Finite Group Databasebeta

← #30603561

Subgroups — #30603561

Order 15616.

770 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840636C211yesmaximal, characteristic
2C2×#16840635C211yesmaximal, characteristic
3C2×#16840635C211yesmaximal, characteristic
4C2×(C2×#6923)⋊C8C211yesmaximal, characteristic
5#21460996C211yesmaximal, characteristic
6#21460996C211yesmaximal, characteristic
7#340×D61C211yesmaximal, characteristic
8C22×D61⋊C8C2211yescharacteristic
9C22×C4⋊#6923C2211yescharacteristic
10C22×C4⋊#6923C2211yescharacteristic
11C22×C4×#6923C2211yescharacteristic
12C2×(C2×#6923)⋊C4—21no—
13C2×(C2×#6923)⋊C4—21no—
14C2×(C2×#6923)⋊C4—21no—
15C2×(C2×#6923)⋊C4—21no—
16#16840636—22no—
17#16840635—22no—
18#16840635—22no—
19(C2×#6923)⋊C8—22no—
20C22×C8×D61C2211yescharacteristic
21C2×C4⋊C4×D61C2211yescharacteristic
22C2×C4⋊C4×D61C2211yescharacteristic
23#16839525C411yescharacteristic, complemented
24#16839524C411yescharacteristic, complemented
25#16839524C411yescharacteristic, complemented
26C61×#340C411yescharacteristic, complemented
27C23×#6923—21no—
28C23×#6923—21no—
29C23×#6923D411yescharacteristic
30C23×#6923D411yescharacteristic
31C2×D61⋊C8—21no—
32C2×D61⋊C8—21no—
33C2×D61⋊C8—21no—
34C2×D61⋊C8—21no—
35C2×D61⋊C8—21no—
36C2×D61⋊C8D412yes—
37C22×#92420—21no—
38C2×C4⋊#6923—21no—
39C2×C4⋊#6923—21no—
40C2×C4⋊#6923—21no—
41C2×C4⋊#6923—21no—
42C2×C4⋊#6923—21no—
43C2×C4⋊#6923—21no—
44C2×C4⋊#6923—21no—
45C2×C4⋊#6923—21no—
46C2×C4⋊#6923—21no—
47C2×C4⋊#6923—21no—
48C2×C4⋊#6923D412yes—
49C2×C4⋊#6923Q812yes—
50C2×C4×#6923—21no—
51C2×C4×#6923—21no—
52C2×C4×#6923—21no—
53C2×C4×#6923—21no—
54C2×C4×#6923—21no—
55C2×C4×#6923—21no—
56(C2×#6923)⋊C4—42no—
57(C2×#6923)⋊C4—42no—
58(C2×#6923)⋊C4—42no—
59(C2×#6923)⋊C4—42no—
60C22×C4×D61—21no—
61C22×C4×D61—21no—
62C22×C4×D61C2311yescharacteristic
63C22×#92418C2×C411yescharacteristic
64C2×C8×D61—21no—
65C2×C8×D61—21no—
66C2×C8×D61—21no—
67C2×C8×D61—21no—
68C2×C8×D61—21no—
69C2×C8×D61—21no—
70C2×C4⋊Dic61C2×C411yescharacteristic
71C2×C4⋊Dic61C2×C411yescharacteristic
72C2×#11758196—21no—
73C2×#11758196—21no—
74C4⋊C4×D61—21no—
75C4⋊C4×D61—21no—
76C4⋊C4×D61—21no—
77C4⋊C4×D61—21no—
78C4⋊C4×D61—21no—
79C4⋊C4×D61—21no—
80C4⋊C4×D61—21no—
81C4⋊C4×D61—21no—
82C22×C8×C61C2×C411yescharacteristic
83C2×C4⋊C4×C61C2×C411yescharacteristic
84C2×C4⋊C4×C61C2×C411yescharacteristic
85C23×D61C2×D411yescharacteristic
86C22×#6923—21no—
87C22×#6923—21no—
88C22×#6923—21no—
89C22×#6923—21no—
90C22×#6923—21no—
91C22×#6923—21no—
92C22×#6923—21no—
93C22×#6923—21no—
94C22×#6923—21no—
95C22×#6923—21no—
96C22×#6923—21no—
97C22×#6923—21no—
98C22×#6923—22no—
99C22×#6923—22no—
100C22×#6923—41no—
101C22×#6923—41no—
102C22×#6923—41no—
103C22×#6923—41no—
104C22×#6923—41no—
105C22×#6923—41no—
106C22×#6923—41no—
107C22×#6923—41no—
108C22×#6923—41no—
109C22×#6923—41no—
110C22×#6923—41no—
111C22×#6923—41no—
112C22×#6923D812yes—
113C22×#6923SD1612yes—
114C22×C4×C61—21no—
115C22×C4×C61—21no—
116C22×C4×C61C22×C411yescharacteristic
117C22×Dic61—21no—
118C22×Dic61—21no—
119C22×Dic61#4111yescharacteristic
120C2×C4×D61—41no—
121C2×C4×D61—41no—
122C2×C4×D61—41no—
123C2×C4×D61—41no—
124C2×C4×D61—41no—
125C2×C4×D61—41no—
126C2×C4×D61—41no—
127C2×C4×D61—41no—
128C2×C4×D61—41no—
129C2×C4×D61—41no—
130C2×C4×D61—41no—
131C2×C4×D61—41no—
132C2×C4×D61C2×D411yescharacteristic
133C2×C4×D61C2×D411yescharacteristic
134C2×C4×D61C2×Q811yescharacteristic
135C2×C4×D61#4111yescharacteristic
136C2×C4×D61#4111yescharacteristic
137C2×C4×D61#4111yescharacteristic
138C2×C4×D61#4111yescharacteristic
139C2×C4×D61#4111yescharacteristic
140C2×C4×D61#4111yescharacteristic
141C2×C4×D61#4111yescharacteristic
142C2×C4×D61#4111yescharacteristic
143C2×C4×D61#4111yescharacteristic
144C2×#92420—22no—
145C2×#92420—41no—
146C2×#92420—41no—
147C4⋊#6923—22no—
148C4⋊#6923—22no—
149C4⋊#6923—22no—
150C4⋊#6923—22no—
151C4⋊#6923—41no—
152C4⋊#6923—41no—
153C4⋊#6923—41no—
154C4⋊#6923—41no—
155C4×#6923—41no—
156C4×#6923—41no—
157C4×#6923—41no—
158C4×#6923—41no—
159D61⋊C8—22no—
160D61⋊C8—22no—
161D61⋊C8—41no—
162D61⋊C8—41no—
163C2×C8×C61—21no—
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊Dic61—21no—
171C4⋊Dic61—21no—
172C4⋊Dic61—21no—
173C4⋊Dic61—21no—
174#11758196—41no—
175#11758196—41no—
176#11758196—41no—
177#11758196—41no—
178C2×#92418—21no—
179C2×#92418—21no—
180C2×#92418—21no—
181C8×D61—41no—
182C8×D61—41no—
183C8×D61—41no—
184C8×D61—41no—
185C23×C61C4×D411yescharacteristic
186C22×D61#12111yescharacteristic
187C22×D61#12111yescharacteristic
188C22×D61C22⋊Q811yescharacteristic
189C22×D61#12311yescharacteristic
190C22×D61#12311yescharacteristic
191C22×D61#12411yescharacteristic
192C22×D61C2×D811yescharacteristic
193C22×D61C2×SD1611yescharacteristic
194C22×D61#13511yescharacteristic
195C22×D61#13511yescharacteristic
196C22×D61AGL(1,ℤ/8)11yescharacteristic
197C22×D61#13711yescharacteristic
198C22×D61#13711yescharacteristic
199C22×D61#13711yescharacteristic
200C2×#6923—22no—
201C2×#6923—22no—
202C2×#6923—22no—
203C2×#6923—22no—
204C2×#6923—22no—
205C2×#6923—22no—
206C2×#6923—41no—
207C2×#6923—41no—
208C2×#6923—41no—
209C2×#6923—41no—
210C2×#6923—41no—
211C2×#6923—41no—
212C2×#6923—41no—
213C2×#6923—41no—
214C2×#6923—42no—
215C2×#6923—42no—
216C2×#6923—42no—
217C2×#6923—42no—
218C2×#6923—42no—
219C2×#6923—42no—
220C2×#6923—81no—
221C2×#6923—81no—
222C2×#6923—81no—
223C2×#6923—81no—
224C2×#6923—81no—
225C2×#6923—81no—
226C2×#6923—81no—
227C2×#6923—81no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61#11711yescharacteristic
235C2×C4×C61#11711yescharacteristic
236C2×C4×C61#11711yescharacteristic
237C2×C4×C61C4×D411yescharacteristic
238C2×C4×C61C4×D411yescharacteristic
239C2×C4×C61C4×Q811yescharacteristic
240C2×Dic61—41no—
241C2×Dic61—41no—
242C2×Dic61—41no—
243C2×Dic61—41no—
244C2×Dic61—41no—
245C2×Dic61—41no—
246C2×Dic61#12311yescharacteristic
247C2×Dic61#12411yescharacteristic
248C2×Dic61#12511yescharacteristic
249C2×Dic61#12611yescharacteristic
250C2×Dic61#12611yescharacteristic
251C2×Dic61#12611yescharacteristic
252C4×D61—81no—
253C4×D61—81no—
254C4×D61—81no—
255C4×D61—81no—
256C4×D61—81no—
257C4×D61—81no—
258C4×D61—81no—
259C4×D61—81no—
260C4×D61#12111yescharacteristic
261C4×D61C22⋊Q811yescharacteristic
262C4×D61C22⋊Q811yescharacteristic
263C4×D61#12311yescharacteristic
264C4×D61#12311yescharacteristic
265C4×D61#12311yescharacteristic
266C4×D61#12411yescharacteristic
267C4×D61#12511yescharacteristic
268C4×D61#12511yescharacteristic
269C4×D61#12611yescharacteristic
270C4×D61#12611yescharacteristic
271C4×D61#12611yescharacteristic
272C4×D61#12611yescharacteristic
273C4×D61#12611yescharacteristic
274C4×D61#12611yescharacteristic
275C4×D61#12611yescharacteristic
276#92420—42no—
277C8×C61—41no—
278#92418—41no—
279#11315—611nomaximal, Sylow
280C22×C61#38711yescharacteristic
281C22×C61#38811yescharacteristic
282C22×C61#38811yescharacteristic
283C22×C61C4×D811yescharacteristic
284C22×C61C4×SD1611yescharacteristic
285C22×C61#44011yescharacteristic
286C22×C61#44111yescharacteristic
287C2×D61#39611yescharacteristic
288C2×D61#39711yescharacteristic
289C2×D61#39711yescharacteristic
290C2×D61#40011yescharacteristic
291C2×D61#45911yescharacteristic
292C2×D61#46111yescharacteristic
293C2×D61#46411yescharacteristic
294C2×D61#46411yescharacteristic
295C2×D61#46511yescharacteristic
296C2×D61#46611yescharacteristic
297C2×D61#46811yescharacteristic
298C2×D61#47011yescharacteristic
299C2×D61#47411yescharacteristic
300C2×D61#47511yescharacteristic
301C2×D61#47811yescharacteristic
302C2×D61#47911yescharacteristic
303C2×D61#48011yescharacteristic
304C2×D61#48011yescharacteristic
305C2×D61#48111yescharacteristic
306C2×D61#48211yescharacteristic
307C2×D61#48311yescharacteristic
308C2×D61#48511yescharacteristic
309C2×D61#48511yescharacteristic
310C2×D61#48511yescharacteristic
311C2×D61#48611yescharacteristic
312C2×D61#48811yescharacteristic
313C2×D61#48911yescharacteristic
314C2×D61#49111yescharacteristic
315#6923—42no—
316#6923—42no—
317#6923—82no—
318#6923—82no—
319C4×C61—81no—
320C4×C61—81no—
321C4×C61#38311yescharacteristic
322C4×C61#38711yescharacteristic
323C4×C61#38711yescharacteristic
324C4×C61#38811yescharacteristic
325Dic61—81no—
326Dic61—81no—
327Dic61#39711yescharacteristic
328Dic61#40011yescharacteristic
329Dic61#40011yescharacteristic
330Dic61#40111yescharacteristic
331C2×#340—611no—
332C2×#340—611no—
333C2×#340—611no—
334C2×#340—611no—
335C2×#336—611no—
336C4⋊#95—611no—
337C4⋊#95—611no—
338C2×C61#144311yescharacteristic
339C2×C61#191811yescharacteristic
340C2×C61#191911yescharacteristic
341C2×C61#192511yescharacteristic
342C2×C61#192711yescharacteristic
343C2×C61#193411yescharacteristic
344C2×C61#193511yescharacteristic
345D61#206611yescharacteristic
346D61#206711yescharacteristic
347D61#207111yescharacteristic
348D61#207411yescharacteristic
349D61#207511yescharacteristic
350D61#207711yescharacteristic
351D61#209911yescharacteristic
352D61#210111yescharacteristic
353C23×C8—611no—
354C23×C8—611no—
355C22×C4⋊C4—611no—
356C22×C4⋊C4—611no—
357C22×C4⋊C4—611no—
358C22×C4⋊C4—611no—
359C22×C42—611no—
360C2×#95—1221no—
361C2×#95—1221no—
362C2×#95—1221no—
363C2×#95—1221no—
364#340—611no—
365#340—611no—
366#340—611no—
367#340—1222no—
368#340—1222no—
369#340—1222no—
370#340#692311yescharacteristic, complemented
371#336—1222no—
372C61#1131511yescharacteristic, complemented, Sylow
373C23×C4—611no—
374C23×C4—611no—
375C23×C4—611no—
376C23×C4—1221no—
377C23×C4—1221no—
378C23×C4—1221no—
379C23×C4—1221no—
380C22×C8—612no—
381C22×C8—611no—
382C22×C8—1221no—
383C22×C8—1221no—
384C22×C8—1221no—
385C22×C8—1221no—
386C22×C8—1221no—
387C22×C8—1221no—
388C22×C8—1221no—
389C22×C8—1221no—
390C22×C8—1221no—
391C22×C8—1221no—
392C22×C8—1221no—
393C22×C8—1221no—
394C22×C8C2×#692311yescharacteristic
395C2×C4⋊C4—612no—
396C2×C4⋊C4—612no—
397C2×C4⋊C4—611no—
398C2×C4⋊C4—611no—
399C2×C4⋊C4—1221no—
400C2×C4⋊C4—1221no—
401C2×C4⋊C4—1221no—
402C2×C4⋊C4—1221no—
403C2×C4⋊C4—1221no—
404C2×C4⋊C4—1221no—
405C2×C4⋊C4—1221no—
406C2×C4⋊C4—1221no—
407C2×C4⋊C4—1221no—
408C2×C4⋊C4—1221no—
409C2×C4⋊C4—1221no—
410C2×C4⋊C4—1221no—
411C2×C4⋊C4—1221no—
412C2×C4⋊C4—1221no—
413C2×C4⋊C4—1221no—
414C2×C4⋊C4—1221no—
415C2×C4⋊C4—1221no—
416C2×C4⋊C4—1221no—
417C2×C4⋊C4—1221no—
418C2×C4⋊C4—1221no—
419C2×C4⋊C4C2×#692311yescharacteristic
420C2×C4⋊C4C2×#692311yescharacteristic
421C2×C42—1221no—
422C2×C42—1221no—
423C2×C42—1221no—
424C2×C42—1221no—
425C2×C42—1221no—
426C2×C42—1221no—
427#95—2442no—
428#95—2442no—
429#95—2442no—
430#95—2442no—
431C24—611no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—611no—
435C22×C4—611no—
436C22×C4—611no—
437C22×C4—611no—
438C22×C4—611no—
439C22×C4—611no—
440C22×C4—611no—
441C22×C4—611no—
442C22×C4—611no—
443C22×C4—611no—
444C22×C4—611no—
445C22×C4—611no—
446C22×C4—611no—
447C22×C4—612no—
448C22×C4—612no—
449C22×C4—1221no—
450C22×C4—1221no—
451C22×C4—1221no—
452C22×C4—1221no—
453C22×C4—1221no—
454C22×C4—1221no—
455C22×C4—1221no—
456C22×C4—1221no—
457C22×C4—1221no—
458C22×C4—1221no—
459C22×C4—1221no—
460C22×C4—1221no—
461C22×C4—1222no—
462C22×C4—1222no—
463C22×C4—1221no—
464C22×C4—1221no—
465C22×C4—2441no—
466C22×C4—2441no—
467C22×C4—2441no—
468C22×C4—2441no—
469C22×C4—2441no—
470C22×C4—2441no—
471C22×C4—2441no—
472C22×C4—2441no—
473C22×C4—2441no—
474C22×C4—2441no—
475C22×C4—2441no—
476C22×C4—2441no—
477C22×C4—2441no—
478C22×C4—2441no—
479C22×C4—2441no—
480C22×C4—2441no—
481C22×C4—2441no—
482C22×C4—2441no—
483C22×C4—2441no—
484C22×C4—2441no—
485C22×C4—2441no—
486C22×C4—2441no—
487C22×C4—2441no—
488C22×C4—2441no—
489C22×C4C22×#692311yescharacteristic
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—1222no—
494C2×C8—1222no—
495C2×C8—1222no—
496C2×C8—1221no—
497C2×C8—1221no—
498C2×C8—1221no—
499C2×C8—2441no—
500C2×C8—2441no—
501C2×C8—2441no—
502C2×C8—2441no—
503C2×C8—2441no—
504C2×C8—2441no—
505C2×C8—2441no—
506C2×C8—2441no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—1222no—
512C4⋊C4—1222no—
513C4⋊C4—1222no—
514C4⋊C4—1222no—
515C4⋊C4—1221no—
516C4⋊C4—1221no—
517C4⋊C4—1221no—
518C4⋊C4—1221no—
519C4⋊C4—2441no—
520C4⋊C4—2441no—
521C4⋊C4—2441no—
522C4⋊C4—2441no—
523C4⋊C4—2441no—
524C4⋊C4—2441no—
525C4⋊C4—2441no—
526C4⋊C4—2441no—
527C42—2441no—
528C42—2441no—
529C42—2441no—
530C42—2441no—
531C23—611no—
532C23—611no—
533C23—611no—
534C23—611no—
535C23—611no—
536C23—611no—
537C23—611no—
538C23—611no—
539C23—611no—
540C23—611no—
541C23—611no—
542C23—611no—
543C23—611no—
544C23—611no—
545C23D4×#692311yescharacteristic
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—611no—
553C2×C4—611no—
554C2×C4—611no—
555C2×C4—611no—
556C2×C4—611no—
557C2×C4—611no—
558C2×C4—611no—
559C2×C4—611no—
560C2×C4—611no—
561C2×C4—611no—
562C2×C4—611no—
563C2×C4—611no—
564C2×C4—611no—
565C2×C4—611no—
566C2×C4—611no—
567C2×C4—611no—
568C2×C4—611no—
569C2×C4—611no—
570C2×C4—611no—
571C2×C4—611no—
572C2×C4—611no—
573C2×C4—611no—
574C2×C4—1222no—
575C2×C4—1222no—
576C2×C4—1222no—
577C2×C4—1222no—
578C2×C4—1222no—
579C2×C4—1222no—
580C2×C4—4881no—
581C2×C4—4881no—
582C2×C4—4881no—
583C2×C4—4881no—
584C2×C4—4881no—
585C2×C4—4881no—
586C2×C4—4881no—
587C2×C4—4881no—
588C2×C4—4881no—
589C2×C4—4881no—
590C2×C4—4881no—
591C2×C4—4881no—
592C2×C4—4881no—
593C2×C4—4881no—
594C2×C4—4881no—
595C2×C4—4881no—
596C2×C4—2442no—
597C2×C4—2442no—
598C2×C4—2442no—
599C2×C4—2442no—
600C2×C4—2442no—
601C2×C4—2442no—
602C2×C4—2441no—
603C2×C4—2441no—
604C2×C4—2441no—
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×C4—2441no—
614C2×C4—2441no—
615C2×C4—2441no—
616C2×C4#1451985611yescharacteristic
617C2×C4#1451985611yescharacteristic
618C2×C4#1451985611yescharacteristic
619C2×C4D4×#692311yescharacteristic
620C2×C4D4×#692311yescharacteristic
621C2×C4Q8×#692311yescharacteristic
622C8—41no—
623C8—2442no—
624C8—2441no—
625C22—611no—
626C22—611no—
627C22—611no—
628C22—611no—
629C22—611no—
630C22—611no—
631C22—611no—
632C22—611no—
633C22—611no—
634C22—611no—
635C22—611no—
636C22—611no—
637C22—611no—
638C22—611no—
639C22—611no—
640C22—611no—
641C22—611no—
642C22—611no—
643C22—611no—
644C22—611no—
645C22—611no—
646C22—611no—
647C22—611no—
648C22—611no—
649C22—611no—
650C22—611no—
651C22—611no—
652C22—611no—
653C22#1684071111yescharacteristic
654C22#1684071211yescharacteristic
655C22#1684071211yescharacteristic
656C22D8×#692311yescharacteristic
657C22SD16×#692311yescharacteristic
658C22#1684080111yescharacteristic
659C22#1684080211yescharacteristic
660C4—81no—
661C4—81no—
662C4—611no—
663C4—611no—
664C4—611no—
665C4—611no—
666C4—4882no—
667C4—4882no—
668C4—4881no—
669C4—4881no—
670C4—2442no—
671C4—2442no—
672C4#1684070711yescharacteristic
673C4#1684071111yescharacteristic
674C4#1684071111yescharacteristic
675C4#1684071211yescharacteristic
676C2—611no—
677C2—611no—
678C2—611no—
679C2—611no—
680C2—611no—
681C2—611no—
682C2—611no—
683C2—611no—
684C2#2146100611yescharacteristic
685C2#2146188011yescharacteristic
686C2#2146188111yescharacteristic
687C2#2146189611yescharacteristic
688C2#2146189811yescharacteristic
689C2#2146190911yescharacteristic
690C2#2146191011yescharacteristic
subgroupG/H
centerC23D4×#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#340C4
socleC23×C61C4×D4
prime radicalC23×D61C2×D4
cosocleC22×C4×D61C23
hypercenter#340#6923
hypocenterC61#11315
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
23. #16839525C4semidirect
24. #16839524C4semidirect
25. #16839524C4semidirect
26. C61×#340C4semidirect
370. #340#6923semidirect
372. C61#11315semidirect

Maximal subgroups

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

subgroupindex
C2×#168406362
C2×#168406352
C2×(C2×#6923)⋊C82
#214609962
#340×D612
#1131561