Finite Group Databasebeta

← #21461836

Subgroups — #21461836

Order 7808.

442 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 76 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
1C22×C4×#6923C211yesmaximal, characteristic, complemented
2C2×#14519842C212yesmaximal, complemented
3#16840733C211yesmaximal, characteristic, complemented
4#16840632C212yesmaximal, complemented
5#16840275C211yesmaximal, characteristic
6C23×#6923—21no—
7C2×#11758213C2212yes—
8C2×C4×#6923—21no—
9C2×C4×#6923—24no—
10C2×C4×#6923C2212yes—
11#14519842—24no—
12#14519834—21no—
13C22⋊#92420—21no—
14C2×#11758226C2211yescharacteristic
15C22×C4×D61C2211yescharacteristic
16#14519762—21no—
17#14519753C411yescharacteristic, complemented
18#14519752C411yescharacteristic, complemented
19#14519751C411yescharacteristic, complemented
20#14519747—21no—
21#14519739—21no—
22#14519737—21no—
23#14519735C2211yescharacteristic
24C22⋊Q8×C61C411yescharacteristic, complemented
25C23×D61D411yescharacteristic
26C22×#6923—24no—
27C22×#6923—24no—
28C22×#6923—24no—
29C22×#6923—22no—
30C2×Q8×C61C2×C411yescharacteristic, complemented
31C22×C4×C61C2×C411yescharacteristic
32C2×C22⋊D61—21no—
33C22×Dic61D411yescharacteristic
34#11758226—22no—
35#11758226—22no—
36C2×D244—21no—
37C2×D244—21no—
38C2×D244C2×C411yescharacteristic, complemented
39C2×C4×D61—22no—
40C2×C4×D61—22no—
41C2×C4×D61—21no—
42C2×C4×D61C2×C411yescharacteristic
43C2×C4×D61D411yescharacteristic
44C2×C4×D61D411yescharacteristic
45C2×C4×D61C2311yescharacteristic
46C2×#92420—22no—
47C4×#6923—24no—
48C4×#6923—22no—
49C4×#6923D414yescomplemented
50#11758213—22no—
51#11758213—22no—
52C4⋊C4×C61—21no—
53C4⋊C4×C61C2×C411yescharacteristic, complemented
54C22⋊C4×C61—21no—
55#11758198—21no—
56#11758198—21no—
57#11758198—21no—
58#11758198—21no—
59C4⋊Dic61C2×C411yescharacteristic, complemented
60#11758196—21no—
61C4×Dic61—21no—
62C23×C61C22⋊C411yescharacteristic
63C22×D61—22no—
64C22×D61—22no—
65C22×D61—21no—
66C22×D61—21no—
67C22×D61—21no—
68C22×D61C22⋊C411yescharacteristic
69C22×D61C2×D411yescharacteristic
70C2×#6923—216no—
71C2×#6923—24no—
72C2×#6923—24no—
73C2×#6923—24no—
74Q8×C61—22no—
75C2×C4×C61—22no—
76C2×C4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61C22⋊C411yescharacteristic
79C2×C4×C61C22×C411yescharacteristic
80C22⋊D61—42no—
81C2×Dic61—22no—
82C2×Dic61—21no—
83C2×Dic61C22⋊C411yescharacteristic
84C2×Dic61C2×D411yescharacteristic
85D244—22no—
86D244—42no—
87D244—41no—
88D244—41no—
89C4×D61—21no—
90C4×D61—21no—
91C4×D61—22no—
92C4×D61—22no—
93C4×D61—42no—
94C4×D61C2×D412yes—
95C4×D61#4112yes—
96#92420—42no—
97C22×C61—21no—
98C22×C61—21no—
99C22×C61#10412yescomplemented
100C22×C61C2×C22⋊C411yescharacteristic
101C2×D61—24no—
102C2×D61—24no—
103C2×D61—21no—
104C2×D61—21no—
105C2×D61—21no—
106C2×D61—21no—
107C2×D61—41no—
108C2×D61—41no—
109C2×D61—41no—
110C2×D61#10412yescomplemented
111C2×D61#12011yescharacteristic
112C2×D61#12311yescharacteristic
113#6923—28no—
114C4×C61—21no—
115C4×C61—41no—
116C4×C61—41no—
117C4×C61C4×D412yes—
118Dic61—21no—
119Dic61—41no—
120Dic61#12112yes—
121#1896—611nomaximal, Sylow
122C2×C61—22no—
123C2×C61#38611yescharacteristic
124C2×C61C2×#10411yescharacteristic
125C2×C61C2×#10411yescharacteristic
126D61—21no—
127D61—22no—
128D61—21no—
129D61—81no—
130#525—611no—
131C22×C42—611no—
132C2×#104—612no—
133#407—611no—
134#339—612no—
135C61#189611yescharacteristic, complemented, Sylow
136C2×#41—611no—
137C23×C4—611no—
138C23×C4—1221no—
139C2×M16—612no—
140#123—1221no—
141C22⋊Q8—611no—
142C22⋊Q8#692311yescharacteristic, complemented
143#121—611no—
144#121—611no—
145#120—1221no—
146C4×D4—1221no—
147C4×D4—1221no—
148#117—611no—
149C2×C42—612no—
150C2×C42—1224no—
151C2×C42—1221no—
152#104—1224no—
153C22⋊C8—1221no—
154C22⋊C8—1221no—
155C24—611no—
156#41—1222no—
157#41—1222no—
158C2×Q8C2×#692311yescharacteristic, complemented
159C2×D4—611no—
160C2×D4—1221no—
161C2×D4—1221no—
162C2×D4—1221no—
163C22×C4—611no—
164C22×C4—611no—
165C22×C4—611no—
166C22×C4—611no—
167C22×C4—611no—
168C22×C4—1222no—
169C22×C4—1222no—
170C22×C4—1221no—
171C22×C4—1222no—
172C22×C4—1224no—
173C22×C4—1224no—
174C22×C4—1224no—
175C22×C4C2×#692311yescharacteristic
176M16—1222no—
177M16—1222no—
178C2×C8—1222no—
179C4⋊C4—21no—
180C4⋊C4—611no—
181C4⋊C4—1221no—
182C4⋊C4C2×#692311yescharacteristic, complemented
183C22⋊C4—21no—
184C22⋊C4—1221no—
185C22⋊C4—1221no—
186C22⋊C4—1221no—
187C22⋊C4—1221no—
188C42—614no—
189C42—1221no—
190C42—1222no—
191C42—1224no—
192C23—611no—
193C23—611no—
194C23—1221no—
195C23—1221no—
196C23—1222no—
197C23—1222no—
198C23—1221no—
199C23C22⋊#692311yescharacteristic
200Q8—22no—
201D4—1222no—
202D4—2442no—
203D4—2441no—
204D4—2441no—
205D4—2442no—
206C2×C4—22no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—611no—
210C2×C4—612no—
211C2×C4—612no—
212C2×C4—611no—
213C2×C4—1222no—
214C2×C4—1221no—
215C2×C4—1221no—
216C2×C4—1222no—
217C2×C4—1224no—
218C2×C4—12216no—
219C2×C4—1224no—
220C2×C4—1224no—
221C2×C4—1222no—
222C2×C4—1221no—
223C2×C4—2442no—
224C2×C4C22⋊#692311yescharacteristic
225C2×C4C22×#692311yescharacteristic
226C8—2442no—
227C22—21no—
228C22—21no—
229C22—611no—
230C22—611no—
231C22—612no—
232C22—1224no—
233C22—1224no—
234C22—1221no—
235C22—1221no—
236C22—1221no—
237C22—1221no—
238C22—2441no—
239C22—2441no—
240C22—2441no—
241C22#1451984212yescomplemented
242C22C2×C22⋊#692311yescharacteristic
243C4—21no—
244C4—41no—
245C4—41no—
246C4—612no—
247C4—1228no—
248C4—1221no—
249C4—2441no—
250C4D4×#692312yes—
251C2—22no—
252C2—1221no—
253C2—1221no—
254C2—1222no—
255C2—4881no—
256C2#1684071011yescharacteristic
257C2D61⋊#10411yescharacteristic
258C2C2×#1451984211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC22⋊Q8×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC22⋊Q8#6923
hypocenterC61#1896
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×C4×#6923C2semidirect
2. C2×#14519842C2semidirect
3. #16840733C2semidirect
4. #16840632C2semidirect
17. #14519753C4semidirect
18. #14519752C4semidirect
19. #14519751C4semidirect
24. C22⋊Q8×C61C4semidirect
30. C2×Q8×C61C2×C4semidirect
38. C2×D244C2×C4semidirect
49. C4×#6923D4semidirect
53. C4⋊C4×C61C2×C4semidirect
59. C4⋊Dic61C2×C4semidirect
99. C22×C61#104semidirect
110. C2×D61#104semidirect
135. C61#1896semidirect
142. C22⋊Q8#6923semidirect
158. C2×Q8C2×#6923semidirect
182. C4⋊C4C2×#6923semidirect
241. C22#14519842semidirect