
103C23×D61—21no—
104C23×D61—21no—
105C23×D61—22no—
106C23×D61—22no—
107C23×D61—22no—
108C23×D61C22×C411yescharacteristic
109C23×D61C22×C414yes—
110C23×D61C2411yescharacteristic
111C22×#6923—22no—
112C22×#6923—22no—
113C22×#6923—22no—
114C22×#6923—22no—
115C22×#6923—22no—
116C22×#6923—22no—
117C22×#6923—22no—
118C22×#6923—22no—
119C22×#6923—22no—
120C22×#6923—22no—
121C22×#6923—22no—
122C22×#6923—22no—
123C22×#6923—22no—
124C22×#6923—22no—
125C22×#6923—22no—
126C22×#6923—22no—
127C22×#6923—22no—
128C22×#6923—22no—
129C22×#6923—22no—
130C22×#6923—22no—
131C22×#6923—22no—
132C22×#6923—22no—
133C22×#6923—22no—
134C22×#6923—22no—
135C22×#6923C22×C414yes—
136C22×#6923C22×C414yes—
137C22×#6923C22×C414yes—
138C22×#6923C22×C414yes—
139C22×C4×C61—42no—
140C22×C4×C61—41no—
141C22×C4×C61C22×C412yes—
142C22×C4×C61C22×C411yescharacteristic
143C22×C4×C61C22×C411yescharacteristic
144C22×C4×C61C22×C412yes—
145C22×Dic61—42no—
146C22×Dic61—41no—
147C22×Dic61C22×C412yes—
148C22×Dic61C22×C411yescharacteristic
149C22×Dic61C22×C411yescharacteristic
150C22×Dic61C22×C412yes—
151C2×C4×D61—22no—
152C2×C4×D61—22no—
153C2×C4×D61—22no—
154C2×C4×D61—22no—
155C2×C4×D61—22no—
156C2×C4×D61—22no—
157C2×C4×D61—22no—
158C2×C4×D61—22no—
159C2×C4×D61—22no—
160C2×C4×D61—22no—
161C2×C4×D61—22no—
162C2×C4×D61—21no—
163C2×C4×D61—21no—
164C2×C4×D61—22no—
165C2×C4×D61—21no—
166C2×C4×D61—21no—
167C2×C4×D61—22no—
168C2×C4×D61—22no—
169C2×C4×D61—42no—
170C2×C4×D61—42no—
171C2×C4×D61—42no—
172C2×C4×D61—44no—
173C2×C4×D61—48no—
174C2×C4×D61—44no—
175C2×C4×D61C22×C414yes—
176C2×C4×D61C22×C414yes—
177C22⋊#6923—48no—
178C22⋊#6923—48no—
179C4⋊#6923—48no—
180C4×#6923—48no—
181C4×#6923—44no—
182C4×#6923—44no—
183C4⋊C4×C61—42no—
184C22⋊C4×C61—41no—
185C22⋊C4×C61C4214yescomplemented
186C22⋊Dic61—41no—
187C22⋊Dic61C4214yescomplemented
188#11758198—41no—
189#11758198—41no—
190#11758198C4218yescomplemented
191C4⋊Dic61—42no—
192#11758196—42no—
193#11758196—42no—
194C23×C61—21no—
195C23×C61—22no—
196C23×C61—21no—
197C23×C61—22no—
198C23×C61C2×C4212yes—
199C23×C61C23×C411yescharacteristic
200C22×D61—21no—
201C22×D61—22no—
202C22×D61—21no—
203C22×D61—22no—
204C22×D61—24no—
205C22×D61—24no—
206C22×D61—24no—
207C22×D61—24no—
208C22×D61—24no—
209C22×D61—24no—
210C22×D61—41no—
211C22×D61—42no—
212C22×D61—41no—
213C22×D61—41no—
214C22×D61—42no—
215C22×D61—42no—
216C22×D61—42no—
217C22×D61—41no—
218C22×D61—42no—
219C22×D61—42no—
220C22×D61C2×C4212yes—
221C22×D61C23×C412yes—
222C22×D61H(5,𝔽2)12yes—
223C22×D61H(5,𝔽2)12yes—
224C22×D61H(5,𝔽2)12yes—
225C22×D61H(5,𝔽2)11yescharacteristic
226C22×D61H(5,𝔽2)11yescharacteristic
227C22×D612−1+412yes—
228C22×D612−1+412yes—
229C2×#6923—24no—
230C2×#6923—24no—
231C2×#6923—24no—
232C2×#6923—24no—
233C2×#6923—24no—
234C2×#6923—24no—
235C2×#6923—24no—
236C2×#6923—24no—
237C2×#6923—24no—
238C2×#6923—24no—
239C2×#6923—24no—
240C2×#6923—24no—
241C2×#6923—42no—
242C2×#6923—42no—
243C2×#6923—42no—
244C2×#6923—42no—
245C2×#6923—42no—
246C2×#6923—42no—
247C2×#6923—42no—
248C2×#6923—42no—
249C2×#6923—42no—
250C2×#6923—42no—
251C2×#6923—42no—
252C2×#6923—42no—
253C2×#6923—42no—
254C2×#6923—42no—
255C2×#6923—42no—
256C2×#6923—42no—
257C2×C4×C61—22no—
258C2×C4×C61—22no—
259C2×C4×C61—22no—
260C2×C4×C61—22no—
261C2×C4×C61—21no—
262C2×C4×C61—21no—
263C2×C4×C61—22no—
264C2×C4×C61—22no—
265C2×C4×C61—22no—
266C2×C4×C61—44no—
267C2×C4×C61C2×C4214yes—
268C2×Dic61—22no—
269C2×Dic61—22no—
270C2×Dic61—22no—
271C2×Dic61—22no—
272C2×Dic61—21no—
273C2×Dic61—21no—
274C2×Dic61—22no—
275C2×Dic61—22no—
276C2×Dic61—22no—
277C2×Dic61—44no—
278C2×Dic61C2×C4214yes—
279C4×D61—24no—
280C4×D61—24no—
281C4×D61—24no—
282C4×D61—24no—
283C4×D61—48no—
284C4×D61—41no—
285C4×D61—41no—
286C4×D61—42no—
287C4×D61—42no—
288C4×D61—42no—
289C4×D61—42no—
290C4×D61—41no—
291C4×D61—42no—
292C4×D61—42no—
293C4×D61—41no—
294#13831—611nomaximal, Sylow
295C22×C61—22no—
296C22×C61—24no—
297C22×C61—41no—
298C22×C61—41no—
299C22×C61—42no—
300C22×C61C22×C4211yescharacteristic
301C22×C61#51811yescharacteristic
302C22×C61#51812yes—
303C22×C61#51911yescharacteristic
304C22×C61#52012yes—
305C2×D61—22no—
306C2×D61—24no—
307C2×D61—41no—
308C2×D61—41no—
309C2×D61—42no—
310C2×D61—44no—
311C2×D61—44no—
312C2×D61—44no—
313C2×D61—44no—
314C2×D61#51812yes—
315C2×D61#51812yes—
316C2×D61#52012yes—
317C2×D61#52012yes—
318C2×D61#52012yes—
319C2×D61#52012yes—
320C2×D61#56011yescharacteristic
321C2×D61#56011yescharacteristic
322C2×D61#56012yes—
323C2×D61H(3,𝔽4)11yescharacteristic
324C2×D61#56212yes—
325C2×D61#56212yes—
326C2×D61#56212yes—
327C2×D61#56312yes—
328C2×D61#56312yes—
329C2×D61#56311yescharacteristic
330#6923—44no—
331#6923—44no—
332#6923—44no—
333#6923—44no—
334C4×C61—24no—
335C4×C61—42no—
336C4×C61—41no—
337C4×C61—41no—
338Dic61—24no—
339Dic61—42no—
340Dic61—41no—
341Dic61—41no—
342C2×#388—612no—
343C2×#385—611no—
344#1437—611no—
345#1437—611no—
346#1436—612no—
347#1436—612no—
348C4⋊#95—612no—
349#1434—612no—
350C22⋊#95—612no—
351C2×C61—42no—
352C2×C61#227411yescharacteristic
353C2×C61#227512yes—
354C2×C61#237511yescharacteristic
355C2×C61#237611yescharacteristic
356C2×C61#237812yes—
357D61—42no—
358D61#237612yes—
359D61#237712yes—
360D61#237912yes—
361D61#238312yes—
362C24×C4—611no—
363C22×C4⋊C4—612no—
364C22×C4⋊C4—612no—
365C22×C22⋊C4—611no—
366C22×C22⋊C4—612no—
367C22×C22⋊C4—612no—
368C22×C22⋊C4—611no—
369C22×C42—612no—
370C22×C42—611no—
371C22×C42—611no—
372#388—6116no—
373#385—611no—
374#385—612no—
375#385—611no—
376#385—611no—
377#385—612no—
378#385#692311yescharacteristic, complemented
379C2×#95—612no—
380C2×#95—612no—
381C2×#95—612no—
382C2×#95—612no—
383C2×#95—612no—
384C2×#95—612no—
385C2×#95—612no—
386C2×#95—611no—
387C2×#95—612no—
388C2×#95—611no—
389C2×#95—612no—
390C61#1383111yescharacteristic, complemented, Sylow
391C25—611no—
392C23×C4—612no—
393C23×C4—612no—
394C23×C4—612no—
395C23×C4—612no—
396C23×C4—612no—
397C23×C4—611no—
398C23×C4—611no—
399C23×C4—611no—
400C23×C4—612no—
401C23×C4—612no—
402C23×C4—2441no—
403C23×C4—2441no—
404C23×C4—2442no—
405C23×C4—2442no—
406C23×C4C2×#692311yescharacteristic
407C2×C4⋊C4—618no—
408C2×C4⋊C4—612no—
409C2×C4⋊C4—612no—
410C2×C4⋊C4—612no—
411C2×C4⋊C4—2442no—
412C2×C4⋊C4—2442no—
413C2×C4⋊C4—2442no—
414C2×C4⋊C4—2442no—
415C2×C4⋊C4C2×#692312yes—
416C2×C22⋊C4—611no—
417C2×C22⋊C4—612no—
418C2×C22⋊C4—618no—
419C2×C22⋊C4—618no—
420C2×C22⋊C4—618no—
421C2×C22⋊C4—611no—
422C2×C22⋊C4—611no—
423C2×C22⋊C4—611no—
424C2×C22⋊C4—2441no—
425C2×C22⋊C4—2441no—
426C2×C22⋊C4—2442no—
427C2×C22⋊C4—2442no—
428C2×C22⋊C4—2442no—
429C2×C22⋊C4—2442no—
430C2×C22⋊C4C2×#692311yescharacteristic
431C2×C22⋊C4C2×#692311yescharacteristic
432C2×C42—618no—
433C2×C42—2442no—
434C2×C42—2442no—
435C2×C42—2442no—
436C2×C42—2441no—
437C2×C42—2441no—
438C2×C42—2442no—
439#95—618no—
440#95—618no—
441#95—612no—
442#95—612no—
443#95—612no—
444#95—2442no—
445#95—2441no—
446#95—2441no—
447#95—2442no—
448#95—2442no—
449#95—2442no—
450#95—2442no—
451#95—2442no—
452#95C2×#692312yes—
453C24—611no—
454C24—614no—
455C24—611no—
456C24—1222no—
457C24—1221no—
458C24—1221no—
459C24—1222no—
460C24—1222no—
461C24—1222no—
462C24—1222no—
463C24C22×#692311yescharacteristic
464C22×C4—42no—
465C22×C4—41no—
466C22×C4—612no—
467C22×C4—614no—
468C22×C4—614no—
469C22×C4—614no—
470C22×C4—614no—
471C22×C4—614no—
472C22×C4—614no—
473C22×C4—611no—
474C22×C4—612no—
475C22×C4—611no—
476C22×C4—1222no—
477C22×C4—1222no—
478C22×C4—1222no—
479C22×C4—1222no—
480C22×C4—1222no—
481C22×C4—1221no—
482C22×C4—1221no—
483C22×C4—1222no—
484C22×C4—1222no—
485C22×C4—1222no—
486C22×C4—1222no—
487C22×C4—1222no—
488C22×C4—1221no—
489C22×C4—1221no—
490C22×C4—1222no—
491C22×C4—1222no—
492C22×C4—1222no—
493C22×C4—1222no—
494C22×C4—1222no—
495C22×C4—1222no—
496C22×C4—1222no—
497C22×C4—1222no—
498C22×C4—1222no—
499C22×C4—1222no—
500C22×C4—1222no—
501C22×C4—1222no—
502C22×C4—1222no—
503C22×C4—1222no—
504C22×C4—1222no—
505C22×C4—1222no—
506C22×C4—1222no—
507C22×C4—1222no—
508C22×C4—1222no—
509C22×C4—1222no—
510C22×C4—1222no—
511C22×C4—1222no—
512C22×C4—1222no—
513C22×C4—1222no—
514C22×C4—1222no—
515C22×C4—1222no—
516C22×C4—1222no—
517C22×C4—1222no—
518C22×C4—2442no—
519C22×C4—2442no—
520C22×C4—2442no—
521C22×C4—2448no—
522C22×C4—2444no—
523C22×C4—2444no—
524C22×C4—2442no—
525C22×C4—2441no—
526C22×C4C22×#692311yescharacteristic
527C22×C4C22×#692312yes—
528C22×C4C22×#692311yescharacteristic
529C22×C4C22×#692312yes—
530C4⋊C4—42no—
531C4⋊C4—2442no—
532C4⋊C4—2442no—
533C4⋊C4—2442no—
534C4⋊C4—2448no—
535C22⋊C4—41no—
536C22⋊C4—614no—
537C22⋊C4—618no—
538C22⋊C4—2441no—
539C22⋊C4—2441no—
540C22⋊C4—2441no—
541C22⋊C4—2448no—
542C22⋊C4—2448no—
543C22⋊C4C4×#692314yescomplemented
544C42—2448no—
545C42—2444no—
546C42—2444no—
547C23—21no—
548C23—22no—
549C23—21no—
550C23—22no—
551C23—612no—
552C23—611no—
553C23—612no—
554C23—611no—
555C23—612no—
556C23—612no—
557C23—612no—
558C23—612no—
559C23—612no—
560C23—1224no—
561C23—1224no—
562C23—1224no—
563C23—1224no—
564C23—1224no—
565C23—1224no—
566C23—1221no—
567C23—1222no—
568C23—1221no—
569C23—1222no—
570C23—2442no—
571C23—2441no—
572C23—2441no—
573C23—2441no—
574C23—2442no—
575C23—2441no—
576C23—2442no—
577C23—2442no—
578C23—2442no—
579C23—2442no—
580C23C2×C4×#692312yes—
581C23C23×#692311yescharacteristic
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—44no—
592C2×C4—614no—
593C2×C4—1224no—
594C2×C4—1224no—
595C2×C4—1224no—
596C2×C4—1224no—
597C2×C4—1222no—
598C2×C4—1222no—
599C2×C4—1224no—
600C2×C4—1224no—
601C2×C4—1224no—
602C2×C4—1224no—
603C2×C4—1224no—
604C2×C4—1224no—
605C2×C4—1224no—
606C2×C4—1224no—
607C2×C4—1224no—
608C2×C4—1224no—
609C2×C4—1224no—
610C2×C4—1224no—
611C2×C4—1221no—
612C2×C4—1221no—
613C2×C4—1222no—
614C2×C4—1222no—
615C2×C4—1222no—
616C2×C4—1222no—
617C2×C4—1222no—
618C2×C4—2441no—
619C2×C4—2441no—
620C2×C4—2442no—
621C2×C4—2441no—
622C2×C4—2442no—
623C2×C4—2441no—
624C2×C4—2442no—
625C2×C4—2442no—
626C2×C4—2442no—
627C2×C4—2442no—
628C2×C4—2448no—
629C2×C4—2444no—
630C2×C4—2442no—
631C2×C4—2442no—
632C2×C4—2442no—
633C2×C4—2442no—
634C2×C4—2442no—
635C2×C4—2442no—
636C2×C4—2442no—
637C2×C4—2442no—
638C2×C4—2442no—
639C2×C4—2442no—
640C2×C4—2442no—
641C2×C4—2442no—
642C2×C4—2442no—
643C2×C4—2442no—
644C2×C4—2442no—
645C2×C4—2442no—
646C2×C4C2×C4×#692314yes—
647C22—22no—
648C22—24no—
649C22—41no—
650C22—41no—
651C22—42no—
652C22—612no—
653C22—611no—
654C22—611no—
655C22—611no—
656C22—612no—
657C22—611no—
658C22—612no—
659C22—612no—
660C22—612no—
661C22—612no—
662C22—612no—
663C22—612no—
664C22—612no—
665C22—612no—
666C22—612no—
667C22—612no—
668C22—1222no—
669C22—1224no—
670C22—2444no—
671C22—2444no—
672C22—2444no—
673C22—2444no—
674C22—2441no—
675C22—2441no—
676C22—2442no—
677C22C22×C4×#692311yescharacteristic
678C22#1684082911yescharacteristic
679C22#1684082912yes—
680C22#1684083011yescharacteristic
681C22#1684083112yes—
682C4—24no—
683C4—42no—
684C4—41no—
685C4—41no—
686C4—1224no—
687C4—2444no—
688C4—2444no—
689C4—2444no—
690C4—2444no—
691C4—2441no—
692C4—2442no—
693C4—2441no—
694C2—42no—
695C2—612no—
696C2—612no—
697C2—612no—
698C2—612no—
699C2—2442no—
700C2#2146225711yescharacteristic
701C2#2146225812yes—
702C2#2146235811yescharacteristic
703C2#2146235911yescharacteristic
704C2#2146236112yes—
subgroupG/H
center, FrattiniC23C23×#6923
commutatorC22×C61C22×C42
FittingC61×#385C4
socleC23×C61C23×C4
prime radicalC24×D61C23
cosocleC23×D61C24
hypercenter#385#6923
hypocenterC61#13831
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
4. #21460999C2semidirect
5. #21460998C2semidirect
6. #21460996C2semidirect
7. #21460994C2semidirect
16. #16840712C4semidirect
31. #16839637C4semidirect
32. #16839636C4semidirect
33. #16839635C4semidirect
34. #16839634C4semidirect
35. #16839633C4semidirect
37. C61×#385C4semidirect
44. C2×C4⋊#6923C2×C4semidirect
57. C2×C4×#6923C2×C4semidirect
66. (C2×#6923)⋊C4C2×C4semidirect
67. (C2×#6923)⋊C4C2×C4semidirect
185. C22⋊C4×C61C42semidirect
187. C22⋊Dic61C42semidirect
190. #11758198C42semidirect
378. #385#6923semidirect
390. C61#13831semidirect
543. C22⋊C4C4×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168407122
#214610002
#214609992
#214609982
#214609962
#214609942
#214609932
#385×D612
#1383161