Finite Group Databasebeta

← #21444207

Subgroups — #21444207

Order 7808.

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

normal subgroups only

This group has 264 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
1C4×#11758222C211yesmaximal, characteristic
2C2×C4⋊#92418C211yesmaximal, characteristic, complemented
3#16839494C212yesmaximal, complemented
4#16839491C212yesmaximal, complemented
5C61×#431C211yesmaximal, characteristic, complemented
6C2×#11758222C411yescharacteristic
7C22×#92418—21no—
8C4×Dic122C411yescharacteristic
9C4×Dic122C2211yescharacteristic
10C4×D244C411yescharacteristic
11C4×D244C2211yescharacteristic
12C4×C22⋊D61—21no—
13C4×C22⋊D61—21no—
14#14519736C411yescharacteristic
15#14519734—21no—
16C42×D61—21no—
17C4⋊#92418—21no—
18C4⋊#92418C2212yes—
19C2×C42×C61C2211yescharacteristic
20C4⋊C8×C61—21no—
21C22⋊C8×C61—21no—
22C4×C8×C61C2212yes—
23C22×C4×C61C2×C411yescharacteristic
24C22×C4×C61D411yescharacteristic
25C22×C4×C61D411yescharacteristic
26C2×C22⋊D61—21no—
27#11758222—22no—
28#11758222C814yescomplemented
29C2×D244C2×C411yescharacteristic
30C2×C4×D61—21no—
31C2×C4×D61—21no—
32C2×C4×D61—21no—
33C2×Dic122C2×C411yescharacteristic
34C2×C8×C61—22no—
35C42×C61C2×C411yescharacteristic
36C42×C61D411yescharacteristic
37C42×C61D411yescharacteristic
38C42×C61C2311yescharacteristic
39C22⋊Dic61—21no—
40#11758198—21no—
41#11758198—21no—
42C4⋊Dic61C2×C411yescharacteristic
43C4⋊Dic61C2×C411yescharacteristic
44#11758196—21no—
45#11758196—21no—
46C4×Dic61—21no—
47C4×Dic61—21no—
48C4×Dic61—21no—
49C2×#92418—22no—
50C2×#92418—42no—
51C23×C61C22⋊C411yescharacteristic
52C22×D61—21no—
53C2×C4×C61—21no—
54C2×C4×C61—21no—
55C2×C4×C61—41no—
56C2×C4×C61C22⋊C411yescharacteristic
57C2×C4×C61C22⋊C411yescharacteristic
58C2×C4×C61C22⋊C411yescharacteristic
59C2×C4×C61C2×C812yes—
60C2×C4×C61M1612yes—
61C2×C4×C61C22×C411yescharacteristic
62C2×C4×C61C2×D411yescharacteristic
63C2×C4×C61C2×D411yescharacteristic
64C22⋊D61—24no—
65C2×Dic61—21no—
66C2×Dic61—21no—
67C2×Dic61—21no—
68D244—21no—
69D244C2×C812yescomplemented
70C4×D61—24no—
71C4×D61—42no—
72C4×D61—41no—
73C4×D61—41no—
74Dic122—21no—
75Dic122C2×C812yescomplemented
76C8×C61—42no—
77#92418—42no—
78C22×C61—21no—
79C22×C61—21no—
80C22×C61C22⋊C812yes—
81C22×C61C2×C22⋊C411yescharacteristic
82C2×D61—22no—
83C2×D61—41no—
84C2×D61—41no—
85C4×C61—21no—
86C4×C61—21no—
87C4×C61—21no—
88C4×C61C22⋊C812yes—
89C4×C61C22×C811yescharacteristic
90C4×C61C2×M1611yescharacteristic
91C4×C61AGL(1,ℤ/8)11yescharacteristic
92C4×C61#13711yescharacteristic
93Dic61—22no—
94Dic61—41no—
95Dic61—41no—
96#1477—611nomaximal, Sylow
97C2×C61—22no—
98C2×C61C2×C22⋊C811yescharacteristic
99C2×C61#41711yescharacteristic
100C2×C61#42111yescharacteristic
101D61—42no—
102C4×#41—611no—
103#431D6111yescharacteristic, complemented
104C2×C4⋊C8—611no—
105Q8⋊C8—612no—
106D4⋊C8—612no—
107C61#147711yescharacteristic, complemented, Sylow
108C2×#41—611no—
109C22×C8—1221no—
110C4×Q8—611no—
111C4×Q8—611no—
112C4×D4—611no—
113C4×D4—611no—
114C4×D4—1221no—
115C4×D4—1221no—
116#117—611no—
117#117—1221no—
118C2×C42—1221no—
119C2×C42C2×D6111yescharacteristic
120C4⋊C8—21no—
121C4⋊C8—612no—
122C4⋊C8—1221no—
123C22⋊C8—21no—
124C4×C8C2×D6112yes—
125#41—614no—
126#41—1222no—
127C2×Q8—611no—
128C2×D4—611no—
129C2×D4—1221no—
130C22×C4—1221no—
131C22×C4—1221no—
132C22×C4—1221no—
133C22×C4C4×D6111yescharacteristic
134C22×C4D24411yescharacteristic
135C22×C4C22⋊D6111yescharacteristic
136C2×C8—22no—
137C2×C8—1222no—
138C2×C8—2442no—
139C4⋊C4—611no—
140C4⋊C4—611no—
141C4⋊C4—1221no—
142C4⋊C4—1221no—
143C22⋊C4—1221no—
144C22⋊C4—1221no—
145C22⋊C4—1221no—
146C42—1221no—
147C42—1221no—
148C42—1221no—
149C42C4×D6111yescharacteristic
150C42D24411yescharacteristic
151C42C22⋊D6111yescharacteristic
152C42C22×D6111yescharacteristic
153C23—1221no—
154C23#1175819811yescharacteristic
155Q8—612no—
156Q8—1221no—
157D4—612no—
158D4—1224no—
159D4—1221no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—41no—
163C2×C4—1221no—
164C2×C4—1224no—
165C2×C4—1221no—
166C2×C4—1221no—
167C2×C4—2442no—
168C2×C4—2441no—
169C2×C4—2441no—
170C2×C4C8×D6112yes—
171C2×C4#1175818912yes—
172C2×C4#1175819811yescharacteristic
173C2×C4#1175819811yescharacteristic
174C2×C4#1175819811yescharacteristic
175C2×C4C2×C4×D6111yescharacteristic
176C2×C4C2×D24411yescharacteristic
177C2×C4C2×C22⋊D6111yescharacteristic
178C8—42no—
179C8—2442no—
180C22—21no—
181C22—21no—
182C22—1222no—
183C22—2441no—
184C22—2441no—
185C22#1451968912yes—
186C22C2×#1175819811yescharacteristic
187C4—21no—
188C4—21no—
189C4—21no—
190C4—1222no—
191C4—2441no—
192C4—2441no—
193C4#1451968912yes—
194C4C2×C8×D6111yescharacteristic
195C4C2×#1175818911yescharacteristic
196C4#1451980511yescharacteristic
197C4#1451981011yescharacteristic
198C2—22no—
199C2—2442no—
200C2C2×#1451968911yescharacteristic
201C2#1683976411yescharacteristic
202C2#1683978011yescharacteristic
subgroupG/H
centerC2×C4C2×D244
commutatorC4×C61C22×C8
FrattiniC42C22×D61
FittingC61×#431C2
socleC22×C61C2×C22⋊C4
hypercenter#431D61
hypocenterC61#1477
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊#92418C2semidirect
3. #16839494C2semidirect
4. #16839491C2semidirect
5. C61×#431C2semidirect
28. #11758222C8semidirect
69. D244C2×C8semidirect
75. Dic122C2×C8semidirect
103. #431D61semidirect
107. C61#1477semidirect