Finite Group Databasebeta

← #44529563

Subgroups — #44529563

Order 31168.

330 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 109 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×#21441262C211yesmaximal, characteristic, complemented
2C22×C4×D487C211yesmaximal, characteristic, complemented
3#29510200C212yesmaximal, complemented
4#29510191C211yesmaximal, characteristic, complemented
5#29510190C211yesmaximal, characteristic, complemented
6#29510189C211yesmaximal, characteristic, complemented
7#29510185C212yesmaximal, complemented
8#29510177C212yesmaximal, complemented
9(C22⋊D487)⋊C4C212yesmaximal, complemented
10#29510173C211yesmaximal, characteristic, complemented
11C22⋊Q8×C487C211yesmaximal, characteristic, complemented
12C23×D487C2211yescharacteristic
13#21441262—24no—
14C2×D1948C2212yes—
15C2×D1948C2212yes—
16C2×D1948C2211yescharacteristic, complemented
17C2×C22⋊D487C2212yes—
18C22×Dic487C2211yescharacteristic
19C2×C4×D487—24no—
20C2×C4×D487C2211yescharacteristic
21C2×C4×D487C2211yescharacteristic
22C2×C4×D487C2211yescharacteristic
23C2×C4×D487C2211yescharacteristic
24C2×C4×D487C2212yescomplemented
25C4⋊Dic487C2211yescharacteristic, complemented
26Dic487⋊C4C2212yescomplemented
27(C2×D487)⋊C4C2212yes—
28(C2×D487)⋊C4C2212yes—
29(C2×D487)⋊C4C2212yescomplemented
30(C2×D487)⋊C4C2212yescomplemented
31C4×Dic487C2212yescomplemented
32C2×Q8×C487C2211yescharacteristic, complemented
33C22×C4×C487C2211yescharacteristic
34C4⋊C4×C487C2211yescharacteristic, complemented
35C4⋊C4×C487C2212yescomplemented
36C22⋊C4×C487C2212yes—
37C22×D487—22no—
38C22×D487—22no—
39C22×D487—22no—
40C22×D487C2312yes—
41C22×D487C2311yescharacteristic
42C22×D487C2311yescharacteristic
43D1948—24no—
44D1948—24no—
45D1948—22no—
46C22⋊D487—24no—
47C2×Dic487—22no—
48C2×Dic487C2312yes—
49C2×Dic487C2311yescharacteristic
50C2×Dic487C2311yescharacteristic
51C4×D487—22no—
52C4×D487—22no—
53C4×D487—22no—
54C4×D487—24no—
55C4×D487D414yescomplemented
56C23×C487C2311yescharacteristic
57Q8×C487—22no—
58C2×C4×C487—22no—
59C2×C4×C487C2312yes—
60C2×C4×C487C2312yes—
61C2×C4×C487C2311yescharacteristic
62C2×C4×C487C2311yescharacteristic
63C22×C487—21no—
64C22×C487—21no—
65C22×C487#4112yescomplemented
66C22×C487C2411yescharacteristic
67C2×D487—28no—
68C2×D487—21no—
69C2×D487—21no—
70C2×D487—21no—
71C2×D487—21no—
72C2×D487—22no—
73C2×D487—22no—
74C2×D487—22no—
75C2×D487C2×D412yes—
76C2×D487#4112yescomplemented
77C4×C487—21no—
78C4×C487—22no—
79C4×C487—22no—
80C4×C487C2×D412yes—
81Dic487—21no—
82Dic487—22no—
83Dic487C2×D412yes—
84C2×C487—22no—
85C2×C487C22×D411yescharacteristic
86C2×C487C2×#4111yescharacteristic
87C2×C487C2×#4111yescharacteristic
88D487—22no—
89D487—22no—
90D487—42no—
91C487#52511yescharacteristic, complemented, Sylow
92#525—4871nomaximal, Sylow
93C2×#41—4871no—
94C23×C4—4871no—
95#123—4872no—
96C22⋊Q8—4871no—
97C22⋊Q8D48711yescharacteristic, complemented
98#121—4871no—
99#121—4871no—
100#120—4872no—
101C4×D4—4872no—
102C4×D4—4872no—
103#117—4871no—
104C24—4871no—
105#41—9744no—
106C2×Q8C2×D48711yescharacteristic, complemented
107C2×D4—4872no—
108C2×D4—4872no—
109C2×D4—4872no—
110C2×D4—4871no—
111C22×C4—9744no—
112C22×C4—4871no—
113C22×C4—4871no—
114C22×C4—4872no—
115C22×C4—4871no—
116C22×C4—4871no—
117C22×C4—4871no—
118C22×C4C2×D48711yescharacteristic
119C4⋊C4—4871no—
120C4⋊C4—4872no—
121C4⋊C4C2×D48711yescharacteristic, complemented
122C4⋊C4C2×D48712yescomplemented
123C22⋊C4—4872no—
124C22⋊C4—4872no—
125C22⋊C4—4872no—
126C22⋊C4—4872no—
127C22⋊C4C2×D48712yes—
128C42—4872no—
129C23—9742no—
130C23—9742no—
131C23—9742no—
132C23—4872no—
133C23—4871no—
134C23—4871no—
135C23C22×D48711yescharacteristic
136Q8—22no—
137D4—9744no—
138D4—9744no—
139D4—9744no—
140D4—9742no—
141C2×C4—22no—
142C2×C4—9742no—
143C2×C4—9742no—
144C2×C4—9744no—
145C2×C4—9742no—
146C2×C4—9742no—
147C2×C4—4872no—
148C2×C4—4871no—
149C2×C4—4871no—
150C2×C4—4874no—
151C2×C4C22×D48712yes—
152C2×C4C22×D48711yescharacteristic
153C2×C4C22×D48712yes—
154C2×C4C22×D48711yescharacteristic
155C22—21no—
156C22—21no—
157C22—9748no—
158C22—9742no—
159C22—9742no—
160C22—9742no—
161C22—9741no—
162C22—9741no—
163C22—9741no—
164C22—9741no—
165C22—4872no—
166C22—4872no—
167C22#2144126212yescomplemented
168C22C23×D48711yescharacteristic
169C4—21no—
170C4—22no—
171C4—22no—
172C4—9741no—
173C4—9742no—
174C4—4872no—
175C4D4×D48712yes—
176C2—22no—
177C2—19482no—
178C2—9742no—
179C2—9742no—
180C2C2×D4×D48711yescharacteristic
181C2#41×D48711yescharacteristic
182C2C2×#2144126211yescharacteristic
subgroupG/H
center, FrattiniC22C23×D487
commutator, socle, cosocleC22×C487C24
FittingC22⋊Q8×C487C2
hypercenterC22⋊Q8D487
hypocenterC487#525
LCSG ▷ C22×C487 ▷ C487
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#21441262C2semidirect
2. C22×C4×D487C2semidirect
3. #29510200C2semidirect
4. #29510191C2semidirect
5. #29510190C2semidirect
6. #29510189C2semidirect
7. #29510185C2semidirect
8. #29510177C2semidirect
9. (C22⋊D487)⋊C4C2semidirect
10. #29510173C2semidirect
11. C22⋊Q8×C487C2semidirect
16. C2×D1948C22semidirect
24. C2×C4×D487C22semidirect
25. C4⋊Dic487C22semidirect
26. Dic487⋊C4C22semidirect
29. (C2×D487)⋊C4C22semidirect
30. (C2×D487)⋊C4C22semidirect
31. C4×Dic487C22semidirect
32. C2×Q8×C487C22semidirect
34. C4⋊C4×C487C22semidirect
35. C4⋊C4×C487C22semidirect
55. C4×D487D4semidirect
65. C22×C487#41semidirect
76. C2×D487#41semidirect
91. C487#525semidirect
97. C22⋊Q8D487semidirect
106. C2×Q8C2×D487semidirect
121. C4⋊C4C2×D487semidirect
122. C4⋊C4C2×D487semidirect
167. C22#21441262semidirect

Maximal subgroups

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

subgroupindex
C2×#214412622
C22×C4×D4872
#295102002
#295101912
#295101902
#295101892
#295101852
#295101772
(C22⋊D487)⋊C42
#295101732
C22⋊Q8×C4872
#525487