Finite Group Databasebeta

← #21450130

Subgroups — #21450130

Order 7808.

584 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 173 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×C4×C22⋊D61C211yesmaximal, characteristic
2#16839700C212yesmaximal, complemented
3#16839697C212yesmaximal, complemented
4#16839658C212yesmaximal, complemented
5#16839641C212yesmaximal
6#16839635C212yesmaximal, complemented
7#16839622C211yesmaximal, characteristic, complemented
8#16839619C212yesmaximal, complemented
9C22×C4⋊C4×C61C211yesmaximal, characteristic, complemented
10C22×C22⋊D61C2211yescharacteristic
11C22×C4×D61C2211yescharacteristic
12C4×C22⋊D61—24no—
13C2×C4⋊Dic61C2212yes—
14C2×#11758196C2211yescharacteristic
15C2×#11758196C2214yes—
16C2×C22⋊Dic61C2211yescharacteristic
17C2×C22⋊Dic61C2212yes—
18C2×#11758198C2211yescharacteristic
19C2×#11758198C2214yes—
20C2×C4×Dic61C2211yescharacteristic
21#14519684C2212yes—
22#14519684C2214yes—
23#14519684C2214yes—
24C23×C4×C61C2211yescharacteristic
25C23×C4×C61C2212yes—
26C2×C4⋊C4×C61—24no—
27C2×C4⋊C4×C61C2212yes—
28C2×C4⋊C4×C61C2212yes—
29C24×C61C2311yescharacteristic
30C23×D61C2311yescharacteristic
31C22×C4×C61—24no—
32C22×C4×C61—24no—
33C22×C4×C61—44no—
34C22×C4×C61D414yes—
35C22×C4×C61C2314yes—
36C22×C4×C61C2311yescharacteristic
37C22×C4×C61C2311yescharacteristic
38C2×C22⋊D61—22no—
39C2×C22⋊D61—22no—
40C2×C22⋊D61Q814yes—
41C22×Dic61C2311yescharacteristic
42C22×Dic61C2314yes—
43C22×Dic61C2311yescharacteristic
44C22×Dic61C2311yescharacteristic
45C2×C4×D61—22no—
46C2×C4×D61—24no—
47C4⋊C4×C61—24no—
48C4⋊C4×C61—24no—
49C22⋊Dic61—22no—
50C22⋊Dic61—24no—
51#11758198—22no—
52#11758198—44no—
53C4⋊Dic61—24no—
54#11758196—22no—
55#11758196—44no—
56C4×Dic61—22no—
57C23×C61—22no—
58C23×C61—22no—
59C23×C61C2×D412yes—
60C23×C61C2×Q812yes—
61C23×C61#4112yes—
62C23×C61C2411yescharacteristic
63C22×D61—21no—
64C22×D61—22no—
65C22×D61—21no—
66C22×D61—22no—
67C22×D61C2×Q812yes—
68C2×C4×C61—22no—
69C2×C4×C61—28no—
70C2×C4×C61—24no—
71C2×C4×C61—24no—
72C2×C4×C61—24no—
73C2×C4×C61—48no—
74C2×C4×C61C2×D412yes—
75C2×C4×C61C2×D412yes—
76C2×C4×C61#4114yes—
77C22⋊D61—28no—
78C2×Dic61—21no—
79C2×Dic61—21no—
80C2×Dic61—21no—
81C2×Dic61—21no—
82C2×Dic61—24no—
83C2×Dic61—24no—
84C2×Dic61—22no—
85C2×Dic61—22no—
86C2×Dic61—24no—
87C2×Dic61C2×Q812yes—
88C4×D61—44no—
89C22×C61—22no—
90C22×C61—22no—
91C22×C61—24no—
92C22×C61—24no—
93C22×C61C22⋊Q814yes—
94C22×C61C22×D411yescharacteristic
95C22×C61C22×Q811yescharacteristic
96C22×C61C2×#4112yes—
97C22×C61C2×#4111yescharacteristic
98C22×C61H(5,𝔽2)12yes—
99C2×D61—22no—
100C2×D61—24no—
101C2×D61—41no—
102C2×D61—41no—
103C2×D61—42no—
104C4×C61—22no—
105C4×C61—44no—
106C4×C61#12314yes—
107Dic61—22no—
108Dic61—41no—
109Dic61—41no—
110Dic61—44no—
111#2487—611nomaximal, Sylow
112C2×C61—24no—
113C2×C61C2×C22⋊Q811yescharacteristic
114C2×C61C2×#12311yescharacteristic
115C2×C61#53511yescharacteristic
116C2×C61#55312yes—
117C2×C61#55412yes—
118D61—42no—
119C2×C4×D4—611no—
120C22×C4⋊C4D6111yescharacteristic, complemented
121#400—612no—
122#399—612no—
123#389—612no—
124#386—612no—
125#385—612no—
126#380—611no—
127#380—612no—
128C61#248711yescharacteristic, complemented, Sylow
129C22×D4—611no—
130C23×C4—611no—
131C23×C4C2×D6111yescharacteristic
132C23×C4C2×D6112yes—
133C4×D4—1224no—
134C2×C4⋊C4—24no—
135C2×C4⋊C4—611no—
136C2×C4⋊C4—612no—
137C2×C4⋊C4—614no—
138C2×C4⋊C4C2×D6112yes—
139C2×C4⋊C4C2×D6112yes—
140C2×C22⋊C4—611no—
141C2×C22⋊C4—612no—
142C2×C22⋊C4—611no—
143C2×C22⋊C4—614no—
144C2×C42—611no—
145#95—614no—
146#95—612no—
147#95—614no—
148C24—611no—
149C24C22×D6111yescharacteristic
150C2×D4—614no—
151C2×D4—1222no—
152C2×D4—1222no—
153C22×C4—24no—
154C22×C4—24no—
155C22×C4—44no—
156C22×C4—611no—
157C22×C4—611no—
158C22×C4—614no—
159C22×C4—611no—
160C22×C4—1224no—
161C22×C4—1222no—
162C22×C4C22⋊D6114yes—
163C22×C4C22×D6114yes—
164C22×C4C22×D6111yescharacteristic
165C22×C4C22×D6111yescharacteristic
166C4⋊C4—24no—
167C4⋊C4—24no—
168C4⋊C4—1224no—
169C4⋊C4—1222no—
170C4⋊C4—2444no—
171C22⋊C4—1224no—
172C22⋊C4—1222no—
173C22⋊C4—1222no—
174C22⋊C4—2444no—
175C42—1222no—
176C23—22no—
177C23—22no—
178C23—612no—
179C23—1221no—
180C23—1222no—
181C23—1221no—
182C23—1222no—
183C23Q8×D6112yes—
184C23#1175822612yes—
185C23C2×C22⋊D6112yes—
186C23C23×D6111yescharacteristic
187D4—1228no—
188C2×C4—22no—
189C2×C4—28no—
190C2×C4—24no—
191C2×C4—24no—
192C2×C4—24no—
193C2×C4—48no—
194C2×C4—612no—
195C2×C4—1221no—
196C2×C4—1221no—
197C2×C4—1221no—
198C2×C4—1221no—
199C2×C4—1224no—
200C2×C4—1222no—
201C2×C4—1224no—
202C2×C4—1224no—
203C2×C4—1222no—
204C2×C4—2444no—
205C2×C4#1175822214yes—
206C2×C4C2×C22⋊D6112yes—
207C2×C4C2×C22⋊D6112yes—
208C22—24no—
209C22—24no—
210C22—22no—
211C22—22no—
212C22—1224no—
213C22—1222no—
214C22—2442no—
215C22—2441no—
216C22—2441no—
217C22#1451975314yes—
218C22C22×C22⋊D6111yescharacteristic
219C22C2×Q8×D6111yescharacteristic
220C22C2×#1175822212yes—
221C22C2×#1175822611yescharacteristic
222C22#1451982212yes—
223C4—22no—
224C4—44no—
225C4—1222no—
226C4—2444no—
227C4—2441no—
228C4—2441no—
229C4#1451976014yes—
230C2—24no—
231C2—2442no—
232C2C2×#1451975311yescharacteristic
233C2C2×#1451976011yescharacteristic
234C2#1684032911yescharacteristic
235C2#1684046012yes—
236C2#1684046712yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC22×C4⋊C4×C61C2
hypercenterC22×C4⋊C4D61
hypocenterC61#2487
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #16839700C2semidirect
3. #16839697C2semidirect
4. #16839658C2semidirect
6. #16839635C2semidirect
7. #16839622C2semidirect
8. #16839619C2semidirect
9. C22×C4⋊C4×C61C2semidirect
120. C22×C4⋊C4D61semidirect
128. C61#2487semidirect