Finite Group Databasebeta

← #21444511

Subgroups — #21444511

Order 7808.

252 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 67 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#16840310C211yesmaximal, characteristic
2#16839818C211yesmaximal, characteristic, complemented
3C4⋊C8×D61C211yesmaximal, characteristic, complemented
4#16839510C211yesmaximal, characteristic, complemented
5#16839510C211yesmaximal, characteristic, complemented
6#16839506C211yesmaximal, characteristic, complemented
7C61×#331C211yesmaximal, characteristic, complemented
8C2×#11758224C412yes—
9C2×C8×D61—21no—
10#14519777C2211yescharacteristic
11#14519764C412yes—
12#14519748—21no—
13#14519748—21no—
14D4×Dic61—21no—
15D4×Dic61—21no—
16C42×D61C2211yescharacteristic
17C4⋊#92418C2211yescharacteristic
18C4⋊#92418C2211yescharacteristic
19#14519706—21no—
20#14519689—21no—
21#14519687—21no—
22#127×C61C2211yescharacteristic
23C4⋊C8×C61C2211yescharacteristic
24C4⋊C8×C61C2211yescharacteristic
25C2×D4×C61—21no—
26C2×D4×C61—21no—
27C2×D4×C61C2×C412yes—
28C2×C22⋊D61—22no—
29C22×Dic61—22no—
30#11758224—44no—
31C2×C4×D61C2×C411yescharacteristic
32C2×C4×D61D411yescharacteristic
33C2×C4×D61D411yescharacteristic
34C2×Dic122C2×C412yes—
35C2×C8×C61—21no—
36C2×C8×C61—21no—
37C42×C61C2311yescharacteristic
38C22⋊Dic61—22no—
39C22⋊Dic61—22no—
40C4⋊Dic61—21no—
41C4⋊Dic61—21no—
42C4×Dic61C2×C411yescharacteristic
43C4×Dic61D411yescharacteristic
44C4×Dic61D411yescharacteristic
45C2×#92418—21no—
46C2×#92418—21no—
47C8×D61—42no—
48C23×C61—22no—
49C22×D61C22⋊C411yescharacteristic
50D4×C61—42no—
51D4×C61—41no—
52D4×C61—41no—
53D4×C61—41no—
54D4×C61—41no—
55C2×C4×C61C22×C411yescharacteristic
56C2×C4×C61C2×D411yescharacteristic
57C2×C4×C61C2×D411yescharacteristic
58C22⋊D61—44no—
59C2×Dic61—22no—
60C2×Dic61—44no—
61C2×Dic61C22⋊C411yescharacteristic
62C2×Dic61C22⋊C411yescharacteristic
63C2×Dic61C22⋊C411yescharacteristic
64C4×D61—22no—
65C4×D61—21no—
66C4×D61—21no—
67C4×D61—21no—
68C4×D61—21no—
69Dic122—42no—
70C8×C61—41no—
71C8×C61—41no—
72#92418—41no—
73#92418—41no—
74C22×C61—42no—
75C22×C61—42no—
76C22×C61—42no—
77C22×C61C2×C22⋊C411yescharacteristic
78C2×D61—21no—
79C2×D61—21no—
80C2×D61#10012yes—
81C4×C61—21no—
82C4×C61#13511yescharacteristic
83C4×C61#13511yescharacteristic
84C4×C61AGL(1,ℤ/8)11yescharacteristic
85C4×C61#13711yescharacteristic
86Dic61—21no—
87Dic61—21no—
88Dic61—21no—
89Dic61—42no—
90#1551—611nomaximal, Sylow
91C2×C61—82no—
92C2×C61C2×#10011yescharacteristic
93C2×C61#41611yescharacteristic
94C2×C61#41711yescharacteristic
95D61—22no—
96#532—611no—
97#432—611no—
98C2×C4⋊C8—611no—
99#333—611no—
100#333—611no—
101#331—611no—
102#331D6111yescharacteristic, complemented
103C61#155111yescharacteristic, complemented, Sylow
104C2×#41—612no—
105C22×C8—1221no—
106C4⋊Q8—611no—
107#127C2×D6111yescharacteristic
108#124—612no—
109#121—1221no—
110#121—1221no—
111C4×D4—1221no—
112C4×D4—1221no—
113C2×C42—611no—
114C4⋊C8—611no—
115C4⋊C8—611no—
116C4⋊C8—1221no—
117C4⋊C8C2×D6111yescharacteristic
118C4⋊C8C2×D6111yescharacteristic
119C22⋊C8—1221no—
120#97—1221no—
121#41—2444no—
122C2×Q8—612no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—1222no—
126C2×D4C4×D6112yes—
127C22×C4—611no—
128C22×C4—611no—
129C22×C4—611no—
130C22×C4—1222no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—1221no—
134C2×C8—1221no—
135C2×C8—2442no—
136C4⋊C4—1221no—
137C4⋊C4—1221no—
138C22⋊C4—1222no—
139C22⋊C4—1222no—
140C42—611no—
141C42—611no—
142C42—611no—
143C42C22×D6111yescharacteristic
144C23—22no—
145C23—611no—
146Q8—2442no—
147D4—42no—
148D4—41no—
149D4—41no—
150D4—41no—
151D4—41no—
152D4—2444no—
153C2×C4—611no—
154C2×C4—611no—
155C2×C4—611no—
156C2×C4—1222no—
157C2×C4—1221no—
158C2×C4—1221no—
159C2×C4—1221no—
160C2×C4—1221no—
161C2×C4—1222no—
162C2×C4—2444no—
163C2×C4C2×C4×D6111yescharacteristic
164C2×C4D4×D6111yescharacteristic
165C2×C4D4×D6111yescharacteristic
166C8—41no—
167C8—41no—
168C8—2441no—
169C8—2441no—
170C22—42no—
171C22—42no—
172C22—42no—
173C22—612no—
174C22—1221no—
175C22—1221no—
176C22C22⋊C4×D6111yescharacteristic
177C4—21no—
178C4—1221no—
179C4—1221no—
180C4—1221no—
181C4—2442no—
182C4#1451979611yescharacteristic
183C4#1451979811yescharacteristic
184C4#1451980111yescharacteristic
185C4#1451980611yescharacteristic
186C2—82no—
187C2—1222no—
188C2#100×D6111yescharacteristic
189C2#1683975511yescharacteristic
190C2#1683976011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D61
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC61×#331C2
socleC22×C61C2×C22⋊C4
hypercenter#331D61
hypocenterC61#1551
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #16839818C2semidirect
3. C4⋊C8×D61C2semidirect
4. #16839510C2semidirect
5. #16839510C2semidirect
6. #16839506C2semidirect
7. C61×#331C2semidirect
102. #331D61semidirect
103. C61#1551semidirect