Finite Group Databasebeta

← #16829742

Subgroups — #16829742

Order 3712.

394 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271774C211yesmaximal, characteristic, complemented
2#14271635C211yesmaximal, characteristic
3#14271503C211yesmaximal, characteristic, complemented
4#14271502C211yesmaximal, characteristic, complemented
5#14271464C211yesmaximal, characteristic, complemented
6#14271463C211yesmaximal, characteristic, complemented
7#14271365C211yesmaximal, characteristic, complemented
8#14271312C211yesmaximal, characteristic
9#14271312C211yesmaximal, characteristic
10#14271266C211yesmaximal, characteristic, complemented
11#14271264C211yesmaximal, characteristic, complemented
12SD16×Dic29C211yesmaximal, characteristic, complemented
13#14271248C211yesmaximal, characteristic, complemented
14#14271223C211yesmaximal, characteristic, complemented
15C29×#461C211yesmaximal, characteristic, complemented
16C2×D4×D29C2211yescharacteristic
17C2×SD16×C29C2211yescharacteristic
18C2×SD16×C29C2211yescharacteristic
19C29×C4⋊Q8C2211yescharacteristic, complemented
20C4×D4×C29C2211yescharacteristic
21#11745308C2211yescharacteristic
22#11745308C2211yescharacteristic
23Q8×Dic29C2211yescharacteristic, complemented
24Q8×Dic29C2211yescharacteristic, complemented
25C2×#90784C2211yescharacteristic
26C2×#90784C2211yescharacteristic
27D4×Dic29C2211yescharacteristic
28C4×C22⋊D29—21no—
29C2×#90781—21no—
30#11745260—21no—
31#11745260—21no—
32#11745255C2211yescharacteristic
33#11745254C2211yescharacteristic
34#11745251—21no—
35#11745251—21no—
36#11745243—21no—
37C22⋊C4×D29—21no—
38C4×D116C2211yescharacteristic
39#11745234C2211yescharacteristic
40#11745232C2211yescharacteristic, complemented
41C29×C4⋊C8C2211yescharacteristic, complemented
42C29×#103C2211yescharacteristic, complemented
43C29×#103C2211yescharacteristic, complemented
44#11745183C2211yescharacteristic, complemented
45#11745183C2211yescharacteristic, complemented
46#11745180C2211yescharacteristic
47#11745180C2211yescharacteristic
48#11745169C2211yescharacteristic
49#11745169C2211yescharacteristic
50#11745168C2211yescharacteristic
51#11745168C2211yescharacteristic
52#11745166C2211yescharacteristic, complemented
53#11745165C2211yescharacteristic, complemented
54#11745163C2211yescharacteristic, complemented
55C8×Dic29C2211yescharacteristic, complemented
56#11745156C2211yescharacteristic, complemented
57#11745155C2211yescharacteristic, complemented
58C4⋊#6597C2211yescharacteristic, complemented
59C23×D29—21no—
60C2×Q8×C29C2311yescharacteristic
61C2×Q8×C29C2311yescharacteristic
62C2×D4×C29C2311yescharacteristic
63C22×C4×C29—21no—
64C2×C22⋊D29—21no—
65C22×Dic29—21no—
66D4×D29—22no—
67D4×D29—22no—
68C2×D116C2311yescharacteristic
69C2×C4×D29—21no—
70C2×C4×D29—21no—
71C2×C4×D29C2311yescharacteristic
72SD16×C29—22no—
73SD16×C29—22no—
74C2×C8×C29C2311yescharacteristic
75C2×C8×C29C2311yescharacteristic
76C4⋊C4×C29—21no—
77C4⋊C4×C29—21no—
78C4⋊C4×C29C2311yescharacteristic
79C22⋊C4×C29—21no—
80C42×C29C2311yescharacteristic
81C22⋊Dic29—21no—
82#90784—22no—
83#90784—22no—
84#90781—21no—
85#90781—21no—
86#90781—21no—
87#90781—21no—
88#90781—21no—
89#90781D411yescharacteristic
90#90781D411yescharacteristic
91C4⋊Dic29—21no—
92C4⋊Dic29—21no—
93C4⋊Dic29C2311yescharacteristic
94C4⋊Dic29C2311yescharacteristic
95C4⋊Dic29C2311yescharacteristic
96#90779—21no—
97#90779—21no—
98#90779—21no—
99#90779—21no—
100#90779D411yescharacteristic
101#90779D411yescharacteristic
102C4×Dic29—21no—
103C4×Dic29—21no—
104C4×Dic29—21no—
105C4×Dic29C2311yescharacteristic
106C2×#6597C2311yescharacteristic
107C2×#6597C2311yescharacteristic
108C23×C29—21no—
109C22×D29—21no—
110C22×D29—24no—
111C22×D29—81no—
112C22×D29—81no—
113C22×D29C2×D411yescharacteristic
114Q8×C29—21no—
115Q8×C29—21no—
116Q8×C29—21no—
117Q8×C29—21no—
118D4×C29—21no—
119D4×C29#4112yes—
120C2×C4×C29—21no—
121C2×C4×C29—21no—
122C2×C4×C29—21no—
123C2×C4×C29—81no—
124C2×C4×C29C2×D411yescharacteristic
125C2×C4×C29C2×D411yescharacteristic
126C2×C4×C29C2411yescharacteristic
127C22⋊D29—24no—
128C2×Dic29—21no—
129C2×Dic29—21no—
130C2×Dic29—21no—
131C2×Dic29—81no—
132C2×Dic29C2×D411yescharacteristic
133C2×Dic29C2×D411yescharacteristic
134C2×Dic29C2×D411yescharacteristic
135D116—21no—
136D116#4112yes—
137C4×D29—21no—
138C4×D29—21no—
139C4×D29—81no—
140C4×D29—81no—
141C8×C29—21no—
142C8×C29—21no—
143#6597—21no—
144#6597—21no—
145#3123—291nomaximal, Sylow
146C22×C29—22no—
147C22×C29—41no—
148C22×C29—41no—
149C22×C29C22×D411yescharacteristic
150C2×D29—21no—
151C2×D29—22no—
152C2×D29—21no—
153C2×D29—21no—
154C2×D29—41no—
155C2×D29—41no—
156C2×D29—84no—
157C4×C29—21no—
158C4×C29—21no—
159C4×C29—41no—
160C4×C29—41no—
161C4×C29—41no—
162C4×C29C2×#4111yescharacteristic
163C4×C29C2×#4111yescharacteristic
164Dic29—21no—
165Dic29—21no—
166Dic29—21no—
167Dic29—41no—
168Dic29—41no—
169Dic29—41no—
170#541—291no—
171#518—291no—
172#485—291no—
173#485—291no—
174#478—291no—
175#478—291no—
176#461—291no—
177#461D2911yescharacteristic, complemented
178#450—291no—
179#450—291no—
180#440—291no—
181#440—291no—
182C4×SD16—291no—
183C4×SD16—291no—
184#433—291no—
185C2×C29—42no—
186C2×C29#52511yescharacteristic
187C2×C29#57711yescharacteristic
188C2×C29#57711yescharacteristic
189D29—41no—
190D29—42no—
191C22×D4—291no—
192C2×SD16—291no—
193C2×SD16—291no—
194C2×SD16C2×D2911yescharacteristic
195C2×SD16C2×D2911yescharacteristic
196C4⋊Q8C2×D2911yescharacteristic, complemented
197#126—581no—
198#126—581no—
199#125—291no—
200#125—581no—
201#125—581no—
202C22⋊Q8—291no—
203C22⋊Q8—291no—
204C4×Q8—291no—
205C4×Q8—291no—
206C4×D4—291no—
207C4×D4—291no—
208C4×D4—291no—
209C4×D4—581no—
210C4×D4—581no—
211C4×D4C2×D2911yescharacteristic
212#117—291no—
213#117—291no—
214C2×C22⋊C4—581no—
215C2×C22⋊C4—581no—
216#107—291no—
217#107—291no—
218#106—291no—
219#106—291no—
220C4⋊C8—291no—
221C4⋊C8C2×D2911yescharacteristic, complemented
222#103—291no—
223#103—291no—
224#103C2×D2911yescharacteristic, complemented
225#103C2×D2911yescharacteristic, complemented
226#102—291no—
227#102—291no—
228#102—291no—
229#102—291no—
230C22⋊C8—291no—
231C22⋊C8—291no—
232#97—291no—
233C4×C8—291no—
234C29#312311yescharacteristic, complemented, Sylow
235C24—581no—
236C2×Q8C22×D2911yescharacteristic
237C2×Q8C22×D2911yescharacteristic
238C2×D4—291no—
239C2×D4—581no—
240C2×D4—582no—
241C2×D4—582no—
242C2×D4C22×D2911yescharacteristic
243C22×C4—21no—
244C22×C4—291no—
245C22×C4—581no—
246C22×C4—581no—
247C22×C4—581no—
248SD16—22no—
249SD16—22no—
250SD16—582no—
251SD16—582no—
252C2×C8—291no—
253C2×C8—291no—
254C2×C8C22×D2911yescharacteristic
255C2×C8C22×D2911yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—291no—
259C4⋊C4—291no—
260C4⋊C4—291no—
261C4⋊C4—291no—
262C4⋊C4—291no—
263C4⋊C4—581no—
264C4⋊C4—581no—
265C4⋊C4—581no—
266C4⋊C4—581no—
267C4⋊C4—581no—
268C4⋊C4—581no—
269C4⋊C4C22×D2911yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—291no—
272C22⋊C4—291no—
273C22⋊C4—581no—
274C22⋊C4—581no—
275C22⋊C4—581no—
276C22⋊C4—581no—
277C22⋊C4—581no—
278C22⋊C4—581no—
279C42—291no—
280C42—581no—
281C42—581no—
282C42—581no—
283C42C22×D2911yescharacteristic
284C23—21no—
285C23—291no—
286C23—584no—
287C23—581no—
288C23—2321no—
289C23—2321no—
290Q8—21no—
291Q8—21no—
292Q8—21no—
293Q8—21no—
294D4—21no—
295D4—292no—
296D4—584no—
297D4—581no—
298D4#9080712yes—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—81no—
303C2×C4—291no—
304C2×C4—291no—
305C2×C4—291no—
306C2×C4—581no—
307C2×C4—581no—
308C2×C4—581no—
309C2×C4—581no—
310C2×C4—581no—
311C2×C4—2321no—
312C2×C4—2321no—
313C2×C4—2321no—
314C2×C4D4×D2911yescharacteristic
315C2×C4D4×D2911yescharacteristic
316C2×C4C23×D2911yescharacteristic
317C8—21no—
318C8—21no—
319C8—581no—
320C8—581no—
321C22—22no—
322C22—41no—
323C22—41no—
324C22—581no—
325C22—582no—
326C22—581no—
327C22—581no—
328C22—1161no—
329C22—1161no—
330C22—2324no—
331C22C2×D4×D2911yescharacteristic
332C4—21no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—581no—
338C4—581no—
339C4—581no—
340C4—1161no—
341C4—1161no—
342C4—1161no—
343C4C2×#9080711yescharacteristic
344C4#41×D2911yescharacteristic
345C2—42no—
346C2—1161no—
347C2—1162no—
348C2#1427167311yescharacteristic
349C2#1427196911yescharacteristic
350C2#1427197211yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#461C2
socleC22×C29C22×D4
prime radicalC2×D4×D29C22
hypercenter#461D29
hypocenterC29#3123
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #14271774C2semidirect
3. #14271503C2semidirect
4. #14271502C2semidirect
5. #14271464C2semidirect
6. #14271463C2semidirect
7. #14271365C2semidirect
10. #14271266C2semidirect
11. #14271264C2semidirect
12. SD16×Dic29C2semidirect
13. #14271248C2semidirect
14. #14271223C2semidirect
15. C29×#461C2semidirect
19. C29×C4⋊Q8C22semidirect
23. Q8×Dic29C22semidirect
24. Q8×Dic29C22semidirect
40. #11745232C22semidirect
41. C29×C4⋊C8C22semidirect
42. C29×#103C22semidirect
43. C29×#103C22semidirect
44. #11745183C22semidirect
45. #11745183C22semidirect
52. #11745166C22semidirect
53. #11745165C22semidirect
54. #11745163C22semidirect
55. C8×Dic29C22semidirect
56. #11745156C22semidirect
57. #11745155C22semidirect
58. C4⋊#6597C22semidirect
177. #461D29semidirect
196. C4⋊Q8C2×D29semidirect
221. C4⋊C8C2×D29semidirect
224. #103C2×D29semidirect
225. #103C2×D29semidirect
234. C29#3123semidirect

Maximal subgroups

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

subgroupindex
#142717742
#142716352
#142715032
#142715022
#142714642
#142714632
#142713652
#142713122
#142712662
#142712642
SD16×Dic292
#142712482
#142712232
C29×#4612
#312329