Finite Group Databasebeta

← #21451728

Subgroups — #21451728

Order 7808.

450 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 129 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×#14519770C211yesmaximal, characteristic
2C2×#14519742C211yesmaximal, characteristic, complemented
3#16839696C212yesmaximal, complemented
4#16839693C211yesmaximal, characteristic, complemented
5#16839685C212yesmaximal
6#16839683C211yesmaximal, characteristic, complemented
7#16839674C211yesmaximal, characteristic
8#16839656C212yesmaximal
9#16839645C212yesmaximal, complemented
10#16839626C211yesmaximal, characteristic, complemented
11C61×#397C211yesmaximal, characteristic
12C22×Dic122C2211yescharacteristic
13#14519770—24no—
14#14519742—24no—
15C2×C4⋊Dic61C2212yes—
16C2×C4⋊Dic61C2211yescharacteristic
17C2×#11758196C2211yescharacteristic
18C2×#11758196C2212yes—
19C2×#11758196C2211yescharacteristic
20C2×#11758196C2212yes—
21C2×#11758196C2212yes—
22C2×C22⋊Dic61C2211yescharacteristic
23C2×C22⋊Dic61C2212yes—
24C2×C22⋊Dic61C2211yescharacteristic
25C2×C4×Dic61C2212yes—
26C2×C4×Dic61C2211yescharacteristic
27#14519684C2212yes—
28#14519684C2212yes—
29#14519684C2211yescharacteristic
30#14519684C2212yes—
31#14519684C2212yes—
32C2×C4⋊C4×C61C2211yescharacteristic
33C2×C22⋊C4×C61C2211yescharacteristic
34C2×C22⋊C4×C61C2212yes—
35#95×C61C2211yescharacteristic
36#95×C61C2212yes—
37C24×C61C2311yescharacteristic
38C22×C4×C61C2311yescharacteristic
39C22×C4×C61C2312yes—
40C22×C4×C61C2312yes—
41C22×C4×C61C2311yescharacteristic
42C22×Dic61C2312yes—
43C22×Dic61C2311yescharacteristic
44C22×Dic61C2311yescharacteristic
45C22×Dic61C2311yescharacteristic
46C22×Dic61C2311yescharacteristic
47C22×Dic61C2312yes—
48C2×Dic122—22no—
49C2×Dic122—24no—
50C4⋊C4×C61—22no—
51C22⋊C4×C61—22no—
52C22⋊C4×C61—42no—
53C22⋊Dic61—22no—
54C22⋊Dic61—22no—
55C22⋊Dic61—24no—
56C4⋊Dic61—22no—
57C4⋊Dic61—24no—
58#11758196—22no—
59#11758196—24no—
60#11758196—22no—
61#11758196—42no—
62#11758196—42no—
63C4×Dic61—24no—
64C4×Dic61D414yes—
65C23×C61—21no—
66C23×C61—22no—
67C23×C61—21no—
68C23×C61—22no—
69C23×C61—21no—
70C23×C61C2411yescharacteristic
71C2×C4×C61—22no—
72C2×C4×C61—22no—
73C2×C4×C61—21no—
74C2×C4×C61—22no—
75C2×C4×C61—22no—
76C2×C4×C61—22no—
77C2×C4×C61—22no—
78C2×C4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61C2×D412yes—
81C2×Dic61—22no—
82C2×Dic61—22no—
83C2×Dic61—21no—
84C2×Dic61—22no—
85C2×Dic61—21no—
86C2×Dic61—21no—
87C2×Dic61—21no—
88C2×Dic61—22no—
89C2×Dic61—22no—
90C2×Dic61—21no—
91C2×Dic61—22no—
92C2×Dic61—21no—
93C2×Dic61—22no—
94C2×Dic61C2×D412yes—
95C2×Dic61C2×D412yes—
96C2×Dic61#4114yes—
97Dic122—28no—
98C22×C61—41no—
99C22×C61—41no—
100C22×C61—41no—
101C22×C61—42no—
102C22×C61—42no—
103C22×C61C22×D411yescharacteristic
104C22×C61C2×#4112yes—
105C22×C61H(5,𝔽2)11yescharacteristic
106C22×C612−1+412yes—
107C22×C612−1+411yescharacteristic
108C4×C61—22no—
109C4×C61—41no—
110C4×C61—42no—
111C4×C61—42no—
112Dic61—24no—
113Dic61—22no—
114Dic61—22no—
115Dic61—41no—
116Dic61—41no—
117Dic61—42no—
118#2637—611nomaximal, Sylow
119C2×C61—81no—
120C2×C61#52511yescharacteristic
121C2×C61#53611yescharacteristic
122C2×C61#53711yescharacteristic
123C2×C61#54112yes—
124C2×C61#54212yes—
125C2×#126—611no—
126C2×C4×Q8—611no—
127#398—611no—
128#398—612no—
129#397D6111yescharacteristic
130#396—612no—
131#395—611no—
132#393—611no—
133#388—612no—
134#387—612no—
135#382—611no—
136C61#263711yescharacteristic, complemented, Sylow
137C22×Q8—611no—
138#126—1224no—
139C4×Q8—1224no—
140C2×C4⋊C4—612no—
141C2×C4⋊C4—611no—
142C2×C4⋊C4—611no—
143C2×C4⋊C4—611no—
144C2×C4⋊C4—612no—
145C2×C4⋊C4—612no—
146C2×C4⋊C4—612no—
147C2×C4⋊C4C2×D6111yescharacteristic
148C2×C22⋊C4—611no—
149C2×C22⋊C4—611no—
150C2×C22⋊C4—612no—
151C2×C22⋊C4C2×D6111yescharacteristic
152C2×C22⋊C4C2×D6112yes—
153C2×C42—611no—
154C2×C42—612no—
155#95—612no—
156#95—611no—
157#95—612no—
158#95—612no—
159#95—612no—
160#95C2×D6111yescharacteristic
161#95C2×D6112yes—
162C24C22×D6111yescharacteristic
163C2×Q8—1224no—
164C2×Q8—1222no—
165C22×C4—611no—
166C22×C4—612no—
167C22×C4—611no—
168C22×C4—612no—
169C22×C4—611no—
170C22×C4—611no—
171C22×C4C22×D6111yescharacteristic
172C22×C4C22×D6112yes—
173C22×C4C22×D6112yes—
174C22×C4C22×D6111yescharacteristic
175C4⋊C4—22no—
176C4⋊C4—1224no—
177C4⋊C4—1222no—
178C4⋊C4—1224no—
179C4⋊C4—1222no—
180C4⋊C4—1222no—
181C4⋊C4—2442no—
182C4⋊C4—2442no—
183C22⋊C4—22no—
184C22⋊C4—42no—
185C22⋊C4—1224no—
186C22⋊C4—1222no—
187C22⋊C4—1222no—
188C42—614no—
189C42—1224no—
190C23—21no—
191C23—22no—
192C23—21no—
193C23—22no—
194C23—21no—
195C23C23×D6111yescharacteristic
196Q8—1228no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—612no—
207C2×C4—612no—
208C2×C4—614no—
209C2×C4—1222no—
210C2×C4—1222no—
211C2×C4—1221no—
212C2×C4—1222no—
213C2×C4—1221no—
214C2×C4—1221no—
215C2×C4—1221no—
216C2×C4—1222no—
217C2×C4—1222no—
218C2×C4—1221no—
219C2×C4—1222no—
220C2×C4—1221no—
221C2×C4—1222no—
222C2×C4D4×D6112yes—
223C22—41no—
224C22—41no—
225C22—41no—
226C22—42no—
227C22—42no—
228C22C2×D4×D6111yescharacteristic
229C22#41×D6112yes—
230C22#1451982211yescharacteristic
231C22#1451982412yes—
232C22#1451982411yescharacteristic
233C4—22no—
234C4—41no—
235C4—42no—
236C4—42no—
237C4—1224no—
238C4—1222no—
239C4—1222no—
240C4—2441no—
241C4—2441no—
242C4—2442no—
243C2—81no—
244C2#1684027011yescharacteristic
245C2#1684033211yescharacteristic
246C2#1684034111yescharacteristic
247C2#1684036912yes—
248C2#1684038012yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#397C2
hypercenter#397D61
hypocenterC61#2637
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
2. C2×#14519742C2semidirect
3. #16839696C2semidirect
4. #16839693C2semidirect
6. #16839683C2semidirect
9. #16839645C2semidirect
10. #16839626C2semidirect
136. C61#2637semidirect