Finite Group Databasebeta

← #21451451

Subgroups — #21451451

Order 7808.

470 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 145 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×#14519771C211yesmaximal, characteristic
2#16839700C211yesmaximal, characteristic, complemented
3#16839697C211yesmaximal, characteristic
4#16839681C211yesmaximal, characteristic, complemented
5#16839673C211yesmaximal, characteristic
6#16839657C212yesmaximal, complemented
7#16839653C212yesmaximal
8#16839652C212yesmaximal
9#16839646C212yesmaximal, complemented
10#16839608C211yesmaximal, characteristic, complemented
11C2×C4×Q8×C61C211yesmaximal, characteristic, complemented
12#14519771—24no—
13C2×#11758196C2211yescharacteristic
14C2×#11758196C2212yes—
15C2×#11758196C2212yes—
16C2×#11758196C2211yescharacteristic
17C2×#11758196C2211yescharacteristic
18C2×#11758198C2211yescharacteristic
19C2×#11758198C2212yes—
20C2×#11758198C2211yescharacteristic
21C2×#11758198C2211yescharacteristic
22C2×#11758198C2212yes—
23C2×C4×Dic61C2212yes—
24#14519684C2211yescharacteristic
25#14519684C2212yes—
26#14519684C2211yescharacteristic
27#14519684C2212yes—
28#14519684C2212yes—
29#14519684C2212yes—
30#14519684C2212yes—
31C22×Q8×C61C2211yescharacteristic
32C4×Q8×C61—24no—
33C2×C4⋊C4×C61C2211yescharacteristic
34C2×C4⋊C4×C61C2212yes—
35C2×C42×C61C2212yes—
36C2×C42×C61C2211yescharacteristic
37C23×D61C2311yescharacteristic
38C2×Q8×C61—22no—
39C2×Q8×C61—24no—
40C22×C4×C61C2312yes—
41C22×C4×C61C2311yescharacteristic
42C22×C4×C61C2311yescharacteristic
43C22×C4×C61C2311yescharacteristic
44C22×C4×C61C2312yes—
45C22×Dic61C2312yes—
46C22×Dic61C2311yescharacteristic
47C22×Dic61C2311yescharacteristic
48C22×Dic61C2311yescharacteristic
49C22×Dic61C2312yes—
50C4⋊C4×C61—24no—
51C4⋊C4×C61—22no—
52C42×C61—24no—
53C42×C61D414yes—
54#11758198—22no—
55#11758198—22no—
56#11758198—22no—
57#11758198—24no—
58#11758198—24no—
59#11758196—22no—
60#11758196—22no—
61#11758196—22no—
62#11758196—24no—
63#11758196—24no—
64C4×Dic61—24no—
65C23×C61C2411yescharacteristic
66C22×D61—21no—
67C22×D61—22no—
68C22×D61—22no—
69C22×D61—21no—
70C22×D61—21no—
71Q8×C61—28no—
72C2×C4×C61—22no—
73C2×C4×C61—22no—
74C2×C4×C61—22no—
75C2×C4×C61—22no—
76C2×C4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61—22no—
81C2×C4×C61C2×D412yes—
82C2×C4×C61C2×D412yes—
83C2×C4×C61C2×D412yes—
84C2×C4×C61#4114yes—
85C2×Dic61—22no—
86C2×Dic61—22no—
87C2×Dic61—21no—
88C2×Dic61—21no—
89C2×Dic61—21no—
90C2×Dic61—22no—
91C2×Dic61—22no—
92C2×Dic61—22no—
93C2×Dic61—22no—
94C2×Dic61—21no—
95C2×Dic61—21no—
96C2×Dic61—22no—
97C2×Dic61#4114yes—
98C22×C61C22×D411yescharacteristic
99C22×C61C2×#4112yes—
100C22×C61C2×#4112yes—
101C22×C612−1+411yescharacteristic
102C22×C612−1+411yescharacteristic
103C2×D61—41no—
104C2×D61—41no—
105C2×D61—41no—
106C2×D61—42no—
107C2×D61—42no—
108C4×C61—22no—
109C4×C61—24no—
110C4×C61—22no—
111C4×C61—22no—
112C4×C61—42no—
113Dic61—24no—
114Dic61—41no—
115Dic61—41no—
116Dic61—41no—
117Dic61—42no—
118#2604—611nomaximal, Sylow
119C2×C61#52511yescharacteristic
120C2×C61#53211yescharacteristic
121C2×C61#53611yescharacteristic
122C2×C61#55212yes—
123C2×C61#55612yes—
124D61—81no—
125C2×#126—611no—
126C2×C4×Q8D6111yescharacteristic, complemented
127#400—611no—
128#399—611no—
129#395—611no—
130#393—611no—
131#389—612no—
132#388—612no—
133#388—612no—
134#387—612no—
135#376—611no—
136C61#260411yescharacteristic, complemented, Sylow
137C22×Q8C2×D6111yescharacteristic
138#126—1224no—
139C4×Q8—24no—
140C2×C4⋊C4—611no—
141C2×C4⋊C4—611no—
142C2×C4⋊C4—611no—
143C2×C4⋊C4—612no—
144C2×C4⋊C4—612no—
145C2×C4⋊C4C2×D6112yes—
146C2×C4⋊C4C2×D6111yescharacteristic
147C2×C22⋊C4—611no—
148C2×C22⋊C4—611no—
149C2×C22⋊C4—611no—
150C2×C22⋊C4—612no—
151C2×C22⋊C4—612no—
152C2×C42—612no—
153C2×C42C2×D6112yes—
154C2×C42C2×D6111yescharacteristic
155#95—612no—
156#95—611no—
157#95—611no—
158#95—612no—
159#95—612no—
160#95—612no—
161#95—612no—
162C24—611no—
163C2×Q8—24no—
164C2×Q8—22no—
165C22×C4—612no—
166C22×C4—612no—
167C22×C4—611no—
168C22×C4—611no—
169C22×C4—611no—
170C22×C4C22×D6112yes—
171C22×C4C22×D6112yes—
172C22×C4C22×D6111yescharacteristic
173C22×C4C22×D6111yescharacteristic
174C22×C4C22×D6111yescharacteristic
175C4⋊C4—24no—
176C4⋊C4—22no—
177C4⋊C4—1224no—
178C4⋊C4—1224no—
179C4⋊C4—1222no—
180C4⋊C4—1222no—
181C4⋊C4—1222no—
182C22⋊C4—1224no—
183C22⋊C4—1224no—
184C22⋊C4—1222no—
185C22⋊C4—1222no—
186C22⋊C4—1222no—
187C42—24no—
188C42—1224no—
189C42C22⋊D6114yes—
190C23—1221no—
191C23—1222no—
192C23—1222no—
193C23—1221no—
194C23—1221no—
195C23C23×D6111yescharacteristic
196Q8—28no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—614no—
207C2×C4—1222no—
208C2×C4—1222no—
209C2×C4—1221no—
210C2×C4—1221no—
211C2×C4—1221no—
212C2×C4—1222no—
213C2×C4—1222no—
214C2×C4—1222no—
215C2×C4—1222no—
216C2×C4—1222no—
217C2×C4—1221no—
218C2×C4—1221no—
219C2×C4#1175822214yes—
220C2×C4C2×C22⋊D6112yes—
221C2×C4C2×C22⋊D6112yes—
222C2×C4C2×C22⋊D6112yes—
223C22—2442no—
224C22—2442no—
225C22—2441no—
226C22—2441no—
227C22—2441no—
228C22C22×C22⋊D6111yescharacteristic
229C22#41×D6112yes—
230C22C2×#1175822212yes—
231C22#1451982511yescharacteristic
232C22#1451982511yescharacteristic
233C4—24no—
234C4—22no—
235C4—22no—
236C4—22no—
237C4—42no—
238C4—1224no—
239C4—2442no—
240C4—2441no—
241C4—2441no—
242C4—2441no—
243C2—4881no—
244C2#1684027311yescharacteristic
245C2#1684030811yescharacteristic
246C2#1684033611yescharacteristic
247C2#1684045312yes—
248C2#1684048412yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×C4×Q8×C61C2
hypercenterC2×C4×Q8D61
hypocenterC61#2604
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
2. #16839700C2semidirect
4. #16839681C2semidirect
6. #16839657C2semidirect
9. #16839646C2semidirect
10. #16839608C2semidirect
11. C2×C4×Q8×C61C2semidirect
126. C2×C4×Q8D61semidirect
136. C61#2604semidirect