Finite Group Databasebeta

← #21449466

Subgroups — #21449466

Order 7808.

1088 conjugacy classes of subgroups; only the 197 normal subgroups are shown.

normal subgroups only

This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 197 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×#14519764C212yesmaximal, complemented
2C2×#14519756C211yesmaximal, characteristic, complemented
3#16839676C214yesmaximal, complemented
4#16839665C212yesmaximal, complemented
5#16839618C214yesmaximal, complemented
6C4×C22⋊Dic61C211yesmaximal, characteristic, complemented
7C23×D4×C61C211yesmaximal, characteristic
8C22×Dic122C2211yescharacteristic, complemented
9#14519764—28no—
10#14519756—24no—
11C2×C4⋊Dic61C2211yescharacteristic, complemented
12C2×#11758196C2212yescomplemented
13C2×C22⋊Dic61C2212yes—
14C2×C22⋊Dic61C2212yes—
15C2×C22⋊Dic61C2218yescomplemented
16C2×C22⋊Dic61C2218yescomplemented
17C2×C4×Dic61C2212yescomplemented
18#14519684C2212yescomplemented
19C25×C61C2212yes—
20C22×D4×C61—28no—
21C22×D4×C61—24no—
22C22×D4×C61C2212yes—
23C22×D4×C61C2212yes—
24C23×C4×C61C2211yescharacteristic
25C24×C61—28no—
26C24×C61—24no—
27C24×C61—28no—
28C24×C61—44no—
29C24×C61C2314yes—
30C24×C61C2311yescharacteristic
31C2×D4×C61—232no—
32C2×D4×C61—28no—
33C2×D4×C61—24no—
34C2×D4×C61—24no—
35C2×D4×C61—24no—
36C2×D4×C61D418yes—
37C22×C4×C61—24no—
38C22×C4×C61D414yes—
39C22×C4×C61C2311yescharacteristic
40C22×C4×C61C2311yescharacteristic
41C22×Dic61C2312yes—
42C22×Dic61C2314yes—
43C22×Dic61C2312yes—
44C2×Dic122—22no—
45C2×Dic122—24no—
46C22⋊Dic61—24no—
47C22⋊Dic61—216no—
48C22⋊Dic61—24no—
49C22⋊Dic61—48no—
50C4⋊Dic61—22no—
51#11758196—24no—
52C4×Dic61—24no—
53C23×C61—22no—
54C23×C61—22no—
55C23×C61—216no—
56C23×C61—24no—
57C23×C61—24no—
58C23×C61—28no—
59C23×C61—28no—
60C23×C61—432no—
61C23×C61—48no—
62C23×C61—48no—
63C23×C61C2×D418yes—
64C23×C61C2×D412yes—
65C23×C61#4114yes—
66C23×C61C2411yescharacteristic
67D4×C61—216no—
68D4×C61—216no—
69C2×C4×C61—22no—
70C2×C4×C61—28no—
71C2×C4×C61C2×D412yes—
72C2×C4×C61C2×D414yes—
73C2×C4×C61C2×D412yes—
74C2×Dic61—24no—
75C2×Dic61—22no—
76C2×Dic61—22no—
77C2×Dic61—24no—
78C2×Dic61—24no—
79C2×Dic61—24no—
80C2×Dic61—24no—
81Dic122—44no—
82C22×C61—22no—
83C22×C61—22no—
84C22×C61—28no—
85C22×C61—28no—
86C22×C61—216no—
87C22×C61—432no—
88C22×C61—44no—
89C22×C61—44no—
90C22×C61—48no—
91C22×C61#12414yescomplemented
92C22×C61C22×D411yescharacteristic
93C22×C61C22×D412yes—
94C22×C61C2×#4112yes—
95C22×C61H(5,𝔽2)12yes—
96C4×C61—22no—
97C4×C61#12014yes—
98Dic61—42no—
99Dic61—42no—
100Dic61—44no—
101#2435—611nomaximal, Sylow
102C2×C61—24no—
103C2×C61—48no—
104C2×C61C2×#12011yescharacteristic
105C2×C61C2×#12411yescharacteristic
106C2×C61#53511yescharacteristic
107C2×C61#54614yes—
108C23×D4D6111yescharacteristic
109C2×#124—612no—
110C2×C22⋊Q8—611no—
111#394—614no—
112#390—612no—
113#379—614no—
114C4×C22⋊C4—611no—
115C61#243511yescharacteristic, complemented, Sylow
116C25C2×D6112yes—
117C22×Q8—611no—
118C22×D4—28no—
119C22×D4—24no—
120C22×D4C2×D6112yes—
121C22×D4C2×D6112yes—
122C23×C4C2×D6111yescharacteristic
123#124—1228no—
124C22⋊Q8—1224no—
125C2×C4⋊C4—611no—
126C2×C4⋊C4—612no—
127C2×C22⋊C4—612no—
128C2×C22⋊C4—618no—
129C2×C22⋊C4—612no—
130C2×C22⋊C4—618no—
131C2×C42—612no—
132#95—612no—
133C24—28no—
134C24—24no—
135C24—28no—
136C24—44no—
137C24C22×D6114yes—
138C24C22×D6111yescharacteristic
139C2×Q8—1222no—
140C2×Q8—1224no—
141C2×D4—232no—
142C2×D4—28no—
143C2×D4—24no—
144C2×D4—24no—
145C2×D4—24no—
146C2×D4C22⋊D6118yes—
147C22×C4—24no—
148C22×C4—614no—
149C22×C4—612no—
150C22×C4—612no—
151C22×C4C22⋊D6114yes—
152C22×C4C22×D6111yescharacteristic
153C22×C4C22×D6111yescharacteristic
154C4⋊C4—1224no—
155C4⋊C4—1222no—
156C22⋊C4—1224no—
157C22⋊C4—1224no—
158C22⋊C4—12216no—
159C22⋊C4—2448no—
160C42—1224no—
161C23—22no—
162C23—22no—
163C23—216no—
164C23—24no—
165C23—24no—
166C23—28no—
167C23—28no—
168C23—432no—
169C23—48no—
170C23—48no—
171C23#1175822414yes—
172C23C2×C22⋊D6118yes—
173C23C2×C22⋊D6112yes—
174C23C23×D6111yescharacteristic
175Q8—2444no—
176D4—216no—
177D4—216no—
178C2×C4—22no—
179C2×C4—28no—
180C2×C4—1224no—
181C2×C4—1224no—
182C2×C4—1222no—
183C2×C4—1222no—
184C2×C4—1224no—
185C2×C4—1224no—
186C2×C4—1224no—
187C2×C4C2×C22⋊D6112yes—
188C2×C4C2×C22⋊D6114yes—
189C2×C4C2×C22⋊D6112yes—
190C22—22no—
191C22—22no—
192C22—28no—
193C22—28no—
194C22—216no—
195C22—432no—
196C22—44no—
197C22—44no—
198C22—48no—
199C22#1451976414yescomplemented
200C22C22×C22⋊D6111yescharacteristic
201C22C22×C22⋊D6112yes—
202C22C2×#1175822412yes—
203C22#1451982212yes—
204C4—22no—
205C4—2442no—
206C4—2442no—
207C4—2444no—
208C4#1451974614yes—
209C2—24no—
210C2—48no—
211C2C2×#1451974611yescharacteristic
212C2C2×#1451976411yescharacteristic
213C2#1684032911yescharacteristic
214C2#1684040614yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC23×D4×C61C2
hypercenterC23×D4D61
hypocenterC61#2435
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. C2×#14519764C2semidirect
2. C2×#14519756C2semidirect
3. #16839676C2semidirect
4. #16839665C2semidirect
5. #16839618C2semidirect
6. C4×C22⋊Dic61C2semidirect
8. C22×Dic122C22semidirect
11. C2×C4⋊Dic61C22semidirect
12. C2×#11758196C22semidirect
15. C2×C22⋊Dic61C22semidirect
16. C2×C22⋊Dic61C22semidirect
17. C2×C4×Dic61C22semidirect
18. #14519684C22semidirect
91. C22×C61#124semidirect
115. C61#2435semidirect
199. C22#14519764semidirect