Finite Group Databasebeta

← #21448444

Subgroups — #21448444

Order 7808.

600 conjugacy classes of subgroups; only the 229 normal subgroups are shown.

normal subgroups only

This group has 600 conjugacy classes of subgroups — too many to draw. Only its 229 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×#14519735C211yesmaximal, characteristic
2C2×#14519734C211yesmaximal, characteristic
3C2×C4⋊C4×D61C211yesmaximal, characteristic
4#16839659C214yesmaximal, complemented
5#16839636C214yesmaximal
6#16839632C211yesmaximal, characteristic, complemented
7#16839631C211yesmaximal, characteristic, complemented
8#16839627C211yesmaximal, characteristic, complemented
9C61×#382C211yesmaximal, characteristic, complemented
10C22×C4×D61C2212yes—
11C22×C4×D61C2211yescharacteristic
12#14519735—24no—
13#14519734C418yescomplemented
14C2×C4⋊Dic61C2211yescharacteristic
15C2×C4⋊Dic61C2211yescharacteristic
16C2×C4⋊Dic61C2214yes—
17C2×#11758196C2212yes—
18C2×#11758196C2214yes—
19C2×#11758196C2212yes—
20C4⋊C4×D61—24no—
21C2×#11758198C2212yes—
22C2×#11758198C2212yes—
23C2×C4×Dic61C2212yes—
24C2×C4×Dic61C2211yescharacteristic
25#14519684C2214yes—
26C2×C4⋊C4×C61C2211yescharacteristic
27C2×C4⋊C4×C61C2211yescharacteristic
28C2×C42×C61C2211yescharacteristic
29#95×C61C2214yes—
30C23×D61C2311yescharacteristic
31C22×C4×C61C2312yes—
32C22×C4×C61C2312yes—
33C22×C4×C61C2312yes—
34C22×C4×C61C2311yescharacteristic
35C22×Dic61C2312yes—
36C22×Dic61C2312yes—
37C22×Dic61C2312yes—
38C22×Dic61C2311yescharacteristic
39C2×C4×D61—24no—
40C2×C4×D61—44no—
41C2×C4×D61C2×C414yes—
42C2×C4×D61D414yes—
43C2×C4×D61Q814yes—
44C4⋊C4×C61—22no—
45C4⋊C4×C61—22no—
46C42×C61C2×C414yescomplemented
47#11758198—24no—
48#11758198C2×C418yes—
49C4⋊Dic61—22no—
50C4⋊Dic61—22no—
51C4⋊Dic61—44no—
52#11758196—24no—
53#11758196—44no—
54#11758196C2×C418yescomplemented
55C4×Dic61—24no—
56C4×Dic61C2×C414yescomplemented
57C23×C61C2411yescharacteristic
58C22×D61—22no—
59C22×D61—22no—
60C22×D61C22×C412yes—
61C22×D61C2×D412yes—
62C22×D61C2×Q812yes—
63C2×C4×C61—22no—
64C2×C4×C61—22no—
65C2×C4×C61—22no—
66C2×C4×C61—22no—
67C2×C4×C61—24no—
68C2×C4×C61—24no—
69C2×C4×C61C22×C414yes—
70C2×C4×C61C22×C412yes—
71C2×C4×C61C2×D412yes—
72C2×C4×C61C2×Q812yes—
73C2×Dic61—22no—
74C2×Dic61—22no—
75C2×Dic61—22no—
76C2×Dic61—22no—
77C2×Dic61—24no—
78C2×Dic61—24no—
79C2×Dic61C22×C414yes—
80C2×Dic61C22×C412yes—
81C2×Dic61C2×D412yes—
82C2×Dic61C2×Q812yes—
83C4×D61—48no—
84C4×D61C4⋊C4116yescomplemented
85C22×C61C23×C411yescharacteristic
86C22×C61C22×D411yescharacteristic
87C22×C61C22×Q811yescharacteristic
88C22×C61H(5,𝔽2)12yes—
89C22×C612−1+412yes—
90C2×D61—24no—
91C2×D61—22no—
92C2×D61—22no—
93C2×D61—24no—
94C2×D61C2×C4⋊C414yes—
95C4×C61—24no—
96C4×C61—42no—
97C4×C61—42no—
98C4×C61C2×C4⋊C414yes—
99Dic61—24no—
100Dic61—42no—
101Dic61—42no—
102Dic61C2×C4⋊C414yes—
103#2317—611nomaximal, Sylow
104C2×C61C22×C4⋊C411yescharacteristic
105C2×C61#52012yes—
106C2×C61#53511yescharacteristic
107C2×C61#53611yescharacteristic
108C2×C61#54412yes—
109D61—24no—
110C2×#117—611no—
111C2×#117—611no—
112C22×C4⋊C4—611no—
113#389—614no—
114#385—614no—
115#384—611no—
116#384—611no—
117#382—611no—
118#382D6111yescharacteristic, complemented
119C61#231711yescharacteristic, complemented, Sylow
120C23×C4—611no—
121C23×C4—612no—
122#117—618no—
123#117—1224no—
124C2×C4⋊C4—612no—
125C2×C4⋊C4—611no—
126C2×C4⋊C4—612no—
127C2×C4⋊C4—611no—
128C2×C4⋊C4—614no—
129C2×C4⋊C4—614no—
130C2×C4⋊C4—1224no—
131C2×C4⋊C4C2×D6111yescharacteristic
132C2×C4⋊C4C2×D6111yescharacteristic
133C2×C22⋊C4—612no—
134C2×C22⋊C4—612no—
135C2×C42—611no—
136C2×C42—612no—
137C2×C42C2×D6111yescharacteristic
138#95—614no—
139#95C2×D6114yes—
140C24—611no—
141C22×C4—611no—
142C22×C4—614no—
143C22×C4—614no—
144C22×C4—614no—
145C22×C4—612no—
146C22×C4—612no—
147C22×C4—612no—
148C22×C4—1224no—
149C22×C4—2444no—
150C22×C4C22×D6112yes—
151C22×C4C22×D6112yes—
152C22×C4C22×D6112yes—
153C22×C4C22×D6111yescharacteristic
154C4⋊C4—22no—
155C4⋊C4—22no—
156C4⋊C4—618no—
157C4⋊C4—1224no—
158C4⋊C4—1222no—
159C4⋊C4—1222no—
160C4⋊C4—2444no—
161C4⋊C4—2444no—
162C22⋊C4—618no—
163C22⋊C4—1224no—
164C42—614no—
165C42—1224no—
166C42C4×D6114yescomplemented
167C23—612no—
168C23—612no—
169C23—612no—
170C23—1222no—
171C23—1222no—
172C23C23×D6111yescharacteristic
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—24no—
178C2×C4—24no—
179C2×C4—612no—
180C2×C4—612no—
181C2×C4—612no—
182C2×C4—6116no—
183C2×C4—614no—
184C2×C4—1222no—
185C2×C4—1222no—
186C2×C4—1222no—
187C2×C4—1222no—
188C2×C4—1224no—
189C2×C4—1224no—
190C2×C4—2448no—
191C2×C4C2×C4×D6114yes—
192C2×C4C2×C4×D6112yes—
193C2×C4D4×D6112yes—
194C2×C4Q8×D6112yes—
195C22—614no—
196C22—1224no—
197C22—1222no—
198C22—1222no—
199C22—1224no—
200C22C22×C4×D6111yescharacteristic
201C22C2×D4×D6111yescharacteristic
202C22C2×Q8×D6111yescharacteristic
203C22#1451982312yes—
204C22#1451982412yes—
205C4—24no—
206C4—42no—
207C4—42no—
208C4—614no—
209C4—1224no—
210C4—2442no—
211C4—2442no—
212C4C4⋊C4×D6114yes—
213C2—1224no—
214C2C2×C4⋊C4×D6111yescharacteristic
215C2#1684024212yes—
216C2#1684033011yescharacteristic
217C2#1684033211yescharacteristic
218C2#1684039212yes—
subgroupG/H
center, FrattiniC23C23×D61
commutatorC22×C61C23×C4
FittingC61×#382C2
socleC23×C61C24
hypercenter#382D61
hypocenterC61#2317
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
4. #16839659C2semidirect
6. #16839632C2semidirect
7. #16839631C2semidirect
8. #16839627C2semidirect
9. C61×#382C2semidirect
13. #14519734C4semidirect
46. C42×C61C2×C4semidirect
54. #11758196C2×C4semidirect
56. C4×Dic61C2×C4semidirect
84. C4×D61C4⋊C4semidirect
118. #382D61semidirect
119. C61#2317semidirect
166. C42C4×D61semidirect