Finite Group Databasebeta

← #29742889

Subgroups — #29742889

Order 15616.

860 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840065C211yesmaximal, characteristic, complemented
2#21449537C211yesmaximal, characteristic, complemented
3#21448857C211yesmaximal, characteristic
4#21447341C211yesmaximal, characteristic, complemented
5#21447318C211yesmaximal, characteristic, complemented
6#21447188C211yesmaximal, characteristic, complemented
7#21447159C211yesmaximal, characteristic, complemented
8#21446584C211yesmaximal, characteristic, complemented
9#21446392C211yesmaximal, characteristic, complemented
10#21446257C211yesmaximal, characteristic
11#21446136C211yesmaximal, characteristic
12#21446063C211yesmaximal, characteristic, complemented
13#21446018C211yesmaximal, characteristic, complemented
14#21446002C211yesmaximal, characteristic, complemented
15C2×C61×#428C211yesmaximal, characteristic, complemented
16C2×#14519768C2211yescharacteristic
17C2×#14519751C2211yescharacteristic
18C2×#14519739C2211yescharacteristic
19#16840065—24no—
20C2×#14519710C2211yescharacteristic
21C2×#14519708C2211yescharacteristic
22C2×#14519706C2211yescharacteristic
23C2×#14519706C2211yescharacteristic
24C2×#14519699C2211yescharacteristic
25C2×#14519699C2211yescharacteristic
26C2×#14519697C2211yescharacteristic
27C2×#14519697C2211yescharacteristic
28C2×C22⋊#92418C2211yescharacteristic
29#16839701—21no—
30#16839695—21no—
31#16839663C2211yescharacteristic
32#16839662—21no—
33#16839661C2211yescharacteristic
34#16839658C2211yescharacteristic
35#16839658C2211yescharacteristic
36#16839653—21no—
37#16839638—21no—
38#16839635—21no—
39#16839627C2211yescharacteristic
40#16839622—21no—
41#16839622C2211yescharacteristic
42C4⋊C4×Dic61C2211yescharacteristic
43C4×#11758198—21no—
44C4×C22⋊Dic61C2211yescharacteristic
45#16839525C2211yescharacteristic
46#16839525C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839516C2211yescharacteristic
52#16839516C2211yescharacteristic
53C22×M16×C61C2211yescharacteristic
54C2×#117×C61C2211yescharacteristic
55C22×C4⋊C4×C61C2211yescharacteristic
56C61×#428—24no—
57C2×#107×C61C2211yescharacteristic
58C2×#107×C61C2211yescharacteristic
59C2×#106×C61C2211yescharacteristic
60C2×#106×C61C2211yescharacteristic
61C22×D244C2311yescharacteristic
62C22×C22⋊D61—21no—
63C22×C4×D61—21no—
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66#14519768—22no—
67#14519768—41no—
68#14519751—22no—
69#14519751Q814yes—
70#14519739—22no—
71#14519739—41no—
72C2×C4⋊Dic61—21no—
73C2×C4⋊Dic61—21no—
74C2×C4⋊Dic61C2311yescharacteristic
75C2×C4⋊Dic61C2311yescharacteristic
76C2×C4⋊Dic61C2311yescharacteristic
77C2×#11758196—21no—
78C2×#11758196—21no—
79C2×#11758196—21no—
80C2×C22⋊Dic61—21no—
81C2×C22⋊Dic61D411yescharacteristic
82C2×C22⋊Dic61D411yescharacteristic
83C2×#11758198—21no—
84C2×#11758198—21no—
85C2×#11758198—21no—
86C2×#11758198—21no—
87C2×C4×Dic61—21no—
88C2×C4×Dic61C2311yescharacteristic
89C2×C4×Dic61C2311yescharacteristic
90#14519710—41no—
91#14519708—22no—
92#14519706—22no—
93#14519706—22no—
94#14519699—22no—
95#14519699—22no—
96#14519697—22no—
97#14519697—41no—
98C22⋊#92418—22no—
99#14519684—21no—
100#14519684—21no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105#14519684—21no—
106#14519684D411yescharacteristic
107#14519684D411yescharacteristic
108C23×C4×C61—21no—
109C23×C4×C61C2311yescharacteristic
110C2×M16×C61—22no—
111C2×M16×C61—22no—
112C2×M16×C61—22no—
113C22×C8×C61C2311yescharacteristic
114C22×C8×C61C2311yescharacteristic
115#117×C61—22no—
116#117×C61—41no—
117C2×C4⋊C4×C61—22no—
118C2×C4⋊C4×C61—21no—
119C2×C4⋊C4×C61—41no—
120C2×C4⋊C4×C61C2311yescharacteristic
121C2×C4⋊C4×C61C2311yescharacteristic
122C2×C4⋊C4×C61C2311yescharacteristic
123C2×C4⋊C4×C61C2311yescharacteristic
124C2×C22⋊C4×C61—21no—
125C2×C42×C61—21no—
126#107×C61—22no—
127#107×C61D414yescomplemented
128#106×C61—22no—
129#106×C61—22no—
130C24×C61C2×D411yescharacteristic
131C23×D61—21no—
132C22×C4×C61—21no—
133C22×C4×C61—21no—
134C22×C4×C61—21no—
135C22×C4×C61—21no—
136C22×C4×C61—21no—
137C22×C4×C61—21no—
138C22×C4×C61—21no—
139C22×C4×C61—21no—
140C22×C4×C61—42no—
141C22×C4×C61—42no—
142C22×C4×C61—81no—
143C22×C4×C61C2×D411yescharacteristic
144C22×C4×C61C2×Q812yes—
145C22×C4×C61#4112yes—
146C22×C4×C61C2411yescharacteristic
147C2×C22⋊D61—24no—
148C2×C22⋊D61—81no—
149C2×C22⋊D61—81no—
150C22×Dic61—21no—
151C22×Dic61—21no—
152C22×Dic61—21no—
153C22×Dic61C2×D411yescharacteristic
154C22×Dic61C2×D411yescharacteristic
155C22×Dic61C2×D411yescharacteristic
156C22×Dic61C2×D411yescharacteristic
157C2×D244—21no—
158C2×D244—21no—
159C2×D244—21no—
160C2×D244—21no—
161C2×D244—21no—
162C2×D244C2×Q812yes—
163C2×C4×D61—42no—
164C2×C4×D61—42no—
165C2×C4×D61—81no—
166M16×C61—28no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C2×C8×C61—21no—
170C2×C8×C61—21no—
171C2×C8×C61C2×D412yes—
172C2×C8×C61#4112yes—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61—21no—
177C4⋊C4×C61—21no—
178C4⋊C4×C61—21no—
179C4⋊C4×C61—42no—
180C4⋊C4×C61C2×D412yes—
181C4⋊C4×C61C2×D412yes—
182C22⋊C4×C61—42no—
183C42×C61—42no—
184C22⋊Dic61—41no—
185C22⋊Dic61—41no—
186C22⋊Dic61—42no—
187#11758198—24no—
188#11758198—42no—
189#11758198—42no—
190#11758198—81no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61—21no—
196C4⋊Dic61—42no—
197C4⋊Dic61—81no—
198C4⋊Dic61C2×Q812yes—
199#11758196—42no—
200#11758196—81no—
201#11758196—81no—
202C4×Dic61—21no—
203C4×Dic61—21no—
204C4×Dic61—21no—
205C4×Dic61—21no—
206C4×Dic61—81no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—21no—
210C2×#92418—21no—
211C2×#92418—21no—
212C2×#92418—21no—
213C23×C61—21no—
214C23×C61—21no—
215C23×C61—21no—
216C23×C61—21no—
217C23×C61—21no—
218C23×C61—21no—
219C23×C61C22⋊Q812yes—
220C23×C61C22×D411yescharacteristic
221C22×D61—22no—
222C22×D61—41no—
223C22×D61—41no—
224C22×D61—41no—
225C22×D61—41no—
226C22×D61—41no—
227C22×D61—41no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—22no—
231C2×C4×C61—22no—
232C2×C4×C61—22no—
233C2×C4×C61—22no—
234C2×C4×C61—22no—
235C2×C4×C61—22no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61—41no—
240C2×C4×C61—41no—
241C2×C4×C61—41no—
242C2×C4×C61—41no—
243C2×C4×C61—41no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61—84no—
247C2×C4×C61C22⋊Q812yes—
248C2×C4×C61C22×D411yescharacteristic
249C2×C4×C61C22×Q811yescharacteristic
250C2×C4×C61C2×#4111yescharacteristic
251C2×C4×C61C2×#4111yescharacteristic
252C2×C4×C61H(5,𝔽2)11yescharacteristic
253C2×C4×C612−1+411yescharacteristic
254C22⋊D61—84no—
255C2×Dic61—22no—
256C2×Dic61—21no—
257C2×Dic61—21no—
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—21no—
268C2×Dic61—41no—
269C2×Dic61—41no—
270C2×Dic61—41no—
271C2×Dic61—41no—
272C2×Dic61—41no—
273C2×Dic61—41no—
274C2×Dic61—41no—
275C2×Dic61—41no—
276D244—22no—
277D244—22no—
278D244—41no—
279D244—41no—
280C4×D61—84no—
281C8×C61—22no—
282C8×C61—22no—
283#92418—41no—
284#92418—41no—
285#26363—611nomaximal, Sylow
286C22×C61—22no—
287C22×C61—22no—
288C22×C61—22no—
289C22×C61—41no—
290C22×C61—41no—
291C22×C61—41no—
292C22×C61—41no—
293C22×C61C2×C22⋊Q811yescharacteristic
294C22×C61D4211yescharacteristic
295C22×C61#54711yescharacteristic
296C22×C61#57511yescharacteristic
297C22×C61#57511yescharacteristic
298C22×C61#57611yescharacteristic
299C22×C61#57711yescharacteristic
300C2×D61—42no—
301C2×D61—42no—
302C2×D61—42no—
303C2×D61—81no—
304C2×D61—81no—
305C2×D61—81no—
306C2×D61—81no—
307C4×C61—22no—
308C4×C61—42no—
309C4×C61—42no—
310C4×C61—81no—
311C4×C61—81no—
312C4×C61#52511yescharacteristic
313C4×C61#53911yescharacteristic
314C4×C61D4×Q811yescharacteristic
315C4×C61#55411yescharacteristic
316Dic61—42no—
317Dic61—41no—
318Dic61—41no—
319Dic61—41no—
320Dic61—41no—
321Dic61—81no—
322Dic61—81no—
323C2×#478—611no—
324C2×#428D6111yescharacteristic, complemented
325#2442—611no—
326#2363—611no—
327#2092—611no—
328#2088—611no—
329#2065—611no—
330#2059—611no—
331#1949—611no—
332#1918—611no—
333#1895—611no—
334#1874—611no—
335#1862—611no—
336#1854—611no—
337#1851—611no—
338C2×C61—42no—
339C2×C61#244911yescharacteristic
340C2×C61#308011yescharacteristic
341C2×C61#308111yescharacteristic
342C2×C61#327111yescharacteristic
343C2×C61#327311yescharacteristic
344C2×C61#334811yescharacteristic
345C2×C61#335511yescharacteristic
346D61—82no—
347C22×M16C2×D6111yescharacteristic
348C2×#125—611no—
349C2×#121—611no—
350C2×C4×D4—611no—
351C2×#117C2×D6111yescharacteristic
352C22×C4⋊C4C2×D6111yescharacteristic
353#478—1224no—
354#428—24no—
355C2×#107—611no—
356C2×#107C2×D6111yescharacteristic
357C2×#107C2×D6111yescharacteristic
358C2×#106—611no—
359C2×#106C2×D6111yescharacteristic
360C2×#106C2×D6111yescharacteristic
361C2×C4⋊C8—611no—
362C2×C4⋊C8—611no—
363C2×#102—611no—
364C2×#102—611no—
365C2×#102—611no—
366C2×#102—611no—
367C2×C22⋊C8—611no—
368#400—1221no—
369#398—1221no—
370#390—611no—
371#390—1221no—
372#389—611no—
373#389—611no—
374#389—611no—
375#388—1221no—
376#386—1221no—
377#385—1221no—
378#382—611no—
379#380—611no—
380#380—1221no—
381C4×C4⋊C4—611no—
382C4×C22⋊C4—611no—
383C4×C22⋊C4—1221no—
384#340—611no—
385#340—611no—
386#340—611no—
387#340—611no—
388#340—611no—
389#340—611no—
390#336—611no—
391#336—611no—
392C61#2636311yescharacteristic, complemented, Sylow
393C22×D4—611no—
394C22×D4—1221no—
395C23×C4—21no—
396C23×C4—1221no—
397C23×C4C22×D6111yescharacteristic
398C2×M16—22no—
399C2×M16—22no—
400C2×M16—22no—
401C22×C8—611no—
402C22×C8—611no—
403C22×C8C22×D6111yescharacteristic
404C22×C8C22×D6111yescharacteristic
405#125—1222no—
406#125—2441no—
407#121—614no—
408#121—1222no—
409C4×D4—1222no—
410C4×D4—2441no—
411#117—22no—
412#117—41no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—41no—
416C2×C4⋊C4—611no—
417C2×C4⋊C4—611no—
418C2×C4⋊C4—611no—
419C2×C4⋊C4—1221no—
420C2×C4⋊C4—1221no—
421C2×C4⋊C4—1221no—
422C2×C4⋊C4—1221no—
423C2×C4⋊C4—1221no—
424C2×C4⋊C4C22×D6111yescharacteristic
425C2×C4⋊C4C22×D6111yescharacteristic
426C2×C4⋊C4C22×D6111yescharacteristic
427C2×C4⋊C4C22×D6111yescharacteristic
428C2×C22⋊C4—21no—
429C2×C22⋊C4—611no—
430C2×C22⋊C4—611no—
431C2×C22⋊C4—1221no—
432C2×C22⋊C4—1221no—
433C2×C22⋊C4—1221no—
434C2×C22⋊C4—1221no—
435C2×C22⋊C4—1221no—
436C2×C42—21no—
437C2×C42—611no—
438C2×C42—611no—
439C2×C42—1221no—
440#107—22no—
441#107—2441no—
442#107C22⋊D6114yescomplemented
443#106—22no—
444#106—22no—
445#106—1222no—
446C4⋊C8—1222no—
447C4⋊C8—1222no—
448#102—1222no—
449#102—1222no—
450#102—1222no—
451#102—2441no—
452C22⋊C8—1222no—
453#95—611no—
454#95—611no—
455#95—1221no—
456#95—1221no—
457#95—1221no—
458#95—1221no—
459#95—1221no—
460#95—1221no—
461#95—1221no—
462C24—1221no—
463C24D4×D6111yescharacteristic
464C2×D4—612no—
465C2×D4—1224no—
466C2×D4—1221no—
467C2×D4—1221no—
468C2×D4—1221no—
469C2×D4—1221no—
470C2×D4—1221no—
471C2×D4—4881no—
472C2×D4—4881no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—81no—
484C22×C4—611no—
485C22×C4—611no—
486C22×C4—611no—
487C22×C4—611no—
488C22×C4—1221no—
489C22×C4—1221no—
490C22×C4—1221no—
491C22×C4—4881no—
492C22×C4—2442no—
493C22×C4—2442no—
494C22×C4#1175822212yes—
495C22×C4D4×D6111yescharacteristic
496C22×C4Q8×D6112yes—
497C22×C4C23×D6111yescharacteristic
498M16—28no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—1221no—
504C2×C8—1221no—
505C2×C8—1221no—
506C2×C8—1221no—
507C2×C8—1221no—
508C2×C8—1221no—
509C2×C8#1175822212yes—
510C2×C8C2×C22⋊D6112yes—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—42no—
518C4⋊C4—612no—
519C4⋊C4—1221no—
520C4⋊C4—1221no—
521C4⋊C4—1221no—
522C4⋊C4—1221no—
523C4⋊C4—1221no—
524C4⋊C4—4881no—
525C4⋊C4—4881no—
526C4⋊C4—4881no—
527C4⋊C4—2442no—
528C4⋊C4—2442no—
529C4⋊C4C2×C22⋊D6112yes—
530C4⋊C4C2×C22⋊D6112yes—
531C22⋊C4—42no—
532C22⋊C4—1224no—
533C22⋊C4—4881no—
534C22⋊C4—2442no—
535C22⋊C4—2442no—
536C22⋊C4—2441no—
537C22⋊C4—2441no—
538C22⋊C4—2442no—
539C42—42no—
540C42—1221no—
541C42—1221no—
542C42—1221no—
543C42—1221no—
544C42—4881no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—1222no—
552C23—2441no—
553C23—2441no—
554C23—2441no—
555C23—2441no—
556C23—2441no—
557C23—2441no—
558C23#1451975512yes—
559C23C2×D4×D6111yescharacteristic
560D4—1222no—
561D4—1222no—
562D4—4884no—
563D4—2441no—
564D4—2441no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—84no—
584C2×C4—1222no—
585C2×C4—1221no—
586C2×C4—1221no—
587C2×C4—1221no—
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—4884no—
598C2×C4—2441no—
599C2×C4—2441no—
600C2×C4—2441no—
601C2×C4—2441no—
602C2×C4—2441no—
603C2×C4—2441no—
604C2×C4—2441no—
605C2×C4—2441no—
606C2×C4#1451975512yes—
607C2×C4C22×C22⋊D6111yescharacteristic
608C2×C4C2×Q8×D6111yescharacteristic
609C2×C4C2×#1175822211yescharacteristic
610C2×C4C2×#1175822211yescharacteristic
611C2×C4#1451982211yescharacteristic
612C2×C4#1451982511yescharacteristic
613C8—22no—
614C8—22no—
615C8—2441no—
616C8—2441no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—4881no—
625C22—4881no—
626C22—4881no—
627C22—4881no—
628C22—2442no—
629C22—2442no—
630C22—2442no—
631C22C2×#1451975511yescharacteristic
632C22D4×C22⋊D6111yescharacteristic
633C22#1684041311yescharacteristic
634C22#1684055811yescharacteristic
635C22#1684056111yescharacteristic
636C22#1684056611yescharacteristic
637C22#1684057111yescharacteristic
638C4—22no—
639C4—42no—
640C4—42no—
641C4—81no—
642C4—81no—
643C4—4881no—
644C4—4881no—
645C4—2441no—
646C4—2442no—
647C4—2441no—
648C4—2441no—
649C4—2441no—
650C4#1684027311yescharacteristic
651C4#1684035911yescharacteristic
652C4Q8×C22⋊D6111yescharacteristic
653C4#1684046711yescharacteristic
654C2—42no—
655C2—4882no—
656C2#2144962811yescharacteristic
657C2#2145564011yescharacteristic
658C2#2145564811yescharacteristic
659C2#2145739811yescharacteristic
660C2#2145742411yescharacteristic
661C2#2145833511yescharacteristic
662C2#2145842111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#428C2
socleC23×C61C22×D4
prime radicalC2×#14519751C22
hypercenterC2×#428D61
hypocenterC61#26363
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
1. C2×#16840065C2semidirect
2. #21449537C2semidirect
4. #21447341C2semidirect
5. #21447318C2semidirect
6. #21447188C2semidirect
7. #21447159C2semidirect
8. #21446584C2semidirect
9. #21446392C2semidirect
12. #21446063C2semidirect
13. #21446018C2semidirect
14. #21446002C2semidirect
15. C2×C61×#428C2semidirect
127. #107×C61D4semidirect
324. C2×#428D61semidirect
392. C61#26363semidirect
442. #107C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168400652
#214495372
#214488572
#214473412
#214473182
#214471882
#214471592
#214465842
#214463922
#214462572
#214461362
#214460632
#214460182
#214460022
C2×C61×#4282
#2636361