Finite Group Databasebeta

← #37565810

Subgroups — #37565810

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×#20258606C211yesmaximal, characteristic, complemented
2C2×D4×D379C211yesmaximal, characteristic, complemented
3#27131327C212yesmaximal, complemented
4#27131317C212yesmaximal, complemented
5#27131306C211yesmaximal, characteristic, complemented
6#27131305C211yesmaximal, characteristic, complemented
7#27131302C211yesmaximal, characteristic, complemented
8#27131301C212yesmaximal, complemented
9#27131299C212yesmaximal, complemented
10#27131289C211yesmaximal, characteristic, complemented
11#121×C379C211yesmaximal, characteristic, complemented
12C23×D379C2212yes—
13#20258606—24no—
14C2×Dic758C2211yescharacteristic, complemented
15C2×D1516C2211yescharacteristic
16C2×D1516C2211yescharacteristic
17C2×D1516C2212yescomplemented
18C2×C22⋊D379C2211yescharacteristic
19C2×C22⋊D379C2212yes—
20C2×C22⋊D379C2211yescharacteristic, complemented
21C2×C22⋊D379C2212yescomplemented
22C2×C22⋊D379C2212yescomplemented
23D4×D379—24no—
24C2×C4×D379C2211yescharacteristic
25C2×C4×D379C2211yescharacteristic, complemented
26C4⋊Dic379C2211yescharacteristic, complemented
27C22⋊Dic379C2212yescomplemented
28(C2×D379)⋊C4C2212yes—
29(C2×D379)⋊C4C2212yescomplemented
30(C2×D379)⋊C4C2212yescomplemented
31C4×Dic379C2212yescomplemented
32C2×D4×C379C2211yescharacteristic
33C2×D4×C379C2212yescomplemented
34C22×C4×C379C2211yescharacteristic, complemented
35C4⋊C4×C379C2211yescharacteristic, complemented
36C22⋊C4×C379C2212yescomplemented
37C22×D379—24no—
38C22×D379—42no—
39C22×D379—42no—
40C22×D379C2312yes—
41C22×D379C2311yescharacteristic
42C22×D379C2311yescharacteristic
43Dic758—22no—
44D1516—22no—
45D1516—22no—
46D1516—42no—
47C22⋊D379—22no—
48C22⋊D379—24no—
49C22⋊D379—22no—
50C22⋊D379—42no—
51C22⋊D379—42no—
52C2×Dic379C2312yes—
53C2×Dic379C2311yescharacteristic
54C2×Dic379C2311yescharacteristic
55C4×D379—22no—
56C4×D379D414yescomplemented
57C23×C379C2312yes—
58C23×C379C2311yescharacteristic
59D4×C379—22no—
60D4×C379—42no—
61C2×C4×C379—22no—
62C2×C4×C379C2311yescharacteristic
63C2×C4×C379C2312yes—
64C2×C4×C379C2311yescharacteristic
65C22×C379—21no—
66C22×C379—22no—
67C22×C379—21no—
68C22×C379—22no—
69C22×C379—21no—
70C22×C379—22no—
71C22×C379C2411yescharacteristic
72C2×D379—21no—
73C2×D379—21no—
74C2×D379—21no—
75C2×D379—22no—
76C2×D379—21no—
77C2×D379—22no—
78C2×D379—21no—
79C2×D379—22no—
80C2×D379—48no—
81C2×D379C2×D412yes—
82C4×C379—21no—
83C4×C379—22no—
84C4×C379C2×D412yes—
85Dic379—21no—
86Dic379—22no—
87Dic379C2×D412yes—
88C2×C379—42no—
89C2×C379—41no—
90C2×C379C22×D411yescharacteristic
91C2×C379H(5,𝔽2)11yescharacteristic
92C2×C379H(5,𝔽2)11yescharacteristic
93D379—22no—
94D379—41no—
95D379—42no—
96C379#53511yescharacteristic, complemented, Sylow
97#535—3791nomaximal, Sylow
98C2×#41—3791no—
99C22×D4—3791no—
100#127—3792no—
101#124—3792no—
102#121—3791no—
103#121—3791no—
104#121—3791no—
105#121D37911yescharacteristic, complemented
106#120—3792no—
107#120—3792no—
108#117—3791no—
109C24—3792no—
110#41—7584no—
111C2×Q8—3791no—
112C2×D4—3792no—
113C2×D4—3792no—
114C2×D4—3791no—
115C2×D4—3792no—
116C2×D4—3791no—
117C2×D4—3792no—
118C2×D4—3791no—
119C2×D4—3791no—
120C2×D4—7584no—
121C2×D4C2×D37911yescharacteristic
122C2×D4C2×D37912yescomplemented
123C22×C4—3791no—
124C22×C4—3791no—
125C22×C4C2×D37911yescharacteristic, complemented
126C4⋊C4—3791no—
127C4⋊C4C2×D37911yescharacteristic, complemented
128C22⋊C4—3792no—
129C22⋊C4—3792no—
130C22⋊C4—3792no—
131C22⋊C4—3792no—
132C22⋊C4C2×D37912yescomplemented
133C42—3792no—
134C23—3791no—
135C23—3792no—
136C23—3791no—
137C23—15162no—
138C23—15162no—
139C23—7584no—
140C23C22×D37912yes—
141C23C22×D37911yescharacteristic
142Q8—7582no—
143D4—22no—
144D4—42no—
145D4—15162no—
146D4—15162no—
147D4—15162no—
148D4—7582no—
149D4—7584no—
150D4—7582no—
151D4—7582no—
152D4—7582no—
153C2×C4—22no—
154C2×C4—3791no—
155C2×C4—3794no—
156C2×C4—3792no—
157C2×C4—3791no—
158C2×C4—7582no—
159C2×C4C22×D37912yes—
160C2×C4C22×D37911yescharacteristic
161C2×C4C22×D37911yescharacteristic
162C22—21no—
163C22—22no—
164C22—21no—
165C22—22no—
166C22—21no—
167C22—22no—
168C22—3792no—
169C22—15168no—
170C22—7581no—
171C22—7582no—
172C22—7581no—
173C22—7582no—
174C22—7581no—
175C22—7582no—
176C22—7581no—
177C22—7581no—
178C22C23×D37911yescharacteristic
179C4—21no—
180C4—22no—
181C4—3792no—
182C4—7581no—
183C4—7582no—
184C4D4×D37912yes—
185C2—42no—
186C2—41no—
187C2—15162no—
188C2—15161no—
189C2—7582no—
190C2C2×D4×D37911yescharacteristic
191C2#2713137611yescharacteristic
192C2#2713137711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D379
commutator, socle, cosocleC22×C379C24
Fitting#121×C379C2
hypercenter#121D379
hypocenterC379#535
LCSG ▷ C22×C379 ▷ C379
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×#20258606C2semidirect
2. C2×D4×D379C2semidirect
3. #27131327C2semidirect
4. #27131317C2semidirect
5. #27131306C2semidirect
6. #27131305C2semidirect
7. #27131302C2semidirect
8. #27131301C2semidirect
9. #27131299C2semidirect
10. #27131289C2semidirect
11. #121×C379C2semidirect
14. C2×Dic758C22semidirect
17. C2×D1516C22semidirect
20. C2×C22⋊D379C22semidirect
21. C2×C22⋊D379C22semidirect
22. C2×C22⋊D379C22semidirect
25. C2×C4×D379C22semidirect
26. C4⋊Dic379C22semidirect
27. C22⋊Dic379C22semidirect
29. (C2×D379)⋊C4C22semidirect
30. (C2×D379)⋊C4C22semidirect
31. C4×Dic379C22semidirect
33. C2×D4×C379C22semidirect
34. C22×C4×C379C22semidirect
35. C4⋊C4×C379C22semidirect
36. C22⋊C4×C379C22semidirect
56. C4×D379D4semidirect
96. C379#535semidirect
105. #121D379semidirect
122. C2×D4C2×D379semidirect
125. C22×C4C2×D379semidirect
127. C4⋊C4C2×D379semidirect
132. C22⋊C4C2×D379semidirect

Maximal subgroups

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

subgroupindex
C2×#202586062
C2×D4×D3792
#271313272
#271313172
#271313062
#271313052
#271313022
#271313012
#271312992
#271312892
#121×C3792
#535379