Finite Group Databasebeta

← #21451188

Subgroups — #21451188

Order 7808.

484 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 161 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×#14519742C212yesmaximal
2#16839695C212yesmaximal
3#16839692C211yesmaximal, characteristic
4#16839666C212yesmaximal
5#16839666C212yesmaximal
6#16839659C212yesmaximal
7#16839657C212yesmaximal
8#16839631C211yesmaximal, characteristic
9C61×#398C211yesmaximal, characteristic
10C22×Dic122C2212yes—
11#14519742—28no—
12C2×C4⋊Dic61C2211yescharacteristic
13C2×C4⋊Dic61C2211yescharacteristic
14C2×#11758196C2212yes—
15C2×#11758196C2212yes—
16C2×#11758196C2212yes—
17C2×#11758196C2212yes—
18C2×#11758196C2212yes—
19C2×C4×Dic61C2212yes—
20C2×C4×Dic61C2212yes—
21C2×C4×Dic61C2211yescharacteristic
22#14519684C2212yes—
23#14519684C2211yescharacteristic
24#14519684C2212yes—
25#14519684C2212yes—
26#14519684C2212yes—
27C2×C4⋊C4×C61C2212yes—
28C2×C4⋊C4×C61C2211yescharacteristic
29C2×C4⋊C4×C61C2211yescharacteristic
30#95×C61C2212yes—
31#95×C61C2211yescharacteristic
32C22×C4×C61C2311yescharacteristic
33C22×C4×C61C2311yescharacteristic
34C22×C4×C61C2312yes—
35C22×C4×C61C2311yescharacteristic
36C22×C4×C61C2312yes—
37C22×Dic61C2312yes—
38C22×Dic61C2312yes—
39C22×Dic61C2312yes—
40C22×Dic61C2312yes—
41C2×Dic122—24no—
42C2×Dic122—24no—
43C2×Dic122Q818yescomplemented
44C4⋊C4×C61—24no—
45C4⋊C4×C61—41no—
46C4⋊C4×C61—41no—
47C4⋊Dic61—41no—
48C4⋊Dic61—41no—
49#11758196—24no—
50#11758196—24no—
51#11758196—24no—
52#11758196—24no—
53#11758196—42no—
54C4×Dic61—24no—
55C4×Dic61—24no—
56C4×Dic61D414yes—
57C23×C61C2411yescharacteristic
58C2×C4×C61—22no—
59C2×C4×C61—22no—
60C2×C4×C61—21no—
61C2×C4×C61—21no—
62C2×C4×C61—22no—
63C2×C4×C61—22no—
64C2×C4×C61—22no—
65C2×C4×C61—22no—
66C2×C4×C61—21no—
67C2×C4×C61—21no—
68C2×C4×C61—22no—
69C2×C4×C61C2×D412yes—
70C2×C4×C61C2×Q814yes—
71C2×Dic61—22no—
72C2×Dic61—22no—
73C2×Dic61—22no—
74C2×Dic61—22no—
75C2×Dic61—22no—
76C2×Dic61—22no—
77C2×Dic61—22no—
78C2×Dic61—22no—
79C2×Dic61C2×D414yes—
80C2×Dic61C2×Q814yes—
81C2×Dic61C2×Q814yes—
82C2×Dic61#4114yes—
83Dic122—216no—
84C22×C61C22×D411yescharacteristic
85C22×C61C22×Q812yes—
86C22×C61C2×#4112yes—
87C22×C61H(5,𝔽2)11yescharacteristic
88C22×C612−1+411yescharacteristic
89C4×C61—24no—
90C4×C61—22no—
91C4×C61—42no—
92C4×C61—41no—
93C4×C61—41no—
94Dic61—24no—
95Dic61—42no—
96Dic61—42no—
97Dic61C22⋊Q818yes—
98#2582—611nomaximal, Sylow
99C2×C61C2×C22⋊Q812yes—
100C2×C61#53711yescharacteristic
101C2×C61#55712yes—
102C2×C61Q8211yescharacteristic
103C2×C61#55911yescharacteristic
104C2×C4×Q8—612no—
105#398—611no—
106#398—612no—
107#398D6111yescharacteristic
108#391—612no—
109#391—612no—
110#389—612no—
111#389—612no—
112#384—611no—
113C61#258211yescharacteristic, complemented, Sylow
114C22×Q8—612no—
115C4×Q8—1228no—
116C2×C4⋊C4—612no—
117C2×C4⋊C4—612no—
118C2×C4⋊C4—612no—
119C2×C4⋊C4—612no—
120C2×C4⋊C4—611no—
121C2×C4⋊C4—612no—
122C2×C4⋊C4—611no—
123C2×C4⋊C4C2×D6112yes—
124C2×C4⋊C4C2×D6111yescharacteristic
125C2×C4⋊C4C2×D6111yescharacteristic
126C2×C42—611no—
127C2×C42—612no—
128C2×C42—612no—
129#95—612no—
130#95—612no—
131#95—612no—
132#95—611no—
133#95—612no—
134#95C2×D6112yes—
135#95C2×D6111yescharacteristic
136C2×Q8—618no—
137C2×Q8—1224no—
138C2×Q8—1224no—
139C22×C4—612no—
140C22×C4—612no—
141C22×C4—612no—
142C22×C4—612no—
143C22×C4C22×D6111yescharacteristic
144C22×C4C22×D6111yescharacteristic
145C22×C4C22×D6112yes—
146C22×C4C22×D6111yescharacteristic
147C22×C4C22×D6112yes—
148C4⋊C4—24no—
149C4⋊C4—41no—
150C4⋊C4—41no—
151C4⋊C4—1224no—
152C4⋊C4—1224no—
153C4⋊C4—1224no—
154C4⋊C4—1224no—
155C4⋊C4—2442no—
156C4⋊C4—2441no—
157C4⋊C4—2441no—
158C42—614no—
159C42—1224no—
160C42—1224no—
161C23C23×D6111yescharacteristic
162Q8—12216no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—614no—
175C2×C4—614no—
176C2×C4—614no—
177C2×C4—614no—
178C2×C4—1222no—
179C2×C4—1222no—
180C2×C4—1222no—
181C2×C4—1222no—
182C2×C4—1222no—
183C2×C4—1222no—
184C2×C4—1222no—
185C2×C4—1222no—
186C2×C4D4×D6112yes—
187C2×C4Q8×D6114yes—
188C22C2×D4×D6111yescharacteristic
189C22C2×Q8×D6112yes—
190C22#41×D6112yes—
191C22#1451982211yescharacteristic
192C22#1451982411yescharacteristic
193C4—24no—
194C4—22no—
195C4—41no—
196C4—41no—
197C4—42no—
198C4—618no—
199C4—1224no—
200C4—2442no—
201C4—2442no—
202C2C22⋊Q8×D6112yes—
203C2#1684033911yescharacteristic
204C2#1684048912yes—
205C2#1684049211yescharacteristic
206C2#1684049611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#398C2
hypercenter#398D61
hypocenterC61#2582
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
43. C2×Dic122Q8semidirect
113. C61#2582semidirect