Finite Group Databasebeta

← #21450728

Subgroups — #21450728

Order 7808.

604 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 165 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×#14519756C212yesmaximal, complemented
2C2×C4×Dic122C211yesmaximal, characteristic, complemented
3#16839693C212yesmaximal, complemented
4#16839676C212yesmaximal
5#16839650C214yesmaximal, complemented
6#16839628C211yesmaximal, characteristic, complemented
7#16839622C212yesmaximal, complemented
8C2×C4×D4×C61C211yesmaximal, characteristic
9C22×Dic122C2211yescharacteristic
10#14519756—28no—
11C4×Dic122—24no—
12C2×C4⋊Dic61C2211yescharacteristic
13C2×C4⋊Dic61C2212yes—
14C2×#11758196C2212yes—
15C2×#11758196C2214yes—
16C2×C22⋊Dic61C2214yes—
17C2×C22⋊Dic61C2214yes—
18C2×C4×Dic61C2212yes—
19#14519684C2214yes—
20#14519684C2212yes—
21#14519684C2212yes—
22C22×D4×C61C2211yescharacteristic
23C23×C4×C61C2212yes—
24C4×D4×C61—24no—
25C2×C4⋊C4×C61C2211yescharacteristic
26C2×C22⋊C4×C61C2212yes—
27C2×C42×C61C2211yescharacteristic
28C24×C61C2312yes—
29C2×D4×C61—24no—
30C2×D4×C61—22no—
31C22×C4×C61—24no—
32C22×C4×C61—24no—
33C22×C4×C61—24no—
34C22×C4×C61C2312yes—
35C22×C4×C61C2311yescharacteristic
36C22×C4×C61C2311yescharacteristic
37C22×C4×C61C2311yescharacteristic
38C22×Dic61C2314yes—
39C22×Dic61C2312yes—
40C22×Dic61C2312yes—
41C2×Dic122—22no—
42C2×Dic122—22no—
43C2×Dic122D414yescomplemented
44C4⋊C4×C61—22no—
45C22⋊C4×C61—24no—
46C42×C61D414yes—
47C22⋊Dic61—28no—
48C22⋊Dic61—28no—
49C4⋊Dic61—22no—
50C4⋊Dic61—24no—
51#11758196—24no—
52#11758196—28no—
53C4×Dic61—24no—
54C23×C61—22no—
55C23×C61—22no—
56C23×C61—22no—
57C23×C61—22no—
58C23×C61—22no—
59C23×C61—22no—
60C23×C61#4114yes—
61C23×C61C2411yescharacteristic
62D4×C61—28no—
63C2×C4×C61—22no—
64C2×C4×C61—22no—
65C2×C4×C61—22no—
66C2×C4×C61—22no—
67C2×C4×C61—22no—
68C2×C4×C61—48no—
69C2×C4×C61C2×D412yes—
70C2×C4×C61C2×D412yes—
71C2×C4×C61C2×D412yes—
72C2×C4×C61C2×D412yes—
73C2×C4×C61#4112yes—
74C2×Dic61—22no—
75C2×Dic61—22no—
76C2×Dic61—22no—
77C2×Dic61—24no—
78C2×Dic61—24no—
79C2×Dic61—24no—
80C2×Dic61—24no—
81C2×Dic61C2×D414yes—
82Dic122—28no—
83C22×C61—24no—
84C22×C61—24no—
85C22×C61—24no—
86C22×C61—42no—
87C22×C61—42no—
88C22×C61—42no—
89C22×C61—42no—
90C22×C61C22×D411yescharacteristic
91C22×C61C22×D411yescharacteristic
92C22×C61C2×#4111yescharacteristic
93C22×C61C2×#4112yes—
94C22×C612−1+412yes—
95C4×C61—22no—
96C4×C61—22no—
97C4×C61—42no—
98C4×C61#12114yes—
99Dic61—24no—
100Dic61—42no—
101Dic61—44no—
102#2536—611nomaximal, Sylow
103C2×C61—44no—
104C2×C61C2×#12111yescharacteristic
105C2×C61#52511yescharacteristic
106C2×C61#53611yescharacteristic
107C2×C61#54812yes—
108C2×C61#55212yes—
109C2×C22⋊Q8—612no—
110C2×C4×Q8—611no—
111C2×C4×D4D6111yescharacteristic
112#398—612no—
113#394—612no—
114#388—614no—
115#382—611no—
116#380—612no—
117C61#253611yescharacteristic, complemented, Sylow
118C22×Q8—611no—
119C22×D4C2×D6111yescharacteristic
120C23×C4C2×D6112yes—
121C22⋊Q8—1228no—
122C4×Q8—1224no—
123C4×D4—24no—
124C2×C4⋊C4—611no—
125C2×C4⋊C4—612no—
126C2×C4⋊C4—612no—
127C2×C4⋊C4—614no—
128C2×C4⋊C4C2×D6111yescharacteristic
129C2×C22⋊C4—614no—
130C2×C22⋊C4—614no—
131C2×C22⋊C4C2×D6112yes—
132C2×C42—612no—
133C2×C42C2×D6111yescharacteristic
134#95—614no—
135#95—612no—
136#95—612no—
137C24C22×D6112yes—
138C2×Q8—614no—
139C2×Q8—1222no—
140C2×Q8—1222no—
141C2×D4—24no—
142C2×D4—22no—
143C22×C4—24no—
144C22×C4—24no—
145C22×C4—24no—
146C22×C4—612no—
147C22×C4—614no—
148C22×C4—612no—
149C22×C4C22×D6112yes—
150C22×C4C22×D6111yescharacteristic
151C22×C4C22×D6111yescharacteristic
152C22×C4C22×D6111yescharacteristic
153C4⋊C4—22no—
154C4⋊C4—1228no—
155C4⋊C4—1224no—
156C4⋊C4—1224no—
157C4⋊C4—1222no—
158C22⋊C4—24no—
159C22⋊C4—1228no—
160C22⋊C4—1228no—
161C42—1224no—
162C42C22⋊D6114yes—
163C23—22no—
164C23—22no—
165C23—22no—
166C23—22no—
167C23—22no—
168C23—22no—
169C23#1175822214yes—
170C23C23×D6111yescharacteristic
171Q8—1228no—
172D4—28no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—48no—
179C2×C4—614no—
180C2×C4—1222no—
181C2×C4—1222no—
182C2×C4—1224no—
183C2×C4—1222no—
184C2×C4—1224no—
185C2×C4—1224no—
186C2×C4—1224no—
187C2×C4D4×D6112yes—
188C2×C4#1175822412yes—
189C2×C4C2×C22⋊D6112yes—
190C2×C4C2×C22⋊D6112yes—
191C2×C4C2×C22⋊D6112yes—
192C22—24no—
193C22—24no—
194C22—24no—
195C22—42no—
196C22—42no—
197C22—42no—
198C22—42no—
199C22C2×D4×D6111yescharacteristic
200C22C22×C22⋊D6111yescharacteristic
201C22C2×#1175822411yescharacteristic
202C22C2×#1175822212yes—
203C22#1451982412yes—
204C4—22no—
205C4—22no—
206C4—42no—
207C4—1224no—
208C4—2442no—
209C4—2444no—
210C4#1451974814yes—
211C2—44no—
212C2C2×#1451974811yescharacteristic
213C2#1684027311yescharacteristic
214C2#1684033311yescharacteristic
215C2#1684042112yes—
216C2#1684045212yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×C4×D4×C61C2
hypercenterC2×C4×D4D61
hypocenterC61#2536
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#14519756C2semidirect
2. C2×C4×Dic122C2semidirect
3. #16839693C2semidirect
5. #16839650C2semidirect
6. #16839628C2semidirect
7. #16839622C2semidirect
43. C2×Dic122D4semidirect
117. C61#2536semidirect