Finite Group Databasebeta

← #21456625

Subgroups — #21456625

Order 7808.

462 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 125 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
2#16840097C212yesmaximal, complemented
3#16840073C212yesmaximal, complemented
4#16840006C214yesmaximal, complemented
5#16839913C212yesmaximal, complemented
6#16839900C212yesmaximal, complemented
7#16839726C211yesmaximal, characteristic, complemented
8C2×#121×C61C211yesmaximal, characteristic
9C22×Dic122C2211yescharacteristic, complemented
10C2×#11758200C2214yescomplemented
11C2×#11758194C2212yescomplemented
12#14519756—21no—
13#14519756—21no—
14#14519756C2212yes—
15#14519756C2212yescomplemented
16C2×C4⋊Dic61C2211yescharacteristic, complemented
17C2×#11758196—21no—
18C2×C22⋊Dic61—21no—
19#14519710C2214yescomplemented
20#14519700C2214yescomplemented
21#14519698C2214yescomplemented
22C22⋊#92418C2212yes—
23C22⋊#92418C2212yescomplemented
24C22×D4×C61—21no—
25C22×D4×C61C2211yescharacteristic
26C23×C4×C61C2211yescharacteristic
27#121×C61—21no—
28#121×C61—21no—
29#121×C61C2212yes—
30#121×C61C2212yes—
31C2×C4⋊C4×C61C2211yescharacteristic
32C2×C22⋊C4×C61—21no—
33C24×C61—21no—
34C24×C61D411yescharacteristic
35C2×D4×C61—22no—
36C2×D4×C61—22no—
37C2×D4×C61—21no—
38C2×D4×C61—42no—
39C2×D4×C61—44no—
40C2×D4×C61C2312yes—
41C22×C4×C61—21no—
42C22×C4×C61—42no—
43C22×C4×C61D411yescharacteristic
44C22×C4×C61D411yescharacteristic
45C22×C4×C61D411yescharacteristic
46C22×C4×C61C2311yescharacteristic
47C22×C4×C61C2311yescharacteristic
48C22×C4×C61C2311yescharacteristic
49C22×Dic61—21no—
50C22×Dic61—21no—
51C2×Dic122—21no—
52C2×Dic122—42no—
53C2×Dic122C2312yes—
54C4⋊C4×C61—21no—
55C4⋊C4×C61C2312yes—
56C22⋊C4×C61—22no—
57C22⋊C4×C61—22no—
58C22⋊Dic61—22no—
59C22⋊Dic61—22no—
60#11758200—44no—
61C4⋊Dic61—21no—
62C4⋊Dic61C2312yes—
63#11758196—22no—
64#11758196—22no—
65#11758194—42no—
66C2×#92418C2314yes—
67C23×C61—22no—
68C23×C61—22no—
69C23×C61—22no—
70C23×C61—41no—
71C23×C61—42no—
72C23×C61—42no—
73C23×C61—42no—
74C23×C61C2×D411yescharacteristic
75C23×C61C2×D411yescharacteristic
76C23×C61C2×D411yescharacteristic
77D4×C61—24no—
78D4×C61—42no—
79D4×C61—44no—
80D4×C61—44no—
81C2×C4×C61—22no—
82C2×C4×C61—22no—
83C2×C4×C61—22no—
84C2×C4×C61—22no—
85C2×C4×C61—41no—
86C2×C4×C61—41no—
87C2×C4×C61—41no—
88C2×C4×C61—42no—
89C2×C4×C61C2×D411yescharacteristic
90C2×C4×C61C2×D411yescharacteristic
91C2×C4×C61C2×D411yescharacteristic
92C2×C4×C61C2411yescharacteristic
93C2×Dic61—22no—
94C2×Dic61—22no—
95C2×Dic61—42no—
96C2×Dic61—42no—
97Dic122—24no—
98Dic122—42no—
99#92418—24no—
100C22×C61—21no—
101C22×C61—21no—
102C22×C61—21no—
103C22×C61—21no—
104C22×C61—21no—
105C22×C61—21no—
106C22×C61—21no—
107C22×C61—44no—
108C22×C61—42no—
109C22×C61—42no—
110C22×C61—42no—
111C22×C61—84no—
112C22×C61AGL(1,ℤ/8)12yes—
113C22×C61#13712yes—
114C22×C61C22×D411yescharacteristic
115C4×C61—21no—
116C4×C61—21no—
117C4×C61—21no—
118C4×C61—42no—
119C4×C61H(5,𝔽2)12yes—
120Dic61—42no—
121Dic61—42no—
122#3193—611nomaximal, Sylow
123C2×C61—22no—
124C2×C61—22no—
125C2×C61—41no—
126C2×C61—82no—
127C2×C61#53411yescharacteristic
128C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
129C2×C61C2×#13711yescharacteristic
130C2×C22⋊Q8—611no—
131C2×#121D6111yescharacteristic
132#484—612no—
133#480—612no—
134#468—614no—
135#450—612no—
136#448—612no—
137#407—611no—
138C61#319311yescharacteristic, complemented, Sylow
139C22×Q8—611no—
140C22×D4—21no—
141C22×D4C2×D6111yescharacteristic
142C23×C4C2×D6111yescharacteristic
143C2×SD16—614no—
144C2×M16—612no—
145C22⋊Q8—612no—
146C22⋊Q8—612no—
147C22⋊Q8—1221no—
148C22⋊Q8—1221no—
149#121—21no—
150#121—21no—
151#121C2×D6112yes—
152#121C2×D6112yes—
153C2×C4⋊C4—611no—
154C2×C4⋊C4—1221no—
155C2×C4⋊C4C2×D6111yescharacteristic
156C2×C22⋊C4—21no—
157C2×C22⋊C4—1221no—
158#107—614no—
159#103—614no—
160#102—614no—
161C22⋊C8—612no—
162C22⋊C8—612no—
163C24—21no—
164C24C22⋊D6111yescharacteristic
165C2×Q8—612no—
166C2×Q8—1221no—
167C2×Q8—2442no—
168C2×D4—22no—
169C2×D4—22no—
170C2×D4—21no—
171C2×D4—42no—
172C2×D4—44no—
173C2×D4C22×D6112yes—
174C22×C4—21no—
175C22×C4—42no—
176C22×C4—1221no—
177C22×C4—1221no—
178C22×C4C22⋊D6111yescharacteristic
179C22×C4C22⋊D6111yescharacteristic
180C22×C4C22⋊D6111yescharacteristic
181C22×C4C22×D6111yescharacteristic
182C22×C4C22×D6111yescharacteristic
183C22×C4C22×D6111yescharacteristic
184SD16—2444no—
185M16—2442no—
186C2×C8—614no—
187C4⋊C4—21no—
188C4⋊C4—612no—
189C4⋊C4—1221no—
190C4⋊C4—1222no—
191C4⋊C4—1222no—
192C4⋊C4C22×D6112yes—
193C22⋊C4—22no—
194C22⋊C4—22no—
195C22⋊C4—1222no—
196C22⋊C4—1222no—
197C23—22no—
198C23—22no—
199C23—22no—
200C23—41no—
201C23—42no—
202C23—42no—
203C23—42no—
204C23C2×C22⋊D6111yescharacteristic
205C23C2×C22⋊D6111yescharacteristic
206C23C2×C22⋊D6111yescharacteristic
207Q8—1224no—
208Q8—2442no—
209D4—24no—
210D4—42no—
211D4—44no—
212D4—44no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—42no—
221C2×C4—1222no—
222C2×C4—1222no—
223C2×C4—2442no—
224C2×C4—2442no—
225C2×C4C2×C22⋊D6111yescharacteristic
226C2×C4C2×C22⋊D6111yescharacteristic
227C2×C4C2×C22⋊D6111yescharacteristic
228C2×C4C23×D6111yescharacteristic
229C8—1224no—
230C22—21no—
231C22—21no—
232C22—21no—
233C22—21no—
234C22—21no—
235C22—21no—
236C22—21no—
237C22—44no—
238C22—42no—
239C22—42no—
240C22—42no—
241C22—84no—
242C22#1451980312yes—
243C22#1451980712yes—
244C22C22×C22⋊D6111yescharacteristic
245C4—21no—
246C4—21no—
247C4—21no—
248C4—42no—
249C4—2442no—
250C4—2442no—
251C4#1451982212yes—
252C2—22no—
253C2—22no—
254C2—41no—
255C2—82no—
256C2#1684032111yescharacteristic
257C2C2×#1451980311yescharacteristic
258C2C2×#1451980711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×#121×C61C2
socleC22×C61C22×D4
hypercenterC2×#121D61
hypocenterC61#3193
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#14519756C2semidirect
2. #16840097C2semidirect
3. #16840073C2semidirect
4. #16840006C2semidirect
5. #16839913C2semidirect
6. #16839900C2semidirect
7. #16839726C2semidirect
9. C22×Dic122C22semidirect
10. C2×#11758200C22semidirect
11. C2×#11758194C22semidirect
15. #14519756C22semidirect
16. C2×C4⋊Dic61C22semidirect
19. #14519710C22semidirect
20. #14519700C22semidirect
21. #14519698C22semidirect
23. C22⋊#92418C22semidirect
138. C61#3193semidirect