Finite Group Databasebeta

← #21451961

Subgroups — #21451961

Order 7808.

534 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 133 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, complemented
2C2×#14519764C211yesmaximal, characteristic, complemented
3#16839685C212yesmaximal, complemented
4#16839683C211yesmaximal, characteristic, complemented
5#16839676C211yesmaximal, characteristic, complemented
6#16839676C212yesmaximal, complemented
7#16839674C211yesmaximal, characteristic, complemented
8#16839665C212yesmaximal, complemented
9#16839655C212yesmaximal, complemented
10#16839613C211yesmaximal, characteristic, complemented
11C61×#392C211yesmaximal, characteristic
12C22×Dic122C2211yescharacteristic
13#14519770—24no—
14#14519764—24no—
15C2×C4⋊Dic61C2211yescharacteristic
16C2×C4⋊Dic61C2212yes—
17C2×#11758196C2211yescharacteristic
18C2×#11758196C2211yescharacteristic
19C2×#11758196C2212yes—
20C2×C22⋊Dic61C2212yes—
21C2×C22⋊Dic61C2212yes—
22C2×C22⋊Dic61C2211yescharacteristic
23C2×C22⋊Dic61C2211yescharacteristic
24C2×C22⋊Dic61C2212yes—
25C2×C22⋊Dic61C2212yes—
26C2×C22⋊Dic61C2212yes—
27C2×C4×Dic61C2212yes—
28C2×C4×Dic61C2211yescharacteristic
29#14519684C2212yes—
30#14519684C2212yes—
31#14519684C2211yescharacteristic
32C22×D4×C61C2211yescharacteristic
33C22×D4×C61C2212yes—
34C2×C22⋊C4×C61C2212yes—
35C2×C22⋊C4×C61C2211yescharacteristic
36#95×C61C2211yescharacteristic
37C24×C61C2311yescharacteristic
38C24×C61C2312yes—
39C2×D4×C61—22no—
40C2×D4×C61—24no—
41C2×D4×C61—42no—
42C2×D4×C61—42no—
43C2×D4×C61—42no—
44C22×C4×C61C2311yescharacteristic
45C22×C4×C61C2311yescharacteristic
46C22×C4×C61C2312yes—
47C22×Dic61C2312yes—
48C22×Dic61C2312yes—
49C22×Dic61C2311yescharacteristic
50C22×Dic61C2311yescharacteristic
51C22×Dic61C2311yescharacteristic
52C22×Dic61C2311yescharacteristic
53C2×Dic122—22no—
54C2×Dic122—42no—
55C22⋊C4×C61—22no—
56C22⋊C4×C61—24no—
57C22⋊Dic61—24no—
58C22⋊Dic61—24no—
59C22⋊Dic61—22no—
60C22⋊Dic61—22no—
61C22⋊Dic61—42no—
62C22⋊Dic61—42no—
63C22⋊Dic61—42no—
64C4⋊Dic61—22no—
65C4⋊Dic61—42no—
66#11758196—22no—
67#11758196—24no—
68#11758196—22no—
69C4×Dic61—42no—
70C4×Dic61D414yescomplemented
71C23×C61—21no—
72C23×C61—22no—
73C23×C61—22no—
74C23×C61—22no—
75C23×C61—22no—
76C23×C61—22no—
77C23×C61—22no—
78C23×C61—22no—
79C23×C61—22no—
80C23×C61—21no—
81C23×C61—21no—
82C23×C61—22no—
83C23×C61C2411yescharacteristic
84D4×C61—44no—
85D4×C61—48no—
86C2×C4×C61—22no—
87C2×C4×C61—22no—
88C2×C4×C61—22no—
89C2×C4×C61—21no—
90C2×C4×C61—22no—
91C2×C4×C61C2×D412yes—
92C2×C4×C61#4114yes—
93C2×Dic61—22no—
94C2×Dic61—21no—
95C2×Dic61—21no—
96C2×Dic61—21no—
97C2×Dic61—21no—
98C2×Dic61—22no—
99C2×Dic61—22no—
100C2×Dic61—22no—
101C2×Dic61—22no—
102C2×Dic61—22no—
103C2×Dic61—21no—
104C2×Dic61—22no—
105C2×Dic61—22no—
106C2×Dic61—21no—
107C2×Dic61C2×D412yes—
108C2×Dic61C2×D412yes—
109Dic122—44no—
110C22×C61—41no—
111C22×C61—42no—
112C22×C61—42no—
113C22×C61—41no—
114C22×C61—41no—
115C22×C61—42no—
116C22×C61—42no—
117C22×C61—42no—
118C22×C61—42no—
119C22×C61—42no—
120C22×C61—42no—
121C22×C61—42no—
122C22×C61C22×D411yescharacteristic
123C22×C61C2×#4112yes—
124C22×C61H(5,𝔽2)12yes—
125C22×C61H(5,𝔽2)11yescharacteristic
126C22×C612−1+411yescharacteristic
127C4×C61—22no—
128C4×C61—24no—
129C4×C61—41no—
130Dic61—22no—
131Dic61—22no—
132Dic61—42no—
133Dic61—41no—
134Dic61—41no—
135Dic61—42no—
136#2662—611nomaximal, Sylow
137C2×C61—82no—
138C2×C61—81no—
139C2×C61#53211yescharacteristic
140C2×C61#53511yescharacteristic
141C2×C61#53711yescharacteristic
142C2×C61#53812yes—
143C2×C61#54212yes—
144C2×#126—611no—
145C2×#124—611no—
146#396—612no—
147#395—611no—
148#394—611no—
149#394—612no—
150#393—611no—
151#392D6111yescharacteristic
152#390—612no—
153#388—612no—
154C4×C4⋊C4—611no—
155C61#266211yescharacteristic, complemented, Sylow
156C22×Q8—611no—
157C22×D4C2×D6111yescharacteristic
158C22×D4C2×D6112yes—
159#126—1224no—
160#124—1224no—
161C2×C4⋊C4—611no—
162C2×C4⋊C4—611no—
163C2×C4⋊C4—611no—
164C2×C4⋊C4—612no—
165C2×C4⋊C4—612no—
166C2×C22⋊C4—612no—
167C2×C22⋊C4—612no—
168C2×C22⋊C4—611no—
169C2×C22⋊C4—611no—
170C2×C22⋊C4—612no—
171C2×C22⋊C4—612no—
172C2×C22⋊C4—612no—
173C2×C22⋊C4C2×D6111yescharacteristic
174C2×C22⋊C4C2×D6112yes—
175C2×C42—611no—
176C2×C42—612no—
177#95—611no—
178#95—612no—
179#95—612no—
180#95C2×D6111yescharacteristic
181C24C22×D6111yescharacteristic
182C24C22×D6112yes—
183C2×Q8—1222no—
184C2×Q8—2442no—
185C2×D4—22no—
186C2×D4—24no—
187C2×D4—42no—
188C2×D4—42no—
189C2×D4—42no—
190C22×C4—611no—
191C22×C4—611no—
192C22×C4—612no—
193C22×C4—611no—
194C22×C4—612no—
195C22×C4—611no—
196C22×C4C22×D6111yescharacteristic
197C22×C4C22×D6111yescharacteristic
198C22×C4C22×D6112yes—
199C4⋊C4—1222no—
200C4⋊C4—1222no—
201C4⋊C4—1222no—
202C4⋊C4—1224no—
203C4⋊C4—2442no—
204C22⋊C4—22no—
205C22⋊C4—24no—
206C22⋊C4—1224no—
207C22⋊C4—1224no—
208C22⋊C4—1222no—
209C22⋊C4—1222no—
210C22⋊C4—2442no—
211C22⋊C4—2442no—
212C22⋊C4—2442no—
213C42—614no—
214C42—2442no—
215C23—21no—
216C23—22no—
217C23—22no—
218C23—22no—
219C23—22no—
220C23—22no—
221C23—22no—
222C23—22no—
223C23—22no—
224C23—21no—
225C23—21no—
226C23—22no—
227C23C23×D6111yescharacteristic
228Q8—2444no—
229D4—44no—
230D4—48no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—612no—
237C2×C4—612no—
238C2×C4—1222no—
239C2×C4—1221no—
240C2×C4—1221no—
241C2×C4—1222no—
242C2×C4—1221no—
243C2×C4—1221no—
244C2×C4—1222no—
245C2×C4—1222no—
246C2×C4—1221no—
247C2×C4—1222no—
248C2×C4—1222no—
249C2×C4—1222no—
250C2×C4—1222no—
251C2×C4—1221no—
252C2×C4D4×D6112yes—
253C2×C4#1175822414yes—
254C22—41no—
255C22—42no—
256C22—42no—
257C22—41no—
258C22—41no—
259C22—42no—
260C22—42no—
261C22—42no—
262C22—42no—
263C22—42no—
264C22—42no—
265C22—42no—
266C22C2×D4×D6111yescharacteristic
267C22C2×#1175822412yes—
268C22#1451982212yes—
269C22#1451982211yescharacteristic
270C22#1451982411yescharacteristic
271C4—22no—
272C4—24no—
273C4—41no—
274C4—1222no—
275C4—1222no—
276C4—2441no—
277C4—2442no—
278C4—2441no—
279C4—2442no—
280C2—82no—
281C2—81no—
282C2#1684031011yescharacteristic
283C2#1684032711yescharacteristic
284C2#1684034111yescharacteristic
285C2#1684034712yes—
286C2#1684037912yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#392C2
hypercenter#392D61
hypocenterC61#2662
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#14519770C2semidirect
2. C2×#14519764C2semidirect
3. #16839685C2semidirect
4. #16839683C2semidirect
5. #16839676C2semidirect
6. #16839676C2semidirect
7. #16839674C2semidirect
8. #16839665C2semidirect
9. #16839655C2semidirect
10. #16839613C2semidirect
70. C4×Dic61D4semidirect
155. C61#2662semidirect