Finite Group Databasebeta

← #21451497

Subgroups — #21451497

Order 7808.

540 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 137 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×#14519735C212yesmaximal, complemented
2#16839684C212yesmaximal, complemented
3#16839679C211yesmaximal, characteristic
4#16839652C212yesmaximal, complemented
5#16839649C212yesmaximal, complemented
6#16839640C212yesmaximal
7#16839636C212yesmaximal, complemented
8#16839627C211yesmaximal, characteristic, complemented
9C61×#398C211yesmaximal, characteristic, complemented
10C22×D244C2211yescharacteristic
11C22×C4×D61C2212yes—
12#14519735—28no—
13C2×C4⋊Dic61C2212yes—
14C2×C4⋊Dic61C2211yescharacteristic
15C2×#11758196C2212yes—
16C2×#11758198C2212yes—
17C2×#11758198C2212yes—
18C2×#11758198C2212yes—
19C2×#11758198C2212yes—
20C2×#11758198C2212yes—
21C2×C4×Dic61C2212yes—
22C2×C4×Dic61C2211yescharacteristic
23#14519684C2212yes—
24#14519684C2212yes—
25#14519684C2212yes—
26#14519684C2211yescharacteristic
27C2×C4⋊C4×C61C2212yes—
28C2×C4⋊C4×C61C2211yescharacteristic
29C2×C4⋊C4×C61C2211yescharacteristic
30#95×C61C2211yescharacteristic
31#95×C61C2212yes—
32C23×D61C2312yes—
33C22×C4×C61C2311yescharacteristic
34C22×C4×C61C2311yescharacteristic
35C22×C4×C61C2312yes—
36C22×C4×C61C2311yescharacteristic
37C22×C4×C61C2312yes—
38C22×Dic61C2312yes—
39C22×Dic61C2312yes—
40C22×Dic61C2312yes—
41C2×D244—24no—
42C2×D244—41no—
43C2×C4×D61—24no—
44C2×C4×D61—24no—
45C2×C4×D61—24no—
46C4⋊C4×C61—24no—
47C4⋊C4×C61—41no—
48C4⋊C4×C61—41no—
49#11758198—24no—
50#11758198—24no—
51#11758198—24no—
52#11758198—24no—
53#11758198—42no—
54C4⋊Dic61—24no—
55C4⋊Dic61—41no—
56#11758196—24no—
57C4×Dic61—24no—
58C4×Dic61D414yescomplemented
59C23×C61C2411yescharacteristic
60C22×D61—22no—
61C22×D61—22no—
62C22×D61—22no—
63C22×D61—22no—
64C22×D61—22no—
65C22×D61—22no—
66C22×D61#4114yes—
67C2×C4×C61—22no—
68C2×C4×C61—22no—
69C2×C4×C61—21no—
70C2×C4×C61—21no—
71C2×C4×C61—22no—
72C2×C4×C61—22no—
73C2×C4×C61—22no—
74C2×C4×C61—22no—
75C2×C4×C61—21no—
76C2×C4×C61—21no—
77C2×C4×C61—22no—
78C2×C4×C61C2×D412yes—
79C2×C4×C61#4114yes—
80C2×Dic61—22no—
81C2×Dic61—22no—
82C2×Dic61—22no—
83C2×Dic61—22no—
84C2×Dic61—22no—
85C2×Dic61—22no—
86C2×Dic61—22no—
87C2×Dic61—22no—
88C2×Dic61C2×D414yes—
89D244—44no—
90C4×D61—216no—
91C22×C61C22×D411yescharacteristic
92C22×C61C2×#4112yes—
93C22×C61C2×#4112yes—
94C22×C61H(5,𝔽2)11yescharacteristic
95C22×C612−1+411yescharacteristic
96C2×D61—24no—
97C2×D61—24no—
98C2×D61—24no—
99C2×D61—42no—
100C2×D61—42no—
101C2×D61—42no—
102C2×D61—42no—
103C4×C61—24no—
104C4×C61—22no—
105C4×C61—42no—
106C4×C61—41no—
107C4×C61—41no—
108Dic61—24no—
109Dic61—42no—
110Dic61—42no—
111#2609—611nomaximal, Sylow
112C2×C61#52512yes—
113C2×C61#53711yescharacteristic
114C2×C61#55111yescharacteristic
115C2×C61#55212yes—
116C2×C61#55511yescharacteristic
117D61—44no—
118C2×#117—612no—
119#398D6111yescharacteristic, complemented
120#396—612no—
121#394—611no—
122#388—612no—
123#387—612no—
124#386—612no—
125#385—612no—
126#382—611no—
127C61#260911yescharacteristic, complemented, Sylow
128C22×D4—611no—
129C23×C4—612no—
130#117—1228no—
131C2×C4⋊C4—612no—
132C2×C4⋊C4—612no—
133C2×C4⋊C4—611no—
134C2×C4⋊C4C2×D6112yes—
135C2×C4⋊C4C2×D6111yescharacteristic
136C2×C4⋊C4C2×D6111yescharacteristic
137C2×C22⋊C4—612no—
138C2×C22⋊C4—612no—
139C2×C22⋊C4—612no—
140C2×C22⋊C4—612no—
141C2×C22⋊C4—612no—
142C2×C42—611no—
143C2×C42—612no—
144#95—612no—
145#95—612no—
146#95—611no—
147#95—612no—
148#95C2×D6111yescharacteristic
149#95C2×D6112yes—
150C24—612no—
151C2×D4—1224no—
152C2×D4—2441no—
153C22×C4—612no—
154C22×C4—612no—
155C22×C4—612no—
156C22×C4—1224no—
157C22×C4—1224no—
158C22×C4—1224no—
159C22×C4C22×D6111yescharacteristic
160C22×C4C22×D6111yescharacteristic
161C22×C4C22×D6112yes—
162C22×C4C22×D6111yescharacteristic
163C22×C4C22×D6112yes—
164C4⋊C4—24no—
165C4⋊C4—41no—
166C4⋊C4—41no—
167C4⋊C4—1224no—
168C4⋊C4—1224no—
169C4⋊C4—2441no—
170C22⋊C4—1224no—
171C22⋊C4—1224no—
172C22⋊C4—1224no—
173C22⋊C4—1224no—
174C22⋊C4—2442no—
175C42—614no—
176C42—1224no—
177C23—614no—
178C23—1222no—
179C23—1222no—
180C23—1222no—
181C23—1222no—
182C23—1222no—
183C23—1222no—
184C23C23×D6111yescharacteristic
185D4—2444no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—22no—
197C2×C4—614no—
198C2×C4—12216no—
199C2×C4—1222no—
200C2×C4—1222no—
201C2×C4—1222no—
202C2×C4—1222no—
203C2×C4—1222no—
204C2×C4—1222no—
205C2×C4—1222no—
206C2×C4—1222no—
207C2×C4D4×D6112yes—
208C2×C4#1175822614yes—
209C22—1224no—
210C22—1224no—
211C22—1224no—
212C22—2442no—
213C22—2442no—
214C22—2442no—
215C22—2442no—
216C22C2×D4×D6111yescharacteristic
217C22#41×D6112yes—
218C22C2×#1175822612yes—
219C22#1451982211yescharacteristic
220C22#1451982411yescharacteristic
221C4—24no—
222C4—22no—
223C4—42no—
224C4—41no—
225C4—41no—
226C4—1224no—
227C4—2442no—
228C4—2442no—
229C2—2444no—
230C2#1684027512yes—
231C2#1684033911yescharacteristic
232C2#1684044011yescharacteristic
233C2#1684045012yes—
234C2#1684047811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#398C2
hypercenter#398D61
hypocenterC61#2609
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#14519735C2semidirect
2. #16839684C2semidirect
4. #16839652C2semidirect
5. #16839649C2semidirect
7. #16839636C2semidirect
8. #16839627C2semidirect
9. C61×#398C2semidirect
58. C4×Dic61D4semidirect
119. #398D61semidirect
127. C61#2609semidirect