Finite Group Databasebeta

← #21455759

Subgroups — #21455759

Order 7808.

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

normal subgroups only

This group has 462 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×#14519751C211yesmaximal, characteristic
2#16840086C214yesmaximal, complemented
3#16840080C212yesmaximal, complemented
4#16840075C212yesmaximal, complemented
5#16839805C212yesmaximal, complemented
6#16839766C212yesmaximal, complemented
7#16839726C211yesmaximal, characteristic, complemented
8C2×#117×C61C211yesmaximal, characteristic, complemented
9C22×D244C2211yescharacteristic
10C22×C22⋊D61—21no—
11C2×#11758194C2212yes—
12#14519751—21no—
13#14519751—21no—
14#14519751C2212yes—
15#14519751C2212yes—
16C2×C4⋊Dic61C2211yescharacteristic
17C2×#11758198—21no—
18#14519710C2214yescomplemented
19#14519708C2214yescomplemented
20#14519697C2214yescomplemented
21#14519697C2214yescomplemented
22C22⋊#92418C2212yescomplemented
23C22⋊#92418C2212yescomplemented
24C23×C4×C61C2211yescharacteristic
25#117×C61—21no—
26#117×C61—21no—
27#117×C61C2212yes—
28#117×C61C2212yescomplemented
29C2×C4⋊C4×C61C2211yescharacteristic, complemented
30C2×C4⋊C4×C61C2211yescharacteristic, complemented
31C2×C22⋊C4×C61—21no—
32C2×C42×C61—21no—
33C24×C61D411yescharacteristic
34C23×D61—21no—
35C22×C4×C61—24no—
36C22×C4×C61—21no—
37C22×C4×C61—21no—
38C22×C4×C61D411yescharacteristic
39C22×C4×C61D411yescharacteristic
40C22×C4×C61D411yescharacteristic
41C22×C4×C61C2311yescharacteristic
42C22×C4×C61C2311yescharacteristic
43C22×C4×C61C2311yescharacteristic
44C2×C22⋊D61—22no—
45C2×C22⋊D61—22no—
46C2×C22⋊D61—44no—
47C22×Dic61—21no—
48C2×D244—24no—
49C2×D244—21no—
50C2×D244C2312yes—
51C4⋊C4×C61—21no—
52C4⋊C4×C61—21no—
53C4⋊C4×C61C2312yes—
54C4⋊C4×C61C2312yes—
55C22⋊C4×C61—22no—
56C22⋊C4×C61—22no—
57C42×C61—22no—
58C42×C61—22no—
59#11758198—22no—
60#11758198—22no—
61C4⋊Dic61—21no—
62C4⋊Dic61C2312yes—
63#11758194—24no—
64C2×#92418C2314yes—
65C23×C61—22no—
66C23×C61—22no—
67C23×C61—41no—
68C23×C61C2×D411yescharacteristic
69C23×C61C2×D411yescharacteristic
70C23×C61C2×D411yescharacteristic
71C22×D61—22no—
72C22×D61—42no—
73C22×D61—42no—
74C22×D61—42no—
75C2×C4×C61—22no—
76C2×C4×C61—22no—
77C2×C4×C61—22no—
78C2×C4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61—22no—
81C2×C4×C61—22no—
82C2×C4×C61—42no—
83C2×C4×C61—42no—
84C2×C4×C61C2×D411yescharacteristic
85C2×C4×C61C2×D411yescharacteristic
86C2×C4×C61C2×D411yescharacteristic
87C2×C4×C61#4114yes—
88C2×C4×C61C2411yescharacteristic
89C22⋊D61—44no—
90C22⋊D61—44no—
91C2×Dic61—22no—
92C2×Dic61—42no—
93D244—24no—
94D244—42no—
95#92418—24no—
96C22×C61—21no—
97C22×C61—21no—
98C22×C61—21no—
99C22×C61—21no—
100C22×C61—21no—
101C22×C61—21no—
102C22×C61—21no—
103C22×C61—44no—
104C22×C61#12312yes—
105C22×C61AGL(1,ℤ/8)12yes—
106C22×C61C22×D411yescharacteristic
107C2×D61—42no—
108C2×D61—42no—
109C2×D61—42no—
110C2×D61—84no—
111C4×C61—21no—
112C4×C61—21no—
113C4×C61—42no—
114C4×C61—42no—
115C4×C61#12312yes—
116C4×C61C2×#4112yes—
117Dic61—42no—
118#3094—611nomaximal, Sylow
119C2×C61—22no—
120C2×C61—22no—
121C2×C61—41no—
122C2×C61C2×#12311yescharacteristic
123C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
124C2×C61#57511yescharacteristic
125D61—82no—
126C2×#121—611no—
127C2×#117D6111yescharacteristic, complemented
128#482—614no—
129#481—612no—
130#480—612no—
131#428—612no—
132#418—612no—
133#407—611no—
134C61#309411yescharacteristic, complemented, Sylow
135C22×D4—611no—
136C22×D4—1221no—
137C23×C4C2×D6111yescharacteristic
138C2×M16—612no—
139#121—612no—
140#121—612no—
141#121—1221no—
142#121—1221no—
143#117—21no—
144#117—21no—
145#117C2×D6112yes—
146#117C2×D6112yescomplemented
147C2×C4⋊C4—611no—
148C2×C4⋊C4C2×D6111yescharacteristic, complemented
149C2×C4⋊C4C2×D6111yescharacteristic, complemented
150C2×C22⋊C4—21no—
151C2×C22⋊C4—1221no—
152C2×C42—21no—
153#107—614no—
154#106—614no—
155#102—614no—
156#102—614no—
157C22⋊C8—612no—
158C22⋊C8—612no—
159C24—1221no—
160C24C22⋊D6111yescharacteristic
161C2×D4—612no—
162C2×D4—1222no—
163C2×D4—1222no—
164C2×D4—1224no—
165C2×D4—1221no—
166C2×D4—2444no—
167C22×C4—24no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—1221no—
171C22×C4C22⋊D6111yescharacteristic
172C22×C4C22⋊D6111yescharacteristic
173C22×C4C22⋊D6111yescharacteristic
174C22×C4C22×D6111yescharacteristic
175C22×C4C22×D6111yescharacteristic
176C22×C4C22×D6111yescharacteristic
177M16—1224no—
178C2×C8—614no—
179C4⋊C4—21no—
180C4⋊C4—21no—
181C4⋊C4—612no—
182C4⋊C4—1221no—
183C4⋊C4C22×D6112yes—
184C4⋊C4C22×D6112yes—
185C22⋊C4—22no—
186C22⋊C4—22no—
187C22⋊C4—1222no—
188C22⋊C4—1222no—
189C42—22no—
190C42—22no—
191C23—22no—
192C23—22no—
193C23—41no—
194C23—1222no—
195C23—2442no—
196C23—2442no—
197C23—2442no—
198C23C2×C22⋊D6111yescharacteristic
199C23C2×C22⋊D6111yescharacteristic
200C23C2×C22⋊D6111yescharacteristic
201D4—1224no—
202D4—2444no—
203D4—2444no—
204D4—2442no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—1222no—
215C2×C4—2442no—
216C2×C4#1175822214yes—
217C2×C4C2×C22⋊D6111yescharacteristic
218C2×C4C2×C22⋊D6111yescharacteristic
219C2×C4C2×C22⋊D6111yescharacteristic
220C2×C4C23×D6111yescharacteristic
221C8—1224no—
222C22—21no—
223C22—21no—
224C22—21no—
225C22—21no—
226C22—21no—
227C22—21no—
228C22—21no—
229C22—44no—
230C22—4884no—
231C22—2442no—
232C22—2442no—
233C22—2442no—
234C22#1451976012yes—
235C22#1451980212yes—
236C22C22×C22⋊D6111yescharacteristic
237C4—21no—
238C4—21no—
239C4—42no—
240C4—42no—
241C4—2442no—
242C4#1451976012yes—
243C4C2×#1175822212yes—
244C2—22no—
245C2—22no—
246C2—41no—
247C2—4882no—
248C2C2×#1451976011yescharacteristic
249C2C2×#1451980211yescharacteristic
250C2#1684056011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×#117×C61C2
socleC22×C61C22×D4
hypercenterC2×#117D61
hypocenterC61#3094
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #16840086C2semidirect
3. #16840080C2semidirect
4. #16840075C2semidirect
5. #16839805C2semidirect
6. #16839766C2semidirect
7. #16839726C2semidirect
8. C2×#117×C61C2semidirect
18. #14519710C22semidirect
19. #14519708C22semidirect
20. #14519697C22semidirect
21. #14519697C22semidirect
22. C22⋊#92418C22semidirect
23. C22⋊#92418C22semidirect
28. #117×C61C22semidirect
29. C2×C4⋊C4×C61C22semidirect
30. C2×C4⋊C4×C61C22semidirect
127. C2×#117D61semidirect
134. C61#3094semidirect
146. #117C2×D61semidirect
148. C2×C4⋊C4C2×D61semidirect
149. C2×C4⋊C4C2×D61semidirect