Finite Group Databasebeta

← #21451609

Subgroups — #21451609

Order 7808.

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

normal subgroups only

This group has 548 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, complemented
2#16839698C212yesmaximal, complemented
3#16839687C212yesmaximal, complemented
4#16839676C214yesmaximal, complemented
5#16839665C212yesmaximal, complemented
6#16839658C212yesmaximal, complemented
7#16839622C211yesmaximal, characteristic, complemented
8C2×#121×C61C211yesmaximal, characteristic
9#14519736—24no—
10C2×C4⋊Dic61C2211yescharacteristic
11C2×C4⋊Dic61C2211yescharacteristic
12C2×C4⋊Dic61C2212yes—
13C2×#11758196C2214yes—
14C2×C22⋊Dic61C2212yes—
15C2×C22⋊Dic61C2214yes—
16C2×C22⋊Dic61C2214yes—
17C2×C22⋊Dic61C2212yes—
18C2×C4×Dic61C2212yes—
19#14519684C2212yes—
20#14519684C2214yes—
21C22×D4×C61C2211yescharacteristic
22C22×D4×C61C2212yes—
23C23×C4×C61C2211yescharacteristic
24#121×C61—24no—
25C2×C4⋊C4×C61C2211yescharacteristic
26C2×C22⋊C4×C61C2212yes—
27C24×C61C2312yes—
28C24×C61C2311yescharacteristic
29C2×D4×C61—24no—
30C2×D4×C61—22no—
31C2×D4×C61—24no—
32C2×D4×C61—44no—
33C22×C4×C61—24no—
34C22×C4×C61D414yes—
35C22×C4×C61C2312yes—
36C22×C4×C61C2311yescharacteristic
37C22×C4×C61C2311yescharacteristic
38C22×Dic61C2312yes—
39C22×Dic61C2314yes—
40C22×Dic61C2312yes—
41C4⋊C4×C61—22no—
42C22⋊C4×C61—24no—
43C22⋊Dic61—24no—
44C22⋊Dic61—44no—
45C22⋊Dic61—42no—
46C22⋊Dic61—44no—
47C4⋊Dic61—22no—
48C4⋊Dic61—22no—
49C4⋊Dic61—24no—
50#11758196—44no—
51C4×Dic61—24no—
52C23×C61—22no—
53C23×C61—21no—
54C23×C61—22no—
55C23×C61—21no—
56C23×C61—22no—
57C23×C61—24no—
58C23×C61—22no—
59C23×C61—24no—
60C23×C61—22no—
61C23×C61C2×D412yes—
62C23×C61C2411yescharacteristic
63D4×C61—48no—
64D4×C61—44no—
65C2×C4×C61—22no—
66C2×C4×C61—28no—
67C2×C4×C61—22no—
68C2×C4×C61—24no—
69C2×C4×C61C2×D412yes—
70C2×C4×C61C2×D412yes—
71C2×C4×C61#4114yes—
72C2×Dic61—22no—
73C2×Dic61—22no—
74C2×Dic61—24no—
75C2×Dic61—22no—
76C2×Dic61—24no—
77C2×Dic61—22no—
78C2×Dic61—22no—
79C2×Dic61—24no—
80C2×Dic61—22no—
81C22×C61—22no—
82C22×C61—22no—
83C22×C61—22no—
84C22×C61—42no—
85C22×C61—42no—
86C22×C61—42no—
87C22×C61—42no—
88C22×C61—42no—
89C22×C61—44no—
90C22×C61—44no—
91C22×C61C22×D411yescharacteristic
92C22×C61C2×#4112yes—
93C22×C61H(5,𝔽2)12yes—
94C22×C61H(5,𝔽2)11yescharacteristic
95C22×C612−1+411yescharacteristic
96C4×C61—22no—
97C4×C61—42no—
98C4×C61#12314yes—
99Dic61—42no—
100Dic61—42no—
101Dic61—44no—
102#2624—611nomaximal, Sylow
103C2×C61—42no—
104C2×C61—82no—
105C2×C61C2×#12311yescharacteristic
106C2×C61#53511yescharacteristic
107C2×C61#53711yescharacteristic
108C2×C61#54012yes—
109C2×C61#54212yes—
110C2×#121D6111yescharacteristic
111C2×#117—611no—
112#399—612no—
113#397—612no—
114#394—614no—
115#390—612no—
116#389—612no—
117#380—611no—
118C61#262411yescharacteristic, complemented, Sylow
119C22×D4C2×D6111yescharacteristic
120C22×D4C2×D6112yes—
121C23×C4C2×D6111yescharacteristic
122#121—24no—
123#117—1224no—
124C2×C4⋊C4—611no—
125C2×C4⋊C4—611no—
126C2×C4⋊C4—612no—
127C2×C4⋊C4—614no—
128C2×C4⋊C4C2×D6111yescharacteristic
129C2×C22⋊C4—612no—
130C2×C22⋊C4—612no—
131C2×C22⋊C4—614no—
132C2×C22⋊C4—614no—
133C2×C22⋊C4C2×D6112yes—
134C2×C42—612no—
135#95—612no—
136#95—614no—
137C24C22×D6112yes—
138C24C22×D6111yescharacteristic
139C2×D4—24no—
140C2×D4—24no—
141C2×D4—22no—
142C2×D4—44no—
143C22×C4—24no—
144C22×C4—612no—
145C22×C4—614no—
146C22×C4—612no—
147C22×C4C22⋊D6114yes—
148C22×C4C22×D6112yes—
149C22×C4C22×D6111yescharacteristic
150C22×C4C22×D6111yescharacteristic
151C4⋊C4—22no—
152C4⋊C4—1224no—
153C4⋊C4—1222no—
154C4⋊C4—1222no—
155C4⋊C4—2444no—
156C22⋊C4—24no—
157C22⋊C4—1224no—
158C22⋊C4—2444no—
159C22⋊C4—2442no—
160C22⋊C4—2444no—
161C42—1224no—
162C23—22no—
163C23—22no—
164C23—21no—
165C23—21no—
166C23—22no—
167C23—24no—
168C23—24no—
169C23—22no—
170C23—22no—
171C23C2×C22⋊D6112yes—
172C23C23×D6111yescharacteristic
173D4—48no—
174D4—44no—
175C2×C4—22no—
176C2×C4—28no—
177C2×C4—22no—
178C2×C4—24no—
179C2×C4—1222no—
180C2×C4—1222no—
181C2×C4—1224no—
182C2×C4—1222no—
183C2×C4—1224no—
184C2×C4—1222no—
185C2×C4—1222no—
186C2×C4—1224no—
187C2×C4—1222no—
188C2×C4#1175822414yes—
189C2×C4C2×C22⋊D6112yes—
190C2×C4C2×C22⋊D6112yes—
191C22—22no—
192C22—22no—
193C22—22no—
194C22—42no—
195C22—42no—
196C22—42no—
197C22—42no—
198C22—42no—
199C22—44no—
200C22—44no—
201C22C22×C22⋊D6111yescharacteristic
202C22C2×#1175822412yes—
203C22#1451982212yes—
204C22#1451982311yescharacteristic
205C22#1451982411yescharacteristic
206C4—22no—
207C4—42no—
208C4—2442no—
209C4—2442no—
210C4—2444no—
211C4#1451975814yes—
212C2—42no—
213C2—82no—
214C2C2×#1451975811yescharacteristic
215C2#1684032911yescharacteristic
216C2#1684034011yescharacteristic
217C2#1684036512yes—
218C2#1684037912yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×#121×C61C2
hypercenterC2×#121D61
hypocenterC61#2624
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#14519736C2semidirect
2. #16839698C2semidirect
3. #16839687C2semidirect
4. #16839676C2semidirect
5. #16839665C2semidirect
6. #16839658C2semidirect
7. #16839622C2semidirect
118. C61#2624semidirect