Finite Group Databasebeta

← #21451697

Subgroups — #21451697

Order 7808.

416 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 129 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×#14519767C211yesmaximal, characteristic
2C2×#14519742C211yesmaximal, characteristic
3#16839703C212yesmaximal
4#16839700C211yesmaximal, characteristic
5#16839696C212yesmaximal
6#16839683C211yesmaximal, characteristic
7#16839682C211yesmaximal, characteristic
8#16839649C212yesmaximal
9#16839645C212yesmaximal
10#16839629C211yesmaximal, characteristic
11C61×#400C211yesmaximal, characteristic
12C22×Dic122C2211yescharacteristic
13#14519767—24no—
14#14519742—24no—
15C2×C4⋊Dic61C2212yes—
16C2×C4⋊Dic61C2211yescharacteristic
17C2×#11758196C2212yes—
18C2×#11758196C2211yescharacteristic
19C2×#11758196C2211yescharacteristic
20C2×#11758196C2212yes—
21C2×#11758196C2211yescharacteristic
22C2×#11758196C2211yescharacteristic
23C2×C4×Dic61C2212yes—
24C2×C4×Dic61C2211yescharacteristic
25#14519684C2211yescharacteristic
26#14519684C2212yes—
27#14519684C2212yes—
28#14519684C2212yes—
29#14519684C2212yes—
30#14519684C2212yes—
31#14519684C2212yes—
32C2×C4⋊C4×C61C2211yescharacteristic
33C2×C4⋊C4×C61C2211yescharacteristic
34#95×C61C2211yescharacteristic
35#95×C61C2212yes—
36#95×C61C2212yes—
37C22×C4×C61C2312yes—
38C22×C4×C61C2312yes—
39C22×C4×C61C2311yescharacteristic
40C22×C4×C61C2311yescharacteristic
41C22×C4×C61C2311yescharacteristic
42C22×Dic61C2312yes—
43C22×Dic61C2311yescharacteristic
44C22×Dic61C2311yescharacteristic
45C22×Dic61C2311yescharacteristic
46C22×Dic61C2311yescharacteristic
47C22×Dic61C2312yes—
48C2×Dic122—22no—
49C2×Dic122—24no—
50C4⋊C4×C61—22no—
51C4⋊C4×C61—22no—
52C4⋊Dic61—22no—
53C4⋊Dic61—24no—
54#11758196—22no—
55#11758196—24no—
56#11758196—22no—
57#11758196—22no—
58#11758196—22no—
59#11758196—24no—
60C4×Dic61—24no—
61C4×Dic61D414yes—
62C23×C61C2411yescharacteristic
63C2×C4×C61—22no—
64C2×C4×C61—22no—
65C2×C4×C61—21no—
66C2×C4×C61—21no—
67C2×C4×C61—22no—
68C2×C4×C61—22no—
69C2×C4×C61—24no—
70C2×C4×C61—21no—
71C2×C4×C61—21no—
72C2×C4×C61—22no—
73C2×C4×C61—22no—
74C2×C4×C61C2×D412yes—
75C2×Dic61—22no—
76C2×Dic61—22no—
77C2×Dic61—21no—
78C2×Dic61—22no—
79C2×Dic61—21no—
80C2×Dic61—21no—
81C2×Dic61—21no—
82C2×Dic61—22no—
83C2×Dic61—22no—
84C2×Dic61—21no—
85C2×Dic61—21no—
86C2×Dic61—22no—
87C2×Dic61—22no—
88C2×Dic61C2×D412yes—
89C2×Dic61C2×D412yes—
90C2×Dic61#4114yes—
91Dic122—28no—
92C22×C61C22×D411yescharacteristic
93C22×C61C2×#4112yes—
94C22×C612−1+412yes—
95C22×C612−1+411yescharacteristic
96C22×C612−1+411yescharacteristic
97C4×C61—22no—
98C4×C61—41no—
99C4×C61—42no—
100C4×C61—41no—
101C4×C61—42no—
102Dic61—24no—
103Dic61—22no—
104Dic61—22no—
105Dic61—41no—
106Dic61—41no—
107Dic61—42no—
108#2634—611nomaximal, Sylow
109C2×C61#52511yescharacteristic
110C2×C61#53611yescharacteristic
111C2×C61#53611yescharacteristic
112C2×C61#54112yes—
113C2×C61#54112yes—
114C2×#125—611no—
115C2×C4×Q8—611no—
116#400—611no—
117#400—612no—
118#400D6111yescharacteristic
119#398—612no—
120#395—611no—
121#395—611no—
122#387—612no—
123#387—612no—
124#383—611no—
125C61#263411yescharacteristic, complemented, Sylow
126C22×Q8—611no—
127#125—1224no—
128C4×Q8—1224no—
129C2×C4⋊C4—612no—
130C2×C4⋊C4—611no—
131C2×C4⋊C4—611no—
132C2×C4⋊C4—611no—
133C2×C4⋊C4—611no—
134C2×C4⋊C4—611no—
135C2×C4⋊C4—612no—
136C2×C4⋊C4—612no—
137C2×C4⋊C4C2×D6111yescharacteristic
138C2×C4⋊C4C2×D6111yescharacteristic
139C2×C42—611no—
140C2×C42—612no—
141#95—612no—
142#95—611no—
143#95—612no—
144#95—612no—
145#95—612no—
146#95—612no—
147#95—612no—
148#95C2×D6111yescharacteristic
149#95C2×D6112yes—
150#95C2×D6112yes—
151C2×Q8—1224no—
152C2×Q8—1222no—
153C22×C4—611no—
154C22×C4—611no—
155C22×C4—612no—
156C22×C4—612no—
157C22×C4—611no—
158C22×C4—611no—
159C22×C4C22×D6112yes—
160C22×C4C22×D6112yes—
161C22×C4C22×D6111yescharacteristic
162C22×C4C22×D6111yescharacteristic
163C22×C4C22×D6111yescharacteristic
164C4⋊C4—22no—
165C4⋊C4—22no—
166C4⋊C4—1224no—
167C4⋊C4—1224no—
168C4⋊C4—1222no—
169C4⋊C4—1222no—
170C4⋊C4—1222no—
171C4⋊C4—1224no—
172C4⋊C4—1222no—
173C4⋊C4—1222no—
174C42—614no—
175C42—1224no—
176C23C23×D6111yescharacteristic
177Q8—1228no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—24no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—21no—
189C2×C4—612no—
190C2×C4—612no—
191C2×C4—614no—
192C2×C4—1222no—
193C2×C4—1222no—
194C2×C4—1222no—
195C2×C4—1221no—
196C2×C4—1221no—
197C2×C4—1221no—
198C2×C4—1221no—
199C2×C4—1222no—
200C2×C4—1222no—
201C2×C4—1221no—
202C2×C4—1222no—
203C2×C4—1221no—
204C2×C4—1222no—
205C2×C4D4×D6112yes—
206C22C2×D4×D6111yescharacteristic
207C22#41×D6112yes—
208C22#1451982412yes—
209C22#1451982411yescharacteristic
210C22#1451982511yescharacteristic
211C4—22no—
212C4—41no—
213C4—42no—
214C4—41no—
215C4—42no—
216C4—1224no—
217C4—1222no—
218C4—1222no—
219C4—2441no—
220C4—2441no—
221C4—2442no—
222C2#1684027011yescharacteristic
223C2#1684033211yescharacteristic
224C2#1684033511yescharacteristic
225C2#1684036912yes—
226C2#1684037112yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#400C2
hypercenter#400D61
hypocenterC61#2634
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
125. C61#2634semidirect