Finite Group Databasebeta

← #21444378

Subgroups — #21444378

Order 7808.

264 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 85 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#16840312C211yesmaximal, characteristic
2#16839815C211yesmaximal, characteristic, complemented
3#16839495C214yesmaximal, complemented
4C61×#382C211yesmaximal, characteristic, complemented
5C2×#11758222—21no—
6#14519777C411yescharacteristic, complemented
7#14519774C411yescharacteristic, complemented
8#14519765—21no—
9#14519751—21no—
10#14519751C2212yes—
11C4×D244—21no—
12C4×D244C412yescomplemented
13C4⋊#92418—21no—
14C22⋊#92418C2212yes—
15C4×#92418—21no—
16C2×C4⋊C4×C61—21no—
17C2×C42×C61C2211yescharacteristic
18#95×C61—21no—
19#95×C61C2212yes—
20C22×C4×C61—22no—
21C22×C4×C61D411yescharacteristic
22C22×C4×C61D411yescharacteristic
23C22×C4×C61C2311yescharacteristic
24C2×C22⋊D61—22no—
25#11758222—42no—
26#11758222—42no—
27C2×D244—21no—
28C2×D244—21no—
29C2×D244C2×C412yes—
30C2×C4×D61—22no—
31C2×Dic122—21no—
32C4⋊C4×C61—42no—
33C42×C61C2×C411yescharacteristic
34C42×C61C2×C411yescharacteristic
35C42×C61D411yescharacteristic
36C42×C61D411yescharacteristic
37#11758198—22no—
38#11758198—22no—
39C4⋊Dic61—21no—
40C4⋊Dic61C2×C412yes—
41C2×#92418—22no—
42C23×C61C2×D411yescharacteristic
43C22×D61—22no—
44C2×C4×C61—41no—
45C2×C4×C61—41no—
46C2×C4×C61—42no—
47C2×C4×C61—42no—
48C2×C4×C61—42no—
49C2×C4×C61C22⋊C411yescharacteristic
50C2×C4×C61C22⋊C411yescharacteristic
51C2×C4×C61C22⋊C411yescharacteristic
52C2×C4×C61C22⋊C411yescharacteristic
53C2×C4×C61D812yes—
54C2×C4×C61SD1612yes—
55C2×C4×C61C22×C411yescharacteristic
56C2×C4×C61C2×D411yescharacteristic
57C22⋊D61—42no—
58C22⋊D61—42no—
59C2×Dic61—22no—
60D244—42no—
61D244—42no—
62D244—42no—
63C4×D61—44no—
64Dic122—42no—
65#92418—42no—
66C22×C61—21no—
67C22×C61—21no—
68C22×C61C2×C22⋊C411yescharacteristic
69C22×C61C2×D811yescharacteristic
70C22×C61C2×SD1611yescharacteristic
71C2×D61—42no—
72C2×D61—42no—
73C2×D61—42no—
74C4×C61—21no—
75C4×C61—21no—
76C4×C61—21no—
77C4×C61—21no—
78C4×C61—82no—
79C4×C61#10212yes—
80C4×C61#10212yes—
81Dic61—42no—
82#1517—611nomaximal, Sylow
83C2×C61—21no—
84C2×C61—21no—
85C2×C61#41011yescharacteristic
86C2×C61C2×#10211yescharacteristic
87C2×C61#42111yescharacteristic
88D61—82no—
89#532—611no—
90#431—611no—
91#382D6111yescharacteristic, complemented
92#327—614no—
93C61#151711yescharacteristic, complemented, Sylow
94C2×#41—1221no—
95C4⋊Q8—611no—
96#127—611no—
97#124—1221no—
98#121—612no—
99#121—1221no—
100C4×D4—612no—
101C4×D4—1221no—
102C2×C4⋊C4—21no—
103C2×C42C2×D6111yescharacteristic
104C4⋊C8—1221no—
105C22⋊C8—612no—
106C4×C8—1221no—
107#95—21no—
108#95C2×D6112yes—
109#41—2442no—
110#41—2442no—
111C2×Q8—1221no—
112C2×D4—612no—
113C2×D4—1222no—
114C2×D4—1221no—
115C2×D4—1221no—
116C22×C4—22no—
117C22×C4—1222no—
118C22×C4C22⋊D6111yescharacteristic
119C22×C4C22⋊D6111yescharacteristic
120C22×C4C22×D6111yescharacteristic
121C2×C8—1222no—
122C4⋊C4—42no—
123C4⋊C4—612no—
124C4⋊C4—1221no—
125C22⋊C4—1222no—
126C22⋊C4—1222no—
127C42C4×D6111yescharacteristic
128C42C4×D6111yescharacteristic
129C42D24411yescharacteristic
130C42D24411yescharacteristic
131C23—1222no—
132C23C2×C22⋊D6111yescharacteristic
133Q8—2442no—
134D4—2442no—
135D4—2442no—
136D4—2442no—
137D4—2442no—
138D4—2442no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—42no—
142C2×C4—42no—
143C2×C4—42no—
144C2×C4—1222no—
145C2×C4—2444no—
146C2×C4#1175819811yescharacteristic
147C2×C4#1175819811yescharacteristic
148C2×C4#1175819811yescharacteristic
149C2×C4#1175819811yescharacteristic
150C2×C4#1175819912yes—
151C2×C4#1175820112yes—
152C2×C4C2×C4×D6111yescharacteristic
153C2×C4C2×D24411yescharacteristic
154C8—2442no—
155C22—21no—
156C22—21no—
157C22—2442no—
158C22—2442no—
159C22—2442no—
160C22C2×#1175819811yescharacteristic
161C22C2×#1175819911yescharacteristic
162C22C2×#1175820111yescharacteristic
163C4—21no—
164C4—21no—
165C4—21no—
166C4—21no—
167C4—82no—
168C4—2442no—
169C4#1451969712yes—
170C4#1451969712yes—
171C2—21no—
172C2—21no—
173C2—4882no—
174C2#1683973511yescharacteristic
175C2C2×#1451969711yescharacteristic
176C2#1683978011yescharacteristic
subgroupG/H
centerC22C2×#11758198
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#382C2
socleC22×C61C2×C22⋊C4
hypercenter#382D61
hypocenterC61#1517
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #382

Complements

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

NH ≅ G/Ntype
2. #16839815C2semidirect
3. #16839495C2semidirect
4. C61×#382C2semidirect
6. #14519777C4semidirect
7. #14519774C4semidirect
12. C4×D244C4semidirect
91. #382D61semidirect
93. C61#1517semidirect