Finite Group Databasebeta

← #30616503

Subgroups — #30616503

Order 15616.

1114 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840765C211yesmaximal, characteristic
2C2×C4×#11758217C211yesmaximal, characteristic
3#21462013C214yesmaximal, complemented
4#21462012C212yesmaximal, complemented
5#21462011C212yesmaximal, complemented
6#21461525C214yesmaximal
7C2×#16840314C211yesmaximal, characteristic
8C22×#11758217C2212yes—
9C22×#11758217C2212yes—
10#16840765—21no—
11#16840765—21no—
12#16840765C2212yes—
13#16840765C2212yes—
14C2×#14519844—21no—
15C2×C4⋊#92420—21no—
16C4×#11758217—21no—
17C4×#11758217—21no—
18C4×#11758217C2212yes—
19C4×#11758217C2212yes—
20C2×#14519832—21no—
21C2×C4×#92420—21no—
22#16840642C2218yes—
23#16840642C2218yes—
24#16840314—21no—
25#16840314—21no—
26#16840314—21no—
27#16840314—21no—
28#16840314—21no—
29#16840314—21no—
30#16840314—21no—
31#16840314—21no—
32C2×#14519776C2211yescharacteristic
33C2×#14519775C2211yescharacteristic
34C2×#14519767C2212yes—
35C2×#14519756C411yescharacteristic
36C2×#14519754C412yes—
37C2×Q8×Dic61C411yescharacteristic
38C2×#14519742C412yes—
39C2×#14519742C411yescharacteristic
40C2×#14519733C2212yes—
41C22×C4×Dic61C2211yescharacteristic
42C2×C22⋊Q8×C61C411yescharacteristic
43C2×#11758217—22no—
44C2×#11758217—24no—
45C2×#11758217—22no—
46C2×#11758217—28no—
47C2×#11758217Q818yescomplemented
48C2×#11758217C2314yes—
49C2×#11758217C2314yes—
50C22×#92420—22no—
51C22×#92420—22no—
52#14519844—22no—
53#14519844—22no—
54C4⋊#92420—22no—
55C4⋊#92420—22no—
56#14519832—22no—
57#14519832—22no—
58C4×#92420—22no—
59C4×#92420—22no—
60C22×Dic122C2×C412yes—
61C22×Dic122C2×C411yescharacteristic
62C23×Dic61C2×C411yescharacteristic
63C23×Dic61C2311yescharacteristic
64#14519776—21no—
65#14519776—21no—
66#14519776—21no—
67#14519776—21no—
68#14519775—21no—
69#14519775—21no—
70#14519775—21no—
71#14519775—21no—
72#14519767—22no—
73#14519767—22no—
74#14519767—22no—
75#14519767—22no—
76#14519756—21no—
77#14519756—21no—
78#14519756—21no—
79#14519756—21no—
80#14519754—22no—
81#14519754—22no—
82#14519754—22no—
83#14519754—22no—
84Q8×Dic61—21no—
85Q8×Dic61—21no—
86Q8×Dic61—21no—
87Q8×Dic61—21no—
88#14519742—21no—
89#14519742—21no—
90#14519742—21no—
91#14519742—21no—
92#14519742—22no—
93#14519742—22no—
94#14519742—22no—
95#14519742—22no—
96#14519733—22no—
97#14519733—22no—
98#14519733—22no—
99#14519733—22no—
100C2×C4⋊Dic61C2×C412yes—
101C2×C4⋊Dic61C2×C411yescharacteristic
102C2×#11758196C2×C412yes—
103C2×#11758196C2×C412yes—
104C2×#11758196C2×C412yes—
105C2×#11758196C2312yes—
106C2×#11758196C2312yes—
107C2×C22⋊Dic61C2×C412yes—
108C2×C4×Dic61C2×C412yes—
109C2×C4×Dic61C2×C412yes—
110C2×C4×Dic61C2×C411yescharacteristic
111C2×C4×Dic61C2×C411yescharacteristic
112C2×C4×Dic61D411yescharacteristic
113C2×C4×Dic61D411yescharacteristic
114C2×C4×Dic61D411yescharacteristic
115C2×C4×Dic61D411yescharacteristic
116C2×C4×Dic61D411yescharacteristic
117C2×C4×Dic61D411yescharacteristic
118C2×C4×Dic61D411yescharacteristic
119C2×C4×Dic61D411yescharacteristic
120C2×C4×Dic61C2311yescharacteristic
121C2×C4×Dic61C2311yescharacteristic
122C22×Q8×C61C2×C411yescharacteristic
123C23×C4×C61C2×C411yescharacteristic
124C22⋊Q8×C61—21no—
125C22⋊Q8×C61—21no—
126C22⋊Q8×C61—21no—
127C22⋊Q8×C61—21no—
128C2×C4⋊C4×C61C2×C412yes—
129C2×C4⋊C4×C61C2×C411yescharacteristic
130C2×C22⋊C4×C61C2×C412yes—
131C24×C61C22×C411yescharacteristic
132C2×Q8×C61—21no—
133C2×Q8×C61—21no—
134C2×Q8×C61—42no—
135C22×C4×C61—42no—
136C22×C4×C61C22⋊C411yescharacteristic
137C22×C4×C61C22⋊C411yescharacteristic
138C22×C4×C61C22⋊C411yescharacteristic
139C22×C4×C61C22⋊C411yescharacteristic
140C22×C4×C61C22×C411yescharacteristic
141C22×C4×C61C22×C412yes—
142C22×C4×C61C22×C412yes—
143C22×C4×C61C22×C411yescharacteristic
144C22×Dic61—42no—
145C22×Dic61C22⋊C411yescharacteristic
146C22×Dic61C22⋊C411yescharacteristic
147C22×Dic61C22⋊C411yescharacteristic
148C22×Dic61C22⋊C411yescharacteristic
149C22×Dic61C22×C411yescharacteristic
150C22×Dic61C22×C412yes—
151C22×Dic61C22×C412yes—
152C22×Dic61C22×C411yescharacteristic
153C22×Dic61C22×C411yescharacteristic
154C22×Dic61C2×D411yescharacteristic
155C22×Dic61C2×D411yescharacteristic
156C22×Dic61C2×D411yescharacteristic
157C22×Dic61C2×D411yescharacteristic
158C22×Dic61C2×Q814yes—
159C22×Dic61#4114yes—
160C22×Dic61C2411yescharacteristic
161C2×Dic122—21no—
162C2×Dic122—21no—
163C2×Dic122—22no—
164C2×Dic122—22no—
165C2×Dic122—44no—
166C2×Dic122—42no—
167#11758217—28no—
168#11758217—24no—
169#11758217—28no—
170#11758217—44no—
171#11758217C2×Q818yes—
172C2×#92420—28no—
173C2×#92420—24no—
174C2×#92420—24no—
175C2×#92420—44no—
176C4⋊C4×C61—22no—
177C4⋊C4×C61—22no—
178C4⋊C4×C61—21no—
179C4⋊C4×C61—21no—
180C22⋊C4×C61—22no—
181C22⋊C4×C61—22no—
182C22⋊Dic61—22no—
183C22⋊Dic61—22no—
184C4⋊Dic61—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61—22no—
187C4⋊Dic61—22no—
188#11758196—22no—
189#11758196—22no—
190#11758196—22no—
191#11758196—22no—
192#11758196—22no—
193#11758196—22no—
194#11758196—22no—
195#11758196—22no—
196#11758196—22no—
197#11758196—22no—
198C4×Dic61—22no—
199C4×Dic61—22no—
200C4×Dic61—22no—
201C4×Dic61—22no—
202C4×Dic61C22⋊C411yescharacteristic
203C4×Dic61C22⋊C411yescharacteristic
204C4×Dic61C22⋊C411yescharacteristic
205C4×Dic61C22⋊C411yescharacteristic
206C4×Dic61C22⋊C411yescharacteristic
207C4×Dic61C22⋊C411yescharacteristic
208C4×Dic61C22⋊C411yescharacteristic
209C4×Dic61C22⋊C411yescharacteristic
210C4×Dic61C2×D411yescharacteristic
211C4×Dic61C2×D411yescharacteristic
212C4×Dic61C2×D411yescharacteristic
213C4×Dic61C2×D411yescharacteristic
214C4×Dic61C2×D411yescharacteristic
215C4×Dic61C2×D411yescharacteristic
216C4×Dic61C2×D411yescharacteristic
217C4×Dic61C2×D411yescharacteristic
218C23×C61—41no—
219C23×C61—41no—
220C23×C61C2×C22⋊C411yescharacteristic
221C23×C61C2×C22⋊C411yescharacteristic
222C23×C61C4×Q814yes—
223C23×C61C23×C411yescharacteristic
224Q8×C61—42no—
225Q8×C61—42no—
226C2×C4×C61—22no—
227C2×C4×C61—22no—
228C2×C4×C61—22no—
229C2×C4×C61—22no—
230C2×C4×C61—22no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—42no—
235C2×C4×C61—42no—
236C2×C4×C61C2×C22⋊C411yescharacteristic
237C2×C4×C61C2×C22⋊C411yescharacteristic
238C2×C4×C61C2×C22⋊C411yescharacteristic
239C2×C4×C61C2×C22⋊C411yescharacteristic
240C2×Dic61—22no—
241C2×Dic61—22no—
242C2×Dic61—22no—
243C2×Dic61—22no—
244C2×Dic61—22no—
245C2×Dic61—41no—
246C2×Dic61—41no—
247C2×Dic61—41no—
248C2×Dic61—42no—
249C2×Dic61—42no—
250C2×Dic61C2×C22⋊C411yescharacteristic
251C2×Dic61C2×C22⋊C411yescharacteristic
252C2×Dic61C2×C22⋊C411yescharacteristic
253C2×Dic61C2×C22⋊C411yescharacteristic
254C2×Dic61C2×C22⋊C411yescharacteristic
255C2×Dic61C2×C22⋊C411yescharacteristic
256C2×Dic61C4×Q814yes—
257C2×Dic61C22⋊Q814yes—
258C2×Dic61C22⋊Q814yes—
259C2×Dic61#12412yes—
260C2×Dic61#12412yes—
261C2×Dic61C4⋊Q812yes—
262C2×Dic61C4⋊Q812yes—
263C2×Dic61C22×D411yescharacteristic
264C2×Dic61C22×D411yescharacteristic
265C2×Dic61C22×Q812yes—
266C2×Dic61C2×#4112yes—
267Dic122—44no—
268Dic122—42no—
269Dic122—42no—
270Dic122—44no—
271#92420—28no—
272#92420—44no—
273#21337—611nomaximal, Sylow
274C22×C61—21no—
275C22×C61—21no—
276C22×C61—21no—
277C22×C61—21no—
278C22×C61—21no—
279C22×C61—21no—
280C22×C61—44no—
281C22×C61#39112yes—
282C22×C61#39112yes—
283C22×C61C22×C22⋊C411yescharacteristic
284C22×C61C2×C4×Q812yes—
285C4×C61—21no—
286C4×C61—21no—
287C4×C61—21no—
288C4×C61—42no—
289C4×C61—42no—
290C4×C61#41312yes—
291Dic61—21no—
292Dic61—21no—
293Dic61—21no—
294Dic61—42no—
295Dic61—42no—
296Dic61#39112yes—
297Dic61#39112yes—
298Dic61#41312yes—
299Dic61C2×C22⋊Q812yes—
300Dic61C2×#12411yescharacteristic
301Dic61C2×C4⋊Q811yescharacteristic
302C2×#533—611no—
303C2×#423—611no—
304C2×C4×M16—611no—
305#1998—614no—
306#1997—612no—
307#1997—612no—
308#1742—614no—
309C2×C61—22no—
310C2×C61—22no—
311C2×C61—22no—
312C2×C61C2×#39111yescharacteristic
313C2×C61C2×#41311yescharacteristic
314C2×C61C2×#41311yescharacteristic
315C22×M16—612no—
316C22×M16—612no—
317#533—1221no—
318#533—1221no—
319#533—1221no—
320#533—1221no—
321#533—1221no—
322#533—1221no—
323#533—1221no—
324#533—1221no—
325C2×C4⋊Q8—611no—
326C2×C4⋊Q8—611no—
327C2×#125—612no—
328C2×C22⋊Q8—611no—
329C2×C22⋊Q8—612no—
330C2×C22⋊Q8#692311yescharacteristic
331C2×C4×Q8—611no—
332C2×C4×Q8—611no—
333C2×C4×Q8—612no—
334C2×#117—612no—
335C22×C42—611no—
336#423—612no—
337#423—612no—
338#423—1221no—
339#423—1221no—
340C2×C4⋊C8—1221no—
341C2×C4⋊C8—1221no—
342C4×M16—612no—
343C4×M16—612no—
344C4×M16—1221no—
345C4×M16—1221no—
346C2×#97—1221no—
347C2×C4×C8—1221no—
348#343—618no—
349#343—618no—
350C61#2133711yescharacteristic, complemented, Sylow
351C22×Q8—612no—
352C22×Q8—611no—
353C22×Q8C2×#692311yescharacteristic
354C23×C4—611no—
355C23×C4—611no—
356C23×C4C2×#692311yescharacteristic
357C2×M16—618no—
358C2×M16—614no—
359C2×M16—614no—
360C2×M16—1224no—
361C2×M16—1222no—
362C2×M16—1222no—
363C2×M16—1228no—
364C22×C8—1222no—
365C22×C8—1222no—
366C4⋊Q8—1221no—
367C4⋊Q8—1221no—
368C4⋊Q8—1221no—
369C4⋊Q8—1221no—
370C4⋊Q8—1221no—
371C4⋊Q8—1221no—
372C4⋊Q8—1221no—
373C4⋊Q8—1221no—
374#125—1222no—
375#125—1222no—
376#125—1222no—
377#125—1222no—
378C22⋊Q8—21no—
379C22⋊Q8—21no—
380C22⋊Q8—21no—
381C22⋊Q8—21no—
382C22⋊Q8—1222no—
383C22⋊Q8—1222no—
384C22⋊Q8—1222no—
385C22⋊Q8—1222no—
386C22⋊Q8—1221no—
387C22⋊Q8—1221no—
388C22⋊Q8—1221no—
389C22⋊Q8—1221no—
390C4×Q8—1222no—
391C4×Q8—1222no—
392C4×Q8—1222no—
393C4×Q8—1222no—
394C4×Q8—1221no—
395C4×Q8—1221no—
396C4×Q8—1221no—
397C4×Q8—1221no—
398C4×Q8—1221no—
399C4×Q8—1221no—
400C4×Q8—1221no—
401C4×Q8—1221no—
402#117—1222no—
403#117—1222no—
404#117—1222no—
405#117—1222no—
406C2×C4⋊C4—612no—
407C2×C4⋊C4—612no—
408C2×C4⋊C4—612no—
409C2×C4⋊C4—612no—
410C2×C4⋊C4—612no—
411C2×C4⋊C4—612no—
412C2×C4⋊C4—611no—
413C2×C4⋊C4C2×#692312yes—
414C2×C4⋊C4C2×#692311yescharacteristic
415C2×C22⋊C4—612no—
416C2×C22⋊C4C2×#692312yes—
417C2×C42—611no—
418C2×C42—611no—
419C2×C42—611no—
420C2×C42—611no—
421C2×C42—611no—
422C2×C42—611no—
423C2×C42—611no—
424C2×C42—611no—
425C2×C42—611no—
426C2×C42—611no—
427C2×C42—611no—
428C2×C42—611no—
429C2×C42—612no—
430C2×C42—612no—
431C4⋊C8—1222no—
432C4⋊C8—1222no—
433C4⋊C8—1222no—
434C4⋊C8—1222no—
435#97—1222no—
436#97—1222no—
437C4×C8—1222no—
438C4×C8—1222no—
439C24C22×#692311yescharacteristic
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—42no—
443C2×Q8—1222no—
444C2×Q8—1222no—
445C2×Q8—1221no—
446C2×Q8—1221no—
447C2×Q8—2442no—
448C2×Q8—2444no—
449C22×C4—42no—
450C22×C4—611no—
451C22×C4—611no—
452C22×C4—611no—
453C22×C4—611no—
454C22×C4—614no—
455C22×C4—614no—
456C22×C4—611no—
457C22×C4—611no—
458C22×C4—611no—
459C22×C4—611no—
460C22×C4—611no—
461C22×C4—611no—
462C22×C4—611no—
463C22×C4—611no—
464C22×C4—612no—
465C22×C4—612no—
466C22×C4—2442no—
467C22×C4C22⋊#692311yescharacteristic
468C22×C4C22⋊#692311yescharacteristic
469C22×C4C22⋊#692311yescharacteristic
470C22×C4C22⋊#692311yescharacteristic
471C22×C4C22×#692311yescharacteristic
472C22×C4C22×#692312yes—
473C22×C4C22×#692312yes—
474C22×C4C22×#692311yescharacteristic
475M16—618no—
476M16—1228no—
477M16—1224no—
478M16—1228no—
479M16—2444no—
480C2×C8—1224no—
481C2×C8—1228no—
482C2×C8—1224no—
483C2×C8—2444no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—1222no—
489C4⋊C4—1222no—
490C4⋊C4—1222no—
491C4⋊C4—1222no—
492C4⋊C4—1222no—
493C4⋊C4—1222no—
494C4⋊C4—1222no—
495C4⋊C4—1222no—
496C4⋊C4—1222no—
497C4⋊C4—1222no—
498C4⋊C4—1222no—
499C4⋊C4—1222no—
500C4⋊C4—1221no—
501C4⋊C4—1221no—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C22⋊C4—1222no—
505C22⋊C4—1222no—
506C42—611no—
507C42—611no—
508C42—611no—
509C42—611no—
510C42—611no—
511C42—611no—
512C42—611no—
513C42—611no—
514C42—611no—
515C42—611no—
516C42—611no—
517C42—611no—
518C42—611no—
519C42—611no—
520C42—611no—
521C42—611no—
522C42—1222no—
523C42—1222no—
524C42—1222no—
525C42—1222no—
526C23—41no—
527C23—41no—
528C23C2×C22⋊#692311yescharacteristic
529C23C2×C22⋊#692311yescharacteristic
530C23Q8×#692314yes—
531C23C23×#692311yescharacteristic
532Q8—42no—
533Q8—42no—
534Q8—2442no—
535Q8—2444no—
536Q8—2444no—
537Q8—2442no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—614no—
549C2×C4—614no—
550C2×C4—612no—
551C2×C4—612no—
552C2×C4—612no—
553C2×C4—612no—
554C2×C4—611no—
555C2×C4—611no—
556C2×C4—611no—
557C2×C4—611no—
558C2×C4—611no—
559C2×C4—614no—
560C2×C4—612no—
561C2×C4—612no—
562C2×C4—611no—
563C2×C4—611no—
564C2×C4—611no—
565C2×C4—1222no—
566C2×C4—1222no—
567C2×C4—1222no—
568C2×C4—1222no—
569C2×C4—1222no—
570C2×C4—2441no—
571C2×C4—2441no—
572C2×C4—2441no—
573C2×C4—2442no—
574C2×C4—2442no—
575C2×C4C2×C22⋊#692311yescharacteristic
576C2×C4C2×C22⋊#692311yescharacteristic
577C2×C4C2×C22⋊#692311yescharacteristic
578C2×C4C2×C22⋊#692311yescharacteristic
579C8—1228no—
580C8—2444no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—21no—
585C22—21no—
586C22—21no—
587C22—44no—
588C22(C2×#6923)⋊Q812yes—
589C22(C2×#6923)⋊Q812yes—
590C22C22×C22⋊#692311yescharacteristic
591C22C2×Q8×#692312yes—
592C4—21no—
593C4—21no—
594C4—21no—
595C4—42no—
596C4—42no—
597C4—612no—
598C4—611no—
599C4—611no—
600C4—612no—
601C4—612no—
602C4—612no—
603C4—1221no—
604C4—1221no—
605C4—1221no—
606C4—2442no—
607C4—2442no—
608C4#1684074912yes—
609C2—22no—
610C2—22no—
611C2—22no—
612C2C2×(C2×#6923)⋊Q811yescharacteristic
613C2D61⋊#41311yescharacteristic
614C2C2×#1684074911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×C22⋊Q8×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC24×C61C22×C4
cosocleC22×Dic61C24
hypercenterC2×C22⋊Q8#6923
hypocenterC61#21337
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #21462013C2semidirect
4. #21462012C2semidirect
5. #21462011C2semidirect
47. C2×#11758217Q8semidirect
350. C61#21337semidirect

Maximal subgroups

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

subgroupindex
C2×#168407652
C2×C4×#117582172
#214620132
#214620122
#214620112
#214615252
C2×#168403142
#2133761