Finite Group Databasebeta

← #30682614

Subgroups — #30682614

Order 16832.

248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 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#22554463C211yesmaximal, characteristic, complemented
2#22554463C211yesmaximal, characteristic, complemented
3#22554456C211yesmaximal, characteristic, complemented
4#22554454C211yesmaximal, characteristic, complemented
5#22554453C211yesmaximal, characteristic, complemented
6#22554452C211yesmaximal, characteristic, complemented
7#22554449C211yesmaximal, characteristic, complemented
8#22554447C211yesmaximal, characteristic, complemented
9#22554439C211yesmaximal, characteristic
10C4×C22⋊D263C211yesmaximal, characteristic, complemented
11(C22⋊D263)⋊C4C211yesmaximal, characteristic, complemented
12#22554429C211yesmaximal, characteristic, complemented
13#22554426C211yesmaximal, characteristic, complemented
14C2×C22⋊Dic263C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×C263C211yesmaximal, characteristic, complemented
16C2×Dic526C2211yescharacteristic, complemented
17C2×C22⋊D263C2211yescharacteristic
18C2×C22⋊D263C2211yescharacteristic
19C2×C22⋊D263C2211yescharacteristic
20C22×Dic263C2211yescharacteristic
21C22×Dic263C2211yescharacteristic
22C2×C4×D263C2211yescharacteristic, complemented
23C4⋊Dic263C2211yescharacteristic, complemented
24C4⋊Dic263C2211yescharacteristic, complemented
25C4⋊Dic263C2211yescharacteristic, complemented
26Dic263⋊C4C2211yescharacteristic, complemented
27Dic263⋊C4C2211yescharacteristic, complemented
28Dic263⋊C4C2211yescharacteristic, complemented
29Dic263⋊C4C2211yescharacteristic, complemented
30Dic263⋊C4C2211yescharacteristic, complemented
31C22⋊Dic263C2211yescharacteristic
32C22⋊Dic263C2211yescharacteristic
33C22⋊Dic263C2211yescharacteristic
34C22⋊Dic263C2211yescharacteristic
35C22⋊Dic263C2211yescharacteristic
36C22⋊Dic263C2211yescharacteristic
37C22⋊Dic263C2211yescharacteristic
38(C2×D263)⋊C4C2211yescharacteristic, complemented
39(C2×D263)⋊C4C2211yescharacteristic, complemented
40(C2×D263)⋊C4C2211yescharacteristic, complemented
41C4×Dic263C2211yescharacteristic, complemented
42C4×Dic263C2211yescharacteristic, complemented
43C4×Dic263C2211yescharacteristic, complemented
44C24×C263C2211yescharacteristic
45C22×C4×C263C2211yescharacteristic
46C22×C4×C263C2211yescharacteristic
47C22⋊C4×C263C2211yescharacteristic
48C22⋊C4×C263C2211yescharacteristic
49C22⋊C4×C263C2211yescharacteristic
50C22⋊C4×C263C2211yescharacteristic
51C22×D263C2311yescharacteristic
52Dic526—41no—
53C22⋊D263—22no—
54C22⋊D263—22no—
55C22⋊D263—41no—
56C2×Dic263—22no—
57C2×Dic263—41no—
58C2×Dic263C2311yescharacteristic
59C2×Dic263C2311yescharacteristic
60C2×Dic263C2311yescharacteristic
61C2×Dic263C2311yescharacteristic
62C2×Dic263C2311yescharacteristic
63C2×Dic263C2311yescharacteristic
64C2×Dic263C2311yescharacteristic
65C4×D263—41no—
66C23×C263—22no—
67C23×C263—22no—
68C23×C263—41no—
69C23×C263C2311yescharacteristic
70C23×C263C2311yescharacteristic
71C23×C263C2311yescharacteristic
72C2×C4×C263—22no—
73C2×C4×C263—41no—
74C2×C4×C263C2311yescharacteristic
75C2×C4×C263C2311yescharacteristic
76C2×C4×C263C2311yescharacteristic
77C2×C4×C263C2311yescharacteristic
78C22×C263—21no—
79C22×C263—21no—
80C22×C263—21no—
81C22×C263—21no—
82C22×C263—21no—
83C22×C263—21no—
84C22×C263—21no—
85C22×C263—44no—
86C22×C263#4112yes—
87C22×C263#4112yes—
88C22×C263C2411yescharacteristic
89C2×D263—21no—
90C2×D263—21no—
91C2×D263—21no—
92C4×C263—21no—
93C4×C263—21no—
94C4×C263—21no—
95C4×C263—21no—
96Dic263—21no—
97Dic263—21no—
98Dic263—21no—
99Dic263—21no—
100Dic263—21no—
101Dic263—21no—
102Dic263—21no—
103C2×C263—22no—
104C2×C263—22no—
105C2×C263—41no—
106C2×C263C2×#4111yescharacteristic
107C2×C263C2×#4111yescharacteristic
108C2×C263H(5,𝔽2)11yescharacteristic
109D263—41no—
110C263#55111yescharacteristic, complemented, Sylow
111#551—2631nomaximal, Sylow
112#126—2631no—
113#126—2631no—
114#124—2631no—
115#123—2631no—
116#123—2631no—
117#123—2631no—
118C22⋊Q8—2631no—
119C22⋊Q8—2631no—
120#120—2631no—
121C4×D4—2631no—
122C4×D4—2631no—
123#117—2631no—
124#117—2631no—
125C2×C22⋊C4—2631no—
126C2×C22⋊C4D26311yescharacteristic, complemented
127C24C2×D26311yescharacteristic
128C2×Q8—2631no—
129C2×D4—2631no—
130C2×D4—2631no—
131C2×D4—2631no—
132C22×C4—2631no—
133C22×C4—2631no—
134C22×C4—2631no—
135C22×C4C2×D26311yescharacteristic
136C22×C4C2×D26311yescharacteristic
137C4⋊C4—2631no—
138C4⋊C4—2631no—
139C4⋊C4—2631no—
140C4⋊C4—2631no—
141C4⋊C4—2631no—
142C4⋊C4—2631no—
143C4⋊C4—2631no—
144C4⋊C4—2631no—
145C22⋊C4—2631no—
146C22⋊C4—2631no—
147C22⋊C4—2631no—
148C22⋊C4—2631no—
149C22⋊C4—2631no—
150C22⋊C4—2631no—
151C22⋊C4—2631no—
152C22⋊C4—2631no—
153C22⋊C4—2631no—
154C22⋊C4—2631no—
155C22⋊C4C2×D26311yescharacteristic
156C22⋊C4C2×D26311yescharacteristic
157C22⋊C4C2×D26311yescharacteristic
158C22⋊C4C2×D26311yescharacteristic
159C42—2631no—
160C42—2631no—
161C42—2631no—
162C23—22no—
163C23—22no—
164C23—41no—
165C23—2631no—
166C23C22×D26311yescharacteristic
167C23C22×D26311yescharacteristic
168C23C22×D26311yescharacteristic
169Q8—10521no—
170D4—5262no—
171D4—5262no—
172D4—10521no—
173C2×C4—22no—
174C2×C4—41no—
175C2×C4—2631no—
176C2×C4—2631no—
177C2×C4—2631no—
178C2×C4—2631no—
179C2×C4—2631no—
180C2×C4—2631no—
181C2×C4—2631no—
182C2×C4—5262no—
183C2×C4—10521no—
184C2×C4—10521no—
185C2×C4C22×D26311yescharacteristic
186C2×C4C22×D26311yescharacteristic
187C2×C4C22×D26311yescharacteristic
188C2×C4C22×D26311yescharacteristic
189C22—21no—
190C22—21no—
191C22—21no—
192C22—21no—
193C22—21no—
194C22—21no—
195C22—21no—
196C22—44no—
197C22—5261no—
198C22—5261no—
199C22—5261no—
200C22#1686237512yes—
201C22#1686237612yes—
202C22C23×D26311yescharacteristic
203C4—21no—
204C4—21no—
205C4—21no—
206C4—21no—
207C4—5261no—
208C4—5261no—
209C4—5261no—
210C4—5261no—
211C4—5261no—
212C4—5261no—
213C4—5261no—
214C2—22no—
215C2—22no—
216C2—41no—
217C2—10521no—
218C2C2×#1686237511yescharacteristic
219C2C2×#1686237611yescharacteristic
220C2#2255451511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D263
commutator, socle, cosocleC22×C263C24
FittingC2×C22⋊C4×C263C2
prime radical#22554439C2
hypercenterC2×C22⋊C4D263
hypocenterC263#551
LCSG ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #22554463C2semidirect
2. #22554463C2semidirect
3. #22554456C2semidirect
4. #22554454C2semidirect
5. #22554453C2semidirect
6. #22554452C2semidirect
7. #22554449C2semidirect
8. #22554447C2semidirect
10. C4×C22⋊D263C2semidirect
11. (C22⋊D263)⋊C4C2semidirect
12. #22554429C2semidirect
13. #22554426C2semidirect
14. C2×C22⋊Dic263C2semidirect
15. C2×C22⋊C4×C263C2semidirect
16. C2×Dic526C22semidirect
22. C2×C4×D263C22semidirect
23. C4⋊Dic263C22semidirect
24. C4⋊Dic263C22semidirect
25. C4⋊Dic263C22semidirect
26. Dic263⋊C4C22semidirect
27. Dic263⋊C4C22semidirect
28. Dic263⋊C4C22semidirect
29. Dic263⋊C4C22semidirect
30. Dic263⋊C4C22semidirect
38. (C2×D263)⋊C4C22semidirect
39. (C2×D263)⋊C4C22semidirect
40. (C2×D263)⋊C4C22semidirect
41. C4×Dic263C22semidirect
42. C4×Dic263C22semidirect
43. C4×Dic263C22semidirect
110. C263#551semidirect
126. C2×C22⋊C4D263semidirect

Maximal subgroups

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

subgroupindex
#225544632
#225544562
#225544542
#225544532
#225544522
#225544492
#225544472
#225544392
C4×C22⋊D2632
(C22⋊D263)⋊C42
#225544292
#225544262
C2×C22⋊Dic2632
C2×C22⋊C4×C2632
#551263