Finite Group Databasebeta

← #21461680

Subgroups — #21461680

Order 7808.

380 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 80 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×#14519836C212yesmaximal
2#16840704C212yesmaximal, complemented
3#16840640C212yesmaximal, complemented
4C2×C4×D244C211yesmaximal, characteristic
5C2×C4⋊#6923—22no—
6C2×C22⋊#6923C2214yes—
7#14519836—24no—
8(C2×#6923)⋊C4—22no—
9C22×D244C2211yescharacteristic
10C22×C4×D61C411yescharacteristic, complemented
11C22×C4×D61C2211yescharacteristic
12C4×D244—22no—
13C4×D244—22no—
14C2×C4⋊Dic61C411yescharacteristic, complemented
15C2×#11758198C411yescharacteristic, complemented
16C2×#11758198C2211yescharacteristic
17C2×C42×C61C411yescharacteristic, complemented
18C23×D61C2×C411yescharacteristic
19C23×D61C2311yescharacteristic
20C22×#6923—24no—
21C22×C4×C61C2×C411yescharacteristic
22C22×C4×C61C2×C411yescharacteristic
23C22×C4×C61C2×C411yescharacteristic
24C22×Dic61C2×C411yescharacteristic
25C22×Dic61C2×C411yescharacteristic
26C2×D244—22no—
27C2×D244—22no—
28C2×D244D412yes—
29C2×D244Q812yes—
30C2×C4×D61—21no—
31C2×C4×D61—21no—
32C2×C4×D61—42no—
33C2×C4×D61—42no—
34C2×C4×D61D412yes—
35C2×C4×D61D412yes—
36C22⋊#6923—24no—
37C22⋊#6923—24no—
38C4⋊#6923—44no—
39C42×C61—21no—
40C42×C61—21no—
41#11758198—22no—
42#11758198—22no—
43C4⋊Dic61—22no—
44C23×C61C22×C411yescharacteristic
45C22×D61—21no—
46C22×D61—21no—
47C22×D61—41no—
48C22×D61—41no—
49C22×D61—41no—
50C22×D61—41no—
51C22×D61C4⋊C412yescomplemented
52C22×D61C2×D412yes—
53C22×D61C2×D411yescharacteristic
54C22×D61C2×Q811yescharacteristic
55C22×D61#4112yes—
56C2×#6923—44no—
57C2×#6923—44no—
58C2×#6923—44no—
59C2×C4×C61—21no—
60C2×C4×C61—21no—
61C2×C4×C61—22no—
62C2×C4×C61—21no—
63C2×C4×C61—41no—
64C2×C4×C61C22⋊C411yescharacteristic
65C2×C4×C61C22⋊C411yescharacteristic
66C2×C4×C61C4⋊C412yescomplemented
67C2×Dic61—21no—
68C2×Dic61—41no—
69C2×Dic61—41no—
70C2×Dic61C22⋊C412yes—
71D244—24no—
72D244—24no—
73C4×D61—24no—
74C4×D61—42no—
75C4×D61—42no—
76C4×D61—42no—
77C22×C61—21no—
78C22×C61—21no—
79C22×C61C2×C22⋊C411yescharacteristic
80C22×C61C2×C4⋊C411yescharacteristic
81C22×C61#11711yescharacteristic
82C2×D61—22no—
83C2×D61—22no—
84C2×D61—22no—
85C2×D61—41no—
86C2×D61—41no—
87C2×D61—42no—
88C2×D61—42no—
89C2×D61—41no—
90C2×D61—41no—
91C2×D61—42no—
92C2×D61#12112yes—
93C2×D61C22⋊Q812yes—
94#6923—84no—
95C4×C61—22no—
96C4×C61—21no—
97C4×C61—41no—
98C4×C61#9912yescomplemented
99Dic61—22no—
100Dic61—41no—
101#1799—611nomaximal, Sylow
102C2×C61—21no—
103C2×C61—21no—
104C2×C61#38011yescharacteristic
105C2×C61C2×#9911yescharacteristic
106C2×C61#41011yescharacteristic
107D61—22no—
108D61—22no—
109D61—42no—
110C2×C4×D4—611no—
111C2×#99—612no—
112#380—612no—
113#342—612no—
114C61#179911yescharacteristic, complemented, Sylow
115C22×D4—611no—
116C23×C4—611no—
117C23×C4—611no—
118C4×D4—1222no—
119C4×D4—1222no—
120C2×C4⋊C4—611no—
121C2×C4⋊C4—1222no—
122C2×C22⋊C4—611no—
123C2×C22⋊C4—611no—
124C2×C22⋊C4—614no—
125C2×C42#692311yescharacteristic, complemented
126#99—1224no—
127#95—1222no—
128C24—611no—
129C24—611no—
130C2×D4—612no—
131C2×D4—612no—
132C2×D4—1222no—
133C2×D4—1222no—
134C22×C4—611no—
135C22×C4—612no—
136C22×C4—612no—
137C22×C4—611no—
138C22×C4—1221no—
139C22×C4—1221no—
140C22×C4—1224no—
141C22×C4—2442no—
142C22×C4—2442no—
143C22×C4C2×#692311yescharacteristic
144C22×C4C2×#692311yescharacteristic
145C22×C4C2×#692311yescharacteristic
146C4⋊C4—1222no—
147C4⋊C4—2444no—
148C22⋊C4—1222no—
149C22⋊C4—1222no—
150C22⋊C4—1224no—
151C22⋊C4—1224no—
152C42—21no—
153C42—21no—
154C23—612no—
155C23—611no—
156C23—611no—
157C23—612no—
158C23—612no—
159C23—1221no—
160C23—1221no—
161C23—2441no—
162C23—2441no—
163C23—2441no—
164C23—2441no—
165C23C22×#692311yescharacteristic
166D4—1224no—
167D4—1224no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—22no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—612no—
174C2×C4—1224no—
175C2×C4—1221no—
176C2×C4—2442no—
177C2×C4—2442no—
178C2×C4—2441no—
179C2×C4—2444no—
180C2×C4—2444no—
181C2×C4—2444no—
182C2×C4—2442no—
183C2×C4—2441no—
184C2×C4C4⋊#692312yescomplemented
185C2×C4C22⋊#692311yescharacteristic
186C2×C4C22⋊#692311yescharacteristic
187C22—21no—
188C22—21no—
189C22—612no—
190C22—612no—
191C22—1222no—
192C22—1222no—
193C22—1222no—
194C22—2441no—
195C22—2441no—
196C22—2442no—
197C22—2442no—
198C22—2442no—
199C22—2441no—
200C22—2441no—
201C22C2×C22⋊#692311yescharacteristic
202C22C2×C4⋊#692311yescharacteristic
203C22#1451985611yescharacteristic
204C4—22no—
205C4—21no—
206C4—41no—
207C4—1222no—
208C4—4884no—
209C4—2441no—
210C4#1451983612yescomplemented
211C2—21no—
212C2—21no—
213C2—1222no—
214C2—1222no—
215C2—2442no—
216C2#1684070411yescharacteristic
217C2C2×#1451983611yescharacteristic
218C2#1684074111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC23×C61C22×C4
FrattiniC23C22×#6923
FittingC2×C42×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC2×C42#6923
hypocenterC61#1799
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #16840704C2semidirect
3. #16840640C2semidirect
10. C22×C4×D61C4semidirect
14. C2×C4⋊Dic61C4semidirect
15. C2×#11758198C4semidirect
17. C2×C42×C61C4semidirect
51. C22×D61C4⋊C4semidirect
66. C2×C4×C61C4⋊C4semidirect
98. C4×C61#99semidirect
114. C61#1799semidirect
125. C2×C42#6923semidirect
184. C2×C4C4⋊#6923semidirect
210. C4#14519836semidirect