Finite Group Databasebeta

← #21456714

Subgroups — #21456714

Order 7808.

378 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 117 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#16840333C212yesmaximal
2#16840104C214yesmaximal, complemented
3#16840020C212yesmaximal, complemented
4#16840003C212yesmaximal, complemented
5#16839920C214yesmaximal, complemented
6C61×#408C211yesmaximal, characteristic
7C22×Dic122C2212yes—
8C2×Dic244C2212yes—
9C2×Dic244C2212yes—
10#14519775—22no—
11#14519764—22no—
12#14519758—22no—
13#14519758—22no—
14#14519756C2214yes—
15#14519756C2214yes—
16#14519736C2212yes—
17#14519711C2212yes—
18#14519709C2212yes—
19#14519702C2214yes—
20#14519702C2214yes—
21C2×#41×C61C2211yescharacteristic
22C2×M16×C61C2211yescharacteristic
23C22×C8×C61C2211yescharacteristic
24C22⋊C8×C61C2214yes—
25#41×C61—41no—
26#41×C61—41no—
27C2×Q8×C61D411yescharacteristic
28C2×D4×C61D411yescharacteristic
29C2×D4×C61D412yes—
30C22×C4×C61C2312yes—
31C22×C4×C61C2311yescharacteristic
32C22×Dic61—22no—
33C2×Dic122—22no—
34C2×Dic122—42no—
35C2×Dic122—42no—
36C2×Dic122C2314yes—
37M16×C61—41no—
38C2×C8×C61—41no—
39C2×C8×C61C2312yes—
40C2×C8×C61C2312yes—
41C22⋊Dic61—22no—
42C22⋊Dic61—24no—
43C22⋊Dic61—24no—
44C4⋊Dic61C2314yes—
45#11758196—24no—
46#11758196—24no—
47C4×Dic61—22no—
48Dic244—42no—
49Dic244—42no—
50C23×C61C2×D411yescharacteristic
51C23×C61C2×D412yes—
52Q8×C61—41no—
53D4×C61—42no—
54D4×C61—41no—
55C2×C4×C61—21no—
56C2×C4×C61—21no—
57C2×C4×C61—22no—
58C2×C4×C61—22no—
59C2×C4×C61C2×D412yes—
60C2×C4×C61C2×D411yescharacteristic
61C2×C4×C61C2411yescharacteristic
62C2×Dic61—24no—
63C2×Dic61—24no—
64C2×Dic61—44no—
65Dic122—24no—
66Dic122—24no—
67Dic122—44no—
68C8×C61—22no—
69C8×C61—22no—
70C22×C61—22no—
71C22×C61—21no—
72C22×C61—22no—
73C22×C61—24no—
74C22×C61C22×D411yescharacteristic
75C4×C61—22no—
76C4×C61—21no—
77C4×C61H(5,𝔽2)11yescharacteristic
78C4×C61H(5,𝔽2)11yescharacteristic
79Dic61—44no—
80Dic61—44no—
81#3202—611nomaximal, Sylow
82C2×C61—42no—
83C2×C61—41no—
84C2×C61#53411yescharacteristic
85C2×C61#57812yes—
86#536—612no—
87#485—614no—
88#470—612no—
89#467—612no—
90#451—614no—
91#408D6111yescharacteristic
92C61#320211yescharacteristic, complemented, Sylow
93C2×#41C2×D6111yescharacteristic
94C22×Q8—612no—
95C2×Q16—612no—
96C2×Q16—612no—
97C2×M16C2×D6111yescharacteristic
98C22×C8C2×D6111yescharacteristic
99C4⋊Q8—1222no—
100#124—1222no—
101#123—1222no—
102#123—1222no—
103C22⋊Q8—614no—
104C22⋊Q8—614no—
105#117—612no—
106#107—612no—
107#106—612no—
108#103—614no—
109#103—614no—
110C22⋊C8C2×D6114yes—
111#41—41no—
112#41—41no—
113C2×Q8—614no—
114C2×Q8—1222no—
115C2×Q8—2442no—
116C2×Q8—2442no—
117C2×Q8D24411yescharacteristic
118C2×D4D24411yescharacteristic
119C2×D4D24412yes—
120C22×C4—1222no—
121C22×C4C22×D6112yes—
122C22×C4C22×D6111yescharacteristic
123Q16—2442no—
124Q16—2442no—
125M16—41no—
126C2×C8—41no—
127C2×C8C22×D6112yes—
128C2×C8C22×D6112yes—
129C4⋊C4—614no—
130C4⋊C4—1224no—
131C4⋊C4—1224no—
132C22⋊C4—1222no—
133C22⋊C4—1224no—
134C22⋊C4—1224no—
135C42—1222no—
136C23C2×D24411yescharacteristic
137C23C2×D24412yes—
138Q8—41no—
139Q8—1224no—
140Q8—1224no—
141Q8—2444no—
142D4—41no—
143D4—42no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—22no—
147C2×C4—22no—
148C2×C4—1224no—
149C2×C4—1224no—
150C2×C4—2444no—
151C2×C4C2×D24412yes—
152C2×C4C2×D24411yescharacteristic
153C2×C4C23×D6111yescharacteristic
154C8—22no—
155C8—22no—
156C22—22no—
157C22—24no—
158C22—22no—
159C22—21no—
160C22C22×D24411yescharacteristic
161C4—21no—
162C4—22no—
163C4—2444no—
164C4—2444no—
165C4#1451982211yescharacteristic
166C4#1451982211yescharacteristic
167C2—42no—
168C2—41no—
169C2#1684032411yescharacteristic
170C2#1684057912yes—
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#408C2
socleC22×C61C22×D4
hypercenter#408D61
hypocenterC61#3202
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
2. #16840104C2semidirect
3. #16840020C2semidirect
4. #16840003C2semidirect
5. #16839920C2semidirect
92. C61#3202semidirect