Finite Group Databasebeta

← #21451617

Subgroups — #21451617

Order 7808.

464 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14519736C211yesmaximal, characteristic
2#16839701C212yesmaximal, complemented
3#16839692C212yesmaximal, complemented
4#16839690C214yesmaximal
5#16839669C212yesmaximal, complemented
6#16839658C212yesmaximal, complemented
7#16839622C211yesmaximal, characteristic
8C2×C22⋊Q8×C61C211yesmaximal, characteristic
9#14519736—24no—
10C2×C4⋊Dic61C2211yescharacteristic
11C2×C4⋊Dic61C2211yescharacteristic
12C2×C4⋊Dic61C2212yes—
13C2×#11758196C2214yes—
14C2×C22⋊Dic61C2212yes—
15C2×C22⋊Dic61C2212yes—
16C2×C4×Dic61C2212yes—
17#14519684C2214yes—
18#14519684C2214yes—
19#14519684C2214yes—
20#14519684C2212yes—
21C22×Q8×C61C2211yescharacteristic
22C23×C4×C61C2211yescharacteristic
23C22⋊Q8×C61—24no—
24C2×C4⋊C4×C61C2212yes—
25C2×C4⋊C4×C61C2211yescharacteristic
26C2×C22⋊C4×C61C2212yes—
27C24×C61C2311yescharacteristic
28C2×Q8×C61—22no—
29C2×Q8×C61—24no—
30C22×C4×C61—24no—
31C22×C4×C61D414yes—
32C22×C4×C61C2312yes—
33C22×C4×C61C2312yes—
34C22×C4×C61C2311yescharacteristic
35C22×C4×C61C2311yescharacteristic
36C22×Dic61C2312yes—
37C22×Dic61C2314yes—
38C22×Dic61C2312yes—
39C4⋊C4×C61—22no—
40C4⋊C4×C61—24no—
41C22⋊C4×C61—24no—
42C22⋊Dic61—24no—
43C22⋊Dic61—42no—
44C4⋊Dic61—22no—
45C4⋊Dic61—22no—
46C4⋊Dic61—24no—
47#11758196—44no—
48C4×Dic61—24no—
49C23×C61—22no—
50C23×C61—21no—
51C23×C61—22no—
52C23×C61—21no—
53C23×C61C2×D412yes—
54C23×C61C2411yescharacteristic
55Q8×C61—44no—
56C2×C4×C61—22no—
57C2×C4×C61—28no—
58C2×C4×C61—22no—
59C2×C4×C61—22no—
60C2×C4×C61—24no—
61C2×C4×C61—22no—
62C2×C4×C61—22no—
63C2×C4×C61C2×D412yes—
64C2×C4×C61C2×D412yes—
65C2×C4×C61#4114yes—
66C2×Dic61—22no—
67C2×Dic61—22no—
68C2×Dic61—24no—
69C2×Dic61—22no—
70C2×Dic61—24no—
71C2×Dic61—24no—
72C2×Dic61—22no—
73C2×Dic61—24no—
74C22×C61—22no—
75C22×C61—22no—
76C22×C61—22no—
77C22×C61—42no—
78C22×C61—42no—
79C22×C61C22×D411yescharacteristic
80C22×C61C2×#4112yes—
81C22×C61H(5,𝔽2)11yescharacteristic
82C22×C612−1+411yescharacteristic
83C22×C612−1+412yes—
84C4×C61—22no—
85C4×C61—42no—
86C4×C61—42no—
87C4×C61#12314yes—
88Dic61—42no—
89Dic61—42no—
90Dic61—44no—
91#2625—611nomaximal, Sylow
92C2×C61—42no—
93C2×C61C2×#12311yescharacteristic
94C2×C61#53611yescharacteristic
95C2×C61#53711yescharacteristic
96C2×C61#54112yes—
97C2×C61#54212yes—
98C2×C22⋊Q8D6111yescharacteristic
99C2×#117—611no—
100#400—612no—
101#398—612no—
102#397—614no—
103#391—612no—
104#389—612no—
105#380—611no—
106C61#262511yescharacteristic, complemented, Sylow
107C22×Q8C2×D6111yescharacteristic
108C23×C4C2×D6111yescharacteristic
109C22⋊Q8—24no—
110#117—1224no—
111C2×C4⋊C4—611no—
112C2×C4⋊C4—611no—
113C2×C4⋊C4—612no—
114C2×C4⋊C4—614no—
115C2×C4⋊C4C2×D6111yescharacteristic
116C2×C4⋊C4C2×D6112yes—
117C2×C22⋊C4—612no—
118C2×C22⋊C4—612no—
119C2×C22⋊C4C2×D6112yes—
120C2×C42—612no—
121#95—612no—
122#95—614no—
123#95—614no—
124#95—614no—
125C24C22×D6111yescharacteristic
126C2×Q8—24no—
127C2×Q8—22no—
128C22×C4—24no—
129C22×C4—612no—
130C22×C4—614no—
131C22×C4—612no—
132C22×C4C22⋊D6114yes—
133C22×C4C22×D6112yes—
134C22×C4C22×D6112yes—
135C22×C4C22×D6111yescharacteristic
136C22×C4C22×D6111yescharacteristic
137C4⋊C4—22no—
138C4⋊C4—24no—
139C4⋊C4—1224no—
140C4⋊C4—1222no—
141C4⋊C4—1222no—
142C4⋊C4—2444no—
143C22⋊C4—24no—
144C22⋊C4—1224no—
145C22⋊C4—2442no—
146C42—1224no—
147C23—22no—
148C23—21no—
149C23—21no—
150C23—22no—
151C23C2×C22⋊D6112yes—
152C23C23×D6111yescharacteristic
153Q8—44no—
154C2×C4—22no—
155C2×C4—28no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—24no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—1222no—
162C2×C4—1222no—
163C2×C4—1224no—
164C2×C4—1224no—
165C2×C4—1222no—
166C2×C4—1222no—
167C2×C4—1224no—
168C2×C4—1224no—
169C2×C4#1175822414yes—
170C2×C4C2×C22⋊D6112yes—
171C2×C4C2×C22⋊D6112yes—
172C22—22no—
173C22—22no—
174C22—22no—
175C22—42no—
176C22—42no—
177C22C22×C22⋊D6111yescharacteristic
178C22C2×#1175822412yes—
179C22#1451982311yescharacteristic
180C22#1451982411yescharacteristic
181C22#1451982512yes—
182C4—22no—
183C4—42no—
184C4—42no—
185C4—2442no—
186C4—2442no—
187C4—2444no—
188C4#1451975814yes—
189C2—42no—
190C2C2×#1451975811yescharacteristic
191C2#1684033611yescharacteristic
192C2#1684034011yescharacteristic
193C2#1684037212yes—
194C2#1684038512yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×C22⋊Q8×C61C2
hypercenterC2×C22⋊Q8D61
hypocenterC61#2625
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #16839701C2semidirect
3. #16839692C2semidirect
5. #16839669C2semidirect
6. #16839658C2semidirect
106. C61#2625semidirect