Finite Group Databasebeta

← #21448415

Subgroups — #21448415

Order 7808.

672 conjugacy classes of subgroups; only the 189 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 189 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
1C22×C22⋊Dic61C211yesmaximal, characteristic
2#16839656C214yesmaximal, complemented
3#16839650C214yesmaximal, complemented
4#16839620C212yesmaximal, complemented
5#16839618C211yesmaximal, characteristic
6C22⋊C4×Dic61C212yesmaximal, complemented
7C61×#379C211yesmaximal, characteristic
8C23×Dic61C2211yescharacteristic
9C23×Dic61C2211yescharacteristic
10C2×#11758196C2214yescomplemented
11C2×C22⋊Dic61C418yescomplemented
12C2×C22⋊Dic61C2212yes—
13C2×C22⋊Dic61C2212yes—
14C2×C22⋊Dic61C2212yes—
15C2×C22⋊Dic61C2212yes—
16C2×C22⋊Dic61C2212yes—
17C2×C4×Dic61C2214yescomplemented
18#14519684C2214yescomplemented
19#14519684C2214yescomplemented
20C25×C61C2211yescharacteristic
21C2×C22⋊C4×C61C2212yes—
22C2×C22⋊C4×C61C2212yes—
23C2×C22⋊C4×C61C2212yes—
24C24×C61—24no—
25C24×C61—42no—
26C24×C61—42no—
27C24×C61C2×C414yes—
28C24×C61C2311yescharacteristic
29C24×C61C2311yescharacteristic
30C24×C61C2311yescharacteristic
31C22×C4×C61C2314yes—
32C22×Dic61—42no—
33C22×Dic61—42no—
34C22×Dic61C2×C414yes—
35C22×Dic61C2×C414yes—
36C22×Dic61C2314yes—
37C22×Dic61C2312yes—
38C22×Dic61C2312yes—
39C22⋊C4×C61—24no—
40C22⋊C4×C61—42no—
41C22⋊C4×C61—42no—
42C22⋊Dic61—24no—
43C22⋊Dic61—42no—
44C22⋊Dic61—42no—
45C22⋊Dic61C2×C418yes—
46C22⋊Dic61C2×C418yes—
47#11758196—44no—
48C4×Dic61—44no—
49C23×C61—22no—
50C23×C61—22no—
51C23×C61—28no—
52C23×C61—22no—
53C23×C61—22no—
54C23×C61—22no—
55C23×C61—22no—
56C23×C61—22no—
57C23×C61—22no—
58C23×C61—44no—
59C23×C61—44no—
60C23×C61—416no—
61C23×C61C22×C412yes—
62C23×C61C22×C412yes—
63C23×C61C22×C412yes—
64C23×C61#4114yes—
65C23×C61C2411yescharacteristic
66C2×C4×C61—24no—
67C2×C4×C61—24no—
68C2×C4×C61—24no—
69C2×Dic61—24no—
70C2×Dic61—24no—
71C2×Dic61—24no—
72C2×Dic61—24no—
73C2×Dic61—24no—
74C2×Dic61—44no—
75C2×Dic61—44no—
76C2×Dic61C22×C414yes—
77C2×Dic61C22×C414yes—
78C22×C61—22no—
79C22×C61—22no—
80C22×C61—28no—
81C22×C61—22no—
82C22×C61—22no—
83C22×C61—22no—
84C22×C61—22no—
85C22×C61—22no—
86C22×C61—22no—
87C22×C61—416no—
88C22×C61—44no—
89C22×C61—44no—
90C22×C61#11714yes—
91C22×C61C23×C411yescharacteristic
92C22×C61C2×#4112yes—
93C22×C61H(5,𝔽2)12yes—
94C22×C61H(5,𝔽2)12yes—
95C4×C61—44no—
96Dic61—24no—
97Dic61—24no—
98Dic61—44no—
99#2312—611nomaximal, Sylow
100C2×C61—24no—
101C2×C61—42no—
102C2×C61—42no—
103C2×C61C2×#11711yescharacteristic
104C2×C61#51811yescharacteristic
105C2×C61#51811yescharacteristic
106C2×C61#53814yes—
107C22×C22⋊C4—611no—
108#388—614no—
109#388—614no—
110#380—612no—
111#379—611no—
112#379D6111yescharacteristic
113C4×C22⋊C4—612no—
114C61#231211yescharacteristic, complemented, Sylow
115C25C2×D6111yescharacteristic
116C23×C4—611no—
117C23×C4—611no—
118C2×C4⋊C4—614no—
119C2×C22⋊C4—618no—
120C2×C22⋊C4—612no—
121C2×C22⋊C4—612no—
122C2×C22⋊C4—612no—
123C2×C22⋊C4—612no—
124C2×C22⋊C4—612no—
125C2×C22⋊C4C2×D6112yes—
126C2×C22⋊C4C2×D6112yes—
127C2×C22⋊C4C2×D6112yes—
128C2×C42—614no—
129#95—614no—
130#95—614no—
131C24—24no—
132C24—42no—
133C24—42no—
134C24C4×D6114yes—
135C24C22×D6111yescharacteristic
136C24C22×D6111yescharacteristic
137C24C22×D6111yescharacteristic
138C22×C4—612no—
139C22×C4—612no—
140C22×C4—614no—
141C22×C4—614no—
142C22×C4—614no—
143C22×C4—2442no—
144C22×C4—2442no—
145C22×C4C22×D6114yes—
146C4⋊C4—2444no—
147C22⋊C4—24no—
148C22⋊C4—42no—
149C22⋊C4—42no—
150C22⋊C4—618no—
151C22⋊C4—618no—
152C22⋊C4—1224no—
153C22⋊C4—2442no—
154C22⋊C4—2442no—
155C42—2444no—
156C23—22no—
157C23—22no—
158C23—22no—
159C23—22no—
160C23—22no—
161C23—22no—
162C23—22no—
163C23—22no—
164C23—28no—
165C23—44no—
166C23—44no—
167C23—416no—
168C23C2×C4×D6112yes—
169C23C2×C4×D6112yes—
170C23C2×C4×D6112yes—
171C23#1175822414yes—
172C23C23×D6111yescharacteristic
173C2×C4—24no—
174C2×C4—24no—
175C2×C4—24no—
176C2×C4—614no—
177C2×C4—614no—
178C2×C4—1224no—
179C2×C4—1224no—
180C2×C4—1224no—
181C2×C4—1224no—
182C2×C4—1224no—
183C2×C4—2444no—
184C2×C4—2444no—
185C22—22no—
186C22—22no—
187C22—28no—
188C22—22no—
189C22—22no—
190C22—22no—
191C22—22no—
192C22—22no—
193C22—22no—
194C22—416no—
195C22—44no—
196C22—44no—
197C22#1451973314yes—
198C22C22×C4×D6111yescharacteristic
199C22C2×#1175822412yes—
200C22#1451982212yes—
201C22#1451982212yes—
202C4—44no—
203C4—1224no—
204C4—1224no—
205C4—2444no—
206C2—24no—
207C2—42no—
208C2—42no—
209C2C2×#1451973311yescharacteristic
210C2#1684023511yescharacteristic
211C2#1684023511yescharacteristic
212C2#1684034714yes—
subgroupG/H
center, FrattiniC23C23×D61
commutatorC22×C61C23×C4
FittingC61×#379C2
socleC23×C61C24
hypercenter#379D61
hypocenterC61#2312
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
2. #16839656C2semidirect
3. #16839650C2semidirect
4. #16839620C2semidirect
6. C22⋊C4×Dic61C2semidirect
10. C2×#11758196C22semidirect
11. C2×C22⋊Dic61C4semidirect
17. C2×C4×Dic61C22semidirect
18. #14519684C22semidirect
19. #14519684C22semidirect
114. C61#2312semidirect