Finite Group Databasebeta

← #30619895

Subgroups — #30619895

Order 15616.

768 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#21461943C211yesmaximal, characteristic
2#21461920C211yesmaximal, characteristic, complemented
3#21461893C211yesmaximal, characteristic, complemented
4#21461893C211yesmaximal, characteristic, complemented
5#21461892C211yesmaximal, characteristic, complemented
6#21461888C211yesmaximal, characteristic, complemented
7#21461878C211yesmaximal, characteristic, complemented
8#21461874C211yesmaximal, characteristic, complemented
9#21461796C211yesmaximal, characteristic
10#21461766C211yesmaximal, characteristic, complemented
11#21461675C211yesmaximal, characteristic, complemented
12#21461618C211yesmaximal, characteristic, complemented
13#21461561C211yesmaximal, characteristic, complemented
14C4×C22⋊#92420C211yesmaximal, characteristic, complemented
15#21448344C211yesmaximal, characteristic
16C22×#11758217C2211yescharacteristic
17C2×#14519844C2211yescharacteristic
18C2×#14519844C2211yescharacteristic
19C2×#14519844C2211yescharacteristic
20C2×C4⋊#92420C2211yescharacteristic
21C2×C4⋊#92420C2211yescharacteristic
22C2×C22⋊#92420C2211yescharacteristic
23C2×C22⋊#92420C2211yescharacteristic
24C2×C22⋊#92420C2211yescharacteristic
25C2×C22⋊#92420C2211yescharacteristic
26C2×C22⋊#92420C2211yescharacteristic
27C2×C22⋊#92420C2211yescharacteristic
28C2×C22⋊#92420C2211yescharacteristic
29C2×#14519832C2211yescharacteristic
30C2×#14519832C2211yescharacteristic
31C2×#14519832C2211yescharacteristic
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×#14519758C411yescharacteristic
45C2×D4×Dic61C2211yescharacteristic
46C22×C4×Dic61C2211yescharacteristic
47#16839656C411yescharacteristic
48#16839656C411yescharacteristic
49#16839649C411yescharacteristic
50#16839649C411yescharacteristic
51#16839635C411yescharacteristic
52#16839623C411yescharacteristic
53#16839613C2211yescharacteristic
54#16839613C2211yescharacteristic
55C22⋊C4×Dic61C2211yescharacteristic
56C22⋊C4×Dic61C2211yescharacteristic
57C22⋊C4×Dic61C2211yescharacteristic
58C61×#386C411yescharacteristic
59C2×#11758217—22no—
60C2×#11758217—41no—
61C2×#11758217—41no—
62C22×#92420C2311yescharacteristic
63C22×#92420C2311yescharacteristic
64C22×#92420C2311yescharacteristic
65C22×#92420C2311yescharacteristic
66C22×#92420C2311yescharacteristic
67C22×#92420C2311yescharacteristic
68C22×#92420C2311yescharacteristic
69C22×#92420C2311yescharacteristic
70#14519844—41no—
71#14519844—41no—
72#14519844—41no—
73C4⋊#92420—22no—
74C4⋊#92420—41no—
75C22⋊#92420—22no—
76C22⋊#92420—22no—
77C22⋊#92420—22no—
78C22⋊#92420—41no—
79C22⋊#92420—41no—
80C22⋊#92420—41no—
81C22⋊#92420—41no—
82#14519832—22no—
83#14519832—41no—
84#14519832—41no—
85C4×#92420—41no—
86C4×#92420—41no—
87C23×Dic61C2×C411yescharacteristic
88C23×Dic61C2311yescharacteristic
89C23×Dic61C2311yescharacteristic
90#14519758—24no—
91D4×Dic61—41no—
92D4×Dic61—41no—
93C2×C4⋊Dic61C2×C411yescharacteristic
94C2×#11758196C2×C411yescharacteristic
95C2×#11758196C2×C411yescharacteristic
96C2×#11758196C2×C411yescharacteristic
97C2×#11758196C2×C411yescharacteristic
98C2×C22⋊Dic61C2×C411yescharacteristic
99C2×C22⋊Dic61C2×C411yescharacteristic
100C2×C22⋊Dic61C2×C411yescharacteristic
101C2×C22⋊Dic61C2×C411yescharacteristic
102C2×C22⋊Dic61C2×C411yescharacteristic
103C2×C4×Dic61—41no—
104C2×C4×Dic61—41no—
105C2×C4×Dic61C2×C411yescharacteristic
106C2×C4×Dic61C2×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
119#14519684C2×C411yescharacteristic
120C22×D4×C61C2×C411yescharacteristic
121C23×C4×C61C2×C411yescharacteristic
122C2×C22⋊C4×C61C2×C411yescharacteristic
123C2×C22⋊C4×C61C2×C411yescharacteristic
124C2×C22⋊C4×C61C2×C411yescharacteristic
125#95×C61C2×C411yescharacteristic
126#95×C61C2×C411yescharacteristic
127C24×C61C22×C411yescharacteristic
128C24×C61C22×C411yescharacteristic
129C2×D4×C61—22no—
130C2×D4×C61—41no—
131C2×D4×C61—41no—
132C22×C4×C61—22no—
133C22×C4×C61—41no—
134C22×C4×C61—41no—
135C22×C4×C61C22×C411yescharacteristic
136C22×C4×C61C22×C411yescharacteristic
137C22×C4×C61C22×C411yescharacteristic
138C22×C4×C61C22×C411yescharacteristic
139C22×C4×C61C22×C411yescharacteristic
140C22×Dic61—21no—
141C22×Dic61—21no—
142C22×Dic61—21no—
143C22×Dic61—21no—
144C22×Dic61—21no—
145C22×Dic61—21no—
146C22×Dic61—21no—
147C22×Dic61—21no—
148C22×Dic61—21no—
149C22×Dic61—21no—
150C22×Dic61—21no—
151C22×Dic61—21no—
152C22×Dic61—41no—
153C22×Dic61—41no—
154C22×Dic61M1614yescomplemented
155C22×Dic61C22×C411yescharacteristic
156C22×Dic61C22×C411yescharacteristic
157C22×Dic61C22×C411yescharacteristic
158C22×Dic61C22×C411yescharacteristic
159C22×Dic61C22×C411yescharacteristic
160C22×Dic61C22×C411yescharacteristic
161C22×Dic61C22×C411yescharacteristic
162C22×Dic61C2411yescharacteristic
163#11758217—44no—
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—21no—
186C2×#92420#4112yes—
187C2×#92420#4112yes—
188C22⋊C4×C61—22no—
189C22⋊C4×C61—41no—
190C22⋊C4×C61—41no—
191C22⋊Dic61—22no—
192C22⋊Dic61—22no—
193C22⋊Dic61—22no—
194C22⋊Dic61—41no—
195C22⋊Dic61—41no—
196C4⋊Dic61—41no—
197#11758196—22no—
198#11758196—22no—
199#11758196—22no—
200#11758196—41no—
201C4×Dic61—21no—
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—41no—
212C4×Dic61—41no—
213C23×C61—21no—
214C23×C61—21no—
215C23×C61—21no—
216C23×C61—21no—
217C23×C61—21no—
218C23×C61—21no—
219C23×C61—21no—
220C23×C61—21no—
221C23×C61—21no—
222C23×C61—21no—
223C23×C61—21no—
224C23×C61—21no—
225C23×C61—21no—
226C23×C61C2×M1612yes—
227C23×C61C23×C411yescharacteristic
228D4×C61—44no—
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—44no—
244C2×C4×C61#13112yes—
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×Dic61—21no—
261C2×Dic61—21no—
262C2×Dic61—21no—
263C2×Dic61—21no—
264C2×Dic61—44no—
265C2×Dic61—41no—
266C2×Dic61—41no—
267C2×Dic61—41no—
268C2×Dic61—41no—
269C2×Dic61—41no—
270C2×Dic61—41no—
271C2×Dic61—41no—
272C2×Dic61—41no—
273C2×Dic61C2×M1612yes—
274C2×Dic61C2×M1612yes—
275C2×Dic61C2×#4111yescharacteristic
276C2×Dic61C2×#4111yescharacteristic
277C2×Dic61H(5,𝔽2)11yescharacteristic
278C2×Dic61H(5,𝔽2)11yescharacteristic
279C2×Dic61H(5,𝔽2)11yescharacteristic
280C2×Dic612−1+411yescharacteristic
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#22369—611nomaximal, Sylow
290C22×C61—22no—
291C22×C61—22no—
292C22×C61—22no—
293C22×C61—41no—
294C22×C61—41no—
295C22×C61—41no—
296C22×C61—41no—
297C22×C61—41no—
298C22×C61—41no—
299C22×C61—41no—
300C22×C61—41no—
301C22×C61—41no—
302C22×C61—41no—
303C22×C61—41no—
304C22×C61C4×#4111yescharacteristic
305C22×C61#51811yescharacteristic
306C22×C61#52011yescharacteristic
307C22×C61C22×M1611yescharacteristic
308C22×C61C2×#13111yescharacteristic
309C22×C61#56811yescharacteristic
310C22×C61#56811yescharacteristic
311C4×C61—22no—
312C4×C61—41no—
313C4×C61—41no—
314C4×C61—41no—
315C4×C61—41no—
316Dic61—22no—
317Dic61—22no—
318Dic61—41no—
319Dic61—41no—
320Dic61—41no—
321Dic61—41no—
322Dic61—41no—
323Dic61#53811yescharacteristic
324Dic61#53911yescharacteristic
325Dic61#54011yescharacteristic
326Dic61#54211yescharacteristic
327C4×#123—611no—
328#1955—611no—
329#1940—611no—
330#1924—611no—
331#1924—611no—
332#1924—611no—
333#1923—611no—
334#1917—611no—
335#1916—611no—
336#1870—611no—
337#1851—611no—
338#1797—611no—
339#1771—611no—
340#1753—611no—
341C4×C22⋊C8—611no—
342C2×C61—42no—
343C2×C61—81no—
344C2×C61#233511yescharacteristic
345C2×C61#296511yescharacteristic
346C2×C61#296711yescharacteristic
347C2×C61#297311yescharacteristic
348C2×C61#297611yescharacteristic
349C2×C61#298911yescharacteristic
350C2×C61#299311yescharacteristic
351C22×M16—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×#97—611no—
368C2×#97—611no—
369C2×#97—611no—
370C2×C4×C8—611no—
371C2×C4×C8—611no—
372#388—611no—
373#388—611no—
374#387—611no—
375#387—611no—
376#386#692311yescharacteristic
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#2236911yescharacteristic, complemented, Sylow
395C22×D4C2×#692311yescharacteristic
396C23×C4—611no—
397C23×C4—611no—
398C23×C4—611no—
399C23×C4C2×#692311yescharacteristic
400C2×M16—1222no—
401C2×M16—2441no—
402C2×M16—2441no—
403C22×C8—611no—
404C22×C8—611no—
405C22×C8—611no—
406C22×C8—611no—
407C22×C8—611no—
408C22×C8—611no—
409C22×C8—611no—
410C22×C8—611no—
411#123—1224no—
412C4×D4—2441no—
413C4×D4—2441no—
414C2×C4⋊C4—611no—
415C2×C4⋊C4—611no—
416C2×C4⋊C4—611no—
417C2×C4⋊C4—611no—
418C2×C4⋊C4—611no—
419C2×C22⋊C4—611no—
420C2×C22⋊C4—611no—
421C2×C22⋊C4—611no—
422C2×C22⋊C4—611no—
423C2×C22⋊C4—611no—
424C2×C22⋊C4C2×#692311yescharacteristic
425C2×C22⋊C4C2×#692311yescharacteristic
426C2×C22⋊C4C2×#692311yescharacteristic
427C2×C42—611no—
428C2×C42—611no—
429C2×C42—611no—
430C2×C42—611no—
431C2×C42—611no—
432C2×C42—611no—
433C2×C42—611no—
434C2×C42—2441no—
435C2×C42—2441no—
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—
448#97—1222no—
449#97—2441no—
450#97—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#95—611no—
460#95—611no—
461#95C2×#692311yescharacteristic
462#95C2×#692311yescharacteristic
463C24C22×#692311yescharacteristic
464C24C22×#692311yescharacteristic
465C2×D4—22no—
466C2×D4—41no—
467C2×D4—41no—
468C22×C4—22no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—611no—
472C22×C4—611no—
473C22×C4—611no—
474C22×C4—614no—
475C22×C4—611no—
476C22×C4—611no—
477C22×C4—611no—
478C22×C4—611no—
479C22×C4—611no—
480C22×C4—1221no—
481C22×C4—1221no—
482C22×C4—1221no—
483C22×C4—1221no—
484C22×C4—1221no—
485C22×C4—1221no—
486C22×C4—1221no—
487C22×C4—1221no—
488C22×C4—1221no—
489C22×C4—1221no—
490C22×C4—1221no—
491C22×C4—1221no—
492C22×C4—2441no—
493C22×C4—2441no—
494C22×C4C22×#692311yescharacteristic
495C22×C4C22×#692311yescharacteristic
496C22×C4C22×#692311yescharacteristic
497C22×C4C22×#692311yescharacteristic
498C22×C4C22×#692311yescharacteristic
499M16—2444no—
500C2×C8—612no—
501C2×C8—612no—
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—1221no—
524C4⋊C4—1222no—
525C4⋊C4—1222no—
526C4⋊C4—1222no—
527C4⋊C4—2441no—
528C4⋊C4—2441no—
529C22⋊C4—22no—
530C22⋊C4—41no—
531C22⋊C4—41no—
532C22⋊C4—1222no—
533C22⋊C4—1222no—
534C22⋊C4—1222no—
535C22⋊C4—2441no—
536C22⋊C4—2441no—
537C42—1221no—
538C42—1221no—
539C42—1221no—
540C42—1221no—
541C42—1221no—
542C42—1221no—
543C42—1221no—
544C42—1221no—
545C42—1221no—
546C42—1221no—
547C42—2441no—
548C42—2441no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23D61⋊M1612yes—
563C23C23×#692311yescharacteristic
564D4—44no—
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—44no—
580C2×C4—611no—
581C2×C4—611no—
582C2×C4—611no—
583C2×C4—611no—
584C2×C4—611no—
585C2×C4—611no—
586C2×C4—612no—
587C2×C4—612no—
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—1221no—
600C2×C4—1221no—
601C2×C4—1221no—
602C2×C4—1221no—
603C2×C4—1221no—
604C2×C4—1221no—
605C2×C4—1221no—
606C2×C4—1221no—
607C2×C4—2441no—
608C2×C4—2441no—
609C2×C4—2441no—
610C2×C4—2441no—
611C2×C4—2441no—
612C2×C4—2441no—
613C2×C4—2441no—
614C2×C4—2441no—
615C2×C4—2444no—
616C2×C4#1451986412yes—
617C8—1222no—
618C8—1222no—
619C8—2441no—
620C8—2441no—
621C8—2441no—
622C8—2441no—
623C8—2441no—
624C8—2441no—
625C22—22no—
626C22—22no—
627C22—22no—
628C22—41no—
629C22—41no—
630C22—41no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22#41×#692311yescharacteristic
640C22#1684082911yescharacteristic
641C22#1684083111yescharacteristic
642C22C2×D61⋊M1611yescharacteristic
643C22C2×#1451986411yescharacteristic
644C22#1684084011yescharacteristic
645C22#1684084011yescharacteristic
646C4—22no—
647C4—41no—
648C4—41no—
649C4—41no—
650C4—41no—
651C4—611no—
652C4—611no—
653C4—611no—
654C4—611no—
655C4—1222no—
656C4—1222no—
657C4—2441no—
658C4—2441no—
659C4—2441no—
660C4—2441no—
661C4—2441no—
662C2—42no—
663C2—81no—
664C2#2146231811yescharacteristic
665C2#2146262911yescharacteristic
666C2#2146263811yescharacteristic
667C2#2146267311yescharacteristic
668C2#2146268511yescharacteristic
669C2#2146273911yescharacteristic
670C2#2146276111yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#386C4
prime radicalC22×D4×C61C2×C4
cosocleC22×Dic61C24
hypercenter#386#6923
hypocenterC61#22369
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. #21461920C2semidirect
3. #21461893C2semidirect
4. #21461893C2semidirect
5. #21461892C2semidirect
6. #21461888C2semidirect
7. #21461878C2semidirect
8. #21461874C2semidirect
10. #21461766C2semidirect
11. #21461675C2semidirect
12. #21461618C2semidirect
13. #21461561C2semidirect
14. C4×C22⋊#92420C2semidirect
154. C22×Dic61M16semidirect
394. C61#22369semidirect

Maximal subgroups

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

subgroupindex
#214619432
#214619202
#214618932
#214618922
#214618882
#214618782
#214618742
#214617962
#214617662
#214616752
#214616182
#214615612
C4×C22⋊#924202
#214483442
#2236961