Finite Group Databasebeta

← #21448526

Subgroups — #21448526

Order 7808.

612 conjugacy classes of subgroups; only the 205 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 205 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×#14519766C211yesmaximal, characteristic
2C2×C4×D244C211yesmaximal, characteristic
3#16839669C211yesmaximal, characteristic, complemented
4#16839663C211yesmaximal, characteristic
5#16839653C214yesmaximal, complemented
6#16839633C214yesmaximal, complemented
7#16839631C211yesmaximal, characteristic, complemented
8#16839608C211yesmaximal, characteristic, complemented
9C2×C4×Q8×C61C211yesmaximal, characteristic, complemented
10C22×D244C2211yescharacteristic
11C22×C4×D61C2212yes—
12#14519766C418yescomplemented
13C4×D244—24no—
14C2×C4⋊Dic61C2211yescharacteristic
15C2×#11758196C2214yes—
16C2×#11758198C2212yes—
17C2×#11758198C2214yes—
18C2×#11758198C2214yes—
19C2×C4×Dic61C2211yescharacteristic
20C2×C4×Dic61C2211yescharacteristic
21#14519684C2212yes—
22#14519684C2212yes—
23#14519684C2214yes—
24C22×Q8×C61C2211yescharacteristic
25C4×Q8×C61—24no—
26C2×C4⋊C4×C61C2211yescharacteristic
27C2×C4⋊C4×C61C2212yes—
28C2×C42×C61C2212yes—
29C2×C42×C61C2211yescharacteristic
30C23×D61C2312yes—
31C2×Q8×C61—22no—
32C2×Q8×C61—22no—
33C2×Q8×C61C2×C414yescomplemented
34C22×C4×C61C2312yes—
35C22×C4×C61C2312yes—
36C22×C4×C61C2311yescharacteristic
37C22×C4×C61C2311yescharacteristic
38C22×C4×C61C2311yescharacteristic
39C22×Dic61C2312yes—
40C22×Dic61C2312yes—
41C22×Dic61C2312yes—
42C2×D244—22no—
43C2×D244—22no—
44C2×D244C2×C414yes—
45C2×C4×D61—24no—
46C2×C4×D61—44no—
47C4⋊C4×C61—24no—
48C4⋊C4×C61—22no—
49C42×C61—24no—
50C42×C61D414yes—
51#11758198—24no—
52#11758198—44no—
53#11758198C2×C4116yescomplemented
54C4⋊Dic61—22no—
55#11758196—44no—
56C4×Dic61—22no—
57C4×Dic61C2×C414yescomplemented
58C23×C61C2411yescharacteristic
59C22×D61—22no—
60C22×D61—22no—
61C22×D61—24no—
62C22×D61—24no—
63C22×D61C22×C414yes—
64Q8×C61—28no—
65C2×C4×C61—22no—
66C2×C4×C61—22no—
67C2×C4×C61—22no—
68C2×C4×C61—22no—
69C2×C4×C61—22no—
70C2×C4×C61—24no—
71C2×C4×C61C22×C414yes—
72C2×C4×C61C22×C412yes—
73C2×C4×C61C2×D412yes—
74C2×C4×C61C2×D412yes—
75C2×C4×C61C2×D412yes—
76C2×C4×C61#4112yes—
77C2×Dic61—22no—
78C2×Dic61—22no—
79C2×Dic61—22no—
80C2×Dic61—22no—
81C2×Dic61—24no—
82C2×Dic61—22no—
83C2×Dic61—22no—
84C2×Dic61C22×C414yes—
85D244—28no—
86C4×D61—48no—
87C22×C61C23×C411yescharacteristic
88C22×C61C22×D411yescharacteristic
89C22×C61C2×#4111yescharacteristic
90C22×C61H(5,𝔽2)12yes—
91C22×C612−1+412yes—
92C2×D61—24no—
93C2×D61—28no—
94C2×D61—42no—
95C2×D61—42no—
96C2×D61—44no—
97C4×C61—24no—
98C4×C61—22no—
99C4×C61—22no—
100C4×C61—42no—
101C4×C61C4×D414yes—
102Dic61—24no—
103Dic61—42no—
104Dic61—42no—
105#2326—611nomaximal, Sylow
106C2×C61C2×C4×D411yescharacteristic
107C2×C61#52012yes—
108C2×C61#53511yescharacteristic
109C2×C61#53611yescharacteristic
110C2×C61#54212yes—
111D61—44no—
112C2×#124—611no—
113C2×C4×Q8D6111yescharacteristic, complemented
114C2×C4×D4—611no—
115#391—611no—
116#390—611no—
117#388—614no—
118#385—614no—
119#384—611no—
120#376—611no—
121C61#232611yescharacteristic, complemented, Sylow
122C22×Q8C2×D6111yescharacteristic
123C22×D4—611no—
124C23×C4—612no—
125#124—618no—
126C4×Q8—24no—
127C4×D4—1224no—
128C2×C4⋊C4—611no—
129C2×C4⋊C4—614no—
130C2×C4⋊C4C2×D6111yescharacteristic
131C2×C4⋊C4C2×D6112yes—
132C2×C22⋊C4—614no—
133C2×C22⋊C4—612no—
134C2×C22⋊C4—614no—
135C2×C42—611no—
136C2×C42—611no—
137C2×C42C2×D6112yes—
138C2×C42C2×D6111yescharacteristic
139#95—612no—
140#95—612no—
141#95—614no—
142C24—612no—
143C2×Q8—22no—
144C2×Q8—22no—
145C2×Q8C4×D6114yescomplemented
146C2×D4—614no—
147C2×D4—1222no—
148C2×D4—1222no—
149C22×C4—612no—
150C22×C4—612no—
151C22×C4—612no—
152C22×C4—1224no—
153C22×C4—2444no—
154C22×C4C22×D6112yes—
155C22×C4C22×D6112yes—
156C22×C4C22×D6111yescharacteristic
157C22×C4C22×D6111yescharacteristic
158C22×C4C22×D6111yescharacteristic
159C4⋊C4—24no—
160C4⋊C4—22no—
161C4⋊C4—1222no—
162C4⋊C4—2444no—
163C22⋊C4—6116no—
164C22⋊C4—1224no—
165C22⋊C4—2444no—
166C42—24no—
167C42—614no—
168C42—1222no—
169C42C22⋊D6114yes—
170C23—614no—
171C23—1222no—
172C23—1222no—
173C23—1224no—
174C23—1224no—
175C23C23×D6111yescharacteristic
176Q8—28no—
177D4—1228no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—24no—
184C2×C4—614no—
185C2×C4—1222no—
186C2×C4—1222no—
187C2×C4—1222no—
188C2×C4—1222no—
189C2×C4—1222no—
190C2×C4—1224no—
191C2×C4—1222no—
192C2×C4—2448no—
193C2×C4C2×C4×D6114yes—
194C2×C4C2×C4×D6112yes—
195C2×C4#1175822212yes—
196C2×C4C2×C22⋊D6112yes—
197C2×C4C2×C22⋊D6112yes—
198C2×C4C2×C22⋊D6112yes—
199C22—1224no—
200C22—1228no—
201C22—2442no—
202C22—2442no—
203C22—2444no—
204C22C22×C4×D6111yescharacteristic
205C22C22×C22⋊D6111yescharacteristic
206C22C2×#1175822211yescharacteristic
207C22#1451982312yes—
208C22#1451982512yes—
209C4—24no—
210C4—22no—
211C4—22no—
212C4—42no—
213C4—1224no—
214C4—2442no—
215C4—2442no—
216C4C4×C22⋊D6114yes—
217C2—2444no—
218C2C2×C4×C22⋊D6111yescharacteristic
219C2#1684024412yes—
220C2#1684032611yescharacteristic
221C2#1684033611yescharacteristic
222C2#1684038412yes—
subgroupG/H
center, FrattiniC23C23×D61
commutatorC22×C61C23×C4
FittingC2×C4×Q8×C61C2
socleC23×C61C24
hypercenterC2×C4×Q8D61
hypocenterC61#2326
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
3. #16839669C2semidirect
5. #16839653C2semidirect
6. #16839633C2semidirect
7. #16839631C2semidirect
8. #16839608C2semidirect
9. C2×C4×Q8×C61C2semidirect
12. #14519766C4semidirect
33. C2×Q8×C61C2×C4semidirect
53. #11758198C2×C4semidirect
57. C4×Dic61C2×C4semidirect
113. C2×C4×Q8D61semidirect
121. C61#2326semidirect
145. C2×Q8C4×D61semidirect