Finite Group Databasebeta

← #21451641

Subgroups — #21451641

Order 7808.

488 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 157 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×#14519734C211yesmaximal, characteristic
2#16839700C212yesmaximal, complemented
3#16839697C212yesmaximal
4#16839681C212yesmaximal, complemented
5#16839673C212yesmaximal
6#16839658C212yesmaximal, complemented
7#16839628C211yesmaximal, characteristic, complemented
8#16839619C212yesmaximal
9C2×C4⋊Q8×C61C211yesmaximal, characteristic, complemented
10C22×C4×D61C2211yescharacteristic
11#14519734—24no—
12C2×C4⋊Dic61C2212yes—
13C2×#11758196C2211yescharacteristic
14C2×#11758196C2211yescharacteristic
15C2×#11758196C2214yes—
16C2×#11758198C2211yescharacteristic
17C2×#11758198C2211yescharacteristic
18C2×#11758198C2214yes—
19C2×C4×Dic61C2211yescharacteristic
20#14519684C2214yes—
21#14519684C2212yes—
22#14519684C2212yes—
23#14519684C2214yes—
24C22×Q8×C61C2212yes—
25C4⋊Q8×C61—24no—
26C2×C4⋊C4×C61C2212yes—
27C2×C4⋊C4×C61C2212yes—
28C2×C42×C61C2211yescharacteristic
29C23×D61C2311yescharacteristic
30C2×Q8×C61—24no—
31C2×Q8×C61—44no—
32C22×C4×C61C2314yes—
33C22×C4×C61C2311yescharacteristic
34C22×C4×C61C2311yescharacteristic
35C22×C4×C61C2311yescharacteristic
36C22×Dic61C2311yescharacteristic
37C22×Dic61C2314yes—
38C22×Dic61C2311yescharacteristic
39C22×Dic61C2311yescharacteristic
40C2×C4×D61—22no—
41C2×C4×D61—22no—
42C2×C4×D61Q814yescomplemented
43C4⋊C4×C61—24no—
44C4⋊C4×C61—24no—
45C42×C61D414yes—
46#11758198—22no—
47#11758198—22no—
48#11758198—44no—
49C4⋊Dic61—24no—
50#11758196—22no—
51#11758196—22no—
52#11758196—44no—
53C4×Dic61—22no—
54C23×C61C2411yescharacteristic
55C22×D61—21no—
56C22×D61—21no—
57C22×D61—22no—
58C22×D61—22no—
59C22×D61C2×Q812yes—
60Q8×C61—48no—
61C2×C4×C61—22no—
62C2×C4×C61—22no—
63C2×C4×C61—24no—
64C2×C4×C61—24no—
65C2×C4×C61—24no—
66C2×C4×C61C2×D412yes—
67C2×C4×C61C2×D412yes—
68C2×C4×C61C2×D412yes—
69C2×C4×C61C2×Q812yes—
70C2×C4×C61#4112yes—
71C2×Dic61—21no—
72C2×Dic61—21no—
73C2×Dic61—21no—
74C2×Dic61—21no—
75C2×Dic61—24no—
76C2×Dic61—22no—
77C2×Dic61—24no—
78C2×Dic61—22no—
79C2×Dic61—24no—
80C2×Dic61C2×Q812yes—
81C4×D61—28no—
82C22×C61C22×D411yescharacteristic
83C22×C61C22×Q811yescharacteristic
84C22×C61C2×#4111yescharacteristic
85C22×C61H(5,𝔽2)12yes—
86C22×C612−1+412yes—
87C2×D61—22no—
88C2×D61—24no—
89C2×D61—41no—
90C2×D61—41no—
91C2×D61—42no—
92C4×C61—22no—
93C4×C61—22no—
94C4×C61—44no—
95C4×C61C22⋊Q814yes—
96Dic61—22no—
97Dic61—41no—
98Dic61—41no—
99Dic61—44no—
100#2628—611nomaximal, Sylow
101C2×C61C2×C22⋊Q811yescharacteristic
102C2×C61#53511yescharacteristic
103C2×C61#53611yescharacteristic
104C2×C61#54212yes—
105C2×C61#54412yes—
106D61—42no—
107C2×C4⋊Q8D6111yescharacteristic, complemented
108C2×#117—611no—
109#400—612no—
110#399—612no—
111#395—612no—
112#393—612no—
113#389—612no—
114#382—611no—
115#380—612no—
116C61#262811yescharacteristic, complemented, Sylow
117C22×Q8C2×D6112yes—
118C23×C4—611no—
119C4⋊Q8—24no—
120#117—1224no—
121C2×C4⋊C4—611no—
122C2×C4⋊C4—611no—
123C2×C4⋊C4—612no—
124C2×C4⋊C4—614no—
125C2×C4⋊C4C2×D6112yes—
126C2×C4⋊C4C2×D6112yes—
127C2×C22⋊C4—611no—
128C2×C22⋊C4—611no—
129C2×C22⋊C4—614no—
130C2×C42—611no—
131C2×C42C2×D6111yescharacteristic
132#95—614no—
133#95—612no—
134#95—612no—
135#95—614no—
136C24—611no—
137C2×Q8—24no—
138C2×Q8—44no—
139C22×C4—611no—
140C22×C4—614no—
141C22×C4—611no—
142C22×C4—614no—
143C22×C4—611no—
144C22×C4—1222no—
145C22×C4—1222no—
146C22×C4C22×D6114yes—
147C22×C4C22×D6111yescharacteristic
148C22×C4C22×D6111yescharacteristic
149C22×C4C22×D6111yescharacteristic
150C4⋊C4—24no—
151C4⋊C4—24no—
152C4⋊C4—1224no—
153C4⋊C4—1222no—
154C4⋊C4—1222no—
155C4⋊C4—2444no—
156C22⋊C4—1222no—
157C22⋊C4—1222no—
158C22⋊C4—2444no—
159C42—1222no—
160C42C22⋊D6114yes—
161C23—612no—
162C23—1221no—
163C23—1221no—
164C23—1222no—
165C23—1222no—
166C23C23×D6111yescharacteristic
167Q8—48no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—24no—
171C2×C4—24no—
172C2×C4—24no—
173C2×C4—612no—
174C2×C4—1221no—
175C2×C4—1221no—
176C2×C4—1228no—
177C2×C4—1221no—
178C2×C4—1221no—
179C2×C4—1224no—
180C2×C4—1224no—
181C2×C4—1222no—
182C2×C4—1222no—
183C2×C4—1224no—
184C2×C4Q8×D6112yes—
185C2×C4#1175822612yes—
186C2×C4C2×C22⋊D6112yes—
187C2×C4C2×C22⋊D6112yes—
188C2×C4C2×C22⋊D6112yes—
189C22—1222no—
190C22—1224no—
191C22—2441no—
192C22—2441no—
193C22—2442no—
194C22C22×C22⋊D6111yescharacteristic
195C22C2×Q8×D6111yescharacteristic
196C22C2×#1175822611yescharacteristic
197C22#1451982212yes—
198C22#1451982512yes—
199C4—22no—
200C4—22no—
201C4—44no—
202C4—1222no—
203C4—2441no—
204C4—2441no—
205C4—2444no—
206C4#1451975314yes—
207C2—2442no—
208C2C2×#1451975311yescharacteristic
209C2#1684032911yescharacteristic
210C2#1684033611yescharacteristic
211C2#1684038612yes—
212C2#1684038912yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×C4⋊Q8×C61C2
hypercenterC2×C4⋊Q8D61
hypocenterC61#2628
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #16839700C2semidirect
4. #16839681C2semidirect
6. #16839658C2semidirect
7. #16839628C2semidirect
9. C2×C4⋊Q8×C61C2semidirect
42. C2×C4×D61Q8semidirect
107. C2×C4⋊Q8D61semidirect
116. C61#2628semidirect