Finite Group Databasebeta

← #37535394

Subgroups — #37535394

Order 23168.

238 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 55 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#26041849C211yesmaximal, characteristic
2#26041251C212yesmaximal
3#26041074C211yesmaximal, characteristic, complemented
4#26041073C212yesmaximal, complemented
5#354×C181C211yesmaximal, characteristic, complemented
6C2×#15668448C2211yescharacteristic
7C2×Q8×D181C411yescharacteristic, complemented
8#19153816C411yescharacteristic, complemented
9#19153814C411yescharacteristic, complemented
10#19153803C2211yescharacteristic
11#19153798—22no—
12#19153793—22no—
13#19153773C411yescharacteristic, complemented
14#19153772—22no—
15#19153731C2212yes—
16#19153730—22no—
17#124×C181C2211yescharacteristic
18#99×C181C2212yes—
19#15668448—42no—
20C2×Dic362—21no—
21C2×Dic362C2×C411yescharacteristic
22C2×Dic362C2×C411yescharacteristic
23Q8×D181—42no—
24C2×C22⋊D181D412yes—
25C22×Dic181D412yes—
26C2×C4×D181—21no—
27C2×C4×D181C2×C411yescharacteristic
28C4⋊Dic181—22no—
29#15668428—21no—
30#15668428—22no—
31#15668428—42no—
32C22⋊Dic181—22no—
33C22⋊Dic181—22no—
34#15668426—21no—
35C4×Dic181—42no—
36C4×Dic181C2×C411yescharacteristic
37C2×Q8×C181C2×C411yescharacteristic
38C2×D4×C181C2311yescharacteristic
39C22⋊C4×C181—22no—
40C22⋊C4×C181—22no—
41C42×C181C2×C411yescharacteristic
42C22×D181C22⋊C411yescharacteristic
43Dic362—41no—
44Dic362—42no—
45Dic362—41no—
46C22⋊D181—42no—
47C2×Dic181—22no—
48C2×Dic181—22no—
49C2×Dic181—21no—
50C2×Dic181—21no—
51C2×Dic181—42no—
52C2×Dic181C22⋊C412yes—
53C2×Dic181C22⋊C411yescharacteristic
54C4×D181—22no—
55C4×D181—42no—
56C23×C181C2×D412yes—
57Q8×C181—41no—
58D4×C181—41no—
59C2×C4×C181—21no—
60C2×C4×C181—21no—
61C2×C4×C181—42no—
62C2×C4×C181C22×C411yescharacteristic
63C22×C181—22no—
64C22×C181—42no—
65C22×C181C2×C22⋊C411yescharacteristic
66C2×D181—21no—
67C2×D181—41no—
68C4×C181—21no—
69C4×C181—41no—
70C4×C181—41no—
71C4×C181—82no—
72Dic181—22no—
73Dic181—41no—
74Dic181—41no—
75Dic181—82no—
76Dic181#9912yes—
77C2×C181—21no—
78C2×C181—42no—
79C2×C181C2×#9911yescharacteristic
80D181—41no—
81C181#212911yescharacteristic, complemented, Sylow
82#2129—1811nomaximal, Sylow
83#536—1811no—
84#410—1812no—
85#354—1811no—
86#354—1812no—
87#354D18111yescharacteristic, complemented
88C2×#41—1811no—
89C22×Q8—1811no—
90C4⋊Q8—1811no—
91C4⋊Q8—1811no—
92#124—1811no—
93#124C2×D18111yescharacteristic
94#123—3622no—
95C22⋊Q8—3622no—
96#117—3622no—
97#117—1811no—
98#99—3622no—
99#99—1812no—
100#99C2×D18112yes—
101#41—7242no—
102C2×Q8—3621no—
103C2×Q8—1811no—
104C2×Q8—1811no—
105C2×Q8—7242no—
106C2×Q8C4×D18111yescharacteristic
107C2×D4—1812no—
108C2×D4C22×D18111yescharacteristic
109C22×C4—3621no—
110C22×C4—1812no—
111C22×C4—1811no—
112C4⋊C4—3621no—
113C4⋊C4—3622no—
114C4⋊C4—3622no—
115C4⋊C4—7242no—
116C22⋊C4—22no—
117C22⋊C4—22no—
118C22⋊C4—3621no—
119C22⋊C4—3622no—
120C22⋊C4—3622no—
121C42—1811no—
122C42—7242no—
123C42C4×D18111yescharacteristic
124C23—1811no—
125C23D4×D18112yes—
126Q8—41no—
127Q8—7241no—
128Q8—7241no—
129Q8—7242no—
130D4—41no—
131D4—7242no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—42no—
135C2×C4—3622no—
136C2×C4—3622no—
137C2×C4—3622no—
138C2×C4—3621no—
139C2×C4—3621no—
140C2×C4—1812no—
141C2×C4—1811no—
142C2×C4—7242no—
143C2×C4—7242no—
144C2×C4C2×C4×D18111yescharacteristic
145C22—22no—
146C22—42no—
147C22—3621no—
148C22—7241no—
149C22C22⋊C4×D18111yescharacteristic
150C4—21no—
151C4—41no—
152C4—41no—
153C4—82no—
154C4—3622no—
155C4—14482no—
156C4—1812no—
157C4—7241no—
158C4—7241no—
159C2—21no—
160C2—42no—
161C2—7241no—
162C2#99×D18111yescharacteristic
subgroupG/H
centerC2#99×D181
commutatorC2×C4×C181C22×C4
FrattiniC2×D4C22×D181
Fitting#354×C181C2
socleC2×C181C2×#99
prime radicalC2×#15668448C22
cosocleC2×D4×C181C23
hypercenter#354D181
hypocenterC181#2129
LCSG ▷ C2×C4×C181 ▷ C22×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
3. #26041074C2semidirect
4. #26041073C2semidirect
5. #354×C181C2semidirect
7. C2×Q8×D181C4semidirect
8. #19153816C4semidirect
9. #19153814C4semidirect
13. #19153773C4semidirect
81. C181#2129semidirect
87. #354D181semidirect

Maximal subgroups

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

subgroupindex
#260418492
#260412512
#260410742
#260410732
#354×C1812
#2129181