Finite Group Databasebeta

← #21451486

Subgroups — #21451486

Order 7808.

428 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 145 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#16839685C212yesmaximal
2#16839685C212yesmaximal
3#16839660C212yesmaximal, complemented
4#16839659C212yesmaximal, complemented
5#16839649C212yesmaximal, complemented
6#16839646C212yesmaximal, complemented
7#16839625C211yesmaximal, characteristic
8C4×C22⋊Dic61C211yesmaximal, characteristic
9C4×C22⋊C4×C61C211yesmaximal, characteristic
10C2×C4⋊Dic61C2212yes—
11C2×C4⋊Dic61C2212yes—
12C2×#11758196C2212yes—
13C2×#11758196C2212yes—
14C2×#11758196C2212yes—
15C2×#11758196C2212yes—
16C2×C22⋊Dic61C2212yes—
17C2×C22⋊Dic61C2211yescharacteristic
18C2×C22⋊Dic61C2211yescharacteristic
19C2×C4×Dic61C2211yescharacteristic
20C2×C4×Dic61C2211yescharacteristic
21#14519684C2212yes—
22#14519684C2212yes—
23#14519684C2212yes—
24#14519684C2212yes—
25#14519684C2212yes—
26C23×C4×C61C2211yescharacteristic
27C2×C22⋊C4×C61C2212yes—
28C2×C42×C61C2211yescharacteristic
29C2×C42×C61C2211yescharacteristic
30#95×C61C2212yes—
31C24×C61C2311yescharacteristic
32C22×C4×C61—41no—
33C22×C4×C61—41no—
34C22×C4×C61Q814yes—
35C22×C4×C61C2312yes—
36C22×C4×C61C2311yescharacteristic
37C22×C4×C61C2311yescharacteristic
38C22×C4×C61C2312yes—
39C22×Dic61C2312yes—
40C22×Dic61C2312yes—
41C22×Dic61C2312yes—
42C22×Dic61C2312yes—
43C22⋊C4×C61—24no—
44C42×C61—41no—
45C42×C61—41no—
46C22⋊Dic61—24no—
47C22⋊Dic61—41no—
48C22⋊Dic61—41no—
49C4⋊Dic61—24no—
50C4⋊Dic61—42no—
51#11758196—24no—
52#11758196—24no—
53#11758196—24no—
54#11758196—42no—
55C4×Dic61—41no—
56C4×Dic61—41no—
57C23×C61—22no—
58C23×C61—22no—
59C23×C61—21no—
60C23×C61—21no—
61C23×C61C2×Q812yes—
62C23×C61C2411yescharacteristic
63C2×C4×C61—22no—
64C2×C4×C61—21no—
65C2×C4×C61—21no—
66C2×C4×C61—22no—
67C2×C4×C61—21no—
68C2×C4×C61—21no—
69C2×C4×C61—22no—
70C2×C4×C61—22no—
71C2×C4×C61—22no—
72C2×C4×C61—44no—
73C2×C4×C61C2×Q812yes—
74C2×C4×C61C2×Q812yes—
75C2×C4×C61#4114yes—
76C2×Dic61—22no—
77C2×Dic61—22no—
78C2×Dic61—22no—
79C2×Dic61—22no—
80C2×Dic61—22no—
81C2×Dic61—22no—
82C2×Dic61—22no—
83C2×Dic61—22no—
84C2×Dic61—22no—
85C2×Dic61—22no—
86C2×Dic61—22no—
87C2×Dic61#4114yes—
88C22×C61—22no—
89C22×C61—22no—
90C22×C61—22no—
91C22×C61—42no—
92C22×C61—42no—
93C22×C61C22×Q811yescharacteristic
94C22×C61C2×#4112yes—
95C22×C61C2×#4112yes—
96C22×C61H(5,𝔽2)11yescharacteristic
97C22×C61H(5,𝔽2)11yescharacteristic
98C4×C61—22no—
99C4×C61—22no—
100C4×C61—24no—
101C4×C61—42no—
102Dic61—24no—
103Dic61—42no—
104Dic61—42no—
105Dic61—42no—
106#2608—611nomaximal, Sylow
107C2×C61—42no—
108C2×C61#53311yescharacteristic
109C2×C61#53311yescharacteristic
110C2×C61#54311yescharacteristic
111C2×C61#55312yes—
112C2×C61#55312yes—
113#396—612no—
114#396—612no—
115#389—612no—
116#389—612no—
117#387—612no—
118#387—612no—
119#381—611no—
120C4×C22⋊C4—611no—
121C4×C22⋊C4D6111yescharacteristic
122C61#260811yescharacteristic, complemented, Sylow
123C23×C4C2×D6111yescharacteristic
124C2×C4⋊C4—612no—
125C2×C4⋊C4—612no—
126C2×C4⋊C4—612no—
127C2×C4⋊C4—612no—
128C2×C4⋊C4—612no—
129C2×C4⋊C4—612no—
130C2×C22⋊C4—612no—
131C2×C22⋊C4—611no—
132C2×C22⋊C4—611no—
133C2×C22⋊C4C2×D6112yes—
134C2×C42—611no—
135C2×C42—611no—
136C2×C42C2×D6111yescharacteristic
137C2×C42C2×D6111yescharacteristic
138#95—612no—
139#95—612no—
140#95—612no—
141#95—612no—
142#95—612no—
143#95C2×D6112yes—
144C24C22×D6111yescharacteristic
145C22×C4—41no—
146C22×C4—41no—
147C22×C4—612no—
148C22×C4—612no—
149C22×C4—612no—
150C22×C4—612no—
151C22×C4Dic12214yes—
152C22×C4C22×D6112yes—
153C22×C4C22×D6111yescharacteristic
154C22×C4C22×D6111yescharacteristic
155C22×C4C22×D6112yes—
156C4⋊C4—1224no—
157C4⋊C4—1224no—
158C4⋊C4—1224no—
159C4⋊C4—1224no—
160C4⋊C4—2442no—
161C4⋊C4—2442no—
162C22⋊C4—24no—
163C22⋊C4—1224no—
164C22⋊C4—2441no—
165C22⋊C4—2441no—
166C42—41no—
167C42—41no—
168C42—2441no—
169C42—2441no—
170C23—22no—
171C23—22no—
172C23—21no—
173C23—21no—
174C23C2×Dic12212yes—
175C23C23×D6111yescharacteristic
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—44no—
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—1222no—
198C2×C4C2×Dic12212yes—
199C2×C4C2×Dic12212yes—
200C2×C4#1175822214yes—
201C22—22no—
202C22—22no—
203C22—22no—
204C22—42no—
205C22—42no—
206C22C22×Dic12211yescharacteristic
207C22#41×D6112yes—
208C22C2×#1175822212yes—
209C22#1451982211yescharacteristic
210C22#1451982211yescharacteristic
211C4—24no—
212C4—22no—
213C4—22no—
214C4—42no—
215C4—1224no—
216C4—2442no—
217C4—2442no—
218C4—2442no—
219C2—42no—
220C2#1684031511yescharacteristic
221C2#1684031911yescharacteristic
222C2#1684038811yescharacteristic
223C2#1684046112yes—
224C2#1684046212yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC4×C22⋊C4×C61C2
hypercenterC4×C22⋊C4D61
hypocenterC61#2608
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #16839660C2semidirect
4. #16839659C2semidirect
5. #16839649C2semidirect
6. #16839646C2semidirect
122. C61#2608semidirect