Finite Group Databasebeta

← #44537310

Subgroups — #44537310

Order 31424.

250 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 95 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#30628330C211yesmaximal, characteristic, complemented
2#30628330C211yesmaximal, characteristic, complemented
3#30628324C211yesmaximal, characteristic, complemented
4#30628323C211yesmaximal, characteristic, complemented
5#30628319C211yesmaximal, characteristic, complemented
6#30628318C211yesmaximal, characteristic, complemented
7#30628314C211yesmaximal, characteristic, complemented
8#30628309C211yesmaximal, characteristic, complemented
9#30628309C211yesmaximal, characteristic, complemented
10#30628308C211yesmaximal, characteristic, complemented
11#30628306C211yesmaximal, characteristic, complemented
12D4×Dic491C211yesmaximal, characteristic, complemented
13(C22⋊D491)⋊C4C211yesmaximal, characteristic, complemented
14C2×C22⋊Dic491C211yesmaximal, characteristic, complemented
15#120×C491C211yesmaximal, characteristic, complemented
16C2×Dic982C2211yescharacteristic, complemented
17C2×C22⋊D491C2211yescharacteristic
18C2×C22⋊D491C2211yescharacteristic
19C2×C22⋊D491C2211yescharacteristic
20C2×C22⋊D491C2211yescharacteristic, complemented
21C22×Dic491C2211yescharacteristic
22C22×Dic491C2211yescharacteristic
23C22×Dic491C2211yescharacteristic, complemented
24C2×C4×D491C2211yescharacteristic, complemented
25C4⋊Dic491C2211yescharacteristic, complemented
26C4⋊Dic491C2211yescharacteristic, complemented
27Dic491⋊C4C2211yescharacteristic, complemented
28Dic491⋊C4C2211yescharacteristic, complemented
29Dic491⋊C4C2211yescharacteristic, complemented
30Dic491⋊C4C2211yescharacteristic, complemented
31C22⋊Dic491C2211yescharacteristic
32C22⋊Dic491C2211yescharacteristic
33C22⋊Dic491C2211yescharacteristic
34C22⋊Dic491C2211yescharacteristic
35C22⋊Dic491C2211yescharacteristic
36C22⋊Dic491C2211yescharacteristic
37C22⋊Dic491C2211yescharacteristic
38C22⋊Dic491C2211yescharacteristic, complemented
39C22⋊Dic491C2211yescharacteristic, complemented
40(C2×D491)⋊C4C2211yescharacteristic, complemented
41(C2×D491)⋊C4C2211yescharacteristic, complemented
42C4×Dic491C2211yescharacteristic, complemented
43C4×Dic491C2211yescharacteristic, complemented
44C24×C491C2211yescharacteristic
45C2×D4×C491C2211yescharacteristic
46C2×D4×C491C2211yescharacteristic
47C2×D4×C491C2211yescharacteristic
48C22⋊C4×C491C2211yescharacteristic
49C22⋊C4×C491C2211yescharacteristic
50C22⋊C4×C491C2211yescharacteristic
51C22×D491C2311yescharacteristic
52Dic982—41no—
53C22⋊D491—22no—
54C22⋊D491—41no—
55C22⋊D491—41no—
56C22⋊D491—41no—
57C2×Dic491—41no—
58C2×Dic491—41no—
59C2×Dic491—41no—
60C2×Dic491C2311yescharacteristic
61C2×Dic491C2311yescharacteristic
62C2×Dic491C2311yescharacteristic
63C2×Dic491C2311yescharacteristic
64C2×Dic491C2311yescharacteristic
65C2×Dic491C2311yescharacteristic
66C2×Dic491C2311yescharacteristic
67C4×D491—41no—
68C23×C491—22no—
69C23×C491—41no—
70C23×C491—41no—
71C23×C491C2311yescharacteristic
72C23×C491C2311yescharacteristic
73C23×C491C2311yescharacteristic
74C23×C491C2311yescharacteristic
75D4×C491—22no—
76D4×C491—41no—
77D4×C491—41no—
78C2×C4×C491C2311yescharacteristic
79C2×C4×C491C2311yescharacteristic
80C2×C4×C491C2311yescharacteristic
81C22×C491—21no—
82C22×C491—21no—
83C22×C491—21no—
84C22×C491—21no—
85C22×C491—21no—
86C22×C491—21no—
87C22×C491—21no—
88C22×C491—21no—
89C22×C491—21no—
90C22×C491—21no—
91C22×C491—21no—
92C22×C491—44no—
93C22×C491#4112yes—
94C22×C491C2411yescharacteristic
95C2×D491—21no—
96C2×D491—21no—
97C2×D491—21no—
98C4×C491—21no—
99C4×C491—21no—
100C4×C491—21no—
101Dic491—21no—
102Dic491—21no—
103Dic491—21no—
104Dic491—21no—
105Dic491—21no—
106Dic491—21no—
107Dic491—21no—
108C2×C491—22no—
109C2×C491—41no—
110C2×C491—41no—
111C2×C491—41no—
112C2×C491C2×#4111yescharacteristic
113C2×C491H(5,𝔽2)11yescharacteristic
114C2×C491H(5,𝔽2)11yescharacteristic
115D491—41no—
116C491#53811yescharacteristic, complemented, Sylow
117#538—4911nomaximal, Sylow
118#126—4911no—
119#126—4911no—
120#124—4911no—
121#124—4911no—
122#123—4911no—
123#123—4911no—
124C22⋊Q8—4911no—
125#121—4911no—
126#121—4911no—
127#121—4911no—
128#120—4911no—
129#120D49111yescharacteristic, complemented
130C4×D4—4911no—
131C4×D4—4911no—
132C2×C22⋊C4—4911no—
133C24C2×D49111yescharacteristic
134C2×Q8—4911no—
135C2×D4—4911no—
136C2×D4—4911no—
137C2×D4—4911no—
138C2×D4—4911no—
139C2×D4C2×D49111yescharacteristic
140C2×D4C2×D49111yescharacteristic
141C2×D4C2×D49111yescharacteristic
142C22×C4—4911no—
143C22×C4—4911no—
144C22×C4—4911no—
145C22×C4—4911no—
146C4⋊C4—4911no—
147C4⋊C4—4911no—
148C4⋊C4—4911no—
149C4⋊C4—4911no—
150C4⋊C4—4911no—
151C4⋊C4—4911no—
152C22⋊C4—4911no—
153C22⋊C4—4911no—
154C22⋊C4—4911no—
155C22⋊C4—4911no—
156C22⋊C4—4911no—
157C22⋊C4—4911no—
158C22⋊C4—4911no—
159C22⋊C4—4911no—
160C22⋊C4—4911no—
161C22⋊C4—4911no—
162C22⋊C4—4911no—
163C22⋊C4C2×D49111yescharacteristic
164C22⋊C4C2×D49111yescharacteristic
165C22⋊C4C2×D49111yescharacteristic
166C42—4911no—
167C42—4911no—
168C23—22no—
169C23—41no—
170C23—41no—
171C23—4911no—
172C23C22×D49111yescharacteristic
173C23C22×D49111yescharacteristic
174C23C22×D49111yescharacteristic
175C23C22×D49111yescharacteristic
176Q8—19641no—
177D4—22no—
178D4—41no—
179D4—41no—
180D4—19641no—
181D4—19641no—
182D4—19641no—
183D4—9822no—
184C2×C4—19641no—
185C2×C4—19641no—
186C2×C4—19641no—
187C2×C4—19641no—
188C2×C4—4911no—
189C2×C4—4911no—
190C2×C4—4911no—
191C2×C4—4911no—
192C2×C4—4911no—
193C2×C4—4911no—
194C2×C4—4911no—
195C2×C4C22×D49111yescharacteristic
196C2×C4C22×D49111yescharacteristic
197C2×C4C22×D49111yescharacteristic
198C22—21no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—21no—
207C22—21no—
208C22—21no—
209C22—44no—
210C22—9821no—
211C22—9821no—
212C22—9821no—
213C22#2146332712yes—
214C22C23×D49111yescharacteristic
215C4—21no—
216C4—21no—
217C4—21no—
218C4—9821no—
219C4—9821no—
220C4—9821no—
221C4—9821no—
222C4—9821no—
223C4—9821no—
224C4—9821no—
225C2—22no—
226C2—41no—
227C2—41no—
228C2—41no—
229C2—19641no—
230C2C2×#2146332711yescharacteristic
231C2#3062838211yescharacteristic
232C2#3062838211yescharacteristic
subgroupG/H
center, FrattiniC22C23×D491
commutator, socle, cosocleC22×C491C24
Fitting#120×C491C2
hypercenter#120D491
hypocenterC491#538
LCSG ▷ C22×C491 ▷ C491
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. #30628330C2semidirect
2. #30628330C2semidirect
3. #30628324C2semidirect
4. #30628323C2semidirect
5. #30628319C2semidirect
6. #30628318C2semidirect
7. #30628314C2semidirect
8. #30628309C2semidirect
9. #30628309C2semidirect
10. #30628308C2semidirect
11. #30628306C2semidirect
12. D4×Dic491C2semidirect
13. (C22⋊D491)⋊C4C2semidirect
14. C2×C22⋊Dic491C2semidirect
15. #120×C491C2semidirect
16. C2×Dic982C22semidirect
20. C2×C22⋊D491C22semidirect
23. C22×Dic491C22semidirect
24. C2×C4×D491C22semidirect
25. C4⋊Dic491C22semidirect
26. C4⋊Dic491C22semidirect
27. Dic491⋊C4C22semidirect
28. Dic491⋊C4C22semidirect
29. Dic491⋊C4C22semidirect
30. Dic491⋊C4C22semidirect
38. C22⋊Dic491C22semidirect
39. C22⋊Dic491C22semidirect
40. (C2×D491)⋊C4C22semidirect
41. (C2×D491)⋊C4C22semidirect
42. C4×Dic491C22semidirect
43. C4×Dic491C22semidirect
116. C491#538semidirect
129. #120D491semidirect

Maximal subgroups

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

subgroupindex
#306283302
#306283242
#306283232
#306283192
#306283182
#306283142
#306283092
#306283082
#306283062
D4×Dic4912
(C22⋊D491)⋊C42
C2×C22⋊Dic4912
#120×C4912
#538491