Finite Group Databasebeta

← #30616621

Subgroups — #30616621

Order 15616.

714 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462500C211yesmaximal, characteristic
2#21462384C211yesmaximal, characteristic
3#21461935C211yesmaximal, characteristic, complemented
4#21461935C211yesmaximal, characteristic, complemented
5#21461934C211yesmaximal, characteristic, complemented
6#21461933C211yesmaximal, characteristic, complemented
7#21461773C211yesmaximal, characteristic
8#21461773C211yesmaximal, characteristic
9#21461772C211yesmaximal, characteristic
10#21461771C211yesmaximal, characteristic
11#21461639C211yesmaximal, characteristic, complemented
12#21461639C211yesmaximal, characteristic, complemented
13C4×#14519848C211yesmaximal, characteristic, complemented
14C4×#14519847C211yesmaximal, characteristic, complemented
15#433×D61C211yesmaximal, characteristic
16C22×#11758213C2211yescharacteristic
17C2×D61⋊M16C2211yescharacteristic
18#16840787—21no—
19#16840787—21no—
20#16840786—21no—
21#16840786—21no—
22C2×#14519848C2211yescharacteristic
23C2×#14519848C2211yescharacteristic
24C2×#14519848C2211yescharacteristic
25C2×#14519848C2211yescharacteristic
26C2×#14519847C2211yescharacteristic
27C2×#14519847C2211yescharacteristic
28C2×#14519847C2211yescharacteristic
29C2×#14519847C2211yescharacteristic
30#16840767C2211yescharacteristic
31#16840766C2211yescharacteristic
32#16840733C2211yescharacteristic
33#16840733C2211yescharacteristic
34#16840727—21no—
35#16840727—21no—
36#16840726—21no—
37#16840726—21no—
38C4×#11758213C2211yescharacteristic
39C4×#11758213C2211yescharacteristic
40C4×#11758213C2211yescharacteristic
41C4×#11758213C2211yescharacteristic
42C4×#11758213C2211yescharacteristic
43C4×#11758213C2211yescharacteristic
44#16840638C2211yescharacteristic
45#16840638C2211yescharacteristic
46#16840638C2211yescharacteristic
47#16840638C2211yescharacteristic
48#16840638C2211yescharacteristic
49#16840638C2211yescharacteristic
50#16840638C2211yescharacteristic
51#16840638C2211yescharacteristic
52#117×D61C2211yescharacteristic
53#16839824C411yescharacteristic
54#16839823C411yescharacteristic
55#16839822C411yescharacteristic
56#16839822C411yescharacteristic
57#16839821C411yescharacteristic
58#16839820C411yescharacteristic
59#16839820C411yescharacteristic
60C4⋊C8×D61C2211yescharacteristic
61C4⋊C8×D61C2211yescharacteristic
62C22⋊C8×D61C2211yescharacteristic
63C22⋊C8×D61C2211yescharacteristic
64#97×D61C2211yescharacteristic
65C4×C8×D61C2211yescharacteristic
66C61×#433C411yescharacteristic
67C2×#11758213—21no—
68C2×#11758213—22no—
69C2×#11758213—22no—
70C2×#11758213C2311yescharacteristic
71C2×#11758213C2311yescharacteristic
72C2×#11758213C2311yescharacteristic
73C2×#11758213C2311yescharacteristic
74C2×#11758213C2311yescharacteristic
75C2×#11758213C2311yescharacteristic
76C2×#11758213C2311yescharacteristic
77C2×#11758213C2311yescharacteristic
78D61⋊M16—22no—
79D61⋊M16—22no—
80C2×#11758217—21no—
81C2×D61⋊C8—21no—
82C22×#92420—21no—
83#14519848—22no—
84#14519848—22no—
85#14519848—22no—
86#14519848—22no—
87#14519847—22no—
88#14519847—22no—
89#14519847—22no—
90#14519847—22no—
91#14519844—21no—
92#14519844—21no—
93C4⋊#92420—21no—
94C4⋊#92420—21no—
95#14519834—21no—
96#14519834—21no—
97C22⋊#92420—21no—
98C22⋊#92420—21no—
99#14519832—21no—
100#14519832—21no—
101#14519832—21no—
102#14519832—21no—
103#14519832—21no—
104#14519832—21no—
105C4×#92420—21no—
106C4×#92420—21no—
107C4×#92420—21no—
108C4×#92420—21no—
109C4×#92420—21no—
110C4×#92420—21no—
111C22×C4×D61C2311yescharacteristic
112C2×C8×D61C2311yescharacteristic
113C2×C8×D61C2311yescharacteristic
114C2×C8×D61C2311yescharacteristic
115C2×C8×D61C2311yescharacteristic
116#14519736C2×C411yescharacteristic
117#14519735D411yescharacteristic
118#14519735D411yescharacteristic
119#14519734C2×C411yescharacteristic
120#14519734C2×C411yescharacteristic
121#14519733D411yescharacteristic
122#14519733D411yescharacteristic
123C4⋊C4×D61Q811yescharacteristic
124C4⋊C4×D61Q811yescharacteristic
125C22⋊C4×D61Q811yescharacteristic
126C22⋊C4×D61Q811yescharacteristic
127C42×D61C2311yescharacteristic
128C42×D61C2311yescharacteristic
129C4⋊#92418C2×C411yescharacteristic
130C4⋊#92418C2×C411yescharacteristic
131#14519706C2×C411yescharacteristic
132#14519706C2×C411yescharacteristic
133#14519706C2×C411yescharacteristic
134#14519706C2×C411yescharacteristic
135C22⋊#92418C2×C411yescharacteristic
136C22⋊#92418C2×C411yescharacteristic
137#14519689C2×C411yescharacteristic
138#14519689C2×C411yescharacteristic
139#14519689C2×C411yescharacteristic
140#14519689C2×C411yescharacteristic
141#14519688C2×C411yescharacteristic
142#14519687C2×C411yescharacteristic
143#14519687C2×C411yescharacteristic
144C4×#92418C2×C411yescharacteristic
145C8×Dic61C2×C411yescharacteristic
146C8×Dic61C2×C411yescharacteristic
147#117×C61C2×C411yescharacteristic
148C4⋊C8×C61C2×C411yescharacteristic
149C4⋊C8×C61C2×C411yescharacteristic
150C22⋊C8×C61C2×C411yescharacteristic
151C22⋊C8×C61C2×C411yescharacteristic
152#97×C61C2×C411yescharacteristic
153C4×C8×C61C2×C411yescharacteristic
154C23×D61C2×Q811yescharacteristic
155C22×C4×C61C22×C411yescharacteristic
156C22×Dic61C2×D411yescharacteristic
157C2×C4×D61—21no—
158C2×C4×D61—21no—
159C2×C4×D61—21no—
160C2×C4×D61—21no—
161C2×C4×D61C22×C411yescharacteristic
162C2×C4×D61C2×D411yescharacteristic
163C2×C4×D61C2×Q811yescharacteristic
164C2×C4×D61C2×Q811yescharacteristic
165C2×C4×D61C2×Q811yescharacteristic
166C2×C4×D61C2×Q811yescharacteristic
167C2×C4×D61C2×Q811yescharacteristic
168C2×C4×D61C2411yescharacteristic
169#11758217—24no—
170C2×#92420—24no—
171C2×#92420—21no—
172C2×#92420—21no—
173C2×#92420—21no—
174C2×#92420—21no—
175C2×#92420—21no—
176C2×#92420—21no—
177C2×#92420—21no—
178C2×#92420—21no—
179#11758213—24no—
180#11758213—21no—
181#11758213—21no—
182#11758213—21no—
183#11758213—21no—
184#11758213—21no—
185#11758213—21no—
186#11758213—21no—
187#11758213—21no—
188#11758213—21no—
189#11758213—21no—
190#11758213—21no—
191#11758213—21no—
192#11758213#4112yes—
193#11758213#4112yes—
194#11758213#4112yes—
195#11758213#4112yes—
196D61⋊C8—24no—
197C2×C8×C61C22×C411yescharacteristic
198C2×C8×C61C22×C411yescharacteristic
199C2×C8×C61C22×C411yescharacteristic
200C2×C8×C61C22×C411yescharacteristic
201C4⋊C4×C61C4⋊C411yescharacteristic
202C4⋊C4×C61C4⋊C411yescharacteristic
203C22⋊C4×C61C4⋊C411yescharacteristic
204C22⋊C4×C61C4⋊C411yescharacteristic
205C42×C61C22×C411yescharacteristic
206C42×C61C22×C411yescharacteristic
207C22⋊Dic61C4⋊C411yescharacteristic
208C22⋊Dic61C4⋊C411yescharacteristic
209#11758198C4⋊C411yescharacteristic
210#11758198C4⋊C411yescharacteristic
211#11758198C4⋊C411yescharacteristic
212#11758198C4⋊C411yescharacteristic
213C4⋊Dic61C4⋊C411yescharacteristic
214C4⋊Dic61C4⋊C411yescharacteristic
215#11758196C4⋊C411yescharacteristic
216#11758196C4⋊C411yescharacteristic
217#11758196C4⋊C411yescharacteristic
218#11758196C4⋊C411yescharacteristic
219C4×Dic61C22×C411yescharacteristic
220C4×Dic61C22×C411yescharacteristic
221C4×Dic61C2×D411yescharacteristic
222C4×Dic61C2×D411yescharacteristic
223C4×Dic61C2×D411yescharacteristic
224C4×Dic61C2×D411yescharacteristic
225C2×#92418C22×C411yescharacteristic
226C2×#92418C22×C411yescharacteristic
227C2×#92418C22×C411yescharacteristic
228C2×#92418C22×C411yescharacteristic
229C8×D61—21no—
230C8×D61—21no—
231C8×D61—21no—
232C8×D61—21no—
233C8×D61—21no—
234C8×D61—21no—
235C8×D61—21no—
236C8×D61—21no—
237C23×C61C2×C4⋊C411yescharacteristic
238C22×D61—21no—
239C22×D61—21no—
240C22×D61—41no—
241C22×D61—41no—
242C22×D61C2×C4⋊C411yescharacteristic
243C22×D61C22×Q811yescharacteristic
244C2×C4×C61—21no—
245C2×C4×C61—21no—
246C2×C4×C61C2×C4⋊C411yescharacteristic
247C2×C4×C61C2×C4⋊C411yescharacteristic
248C2×C4×C61C2×C4⋊C411yescharacteristic
249C2×C4×C61C2×C4⋊C411yescharacteristic
250C2×C4×C61C2×C4⋊C411yescharacteristic
251C2×C4×C61C23×C411yescharacteristic
252C2×Dic61—21no—
253C2×Dic61—21no—
254C2×Dic61C2×C4⋊C411yescharacteristic
255C2×Dic61C2×C4⋊C411yescharacteristic
256C2×Dic61C2×C4⋊C411yescharacteristic
257C2×Dic61C2×C4⋊C411yescharacteristic
258C2×Dic61C2×C4⋊C411yescharacteristic
259C2×Dic61C22×D411yescharacteristic
260C4×D61—21no—
261C4×D61—21no—
262C4×D61—21no—
263C4×D61—21no—
264C4×D61—21no—
265C4×D61—21no—
266C4×D61—41no—
267C4×D61—41no—
268C4×D61—41no—
269C4×D61—41no—
270C4×D61C2×#4111yescharacteristic
271C4×D61C2×#4111yescharacteristic
272C4×D61C2×#4111yescharacteristic
273C4×D61C2×#4111yescharacteristic
274#92420—22no—
275#92420—22no—
276#92420—22no—
277#92420—22no—
278#92420—41no—
279#92420—41no—
280#92420—41no—
281#92420—41no—
282C8×C61—21no—
283C8×C61—21no—
284C8×C61—21no—
285C8×C61—21no—
286#92418—21no—
287#92418—21no—
288#92418—21no—
289#92418—21no—
290#21372—611nomaximal, Sylow
291C22×C61—21no—
292C22×C61—21no—
293C22×C61—21no—
294C22×C61C22×C4⋊C411yescharacteristic
295C2×D61—21no—
296C2×D61—21no—
297C2×D61—21no—
298C2×D61—21no—
299C2×D61—21no—
300C2×D61—81no—
301C2×D61—81no—
302C2×D61#53311yescharacteristic
303C2×D61#53311yescharacteristic
304C4×C61—21no—
305C4×C61—21no—
306C4×C61—21no—
307C4×C61—21no—
308C4×C61—21no—
309C4×C61C4×#4111yescharacteristic
310C4×C61C4×#4111yescharacteristic
311Dic61—21no—
312Dic61—21no—
313Dic61—21no—
314Dic61—21no—
315Dic61—21no—
316Dic61#52511yescharacteristic
317Dic61#52511yescharacteristic
318#2921—611no—
319C2×#433—611no—
320#2873—611no—
321#1950—611no—
322#1950—611no—
323#1950—611no—
324#1950—611no—
325#1855—611no—
326#1855—611no—
327#1855—611no—
328#1855—611no—
329#1778—611no—
330#1778—611no—
331C4×#108—611no—
332C4×#108—611no—
333C2×C61—41no—
334C2×C61#229611yescharacteristic
335C2×C61#291611yescharacteristic
336C2×C61#291611yescharacteristic
337D61—21no—
338D61—21no—
339D61—41no—
340C22×M16—611no—
341C22×M16—611no—
342C2×#117—611no—
343#433—611no—
344#433—611no—
345#433—611no—
346#433—611no—
347#433—611no—
348#433—611no—
349#433—611no—
350#433—1221no—
351#433—1221no—
352#433—1221no—
353#433—1221no—
354#433#692311yescharacteristic
355C2×#108—611no—
356C2×#108—611no—
357C2×#108—611no—
358C2×#108—611no—
359C2×#108—611no—
360C2×#108—611no—
361C2×#108—611no—
362C2×#108—611no—
363#423—611no—
364#423—611no—
365C2×C4⋊C8—611no—
366C2×C4⋊C8—611no—
367#407—611no—
368#407—611no—
369C2×C22⋊C8—611no—
370C2×C22⋊C8—611no—
371#405—1221no—
372#405—1221no—
373#405—1221no—
374#405—1221no—
375C4×M16—611no—
376C4×M16—611no—
377C4×M16—611no—
378C4×M16—611no—
379C4×M16—611no—
380C4×M16—611no—
381C2×#97—611no—
382C2×C4×C8—611no—
383#341—611no—
384#341—611no—
385#341—611no—
386#341—611no—
387#341—611no—
388#341—611no—
389#341—611no—
390#341—611no—
391C61#2137211yescharacteristic, complemented, Sylow
392C23×C4—611no—
393C2×M16—611no—
394C2×M16—611no—
395C2×M16—611no—
396C2×M16—611no—
397C2×M16—611no—
398C2×M16—611no—
399C2×M16—611no—
400C2×M16—611no—
401C2×M16—1222no—
402C2×M16—1222no—
403C2×M16—1222no—
404C2×M16—1222no—
405C2×M16—1221no—
406C2×M16—1221no—
407C22×C8—611no—
408C22×C8—611no—
409C22×C8—611no—
410C22×C8—611no—
411C22×C8—1221no—
412C22×C8—1221no—
413#117—611no—
414#117—611no—
415#117—611no—
416#117—611no—
417#117—611no—
418#117—611no—
419#117—611no—
420#117C2×#692311yescharacteristic
421C2×C4⋊C4—611no—
422C2×C4⋊C4—611no—
423C2×C22⋊C4—611no—
424C2×C22⋊C4—611no—
425C2×C42—611no—
426C2×C42—611no—
427#108—1222no—
428#108—1222no—
429#108—1222no—
430#108—1222no—
431#108—1222no—
432#108—1222no—
433#108—1222no—
434#108—1222no—
435C4⋊C8—611no—
436C4⋊C8—611no—
437C4⋊C8—611no—
438C4⋊C8—611no—
439C4⋊C8—611no—
440C4⋊C8—611no—
441C4⋊C8—1221no—
442C4⋊C8—1221no—
443C4⋊C8—1221no—
444C4⋊C8—1221no—
445C4⋊C8C2×#692311yescharacteristic
446C4⋊C8C2×#692311yescharacteristic
447C22⋊C8—611no—
448C22⋊C8—611no—
449C22⋊C8—611no—
450C22⋊C8—611no—
451C22⋊C8—611no—
452C22⋊C8—611no—
453C22⋊C8—1221no—
454C22⋊C8—1221no—
455C22⋊C8—1221no—
456C22⋊C8—1221no—
457C22⋊C8C2×#692311yescharacteristic
458C22⋊C8C2×#692311yescharacteristic
459#97—611no—
460#97—611no—
461#97—611no—
462#97—1221no—
463#97—1221no—
464#97—1221no—
465#97—1221no—
466#97—1221no—
467#97—1221no—
468#97C2×#692311yescharacteristic
469C4×C8—611no—
470C4×C8—611no—
471C4×C8—611no—
472C4×C8—1221no—
473C4×C8—1221no—
474C4×C8—1221no—
475C4×C8—1221no—
476C4×C8—1221no—
477C4×C8—1221no—
478C4×C8C2×#692311yescharacteristic
479C24—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—1221no—
490C22×C4—1221no—
491C22×C4—1221no—
492C22×C4—1221no—
493C22×C4C22×#692311yescharacteristic
494M16—612no—
495M16—612no—
496M16—612no—
497M16—612no—
498M16—1221no—
499M16—1221no—
500M16—1221no—
501M16—1221no—
502M16—1224no—
503M16—1224no—
504M16—1221no—
505M16—1221no—
506M16—1221no—
507M16—1221no—
508M16—1221no—
509M16—1221no—
510M16—1221no—
511M16—1221no—
512C2×C8—611no—
513C2×C8—611no—
514C2×C8—611no—
515C2×C8—611no—
516C2×C8—1221no—
517C2×C8—1221no—
518C2×C8—1221no—
519C2×C8—1221no—
520C2×C8—1221no—
521C2×C8—1221no—
522C2×C8—1221no—
523C2×C8—1221no—
524C2×C8—1221no—
525C2×C8—1221no—
526C2×C8—1221no—
527C2×C8—1221no—
528C2×C8—1224no—
529C2×C8—1224no—
530C2×C8—1221no—
531C2×C8—1221no—
532C2×C8—1221no—
533C2×C8—1221no—
534C2×C8C22×#692311yescharacteristic
535C2×C8C22×#692311yescharacteristic
536C2×C8C22×#692311yescharacteristic
537C2×C8C22×#692311yescharacteristic
538C4⋊C4—611no—
539C4⋊C4—611no—
540C4⋊C4—611no—
541C4⋊C4—611no—
542C4⋊C4—611no—
543C4⋊C4—611no—
544C4⋊C4C4⋊#692311yescharacteristic
545C4⋊C4C4⋊#692311yescharacteristic
546C22⋊C4—611no—
547C22⋊C4—611no—
548C22⋊C4—611no—
549C22⋊C4—611no—
550C22⋊C4—611no—
551C22⋊C4—611no—
552C22⋊C4C4⋊#692311yescharacteristic
553C22⋊C4C4⋊#692311yescharacteristic
554C42—611no—
555C42—611no—
556C42—611no—
557C42—611no—
558C42—611no—
559C42—611no—
560C42C22×#692311yescharacteristic
561C42C22×#692311yescharacteristic
562C23—611no—
563C23—611no—
564C23—1221no—
565C23—1221no—
566C23—2441no—
567C23—2441no—
568C23C2×C4⋊#692311yescharacteristic
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—611no—
572C2×C4—611no—
573C2×C4—611no—
574C2×C4—611no—
575C2×C4—611no—
576C2×C4—611no—
577C2×C4—611no—
578C2×C4—611no—
579C2×C4—611no—
580C2×C4—611no—
581C2×C4—1221no—
582C2×C4—1221no—
583C2×C4—1221no—
584C2×C4—1221no—
585C2×C4—1221no—
586C2×C4—1221no—
587C2×C4—1221no—
588C2×C4—1221no—
589C2×C4—2441no—
590C2×C4—2441no—
591C2×C4—2441no—
592C2×C4—2441no—
593C2×C4C2×C4⋊#692311yescharacteristic
594C2×C4C2×C4⋊#692311yescharacteristic
595C2×C4C2×C4⋊#692311yescharacteristic
596C2×C4C2×C4⋊#692311yescharacteristic
597C2×C4C2×C4⋊#692311yescharacteristic
598C2×C4C23×#692311yescharacteristic
599C8—21no—
600C8—21no—
601C8—21no—
602C8—21no—
603C8—1222no—
604C8—1222no—
605C8—1222no—
606C8—1222no—
607C8—1221no—
608C8—1221no—
609C8—1221no—
610C8—1221no—
611C8—2441no—
612C8—2441no—
613C8—2441no—
614C8—2441no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—611no—
619C22—611no—
620C22—1221no—
621C22—1221no—
622C22—1221no—
623C22—1221no—
624C22—1221no—
625C22—4881no—
626C22—4881no—
627C22C22×C4⋊#692311yescharacteristic
628C4—21no—
629C4—21no—
630C4—21no—
631C4—21no—
632C4—21no—
633C4—611no—
634C4—611no—
635C4—1221no—
636C4—1221no—
637C4—1221no—
638C4—1221no—
639C4—1221no—
640C4#41×#692311yescharacteristic
641C4#41×#692311yescharacteristic
642C2—41no—
643C2—1221no—
644C2—1221no—
645C2—2441no—
646C2#2146227911yescharacteristic
647C2#2146248011yescharacteristic
648C2#2146248111yescharacteristic
subgroupG/H
centerC22C22×C4⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#433C4
socleC22×C61C22×C4⋊C4
prime radicalC23×D61C2×Q8
cosocleC2×C4×D61C24
hypercenter#433#6923
hypocenterC61#21372
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
3. #21461935C2semidirect
4. #21461935C2semidirect
5. #21461934C2semidirect
6. #21461933C2semidirect
11. #21461639C2semidirect
12. #21461639C2semidirect
13. C4×#14519848C2semidirect
14. C4×#14519847C2semidirect
391. C61#21372semidirect

Maximal subgroups

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

subgroupindex
#214625002
#214623842
#214619352
#214619342
#214619332
#214617732
#214617722
#214617712
#214616392
C4×#145198482
C4×#145198472
#433×D612
#2137261