Finite Group Databasebeta

← #21450720

Subgroups — #21450720

Order 7808.

732 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 732 conjugacy classes of subgroups — too many to draw. Only its 165 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×#14519751C212yesmaximal, complemented
2C2×C4×D244C211yesmaximal, characteristic, complemented
3#16839688C212yesmaximal, complemented
4#16839670C212yesmaximal, complemented
5#16839638C214yesmaximal, complemented
6#16839628C211yesmaximal, characteristic, complemented
7#16839622C212yesmaximal, complemented
8C2×C4×D4×C61C211yesmaximal, characteristic, complemented
9C22×D244C2211yescharacteristic
10C22×C22⋊D61C2214yes—
11C22×C4×D61C2212yes—
12#14519751—28no—
13C4×D244—24no—
14C2×C4⋊Dic61C2211yescharacteristic
15C2×C4⋊Dic61C2212yes—
16C2×C22⋊Dic61C2214yes—
17C2×#11758198C2212yes—
18C2×#11758198C2214yes—
19#14519684C2214yes—
20#14519684C2212yes—
21#14519684C2212yes—
22C22×D4×C61C2211yescharacteristic
23C23×C4×C61C2212yes—
24C4×D4×C61—24no—
25C2×C4⋊C4×C61C2211yescharacteristic
26C2×C22⋊C4×C61C2212yes—
27C2×C42×C61C2211yescharacteristic
28C24×C61C2312yes—
29C23×D61C2312yes—
30C2×D4×C61—24no—
31C2×D4×C61—22no—
32C22×C4×C61—24no—
33C22×C4×C61—24no—
34C22×C4×C61—24no—
35C22×C4×C61C2312yes—
36C22×C4×C61C2311yescharacteristic
37C22×C4×C61C2311yescharacteristic
38C22×C4×C61C2311yescharacteristic
39C2×C22⋊D61—28no—
40C2×C22⋊D61—28no—
41C2×C22⋊D61—44no—
42C22×Dic61C2312yes—
43C22×Dic61C2314yes—
44C2×D244—22no—
45C2×D244—22no—
46C2×D244D414yescomplemented
47C2×C4×D61—24no—
48C2×C4×D61—44no—
49C4⋊C4×C61—22no—
50C22⋊C4×C61—24no—
51C42×C61D414yescomplemented
52C22⋊Dic61—44no—
53#11758198—28no—
54#11758198—24no—
55C4⋊Dic61—22no—
56C4⋊Dic61—24no—
57C23×C61—22no—
58C23×C61—22no—
59C23×C61—22no—
60C23×C61—22no—
61C23×C61—22no—
62C23×C61—22no—
63C23×C61#4114yes—
64C23×C61C2411yescharacteristic
65C22×D61—22no—
66C22×D61—22no—
67C22×D61—24no—
68C22×D61—24no—
69C22×D61C2×D414yes—
70D4×C61—28no—
71C2×C4×C61—22no—
72C2×C4×C61—22no—
73C2×C4×C61—22no—
74C2×C4×C61—22no—
75C2×C4×C61—22no—
76C2×C4×C61—48no—
77C2×C4×C61C2×D412yes—
78C2×C4×C61C2×D412yes—
79C2×C4×C61C2×D412yes—
80C2×C4×C61C2×D412yes—
81C2×C4×C61#4112yes—
82C22⋊D61—416no—
83C2×Dic61—22no—
84C2×Dic61—24no—
85C2×Dic61—24no—
86C2×Dic61—24no—
87C2×Dic61—24no—
88D244—28no—
89C4×D61—48no—
90C22×C61—24no—
91C22×C61—24no—
92C22×C61—24no—
93C22×C61—42no—
94C22×C61—42no—
95C22×C61—42no—
96C22×C61—42no—
97C22×C61C22×D411yescharacteristic
98C22×C61C22×D411yescharacteristic
99C22×C61C2×#4111yescharacteristic
100C22×C61C2×#4112yes—
101C22×C61H(5,𝔽2)12yes—
102C2×D61—24no—
103C2×D61—28no—
104C2×D61—42no—
105C2×D61—42no—
106C2×D61—44no—
107C4×C61—22no—
108C4×C61—22no—
109C4×C61—42no—
110C4×C61#12114yes—
111Dic61—42no—
112Dic61—44no—
113#2535—611nomaximal, Sylow
114C2×C61—44no—
115C2×C61C2×#12111yescharacteristic
116C2×C61#52511yescharacteristic
117C2×C61#53511yescharacteristic
118C2×C61#54612yes—
119C2×C61#55312yes—
120D61—44no—
121C2×#121—612no—
122C2×C4×D4—611no—
123C2×C4×D4D6111yescharacteristic, complemented
124#397—612no—
125#392—612no—
126#386—614no—
127#382—611no—
128#380—612no—
129C61#253511yescharacteristic, complemented, Sylow
130C22×D4—614no—
131C22×D4—611no—
132C22×D4C2×D6111yescharacteristic
133C23×C4—612no—
134C23×C4C2×D6112yes—
135#121—1228no—
136C4×D4—24no—
137C4×D4—1224no—
138C2×C4⋊C4—611no—
139C2×C4⋊C4—612no—
140C2×C4⋊C4C2×D6111yescharacteristic
141C2×C22⋊C4—612no—
142C2×C22⋊C4—614no—
143C2×C22⋊C4—614no—
144C2×C22⋊C4C2×D6112yes—
145C2×C42C2×D6111yescharacteristic
146#95—614no—
147#95—612no—
148#95—612no—
149C24—612no—
150C24C22×D6112yes—
151C2×D4—24no—
152C2×D4—22no—
153C2×D4—614no—
154C2×D4—1228no—
155C2×D4—1228no—
156C2×D4—1222no—
157C2×D4—1222no—
158C2×D4—2444no—
159C22×C4—24no—
160C22×C4—24no—
161C22×C4—24no—
162C22×C4—614no—
163C22×C4—612no—
164C22×C4—1224no—
165C22×C4—2444no—
166C22×C4C22×D6112yes—
167C22×C4C22×D6111yescharacteristic
168C22×C4C22×D6111yescharacteristic
169C22×C4C22×D6111yescharacteristic
170C4⋊C4—22no—
171C4⋊C4—1224no—
172C4⋊C4—1222no—
173C22⋊C4—24no—
174C22⋊C4—1228no—
175C22⋊C4—1224no—
176C22⋊C4—2444no—
177C42C22⋊D6114yescomplemented
178C23—22no—
179C23—22no—
180C23—22no—
181C23—22no—
182C23—22no—
183C23—22no—
184C23—614no—
185C23—1222no—
186C23—1222no—
187C23—1224no—
188C23—1224no—
189C23#1175822214yes—
190C23C23×D6111yescharacteristic
191D4—28no—
192D4—1228no—
193D4—24416no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—48no—
200C2×C4—1224no—
201C2×C4—1222no—
202C2×C4—1224no—
203C2×C4—1224no—
204C2×C4—1224no—
205C2×C4—2448no—
206C2×C4D4×D6112yes—
207C2×C4#1175822412yes—
208C2×C4C2×C22⋊D6112yes—
209C2×C4C2×C22⋊D6112yes—
210C2×C4C2×C22⋊D6112yes—
211C22—24no—
212C22—24no—
213C22—24no—
214C22—42no—
215C22—42no—
216C22—42no—
217C22—42no—
218C22—1224no—
219C22—1228no—
220C22—2444no—
221C22—2442no—
222C22—2442no—
223C22C2×D4×D6111yescharacteristic
224C22C22×C22⋊D6111yescharacteristic
225C22C2×#1175822411yescharacteristic
226C22C2×#1175822212yes—
227C22#1451982312yes—
228C4—22no—
229C4—22no—
230C4—42no—
231C4—2442no—
232C4—2444no—
233C4#1451974814yes—
234C2—44no—
235C2—2444no—
236C2C2×#1451974811yescharacteristic
237C2#1684027311yescharacteristic
238C2#1684032611yescharacteristic
239C2#1684040812yes—
240C2#1684045812yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×C4×D4×C61C2
hypercenterC2×C4×D4D61
hypocenterC61#2535
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#14519751C2semidirect
2. C2×C4×D244C2semidirect
3. #16839688C2semidirect
4. #16839670C2semidirect
5. #16839638C2semidirect
6. #16839628C2semidirect
7. #16839622C2semidirect
8. C2×C4×D4×C61C2semidirect
46. C2×D244D4semidirect
51. C42×C61D4semidirect
123. C2×C4×D4D61semidirect
129. C61#2535semidirect
177. C42C22⋊D61semidirect