Finite Group Databasebeta

← #21451678

Subgroups — #21451678

Order 7808.

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

normal subgroups only

This group has 500 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×#14519763C211yesmaximal, characteristic
2C2×Q8×Dic61C211yesmaximal, characteristic, complemented
3#16839699C211yesmaximal, characteristic, complemented
4#16839698C211yesmaximal, characteristic, complemented
5#16839683C212yesmaximal, complemented
6#16839678C212yesmaximal
7#16839673C211yesmaximal, characteristic, complemented
8#16839655C212yesmaximal, complemented
9#16839651C212yesmaximal, complemented
10#16839629C211yesmaximal, characteristic, complemented
11C61×#393C211yesmaximal, characteristic, complemented
12C22×Dic122C2211yescharacteristic
13C22×C22⋊D61C2211yescharacteristic
14#14519763—24no—
15Q8×Dic61—24no—
16C2×C4⋊Dic61C2212yes—
17C2×C4⋊Dic61C2211yescharacteristic
18C2×C4⋊Dic61C2212yes—
19C2×#11758196C2212yes—
20C2×C22⋊Dic61C2211yescharacteristic
21C2×C22⋊Dic61C2212yes—
22C2×#11758198C2211yescharacteristic
23C2×#11758198C2211yescharacteristic
24C2×#11758198C2212yes—
25C2×#11758198C2212yes—
26C2×C4×Dic61C2212yes—
27C2×C4×Dic61C2211yescharacteristic
28#14519684C2212yes—
29#14519684C2212yes—
30#14519684C2211yescharacteristic
31#14519684C2212yes—
32C22×Q8×C61C2211yescharacteristic
33C2×C22⋊C4×C61C2211yescharacteristic
34C2×C22⋊C4×C61C2212yes—
35#95×C61C2212yes—
36#95×C61C2211yescharacteristic
37C24×C61C2311yescharacteristic
38C23×D61C2311yescharacteristic
39C2×Q8×C61—22no—
40C2×Q8×C61—24no—
41C22×C4×C61C2311yescharacteristic
42C22×C4×C61C2312yes—
43C22×C4×C61C2311yescharacteristic
44C22×C4×C61C2312yes—
45C2×C22⋊D61—22no—
46C2×C22⋊D61—42no—
47C22×Dic61C2311yescharacteristic
48C22×Dic61C2312yes—
49C22×Dic61C2312yes—
50C22×Dic61C2311yescharacteristic
51C22×Dic61C2311yescharacteristic
52C2×Dic122—22no—
53C2×Dic122—42no—
54C22⋊C4×C61—22no—
55C22⋊C4×C61—24no—
56C22⋊Dic61—22no—
57C22⋊Dic61—42no—
58#11758198—22no—
59#11758198—24no—
60#11758198—22no—
61#11758198—42no—
62C4⋊Dic61—22no—
63C4⋊Dic61—24no—
64C4⋊Dic61—42no—
65#11758196—42no—
66C4×Dic61—24no—
67C4×Dic61D414yes—
68C23×C61—21no—
69C23×C61—22no—
70C23×C61—22no—
71C23×C61—21no—
72C23×C61—21no—
73C23×C61C2411yescharacteristic
74C22×D61—21no—
75C22×D61—22no—
76C22×D61—22no—
77C22×D61—21no—
78C22×D61—21no—
79Q8×C61—28no—
80C2×C4×C61—22no—
81C2×C4×C61—22no—
82C2×C4×C61—22no—
83C2×C4×C61—21no—
84C2×C4×C61—22no—
85C2×C4×C61—22no—
86C2×C4×C61—22no—
87C2×C4×C61—22no—
88C2×C4×C61C2×D412yes—
89C2×C4×C61#4114yes—
90C22⋊D61—44no—
91C2×Dic61—22no—
92C2×Dic61—21no—
93C2×Dic61—21no—
94C2×Dic61—22no—
95C2×Dic61—21no—
96C2×Dic61—22no—
97C2×Dic61—22no—
98C2×Dic61—22no—
99C2×Dic61—22no—
100C2×Dic61—22no—
101C2×Dic61—22no—
102C2×Dic61C2×D412yes—
103C2×Dic61C2×D412yes—
104Dic122—44no—
105C22×C61—41no—
106C22×C61—41no—
107C22×C61—41no—
108C22×C61—42no—
109C22×C61—42no—
110C22×C61C22×D411yescharacteristic
111C22×C61C2×#4112yes—
112C22×C61H(5,𝔽2)12yes—
113C22×C612−1+411yescharacteristic
114C22×C612−1+411yescharacteristic
115C2×D61—41no—
116C2×D61—41no—
117C2×D61—41no—
118C2×D61—42no—
119C2×D61—42no—
120C4×C61—22no—
121C4×C61—24no—
122C4×C61—41no—
123C4×C61—42no—
124Dic61—22no—
125Dic61—22no—
126Dic61—41no—
127Dic61—42no—
128Dic61—42no—
129#2632—611nomaximal, Sylow
130C2×C61—81no—
131C2×C61#52511yescharacteristic
132C2×C61#53511yescharacteristic
133C2×C61#53611yescharacteristic
134C2×C61#54212yes—
135C2×C61#54212yes—
136D61—81no—
137C2×#124—611no—
138C2×C4×Q8—611no—
139#399—611no—
140#399—611no—
141#395—612no—
142#394—612no—
143#393—611no—
144#393D6111yescharacteristic, complemented
145#388—612no—
146#388—612no—
147#383—611no—
148C61#263211yescharacteristic, complemented, Sylow
149C22×Q8—611no—
150C22×Q8C2×D6111yescharacteristic
151C22×D4—611no—
152#124—1224no—
153C4×Q8—1224no—
154C2×C4⋊C4—612no—
155C2×C4⋊C4—611no—
156C2×C4⋊C4—612no—
157C2×C4⋊C4—612no—
158C2×C22⋊C4—611no—
159C2×C22⋊C4—611no—
160C2×C22⋊C4—611no—
161C2×C22⋊C4—612no—
162C2×C22⋊C4—612no—
163C2×C22⋊C4—612no—
164C2×C22⋊C4C2×D6111yescharacteristic
165C2×C22⋊C4C2×D6112yes—
166C2×C42—611no—
167C2×C42—612no—
168#95—612no—
169#95—611no—
170#95—612no—
171#95—612no—
172#95C2×D6111yescharacteristic
173#95C2×D6112yes—
174C24—611no—
175C24C22×D6111yescharacteristic
176C2×Q8—22no—
177C2×Q8—24no—
178C2×Q8—1222no—
179C2×Q8—2442no—
180C2×D4—1222no—
181C2×D4—2442no—
182C22×C4—611no—
183C22×C4—611no—
184C22×C4—612no—
185C22×C4—611no—
186C22×C4—612no—
187C22×C4C22×D6112yes—
188C22×C4C22×D6111yescharacteristic
189C22×C4C22×D6111yescharacteristic
190C22×C4C22×D6112yes—
191C4⋊C4—1224no—
192C4⋊C4—1222no—
193C4⋊C4—2442no—
194C4⋊C4—2442no—
195C22⋊C4—22no—
196C22⋊C4—24no—
197C22⋊C4—1222no—
198C22⋊C4—1222no—
199C22⋊C4—1222no—
200C22⋊C4—1224no—
201C22⋊C4—2442no—
202C22⋊C4—2442no—
203C42—614no—
204C42—1224no—
205C23—21no—
206C23—22no—
207C23—22no—
208C23—21no—
209C23—21no—
210C23—1221no—
211C23—1222no—
212C23—1222no—
213C23—1221no—
214C23—1221no—
215C23C23×D6111yescharacteristic
216Q8—28no—
217Q8—2444no—
218D4—2444no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—612no—
228C2×C4—612no—
229C2×C4—1222no—
230C2×C4—1221no—
231C2×C4—1221no—
232C2×C4—1222no—
233C2×C4—1221no—
234C2×C4—1222no—
235C2×C4—1222no—
236C2×C4—1222no—
237C2×C4—1222no—
238C2×C4—1222no—
239C2×C4—1222no—
240C2×C4D4×D6112yes—
241C2×C4#1175822414yes—
242C22—41no—
243C22—41no—
244C22—41no—
245C22—42no—
246C22—42no—
247C22—2441no—
248C22—2441no—
249C22—2441no—
250C22—2442no—
251C22—2442no—
252C22C2×D4×D6111yescharacteristic
253C22C2×#1175822412yes—
254C22#1451982312yes—
255C22#1451982411yescharacteristic
256C22#1451982511yescharacteristic
257C4—22no—
258C4—24no—
259C4—41no—
260C4—42no—
261C4—1222no—
262C4—1222no—
263C4—2442no—
264C4—2441no—
265C4—2442no—
266C2—81no—
267C2—4881no—
268C2#1684026811yescharacteristic
269C2#1684033011yescharacteristic
270C2#1684033511yescharacteristic
271C2#1684038112yes—
272C2#1684038512yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#393C2
hypercenter#393D61
hypocenterC61#2632
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
2. C2×Q8×Dic61C2semidirect
3. #16839699C2semidirect
4. #16839698C2semidirect
5. #16839683C2semidirect
7. #16839673C2semidirect
8. #16839655C2semidirect
9. #16839651C2semidirect
10. #16839629C2semidirect
11. C61×#393C2semidirect
144. #393D61semidirect
148. C61#2632semidirect