Finite Group Databasebeta

← C2×2−1+4×D181 #37548524

Subgroups — C2×2−1+4×D181 #37548524

Order 23168.

5872 conjugacy classes of subgroups; only the 3213 normal subgroups are shown.

normal subgroups only

This group has 5872 conjugacy classes of subgroups — too many to draw. Only its 3213 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×#19153864C215yesmaximal, complemented
2C2×#19153863C2110yesmaximal, complemented
32−1+4×D181C2132yesmaximal, direct product factor
4C2×#41×D181C2110yesmaximal, complemented
5C22×Q8×D181C215yesmaximal, complemented
6C2×2−1+4×C181C211yesmaximal, characteristic, complemented
7#19153864C22180yescomplemented
8#19153863C221160yescomplemented
9C2×#15668450C22110yescomplemented
10C2×#15668449C22130yescomplemented
11C2×#15668448C22130yescomplemented
12#41×D181C221160yescomplemented
13C22×Dic362C22115yescomplemented
14C2×Q8×D181C22110yes—
15C2×Q8×D181C22120yescomplemented
16C2×Q8×D181C22180yescomplemented
17C2×D4×D181C22110yes—
18C22×C4×D181C22115yes—
192−1+4×C181C22116yescomplemented
20C2×#41×C181C22110yescomplemented
21C22×Q8×C181C2215yescomplemented
22C23×D181C2315yes—
23#15668450C23180yescomplemented
24#15668449C231240yescomplemented
25#15668448C231240yescomplemented
26C2×Dic362C23130yes—
27C2×Dic362C231120yescomplemented
28Q8×D181C23180yes—
29Q8×D181C231160yescomplemented
30C2×D724C23110yes—
31C2×C22⋊D181C23120yes—
32D4×D181C23180yes—
33C22×Dic181C23115yes—
34C2×C4×D181C23110yes—
35C2×C4×D181C231120yes—
36C2×C4×D181C23130yes—
37#41×C181C23180yescomplemented
38C2×Q8×C181C23110yes—
39C2×Q8×C181C23140yescomplemented
40C2×D4×C181C23110yes—
41C22×C4×C181C23115yes—
42C22×D181—220no—
43C22×D181C24120yes—
44C22×D181C2415yes—
45C22×D181C2411yescharacteristic
46Dic362C241120yes—
47D724C24140yes—
48C22⋊D181C24180yes—
49C2×Dic181C24110yes—
50C2×Dic181C24160yes—
51C4×D181C24140yes—
52C4×D181C241120yes—
53C23×C181C2415yes—
54Q8×C181C24140yes—
55D4×C181C24140yes—
56C2×C4×C181C24110yes—
57C2×C4×C181C24160yes—
58C22×C181—210no—
59C22×C181C25110yes—
60C22×C181C2511yescharacteristic
61C2×D181—210no—
62C2×D181—240no—
63C2×D1812−1+414yesdirect product factor
64C2×D181C25110yes—
65C2×D181C2512yes—
66C4×C181C25120yes—
67Dic181C25120yes—
68C2×C181—210no—
69C2×C181C2×2−1+412yescomplemented
70C2×C181C2611yescharacteristic
71D181—210no—
72D181C2×2−1+414yesdirect product factor
73C181C22×2−1+411yescharacteristic, complemented, Sylow
74C22×2−1+4—1811nomaximal, Sylow
75C2×2−1+4—18132no—
76C2×2−1+4—18110no—
77C2×2−1+4—1815no—
78C2×2−1+4D18111yescharacteristic, direct product factor
79C22×#41—18110no—
80C23×Q8—1815no—
812−1+4—181160no—
822−1+4—18180no—
832−1+4C2×D181116yesdirect product factor
84C2×#41—181160no—
85C2×#41—18110no—
86C2×#41—18130no—
87C2×#41—18130no—
88C2×#41C2×D181110yescomplemented
89C22×Q8—18110no—
90C22×Q8—18120no—
91C22×Q8—18180no—
92C22×Q8—18115no—
93C22×Q8C2×D18115yescomplemented
94C22×D4—18110no—
95C23×C4—18115no—
96C24—1815no—
97#41—18180no—
98#41—181240no—
99#41—181240no—
100#41C22×D181180yescomplemented
101C2×Q8—18180no—
102C2×Q8—181160no—
103C2×Q8—18130no—
104C2×Q8—181120no—
105C2×Q8C22×D181110yes—
106C2×Q8C22×D181140yescomplemented
107C2×D4—18120no—
108C2×D4—18180no—
109C2×D4—18110no—
110C2×D4C22×D181110yes—
111C22×C4—18115no—
112C22×C4—18110no—
113C22×C4—181120no—
114C22×C4—18130no—
115C22×C4C22×D181115yes—
116C23—36220no—
117C23—18120no—
118C23—1815no—
119C23—1811no—
120C23C23×D18115yes—
121Q8—181120no—
122Q8C23×D181140yes—
123D4—18180no—
124D4—18140no—
125D4C23×D181140yes—
126C2×C4—18160no—
127C2×C4—18110no—
128C2×C4—18140no—
129C2×C4—181120no—
130C2×C4C23×D181160yes—
131C2×C4C23×D181110yes—
132C22—210no—
133C22—36240no—
134C22—36210no—
135C22—18110no—
136C22—1812no—
137C22—1814no—
138C22C24×D181110yes—
139C22C24×D18111yescharacteristic
140C4—18120no—
141C4C24×D181120yes—
142C2—210no—
143C2—36210no—
144C2—1814no—
145C22−1+4×D18112yesdirect product factor
146C2C25×D18111yescharacteristic
subgroupG/H
centerC22C24×D181
commutator, cosocleC2×C181C26
FrattiniC2C25×D181
FittingC2×2−1+4×C181C2
socleC22×C181C25
hypercenterC2×2−1+4D181
hypocenterC181C22×2−1+4
LCSG ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C2×2−1+4

Complements

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

NH ≅ G/Ntype
1. C2×#19153864C2semidirect
2. C2×#19153863C2semidirect
3. 2−1+4×D181C2direct (N × H)
4. C2×#41×D181C2semidirect
5. C22×Q8×D181C2semidirect
6. C2×2−1+4×C181C2semidirect
7. #19153864C22semidirect
8. #19153863C22semidirect
9. C2×#15668450C22semidirect
10. C2×#15668449C22semidirect
11. C2×#15668448C22semidirect
12. #41×D181C22semidirect
13. C22×Dic362C22semidirect
15. C2×Q8×D181C22semidirect
16. C2×Q8×D181C22semidirect
19. 2−1+4×C181C22semidirect
20. C2×#41×C181C22semidirect
21. C22×Q8×C181C22semidirect
23. #15668450C23semidirect
24. #15668449C23semidirect
25. #15668448C23semidirect
27. C2×Dic362C23semidirect
29. Q8×D181C23semidirect
37. #41×C181C23semidirect
39. C2×Q8×C181C23semidirect
63. C2×D1812−1+4direct (N × H)
69. C2×C181C2×2−1+4semidirect
72. D181C2×2−1+4direct (N × H)
73. C181C22×2−1+4semidirect
78. C2×2−1+4D181direct (N × H)
83. 2−1+4C2×D181direct (N × H)
88. C2×#41C2×D181semidirect
93. C22×Q8C2×D181semidirect
100. #41C22×D181semidirect
106. C2×Q8C22×D181semidirect
145. C22−1+4×D181direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191538642
C2×#191538632
2−1+4×D1812
C2×#41×D1812
C22×Q8×D1812
C2×2−1+4×C1812
C22×2−1+4181