Finite Group Databasebeta

← #21453870

Subgroups — #21453870

Order 7808.

464 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C2×#14519769C211yesmaximal, characteristic, complemented
2#16839698C212yesmaximal, complemented
3#16839687C212yesmaximal, complemented
4#16839685C214yesmaximal, complemented
5#16839681C212yesmaximal, complemented
6#16839676C212yesmaximal
7#16839628C211yesmaximal, characteristic, complemented
8C2×#124×C61C211yesmaximal, characteristic
9#14519769—24no—
10C2×C4⋊Dic61C2211yescharacteristic
11C2×C4⋊Dic61C2211yescharacteristic
12C2×C4⋊Dic61C2212yes—
13C2×#11758196C2212yes—
14C2×#11758196C2212yes—
15C2×#11758196C2214yes—
16C2×C22⋊Dic61C2214yes—
17C2×C22⋊Dic61C2214yes—
18#14519684C2214yes—
19#14519684C2212yes—
20#14519684C2212yes—
21C22×Q8×C61C2211yescharacteristic
22C22×D4×C61C2211yescharacteristic
23#124×C61—24no—
24C2×C22⋊C4×C61C2212yes—
25C2×C22⋊C4×C61C2212yes—
26C2×C42×C61C2211yescharacteristic
27C24×C61C2312yes—
28C2×Q8×C61—22no—
29C2×Q8×C61—42no—
30C2×D4×C61—22no—
31C2×D4×C61—42no—
32C22×C4×C61C2312yes—
33C22×C4×C61C2311yescharacteristic
34C22×C4×C61C2311yescharacteristic
35C22×C4×C61C2311yescharacteristic
36C22×Dic61C2314yes—
37C22×Dic61C2312yes—
38C22×Dic61C2312yes—
39C22⋊C4×C61—24no—
40C22⋊C4×C61—24no—
41C42×C61D414yes—
42C22⋊Dic61—44no—
43C22⋊Dic61—44no—
44C4⋊Dic61—22no—
45C4⋊Dic61—22no—
46C4⋊Dic61—42no—
47#11758196—24no—
48#11758196—24no—
49#11758196—44no—
50C23×C61—22no—
51C23×C61—22no—
52C23×C61—24no—
53C23×C61—24no—
54C23×C61—22no—
55C23×C61C2411yescharacteristic
56Q8×C61—44no—
57D4×C61—44no—
58C2×C4×C61—21no—
59C2×C4×C61—22no—
60C2×C4×C61—22no—
61C2×C4×C61—21no—
62C2×C4×C61—22no—
63C2×C4×C61—24no—
64C2×C4×C61C2×D412yes—
65C2×C4×C61C2×D412yes—
66C2×C4×C61C2×D412yes—
67C2×Dic61—22no—
68C2×Dic61—22no—
69C2×Dic61—24no—
70C2×Dic61—24no—
71C2×Dic61—24no—
72C2×Dic61—22no—
73C2×Dic61—22no—
74C2×Dic61—24no—
75C22×C61—42no—
76C22×C61—42no—
77C22×C61—42no—
78C22×C61—44no—
79C22×C61—44no—
80C22×C61C22×D411yescharacteristic
81C22×C61H(5,𝔽2)12yes—
82C22×C61H(5,𝔽2)11yescharacteristic
83C22×C612−1+412yes—
84C22×C612−1+411yescharacteristic
85C4×C61—22no—
86C4×C61—22no—
87C4×C61—22no—
88C4×C61—42no—
89Dic61—42no—
90Dic61—42no—
91Dic61—44no—
92#2820—611nomaximal, Sylow
93C2×C61—82no—
94C2×C61#53511yescharacteristic
95C2×C61#53611yescharacteristic
96C2×C61#53711yescharacteristic
97C2×C61#56212yes—
98C2×C61#56312yes—
99C2×#125—611no—
100C2×#124D6111yescharacteristic
101#399—612no—
102#397—612no—
103#396—614no—
104#395—612no—
105#394—612no—
106#382—611no—
107C61#282011yescharacteristic, complemented, Sylow
108C22×Q8C2×D6111yescharacteristic
109C22×D4C2×D6111yescharacteristic
110#125—1224no—
111#124—24no—
112C2×C4⋊C4—612no—
113C2×C4⋊C4—612no—
114C2×C4⋊C4—611no—
115C2×C4⋊C4—611no—
116C2×C4⋊C4—612no—
117C2×C4⋊C4—614no—
118C2×C22⋊C4—614no—
119C2×C22⋊C4—614no—
120C2×C22⋊C4C2×D6112yes—
121C2×C22⋊C4C2×D6112yes—
122C2×C42C2×D6111yescharacteristic
123#95—612no—
124#95—612no—
125#95—614no—
126C24C22×D6112yes—
127C2×Q8—22no—
128C2×Q8—42no—
129C2×D4—22no—
130C2×D4—42no—
131C22×C4—614no—
132C22×C4—612no—
133C22×C4—612no—
134C22×C4C22×D6112yes—
135C22×C4C22×D6111yescharacteristic
136C22×C4C22×D6111yescharacteristic
137C22×C4C22×D6111yescharacteristic
138C4⋊C4—1224no—
139C4⋊C4—1224no—
140C4⋊C4—1222no—
141C4⋊C4—1222no—
142C4⋊C4—2444no—
143C4⋊C4—2442no—
144C22⋊C4—24no—
145C22⋊C4—24no—
146C22⋊C4—2444no—
147C22⋊C4—2444no—
148C42C22⋊D6114yes—
149C23—22no—
150C23—24no—
151C23—22no—
152C23—24no—
153C23—22no—
154C23C23×D6111yescharacteristic
155Q8—44no—
156D4—44no—
157C2×C4—22no—
158C2×C4—21no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—22no—
162C2×C4—24no—
163C2×C4—1222no—
164C2×C4—1222no—
165C2×C4—1224no—
166C2×C4—1224no—
167C2×C4—1222no—
168C2×C4—1224no—
169C2×C4—1224no—
170C2×C4—1222no—
171C2×C4C2×C22⋊D6112yes—
172C2×C4C2×C22⋊D6112yes—
173C2×C4C2×C22⋊D6112yes—
174C22—44no—
175C22—44no—
176C22—42no—
177C22—42no—
178C22—42no—
179C22C22×C22⋊D6111yescharacteristic
180C22#1451982212yes—
181C22#1451982311yescharacteristic
182C22#1451982412yes—
183C22#1451982411yescharacteristic
184C4—22no—
185C4—22no—
186C4—22no—
187C4—42no—
188C4—2444no—
189C4—2442no—
190C4—2442no—
191C2—82no—
192C2#1684032911yescharacteristic
193C2#1684033311yescharacteristic
194C2#1684034011yescharacteristic
195C2#1684050612yes—
196C2#1684051212yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×#124×C61C2
hypercenterC2×#124D61
hypocenterC61#2820
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#14519769C2semidirect
2. #16839698C2semidirect
3. #16839687C2semidirect
4. #16839685C2semidirect
5. #16839681C2semidirect
7. #16839628C2semidirect
107. C61#2820semidirect