Finite Group Databasebeta

← #21446229

Subgroups — #21446229

Order 7808.

386 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 83 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×#14519760C211yesmaximal, characteristic
2#16840235C211yesmaximal, characteristic
3C2×#14519691C211yesmaximal, characteristic
4#16839625C211yesmaximal, characteristic, complemented
5#16839529C211yesmaximal, characteristic, complemented
6#16839528C211yesmaximal, characteristic, complemented
7C61×#381C211yesmaximal, characteristic, complemented
8C22×C22⋊D61C2211yescharacteristic
9#14519760—22no—
10#14519760C414yescomplemented
11C4×C22⋊D61—22no—
12#14519737—22no—
13#14519733—21no—
14C2×#11758196—21no—
15C2×C22⋊Dic61C2211yescharacteristic
16C2×C22⋊Dic61C2211yescharacteristic
17C2×C22⋊Dic61C2211yescharacteristic
18C2×#11758198—21no—
19C22⋊C4×D61—21no—
20#14519691—22no—
21#14519684—22no—
22C23×C4×C61C2211yescharacteristic
23C2×C22⋊C4×C61C2211yescharacteristic
24C2×C22⋊C4×C61C2211yescharacteristic
25#95×C61—22no—
26C24×C61C2311yescharacteristic
27C23×D61D411yescharacteristic
28C22×C4×C61—21no—
29C22×C4×C61—21no—
30C22×C4×C61—21no—
31C22×C4×C61—21no—
32C22×C4×C61—21no—
33C22×C4×C61—21no—
34C22×C4×C61—21no—
35C22×C4×C61C2×C412yescomplemented
36C22×C4×C61D412yes—
37C2×C22⋊D61—21no—
38C2×C22⋊D61—21no—
39C2×C22⋊D61—21no—
40C2×C22⋊D61—21no—
41C2×C22⋊D61C2×C412yes—
42C2×C22⋊D61D412yes—
43C22×Dic61—21no—
44C22×Dic61—21no—
45C22×Dic61D411yescharacteristic
46C22×Dic61D412yes—
47C2×C4×D61—22no—
48C22⋊C4×C61—21no—
49C22⋊C4×C61—21no—
50C22⋊C4×C61—21no—
51C22⋊C4×C61—21no—
52C22⋊Dic61—21no—
53C22⋊Dic61—21no—
54C22⋊Dic61—21no—
55C22⋊Dic61—21no—
56C22⋊Dic61—21no—
57C22⋊Dic61C2×C412yescomplemented
58#11758198—22no—
59#11758198—24no—
60#11758196—22no—
61#11758196—24no—
62C4×Dic61—22no—
63C23×C61—42no—
64C23×C61C22×C411yescharacteristic
65C23×C61C2×D411yescharacteristic
66C23×C61C2×D411yescharacteristic
67C23×C61C2×D411yescharacteristic
68C23×C61C2×D411yescharacteristic
69C23×C61#4111yescharacteristic
70C23×C61#4111yescharacteristic
71C22×D61—21no—
72C22×D61—21no—
73C22×D61—42no—
74C22×D61C22⋊C412yes—
75C2×C4×C61—22no—
76C2×C4×C61—22no—
77C2×C4×C61—22no—
78C2×C4×C61—22no—
79C2×C4×C61—41no—
80C2×C4×C61—41no—
81C2×C4×C61—41no—
82C2×C4×C61—41no—
83C2×C4×C61—42no—
84C2×C4×C61—42no—
85C2×C4×C61—41no—
86C22⋊D61—22no—
87C22⋊D61—22no—
88C22⋊D61—22no—
89C22⋊D61—22no—
90C2×Dic61—21no—
91C2×Dic61—21no—
92C2×Dic61—22no—
93C2×Dic61—22no—
94C2×Dic61—42no—
95C2×Dic61—42no—
96C2×Dic61—42no—
97C2×Dic61—41no—
98C2×Dic61C22⋊C412yes—
99C4×D61—82no—
100C22×C61—22no—
101C22×C61—22no—
102C22×C61—22no—
103C22×C61—41no—
104C22×C61—41no—
105C22×C61—41no—
106C22×C61—41no—
107C22×C61C2×C22⋊C411yescharacteristic
108C22×C61C4×D411yescharacteristic
109C22×C61C4×D411yescharacteristic
110C22×C61#12011yescharacteristic
111C22×C61#12111yescharacteristic
112C22×C61#12111yescharacteristic
113C22×C61#12311yescharacteristic
114C2×D61—22no—
115C2×D61—42no—
116C2×D61—42no—
117C2×D61—81no—
118C4×C61—42no—
119C4×C61—42no—
120C4×C61—81no—
121Dic61—22no—
122Dic61—42no—
123Dic61—42no—
124Dic61—81no—
125#1890—611nomaximal, Sylow
126C2×C61—21no—
127C2×C61—21no—
128C2×C61—21no—
129C2×C61—21no—
130C2×C61—21no—
131C2×C61—21no—
132C2×C61#38611yescharacteristic
133C2×C61#45812yes—
134D61—42no—
135C2×#123—611no—
136#518—611no—
137C2×#99—611no—
138#381—611no—
139#381D6111yescharacteristic, complemented
140#342—611no—
141#342—611no—
142C61#189011yescharacteristic, complemented, Sylow
143C22×D4—611no—
144C23×C4C2×D6111yescharacteristic
145#123—614no—
146#123—1222no—
147C4×D4—1222no—
148C4×D4—1222no—
149#117—1221no—
150C2×C4⋊C4—1221no—
151C2×C22⋊C4—611no—
152C2×C22⋊C4—611no—
153C2×C22⋊C4—611no—
154C2×C22⋊C4—1221no—
155C2×C22⋊C4—1221no—
156C2×C22⋊C4C2×D6111yescharacteristic
157C2×C22⋊C4C2×D6111yescharacteristic
158#99—1222no—
159#95—22no—
160#95—1222no—
161C24—611no—
162C24C22×D6111yescharacteristic
163C2×D4—612no—
164C2×D4—612no—
165C2×D4—1221no—
166C2×D4—1221no—
167C2×D4—1221no—
168C2×D4—1221no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—611no—
177C22×C4—612no—
178C22×C4—1222no—
179C22×C4—1221no—
180C22×C4—1221no—
181C22×C4C4×D6112yescomplemented
182C22×C4C22⋊D6112yes—
183C4⋊C4—1224no—
184C4⋊C4—1222no—
185C22⋊C4—21no—
186C22⋊C4—21no—
187C22⋊C4—21no—
188C22⋊C4—21no—
189C22⋊C4—612no—
190C22⋊C4—1224no—
191C22⋊C4—1222no—
192C22⋊C4—1221no—
193C22⋊C4—1221no—
194C22⋊C4—1221no—
195C22⋊C4—1221no—
196C22⋊C4—1221no—
197C42—1222no—
198C23—42no—
199C23—612no—
200C23—1221no—
201C23—1221no—
202C23—2442no—
203C23C2×C4×D6111yescharacteristic
204C23#1175822211yescharacteristic
205C23D4×D6111yescharacteristic
206C23D4×D6111yescharacteristic
207C23D4×D6111yescharacteristic
208C23#1175822411yescharacteristic
209C23C2×C22⋊D6111yescharacteristic
210D4—1222no—
211D4—1222no—
212D4—1222no—
213D4—1222no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4—41no—
225C2×C4—612no—
226C2×C4—1221no—
227C2×C4—1221no—
228C2×C4—1222no—
229C2×C4—1222no—
230C2×C4—4882no—
231C2×C4—2442no—
232C2×C4—2441no—
233C2×C4—2442no—
234C2×C4—2442no—
235C22—22no—
236C22—22no—
237C22—22no—
238C22—41no—
239C22—41no—
240C22—41no—
241C22—41no—
242C22—1222no—
243C22—4881no—
244C22—2442no—
245C22—2442no—
246C22C22⋊C4×D6111yescharacteristic
247C22#1451973711yescharacteristic
248C22C4×C22⋊D6111yescharacteristic
249C22#1451974511yescharacteristic
250C22#1451974811yescharacteristic
251C22#1451975011yescharacteristic
252C22#1451975911yescharacteristic
253C4—42no—
254C4—42no—
255C4—81no—
256C4—1222no—
257C4—4881no—
258C4—2442no—
259C4—2442no—
260C2—21no—
261C2—21no—
262C2—21no—
263C2—21no—
264C2—21no—
265C2—21no—
266C2—2442no—
267C2#1683963811yescharacteristic
268C2#1683995112yes—
subgroupG/H
centerC22#14519745
commutatorC23×C61C22×C4
FrattiniC24C22×D61
FittingC61×#381C2
socleC22×C61#120
hypercenter#381D61
hypocenterC61#1890
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ #381

Complements

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

NH ≅ G/Ntype
4. #16839625C2semidirect
5. #16839529C2semidirect
6. #16839528C2semidirect
7. C61×#381C2semidirect
10. #14519760C4semidirect
35. C22×C4×C61C2×C4semidirect
57. C22⋊Dic61C2×C4semidirect
139. #381D61semidirect
142. C61#1890semidirect
181. C22×C4C4×D61semidirect