Finite Group Databasebeta

← #29646250

Subgroups — #29646250

Order 15616.

944 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840447C211yesmaximal, characteristic
2#21454479C212yesmaximal, complemented
3#21444187C212yesmaximal, complemented
4#21444173C212yesmaximal, complemented
5#21444168C212yesmaximal
6#21444161C211yesmaximal, characteristic, complemented
7#21444152C211yesmaximal, characteristic, complemented
8#21444141C211yesmaximal, characteristic, complemented
9#21444132C211yesmaximal, characteristic, complemented
10C2×#16839488C211yesmaximal, characteristic, complemented
11C61×#1463C211yesmaximal, characteristic, complemented
12#16840447—22no—
13#16840447—22no—
14#16840447—22no—
15#16840447—22no—
16C2×#14519772C411yescharacteristic
17C2×#14519772C2211yescharacteristic
18C2×#14519768C411yescharacteristic
19C2×#14519767C411yescharacteristic
20C2×#14519767C2211yescharacteristic
21C2×#14519760C411yescharacteristic
22C2×#14519760C2211yescharacteristic
23C2×#14519757C411yescharacteristic
24C2×#14519756C411yescharacteristic
25C2×#14519742C2211yescharacteristic
26C2×C4×C22⋊D61C411yescharacteristic
27C2×#14519736C411yescharacteristic
28C2×#14519736C2211yescharacteristic
29C2×#14519735C2211yescharacteristic
30#16839820—22no—
31#16839820—22no—
32#16839816C2212yes—
33#16839816C2212yes—
34#16839812C2212yes—
35#16839812C2212yes—
36#16839790—22no—
37C2×C22⋊#92418C2212yes—
38#16839720—22no—
39#16839488C2211yescharacteristic
40#16839488C2211yescharacteristic
41#16839488C2212yes—
42#16839487C2212yes—
43#16839487C2212yes—
44#16839485C2212yes—
45#16839485C2212yes—
46C22×C4⋊C4×C61C2211yescharacteristic
47C61×#407C2212yes—
48C61×#324C2211yescharacteristic
49C61×#324C2211yescharacteristic
50C61×#324C2212yes—
51C22×Dic122C2×C411yescharacteristic
52C22×C22⋊D61C2×C411yescharacteristic
53C22×C4×D61C2×C411yescharacteristic
54C22×#92418—22no—
55#14519772—22no—
56#14519772—22no—
57#14519772—22no—
58#14519772—22no—
59#14519768—22no—
60#14519768—22no—
61#14519767—22no—
62#14519767—22no—
63#14519767—22no—
64#14519767—22no—
65#14519760—22no—
66#14519760—22no—
67#14519760—22no—
68#14519760—22no—
69#14519757—22no—
70#14519757—22no—
71#14519756—22no—
72#14519756—22no—
73#14519742—22no—
74#14519742—22no—
75C4×C22⋊D61—21no—
76C4×C22⋊D61—21no—
77C4×C22⋊D61—21no—
78C4×C22⋊D61—21no—
79#14519736—21no—
80#14519736—21no—
81#14519736—21no—
82#14519736—21no—
83#14519736D412yes—
84#14519736D412yes—
85#14519736D412yes—
86#14519736D412yes—
87#14519735—22no—
88#14519735—22no—
89C2×C4⋊Dic61C2×C411yescharacteristic
90C2×C4⋊Dic61C2×C411yescharacteristic
91C2×C4⋊Dic61C2×C411yescharacteristic
92C2×C4⋊Dic61C2×C411yescharacteristic
93C2×C4⋊Dic61C2×C411yescharacteristic
94C2×#11758196C2×C411yescharacteristic
95C2×#11758196C2×C411yescharacteristic
96C2×#11758196C2×C411yescharacteristic
97C2×#11758196C2×C411yescharacteristic
98C2×#11758196C2×C411yescharacteristic
99C2×#11758196C2×C411yescharacteristic
100C2×#11758196C2311yescharacteristic
101C2×C22⋊Dic61C2×C411yescharacteristic
102C2×C22⋊Dic61C2×C411yescharacteristic
103C2×C22⋊Dic61C2×C411yescharacteristic
104C2×#11758198C2×C411yescharacteristic
105C2×#11758198C2×C411yescharacteristic
106C2×#11758198C2×C411yescharacteristic
107C2×#11758198C2×C411yescharacteristic
108C2×#11758198C2311yescharacteristic
109C2×C4×Dic61C2×C411yescharacteristic
110C2×C4×Dic61C2×C411yescharacteristic
111C2×C4×Dic61C2×C411yescharacteristic
112C2×C4×Dic61C2311yescharacteristic
113C2×C4×Dic61C2311yescharacteristic
114#14519706—22no—
115#14519706—22no—
116#14519706—22no—
117#14519706—22no—
118C22⋊#92418—22no—
119C22⋊#92418C2312yes—
120C22⋊#92418C2312yes—
121#14519687—22no—
122#14519687—22no—
123C8×Dic61—22no—
124C8×Dic61—22no—
125C23×C4×C61C2×C411yescharacteristic
126C23×C4×C61C2×C411yescharacteristic
127C23×C4×C61C2311yescharacteristic
128C2×M16×C61—22no—
129C2×C4⋊C4×C61—22no—
130C2×C4⋊C4×C61—22no—
131C2×C4⋊C4×C61C2×C411yescharacteristic
132C2×C4⋊C4×C61C2×C411yescharacteristic
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C4⋊C4×C61C2311yescharacteristic
135C22⋊C8×C61—22no—
136C22⋊C8×C61C2312yes—
137C22⋊C8×C61C2312yes—
138C24×C61C22×C411yescharacteristic
139C23×D61C22×C411yescharacteristic
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61—22no—
145C22×C4×C61—41no—
146C22×C4×C61—42no—
147C22×C4×C61—42no—
148C22×C4×C61C22×C411yescharacteristic
149C22×C4×C61C22×C411yescharacteristic
150C22×C4×C61C22×C411yescharacteristic
151C22×C4×C61C22×C411yescharacteristic
152C22×C4×C61C22×C411yescharacteristic
153C22×C4×C61C2×D412yes—
154C22×C4×C61C2×D412yes—
155C22×C4×C61C2411yescharacteristic
156C2×C22⋊D61—21no—
157C2×C22⋊D61—21no—
158C2×C22⋊D61—42no—
159C22×Dic61C22×C411yescharacteristic
160C22×Dic61C22×C411yescharacteristic
161C22×Dic61C22×C411yescharacteristic
162C22×Dic61C22×C411yescharacteristic
163C22×Dic61C22×C411yescharacteristic
164C22×Dic61C22×C411yescharacteristic
165C22×Dic61C22×C411yescharacteristic
166C2×C4×D61—22no—
167C2×C4×D61—21no—
168C2×C4×D61—21no—
169C2×C4×D61—41no—
170C2×Dic122—22no—
171C2×Dic122—22no—
172C2×Dic122—41no—
173M16×C61—44no—
174C2×C8×C61—22no—
175C2×C8×C61—22no—
176C4⋊C4×C61—22no—
177C4⋊C4×C61—22no—
178C4⋊C4×C61—22no—
179C4⋊C4×C61—22no—
180C22⋊Dic61—21no—
181C22⋊Dic61—21no—
182C22⋊Dic61C22⋊C411yescharacteristic
183C22⋊Dic61C22⋊C411yescharacteristic
184C22⋊Dic61C22⋊C411yescharacteristic
185C22⋊Dic61C22⋊C411yescharacteristic
186C22⋊Dic61C22⋊C412yes—
187C22⋊Dic61C22⋊C412yes—
188#11758198—22no—
189#11758198—22no—
190#11758198—22no—
191#11758198—21no—
192#11758198—21no—
193#11758198—22no—
194C4⋊Dic61—22no—
195C4⋊Dic61—21no—
196C4⋊Dic61—21no—
197C4⋊Dic61—21no—
198C4⋊Dic61—21no—
199C4⋊Dic61C22⋊C412yes—
200C4⋊Dic61C22⋊C412yes—
201C4⋊Dic61C22⋊C412yes—
202C4⋊Dic61C22⋊C412yes—
203#11758196—22no—
204#11758196—22no—
205#11758196—21no—
206#11758196—21no—
207#11758196—22no—
208#11758196—22no—
209#11758196—22no—
210#11758196—22no—
211C4×Dic61—21no—
212C4×Dic61—21no—
213C4×Dic61—21no—
214C4×Dic61—21no—
215C4×Dic61—21no—
216C4×Dic61—21no—
217C4×Dic61C2×D412yes—
218C4×Dic61C2×D412yes—
219C4×Dic61C2×D412yes—
220C4×Dic61C2×D412yes—
221C2×#92418—22no—
222C2×#92418—22no—
223C2×#92418—44no—
224C23×C61—21no—
225C23×C61—21no—
226C23×C61—22no—
227C23×C61—41no—
228C23×C61C2×C22⋊C411yescharacteristic
229C23×C61C2×C22⋊C411yescharacteristic
230C23×C61C23×C411yescharacteristic
231C22×D61—21no—
232C22×D61—21no—
233C22×D61—21no—
234C22×D61—41no—
235C22×D61—41no—
236C2×C4×C61—21no—
237C2×C4×C61—21no—
238C2×C4×C61—24no—
239C2×C4×C61—21no—
240C2×C4×C61—21no—
241C2×C4×C61—21no—
242C2×C4×C61—21no—
243C2×C4×C61—21no—
244C2×C4×C61—41no—
245C2×C4×C61—42no—
246C2×C4×C61—41no—
247C2×C4×C61—42no—
248C2×C4×C61—42no—
249C2×C4×C61—42no—
250C2×C4×C61—42no—
251C2×C4×C61—41no—
252C2×C4×C61—41no—
253C2×C4×C61C2×C22⋊C412yes—
254C2×C4×C61#13112yes—
255C2×C4×C61C22×D412yes—
256C22⋊D61—42no—
257C22⋊D61—42no—
258C2×Dic61—21no—
259C2×Dic61—21no—
260C2×Dic61—21no—
261C2×Dic61—21no—
262C2×Dic61—21no—
263C2×Dic61—21no—
264C2×Dic61—21no—
265C2×Dic61—21no—
266C2×Dic61—21no—
267C2×Dic61—41no—
268C2×Dic61—41no—
269C2×Dic61—41no—
270C2×Dic61—41no—
271C2×Dic61C2×C22⋊C411yescharacteristic
272C2×Dic61C2×C22⋊C411yescharacteristic
273C2×Dic61C2×C22⋊C411yescharacteristic
274C2×Dic61C2×C22⋊C411yescharacteristic
275C2×Dic61C2×C22⋊C412yes—
276C2×Dic61C2×C22⋊C412yes—
277C4×D61—42no—
278C4×D61—42no—
279Dic122—44no—
280C8×C61—42no—
281C8×C61—42no—
282#92418—42no—
283#92418—42no—
284#17417—611nomaximal, Sylow
285C22×C61—21no—
286C22×C61—21no—
287C22×C61—21no—
288C22×C61—21no—
289C22×C61—21no—
290C22×C61—21no—
291C22×C61—21no—
292C22×C61—42no—
293C22×C61—42no—
294C22×C61#41012yes—
295C22×C61C22×C22⋊C411yescharacteristic
296C22×C61C2×#13111yescharacteristic
297C22×C61#56811yescharacteristic
298C2×D61—41no—
299C2×D61—41no—
300C2×D61—41no—
301C2×D61—81no—
302C2×D61—81no—
303C4×C61—22no—
304C4×C61—22no—
305C4×C61—22no—
306C4×C61—41no—
307C4×C61—41no—
308C4×C61—41no—
309Dic61—22no—
310Dic61—21no—
311Dic61—21no—
312Dic61—21no—
313Dic61—21no—
314Dic61—22no—
315Dic61—41no—
316Dic61—41no—
317Dic61—41no—
318C2×#552—611no—
319#2924—612no—
320#1473—612no—
321#1470—612no—
322#1468—612no—
323#1467—611no—
324#1464—611no—
325#1463D6111yescharacteristic, complemented
326#1461—611no—
327#1458—611no—
328C2×#324—611no—
329C2×C61—21no—
330C2×C61—21no—
331C2×C61—22no—
332C2×C61—41no—
333C2×C61#288011yescharacteristic
334C2×C61C2×#41011yescharacteristic
335C2×C61#288911yescharacteristic
336D61—81no—
337#552—1222no—
338#552—1222no—
339#552—1222no—
340#552—1222no—
341C2×#126—611no—
342C2×#126—611no—
343C2×#125—611no—
344C2×#125—611no—
345C2×#125—611no—
346C2×#123—611no—
347C2×#123—611no—
348C2×C22⋊Q8—611no—
349C2×C22⋊Q8—611no—
350C2×C4×Q8—611no—
351C2×C4×D4—611no—
352C2×#117—611no—
353C2×#117—611no—
354C2×#117—611no—
355C22×C4⋊C4C2×D6111yescharacteristic
356#433—1222no—
357#433—1222no—
358#432—612no—
359#432—612no—
360#431—612no—
361#431—612no—
362#424—1222no—
363#407C2×D6112yes—
364C2×C22⋊C8—612no—
365#405—1222no—
366#324—611no—
367#324—611no—
368#324—612no—
369#324—612no—
370#324—612no—
371#324C2×D6111yescharacteristic
372#324C2×D6111yescharacteristic
373#324C2×D6112yes—
374#323—612no—
375#323—612no—
376C61#1741711yescharacteristic, complemented, Sylow
377C22×Q8—611no—
378C22×D4—611no—
379C23×C4—611no—
380C23×C4C4×D6111yescharacteristic
381C23×C4C4×D6111yescharacteristic
382C23×C4C22×D6111yescharacteristic
383C2×M16—22no—
384C22×C8—1222no—
385#126—1222no—
386#126—1222no—
387#126—1222no—
388#126—1222no—
389#125—1222no—
390#125—1222no—
391#125—1222no—
392#125—1222no—
393#125—1222no—
394#125—1222no—
395#123—1222no—
396#123—1222no—
397#123—1222no—
398#123—1222no—
399C22⋊Q8—1222no—
400C22⋊Q8—1222no—
401C22⋊Q8—1222no—
402C22⋊Q8—1222no—
403C4×Q8—1222no—
404C4×Q8—1222no—
405C4×D4—1221no—
406C4×D4—1221no—
407C4×D4—1221no—
408C4×D4—1221no—
409#117—612no—
410#117—612no—
411#117—612no—
412#117—612no—
413#117—1222no—
414#117—1222no—
415#117—1221no—
416#117—1221no—
417#117—1221no—
418#117—1221no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—611no—
422C2×C4⋊C4—611no—
423C2×C4⋊C4—611no—
424C2×C4⋊C4—611no—
425C2×C4⋊C4—611no—
426C2×C4⋊C4—611no—
427C2×C4⋊C4—611no—
428C2×C4⋊C4—611no—
429C2×C4⋊C4—611no—
430C2×C4⋊C4—611no—
431C2×C4⋊C4—611no—
432C2×C4⋊C4—611no—
433C2×C4⋊C4C4×D6111yescharacteristic
434C2×C4⋊C4C4×D6111yescharacteristic
435C2×C4⋊C4C22×D6111yescharacteristic
436C2×C4⋊C4C22×D6111yescharacteristic
437C2×C22⋊C4—611no—
438C2×C22⋊C4—611no—
439C2×C22⋊C4—611no—
440C2×C22⋊C4—611no—
441C2×C22⋊C4—611no—
442C2×C22⋊C4—611no—
443C2×C22⋊C4—611no—
444C2×C22⋊C4—611no—
445C2×C42—611no—
446C2×C42—611no—
447C2×C42—611no—
448C2×C42—611no—
449C2×C42—611no—
450C4⋊C8—1222no—
451C4⋊C8—1222no—
452C4⋊C8—1222no—
453C4⋊C8—1222no—
454C22⋊C8—22no—
455C22⋊C8—612no—
456C22⋊C8—612no—
457C22⋊C8—1222no—
458C22⋊C8C22×D6112yes—
459C22⋊C8C22×D6112yes—
460#97—1222no—
461#97—1222no—
462C4×C8—1222no—
463C4×C8—1222no—
464C24—611no—
465C24C2×C4×D6111yescharacteristic
466C2×Q8—1222no—
467C2×Q8—1222no—
468C2×Q8—2441no—
469C2×D4—1221no—
470C2×D4—1221no—
471C2×D4—2442no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—41no—
478C22×C4—42no—
479C22×C4—42no—
480C22×C4—611no—
481C22×C4—611no—
482C22×C4—611no—
483C22×C4—611no—
484C22×C4—611no—
485C22×C4—611no—
486C22×C4—611no—
487C22×C4—1221no—
488C22×C4—1221no—
489C22×C4—1222no—
490C22×C4—2441no—
491C22×C4C2×C4×D6111yescharacteristic
492C22×C4C2×C4×D6111yescharacteristic
493C22×C4C2×C4×D6111yescharacteristic
494C22×C4C2×C4×D6111yescharacteristic
495C22×C4C2×C4×D6111yescharacteristic
496C22×C4D4×D6112yes—
497C22×C4D4×D6112yes—
498C22×C4C23×D6111yescharacteristic
499M16—44no—
500C2×C8—22no—
501C2×C8—22no—
502C2×C8—1222no—
503C2×C8—1222no—
504C2×C8—2444no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—612no—
510C4⋊C4—612no—
511C4⋊C4—612no—
512C4⋊C4—612no—
513C4⋊C4—1221no—
514C4⋊C4—1221no—
515C4⋊C4—1222no—
516C4⋊C4—1222no—
517C4⋊C4—1222no—
518C4⋊C4—1222no—
519C4⋊C4—1222no—
520C4⋊C4—1221no—
521C4⋊C4—1221no—
522C4⋊C4—1221no—
523C4⋊C4—1221no—
524C4⋊C4—1222no—
525C4⋊C4—1222no—
526C22⋊C4—611no—
527C22⋊C4—611no—
528C22⋊C4—611no—
529C22⋊C4—611no—
530C22⋊C4—612no—
531C22⋊C4—612no—
532C22⋊C4—1222no—
533C22⋊C4—1221no—
534C22⋊C4—1221no—
535C22⋊C4—1222no—
536C22⋊C4—1221no—
537C22⋊C4—1221no—
538C22⋊C4—1222no—
539C22⋊C4—1222no—
540C42—612no—
541C42—612no—
542C42—612no—
543C42—612no—
544C42—1221no—
545C42—1221no—
546C42—1221no—
547C42—1221no—
548C42—1221no—
549C42—1221no—
550C23—22no—
551C23—21no—
552C23—21no—
553C23—41no—
554C23—1221no—
555C23—1221no—
556C23—1221no—
557C23—2441no—
558C23—2441no—
559C23C22⋊C4×D6111yescharacteristic
560C23C22⋊C4×D6111yescharacteristic
561C23C22×C4×D6111yescharacteristic
562Q8—2444no—
563D4—2442no—
564D4—2442no—
565C2×C4—21no—
566C2×C4—24no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—41no—
574C2×C4—42no—
575C2×C4—41no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—41no—
581C2×C4—41no—
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—2442no—
598C2×C4—2442no—
599C2×C4—2441no—
600C2×C4—2441no—
601C2×C4—2441no—
602C2×C4—2441no—
603C2×C4C22⋊C4×D6112yes—
604C2×C4#1451978512yes—
605C2×C4C2×D4×D6112yes—
606C8—42no—
607C8—42no—
608C8—2442no—
609C8—2442no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—21no—
615C22—21no—
616C22—21no—
617C22—42no—
618C22—42no—
619C22—4881no—
620C22—4881no—
621C22—2441no—
622C22—2441no—
623C22—2441no—
624C22#1683973412yes—
625C22C2×C22⋊C4×D6111yescharacteristic
626C22C2×#1451978511yescharacteristic
627C22#1684052811yescharacteristic
628C4—22no—
629C4—22no—
630C4—22no—
631C4—41no—
632C4—41no—
633C4—41no—
634C4—1221no—
635C4—1221no—
636C4—1222no—
637C4—1221no—
638C4—1221no—
639C4—1222no—
640C4—2441no—
641C4—2441no—
642C4—2441no—
643C2—21no—
644C2—21no—
645C2—22no—
646C2—41no—
647C2—4881no—
648C2#2145426911yescharacteristic
649C2C2×#1683973411yescharacteristic
650C2#2145429911yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1463C2
socleC22×C61C22×C22⋊C4
prime radicalC22×C22⋊D61C2×C4
cosocleC22×C4×C61C24
hypercenter#1463D61
hypocenterC61#17417
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
2. #21454479C2semidirect
3. #21444187C2semidirect
4. #21444173C2semidirect
6. #21444161C2semidirect
7. #21444152C2semidirect
8. #21444141C2semidirect
9. #21444132C2semidirect
10. C2×#16839488C2semidirect
11. C61×#1463C2semidirect
325. #1463D61semidirect
376. C61#17417semidirect

Maximal subgroups

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

subgroupindex
C2×#168404472
#214544792
#214441872
#214441732
#214441682
#214441612
#214441522
#214441412
#214441322
C2×#168394882
C61×#14632
#1741761