Finite Group Databasebeta

← #21456577

Subgroups — #21456577

Order 7808.

468 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 137 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×#14519756C211yesmaximal, characteristic, complemented
2C2×#14519751C211yesmaximal, characteristic
3#16840093C212yesmaximal, complemented
4#16840081C212yesmaximal, complemented
5#16839991C214yesmaximal, complemented
6#16839915C212yesmaximal, complemented
7#16839903C212yesmaximal, complemented
8C2×C22⋊C8×C61C211yesmaximal, characteristic, complemented
9C22×Dic122C2211yescharacteristic, complemented
10C22×D244C2211yescharacteristic
11C22×C22⋊D61—21no—
12C2×#11758190C2214yescomplemented
13#14519756—21no—
14#14519756—21no—
15#14519756C2212yes—
16#14519756C2212yescomplemented
17#14519751—21no—
18#14519751—21no—
19#14519751C2212yes—
20#14519751C2212yes—
21C2×C4⋊Dic61C2211yescharacteristic
22C2×C4⋊Dic61C2211yescharacteristic, complemented
23C2×#11758196—21no—
24C2×C22⋊Dic61—21no—
25C2×#11758198—21no—
26#14519709C2214yescomplemented
27#14519702C2214yescomplemented
28#14519699C2214yescomplemented
29C23×C4×C61C2211yescharacteristic
30C22×C8×C61C2212yescomplemented
31C22⋊C8×C61C2212yes—
32C22⋊C8×C61C2212yescomplemented
33C24×C61D411yescharacteristic
34C23×D61—21no—
35C22×C4×C61—42no—
36C22×C4×C61D411yescharacteristic
37C22×C4×C61D411yescharacteristic
38C22×C4×C61D411yescharacteristic
39C22×C4×C61C2311yescharacteristic
40C22×C4×C61C2311yescharacteristic
41C22×C4×C61C2311yescharacteristic
42C2×C22⋊D61—22no—
43C2×C22⋊D61—22no—
44C2×C22⋊D61—44no—
45C22×Dic61—21no—
46C22×Dic61—21no—
47C22×Dic61—21no—
48C2×D244—21no—
49C2×D244—42no—
50C2×D244C2312yes—
51C2×Dic122—21no—
52C2×Dic122—42no—
53C2×Dic122C2312yes—
54C2×C8×C61—42no—
55C2×C8×C61C2314yes—
56C22⋊Dic61—22no—
57C22⋊Dic61—22no—
58#11758198—22no—
59#11758198—22no—
60C4⋊Dic61—21no—
61C4⋊Dic61—21no—
62C4⋊Dic61C2312yes—
63C4⋊Dic61C2312yes—
64#11758196—22no—
65#11758196—22no—
66#11758190—44no—
67C23×C61—41no—
68C23×C61—41no—
69C23×C61SD1614yescomplemented
70C23×C61C2×D411yescharacteristic
71C23×C61C2×D411yescharacteristic
72C23×C61C2×D411yescharacteristic
73C22×D61—22no—
74C22×D61—42no—
75C22×D61—42no—
76C22×D61—42no—
77C2×C4×C61—22no—
78C2×C4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61—41no—
81C2×C4×C61—41no—
82C2×C4×C61—41no—
83C2×C4×C61C2×D411yescharacteristic
84C2×C4×C61C2×D411yescharacteristic
85C2×C4×C61C2×D411yescharacteristic
86C2×C4×C61C2411yescharacteristic
87C22⋊D61—44no—
88C22⋊D61—44no—
89C2×Dic61—22no—
90C2×Dic61—22no—
91C2×Dic61—22no—
92C2×Dic61—42no—
93C2×Dic61—42no—
94C2×Dic61—42no—
95D244—24no—
96D244—42no—
97Dic122—24no—
98Dic122—42no—
99C8×C61—24no—
100C22×C61—21no—
101C22×C61—21no—
102C22×C61—21no—
103C22×C61—21no—
104C22×C61—21no—
105C22×C61—21no—
106C22×C61—44no—
107C22×C61C2×SD1612yes—
108C22×C61C2×SD1612yes—
109C22×C61C2×SD1612yes—
110C22×C61C22×D411yescharacteristic
111C2×D61—42no—
112C2×D61—42no—
113C2×D61—42no—
114C2×D61—84no—
115C4×C61—21no—
116C4×C61—21no—
117C4×C61—21no—
118C4×C61H(5,𝔽2)12yes—
119Dic61—42no—
120Dic61—42no—
121Dic61—42no—
122#3187—611nomaximal, Sylow
123C2×C61—22no—
124C2×C61—22no—
125C2×C61—22no—
126C2×C61#53411yescharacteristic
127C2×C61C22×SD1611yescharacteristic
128C2×C61#57511yescharacteristic
129D61—82no—
130C2×C22⋊Q8—611no—
131C2×#121—611no—
132#483—612no—
133#481—612no—
134#465—614no—
135#450—612no—
136#448—612no—
137C2×C22⋊C8D6111yescharacteristic, complemented
138C61#318711yescharacteristic, complemented, Sylow
139C22×Q8—611no—
140C22×D4—611no—
141C22×D4—1221no—
142C23×C4C2×D6111yescharacteristic
143C2×SD16—614no—
144C22×C8C2×D6112yescomplemented
145C22⋊Q8—612no—
146C22⋊Q8—612no—
147C22⋊Q8—1221no—
148C22⋊Q8—1221no—
149#121—612no—
150#121—612no—
151#121—1221no—
152#121—1221no—
153C2×C4⋊C4—611no—
154C2×C4⋊C4—611no—
155C2×C4⋊C4—1221no—
156C2×C22⋊C4—1221no—
157C2×C22⋊C4—1221no—
158#106—614no—
159#103—614no—
160#102—614no—
161C22⋊C8C2×D6112yes—
162C22⋊C8C2×D6112yescomplemented
163C24—1221no—
164C24D24411yescharacteristic
165C2×Q8—612no—
166C2×Q8—1221no—
167C2×Q8—2442no—
168C2×D4—612no—
169C2×D4—1222no—
170C2×D4—1222no—
171C2×D4—1221no—
172C2×D4—2442no—
173C2×D4—2444no—
174C22×C4—42no—
175C22×C4—1221no—
176C22×C4—1221no—
177C22×C4—1221no—
178C22×C4D24411yescharacteristic
179C22×C4D24411yescharacteristic
180C22×C4D24411yescharacteristic
181C22×C4C22×D6111yescharacteristic
182C22×C4C22×D6111yescharacteristic
183C22×C4C22×D6111yescharacteristic
184SD16—2444no—
185C2×C8—42no—
186C2×C8C22×D6114yes—
187C4⋊C4—612no—
188C4⋊C4—612no—
189C4⋊C4—1221no—
190C4⋊C4—1221no—
191C4⋊C4—1222no—
192C4⋊C4—1222no—
193C22⋊C4—1222no—
194C22⋊C4—1222no—
195C22⋊C4—1222no—
196C22⋊C4—1222no—
197C23—41no—
198C23—41no—
199C23—1222no—
200C23—2442no—
201C23—2442no—
202C23—2442no—
203C23#1175819014yescomplemented
204C23C2×D24411yescharacteristic
205C23C2×D24411yescharacteristic
206C23C2×D24411yescharacteristic
207Q8—1224no—
208Q8—2442no—
209D4—1224no—
210D4—2442no—
211D4—2444no—
212D4—2444no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4—1222no—
220C2×C4—1222no—
221C2×C4—1222no—
222C2×C4—2442no—
223C2×C4—2442no—
224C2×C4—2442no—
225C2×C4C2×D24411yescharacteristic
226C2×C4C2×D24411yescharacteristic
227C2×C4C2×D24411yescharacteristic
228C2×C4C23×D6111yescharacteristic
229C8—24no—
230C22—21no—
231C22—21no—
232C22—21no—
233C22—21no—
234C22—21no—
235C22—21no—
236C22—44no—
237C22—4884no—
238C22—2442no—
239C22—2442no—
240C22—2442no—
241C22C2×#1175819012yes—
242C22C2×#1175819012yes—
243C22C2×#1175819012yes—
244C22C22×D24411yescharacteristic
245C4—21no—
246C4—21no—
247C4—21no—
248C4—2442no—
249C4—2442no—
250C4—2442no—
251C4#1451982212yes—
252C2—22no—
253C2—22no—
254C2—22no—
255C2—4882no—
256C2#1684032411yescharacteristic
257C2C22×#1175819011yescharacteristic
258C2#1684056211yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×C22⋊C8×C61C2
socleC22×C61C22×D4
hypercenterC2×C22⋊C8D61
hypocenterC61#3187
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#14519756C2semidirect
3. #16840093C2semidirect
4. #16840081C2semidirect
5. #16839991C2semidirect
6. #16839915C2semidirect
7. #16839903C2semidirect
8. C2×C22⋊C8×C61C2semidirect
9. C22×Dic122C22semidirect
12. C2×#11758190C22semidirect
16. #14519756C22semidirect
22. C2×C4⋊Dic61C22semidirect
26. #14519709C22semidirect
27. #14519702C22semidirect
28. #14519699C22semidirect
30. C22×C8×C61C22semidirect
32. C22⋊C8×C61C22semidirect
69. C23×C61SD16semidirect
137. C2×C22⋊C8D61semidirect
138. C61#3187semidirect
144. C22×C8C2×D61semidirect
162. C22⋊C8C2×D61semidirect
203. C23#11758190semidirect