Finite Group Databasebeta

← #21444496

Subgroups — #21444496

Order 7808.

260 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 97 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#16839786C211yesmaximal, characteristic, complemented
2C2×C4⋊#92418C211yesmaximal, characteristic, complemented
3#16839508C212yesmaximal, complemented
4#16839506C212yesmaximal, complemented
5C61×#532C211yesmaximal, characteristic
6C2×#11758194—21no—
7C22×#92418—21no—
8C4⋊#92418—21no—
9C4⋊#92418—21no—
10C4⋊#92418C2212yes—
11C4⋊#92418C2212yes—
12C2×#41×C61—21no—
13C4⋊Q8×C61C2211yescharacteristic
14#127×C61C2211yescharacteristic
15#124×C61—21no—
16#121×C61—21no—
17#121×C61C412yes—
18C4×D4×C61—21no—
19C4×D4×C61C412yes—
20C2×C42×C61C2211yescharacteristic
21#41×C61—42no—
22#41×C61—42no—
23C2×Q8×C61—21no—
24C2×D4×C61—22no—
25C2×D4×C61—21no—
26C2×D4×C61—21no—
27C2×D4×C61C2×C412yes—
28C22×C4×C61—22no—
29C22×C4×C61C2×C411yescharacteristic
30C22×C4×C61D411yescharacteristic
31C22×C4×C61D411yescharacteristic
32C4⋊C4×C61—21no—
33C4⋊C4×C61C2×C412yes—
34C22⋊C4×C61—22no—
35C22⋊C4×C61—22no—
36C42×C61C2×C411yescharacteristic
37C42×C61D411yescharacteristic
38C42×C61D411yescharacteristic
39C42×C61C2311yescharacteristic
40#11758194—42no—
41C2×#92418—22no—
42C2×#92418—22no—
43C2×#92418—42no—
44C23×C61—22no—
45C23×C61C22⋊C411yescharacteristic
46Q8×C61—41no—
47Q8×C61—41no—
48D4×C61—42no—
49D4×C61—44no—
50D4×C61—41no—
51D4×C61—41no—
52D4×C61—41no—
53D4×C61—41no—
54C2×C4×C61—21no—
55C2×C4×C61—21no—
56C2×C4×C61—22no—
57C2×C4×C61—41no—
58C2×C4×C61—44no—
59C2×C4×C61C22⋊C411yescharacteristic
60C2×C4×C61C22⋊C411yescharacteristic
61C2×C4×C61C22⋊C411yescharacteristic
62C2×C4×C61D812yes—
63C2×C4×C61SD1612yes—
64C2×C4×C61C22×C411yescharacteristic
65C2×C4×C61C2×D411yescharacteristic
66C2×C4×C61C2×D411yescharacteristic
67#92418—42no—
68#92418—42no—
69C22×C61—21no—
70C22×C61—21no—
71C22×C61—42no—
72C22×C61—42no—
73C22×C61—42no—
74C22×C61#10212yes—
75C22×C61C2×C22⋊C411yescharacteristic
76C4×C61—21no—
77C4×C61—21no—
78C4×C61—21no—
79C4×C61—42no—
80C4×C61#10212yes—
81C4×C61C2×D811yescharacteristic
82C4×C61C2×SD1611yescharacteristic
83C4×C61AGL(1,ℤ/8)11yescharacteristic
84C4×C61#13711yescharacteristic
85#1547—611nomaximal, Sylow
86C2×C61—22no—
87C2×C61—82no—
88C2×C61#41311yescharacteristic
89C2×C61C2×#10211yescharacteristic
90C2×C61#41711yescharacteristic
91#532D6111yescharacteristic
92#423—611no—
93C2×C4⋊C8—611no—
94#332—612no—
95#331—612no—
96C61#154711yescharacteristic, complemented, Sylow
97C2×#41—21no—
98C2×M16—1221no—
99C22×C8—1221no—
100C4⋊Q8C2×D6111yescharacteristic
101#127C2×D6111yescharacteristic
102#124—21no—
103#121—21no—
104#121Dic6112yes—
105C4×D4—21no—
106C4×D4Dic6112yes—
107C2×C42C2×D6111yescharacteristic
108C4⋊C8—612no—
109C4⋊C8—612no—
110C4⋊C8—1221no—
111C4⋊C8—1221no—
112#41—42no—
113#41—42no—
114C2×Q8—21no—
115C2×D4—22no—
116C2×D4—21no—
117C2×D4—21no—
118C2×D4C2×Dic6112yes—
119C22×C4—22no—
120C22×C4C2×Dic6111yescharacteristic
121C22×C4C22⋊D6111yescharacteristic
122C22×C4C22⋊D6111yescharacteristic
123M16—2442no—
124C2×C8—1222no—
125C2×C8—1222no—
126C2×C8—2442no—
127C4⋊C4—21no—
128C4⋊C4C2×Dic6112yes—
129C22⋊C4—22no—
130C22⋊C4—22no—
131C42C2×Dic6111yescharacteristic
132C42C22⋊D6111yescharacteristic
133C42C22⋊D6111yescharacteristic
134C42C22×D6111yescharacteristic
135C23—22no—
136C23C22⋊Dic6111yescharacteristic
137Q8—41no—
138Q8—41no—
139D4—42no—
140D4—44no—
141D4—41no—
142D4—41no—
143D4—41no—
144D4—41no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—22no—
148C2×C4—41no—
149C2×C4—44no—
150C2×C4#1175819912yes—
151C2×C4#1175820012yes—
152C2×C4C22⋊Dic6111yescharacteristic
153C2×C4C22⋊Dic6111yescharacteristic
154C2×C4C22⋊Dic6111yescharacteristic
155C2×C4C22×Dic6111yescharacteristic
156C2×C4C2×C22⋊D6111yescharacteristic
157C2×C4C2×C22⋊D6111yescharacteristic
158C8—2442no—
159C8—2442no—
160C22—21no—
161C22—21no—
162C22—42no—
163C22—42no—
164C22—42no—
165C22#1451969812yes—
166C22C2×C22⋊Dic6111yescharacteristic
167C4—21no—
168C4—21no—
169C4—21no—
170C4—42no—
171C4#1451969812yes—
172C4C2×#1175819911yescharacteristic
173C4C2×#1175820011yescharacteristic
174C4#1451980211yescharacteristic
175C4#1451980711yescharacteristic
176C2—22no—
177C2—82no—
178C2#1683974611yescharacteristic
179C2C2×#1451969811yescharacteristic
180C2#1683976311yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic61
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC61×#532C2
socleC22×C61C2×C22⋊C4
hypercenter#532D61
hypocenterC61#1547
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. #16839786C2semidirect
2. C2×C4⋊#92418C2semidirect
3. #16839508C2semidirect
4. #16839506C2semidirect
96. C61#1547semidirect