Finite Group Databasebeta

← #21450228

Subgroups — #21450228

Order 7808.

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

normal subgroups only

This group has 412 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
1#16839700C212yesmaximal, complemented
2#16839691C212yesmaximal
3#16839658C211yesmaximal, characteristic, complemented
4#16839652C212yesmaximal
5#16839629C212yesmaximal, complemented
6#16839628C211yesmaximal, characteristic, complemented
7#16839619C211yesmaximal, characteristic
8#16839619C211yesmaximal, characteristic
9C4⋊C4×Dic61C211yesmaximal, characteristic, complemented
10C4×#11758198C211yesmaximal, characteristic
11C61×#389C211yesmaximal, characteristic, complemented
12C22×C4×D61C2211yescharacteristic
13C2×C4⋊Dic61C2211yescharacteristic
14C2×C4⋊Dic61C2211yescharacteristic
15C2×#11758196C2212yes—
16C2×#11758198C2211yescharacteristic
17C2×#11758198C2212yes—
18C2×#11758198C2211yescharacteristic
19C2×#11758198C2212yes—
20C2×C4×Dic61C2211yescharacteristic
21C2×C4×Dic61C2212yes—
22#14519684C2212yes—
23#14519684C2212yes—
24#14519684C2211yescharacteristic
25#14519684C2212yes—
26#14519684C2212yes—
27#14519684C2212yes—
28#14519684C2211yescharacteristic
29#14519684C2212yes—
30C2×C4⋊C4×C61C2211yescharacteristic
31C2×C4⋊C4×C61C2211yescharacteristic
32C2×C4⋊C4×C61C2212yes—
33C2×C42×C61C2211yescharacteristic
34#95×C61C2212yes—
35C23×D61C2311yescharacteristic
36C22×C4×C61C2311yescharacteristic
37C22×C4×C61C2312yes—
38C22×C4×C61C2312yes—
39C22×C4×C61C2311yescharacteristic
40C22×C4×C61C2311yescharacteristic
41C22×Dic61C2311yescharacteristic
42C22×Dic61C2312yes—
43C22×Dic61C2312yes—
44C22×Dic61C2311yescharacteristic
45C22×Dic61C2311yescharacteristic
46C2×C4×D61—22no—
47C2×C4×D61—22no—
48C2×C4×D61—22no—
49C4⋊C4×C61—22no—
50C4⋊C4×C61—22no—
51C4⋊C4×C61—42no—
52C42×C61—22no—
53#11758198—22no—
54#11758198—24no—
55#11758198—22no—
56#11758198—42no—
57C4⋊Dic61—22no—
58C4⋊Dic61—22no—
59#11758196—42no—
60C4×Dic61—22no—
61C4×Dic61—24no—
62C23×C61C2411yescharacteristic
63C22×D61—21no—
64C22×D61—21no—
65C22×D61—21no—
66C22×D61—21no—
67C22×D61—21no—
68C22×D61—21no—
69C22×D61#4112yes—
70C2×C4×C61—22no—
71C2×C4×C61—21no—
72C2×C4×C61—22no—
73C2×C4×C61—21no—
74C2×C4×C61—21no—
75C2×C4×C61—21no—
76C2×C4×C61—22no—
77C2×C4×C61—22no—
78C2×C4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61—21no—
81C2×C4×C61—21no—
82C2×C4×C61#4112yes—
83C2×C4×C61#4112yes—
84C2×C4×C61#4112yes—
85C2×Dic61—21no—
86C2×Dic61—21no—
87C2×Dic61—22no—
88C2×Dic61—21no—
89C2×Dic61—22no—
90C2×Dic61—22no—
91C2×Dic61—22no—
92C2×Dic61—21no—
93C2×Dic61—21no—
94C2×Dic61—21no—
95C2×Dic61—21no—
96C2×Dic61—21no—
97C2×Dic61—22no—
98C2×Dic61—22no—
99C2×Dic61#4112yes—
100C4×D61—44no—
101C22×C61C2×#4111yescharacteristic
102C22×C61C2×#4111yescharacteristic
103C22×C61C2×#4111yescharacteristic
104C22×C61C2×#4111yescharacteristic
105C22×C61C2×#4111yescharacteristic
106C22×C61H(5,𝔽2)11yescharacteristic
107C22×C612−1+411yescharacteristic
108C2×D61—22no—
109C2×D61—22no—
110C2×D61—22no—
111C2×D61—41no—
112C2×D61—41no—
113C2×D61—41no—
114C2×D61—41no—
115C4×C61—41no—
116C4×C61—42no—
117C4×C61—42no—
118C4×C61—41no—
119C4×C61#12614yes—
120Dic61—22no—
121Dic61—41no—
122Dic61—42no—
123Dic61—42no—
124Dic61—41no—
125#2495—611nomaximal, Sylow
126C2×C61C2×#12611yescharacteristic
127C2×C61#52911yescharacteristic
128C2×C61#54211yescharacteristic
129C2×C61#55211yescharacteristic
130C2×C61#55211yescharacteristic
131C2×C61#55311yescharacteristic
132C2×C61#55511yescharacteristic
133D61—42no—
134#400—612no—
135#397—612no—
136#389—611no—
137#389D6111yescharacteristic, complemented
138#388—612no—
139#383—612no—
140#382—611no—
141#380—611no—
142#380—611no—
143C4×C4⋊C4—611no—
144C4×C22⋊C4—611no—
145C61#249511yescharacteristic, complemented, Sylow
146C23×C4—611no—
147C2×C4⋊C4—611no—
148C2×C4⋊C4—611no—
149C2×C4⋊C4—612no—
150C2×C4⋊C4C2×D6111yescharacteristic
151C2×C4⋊C4C2×D6111yescharacteristic
152C2×C4⋊C4C2×D6112yes—
153C2×C22⋊C4—611no—
154C2×C22⋊C4—611no—
155C2×C22⋊C4—612no—
156C2×C22⋊C4—612no—
157C2×C42—611no—
158C2×C42—612no—
159C2×C42C2×D6111yescharacteristic
160#95—611no—
161#95—611no—
162#95—612no—
163#95—612no—
164#95—612no—
165#95—612no—
166#95—612no—
167#95—612no—
168#95C2×D6112yes—
169C24—611no—
170C22×C4—611no—
171C22×C4—611no—
172C22×C4—612no—
173C22×C4—612no—
174C22×C4—611no—
175C22×C4—1222no—
176C22×C4—1222no—
177C22×C4—1222no—
178C22×C4C22×D6111yescharacteristic
179C22×C4C22×D6111yescharacteristic
180C22×C4C22×D6112yes—
181C22×C4C22×D6112yes—
182C22×C4C22×D6111yescharacteristic
183C4⋊C4—22no—
184C4⋊C4—22no—
185C4⋊C4—42no—
186C4⋊C4—1222no—
187C4⋊C4—1222no—
188C4⋊C4—2442no—
189C22⋊C4—1222no—
190C22⋊C4—1222no—
191C22⋊C4—1224no—
192C22⋊C4—2442no—
193C42—22no—
194C42—1224no—
195C42—1222no—
196C23—612no—
197C23—1221no—
198C23—1221no—
199C23—1221no—
200C23—1221no—
201C23—1221no—
202C23—1221no—
203C23C23×D6111yescharacteristic
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—21no—
216C2×C4—612no—
217C2×C4—1221no—
218C2×C4—1221no—
219C2×C4—1222no—
220C2×C4—1221no—
221C2×C4—1222no—
222C2×C4—1221no—
223C2×C4—1221no—
224C2×C4—1221no—
225C2×C4—1222no—
226C2×C4—1222no—
227C2×C4—1221no—
228C2×C4—1222no—
229C2×C4—1221no—
230C2×C4—1222no—
231C2×C4—2444no—
232C2×C4#1175822212yes—
233C2×C4#1175822412yes—
234C2×C4#1175822612yes—
235C22—1222no—
236C22—1222no—
237C22—1222no—
238C22—2441no—
239C22—2441no—
240C22—2441no—
241C22—2441no—
242C22#41×D6111yescharacteristic
243C22#41×D6111yescharacteristic
244C22C2×#1175822411yescharacteristic
245C22C2×#1175822211yescharacteristic
246C22C2×#1175822611yescharacteristic
247C22#1451982211yescharacteristic
248C22#1451982511yescharacteristic
249C4—42no—
250C4—42no—
251C4—41no—
252C4—41no—
253C4—1222no—
254C4—2441no—
255C4—2441no—
256C4—2442no—
257C4—2442no—
258C4#1451977214yes—
259C2—2442no—
260C2C2×#1451977211yescharacteristic
261C2#1684029711yescharacteristic
262C2#1684038611yescharacteristic
263C2#1684044611yescharacteristic
264C2#1684045311yescharacteristic
265C2#1684046211yescharacteristic
266C2#1684047611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#389C2
hypercenter#389D61
hypocenterC61#2495
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
1. #16839700C2semidirect
3. #16839658C2semidirect
5. #16839629C2semidirect
6. #16839628C2semidirect
9. C4⋊C4×Dic61C2semidirect
11. C61×#389C2semidirect
137. #389D61semidirect
145. C61#2495semidirect