Finite Group Databasebeta

← #21445804

Subgroups — #21445804

Order 7808.

380 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 97 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
2C2×#14519691C212yesmaximal
3#16839622C211yesmaximal, characteristic, complemented
4#16839528C212yesmaximal, complemented
5C61×#380C211yesmaximal, characteristic, complemented
6C22×C22⋊D61C2211yescharacteristic
7C22×C4×D61C411yescharacteristic, complemented
8C4×C22⋊D61—21no—
9C4×C22⋊D61—21no—
10C4×C22⋊D61—21no—
11C4×C22⋊D61—21no—
12C2×C4⋊Dic61—21no—
13C2×#11758196C411yescharacteristic, complemented
14C2×C22⋊Dic61C2212yes—
15C2×C22⋊Dic61C2211yescharacteristic
16C2×#11758198C411yescharacteristic, complemented
17C2×C4×Dic61C411yescharacteristic, complemented
18#14519691—24no—
19#14519684—21no—
20C23×C4×C61C2211yescharacteristic
21C2×C4⋊C4×C61—21no—
22C2×C22⋊C4×C61C2212yes—
23#95×C61—21no—
24C24×C61C2311yescharacteristic
25C23×D61C2×C411yescharacteristic
26C22×C4×C61—22no—
27C22×C4×C61—42no—
28C22×C4×C61C2×C411yescharacteristic
29C22×C4×C61C2×C411yescharacteristic
30C22×C4×C61D411yescharacteristic
31C22×C4×C61D411yescharacteristic
32C22×C4×C61D411yescharacteristic
33C22×C4×C61D411yescharacteristic
34C2×C22⋊D61—21no—
35C2×C22⋊D61—21no—
36C2×C22⋊D61—21no—
37C2×C22⋊D61—21no—
38C2×C22⋊D61D412yes—
39C2×C22⋊D61Q812yes—
40C22×Dic61—22no—
41C22×Dic61C2×C411yescharacteristic
42C22×Dic61C2×C411yescharacteristic
43C22×Dic61C2×C411yescharacteristic
44C2×C4×D61—21no—
45C2×C4×D61—21no—
46C2×C4×D61—42no—
47C4⋊C4×C61—42no—
48C22⋊C4×C61—22no—
49C22⋊C4×C61—22no—
50C22⋊Dic61—21no—
51C22⋊Dic61—21no—
52C22⋊Dic61—22no—
53C22⋊Dic61—22no—
54#11758198—21no—
55#11758198—21no—
56C4⋊Dic61—42no—
57#11758196—21no—
58#11758196—21no—
59C4×Dic61—21no—
60C4×Dic61—21no—
61C23×C61—41no—
62C23×C61—41no—
63C23×C61C22×C411yescharacteristic
64C23×C61C2×D411yescharacteristic
65C23×C61C2×D411yescharacteristic
66C23×C61C2×D411yescharacteristic
67C23×C61C2×Q811yescharacteristic
68C23×C61#4111yescharacteristic
69C23×C61#4111yescharacteristic
70C22×D61—21no—
71C22×D61—21no—
72C22×D61—41no—
73C22×D61—41no—
74C22×D61C4⋊C412yescomplemented
75C2×C4×C61—22no—
76C2×C4×C61—22no—
77C2×C4×C61—22no—
78C2×C4×C61—41no—
79C2×C4×C61—41no—
80C2×C4×C61—41no—
81C2×C4×C61—42no—
82C2×C4×C61—42no—
83C2×C4×C61—42no—
84C2×C4×C61C22⋊C411yescharacteristic
85C2×C4×C61C22⋊C411yescharacteristic
86C2×C4×C61C22⋊C411yescharacteristic
87C2×C4×C61C22⋊C411yescharacteristic
88C22⋊D61—22no—
89C22⋊D61—22no—
90C22⋊D61—22no—
91C22⋊D61—22no—
92C2×Dic61—21no—
93C2×Dic61—21no—
94C2×Dic61—21no—
95C2×Dic61—21no—
96C2×Dic61—41no—
97C2×Dic61—41no—
98C2×Dic61—42no—
99C2×Dic61—42no—
100C2×Dic61—42no—
101C2×Dic61C4⋊C412yescomplemented
102C4×D61—42no—
103C4×D61—42no—
104C22×C61—21no—
105C22×C61—21no—
106C22×C61—21no—
107C22×C61—21no—
108C22×C61—21no—
109C22×C61—21no—
110C22×C61—41no—
111C22×C61—41no—
112C22×C61—41no—
113C22×C61—41no—
114C22×C61C2×C22⋊C411yescharacteristic
115C22×C61C2×C4⋊C411yescharacteristic
116C22×C61#11711yescharacteristic
117C22×C61#12111yescharacteristic
118C22×C61#12111yescharacteristic
119C22×C61C22⋊Q811yescharacteristic
120C22×C61C22⋊Q811yescharacteristic
121C2×D61—22no—
122C2×D61—42no—
123C2×D61—41no—
124C2×D61—41no—
125C2×D61—42no—
126C4×C61—21no—
127C4×C61—21no—
128C4×C61—21no—
129C4×C61—82no—
130C4×C61#9912yescomplemented
131Dic61—22no—
132Dic61—41no—
133Dic61—41no—
134Dic61—82no—
135#1799—611nomaximal, Sylow
136C2×C61—21no—
137C2×C61—21no—
138C2×C61—21no—
139C2×C61—21no—
140C2×C61—21no—
141C2×C61—21no—
142C2×C61#38011yescharacteristic
143C2×C61C2×#9911yescharacteristic
144C2×C61#41011yescharacteristic
145D61—42no—
146C2×C4×D4—611no—
147C2×#99—612no—
148#380—611no—
149#380D6111yescharacteristic, complemented
150#342—612no—
151C61#179911yescharacteristic, complemented, Sylow
152C22×D4—611no—
153C23×C4—611no—
154C23×C4C2×D6111yescharacteristic
155C4×D4—1221no—
156C4×D4—1221no—
157C4×D4—1221no—
158C4×D4—1221no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—611no—
161C2×C4⋊C4—1221no—
162C2×C22⋊C4—611no—
163C2×C22⋊C4—611no—
164C2×C22⋊C4—612no—
165C2×C22⋊C4C2×D6112yes—
166C2×C42—611no—
167#99—1224no—
168#95—21no—
169#95—1221no—
170C24—611no—
171C24C22×D6111yescharacteristic
172C2×D4—612no—
173C2×D4—612no—
174C2×D4—1221no—
175C2×D4—1221no—
176C2×D4—1221no—
177C2×D4—1221no—
178C22×C4—22no—
179C22×C4—42no—
180C22×C4—611no—
181C22×C4—611no—
182C22×C4—611no—
183C22×C4—1221no—
184C22×C4—1221no—
185C22×C4—1222no—
186C22×C4—2442no—
187C22×C4C4×D6111yescharacteristic
188C22×C4C4×D6111yescharacteristic
189C22×C4D24411yescharacteristic
190C22×C4D24411yescharacteristic
191C22×C4C22⋊D6111yescharacteristic
192C22×C4C22⋊D6111yescharacteristic
193C4⋊C4—42no—
194C4⋊C4—1221no—
195C4⋊C4—1221no—
196C4⋊C4—2442no—
197C22⋊C4—22no—
198C22⋊C4—22no—
199C22⋊C4—1221no—
200C22⋊C4—1221no—
201C22⋊C4—1221no—
202C22⋊C4—1221no—
203C22⋊C4—1222no—
204C22⋊C4—1222no—
205C42—1221no—
206C42—1221no—
207C23—41no—
208C23—41no—
209C23—612no—
210C23—1221no—
211C23—1221no—
212C23—2441no—
213C23—2441no—
214C23C2×C4×D6111yescharacteristic
215C23C2×D24411yescharacteristic
216C23D4×D6111yescharacteristic
217C23#1175822411yescharacteristic
218C23Q8×D6111yescharacteristic
219C23#1175822611yescharacteristic
220C23C2×C22⋊D6111yescharacteristic
221D4—1222no—
222D4—1222no—
223D4—1222no—
224D4—1222no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—42no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—612no—
235C2×C4—1221no—
236C2×C4—1221no—
237C2×C4—1221no—
238C2×C4—1221no—
239C2×C4—2442no—
240C2×C4—2442no—
241C2×C4—2442no—
242C2×C4—2442no—
243C2×C4—2442no—
244C2×C4—2441no—
245C2×C4—2441no—
246C2×C4#1175819811yescharacteristic
247C2×C4#1175819811yescharacteristic
248C2×C4#1175819811yescharacteristic
249C2×C4#1175819811yescharacteristic
250C22—21no—
251C22—21no—
252C22—21no—
253C22—21no—
254C22—21no—
255C22—21no—
256C22—41no—
257C22—41no—
258C22—41no—
259C22—41no—
260C22—1222no—
261C22—2442no—
262C22—2442no—
263C22—2441no—
264C22—2441no—
265C22C2×#1175819811yescharacteristic
266C22C4⋊C4×D6111yescharacteristic
267C22#1451973511yescharacteristic
268C22#1451974811yescharacteristic
269C22#1451975211yescharacteristic
270C22#1451975311yescharacteristic
271C22#1451975711yescharacteristic
272C4—21no—
273C4—21no—
274C4—21no—
275C4—82no—
276C4—1222no—
277C4—4882no—
278C4—2441no—
279C4—2441no—
280C4#1451969112yescomplemented
281C2—21no—
282C2—21no—
283C2—21no—
284C2—21no—
285C2—21no—
286C2—21no—
287C2—2442no—
288C2#1683961911yescharacteristic
289C2C2×#1451969111yescharacteristic
290C2#1683973511yescharacteristic
subgroupG/H
centerC22C2×#11758198
commutatorC23×C61C22×C4
FrattiniC24C22×D61
FittingC61×#380C2
socleC22×C61C2×C22⋊C4
hypercenter#380D61
hypocenterC61#1799
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
3. #16839622C2semidirect
4. #16839528C2semidirect
5. C61×#380C2semidirect
7. C22×C4×D61C4semidirect
13. C2×#11758196C4semidirect
16. C2×#11758198C4semidirect
17. C2×C4×Dic61C4semidirect
74. C22×D61C4⋊C4semidirect
101. C2×Dic61C4⋊C4semidirect
130. C4×C61#99semidirect
149. #380D61semidirect
151. C61#1799semidirect
280. C4#14519691semidirect