Finite Group Databasebeta

← #21452849

Subgroups — #21452849

Order 7808.

456 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 157 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×#14519775C211yesmaximal, characteristic
2#16839695C212yesmaximal
3#16839682C212yesmaximal
4#16839681C212yesmaximal
5#16839669C211yesmaximal, characteristic
6#16839657C212yesmaximal
7#16839646C212yesmaximal
8#16839643C212yesmaximal
9C2×C4⋊Q8×C61C211yesmaximal, characteristic
10C22×Dic122C2211yescharacteristic
11#14519775—24no—
12C2×C4⋊Dic61C2211yescharacteristic
13C2×#11758196C2212yes—
14C2×#11758196C2212yes—
15C2×#11758196C2212yes—
16C2×#11758196C2212yes—
17C2×#11758196C2212yes—
18C2×C4×Dic61C2211yescharacteristic
19C2×C4×Dic61C2211yescharacteristic
20#14519684C2212yes—
21#14519684C2212yes—
22#14519684C2212yes—
23#14519684C2212yes—
24#14519684C2212yes—
25#14519684C2212yes—
26#14519684C2212yes—
27C22×Q8×C61C2211yescharacteristic
28C22×Q8×C61C2211yescharacteristic
29C4⋊Q8×C61—24no—
30C2×C4⋊C4×C61C2212yes—
31C2×C4⋊C4×C61C2212yes—
32C2×C42×C61C2211yescharacteristic
33C2×Q8×C61—22no—
34C2×Q8×C61—41no—
35C2×Q8×C61—41no—
36C2×Q8×C61—41no—
37C2×Q8×C61—41no—
38C2×Q8×C61D414yes—
39C22×C4×C61C2312yes—
40C22×C4×C61C2311yescharacteristic
41C22×C4×C61C2311yescharacteristic
42C22×C4×C61C2311yescharacteristic
43C22×C4×C61C2312yes—
44C22×Dic61C2312yes—
45C22×Dic61C2312yes—
46C22×Dic61C2312yes—
47C22×Dic61C2312yes—
48C2×Dic122—22no—
49C2×Dic122—41no—
50C2×Dic122—41no—
51C4⋊C4×C61—24no—
52C4⋊C4×C61—24no—
53C42×C61—22no—
54C4⋊Dic61—41no—
55#11758196—24no—
56#11758196—24no—
57#11758196—42no—
58#11758196—42no—
59#11758196Q818yescomplemented
60C4×Dic61—22no—
61C4×Dic61—41no—
62C23×C61C2411yescharacteristic
63Q8×C61—44no—
64Q8×C61—44no—
65C2×C4×C61—22no—
66C2×C4×C61—21no—
67C2×C4×C61—21no—
68C2×C4×C61—21no—
69C2×C4×C61—21no—
70C2×C4×C61—21no—
71C2×C4×C61—21no—
72C2×C4×C61—22no—
73C2×C4×C61—22no—
74C2×C4×C61—22no—
75C2×C4×C61—22no—
76C2×C4×C61C2×D412yes—
77C2×C4×C61C2×D412yes—
78C2×C4×C61C2×D412yes—
79C2×C4×C61C2×Q814yes—
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×Dic61—24no—
89C2×Dic61C2×Q814yes—
90C2×Dic61C2×Q814yes—
91Dic122—44no—
92C22×C61C22×D411yescharacteristic
93C22×C61C22×Q812yes—
94C22×C61H(5,𝔽2)11yescharacteristic
95C22×C61H(5,𝔽2)11yescharacteristic
96C22×C612−1+412yes—
97C4×C61—22no—
98C4×C61—22no—
99C4×C61—22no—
100C4×C61—24no—
101C4×C61—42no—
102Dic61—24no—
103Dic61—24no—
104Dic61—42no—
105Dic61—42no—
106#2734—611nomaximal, Sylow
107C2×C61#53411yescharacteristic
108C2×C61#54412yes—
109C2×C61D4×Q812yes—
110C2×C61Q8211yescharacteristic
111C2×C61#56311yescharacteristic
112C2×C4⋊Q8—611no—
113C2×C4⋊Q8D6111yescharacteristic
114#398—612no—
115#395—612no—
116#395—612no—
117#391—611no—
118#389—612no—
119#387—612no—
120#387—612no—
121C61#273411yescharacteristic, complemented, Sylow
122C22×Q8—611no—
123C22×Q8C2×D6111yescharacteristic
124C22×Q8C2×D6111yescharacteristic
125C4⋊Q8—24no—
126C4⋊Q8—1224no—
127C2×C4⋊C4—612no—
128C2×C4⋊C4—612no—
129C2×C4⋊C4—612no—
130C2×C4⋊C4—612no—
131C2×C4⋊C4—611no—
132C2×C4⋊C4—612no—
133C2×C4⋊C4C2×D6112yes—
134C2×C4⋊C4C2×D6112yes—
135C2×C42—611no—
136C2×C42—611no—
137C2×C42C2×D6111yescharacteristic
138#95—612no—
139#95—612no—
140#95—612no—
141#95—612no—
142#95—612no—
143#95—612no—
144#95—612no—
145C2×Q8—22no—
146C2×Q8—41no—
147C2×Q8—41no—
148C2×Q8—41no—
149C2×Q8—41no—
150C2×Q8—1222no—
151C2×Q8—2441no—
152C2×Q8—2441no—
153C2×Q8C22⋊D6114yes—
154C22×C4—612no—
155C22×C4—612no—
156C22×C4—612no—
157C22×C4—612no—
158C22×C4C22×D6112yes—
159C22×C4C22×D6112yes—
160C22×C4C22×D6111yescharacteristic
161C22×C4C22×D6111yescharacteristic
162C22×C4C22×D6111yescharacteristic
163C4⋊C4—24no—
164C4⋊C4—24no—
165C4⋊C4—618no—
166C4⋊C4—1224no—
167C4⋊C4—1224no—
168C4⋊C4—2442no—
169C4⋊C4—2442no—
170C4⋊C4—2441no—
171C42—22no—
172C42—1222no—
173C42—2441no—
174C23C23×D6111yescharacteristic
175Q8—44no—
176Q8—44no—
177Q8—2444no—
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—614no—
190C2×C4—614no—
191C2×C4—1222no—
192C2×C4—1222no—
193C2×C4—1222no—
194C2×C4—1222no—
195C2×C4—1222no—
196C2×C4—1222no—
197C2×C4—1222no—
198C2×C4—1222no—
199C2×C4—1224no—
200C2×C4Q8×D6114yes—
201C2×C4C2×C22⋊D6112yes—
202C2×C4C2×C22⋊D6112yes—
203C2×C4C2×C22⋊D6112yes—
204C22C22×C22⋊D6111yescharacteristic
205C22C2×Q8×D6112yes—
206C22#1451982211yescharacteristic
207C22#1451982211yescharacteristic
208C22#1451982512yes—
209C4—22no—
210C4—22no—
211C4—22no—
212C4—24no—
213C4—42no—
214C4—1224no—
215C4—1224no—
216C4—2442no—
217C4—2442no—
218C2#1684032111yescharacteristic
219C2#1684038912yes—
220C2Q8×C22⋊D6112yes—
221C2#1684049211yescharacteristic
222C2#1684051111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×C4⋊Q8×C61C2
hypercenterC2×C4⋊Q8D61
hypocenterC61#2734
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
59. #11758196Q8semidirect
121. C61#2734semidirect