Finite Group Databasebeta

← #21454168

Subgroups — #21454168

Order 7808.

644 conjugacy classes of subgroups; only the 189 normal subgroups are shown.

normal subgroups only

This group has 644 conjugacy classes of subgroups — too many to draw. Only its 189 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×#14519775C211yesmaximal, characteristic, complemented
2C2×#14519757C211yesmaximal, characteristic
3C2×#14519753C211yesmaximal, characteristic
4C2×C42×D61C211yesmaximal, characteristic
5#16839668C211yesmaximal, characteristic, complemented
6#16839659C214yesmaximal, complemented
7#16839631C211yesmaximal, characteristic, complemented
8#16839621C214yesmaximal
9C61×#391C211yesmaximal, characteristic, complemented
10C22×Dic122C2211yescharacteristic
11C22×C4×D61C2211yescharacteristic
12C22×C4×D61C2212yes—
13#14519775—24no—
14#14519757—24no—
15#14519753—24no—
16C2×C4⋊Dic61C2211yescharacteristic
17C2×C4⋊Dic61C2212yes—
18C2×#11758196C2212yes—
19C2×#11758196C2214yes—
20C2×#11758196C2214yes—
21C2×#11758198C2212yes—
22C2×#11758198C2212yes—
23C2×C4×Dic61C2212yes—
24C2×C4×Dic61C2211yescharacteristic
25C42×D61—24no—
26#14519684C2214yes—
27C22×Q8×C61C2211yescharacteristic
28C2×C4⋊C4×C61C2211yescharacteristic
29C2×C42×C61C2211yescharacteristic
30#95×C61C2214yes—
31C23×D61C2311yescharacteristic
32C2×Q8×C61—22no—
33C2×Q8×C61—22no—
34C2×Q8×C61—22no—
35C22×C4×C61C2312yes—
36C22×C4×C61C2312yes—
37C22×C4×C61C2312yes—
38C22×C4×C61C2311yescharacteristic
39C22×Dic61C2312yes—
40C22×Dic61C2312yes—
41C22×Dic61C2311yescharacteristic
42C22×Dic61C2312yes—
43C2×C4×D61—22no—
44C2×C4×D61—22no—
45C2×C4×D61—24no—
46C2×C4×D61—24no—
47C2×C4×D61D414yes—
48C2×C4×D61Q818yescomplemented
49C2×Dic122—22no—
50C2×Dic122—22no—
51C2×Dic122—22no—
52C4⋊C4×C61—22no—
53C42×C61—22no—
54#11758198—24no—
55#11758198—24no—
56C4⋊Dic61—22no—
57C4⋊Dic61—24no—
58#11758196—24no—
59#11758196—28no—
60#11758196—28no—
61C4×Dic61—24no—
62C4×Dic61D414yes—
63C23×C61C2411yescharacteristic
64C22×D61—21no—
65C22×D61—21no—
66C22×D61—22no—
67C22×D61C2×D412yes—
68C22×D61C2×Q814yes—
69Q8×C61—44no—
70C2×C4×C61—22no—
71C2×C4×C61—22no—
72C2×C4×C61—22no—
73C2×C4×C61—22no—
74C2×C4×C61—22no—
75C2×C4×C61—24no—
76C2×C4×C61—22no—
77C2×C4×C61C2×D412yes—
78C2×C4×C61C2×D412yes—
79C2×C4×C61C2×Q814yes—
80C2×C4×C61#4112yes—
81C2×Dic61—21no—
82C2×Dic61—21no—
83C2×Dic61—22no—
84C2×Dic61—22no—
85C2×Dic61—22no—
86C2×Dic61—24no—
87C2×Dic61—22no—
88C2×Dic61C2×D412yes—
89C2×Dic61C2×D414yes—
90C2×Dic61C2×Q814yes—
91C2×Dic61#4114yes—
92C4×D61—28no—
93C4×D61—216no—
94Dic122—44no—
95C22×C61C22×D411yescharacteristic
96C22×C61C22×D411yescharacteristic
97C22×C61C22×Q812yes—
98C22×C61C2×#4112yes—
99C22×C61C2×#4111yescharacteristic
100C2×D61—22no—
101C2×D61—24no—
102C2×D61—22no—
103C2×D61—24no—
104C2×D61C4⋊Q814yescomplemented
105C4×C61—24no—
106C4×C61—42no—
107C4×C61—42no—
108C4×C61#12114yes—
109Dic61—22no—
110Dic61—42no—
111Dic61—42no—
112Dic61C22⋊Q818yescomplemented
113#2857—611nomaximal, Sylow
114C2×C61C2×#12111yescharacteristic
115C2×C61C2×C22⋊Q812yes—
116C2×C61C2×C4⋊Q811yescharacteristic
117C2×C61#53211yescharacteristic
118C2×C61#53312yes—
119D61—24no—
120C2×C4⋊Q8—611no—
121C2×C22⋊Q8—611no—
122C2×C22⋊Q8—611no—
123C22×C42—611no—
124#391—611no—
125#391D6111yescharacteristic, complemented
126#389—614no—
127#384—611no—
128#380—614no—
129C61#285711yescharacteristic, complemented, Sylow
130C22×Q8—611no—
131C22×Q8C2×D6111yescharacteristic
132C23×C4—611no—
133C23×C4—612no—
134C4⋊Q8—1224no—
135C22⋊Q8—1224no—
136C22⋊Q8—1224no—
137C2×C4⋊C4—611no—
138C2×C4⋊C4—612no—
139C2×C4⋊C4—612no—
140C2×C4⋊C4—614no—
141C2×C4⋊C4—614no—
142C2×C4⋊C4C2×D6111yescharacteristic
143C2×C22⋊C4—612no—
144C2×C22⋊C4—612no—
145C2×C42—611no—
146C2×C42—612no—
147C2×C42—1224no—
148C2×C42C2×D6111yescharacteristic
149#95—614no—
150#95C2×D6114yes—
151C24—611no—
152C2×Q8—22no—
153C2×Q8—22no—
154C2×Q8—22no—
155C2×Q8—1222no—
156C2×Q8—1222no—
157C2×Q8—1222no—
158C22×C4—612no—
159C22×C4—611no—
160C22×C4—614no—
161C22×C4—618no—
162C22×C4—612no—
163C22×C4—612no—
164C22×C4—1224no—
165C22×C4—1224no—
166C22×C4—1222no—
167C22×C4—1222no—
168C22×C4C22×D6112yes—
169C22×C4C22×D6112yes—
170C22×C4C22×D6112yes—
171C22×C4C22×D6111yescharacteristic
172C4⋊C4—22no—
173C4⋊C4—1228no—
174C4⋊C4—1224no—
175C4⋊C4—1228no—
176C4⋊C4—1224no—
177C4⋊C4—1222no—
178C22⋊C4—1224no—
179C22⋊C4—1224no—
180C42—22no—
181C42—614no—
182C42—1224no—
183C23—612no—
184C23—614no—
185C23—1221no—
186C23—1222no—
187C23—1221no—
188C23C23×D6111yescharacteristic
189Q8—44no—
190Q8—2444no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—24no—
197C2×C4—22no—
198C2×C4—614no—
199C2×C4—614no—
200C2×C4—614no—
201C2×C4—612no—
202C2×C4—12216no—
203C2×C4—1221no—
204C2×C4—1221no—
205C2×C4—1228no—
206C2×C4—1222no—
207C2×C4—1222no—
208C2×C4—1222no—
209C2×C4—1224no—
210C2×C4—1222no—
211C2×C4#1175822212yes—
212C2×C4D4×D6112yes—
213C2×C4D4×D6112yes—
214C2×C4Q8×D6114yes—
215C22—614no—
216C22—1222no—
217C22—1224no—
218C22—1222no—
219C22—1224no—
220C22C2×D4×D6111yescharacteristic
221C22C2×D4×D6111yescharacteristic
222C22C2×Q8×D6112yes—
223C22#41×D6112yes—
224C22C2×#1175822211yescharacteristic
225C4—24no—
226C4—42no—
227C4—42no—
228C4—618no—
229C4—1222no—
230C4—2442no—
231C4—2442no—
232C4#1451975014yes—
233C2—1224no—
234C2C2×#1451975011yescharacteristic
235C2C22⋊Q8×D6112yes—
236C2C4⋊Q8×D6111yescharacteristic
237C2#1684031111yescharacteristic
238C2#1684031612yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#391C2
hypercenter#391D61
hypocenterC61#2857
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
1. C2×#14519775C2semidirect
5. #16839668C2semidirect
6. #16839659C2semidirect
7. #16839631C2semidirect
9. C61×#391C2semidirect
48. C2×C4×D61Q8semidirect
104. C2×D61C4⋊Q8semidirect
112. Dic61C22⋊Q8semidirect
125. #391D61semidirect
129. C61#2857semidirect