Finite Group Databasebeta

← #20295673

Subgroups — #20295673

Order 6976.

334 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 105 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×#13182029C211yesmaximal, characteristic, complemented
2C2×D4×D109C211yesmaximal, characteristic, complemented
3#16812686C211yesmaximal, characteristic, complemented
4#16812681C212yesmaximal, complemented
5#16812679C211yesmaximal, characteristic, complemented
6#16812670C212yesmaximal, complemented
7#16812667C212yesmaximal, complemented
8#16812661C211yesmaximal, characteristic, complemented
9C4×C22⋊D109C211yesmaximal, characteristic, complemented
10C22⋊C4×D109C212yesmaximal, complemented
11#121×C109C211yesmaximal, characteristic, complemented
12C23×D109C2212yes—
13#13182029—24no—
14C2×Dic218C2211yescharacteristic, complemented
15C2×D436C2211yescharacteristic
16C2×C22⋊D109C2211yescharacteristic
17C2×C22⋊D109C2212yes—
18C2×C22⋊D109C2212yescomplemented
19D4×D109—24no—
20C2×C4×D109C2211yescharacteristic
21C2×C4×D109C2212yescomplemented
22C2×C4×D109C2212yescomplemented
23C4⋊Dic109C2212yescomplemented
24#13182008C2211yescharacteristic, complemented
25C22⋊Dic109C2212yescomplemented
26C22⋊Dic109C2211yescharacteristic, complemented
27C22⋊Dic109C2212yescomplemented
28#13182006C2211yescharacteristic
29#13182006C2212yes—
30#13182006C2212yescomplemented
31C4×Dic109C2211yescharacteristic, complemented
32C2×D4×C109C2211yescharacteristic
33C2×D4×C109C2212yescomplemented
34C22×C4×C109C2211yescharacteristic, complemented
35C4⋊C4×C109C2211yescharacteristic, complemented
36C22⋊C4×C109C2212yescomplemented
37C23×C109C2312yes—
38C23×C109C2311yescharacteristic
39C22×D109—24no—
40C22×D109—24no—
41C22×D109—42no—
42C22×D109C2312yes—
43C22×D109C2311yescharacteristic
44D4×C109—22no—
45D4×C109—42no—
46C2×C4×C109—22no—
47C2×C4×C109C2311yescharacteristic
48C2×C4×C109C2312yes—
49C2×C4×C109C2311yescharacteristic
50C22⋊D109—24no—
51C22⋊D109—24no—
52C22⋊D109—22no—
53C2×Dic109C2311yescharacteristic
54C2×Dic109C2311yescharacteristic
55C2×Dic109C2312yes—
56C2×Dic109C2311yescharacteristic
57D436D414yescomplemented
58C4×D109—24no—
59C4×D109—22no—
60C4×D109—42no—
61Dic218—22no—
62C22×C109—21no—
63C22×C109—22no—
64C22×C109—21no—
65C22×C109—22no—
66C22×C109—21no—
67C22×C109—22no—
68C22×C109C2411yescharacteristic
69C2×D109—21no—
70C2×D109—22no—
71C2×D109—22no—
72C2×D109—21no—
73C2×D109—48no—
74C2×D109C2×D414yes—
75C2×D109#4112yescomplemented
76C4×C109—21no—
77C4×C109—22no—
78C4×C109C2×D412yes—
79Dic109—22no—
80Dic109—21no—
81Dic109—21no—
82Dic109—21no—
83C2×C109—42no—
84C2×C109—41no—
85C2×C109C22×D411yescharacteristic
86C2×C109C2×#4111yescharacteristic
87C2×C109H(5,𝔽2)11yescharacteristic
88D109—22no—
89D109—24no—
90C109#54611yescharacteristic, complemented, Sylow
91#546—1091nomaximal, Sylow
92C2×#41—1091no—
93C22×D4—1091no—
94#124—1091no—
95#123—1092no—
96C22⋊Q8—1091no—
97#121—1092no—
98#121D10911yescharacteristic, complemented
99#120—1092no—
100C4×D4—1091no—
101C4×D4—1091no—
102C2×C22⋊C4—1092no—
103C24—1092no—
104#41—2184no—
105C2×Q8—1091no—
106C2×D4—1091no—
107C2×D4—1092no—
108C2×D4—1092no—
109C2×D4—1091no—
110C2×D4—2184no—
111C2×D4C2×D10911yescharacteristic
112C2×D4C2×D10912yescomplemented
113C22×C4—1092no—
114C22×C4—1091no—
115C22×C4—1092no—
116C22×C4C2×D10911yescharacteristic, complemented
117C4⋊C4—1091no—
118C4⋊C4—1092no—
119C4⋊C4C2×D10911yescharacteristic, complemented
120C22⋊C4—1092no—
121C22⋊C4—1091no—
122C22⋊C4—1092no—
123C22⋊C4—1091no—
124C22⋊C4—1092no—
125C22⋊C4—1092no—
126C22⋊C4C2×D10912yescomplemented
127C42—1091no—
128C23—1091no—
129C23—1092no—
130C23—4362no—
131C23—2184no—
132C23—2184no—
133C23C22×D10912yes—
134C23C22×D10911yescharacteristic
135Q8—2182no—
136D4—22no—
137D4—42no—
138D4—1094no—
139D4—2184no—
140D4—2184no—
141D4—2182no—
142C2×C4—22no—
143C2×C4—1091no—
144C2×C4—1091no—
145C2×C4—1092no—
146C2×C4—1091no—
147C2×C4—4362no—
148C2×C4—2184no—
149C2×C4—2182no—
150C2×C4C22×D10912yes—
151C2×C4C22×D10911yescharacteristic
152C2×C4C22×D10911yescharacteristic
153C22—21no—
154C22—22no—
155C22—21no—
156C22—22no—
157C22—21no—
158C22—22no—
159C22—1094no—
160C22—1092no—
161C22—4368no—
162C22—2181no—
163C22—2182no—
164C22—2182no—
165C22—2181no—
166C22C23×D10911yescharacteristic
167C4—21no—
168C4—22no—
169C4—2181no—
170C4—2182no—
171C4—2181no—
172C4—2181no—
173C4D4×D10912yes—
174C2—42no—
175C2—41no—
176C2—2182no—
177C2—2184no—
178C2C2×D4×D10911yescharacteristic
179C2#41×D10911yescharacteristic
180C2#1681274411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D109
commutator, socleC22×C109C24
Fitting#121×C109C2
hypercenter#121D109
hypocenterC109#546
LCSG ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×#13182029C2semidirect
2. C2×D4×D109C2semidirect
3. #16812686C2semidirect
4. #16812681C2semidirect
5. #16812679C2semidirect
6. #16812670C2semidirect
7. #16812667C2semidirect
8. #16812661C2semidirect
9. C4×C22⋊D109C2semidirect
10. C22⋊C4×D109C2semidirect
11. #121×C109C2semidirect
14. C2×Dic218C22semidirect
18. C2×C22⋊D109C22semidirect
21. C2×C4×D109C22semidirect
22. C2×C4×D109C22semidirect
23. C4⋊Dic109C22semidirect
24. #13182008C22semidirect
25. C22⋊Dic109C22semidirect
26. C22⋊Dic109C22semidirect
27. C22⋊Dic109C22semidirect
30. #13182006C22semidirect
31. C4×Dic109C22semidirect
33. C2×D4×C109C22semidirect
34. C22×C4×C109C22semidirect
35. C4⋊C4×C109C22semidirect
36. C22⋊C4×C109C22semidirect
57. D436D4semidirect
75. C2×D109#41semidirect
90. C109#546semidirect
98. #121D109semidirect
112. C2×D4C2×D109semidirect
116. C22×C4C2×D109semidirect
119. C4⋊C4C2×D109semidirect
126. C22⋊C4C2×D109semidirect