Finite Group Databasebeta

← #21451479

Subgroups — #21451479

Order 7808.

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

normal subgroups only

This group has 444 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
1#16839698C212yesmaximal
2#16839674C211yesmaximal, characteristic
3#16839669C212yesmaximal, complemented
4#16839666C212yesmaximal, complemented
5#16839647C212yesmaximal, complemented
6#16839644C212yesmaximal, complemented
7#16839623C211yesmaximal, characteristic
8C22⋊C4×Dic61C212yesmaximal
9C61×#393C211yesmaximal, characteristic
10C22×Dic122C2211yescharacteristic
11C23×Dic61C2211yescharacteristic
12C2×C4⋊Dic61C2212yes—
13C2×#11758196C2212yes—
14C2×#11758196C2212yes—
15C2×C22⋊Dic61C2212yes—
16C2×C22⋊Dic61C2211yescharacteristic
17C2×C4×Dic61C2212yes—
18C2×C4×Dic61C2212yes—
19#14519684C2212yes—
20#14519684C2212yes—
21#14519684C2212yes—
22#14519684C2212yes—
23#14519684C2212yes—
24#14519684C2212yes—
25#14519684C2211yescharacteristic
26C22×Q8×C61C2211yescharacteristic
27C2×C22⋊C4×C61C2212yes—
28C2×C22⋊C4×C61C2211yescharacteristic
29#95×C61C2211yescharacteristic
30#95×C61C2212yes—
31C24×C61C2311yescharacteristic
32C2×Q8×C61—24no—
33C2×Q8×C61—41no—
34C22×C4×C61C2311yescharacteristic
35C22×C4×C61C2312yes—
36C22×C4×C61C2311yescharacteristic
37C22×C4×C61C2312yes—
38C22×Dic61—41no—
39C22×Dic61—41no—
40C22×Dic61Q814yescomplemented
41C22×Dic61C2312yes—
42C22×Dic61C2312yes—
43C22×Dic61C2312yes—
44C22×Dic61C2312yes—
45C2×Dic122—24no—
46C2×Dic122—41no—
47C22⋊C4×C61—24no—
48C22⋊C4×C61—41no—
49C22⋊Dic61—24no—
50C22⋊Dic61—41no—
51C4⋊Dic61—24no—
52#11758196—24no—
53#11758196—42no—
54C4×Dic61—42no—
55C4×Dic61—42no—
56C23×C61—22no—
57C23×C61—22no—
58C23×C61—21no—
59C23×C61—21no—
60C23×C61C2×Q812yes—
61C23×C61C2411yescharacteristic
62Q8×C61—44no—
63C2×C4×C61—22no—
64C2×C4×C61—22no—
65C2×C4×C61—22no—
66C2×C4×C61—22no—
67C2×C4×C61—22no—
68C2×C4×C61—22no—
69C2×C4×C61—22no—
70C2×C4×C61—21no—
71C2×C4×C61—21no—
72C2×C4×C61#4114yes—
73C2×Dic61—22no—
74C2×Dic61—22no—
75C2×Dic61—22no—
76C2×Dic61—22no—
77C2×Dic61—22no—
78C2×Dic61—22no—
79C2×Dic61—22no—
80C2×Dic61—22no—
81C2×Dic61—22no—
82C2×Dic61—22no—
83C2×Dic61—44no—
84C2×Dic61C2×Q814yes—
85C2×Dic61#4114yes—
86Dic122—44no—
87C22×C61—24no—
88C22×C61—22no—
89C22×C61—41no—
90C22×C61—41no—
91C22×C61—42no—
92C22×C61C22×Q811yescharacteristic
93C22×C61C2×#4112yes—
94C22×C61C2×#4112yes—
95C22×C61H(5,𝔽2)11yescharacteristic
96C22×C61H(5,𝔽2)11yescharacteristic
97C4×C61—24no—
98C4×C61—41no—
99C4×C61—41no—
100C4×C61—42no—
101Dic61—24no—
102Dic61—24no—
103Dic61—42no—
104Dic61—42no—
105#2607—611nomaximal, Sylow
106C2×C61—42no—
107C2×C61#53312yes—
108C2×C61#54311yescharacteristic
109C2×C61#55111yescharacteristic
110C2×C61#55111yescharacteristic
111C2×C61#55912yes—
112#399—612no—
113#393—611no—
114#393D6111yescharacteristic
115#391—612no—
116#391—612no—
117#387—612no—
118#387—612no—
119#381—611no—
120C4×C22⋊C4—612no—
121C61#260711yescharacteristic, complemented, Sylow
122C22×Q8—611no—
123C22×Q8C2×D6111yescharacteristic
124C23×C4—611no—
125C2×C4⋊C4—612no—
126C2×C4⋊C4—612no—
127C2×C4⋊C4—612no—
128C2×C22⋊C4—612no—
129C2×C22⋊C4—611no—
130C2×C22⋊C4C2×D6112yes—
131C2×C22⋊C4C2×D6111yescharacteristic
132C2×C42—612no—
133C2×C42—612no—
134#95—612no—
135#95—612no—
136#95—612no—
137#95—612no—
138#95—611no—
139#95—612no—
140#95—612no—
141#95C2×D6111yescharacteristic
142#95C2×D6112yes—
143C24C22×D6111yescharacteristic
144C2×Q8—24no—
145C2×Q8—41no—
146C2×Q8—1224no—
147C2×Q8—2441no—
148C22×C4—612no—
149C22×C4—612no—
150C22×C4—614no—
151C22×C4—612no—
152C22×C4—612no—
153C22×C4—2441no—
154C22×C4—2441no—
155C22×C4C22×D6111yescharacteristic
156C22×C4C22×D6111yescharacteristic
157C22×C4C22×D6112yes—
158C22×C4C22×D6112yes—
159C4⋊C4—1224no—
160C4⋊C4—1224no—
161C4⋊C4—2442no—
162C22⋊C4—24no—
163C22⋊C4—41no—
164C22⋊C4—1224no—
165C22⋊C4—2441no—
166C42—2442no—
167C42—2442no—
168C23—22no—
169C23—22no—
170C23—21no—
171C23—21no—
172C23Q8×D6112yes—
173C23C23×D6111yescharacteristic
174Q8—44no—
175Q8—2444no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—22no—
185C2×C4—614no—
186C2×C4—614no—
187C2×C4—1222no—
188C2×C4—1222no—
189C2×C4—1222no—
190C2×C4—1222no—
191C2×C4—1222no—
192C2×C4—1222no—
193C2×C4—1222no—
194C2×C4—1222no—
195C2×C4—1222no—
196C2×C4—1222no—
197C2×C4—2444no—
198C2×C4#1175822414yes—
199C22—24no—
200C22—22no—
201C22—42no—
202C22—41no—
203C22—41no—
204C22C2×Q8×D6111yescharacteristic
205C22#41×D6112yes—
206C22C2×#1175822412yes—
207C22#1451982211yescharacteristic
208C22#1451982311yescharacteristic
209C4—24no—
210C4—42no—
211C4—41no—
212C4—41no—
213C4—1224no—
214C4—1224no—
215C4—2442no—
216C4—2442no—
217C2—42no—
218C2#1684031412yes—
219C2#1684038711yescharacteristic
220C2#1684044211yescharacteristic
221C2#1684044311yescharacteristic
222C2#1684049412yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#393C2
hypercenter#393D61
hypocenterC61#2607
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
3. #16839669C2semidirect
4. #16839666C2semidirect
5. #16839647C2semidirect
6. #16839644C2semidirect
40. C22×Dic61Q8semidirect
121. C61#2607semidirect