Finite Group Databasebeta

← #21446186

Subgroups — #21446186

Order 7808.

334 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 89 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×#14519807C211yesmaximal, characteristic
2#16840245C211yesmaximal, characteristic
3#16839772C211yesmaximal, characteristic, complemented
4#16839668C211yesmaximal, characteristic, complemented
5#16839530C211yesmaximal, characteristic, complemented
6#16839522C211yesmaximal, characteristic, complemented
7C2×#104×C61C211yesmaximal, characteristic
8C22×Dic122C2211yescharacteristic
9#14519807—22no—
10#14519807C414yescomplemented
11C2×#11758202—21no—
12C2×#11758200—21no—
13C2×#11758194C2211yescharacteristic
14Q8×Dic61—21no—
15D4×Dic61—21no—
16D4×Dic61—22no—
17#14519736—21no—
18#14519736C2211yescharacteristic
19C2×C4⋊Dic61—21no—
20C2×C4⋊Dic61C2211yescharacteristic
21#14519702—21no—
22#14519702—21no—
23#14519684—22no—
24C2×#41×C61C2211yescharacteristic
25C2×M16×C61C2211yescharacteristic
26C2×C42×C61C2211yescharacteristic
27#104×C61—22no—
28#41×C61—21no—
29#41×C61—21no—
30#41×C61C2×C412yes—
31#41×C61D412yes—
32C2×Q8×C61D411yescharacteristic
33C2×D4×C61—21no—
34C2×D4×C61D411yescharacteristic
35C22×C4×C61—21no—
36C22×C4×C61—21no—
37C22×C4×C61C2311yescharacteristic
38C22×Dic61—21no—
39C22×Dic61—22no—
40C22×Dic61D412yes—
41C2×Dic122—21no—
42C2×Dic122—21no—
43C2×Dic122—21no—
44C2×Dic122—21no—
45C2×Dic122—21no—
46C2×Dic122C2×C412yescomplemented
47M16×C61—21no—
48M16×C61—21no—
49C2×C8×C61—21no—
50C42×C61—21no—
51C42×C61—21no—
52C22⋊Dic61—22no—
53C22⋊Dic61—21no—
54#11758202—24no—
55#11758200—24no—
56C4⋊Dic61—22no—
57C4⋊Dic61—21no—
58C4⋊Dic61—21no—
59C4⋊Dic61D411yescharacteristic
60C4⋊Dic61D411yescharacteristic
61C4×Dic61—22no—
62C4×Dic61—21no—
63#11758194—21no—
64#11758194C2×C412yescomplemented
65C2×#92418—21no—
66C23×C61—21no—
67C23×C61C2×D411yescharacteristic
68Q8×C61—21no—
69Q8×C61C22⋊C412yes—
70D4×C61—22no—
71D4×C61—22no—
72D4×C61—21no—
73D4×C61C22⋊C412yes—
74C2×C4×C61—21no—
75C2×C4×C61—22no—
76C2×C4×C61—22no—
77C2×C4×C61—22no—
78C2×C4×C61—41no—
79C2×C4×C61—41no—
80C2×C4×C61C22×C411yescharacteristic
81C2×C4×C61C2×D411yescharacteristic
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61C2×D411yescharacteristic
84C2×C4×C61#4111yescharacteristic
85C2×C4×C61#4111yescharacteristic
86C2×Dic61—22no—
87C2×Dic61—21no—
88C2×Dic61—22no—
89C2×Dic61—21no—
90C2×Dic61—41no—
91C2×Dic61—41no—
92C2×Dic61—42no—
93C2×Dic61—82no—
94Dic122—22no—
95Dic122—22no—
96Dic122—41no—
97Dic122—41no—
98C8×C61—41no—
99#92418—22no—
100C22×C61—21no—
101C22×C61—21no—
102C22×C61—22no—
103C22×C61—41no—
104C22×C61—41no—
105C22×C61C4×D411yescharacteristic
106C22×C61#12011yescharacteristic
107C22×C61#12111yescharacteristic
108C4×C61—22no—
109C4×C61—42no—
110C4×C61C2×C22⋊C411yescharacteristic
111C4×C61C4×D411yescharacteristic
112C4×C61#12111yescharacteristic
113C4×C61#12311yescharacteristic
114Dic61—42no—
115Dic61—42no—
116Dic61—41no—
117Dic61—41no—
118#1882—611nomaximal, Sylow
119C2×C61—21no—
120C2×C61—21no—
121C2×C61—42no—
122C2×C61#38611yescharacteristic
123C2×C61#45511yescharacteristic
124C2×C61#45611yescharacteristic
125C2×#137—611no—
126#520—611no—
127C2×#104D6111yescharacteristic
128#419—611no—
129#391—611no—
130#343—611no—
131#339—611no—
132C61#188211yescharacteristic, complemented, Sylow
133C2×#41C2×D6111yescharacteristic
134C22×Q8—611no—
135#137—614no—
136#137—1222no—
137C2×Q16—1221no—
138C2×SD16—1221no—
139C2×M16—611no—
140C2×M16C2×D6111yescharacteristic
141C4×Q8—1221no—
142C4×D4—1222no—
143C4×D4—1221no—
144#117—611no—
145#117—1221no—
146C2×C4⋊C4—611no—
147C2×C4⋊C4—1221no—
148C2×C42C2×D6111yescharacteristic
149#104—22no—
150#103—1221no—
151#103—1221no—
152#95—1222no—
153#41—21no—
154#41—21no—
155#41C4×D6112yes—
156#41C22⋊D6112yes—
157C2×Q8—612no—
158C2×Q8—1221no—
159C2×Q8—1221no—
160C2×Q8—1221no—
161C2×Q8—1221no—
162C2×Q8—1221no—
163C2×Q8D24411yescharacteristic
164C2×D4—21no—
165C2×D4D24411yescharacteristic
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—612no—
169C22×C4—1222no—
170C22×C4—1221no—
171C22×C4C22×D6111yescharacteristic
172Q16—1224no—
173SD16—1224no—
174M16—21no—
175M16—21no—
176M16—612no—
177M16—1221no—
178C2×C8—21no—
179C2×C8—1221no—
180C4⋊C4—611no—
181C4⋊C4—611no—
182C4⋊C4—1222no—
183C4⋊C4—1221no—
184C4⋊C4—1221no—
185C22⋊C4—1222no—
186C22⋊C4—1221no—
187C42—21no—
188C42—21no—
189C42—1222no—
190C42—1221no—
191C23—21no—
192C23D4×D6111yescharacteristic
193Q8—21no—
194Q8—1222no—
195Q8—1222no—
196Q8—2441no—
197Q8—2441no—
198Q8#1175819812yes—
199D4—22no—
200D4—22no—
201D4—21no—
202D4#1175819812yes—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—1222no—
210C2×C4—1221no—
211C2×C4—1221no—
212C2×C4—1222no—
213C2×C4—4882no—
214C2×C4—2441no—
215C2×C4—2441no—
216C2×C4—2442no—
217C2×C4C2×C4×D6111yescharacteristic
218C2×C4C2×D24411yescharacteristic
219C2×C4D4×D6111yescharacteristic
220C2×C4#1175822411yescharacteristic
221C2×C4#1175822411yescharacteristic
222C2×C4C2×C22⋊D6111yescharacteristic
223C8—41no—
224C8—1222no—
225C22—21no—
226C22—21no—
227C22—22no—
228C22—41no—
229C22—41no—
230C22#1451973711yescharacteristic
231C22#1451974711yescharacteristic
232C22#1451974911yescharacteristic
233C4—22no—
234C4—42no—
235C4—2441no—
236C4—2442no—
237C4—2441no—
238C4—2442no—
239C4C2×#1175819811yescharacteristic
240C4#1451973711yescharacteristic
241C4#1451974911yescharacteristic
242C4#1451976111yescharacteristic
243C2—21no—
244C2—21no—
245C2—42no—
246C2#1683963911yescharacteristic
247C2#1683994111yescharacteristic
248C2#1683994611yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC2×#104×C61C2
socleC22×C61#120
hypercenterC2×#104D61
hypocenterC61#1882
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
3. #16839772C2semidirect
4. #16839668C2semidirect
5. #16839530C2semidirect
6. #16839522C2semidirect
10. #14519807C4semidirect
46. C2×Dic122C2×C4semidirect
64. #11758194C2×C4semidirect
132. C61#1882semidirect