Finite Group Databasebeta

← #21454121

Subgroups — #21454121

Order 7808.

696 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 696 conjugacy classes of subgroups — too many to draw. Only its 169 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×#14519765C211yesmaximal, characteristic, complemented
2C2×#14519757C211yesmaximal, characteristic, complemented
3C2×#14519752C211yesmaximal, characteristic
4C2×C42×D61C211yesmaximal, characteristic, complemented
5#16839667C211yesmaximal, characteristic, complemented
6#16839663C211yesmaximal, characteristic, complemented
7#16839654C214yesmaximal, complemented
8#16839640C214yesmaximal, complemented
9C61×#382C211yesmaximal, characteristic, complemented
10C22×Dic122C2211yescharacteristic
11C22×D244C2211yescharacteristic
12C22×D244C2212yes—
13C22×C4×D61C2212yes—
14C22×C4×D61C2211yescharacteristic
15#14519765—24no—
16#14519757—24no—
17#14519752—24no—
18C2×C4⋊Dic61C2212yes—
19C2×#11758198C2212yes—
20C2×#11758198C2212yes—
21C2×#11758198C2214yes—
22C2×#11758198C2214yes—
23C2×C4×Dic61C2212yes—
24C2×C4×Dic61C2211yescharacteristic
25C42×D61—24no—
26#14519684C2214yes—
27C2×C4⋊C4×C61C2211yescharacteristic
28C2×C4⋊C4×C61C2211yescharacteristic
29C2×C42×C61C2211yescharacteristic
30#95×C61C2214yes—
31C23×D61C2312yes—
32C23×D61C2311yescharacteristic
33C22×C4×C61C2312yes—
34C22×C4×C61C2312yes—
35C22×C4×C61C2312yes—
36C22×C4×C61C2311yescharacteristic
37C22×Dic61C2312yes—
38C22×Dic61C2311yescharacteristic
39C22×Dic61C2312yes—
40C2×D244—24no—
41C2×D244—28no—
42C2×D244—22no—
43C2×D244—22no—
44C2×D244—22no—
45C2×C4×D61—24no—
46C2×C4×D61—24no—
47C2×C4×D61—22no—
48C2×C4×D61—22no—
49C2×C4×D61—24no—
50C2×C4×D61D414yes—
51C2×Dic122—22no—
52C2×Dic122—22no—
53C2×Dic122—22no—
54C4⋊C4×C61—22no—
55C4⋊C4×C61—22no—
56C42×C61D414yescomplemented
57#11758198—24no—
58#11758198—28no—
59#11758198—24no—
60#11758198—28no—
61C4⋊Dic61—24no—
62C4×Dic61—24no—
63C4×Dic61—22no—
64C23×C61C2411yescharacteristic
65C22×D61—21no—
66C22×D61—21no—
67C22×D61—22no—
68C22×D61—22no—
69C22×D61—22no—
70C22×D61—24no—
71C22×D61—22no—
72C22×D61—24no—
73C22×D61C2×D412yes—
74C22×D61#4114yes—
75C2×C4×C61—22no—
76C2×C4×C61—22no—
77C2×C4×C61—22no—
78C2×C4×C61—22no—
79C2×C4×C61—24no—
80C2×C4×C61—24no—
81C2×C4×C61C2×D414yes—
82C2×C4×C61C2×D412yes—
83C2×C4×C61C2×D412yes—
84C2×C4×C61#4112yes—
85C2×Dic61—21no—
86C2×Dic61—22no—
87C2×Dic61—21no—
88C2×Dic61—22no—
89C2×Dic61—22no—
90C2×Dic61—22no—
91C2×Dic61—22no—
92C2×Dic61C2×D412yes—
93C2×Dic61#4114yes—
94D244—48no—
95D244—44no—
96C4×D61—216no—
97C4×D61—28no—
98Dic122—44no—
99C22×C61C22×D411yescharacteristic
100C22×C61C22×D411yescharacteristic
101C22×C61C2×#4112yes—
102C22×C61C2×#4112yes—
103C22×C61C2×#4111yescharacteristic
104C2×D61—22no—
105C2×D61—24no—
106C2×D61—24no—
107C2×D61—22no—
108C2×D61—42no—
109C2×D61—44no—
110C2×D61—42no—
111C2×D61—44no—
112C2×D61—42no—
113C2×D61#12414yescomplemented
114C4×C61—24no—
115C4×C61—42no—
116C4×C61—42no—
117C4×C61#12114yes—
118Dic61—22no—
119Dic61—24no—
120Dic61—42no—
121#2850—611nomaximal, Sylow
122C2×C61C2×#12111yescharacteristic
123C2×C61#52512yes—
124C2×C61C2×#12411yescharacteristic
125C2×C61#52912yes—
126C2×C61#53211yescharacteristic
127D61—24no—
128D61—82no—
129C2×#124—611no—
130C2×C22⋊Q8—611no—
131C2×#121—611no—
132C22×C42—611no—
133#391—611no—
134#390—611no—
135#388—614no—
136#386—614no—
137#382D6111yescharacteristic, complemented
138C61#285011yescharacteristic, complemented, Sylow
139C22×Q8—611no—
140C22×D4—611no—
141C22×D4—612no—
142C23×C4—611no—
143C23×C4—612no—
144#124—1224no—
145C22⋊Q8—1224no—
146#121—1224no—
147C2×C4⋊C4—612no—
148C2×C4⋊C4C2×D6111yescharacteristic
149C2×C4⋊C4C2×D6111yescharacteristic
150C2×C22⋊C4—612no—
151C2×C22⋊C4—612no—
152C2×C22⋊C4—614no—
153C2×C22⋊C4—614no—
154C2×C42—612no—
155C2×C42—611no—
156C2×C42—1224no—
157C2×C42C2×D6111yescharacteristic
158#95—614no—
159#95C2×D6114yes—
160C24—611no—
161C24—612no—
162C2×Q8—1222no—
163C2×Q8—1222no—
164C2×Q8—1222no—
165C2×D4—1224no—
166C2×D4—1228no—
167C2×D4—1222no—
168C2×D4—1222no—
169C2×D4—1222no—
170C22×C4—612no—
171C22×C4—611no—
172C22×C4—614no—
173C22×C4—612no—
174C22×C4—1224no—
175C22×C4—1224no—
176C22×C4—1224no—
177C22×C4—1222no—
178C22×C4—1222no—
179C22×C4C22×D6112yes—
180C22×C4C22×D6112yes—
181C22×C4C22×D6112yes—
182C22×C4C22×D6111yescharacteristic
183C4⋊C4—22no—
184C4⋊C4—22no—
185C4⋊C4—1224no—
186C22⋊C4—1228no—
187C22⋊C4—1224no—
188C22⋊C4—1224no—
189C22⋊C4—1228no—
190C42—1224no—
191C42—1222no—
192C42D24414yescomplemented
193C23—612no—
194C23—614no—
195C23—1221no—
196C23—1222no—
197C23—1221no—
198C23—1222no—
199C23—1222no—
200C23—1224no—
201C23—1224no—
202C23—1222no—
203C23C23×D6111yescharacteristic
204Q8—2444no—
205D4—2448no—
206D4—2444no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—24no—
212C2×C4—24no—
213C2×C4—612no—
214C2×C4—614no—
215C2×C4—12216no—
216C2×C4—1221no—
217C2×C4—1222no—
218C2×C4—1222no—
219C2×C4—1221no—
220C2×C4—1228no—
221C2×C4—1222no—
222C2×C4—1222no—
223C2×C4—1222no—
224C2×C4C2×D24414yes—
225C2×C4C2×D24412yes—
226C2×C4D4×D6112yes—
227C2×C4#1175822612yes—
228C22—614no—
229C22—1222no—
230C22—1224no—
231C22—1224no—
232C22—1222no—
233C22—2442no—
234C22—2444no—
235C22—2442no—
236C22—2444no—
237C22—2442no—
238C22C2×D4×D6111yescharacteristic
239C22C22×D24411yescharacteristic
240C22#41×D6112yes—
241C22#41×D6112yes—
242C22C2×#1175822611yescharacteristic
243C4—24no—
244C4—42no—
245C4—42no—
246C4—1222no—
247C4—1224no—
248C4—2442no—
249C4#1451975214yes—
250C2—1224no—
251C2—4882no—
252C2C2×#1451975211yescharacteristic
253C2#1684027412yes—
254C2#124×D6111yescharacteristic
255C2#1684029712yes—
256C2#1684031111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#382C2
hypercenter#382D61
hypocenterC61#2850
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
1. C2×#14519765C2semidirect
2. C2×#14519757C2semidirect
4. C2×C42×D61C2semidirect
5. #16839667C2semidirect
6. #16839663C2semidirect
7. #16839654C2semidirect
8. #16839640C2semidirect
9. C61×#382C2semidirect
56. C42×C61D4semidirect
113. C2×D61#124semidirect
137. #382D61semidirect
138. C61#2850semidirect
192. C42D244semidirect