Finite Group Databasebeta

← #21461591

Subgroups — #21461591

Order 7808.

324 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 100 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×#14519840C212yesmaximal
2#16840721C211yesmaximal, characteristic
3C4×C4⋊#6923C211yesmaximal, characteristic
4#16840635C212yesmaximal
5C4×Q8×D61C211yesmaximal, characteristic
6C2×D61⋊C8C2212yes—
7C2×C4⋊#6923C2212yes—
8C2×C4×#6923—21no—
9#14519840C418yescomplemented
10#14519832—21no—
11#14519832—21no—
12(C2×#6923)⋊C4—21no—
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—22no—
27Q8×D61C2×C414yes—
28C2×C4×D61—21no—
29C2×C4×D61—21no—
30C2×C4×D61D411yescharacteristic
31C2×C4×D61D411yescharacteristic
32C2×C4×D61C2311yescharacteristic
33C2×Dic122—21no—
34C2×Dic122C2×C411yescharacteristic
35C2×#92420—22no—
36C4⋊#6923—22no—
37C4⋊#6923C2×C414yes—
38C4×#6923—42no—
39D61⋊C8—22no—
40D61⋊C8C2×C414yes—
41C4⋊C4×C61—21no—
42C4⋊C4×C61C2×C411yescharacteristic
43C42×C61—21no—
44C42×C61C2×C411yescharacteristic
45C4⋊Dic61—21no—
46C4⋊Dic61C2×C411yescharacteristic
47#11758196—21no—
48#11758196—21no—
49#11758196—21no—
50C4×Dic61—21no—
51C4×Dic61—21no—
52C4×Dic61—21no—
53C4×Dic61C2×C411yescharacteristic
54C4×Dic61D411yescharacteristic
55C4×Dic61D411yescharacteristic
56C22×D61C2×D411yescharacteristic
57C2×#6923—24no—
58C2×#6923—42no—
59C2×#6923—42no—
60Q8×C61—21no—
61Q8×C61C4212yescomplemented
62C2×C4×C61—21no—
63C2×C4×C61—21no—
64C2×C4×C61C22⋊C411yescharacteristic
65C2×C4×C61C22⋊C411yescharacteristic
66C2×C4×C61C22×C411yescharacteristic
67C2×Dic61—21no—
68C2×Dic61—21no—
69C2×Dic61C22⋊C411yescharacteristic
70C2×Dic61C22⋊C411yescharacteristic
71C2×Dic61C2×D411yescharacteristic
72C4×D61—24no—
73C4×D61—21no—
74C4×D61—21no—
75C4×D61—22no—
76C4×D61—41no—
77C4×D61—41no—
78C4×D61C22×C412yes—
79C4×D61#4112yes—
80Dic122—21no—
81Dic122—24no—
82Dic122C4212yescomplemented
83#92420—24no—
84C22×C61C2×C22⋊C411yescharacteristic
85C2×D61C4×D412yes—
86C2×D61AGL(1,ℤ/8)11yescharacteristic
87C2×D61#13712yes—
88C2×D61#13711yescharacteristic
89#6923—44no—
90C4×C61—22no—
91C4×C61—21no—
92C4×C61—21no—
93C4×C61—41no—
94C4×C61C2×C4211yescharacteristic
95C4×C61#11711yescharacteristic
96Dic61—22no—
97Dic61—21no—
98Dic61—21no—
99Dic61—41no—
100Dic61C4×D412yes—
101#1763—611nomaximal, Sylow
102C2×C61C4×C22⋊C411yescharacteristic
103C2×C61#41711yescharacteristic
104C2×C61#41911yescharacteristic
105D61#44012yes—
106D61#44112yes—
107C2×C4×Q8—611no—
108C2×#103—612no—
109C2×#97—611no—
110C4×C4⋊C4—611no—
111#340—612no—
112C61#176311yescharacteristic, complemented, Sylow
113C22×Q8—611no—
114C22×C8—612no—
115C4×Q8—611no—
116C4×Q8—611no—
117C4×Q8—611no—
118C4×Q8—1221no—
119C4×Q8—1221no—
120C4×Q8#692311yescharacteristic, complemented
121C2×C4⋊C4—612no—
122C2×C4⋊C4—611no—
123C2×C4⋊C4—1221no—
124C2×C42—611no—
125C2×C42—1221no—
126C2×C42—1221no—
127#103—618no—
128#97—1221no—
129#97—1221no—
130#95—1221no—
131C2×Q8—614no—
132C2×Q8—611no—
133C2×Q8—1221no—
134C2×Q8—1222no—
135C2×Q8C2×#692311yescharacteristic
136C22×C4—611no—
137C22×C4—611no—
138C22×C4—611no—
139C22×C4—1221no—
140C22×C4—1221no—
141C22×C4—1222no—
142C2×C8—614no—
143C2×C8—1222no—
144C2×C8—1222no—
145C4⋊C4—21no—
146C4⋊C4—614no—
147C4⋊C4—611no—
148C4⋊C4—1221no—
149C4⋊C4—1221no—
150C4⋊C4—1221no—
151C4⋊C4—1222no—
152C4⋊C4—1221no—
153C4⋊C4C2×#692311yescharacteristic
154C42—21no—
155C42—611no—
156C42—611no—
157C42—611no—
158C42—1221no—
159C42—1221no—
160C42—1221no—
161C42—2442no—
162C42C2×#692311yescharacteristic
163C23—611no—
164Q8—21no—
165Q8—612no—
166Q8—1224no—
167Q8—1221no—
168Q8C4×#692312yescomplemented
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—611no—
172C2×C4—612no—
173C2×C4—612no—
174C2×C4—611no—
175C2×C4—611no—
176C2×C4—1221no—
177C2×C4—1221no—
178C2×C4—1222no—
179C2×C4—1224no—
180C2×C4—1221no—
181C2×C4—1224no—
182C2×C4—1221no—
183C2×C4—2441no—
184C2×C4—2441no—
185C2×C4—2442no—
186C2×C4—2442no—
187C2×C4C22⋊#692311yescharacteristic
188C2×C4C22⋊#692311yescharacteristic
189C2×C4C22×#692311yescharacteristic
190C8—1224no—
191C22—611no—
192C22—611no—
193C22—612no—
194C22—612no—
195C22C2×C22⋊#692311yescharacteristic
196C4—21no—
197C4—21no—
198C4—22no—
199C4—41no—
200C4—612no—
201C4—1221no—
202C4—1221no—
203C4—1222no—
204C4—2444no—
205C4—2441no—
206C4C2×C4×#692311yescharacteristic
207C4#1451985611yescharacteristic
208C2—612no—
209C2—612no—
210C2C4×C22⋊#692311yescharacteristic
211C2#1684075311yescharacteristic
212C2#1684075511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC4×C61C2×C42
FrattiniC2×C4C22×#6923
FittingC4×Q8×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC4×Q8#6923
hypocenterC61#1763
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
9. #14519840C4semidirect
14. Q8×Dic61C4semidirect
16. C4×Dic122C4semidirect
18. #14519742C4semidirect
23. C4×Q8×C61C4semidirect
61. Q8×C61C42semidirect
82. Dic122C42semidirect
112. C61#1763semidirect
120. C4×Q8#6923semidirect
168. Q8C4×#6923semidirect