Finite Group Databasebeta

← #21462009

Subgroups — #21462009

Order 7808.

324 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 74 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
1#16840704C211yesmaximal, characteristic
2C4×C22⋊#6923C211yesmaximal, characteristic
3#16840640C214yesmaximal
4C2×#14519757C211yesmaximal, characteristic
5C2×C4⋊#6923—21no—
6C2×C22⋊#6923C2212yes—
7C2×C22⋊#6923C2212yes—
8C2×C4×#6923—21no—
9(C2×#6923)⋊C4—21no—
10(C2×#6923)⋊C4—21no—
11C22×Dic122C411yescharacteristic, complemented
12C22×C4×D61C2211yescharacteristic
13#14519757—21no—
14#14519757—21no—
15#14519757—21no—
16#14519757—21no—
17C2×C4⋊Dic61C412yescomplemented
18C2×#11758198C2212yes—
19C2×C4⋊C4×C61C411yescharacteristic, complemented
20C23×D61C2311yescharacteristic
21C22×#6923—22no—
22C22×#6923—22no—
23C22×C4×C61C2×C411yescharacteristic
24C22×C4×C61C2×C412yes—
25C22×Dic61C2×C412yes—
26C22×Dic61C2×C411yescharacteristic
27C2×C4×D61—42no—
28C2×C4×D61D411yescharacteristic
29C2×C4×D61D411yescharacteristic
30C2×C4×D61D411yescharacteristic
31C2×C4×D61D411yescharacteristic
32C2×Dic122—21no—
33C2×Dic122—21no—
34C2×Dic122—42no—
35C22⋊#6923—22no—
36C22⋊#6923—24no—
37C22⋊#6923Q814yescomplemented
38C4⋊#6923—42no—
39C4×#6923—42no—
40C4⋊C4×C61—21no—
41C4⋊C4×C61—21no—
42#11758198—22no—
43#11758198—22no—
44C4⋊Dic61—22no—
45C4⋊Dic61—22no—
46C23×C61C22×C411yescharacteristic
47C22×D61—41no—
48C22×D61—41no—
49C22×D61C2×D411yescharacteristic
50C22×D61C2×D411yescharacteristic
51C22×D61C2×Q812yes—
52C22×D61#4112yes—
53C2×#6923—24no—
54C2×#6923—42no—
55C2×#6923—42no—
56C2×#6923—42no—
57C2×#6923—42no—
58C2×#6923—42no—
59C2×C4×C61—22no—
60C2×C4×C61—22no—
61C2×C4×C61—42no—
62C2×C4×C61C22⋊C411yescharacteristic
63C2×C4×C61C22⋊C411yescharacteristic
64C2×Dic61—22no—
65C2×Dic61—41no—
66C2×Dic61—42no—
67C2×Dic61C22⋊C411yescharacteristic
68C2×Dic61C22⋊C411yescharacteristic
69C4×D61—22no—
70C4×D61—22no—
71C4×D61—41no—
72C4×D61—41no—
73Dic122—42no—
74Dic122—42no—
75C22×C61—21no—
76C22×C61—21no—
77C22×C61C2×C22⋊C411yescharacteristic
78C22×C61C4×Q812yes—
79C2×D61—21no—
80C2×D61—21no—
81C2×D61—21no—
82C2×D61—21no—
83C2×D61—42no—
84C2×D61—42no—
85C2×D61C22⋊Q812yes—
86C2×D61#12411yescharacteristic
87C2×D61C4⋊Q811yescharacteristic
88#6923—44no—
89#6923—82no—
90C4×C61—21no—
91C4×C61—42no—
92C4×C61#9912yes—
93Dic61—21no—
94Dic61—21no—
95Dic61—42no—
96#1996—611nomaximal, Sylow
97C2×C61—22no—
98C2×C61#39111yescharacteristic
99C2×C61C2×#9911yescharacteristic
100C2×C61#41011yescharacteristic
101D61—22no—
102D61—21no—
103D61—21no—
104C2×C22⋊Q8—611no—
105#380—611no—
106C4×C22⋊C4—611no—
107#342—614no—
108C61#199611yescharacteristic, complemented, Sylow
109C22×Q8—611no—
110C23×C4—611no—
111C22⋊Q8—1221no—
112C22⋊Q8—1221no—
113C22⋊Q8—1221no—
114C22⋊Q8—1221no—
115C2×C4⋊C4—612no—
116C2×C4⋊C4—1221no—
117C2×C4⋊C4#692311yescharacteristic, complemented
118C2×C22⋊C4—612no—
119C2×C22⋊C4—612no—
120C2×C22⋊C4—612no—
121C2×C42—1221no—
122#95—1221no—
123#95—1221no—
124C24—611no—
125C2×Q8—1221no—
126C2×Q8—1221no—
127C2×Q8—2442no—
128C22×C4—611no—
129C22×C4—611no—
130C22×C4—611no—
131C22×C4—611no—
132C22×C4—611no—
133C22×C4—612no—
134C22×C4—1222no—
135C22×C4—1222no—
136C22×C4—2442no—
137C22×C4C2×#692312yes—
138C22×C4C2×#692311yescharacteristic
139C4⋊C4—21no—
140C4⋊C4—21no—
141C4⋊C4—1222no—
142C4⋊C4—1222no—
143C4⋊C4—2442no—
144C22⋊C4—614no—
145C22⋊C4—1222no—
146C22⋊C4—1222no—
147C22⋊C4—1222no—
148C22⋊C4—1224no—
149C42—2442no—
150C23—611no—
151C23—611no—
152C23—612no—
153C23—612no—
154C23—2441no—
155C23—2441no—
156C23C22×#692311yescharacteristic
157Q8—2442no—
158Q8—2442no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—42no—
162C2×C4—611no—
163C2×C4—611no—
164C2×C4—1222no—
165C2×C4—1222no—
166C2×C4—1224no—
167C2×C4—1222no—
168C2×C4—2441no—
169C2×C4—2441no—
170C2×C4—2441no—
171C2×C4—2442no—
172C2×C4—2442no—
173C2×C4—2442no—
174C2×C4—2442no—
175C2×C4—2442no—
176C2×C4—2442no—
177C2×C4C22⋊#692311yescharacteristic
178C2×C4C22⋊#692311yescharacteristic
179C22—21no—
180C22—21no—
181C22—612no—
182C22—611no—
183C22—611no—
184C22—1221no—
185C22—1221no—
186C22—1221no—
187C22—1221no—
188C22—2442no—
189C22—2442no—
190C22C2×C22⋊#692311yescharacteristic
191C22Q8×#692312yes—
192C4—21no—
193C4—42no—
194C4—1221no—
195C4—1221no—
196C4—4882no—
197C4—2444no—
198C4—2442no—
199C4#1451983612yes—
200C2—22no—
201C2—1221no—
202C2—1222no—
203C2—1221no—
204C2(C2×#6923)⋊Q811yescharacteristic
205C2C2×#1451983611yescharacteristic
206C2#1684074211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC23×C61C22×C4
FrattiniC23C22×#6923
FittingC2×C4⋊C4×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC2×C4⋊C4#6923
hypocenterC61#1996
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
11. C22×Dic122C4semidirect
17. C2×C4⋊Dic61C4semidirect
19. C2×C4⋊C4×C61C4semidirect
37. C22⋊#6923Q8semidirect
108. C61#1996semidirect
117. C2×C4⋊C4#6923semidirect