Finite Group Databasebeta

← #34036694

Subgroups — #34036694

Order 18752.

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×#17989801C211yesmaximal, characteristic, complemented
2C22×C22⋊D293C211yesmaximal, characteristic, complemented
3#22627620C212yesmaximal, complemented
4#22627610C212yesmaximal, complemented
5#22627597C212yesmaximal, complemented
6#22627596C212yesmaximal, complemented
7#22627594C211yesmaximal, characteristic, complemented
8#22627593C211yesmaximal, characteristic, complemented
9#22627592C211yesmaximal, characteristic, complemented
10#22627580C211yesmaximal, characteristic, complemented
11#120×C293C211yesmaximal, characteristic, complemented
12C23×D293C2211yescharacteristic
13#17989801—24no—
14C2×Dic586C2211yescharacteristic, complemented
15C2×D1172C2212yescomplemented
16C2×C22⋊D293—24no—
17C2×C22⋊D293C2211yescharacteristic
18C2×C22⋊D293C2212yes—
19C2×C22⋊D293C2212yes—
20C2×C22⋊D293C2211yescharacteristic, complemented
21C2×C22⋊D293C2212yescomplemented
22C2×C22⋊D293C2212yescomplemented
23C22×Dic293C2211yescharacteristic
24C22×Dic293C2211yescharacteristic, complemented
25C2×C4×D293C2211yescharacteristic, complemented
26#17989781C2212yescomplemented
27C22⋊Dic293C2211yescharacteristic
28C22⋊Dic293C2212yescomplemented
29#17989779C2212yescomplemented
30#17989779C2212yescomplemented
31C4×Dic293C2212yescomplemented
32C24×C293C2211yescharacteristic
33C2×D4×C293C2211yescharacteristic
34C2×D4×C293C2212yescomplemented
35C22⋊C4×C293C2211yescharacteristic
36C22⋊C4×C293C2212yescomplemented
37C22×D293—22no—
38C22×D293—42no—
39C22×D293C2312yes—
40C22×D293C2311yescharacteristic
41Dic586—22no—
42D1172—42no—
43C22⋊D293—22no—
44C22⋊D293—24no—
45C22⋊D293—24no—
46C22⋊D293—22no—
47C22⋊D293—42no—
48C22⋊D293—42no—
49C2×Dic293—22no—
50C2×Dic293D414yescomplemented
51C2×Dic293C2312yes—
52C2×Dic293C2311yescharacteristic
53C2×Dic293C2311yescharacteristic
54C2×Dic293C2311yescharacteristic
55C4×D293—22no—
56C23×C293—22no—
57C23×C293—42no—
58C23×C293C2312yes—
59C23×C293C2311yescharacteristic
60C23×C293C2311yescharacteristic
61D4×C293—22no—
62D4×C293—42no—
63C2×C4×C293C2312yes—
64C2×C4×C293C2311yescharacteristic
65C22×C293—22no—
66C22×C293—21no—
67C22×C293—22no—
68C22×C293—22no—
69C22×C293—22no—
70C22×C293—22no—
71C22×C293—44no—
72C22×C293C2×D412yes—
73C22×C293C2411yescharacteristic
74C2×D293—21no—
75C2×D293—22no—
76C2×D293—22no—
77C2×D293—22no—
78C2×D293—22no—
79C2×D293—44no—
80C4×C293—21no—
81C4×C293—22no—
82Dic293—21no—
83Dic293—22no—
84Dic293C2×D412yes—
85Dic293C2×D412yes—
86C2×C293—22no—
87C2×C293—41no—
88C2×C293—42no—
89C2×C293C22×D411yescharacteristic
90C2×C293H(5,𝔽2)12yes—
91D293—41no—
92D293—42no—
93C293#53511yescharacteristic, complemented, Sylow
94#535—2931nomaximal, Sylow
95C2×#41—2931no—
96C22×D4—2931no—
97#127—2932no—
98#124—2932no—
99#121—2932no—
100#121—2932no—
101#120—2931no—
102#120—2931no—
103#120—2931no—
104#120D29311yescharacteristic, complemented
105#117—2931no—
106C24—2931no—
107C24C2×D29311yescharacteristic
108#41—5864no—
109C2×Q8—2931no—
110C2×D4—2931no—
111C2×D4—2932no—
112C2×D4—2932no—
113C2×D4—2931no—
114C2×D4—2932no—
115C2×D4—2932no—
116C2×D4—2932no—
117C2×D4—5864no—
118C2×D4C2×D29311yescharacteristic
119C2×D4C2×D29312yescomplemented
120C22×C4—2931no—
121C22×C4—2931no—
122C22×C4—2931no—
123C4⋊C4—2932no—
124C22⋊C4—2931no—
125C22⋊C4—2932no—
126C22⋊C4—2932no—
127C22⋊C4—2932no—
128C22⋊C4C2×D29311yescharacteristic
129C22⋊C4C2×D29312yescomplemented
130C42—2932no—
131C23—22no—
132C23—42no—
133C23—2932no—
134C23—2931no—
135C23—5862no—
136C23—11722no—
137C23C22×D29312yes—
138C23C22×D29311yescharacteristic
139C23C22×D29311yescharacteristic
140Q8—5862no—
141D4—22no—
142D4—42no—
143D4—5864no—
144D4—5864no—
145D4—5862no—
146D4—5862no—
147D4—11722no—
148D4—11722no—
149D4—11722no—
150C2×C4—2934no—
151C2×C4—2931no—
152C2×C4—2931no—
153C2×C4—2932no—
154C2×C4—2931no—
155C2×C4—5862no—
156C2×C4—5862no—
157C2×C4C22×D29312yes—
158C2×C4C22×D29311yescharacteristic
159C22—22no—
160C22—21no—
161C22—22no—
162C22—22no—
163C22—22no—
164C22—22no—
165C22—44no—
166C22—5861no—
167C22—5862no—
168C22—5862no—
169C22—5862no—
170C22—5862no—
171C22—11724no—
172C22D4×D29312yes—
173C22C23×D29311yescharacteristic
174C4—21no—
175C4—22no—
176C4—2932no—
177C4—2932no—
178C4—5861no—
179C4—5862no—
180C2—22no—
181C2—42no—
182C2—41no—
183C2—11722no—
184C2—11721no—
185C2C2×D4×D29311yescharacteristic
186C2#2262766912yes—
subgroupG/H
center, FrattiniC22C23×D293
commutator, socle, cosocleC22×C293C24
Fitting#120×C293C2
hypercenter#120D293
hypocenterC293#535
LCSG ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. C2×#17989801C2semidirect
2. C22×C22⋊D293C2semidirect
3. #22627620C2semidirect
4. #22627610C2semidirect
5. #22627597C2semidirect
6. #22627596C2semidirect
7. #22627594C2semidirect
8. #22627593C2semidirect
9. #22627592C2semidirect
10. #22627580C2semidirect
11. #120×C293C2semidirect
14. C2×Dic586C22semidirect
15. C2×D1172C22semidirect
20. C2×C22⋊D293C22semidirect
21. C2×C22⋊D293C22semidirect
22. C2×C22⋊D293C22semidirect
24. C22×Dic293C22semidirect
25. C2×C4×D293C22semidirect
26. #17989781C22semidirect
28. C22⋊Dic293C22semidirect
29. #17989779C22semidirect
30. #17989779C22semidirect
31. C4×Dic293C22semidirect
34. C2×D4×C293C22semidirect
36. C22⋊C4×C293C22semidirect
50. C2×Dic293D4semidirect
93. C293#535semidirect
104. #120D293semidirect
119. C2×D4C2×D293semidirect
129. C22⋊C4C2×D293semidirect

Maximal subgroups

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

subgroupindex
C2×#179898012
C22×C22⋊D2932
#226276202
#226276102
#226275972
#226275962
#226275942
#226275932
#226275922
#226275802
#120×C2932
#535293