Finite Group Databasebeta

← #29646027

Subgroups — #29646027

Order 15616.

988 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840316C211yesmaximal, characteristic
2#21454447C211yesmaximal, characteristic
3#431×D61C211yesmaximal, characteristic
4#21444181C214yesmaximal
5#21444173C214yesmaximal, complemented
6#21444143C211yesmaximal, characteristic, complemented
7#21444142C211yesmaximal, characteristic, complemented
8#21444142C211yesmaximal, characteristic, complemented
9C61×#1461C211yesmaximal, characteristic, complemented
10#16840316—21no—
11#16840316—21no—
12#16840316—21no—
13#16840316—21no—
14#16840316—21no—
15#16840316—21no—
16#16840316—21no—
17#16840316—21no—
18C2×#14519776C411yescharacteristic
19C2×#14519775C411yescharacteristic
20C2×#14519767C2212yes—
21C2×#14519757C411yescharacteristic
22C2×#14519755C2212yes—
23C2×#14519753C411yescharacteristic
24C2×C4×Dic122C412yes—
25C2×C4×Dic122C2211yescharacteristic
26C2×#14519734C412yes—
27C2×C42×D61C2211yescharacteristic
28#16839818—21no—
29#16839816C2212yes—
30#16839815C2211yescharacteristic
31#16839815C2211yescharacteristic
32#16839814—21no—
33#16839813—21no—
34#16839813—21no—
35#16839812C2212yes—
36#16839784—21no—
37C4⋊C8×D61—21no—
38#16839724C2212yes—
39C22⋊C8×D61C2212yes—
40C4×#11758189—21no—
41C4×C8×D61—21no—
42#16839488C2214yes—
43#16839487C2214yes—
44#16839487C2214yes—
45C2×C4×Q8×C61C2211yescharacteristic
46C61×#431C2211yescharacteristic
47C61×#431C2211yescharacteristic
48C61×#324C2214yes—
49C22×Dic122C2×C411yescharacteristic
50C22×Dic122C2×C412yes—
51C22×C4×D61C2×C411yescharacteristic
52C22×C4×D61C2×C411yescharacteristic
53C22×C4×D61C2311yescharacteristic
54C2×#11758189—22no—
55C2×C8×D61—22no—
56#14519776—21no—
57#14519776—21no—
58#14519776—21no—
59#14519776—21no—
60#14519775—21no—
61#14519775—21no—
62#14519775—21no—
63#14519775—21no—
64#14519767—22no—
65#14519767—22no—
66#14519767—22no—
67#14519767—22no—
68#14519757—21no—
69#14519757—21no—
70#14519757—21no—
71#14519757—21no—
72#14519755—22no—
73#14519755—22no—
74#14519755—22no—
75#14519755—22no—
76#14519753—21no—
77#14519753—21no—
78#14519753—21no—
79#14519753—21no—
80C4×Dic122—21no—
81C4×Dic122—21no—
82C4×Dic122—21no—
83C4×Dic122—21no—
84C4×Dic122—22no—
85C4×Dic122—22no—
86C4×Dic122—22no—
87C4×Dic122—22no—
88#14519734—22no—
89#14519734—22no—
90#14519734—22no—
91#14519734—22no—
92C2×C4⋊Dic61C2×C412yes—
93C2×C4⋊Dic61C2×C411yescharacteristic
94C2×#11758196C2×C412yes—
95C2×#11758196C2×C412yes—
96C2×#11758196C2×C412yes—
97C2×#11758196C2×C412yes—
98C2×#11758196C2312yes—
99C2×#11758198C2×C412yes—
100C2×#11758198C2×C412yes—
101C2×C4×Dic61C2×C412yes—
102C2×C4×Dic61C2×C411yescharacteristic
103C2×C4×Dic61C2×C411yescharacteristic
104C2×C4×Dic61C2311yescharacteristic
105C42×D61D411yescharacteristic
106C42×D61D411yescharacteristic
107C42×D61D411yescharacteristic
108C42×D61D411yescharacteristic
109C42×D61D411yescharacteristic
110C42×D61D411yescharacteristic
111C42×D61D411yescharacteristic
112C42×D61D411yescharacteristic
113C4⋊#92418—21no—
114C4⋊#92418—21no—
115#14519706—22no—
116#14519706—22no—
117C22⋊#92418C2312yes—
118C22⋊#92418C2312yes—
119#14519689—22no—
120#14519689—22no—
121#14519687—22no—
122C4×#92418—21no—
123C4×#92418—21no—
124C8×Dic61—22no—
125C22×Q8×C61C2×C411yescharacteristic
126C4×Q8×C61—21no—
127C4×Q8×C61—21no—
128C4×Q8×C61—21no—
129C4×Q8×C61—21no—
130C2×C4⋊C4×C61C2×C411yescharacteristic
131C2×C4⋊C4×C61C2312yes—
132C2×C42×C61C2×C412yes—
133C2×C42×C61C2311yescharacteristic
134C4⋊C8×C61—21no—
135C4⋊C8×C61—21no—
136C22⋊C8×C61C2312yes—
137C22⋊C8×C61C2312yes—
138C4×C8×C61—21no—
139C4×C8×C61—21no—
140C23×D61C22×C411yescharacteristic
141C2×Q8×C61—21no—
142C2×Q8×C61—21no—
143C2×Q8×C61—22no—
144C2×Q8×C61—22no—
145C22×C4×C61C22×C412yes—
146C22×C4×C61C22×C411yescharacteristic
147C22×C4×C61C22×C412yes—
148C22×C4×C61C22×C411yescharacteristic
149C22×C4×C61C2411yescharacteristic
150C22×Dic61C22×C412yes—
151C22×Dic61C22×C411yescharacteristic
152C22×Dic61C22×C411yescharacteristic
153C22×Dic61C22×C411yescharacteristic
154C22×Dic61C22×C412yes—
155C2×C4×D61—22no—
156C2×C4×D61—22no—
157C2×C4×D61—24no—
158C2×C4×D61—42no—
159C2×C4×D61C22⋊C411yescharacteristic
160C2×C4×D61C22⋊C411yescharacteristic
161C2×C4×D61C22⋊C411yescharacteristic
162C2×C4×D61C22⋊C411yescharacteristic
163C2×C4×D61C22⋊C411yescharacteristic
164C2×C4×D61C22⋊C411yescharacteristic
165C2×C4×D61C22⋊C411yescharacteristic
166C2×C4×D61C22⋊C411yescharacteristic
167C2×C4×D61C2×D411yescharacteristic
168C2×C4×D61C2×D411yescharacteristic
169C2×C4×D61C2×D411yescharacteristic
170C2×C4×D61C2×D411yescharacteristic
171C2×Dic122—21no—
172C2×Dic122—21no—
173C2×Dic122—22no—
174C2×Dic122—22no—
175C2×Dic122—22no—
176C2×Dic122—22no—
177C2×Dic122—44no—
178C2×C8×C61—22no—
179C2×C8×C61—22no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—21no—
182C4⋊C4×C61—22no—
183C4⋊C4×C61—22no—
184C42×C61—22no—
185C42×C61—22no—
186C42×C61C2×D411yescharacteristic
187C42×C61C2×D411yescharacteristic
188C42×C61C2×D411yescharacteristic
189C42×C61C2×D411yescharacteristic
190#11758198—22no—
191#11758198—22no—
192#11758198—22no—
193#11758198—22no—
194C4⋊Dic61—21no—
195C4⋊Dic61—21no—
196C4⋊Dic61—22no—
197C4⋊Dic61—22no—
198#11758196—22no—
199#11758196—22no—
200#11758196—22no—
201#11758196—22no—
202#11758196—22no—
203#11758196—22no—
204#11758196—22no—
205#11758196—22no—
206#11758196—22no—
207#11758196—22no—
208C4×Dic61—22no—
209C4×Dic61—22no—
210C4×Dic61C22⋊C411yescharacteristic
211C4×Dic61C22⋊C411yescharacteristic
212C4×Dic61C22⋊C411yescharacteristic
213C4×Dic61C22⋊C411yescharacteristic
214C4×Dic61C22⋊C411yescharacteristic
215C4×Dic61C22⋊C411yescharacteristic
216C4×Dic61C22⋊C411yescharacteristic
217C4×Dic61C22⋊C411yescharacteristic
218C4×Dic61C2×D411yescharacteristic
219C4×Dic61C2×D411yescharacteristic
220C4×Dic61C2×D411yescharacteristic
221C4×Dic61C2×D411yescharacteristic
222C2×#92418—22no—
223C2×#92418—22no—
224#11758189—44no—
225C8×D61—44no—
226C23×C61C23×C411yescharacteristic
227C22×D61—21no—
228C22×D61—21no—
229C22×D61—22no—
230C22×D61—41no—
231C22×D61C2×C22⋊C411yescharacteristic
232C22×D61C2×C22⋊C411yescharacteristic
233Q8×C61—42no—
234Q8×C61—42no—
235C2×C4×C61—22no—
236C2×C4×C61—22no—
237C2×C4×C61—22no—
238C2×C4×C61—22no—
239C2×C4×C61—22no—
240C2×C4×C61—41no—
241C2×C4×C61—42no—
242C2×C4×C61C2×C22⋊C411yescharacteristic
243C2×C4×C61C2×C22⋊C411yescharacteristic
244C2×C4×C61C2×C22⋊C411yescharacteristic
245C2×C4×C61C2×C22⋊C411yescharacteristic
246C2×C4×C61#13112yes—
247C2×C4×C61#13112yes—
248C2×C4×C61C22×D411yescharacteristic
249C2×C4×C61C22×D411yescharacteristic
250C2×Dic61—21no—
251C2×Dic61—21no—
252C2×Dic61—22no—
253C2×Dic61—22no—
254C2×Dic61—22no—
255C2×Dic61—22no—
256C2×Dic61—22no—
257C2×Dic61—22no—
258C2×Dic61—42no—
259C2×Dic61C2×C22⋊C411yescharacteristic
260C2×Dic61C2×C22⋊C411yescharacteristic
261C2×Dic61C2×C22⋊C411yescharacteristic
262C2×Dic61C2×C22⋊C411yescharacteristic
263C2×Dic61C2×C22⋊C411yescharacteristic
264C2×Dic61C2×C22⋊C411yescharacteristic
265C4×D61—22no—
266C4×D61—22no—
267C4×D61—22no—
268C4×D61—22no—
269C4×D61—22no—
270C4×D61—22no—
271C4×D61—22no—
272C4×D61—22no—
273C4×D61—22no—
274C4×D61—41no—
275C4×D61—41no—
276C4×D61#10114yes—
277Dic122—44no—
278Dic122—42no—
279Dic122—42no—
280Dic122—44no—
281C8×C61—42no—
282C8×C61—42no—
283#92418—42no—
284#92418—42no—
285#17385—611nomaximal, Sylow
286C22×C61—21no—
287C22×C61—21no—
288C22×C61C22×C22⋊C411yescharacteristic
289C22×C61C2×#13111yescharacteristic
290C22×C61C2×#13111yescharacteristic
291C2×D61—21no—
292C2×D61—21no—
293C2×D61—21no—
294C2×D61—21no—
295C2×D61—21no—
296C2×D61—42no—
297C2×D61—42no—
298C2×D61C2×#10112yes—
299C4×C61—21no—
300C4×C61—21no—
301C4×C61—21no—
302C4×C61—42no—
303C4×C61—42no—
304C4×C61#40812yes—
305C4×C61#40812yes—
306C4×C61C2×#10112yes—
307Dic61—21no—
308Dic61—21no—
309Dic61—21no—
310Dic61—21no—
311Dic61—42no—
312Dic61—42no—
313Dic61#41012yes—
314Dic61C2×#10112yes—
315C2×#533—611no—
316#2920—611no—
317C2×#431—611no—
318#1472—614no—
319#1470—614no—
320#1461—611no—
321#1461—611no—
322#1461—611no—
323#1461D6111yescharacteristic, complemented
324C2×C61—21no—
325C2×C61—21no—
326C2×C61C2×#40811yescharacteristic
327C2×C61C2×#41011yescharacteristic
328C2×C61C22×#10111yescharacteristic
329D61—22no—
330D61—41no—
331#533—1221no—
332#533—1221no—
333#533—1221no—
334#533—1221no—
335#533—1221no—
336#533—1221no—
337#533—1221no—
338#533—1221no—
339C2×C4⋊Q8—611no—
340C2×C4⋊Q8—611no—
341C2×#125—612no—
342C2×C22⋊Q8—611no—
343C2×C22⋊Q8—611no—
344C2×C22⋊Q8—612no—
345C2×C4×Q8—612no—
346C2×C4×Q8—611no—
347C2×C4×Q8C2×D6111yescharacteristic
348C2×#117—612no—
349C22×C42—611no—
350#432—612no—
351#432—1221no—
352#431—611no—
353#431—611no—
354#431—612no—
355#431—1221no—
356#431—1221no—
357#431—1221no—
358#431C2×D6111yescharacteristic
359#431C2×D6111yescharacteristic
360#423—1221no—
361C2×C4⋊C8—1221no—
362#407—612no—
363C2×C22⋊C8—612no—
364C4×M16—1221no—
365C2×C4×C8—1221no—
366#324—614no—
367#324—614no—
368#324—614no—
369#324C2×D6114yes—
370C61#1738511yescharacteristic, complemented, Sylow
371C22×Q8—611no—
372C22×Q8—612no—
373C22×Q8C4×D6111yescharacteristic
374C23×C4—611no—
375C23×C4—611no—
376C23×C4—611no—
377C2×M16—1222no—
378C22×C8—1222no—
379C4⋊Q8—1221no—
380C4⋊Q8—1221no—
381C4⋊Q8—1221no—
382C4⋊Q8—1221no—
383C4⋊Q8—1221no—
384C4⋊Q8—1221no—
385C4⋊Q8—1221no—
386C4⋊Q8—1221no—
387#125—1222no—
388#125—1222no—
389#125—1222no—
390#125—1222no—
391C22⋊Q8—1222no—
392C22⋊Q8—1222no—
393C22⋊Q8—1222no—
394C22⋊Q8—1222no—
395C22⋊Q8—1221no—
396C22⋊Q8—1221no—
397C22⋊Q8—1221no—
398C22⋊Q8—1221no—
399C22⋊Q8—1221no—
400C22⋊Q8—1221no—
401C22⋊Q8—1221no—
402C22⋊Q8—1221no—
403C4×Q8—21no—
404C4×Q8—21no—
405C4×Q8—21no—
406C4×Q8—21no—
407C4×Q8—1222no—
408C4×Q8—1222no—
409C4×Q8—1222no—
410C4×Q8—1222no—
411C4×Q8—1221no—
412C4×Q8—1221no—
413C4×Q8—1221no—
414C4×Q8—1221no—
415#117—1222no—
416#117—1222no—
417#117—1222no—
418#117—1222no—
419C2×C4⋊C4—612no—
420C2×C4⋊C4—612no—
421C2×C4⋊C4—612no—
422C2×C4⋊C4—612no—
423C2×C4⋊C4—612no—
424C2×C4⋊C4—611no—
425C2×C4⋊C4—612no—
426C2×C4⋊C4C4×D6111yescharacteristic
427C2×C4⋊C4C22×D6112yes—
428C2×C22⋊C4—612no—
429C2×C22⋊C4—612no—
430C2×C42—611no—
431C2×C42—611no—
432C2×C42—611no—
433C2×C42—611no—
434C2×C42—611no—
435C2×C42—611no—
436C2×C42—611no—
437C2×C42—611no—
438C2×C42—611no—
439C2×C42—611no—
440C2×C42—611no—
441C2×C42—612no—
442C2×C42C4×D6112yes—
443C2×C42C22×D6111yescharacteristic
444C4⋊C8—21no—
445C4⋊C8—21no—
446C4⋊C8—1222no—
447C4⋊C8—1222no—
448C4⋊C8—1221no—
449C4⋊C8—1221no—
450C22⋊C8—612no—
451C22⋊C8—612no—
452C22⋊C8—1222no—
453C22⋊C8—1222no—
454C22⋊C8C22×D6112yes—
455C22⋊C8C22×D6112yes—
456#97—1222no—
457C4×C8—21no—
458C4×C8—21no—
459C4×C8—1222no—
460C4×C8—1221no—
461C4×C8—1221no—
462C24—611no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—22no—
466C2×Q8—22no—
467C2×Q8—1222no—
468C2×Q8—1222no—
469C2×Q8—1221no—
470C2×Q8—1221no—
471C2×Q8—1222no—
472C2×Q8—1222no—
473C2×Q8—2444no—
474C22×C4—611no—
475C22×C4—611no—
476C22×C4—611no—
477C22×C4—611no—
478C22×C4—611no—
479C22×C4—611no—
480C22×C4—611no—
481C22×C4—611no—
482C22×C4—611no—
483C22×C4—611no—
484C22×C4—611no—
485C22×C4—611no—
486C22×C4—611no—
487C22×C4—611no—
488C22×C4—611no—
489C22×C4—612no—
490C22×C4—612no—
491C22×C4—1224no—
492C22×C4—1222no—
493C22×C4—1222no—
494C22×C4—2442no—
495C22×C4C2×C4×D6112yes—
496C22×C4C2×C4×D6111yescharacteristic
497C22×C4C2×C4×D6112yes—
498C22×C4C2×C4×D6111yescharacteristic
499C22×C4C23×D6111yescharacteristic
500M16—2444no—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—1222no—
504C2×C8—1222no—
505C2×C8—2444no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—1222no—
511C4⋊C4—1222no—
512C4⋊C4—1222no—
513C4⋊C4—1222no—
514C4⋊C4—1222no—
515C4⋊C4—1222no—
516C4⋊C4—1222no—
517C4⋊C4—1222no—
518C4⋊C4—1222no—
519C4⋊C4—1222no—
520C4⋊C4—1222no—
521C4⋊C4—1222no—
522C4⋊C4—1221no—
523C4⋊C4—1221no—
524C22⋊C4—1222no—
525C22⋊C4—1222no—
526C22⋊C4—1222no—
527C22⋊C4—1222no—
528C42—22no—
529C42—22no—
530C42—611no—
531C42—611no—
532C42—611no—
533C42—611no—
534C42—611no—
535C42—611no—
536C42—611no—
537C42—611no—
538C42—611no—
539C42—611no—
540C42—611no—
541C42—611no—
542C42—1222no—
543C42—1222no—
544C42D4×D6111yescharacteristic
545C42D4×D6111yescharacteristic
546C42D4×D6111yescharacteristic
547C42D4×D6111yescharacteristic
548C23—611no—
549C23—611no—
550C23—1222no—
551C23—1221no—
552C23—1221no—
553C23—2441no—
554C23C22×C4×D6111yescharacteristic
555Q8—42no—
556Q8—42no—
557Q8—2444no—
558Q8—2444no—
559Q8—2442no—
560Q8—2442no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—41no—
567C2×C4—42no—
568C2×C4—611no—
569C2×C4—611no—
570C2×C4—614no—
571C2×C4—611no—
572C2×C4—611no—
573C2×C4—611no—
574C2×C4—611no—
575C2×C4—1222no—
576C2×C4—1222no—
577C2×C4—1222no—
578C2×C4—1222no—
579C2×C4—1222no—
580C2×C4—1222no—
581C2×C4—1221no—
582C2×C4—1221no—
583C2×C4—1222no—
584C2×C4—1222no—
585C2×C4—1222no—
586C2×C4—1222no—
587C2×C4—1222no—
588C2×C4—1222no—
589C2×C4—1222no—
590C2×C4—1222no—
591C2×C4—1222no—
592C2×C4—2441no—
593C2×C4—2441no—
594C2×C4—2442no—
595C2×C4C22⋊C4×D6111yescharacteristic
596C2×C4C22⋊C4×D6111yescharacteristic
597C2×C4C22⋊C4×D6111yescharacteristic
598C2×C4C22⋊C4×D6111yescharacteristic
599C2×C4#1451978312yes—
600C2×C4#1451978512yes—
601C2×C4C2×D4×D6111yescharacteristic
602C2×C4C2×D4×D6111yescharacteristic
603C8—42no—
604C8—42no—
605C8—2442no—
606C8—2442no—
607C22—21no—
608C22—21no—
609C22—612no—
610C22—1221no—
611C22—1221no—
612C22—1221no—
613C22—1221no—
614C22—1221no—
615C22—2442no—
616C22—2442no—
617C22C2×C22⋊C4×D6111yescharacteristic
618C22C2×#1451978311yescharacteristic
619C22C2×#1451978511yescharacteristic
620C4—21no—
621C4—21no—
622C4—21no—
623C4—42no—
624C4—42no—
625C4—612no—
626C4—612no—
627C4—1221no—
628C4—1221no—
629C4—1221no—
630C4—1221no—
631C4—2442no—
632C4—2442no—
633C4#1683972712yes—
634C4#1683972712yes—
635C4#101×D6112yes—
636C2—21no—
637C2—21no—
638C2—1222no—
639C2—2441no—
640C2C2×#1683972711yescharacteristic
641C2#410×D6111yescharacteristic
642C2C2×#101×D6111yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1461C2
socleC22×C61C22×C22⋊C4
prime radicalC23×D61C22×C4
cosocleC22×C4×C61C24
hypercenter#1461D61
hypocenterC61#17385
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1461

Complements

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

NH ≅ G/Ntype
5. #21444173C2semidirect
6. #21444143C2semidirect
7. #21444142C2semidirect
8. #21444142C2semidirect
9. C61×#1461C2semidirect
323. #1461D61semidirect
370. C61#17385semidirect

Maximal subgroups

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

subgroupindex
C2×#168403162
#214544472
#431×D612
#214441812
#214441732
#214441432
#214441422
C61×#14612
#1738561