Finite Group Databasebeta

← #21445849

Subgroups — #21445849

Order 7808.

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

normal subgroups only

This group has 316 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
1C22×#11758189C211yesmaximal, characteristic
2C2×#14519711C211yesmaximal, characteristic, complemented
3#16839619C212yesmaximal
4#16839524C212yesmaximal, complemented
5C2×#106×C61C211yesmaximal, characteristic, complemented
6C22×C4×D61C2211yescharacteristic
7C2×#11758189—22no—
8C2×#11758189—22no—
9C2×#11758189C414yescomplemented
10C22×#92418C2211yescharacteristic
11C2×C4⋊Dic61C2212yes—
12C2×#11758198—22no—
13#14519711—22no—
14#14519684—22no—
15C22×C8×C61C2211yescharacteristic
16C2×C4⋊C4×C61C2212yes—
17#106×C61—22no—
18C23×D61D411yescharacteristic
19C22×C4×C61—22no—
20C22×C4×C61C2311yescharacteristic
21C22×Dic61—22no—
22C22×Dic61D411yescharacteristic
23C2×C4×D61—21no—
24C2×C4×D61—21no—
25C2×C4×D61—21no—
26C2×C4×D61—21no—
27C2×C4×D61C2×C412yes—
28C2×C4×D61Q812yes—
29C2×C8×C61C2×C412yes—
30C2×C8×C61D412yes—
31C2×C8×C61D412yes—
32C4⋊C4×C61—22no—
33C4⋊C4×C61—22no—
34#11758198—44no—
35C4⋊Dic61—22no—
36C4⋊Dic61—22no—
37C2×#92418—21no—
38C2×#92418—21no—
39C2×#92418C2×C412yes—
40#11758189—28no—
41C23×C61C2×D411yescharacteristic
42C22×D61—21no—
43C22×D61—21no—
44C22×D61—22no—
45C22×D61—22no—
46C22×D61C4⋊C412yes—
47C2×C4×C61—42no—
48C2×C4×C61—42no—
49C2×C4×C61—42no—
50C2×C4×C61C22×C411yescharacteristic
51C2×C4×C61C2×D411yescharacteristic
52C2×C4×C61C2×D411yescharacteristic
53C2×C4×C61C2×Q811yescharacteristic
54C2×C4×C61#4111yescharacteristic
55C2×C4×C61#4111yescharacteristic
56C2×Dic61—21no—
57C2×Dic61—21no—
58C2×Dic61—42no—
59C2×Dic61—42no—
60C2×Dic61—42no—
61C2×Dic61C4⋊C412yes—
62C4×D61—22no—
63C4×D61—22no—
64C4×D61—22no—
65C4×D61—22no—
66C8×C61C22⋊C414yescomplemented
67#92418—22no—
68C22×C61C2×C4⋊C411yescharacteristic
69C22×C61#12111yescharacteristic
70C22×C61#12111yescharacteristic
71C22×C61AGL(1,ℤ/8)12yes—
72C22×C61#13712yes—
73C2×D61—22no—
74C2×D61—24no—
75C2×D61—42no—
76C2×D61—41no—
77C2×D61—41no—
78C4×C61—82no—
79C4×C61C2×C22⋊C411yescharacteristic
80C4×C61#11711yescharacteristic
81C4×C61C22⋊Q811yescharacteristic
82C4×C61C22⋊Q811yescharacteristic
83Dic61—22no—
84Dic61—82no—
85#1809—611nomaximal, Sylow
86C2×C61#38011yescharacteristic
87C2×C61#42812yes—
88C2×C61#46812yes—
89C2×C61#46911yescharacteristic
90C2×C61#47011yescharacteristic
91D61—42no—
92C22×M16—611no—
93C2×#107—611no—
94C2×#106D6111yescharacteristic, complemented
95#380—612no—
96#340—612no—
97C61#180911yescharacteristic, complemented, Sylow
98C23×C4—611no—
99C2×M16—614no—
100C2×M16—1222no—
101C2×M16—1222no—
102C22×C8—611no—
103C22×C8C2×D6111yescharacteristic
104C2×C4⋊C4—612no—
105C2×C4⋊C4C2×D6112yes—
106C2×C22⋊C4—1222no—
107#107—1222no—
108#106—22no—
109#95—1222no—
110C24—611no—
111C22×C4—22no—
112C22×C4—611no—
113C22×C4—612no—
114C22×C4—612no—
115C22×C4—1221no—
116C22×C4—1221no—
117C22×C4—1221no—
118C22×C4—1221no—
119C22×C4—1222no—
120C22×C4C22×D6111yescharacteristic
121M16—1228no—
122C2×C8—612no—
123C2×C8—1221no—
124C2×C8—1221no—
125C2×C8C4×D6112yes—
126C2×C8D24412yes—
127C2×C8C22⋊D6112yes—
128C4⋊C4—22no—
129C4⋊C4—22no—
130C4⋊C4—1222no—
131C4⋊C4—1222no—
132C22⋊C4—2444no—
133C23—612no—
134C23—1221no—
135C23—1221no—
136C23—1222no—
137C23—1222no—
138C23D4×D6111yescharacteristic
139C2×C4—42no—
140C2×C4—42no—
141C2×C4—42no—
142C2×C4—612no—
143C2×C4—1221no—
144C2×C4—1221no—
145C2×C4—1222no—
146C2×C4—1222no—
147C2×C4—1222no—
148C2×C4—1222no—
149C2×C4—2442no—
150C2×C4—2442no—
151C2×C4—2442no—
152C2×C4C2×C4×D6111yescharacteristic
153C2×C4C2×D24411yescharacteristic
154C2×C4#1175822411yescharacteristic
155C2×C4Q8×D6111yescharacteristic
156C2×C4#1175822611yescharacteristic
157C2×C4C2×C22⋊D6111yescharacteristic
158C8—1222no—
159C8#1175819814yescomplemented
160C22—1224no—
161C22—1222no—
162C22—2442no—
163C22—2441no—
164C22—2441no—
165C22C4⋊C4×D6111yescharacteristic
166C22#1451974811yescharacteristic
167C22#1451975211yescharacteristic
168C22#1451980412yes—
169C22#1451980612yes—
170C4—82no—
171C4—1222no—
172C4—4882no—
173C4C2×#1175819811yescharacteristic
174C4#1451973511yescharacteristic
175C4#1451975311yescharacteristic
176C4#1451975711yescharacteristic
177C2—2442no—
178C2#1683961911yescharacteristic
179C2#1683980112yes—
180C2#1684000512yes—
181C2#1684001611yescharacteristic
182C2#1684002111yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC2×#106×C61C2
socleC23×C61C2×D4
hypercenterC2×#106D61
hypocenterC61#1809
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
2. C2×#14519711C2semidirect
4. #16839524C2semidirect
5. C2×#106×C61C2semidirect
9. C2×#11758189C4semidirect
66. C8×C61C22⋊C4semidirect
94. C2×#106D61semidirect
97. C61#1809semidirect
159. C8#11758198semidirect