Finite Group Databasebeta

← #21451942

Subgroups — #21451942

Order 7808.

448 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 153 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×#14519776C211yesmaximal, characteristic
2C2×#14519767C211yesmaximal, characteristic
3#16839694C211yesmaximal, characteristic
4#16839693C211yesmaximal, characteristic
5#16839692C211yesmaximal, characteristic
6#16839683C212yesmaximal
7#16839682C212yesmaximal
8#16839631C212yesmaximal
9#16839626C212yesmaximal
10#16839607C211yesmaximal, characteristic
11C61×#398C211yesmaximal, characteristic
12C22×Dic122C2212yes—
13#14519776—24no—
14#14519767—24no—
15C2×C4⋊Dic61C2211yescharacteristic
16C2×C4⋊Dic61C2211yescharacteristic
17C2×C4⋊Dic61C2212yes—
18C2×#11758196C2211yescharacteristic
19C2×#11758196C2211yescharacteristic
20C2×#11758196C2211yescharacteristic
21C2×#11758196C2211yescharacteristic
22C2×#11758196C2212yes—
23C2×#11758196C2212yes—
24C2×#11758196C2212yes—
25C2×C4×Dic61C2211yescharacteristic
26C2×C4×Dic61C2212yes—
27#14519684C2212yes—
28#14519684C2212yes—
29#14519684C2212yes—
30#14519684C2212yes—
31#14519684C2211yescharacteristic
32C2×C4⋊C4×C61C2211yescharacteristic
33C2×C4⋊C4×C61C2211yescharacteristic
34C2×C4⋊C4×C61C2212yes—
35#95×C61C2212yes—
36#95×C61C2211yescharacteristic
37C22×C4×C61C2312yes—
38C22×C4×C61C2311yescharacteristic
39C22×C4×C61C2311yescharacteristic
40C22×C4×C61C2311yescharacteristic
41C22×C4×C61C2312yes—
42C22×Dic61C2312yes—
43C22×Dic61C2311yescharacteristic
44C22×Dic61C2311yescharacteristic
45C22×Dic61C2311yescharacteristic
46C22×Dic61C2312yes—
47C22×Dic61C2311yescharacteristic
48C2×Dic122—24no—
49C2×Dic122—42no—
50C2×Dic122—42no—
51C4⋊C4×C61—22no—
52C4⋊C4×C61—22no—
53C4⋊C4×C61—42no—
54C4⋊Dic61—22no—
55C4⋊Dic61—22no—
56C4⋊Dic61—42no—
57#11758196—22no—
58#11758196—22no—
59#11758196—22no—
60#11758196—22no—
61#11758196—24no—
62#11758196—42no—
63#11758196—42no—
64C4×Dic61D414yes—
65C4×Dic61Q818yescomplemented
66C23×C61C2411yescharacteristic
67C2×C4×C61—22no—
68C2×C4×C61—22no—
69C2×C4×C61—22no—
70C2×C4×C61—21no—
71C2×C4×C61—21no—
72C2×C4×C61—22no—
73C2×C4×C61—21no—
74C2×C4×C61—22no—
75C2×C4×C61—21no—
76C2×C4×C61—22no—
77C2×C4×C61—22no—
78C2×C4×C61C2×D412yes—
79C2×C4×C61C2×Q814yes—
80C2×Dic61—22no—
81C2×Dic61—21no—
82C2×Dic61—21no—
83C2×Dic61—22no—
84C2×Dic61—21no—
85C2×Dic61—21no—
86C2×Dic61—22no—
87C2×Dic61—21no—
88C2×Dic61—22no—
89C2×Dic61—21no—
90C2×Dic61—22no—
91C2×Dic61—22no—
92C2×Dic61C2×D412yes—
93C2×Dic61C2×D412yes—
94C2×Dic61C2×Q814yes—
95C2×Dic61C2×Q814yes—
96Dic122—48no—
97C22×C61C22×D411yescharacteristic
98C22×C61C22×Q812yes—
99C22×C61H(5,𝔽2)11yescharacteristic
100C22×C61H(5,𝔽2)11yescharacteristic
101C22×C612−1+412yes—
102C4×C61—22no—
103C4×C61—24no—
104C4×C61—42no—
105C4×C61—41no—
106C4×C61—41no—
107Dic61—22no—
108Dic61—24no—
109Dic61—42no—
110Dic61—41no—
111Dic61—41no—
112Dic61C4⋊Q814yes—
113#2660—611nomaximal, Sylow
114C2×C61C2×C4⋊Q811yescharacteristic
115C2×C61#53511yescharacteristic
116C2×C61#53611yescharacteristic
117C2×C61#54412yes—
118C2×C61#54412yes—
119C2×C4⋊Q8—611no—
120C2×#125—611no—
121#398—611no—
122#398—611no—
123#398—611no—
124#398D6111yescharacteristic
125#395—612no—
126#395—612no—
127#384—612no—
128#382—612no—
129#376—611no—
130C61#266011yescharacteristic, complemented, Sylow
131C22×Q8—612no—
132C4⋊Q8—1224no—
133#125—1224no—
134C2×C4⋊C4—611no—
135C2×C4⋊C4—611no—
136C2×C4⋊C4—611no—
137C2×C4⋊C4—611no—
138C2×C4⋊C4—611no—
139C2×C4⋊C4—612no—
140C2×C4⋊C4—611no—
141C2×C4⋊C4—612no—
142C2×C4⋊C4—612no—
143C2×C4⋊C4—612no—
144C2×C4⋊C4C2×D6111yescharacteristic
145C2×C4⋊C4C2×D6111yescharacteristic
146C2×C4⋊C4C2×D6112yes—
147C2×C42—611no—
148C2×C42—612no—
149#95—612no—
150#95—611no—
151#95—612no—
152#95—612no—
153#95—612no—
154#95C2×D6111yescharacteristic
155#95C2×D6112yes—
156C2×Q8—1224no—
157C2×Q8—2442no—
158C2×Q8—2442no—
159C22×C4—611no—
160C22×C4—612no—
161C22×C4—611no—
162C22×C4—611no—
163C22×C4—612no—
164C22×C4—611no—
165C22×C4C22×D6111yescharacteristic
166C22×C4C22×D6112yes—
167C22×C4C22×D6111yescharacteristic
168C22×C4C22×D6111yescharacteristic
169C22×C4C22×D6112yes—
170C4⋊C4—22no—
171C4⋊C4—22no—
172C4⋊C4—42no—
173C4⋊C4—1222no—
174C4⋊C4—1222no—
175C4⋊C4—1222no—
176C4⋊C4—1224no—
177C4⋊C4—1222no—
178C4⋊C4—1222no—
179C4⋊C4—1222no—
180C4⋊C4—2442no—
181C4⋊C4—2442no—
182C4⋊C4—2442no—
183C42—614no—
184C42—618no—
185C23C23×D6111yescharacteristic
186Q8—2448no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—612no—
199C2×C4—614no—
200C2×C4—612no—
201C2×C4—614no—
202C2×C4—1221no—
203C2×C4—1222no—
204C2×C4—1221no—
205C2×C4—1222no—
206C2×C4—1221no—
207C2×C4—1221no—
208C2×C4—1222no—
209C2×C4—1221no—
210C2×C4—1222no—
211C2×C4—1221no—
212C2×C4—1222no—
213C2×C4—1222no—
214C2×C4D4×D6112yes—
215C2×C4Q8×D6114yes—
216C22C2×D4×D6111yescharacteristic
217C22C2×Q8×D6112yes—
218C22#1451982211yescharacteristic
219C22#1451982311yescharacteristic
220C22#1451982412yes—
221C4—22no—
222C4—24no—
223C4—41no—
224C4—42no—
225C4—41no—
226C4—614no—
227C4—1222no—
228C4—1224no—
229C4—2441no—
230C4—2442no—
231C4—2441no—
232C2C4⋊Q8×D6111yescharacteristic
233C2#1684032811yescharacteristic
234C2#1684033411yescharacteristic
235C2#1684039112yes—
236C2#1684039212yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#398C2
hypercenter#398D61
hypocenterC61#2660
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
65. C4×Dic61Q8semidirect
130. C61#2660semidirect