Finite Group Databasebeta

← #21452850

Subgroups — #21452850

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×#14519776C212yesmaximal
2#16839695C212yesmaximal
3#16839683C212yesmaximal
4#16839682C212yesmaximal
5#16839668C211yesmaximal, characteristic
6#16839660C211yesmaximal, characteristic
7#16839648C212yesmaximal
8#16839645C212yesmaximal
9C61×#389C211yesmaximal, characteristic
10C22×Dic122C2212yes—
11C22×Dic122C2211yescharacteristic
12#14519776—28no—
13C2×C4⋊Dic61C2212yes—
14C2×C4⋊Dic61C2211yescharacteristic
15C2×C4⋊Dic61C2211yescharacteristic
16C2×C4⋊Dic61C2211yescharacteristic
17C2×#11758196C2212yes—
18C2×#11758196C2212yes—
19C2×#11758196C2212yes—
20C2×C4×Dic61C2212yes—
21#14519684C2212yes—
22#14519684C2212yes—
23#14519684C2212yes—
24#14519684C2212yes—
25#14519684C2212yes—
26#14519684C2212yes—
27C2×C4⋊C4×C61C2212yes—
28C2×C4⋊C4×C61C2211yescharacteristic
29C2×C4⋊C4×C61C2211yescharacteristic
30C2×C42×C61C2211yescharacteristic
31#95×C61C2212yes—
32C22×C4×C61C2312yes—
33C22×C4×C61C2311yescharacteristic
34C22×C4×C61C2311yescharacteristic
35C22×C4×C61C2312yes—
36C22×C4×C61C2311yescharacteristic
37C22×Dic61C2312yes—
38C22×Dic61C2312yes—
39C22×Dic61C2312yes—
40C22×Dic61C2312yes—
41C2×Dic122—24no—
42C2×Dic122—41no—
43C2×Dic122—41no—
44C2×Dic122—42no—
45C2×Dic122—42no—
46C2×Dic122D414yes—
47C4⋊C4×C61—24no—
48C4⋊C4×C61—41no—
49C4⋊C4×C61Q814yescomplemented
50C42×C61—41no—
51C4⋊Dic61—24no—
52C4⋊Dic61—41no—
53C4⋊Dic61—41no—
54C4⋊Dic61Q814yescomplemented
55#11758196—24no—
56#11758196—24no—
57#11758196—42no—
58C4×Dic61—24no—
59C23×C61C2411yescharacteristic
60C2×C4×C61—22no—
61C2×C4×C61—21no—
62C2×C4×C61—21no—
63C2×C4×C61—21no—
64C2×C4×C61—21no—
65C2×C4×C61—21no—
66C2×C4×C61—21no—
67C2×C4×C61—22no—
68C2×C4×C61—22no—
69C2×C4×C61—22no—
70C2×C4×C61—22no—
71C2×C4×C61C2×D412yes—
72C2×C4×C61C2×Q812yes—
73C2×C4×C61C2×Q814yes—
74C2×C4×C61C2×Q812yes—
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—22no—
84C2×Dic61—22no—
85C2×Dic61C2×D414yes—
86C2×Dic61C2×Q814yes—
87Dic122—44no—
88Dic122—48no—
89C22×C61C22×D411yescharacteristic
90C22×C61C22×Q811yescharacteristic
91C22×C61C22×Q811yescharacteristic
92C22×C61H(5,𝔽2)11yescharacteristic
93C22×C61H(5,𝔽2)11yescharacteristic
94C22×C612−1+411yescharacteristic
95C22×C612−1+411yescharacteristic
96C4×C61—22no—
97C4×C61—22no—
98C4×C61—22no—
99C4×C61—24no—
100C4×C61—42no—
101Dic61—24no—
102Dic61—24no—
103Dic61—42no—
104Dic61—42no—
105#2734—611nomaximal, Sylow
106C2×C61#53411yescharacteristic
107C2×C61#54411yescharacteristic
108C2×C61#54411yescharacteristic
109C2×C61D4×Q811yescharacteristic
110C2×C61D4×Q811yescharacteristic
111C2×C61Q8211yescharacteristic
112C2×C61#56311yescharacteristic
113C2×C4⋊Q8—612no—
114#398—612no—
115#395—612no—
116#395—612no—
117#391—611no—
118#389—611no—
119#389D6111yescharacteristic
120#387—612no—
121#387—612no—
122C61#273411yescharacteristic, complemented, Sylow
123C22×Q8—611no—
124C22×Q8—612no—
125C4⋊Q8—1228no—
126C2×C4⋊C4—611no—
127C2×C4⋊C4—612no—
128C2×C4⋊C4—612no—
129C2×C4⋊C4—612no—
130C2×C4⋊C4—611no—
131C2×C4⋊C4—611no—
132C2×C4⋊C4—612no—
133C2×C4⋊C4C2×D6112yes—
134C2×C4⋊C4C2×D6111yescharacteristic
135C2×C4⋊C4C2×D6111yescharacteristic
136C2×C42—612no—
137C2×C42C2×D6111yescharacteristic
138#95—612no—
139#95—612no—
140#95—612no—
141#95—612no—
142#95—612no—
143#95—612no—
144#95C2×D6112yes—
145C2×Q8—614no—
146C2×Q8—1224no—
147C2×Q8—2441no—
148C2×Q8—2441no—
149C2×Q8—2442no—
150C2×Q8—2442no—
151C22×C4—612no—
152C22×C4—612no—
153C22×C4—612no—
154C22×C4—612no—
155C22×C4C22×D6112yes—
156C22×C4C22×D6111yescharacteristic
157C22×C4C22×D6112yes—
158C22×C4C22×D6111yescharacteristic
159C22×C4C22×D6111yescharacteristic
160C4⋊C4—24no—
161C4⋊C4—41no—
162C4⋊C4—614no—
163C4⋊C4—1224no—
164C4⋊C4—1224no—
165C4⋊C4—1224no—
166C4⋊C4—2442no—
167C4⋊C4—2441no—
168C4⋊C4—2441no—
169C4⋊C4Dic12214yescomplemented
170C42—41no—
171C42—1224no—
172C23C23×D6111yescharacteristic
173Q8—2444no—
174Q8—2448no—
175C2×C4—22no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—614no—
187C2×C4—614no—
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×Dic12214yes—
200C2×C4D4×D6112yes—
201C2×C4Q8×D6112yes—
202C22C2×D4×D6111yescharacteristic
203C22C2×Q8×D6111yescharacteristic
204C22C22×Dic12211yescharacteristic
205C22#1451982211yescharacteristic
206C22#1451982311yescharacteristic
207C22#1451982411yescharacteristic
208C22#1451982511yescharacteristic
209C4—22no—
210C4—22no—
211C4—22no—
212C4—24no—
213C4—42no—
214C4—1224no—
215C4—1224no—
216C4—2442no—
217C4—2442no—
218C2#1684032011yescharacteristic
219C2#1684039111yescharacteristic
220C2#1684039311yescharacteristic
221C2#1684042711yescharacteristic
222C2D4×Dic12211yescharacteristic
223C2Q8×Dic12211yescharacteristic
224C2#1684051611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#389C2
hypercenter#389D61
hypocenterC61#2734
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
49. C4⋊C4×C61Q8semidirect
54. C4⋊Dic61Q8semidirect
122. C61#2734semidirect
169. C4⋊C4Dic122semidirect