Finite Group Databasebeta

← #42119804

Subgroups — #42119804

Order 27584.

220 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#28352179C211yesmaximal, characteristic, complemented
2#28352176C211yesmaximal, characteristic, complemented
3#28352175C211yesmaximal, characteristic, complemented
4#28352172C211yesmaximal, characteristic, complemented
5#28352171C211yesmaximal, characteristic, complemented
6#28352170C211yesmaximal, characteristic, complemented
7#28352170C211yesmaximal, characteristic, complemented
8#28352168C211yesmaximal, characteristic, complemented
9#28352167C211yesmaximal, characteristic, complemented
10#28352166C211yesmaximal, characteristic, complemented
11#28352166C211yesmaximal, characteristic, complemented
12#28352161C211yesmaximal, characteristic, complemented
13#28352161C211yesmaximal, characteristic, complemented
14#28352160C211yesmaximal, characteristic, complemented
15#121×C431C211yesmaximal, characteristic, complemented
16C2×Dic862C2211yescharacteristic
17C2×Dic862C2211yescharacteristic
18C2×C22⋊D431C2211yescharacteristic
19C2×C22⋊D431C2211yescharacteristic
20C2×C22⋊D431C2211yescharacteristic
21C22×Dic431C2211yescharacteristic
22C22×Dic431C2211yescharacteristic
23C2×C4×D431C2211yescharacteristic
24C4⋊Dic431C2211yescharacteristic
25C4⋊Dic431C2211yescharacteristic
26Dic431⋊C4C2211yescharacteristic
27Dic431⋊C4C2211yescharacteristic
28Dic431⋊C4C2211yescharacteristic
29Dic431⋊C4C2211yescharacteristic
30Dic431⋊C4C2211yescharacteristic
31Dic431⋊C4C2211yescharacteristic
32Dic431⋊C4C2211yescharacteristic
33C22⋊Dic431C2211yescharacteristic
34C22⋊Dic431C2211yescharacteristic
35C22⋊Dic431C2211yescharacteristic
36C22⋊Dic431C2211yescharacteristic
37C22⋊Dic431C2211yescharacteristic
38C22⋊Dic431C2211yescharacteristic
39C22⋊Dic431C2211yescharacteristic
40(C2×D431)⋊C4C2211yescharacteristic
41(C2×D431)⋊C4C2211yescharacteristic
42(C2×D431)⋊C4C2211yescharacteristic
43C4×Dic431C2211yescharacteristic
44C2×D4×C431C2211yescharacteristic
45C2×D4×C431C2211yescharacteristic
46C2×D4×C431C2211yescharacteristic
47C22×C4×C431C2211yescharacteristic
48C4⋊C4×C431C2211yescharacteristic
49C22⋊C4×C431C2211yescharacteristic
50C22⋊C4×C431C2211yescharacteristic
51C22×D431C2311yescharacteristic
52Dic862—41no—
53Dic862—41no—
54C22⋊D431—41no—
55C22⋊D431—41no—
56C22⋊D431—41no—
57C2×Dic431—41no—
58C2×Dic431—41no—
59C2×Dic431C2311yescharacteristic
60C2×Dic431C2311yescharacteristic
61C2×Dic431C2311yescharacteristic
62C2×Dic431C2311yescharacteristic
63C2×Dic431C2311yescharacteristic
64C2×Dic431C2311yescharacteristic
65C2×Dic431C2311yescharacteristic
66C4×D431—41no—
67C23×C431C2311yescharacteristic
68C23×C431C2311yescharacteristic
69C23×C431C2311yescharacteristic
70D4×C431—41no—
71D4×C431—41no—
72D4×C431—41no—
73C2×C4×C431—41no—
74C2×C4×C431C2311yescharacteristic
75C2×C4×C431C2311yescharacteristic
76C2×C4×C431C2311yescharacteristic
77C2×C4×C431C2311yescharacteristic
78C22×C431—21no—
79C22×C431—21no—
80C22×C431—21no—
81C22×C431—21no—
82C22×C431—21no—
83C22×C431—21no—
84C22×C431—21no—
85C22×C431—21no—
86C22×C431—21no—
87C22×C431C2411yescharacteristic
88C2×D431—21no—
89C2×D431—21no—
90C2×D431—21no—
91C4×C431—21no—
92C4×C431—21no—
93C4×C431—21no—
94C4×C431—21no—
95Dic431—21no—
96Dic431—21no—
97Dic431—21no—
98Dic431—21no—
99Dic431—21no—
100Dic431—21no—
101Dic431—21no—
102C2×C431—41no—
103C2×C431—41no—
104C2×C431—41no—
105C2×C431H(5,𝔽2)11yescharacteristic
106C2×C431H(5,𝔽2)11yescharacteristic
107C2×C4312−1+411yescharacteristic
108D431—41no—
109C431#56211yescharacteristic, complemented, Sylow
110#562—4311nomaximal, Sylow
111#125—4311no—
112#124—4311no—
113#124—4311no—
114#123—4311no—
115#123—4311no—
116#123—4311no—
117#123—4311no—
118C22⋊Q8—4311no—
119C22⋊Q8—4311no—
120C22⋊Q8—4311no—
121C22⋊Q8—4311no—
122#121—4311no—
123#121—4311no—
124#121—4311no—
125#121D43111yescharacteristic, complemented
126C2×Q8—4311no—
127C2×Q8—4311no—
128C2×D4—4311no—
129C2×D4—4311no—
130C2×D4—4311no—
131C2×D4C2×D43111yescharacteristic
132C2×D4C2×D43111yescharacteristic
133C2×D4C2×D43111yescharacteristic
134C22×C4—4311no—
135C22×C4—4311no—
136C22×C4—4311no—
137C22×C4C2×D43111yescharacteristic
138C4⋊C4—4311no—
139C4⋊C4—4311no—
140C4⋊C4—4311no—
141C4⋊C4—4311no—
142C4⋊C4—4311no—
143C4⋊C4—4311no—
144C4⋊C4—4311no—
145C4⋊C4—4311no—
146C4⋊C4—4311no—
147C4⋊C4C2×D43111yescharacteristic
148C22⋊C4—4311no—
149C22⋊C4—4311no—
150C22⋊C4—4311no—
151C22⋊C4—4311no—
152C22⋊C4—4311no—
153C22⋊C4—4311no—
154C22⋊C4—4311no—
155C22⋊C4—4311no—
156C22⋊C4—4311no—
157C22⋊C4—4311no—
158C22⋊C4C2×D43111yescharacteristic
159C22⋊C4C2×D43111yescharacteristic
160C42—4311no—
161C23—4311no—
162C23C22×D43111yescharacteristic
163C23C22×D43111yescharacteristic
164C23C22×D43111yescharacteristic
165Q8—17241no—
166Q8—17241no—
167D4—41no—
168D4—41no—
169D4—41no—
170D4—17241no—
171D4—17241no—
172D4—17241no—
173C2×C4—41no—
174C2×C4—4311no—
175C2×C4—4311no—
176C2×C4—4311no—
177C2×C4—4311no—
178C2×C4—4311no—
179C2×C4—4311no—
180C2×C4—4311no—
181C2×C4—17241no—
182C2×C4—17241no—
183C2×C4—17241no—
184C2×C4C22×D43111yescharacteristic
185C2×C4C22×D43111yescharacteristic
186C2×C4C22×D43111yescharacteristic
187C2×C4C22×D43111yescharacteristic
188C22—21no—
189C22—21no—
190C22—21no—
191C22—21no—
192C22—21no—
193C22—21no—
194C22—21no—
195C22—21no—
196C22—21no—
197C22—8621no—
198C22—8621no—
199C22—8621no—
200C22C23×D43111yescharacteristic
201C4—21no—
202C4—21no—
203C4—21no—
204C4—21no—
205C4—8621no—
206C4—8621no—
207C4—8621no—
208C4—8621no—
209C4—8621no—
210C4—8621no—
211C4—8621no—
212C2—41no—
213C2—41no—
214C2—41no—
215C2—17241no—
216C2#2835223411yescharacteristic
217C2#2835223411yescharacteristic
218C2#2835223611yescharacteristic
subgroupG/H
center, FrattiniC22C23×D431
commutator, socle, cosocleC22×C431C24
Fitting#121×C431C2
hypercenter#121D431
hypocenterC431#562
LCSG ▷ C22×C431 ▷ C431
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #28352179C2semidirect
2. #28352176C2semidirect
3. #28352175C2semidirect
4. #28352172C2semidirect
5. #28352171C2semidirect
6. #28352170C2semidirect
7. #28352170C2semidirect
8. #28352168C2semidirect
9. #28352167C2semidirect
10. #28352166C2semidirect
11. #28352166C2semidirect
12. #28352161C2semidirect
13. #28352161C2semidirect
14. #28352160C2semidirect
15. #121×C431C2semidirect
109. C431#562semidirect
125. #121D431semidirect

Maximal subgroups

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

subgroupindex
#283521792
#283521762
#283521752
#283521722
#283521712
#283521702
#283521682
#283521672
#283521662
#283521612
#283521602
#121×C4312
#562431