Finite Group Databasebeta

← #37565809

Subgroups — #37565809

Order 24256.

334 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 103 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
1C2×#20258605C211yesmaximal, characteristic, complemented
2C22×C22⋊D379C211yesmaximal, characteristic, complemented
3#27131327C212yesmaximal, complemented
4#27131317C212yesmaximal, complemented
5#27131304C212yesmaximal, complemented
6#27131303C212yesmaximal, complemented
7#27131301C211yesmaximal, characteristic, complemented
8#27131300C211yesmaximal, characteristic, complemented
9#27131299C211yesmaximal, characteristic, complemented
10#27131287C211yesmaximal, characteristic, complemented
11#120×C379C211yesmaximal, characteristic, complemented
12C23×D379C2211yescharacteristic
13#20258605—24no—
14C2×Dic758C2211yescharacteristic, complemented
15C2×D1516C2212yescomplemented
16C2×C22⋊D379—24no—
17C2×C22⋊D379C2211yescharacteristic
18C2×C22⋊D379C2212yes—
19C2×C22⋊D379C2212yes—
20C2×C22⋊D379C2211yescharacteristic, complemented
21C2×C22⋊D379C2212yescomplemented
22C2×C22⋊D379C2212yescomplemented
23C22×Dic379C2211yescharacteristic
24C22×Dic379C2211yescharacteristic, complemented
25C2×C4×D379C2211yescharacteristic, complemented
26Dic379⋊C4C2212yescomplemented
27C22⋊Dic379C2211yescharacteristic
28C22⋊Dic379C2212yescomplemented
29(C2×D379)⋊C4C2212yescomplemented
30(C2×D379)⋊C4C2212yescomplemented
31C4×Dic379C2212yescomplemented
32C24×C379C2211yescharacteristic
33C2×D4×C379C2211yescharacteristic
34C2×D4×C379C2212yescomplemented
35C22⋊C4×C379C2211yescharacteristic
36C22⋊C4×C379C2212yescomplemented
37C22×D379—22no—
38C22×D379—42no—
39C22×D379C2312yes—
40C22×D379C2311yescharacteristic
41Dic758—22no—
42D1516—42no—
43C22⋊D379—22no—
44C22⋊D379—24no—
45C22⋊D379—24no—
46C22⋊D379—22no—
47C22⋊D379—42no—
48C22⋊D379—42no—
49C2×Dic379—22no—
50C2×Dic379D414yescomplemented
51C2×Dic379C2312yes—
52C2×Dic379C2311yescharacteristic
53C2×Dic379C2311yescharacteristic
54C2×Dic379C2311yescharacteristic
55C4×D379—22no—
56C23×C379—22no—
57C23×C379—42no—
58C23×C379C2312yes—
59C23×C379C2311yescharacteristic
60C23×C379C2311yescharacteristic
61D4×C379—22no—
62D4×C379—42no—
63C2×C4×C379C2312yes—
64C2×C4×C379C2311yescharacteristic
65C22×C379—22no—
66C22×C379—21no—
67C22×C379—22no—
68C22×C379—22no—
69C22×C379—22no—
70C22×C379—22no—
71C22×C379—44no—
72C22×C379C2×D412yes—
73C22×C379C2411yescharacteristic
74C2×D379—21no—
75C2×D379—22no—
76C2×D379—22no—
77C2×D379—22no—
78C2×D379—22no—
79C2×D379—44no—
80C4×C379—21no—
81C4×C379—22no—
82Dic379—21no—
83Dic379—22no—
84Dic379C2×D412yes—
85Dic379C2×D412yes—
86C2×C379—22no—
87C2×C379—41no—
88C2×C379—42no—
89C2×C379C22×D411yescharacteristic
90C2×C379H(5,𝔽2)12yes—
91D379—41no—
92D379—42no—
93C379#53511yescharacteristic, complemented, Sylow
94#535—3791nomaximal, Sylow
95C2×#41—3791no—
96C22×D4—3791no—
97#127—3792no—
98#124—3792no—
99#121—3792no—
100#121—3792no—
101#120—3791no—
102#120—3791no—
103#120—3791no—
104#120D37911yescharacteristic, complemented
105#117—3791no—
106C24—3791no—
107C24C2×D37911yescharacteristic
108#41—7584no—
109C2×Q8—3791no—
110C2×D4—3792no—
111C2×D4—3792no—
112C2×D4—3791no—
113C2×D4—3792no—
114C2×D4—3792no—
115C2×D4—3791no—
116C2×D4—3792no—
117C2×D4—7584no—
118C2×D4C2×D37911yescharacteristic
119C2×D4C2×D37912yescomplemented
120C22×C4—3791no—
121C22×C4—3791no—
122C22×C4—3791no—
123C4⋊C4—3792no—
124C22⋊C4—3791no—
125C22⋊C4—3792no—
126C22⋊C4—3792no—
127C22⋊C4—3792no—
128C22⋊C4C2×D37911yescharacteristic
129C22⋊C4C2×D37912yescomplemented
130C42—3792no—
131C23—22no—
132C23—42no—
133C23—3792no—
134C23—3791no—
135C23—15162no—
136C23—7582no—
137C23C22×D37912yes—
138C23C22×D37911yescharacteristic
139C23C22×D37911yescharacteristic
140Q8—7582no—
141D4—22no—
142D4—42no—
143D4—15162no—
144D4—15162no—
145D4—15162no—
146D4—7584no—
147D4—7584no—
148D4—7582no—
149D4—7582no—
150C2×C4—3794no—
151C2×C4—3791no—
152C2×C4—3791no—
153C2×C4—3792no—
154C2×C4—3791no—
155C2×C4—7582no—
156C2×C4—7582no—
157C2×C4C22×D37912yes—
158C2×C4C22×D37911yescharacteristic
159C22—22no—
160C22—21no—
161C22—22no—
162C22—22no—
163C22—22no—
164C22—22no—
165C22—44no—
166C22—15164no—
167C22—7581no—
168C22—7582no—
169C22—7582no—
170C22—7582no—
171C22—7582no—
172C22D4×D37912yes—
173C22C23×D37911yescharacteristic
174C4—21no—
175C4—22no—
176C4—3792no—
177C4—3792no—
178C4—7581no—
179C4—7582no—
180C2—22no—
181C2—42no—
182C2—41no—
183C2—15162no—
184C2—15161no—
185C2C2×D4×D37911yescharacteristic
186C2#2713137612yes—
subgroupG/H
center, FrattiniC22C23×D379
commutator, socle, cosocleC22×C379C24
Fitting#120×C379C2
hypercenter#120D379
hypocenterC379#535
LCSG ▷ C22×C379 ▷ C379
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. C2×#20258605C2semidirect
2. C22×C22⋊D379C2semidirect
3. #27131327C2semidirect
4. #27131317C2semidirect
5. #27131304C2semidirect
6. #27131303C2semidirect
7. #27131301C2semidirect
8. #27131300C2semidirect
9. #27131299C2semidirect
10. #27131287C2semidirect
11. #120×C379C2semidirect
14. C2×Dic758C22semidirect
15. C2×D1516C22semidirect
20. C2×C22⋊D379C22semidirect
21. C2×C22⋊D379C22semidirect
22. C2×C22⋊D379C22semidirect
24. C22×Dic379C22semidirect
25. C2×C4×D379C22semidirect
26. Dic379⋊C4C22semidirect
28. C22⋊Dic379C22semidirect
29. (C2×D379)⋊C4C22semidirect
30. (C2×D379)⋊C4C22semidirect
31. C4×Dic379C22semidirect
34. C2×D4×C379C22semidirect
36. C22⋊C4×C379C22semidirect
50. C2×Dic379D4semidirect
93. C379#535semidirect
104. #120D379semidirect
119. C2×D4C2×D379semidirect
129. C22⋊C4C2×D379semidirect

Maximal subgroups

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

subgroupindex
C2×#202586052
C22×C22⋊D3792
#271313272
#271313172
#271313042
#271313032
#271313012
#271313002
#271312992
#271312872
#120×C3792
#535379