Finite Group Databasebeta

← #21451739

Subgroups — #21451739

Order 7808.

520 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 137 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×#14519756C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊D61C211yesmaximal, characteristic
3#16839694C211yesmaximal, characteristic, complemented
4#16839689C211yesmaximal, characteristic, complemented
5#16839687C212yesmaximal, complemented
6#16839683C211yesmaximal, characteristic, complemented
7#16839678C212yesmaximal
8#16839675C211yesmaximal, characteristic, complemented
9#16839647C212yesmaximal, complemented
10#16839636C212yesmaximal, complemented
11C61×#381C211yesmaximal, characteristic, complemented
12C22×Dic122C2211yescharacteristic
13C22×C22⋊D61C2211yescharacteristic
14C22×C4×D61C2211yescharacteristic
15#14519756—24no—
16C4×C22⋊D61—24no—
17C2×C4⋊Dic61C2211yescharacteristic
18C2×C4⋊Dic61C2212yes—
19C2×C4⋊Dic61C2212yes—
20C2×#11758196C2211yescharacteristic
21C2×#11758196C2212yes—
22C2×C22⋊Dic61C2211yescharacteristic
23C2×C22⋊Dic61C2212yes—
24C2×#11758198C2211yescharacteristic
25C2×#11758198C2212yes—
26C2×#11758198C2212yes—
27C2×C4×Dic61C2211yescharacteristic
28#14519684C2212yes—
29#14519684C2212yes—
30#14519684C2212yes—
31#14519684C2212yes—
32C23×C4×C61C2211yescharacteristic
33C2×C22⋊C4×C61C2212yes—
34#95×C61C2211yescharacteristic
35#95×C61C2211yescharacteristic
36#95×C61C2212yes—
37C24×C61C2311yescharacteristic
38C23×D61C2311yescharacteristic
39C22×C4×C61—42no—
40C22×C4×C61D414yes—
41C22×C4×C61C2312yes—
42C22×C4×C61C2312yes—
43C22×C4×C61C2311yescharacteristic
44C22×C4×C61C2311yescharacteristic
45C2×C22⋊D61—22no—
46C2×C22⋊D61—22no—
47C2×C22⋊D61—22no—
48C22×Dic61C2311yescharacteristic
49C22×Dic61C2312yes—
50C22×Dic61C2311yescharacteristic
51C22×Dic61C2312yes—
52C22×Dic61C2311yescharacteristic
53C2×C4×D61—22no—
54C2×C4×D61—42no—
55C2×Dic122—22no—
56C2×Dic122—42no—
57C22⋊C4×C61—42no—
58C22⋊Dic61—22no—
59C22⋊Dic61—24no—
60#11758198—24no—
61#11758198—22no—
62#11758198—42no—
63C4⋊Dic61—22no—
64C4⋊Dic61—24no—
65C4⋊Dic61—42no—
66#11758196—22no—
67#11758196—24no—
68C4×Dic61—22no—
69C23×C61—21no—
70C23×C61—21no—
71C23×C61—22no—
72C23×C61—22no—
73C23×C61C2×D412yes—
74C23×C61C2411yescharacteristic
75C22×D61—21no—
76C22×D61—21no—
77C22×D61—22no—
78C22×D61—22no—
79C22×D61#4112yes—
80C2×C4×C61—22no—
81C2×C4×C61—22no—
82C2×C4×C61—22no—
83C2×C4×C61—22no—
84C2×C4×C61—22no—
85C2×C4×C61—22no—
86C2×C4×C61—22no—
87C2×C4×C61—22no—
88C2×C4×C61—44no—
89C2×C4×C61C2×D412yes—
90C2×C4×C61C2×D412yes—
91C22⋊D61—28no—
92C2×Dic61—21no—
93C2×Dic61—21no—
94C2×Dic61—21no—
95C2×Dic61—22no—
96C2×Dic61—22no—
97C2×Dic61—21no—
98C2×Dic61—22no—
99C2×Dic61—22no—
100C2×Dic61—22no—
101C2×Dic61—22no—
102C2×Dic61—22no—
103C2×Dic61—22no—
104C2×Dic61#4112yes—
105C4×D61—44no—
106Dic122—44no—
107C22×C61—22no—
108C22×C61—22no—
109C22×C61—22no—
110C22×C61—42no—
111C22×C61—42no—
112C22×C61C22×D411yescharacteristic
113C22×C61C2×#4111yescharacteristic
114C22×C61C2×#4111yescharacteristic
115C22×C61H(5,𝔽2)12yes—
116C22×C612−1+412yes—
117C2×D61—22no—
118C2×D61—24no—
119C2×D61—41no—
120C2×D61—41no—
121C2×D61—42no—
122C4×C61—22no—
123C4×C61—22no—
124C4×C61—42no—
125C4×C61—42no—
126Dic61—22no—
127Dic61—42no—
128Dic61—42no—
129Dic61—41no—
130Dic61—41no—
131#2638—611nomaximal, Sylow
132C2×C61—42no—
133C2×C61#52511yescharacteristic
134C2×C61#53411yescharacteristic
135C2×C61#53611yescharacteristic
136C2×C61#53912yes—
137C2×C61#54212yes—
138D61—42no—
139C2×C22⋊Q8—611no—
140C2×C4×D4—611no—
141#398—611no—
142#397—612no—
143#397—611no—
144#395—611no—
145#394—612no—
146#393—611no—
147#387—612no—
148#385—612no—
149#381D6111yescharacteristic, complemented
150C61#263811yescharacteristic, complemented, Sylow
151C22×Q8—611no—
152C22×D4—611no—
153C23×C4—611no—
154C23×C4C2×D6111yescharacteristic
155C22⋊Q8—1224no—
156C4×D4—1224no—
157C2×C4⋊C4—611no—
158C2×C4⋊C4—612no—
159C2×C4⋊C4—611no—
160C2×C4⋊C4—612no—
161C2×C4⋊C4—612no—
162C2×C22⋊C4—611no—
163C2×C22⋊C4—612no—
164C2×C22⋊C4—611no—
165C2×C22⋊C4—612no—
166C2×C22⋊C4—612no—
167C2×C22⋊C4C2×D6112yes—
168C2×C42—611no—
169#95—612no—
170#95—612no—
171#95—612no—
172#95—612no—
173#95C2×D6112yes—
174#95C2×D6111yescharacteristic
175#95C2×D6111yescharacteristic
176C24—611no—
177C24C22×D6111yescharacteristic
178C2×Q8—1222no—
179C2×Q8—2442no—
180C2×D4—1222no—
181C2×D4—1222no—
182C2×D4—1222no—
183C22×C4—42no—
184C22×C4—611no—
185C22×C4—611no—
186C22×C4—612no—
187C22×C4—612no—
188C22×C4—611no—
189C22×C4—1222no—
190C22×C4—2442no—
191C22×C4D24414yes—
192C22×C4C22×D6112yes—
193C22×C4C22×D6112yes—
194C22×C4C22×D6111yescharacteristic
195C22×C4C22×D6111yescharacteristic
196C4⋊C4—1224no—
197C4⋊C4—1222no—
198C4⋊C4—1224no—
199C4⋊C4—1222no—
200C4⋊C4—2442no—
201C22⋊C4—42no—
202C22⋊C4—1224no—
203C22⋊C4—1222no—
204C22⋊C4—1224no—
205C22⋊C4—1222no—
206C22⋊C4—2442no—
207C42—1222no—
208C23—21no—
209C23—21no—
210C23—22no—
211C23—22no—
212C23—612no—
213C23—1221no—
214C23—1221no—
215C23—1222no—
216C23—1222no—
217C23C2×D24412yes—
218C23C23×D6111yescharacteristic
219Q8—2444no—
220D4—1228no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—44no—
230C2×C4—612no—
231C2×C4—1221no—
232C2×C4—1221no—
233C2×C4—1221no—
234C2×C4—1222no—
235C2×C4—1221no—
236C2×C4—1222no—
237C2×C4—1222no—
238C2×C4—1222no—
239C2×C4—1222no—
240C2×C4—1222no—
241C2×C4—1222no—
242C2×C4—1222no—
243C2×C4—2444no—
244C2×C4C2×D24412yes—
245C2×C4C2×D24412yes—
246C22—22no—
247C22—22no—
248C22—22no—
249C22—42no—
250C22—42no—
251C22—1222no—
252C22—1224no—
253C22—2441no—
254C22—2441no—
255C22—2442no—
256C22C22×D24411yescharacteristic
257C22#41×D6111yescharacteristic
258C22#41×D6111yescharacteristic
259C22#1451982212yes—
260C22#1451982412yes—
261C4—22no—
262C4—22no—
263C4—42no—
264C4—42no—
265C4—1222no—
266C4—2442no—
267C4—2441no—
268C4—2442no—
269C4—2441no—
270C2—42no—
271C2—2442no—
272C2#1684027411yescharacteristic
273C2#1684032411yescharacteristic
274C2#1684033811yescharacteristic
275C2#1684035512yes—
276C2#1684038012yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#381C2
hypercenter#381D61
hypocenterC61#2638
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
1. C2×#14519756C2semidirect
3. #16839694C2semidirect
4. #16839689C2semidirect
5. #16839687C2semidirect
6. #16839683C2semidirect
8. #16839675C2semidirect
9. #16839647C2semidirect
10. #16839636C2semidirect
11. C61×#381C2semidirect
149. #381D61semidirect
150. C61#2638semidirect