Finite Group Databasebeta

← #21461688

Subgroups — #21461688

Order 7808.

308 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 94 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
1D61⋊(C4⋊C8)C211yesmaximal, characteristic
2C2×#14519840C212yesmaximal
3#16840708C211yesmaximal, characteristic
4#16840635C212yesmaximal
5C4×Q8×D61C211yesmaximal, characteristic
6C2×D61⋊C8C2212yes—
7C2×C4⋊#6923—21no—
8C2×C4⋊#6923—21no—
9C2×C4⋊#6923C2212yes—
10#14519844—21no—
11C4⋊#92420—21no—
12#14519840—24no—
13C2×Q8×D61C2211yescharacteristic
14Q8×Dic61C411yescharacteristic, complemented
15C4×Dic122—21no—
16C4×Dic122C411yescharacteristic, complemented
17#14519742—21no—
18#14519742C411yescharacteristic, complemented
19C4⋊C4×D61—21no—
20C4⋊C4×D61C2211yescharacteristic
21C42×D61—21no—
22C42×D61C2211yescharacteristic
23C4×Q8×C61C411yescharacteristic, complemented
24C22×#6923—22no—
25C2×Q8×C61C2×C411yescharacteristic
26Q8×D61—21no—
27Q8×D61—21no—
28Q8×D61D412yes—
29Q8×D61Q812yes—
30C2×C4×D61—21no—
31C2×C4×D61—21no—
32C2×C4×D61D411yescharacteristic
33C2×C4×D61D411yescharacteristic
34C2×C4×D61C2311yescharacteristic
35C2×Dic122—21no—
36C2×Dic122C2×C411yescharacteristic
37C2×#92420—22no—
38C4⋊#6923—22no—
39C4⋊#6923—22no—
40C4⋊#6923—42no—
41C4⋊#6923—42no—
42D61⋊C8—22no—
43D61⋊C8—22no—
44C4⋊C4×C61—21no—
45C4⋊C4×C61C2×C411yescharacteristic
46C42×C61—21no—
47C42×C61C2×C411yescharacteristic
48C4⋊Dic61—21no—
49C4⋊Dic61C2×C411yescharacteristic
50#11758196—21no—
51#11758196—21no—
52#11758196—21no—
53C4×Dic61—21no—
54C4×Dic61—21no—
55C4×Dic61—21no—
56C4×Dic61C2×C411yescharacteristic
57C4×Dic61D411yescharacteristic
58C4×Dic61D411yescharacteristic
59C22×D61C2×D411yescharacteristic
60C2×#6923—42no—
61C2×#6923—42no—
62C2×#6923—42no—
63Q8×C61—21no—
64Q8×C61C4⋊C412yescomplemented
65C2×C4×C61—21no—
66C2×C4×C61—21no—
67C2×C4×C61C22⋊C411yescharacteristic
68C2×C4×C61C22⋊C411yescharacteristic
69C2×C4×C61C22×C411yescharacteristic
70C2×Dic61—21no—
71C2×Dic61—21no—
72C2×Dic61C22⋊C411yescharacteristic
73C2×Dic61C22⋊C411yescharacteristic
74C2×Dic61C2×D411yescharacteristic
75C4×D61—22no—
76C4×D61—22no—
77C4×D61—21no—
78C4×D61—21no—
79C4×D61—41no—
80C4×D61—41no—
81C4×D61SD1612yes—
82C4×D61Q1612yes—
83C4×D61C2×D411yescharacteristic
84C4×D61C2×Q811yescharacteristic
85C4×D61#4111yescharacteristic
86C4×D61#4111yescharacteristic
87Dic122—21no—
88Dic122—22no—
89Dic122—22no—
90Dic122C4⋊C412yescomplemented
91#92420—42no—
92C22×C61C2×C22⋊C411yescharacteristic
93C2×D61#12111yescharacteristic
94C2×D61C22⋊Q811yescharacteristic
95C2×D61C2×SD1611yescharacteristic
96C2×D61C2×Q1611yescharacteristic
97C2×D61AGL(1,ℤ/8)11yescharacteristic
98C2×D61#13711yescharacteristic
99#6923—82no—
100C4×C61—22no—
101C4×C61—21no—
102C4×C61—41no—
103C4×C61#10312yescomplemented
104C4×C61C2×C4⋊C411yescharacteristic
105C4×C61#11711yescharacteristic
106Dic61—22no—
107Dic61—21no—
108Dic61—41no—
109Dic61#10312yescomplemented
110Dic61#12111yescharacteristic
111Dic61C22⋊Q811yescharacteristic
112#1803—611nomaximal, Sylow
113C2×C61#38011yescharacteristic
114C2×C61C2×#10311yescharacteristic
115C2×C61#41711yescharacteristic
116D61#46011yescharacteristic
117D61#46211yescharacteristic
118D61#47511yescharacteristic
119D61#47711yescharacteristic
120C2×C4×Q8—611no—
121C2×C4⋊C8—611no—
122C2×#103—612no—
123#384—611no—
124#340—612no—
125C61#180311yescharacteristic, complemented, Sylow
126C22×Q8—611no—
127C22×C8—612no—
128C4×Q8—611no—
129C4×Q8—611no—
130C4×Q8—611no—
131C4×Q8—1221no—
132C4×Q8—1221no—
133C4×Q8#692311yescharacteristic, complemented
134C2×C4⋊C4—611no—
135C2×C4⋊C4—612no—
136C2×C4⋊C4—1221no—
137C2×C4⋊C4—1221no—
138C2×C4⋊C4—1221no—
139C2×C42—611no—
140C2×C42—1221no—
141C4⋊C8—1221no—
142C4⋊C8—1221no—
143#103—1224no—
144C2×Q8—612no—
145C2×Q8—612no—
146C2×Q8—611no—
147C2×Q8—1221no—
148C2×Q8—1221no—
149C2×Q8—1221no—
150C2×Q8C2×#692311yescharacteristic
151C22×C4—611no—
152C22×C4—611no—
153C22×C4—611no—
154C22×C4—1221no—
155C22×C4—1221no—
156C22×C4—1222no—
157C2×C8—1222no—
158C2×C8—1222no—
159C2×C8—1222no—
160C4⋊C4—21no—
161C4⋊C4—611no—
162C4⋊C4—1221no—
163C4⋊C4—1221no—
164C4⋊C4—1221no—
165C4⋊C4—1222no—
166C4⋊C4—1222no—
167C4⋊C4—1221no—
168C4⋊C4—2442no—
169C4⋊C4—2442no—
170C4⋊C4C2×#692311yescharacteristic
171C42—21no—
172C42—611no—
173C42—611no—
174C42—611no—
175C42—1221no—
176C42—1221no—
177C42—1221no—
178C42C2×#692311yescharacteristic
179C23—611no—
180Q8—21no—
181Q8—612no—
182Q8—1222no—
183Q8—1222no—
184Q8—1221no—
185Q8C4⋊#692312yescomplemented
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—611no—
189C2×C4—611no—
190C2×C4—612no—
191C2×C4—612no—
192C2×C4—611no—
193C2×C4—611no—
194C2×C4—611no—
195C2×C4—611no—
196C2×C4—611no—
197C2×C4—1221no—
198C2×C4—1221no—
199C2×C4—1222no—
200C2×C4—1222no—
201C2×C4—1221no—
202C2×C4—1221no—
203C2×C4—2441no—
204C2×C4—2441no—
205C2×C4—2442no—
206C2×C4—2442no—
207C2×C4—2442no—
208C2×C4C22⋊#692311yescharacteristic
209C2×C4C22⋊#692311yescharacteristic
210C2×C4C22×#692311yescharacteristic
211C8—2442no—
212C22—611no—
213C22—611no—
214C22—611no—
215C22—611no—
216C22—611no—
217C22—611no—
218C22C2×C22⋊#692311yescharacteristic
219C4—22no—
220C4—21no—
221C4—41no—
222C4—611no—
223C4—611no—
224C4—612no—
225C4—1222no—
226C4—1221no—
227C4—4882no—
228C4—2441no—
229C4#1451984012yescomplemented
230C4C2×C4⋊#692311yescharacteristic
231C4#1451985611yescharacteristic
232C2—611no—
233C2—611no—
234C2—611no—
235C2—611no—
236C2#1684070411yescharacteristic
237C2C2×#1451984011yescharacteristic
238C2#1684075311yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC4×Q8×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC4×Q8#6923
hypocenterC61#1803
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
14. Q8×Dic61C4semidirect
16. C4×Dic122C4semidirect
18. #14519742C4semidirect
23. C4×Q8×C61C4semidirect
64. Q8×C61C4⋊C4semidirect
90. Dic122C4⋊C4semidirect
103. C4×C61#103semidirect
109. Dic61#103semidirect
125. C61#1803semidirect
133. C4×Q8#6923semidirect
185. Q8C4⋊#6923semidirect
229. C4#14519840semidirect