Finite Group Databasebeta

← #21450753

Subgroups — #21450753

Order 7808.

760 conjugacy classes of subgroups; only the 185 normal subgroups are shown.

normal subgroups only

This group has 760 conjugacy classes of subgroups — too many to draw. Only its 185 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×#14519757C212yesmaximal, complemented
3C2×#14519752C212yesmaximal, complemented
4C2×C4×D244C211yesmaximal, characteristic, complemented
5#16839699C212yesmaximal, complemented
6#16839672C212yesmaximal, complemented
7#16839664C214yesmaximal, complemented
8C4×C4⋊C4×C61C211yesmaximal, characteristic, complemented
9C22×Dic122C2211yescharacteristic
10C22×D244C2211yescharacteristic
11C22×D244C2211yescharacteristic
12C22×D244C2214yes—
13C22×C4×D61C2212yes—
14#14519765—24no—
15#14519757—28no—
16#14519752—28no—
17C4×D244—24no—
18C2×C4⋊Dic61C2211yescharacteristic
19C2×C4⋊Dic61C2214yes—
20C2×#11758198C2214yes—
21C2×#11758198C2212yes—
22C2×#11758198C2212yes—
23C2×#11758198C2214yes—
24C2×#11758198C2212yes—
25C2×C4⋊C4×C61C2212yes—
26C2×C42×C61C2212yes—
27C2×C42×C61C2211yescharacteristic
28#95×C61C2212yes—
29C23×D61C2312yes—
30C23×D61C2312yes—
31C22×C4×C61C2311yescharacteristic
32C22×C4×C61C2314yes—
33C22×C4×C61C2311yescharacteristic
34C22×C4×C61C2311yescharacteristic
35C22×Dic61C2312yes—
36C22×Dic61C2312yes—
37C2×D244—24no—
38C2×D244—22no—
39C2×D244—28no—
40C2×D244—28no—
41C2×D244—24no—
42C2×D244—22no—
43C2×D244—44no—
44C2×C4×D61—24no—
45C2×C4×D61—24no—
46C2×C4×D61—24no—
47C2×Dic122—24no—
48C2×Dic122—22no—
49C4⋊C4×C61D418yescomplemented
50C42×C61—42no—
51C42×C61D414yescomplemented
52#11758198—24no—
53#11758198—28no—
54#11758198—28no—
55#11758198—24no—
56#11758198—24no—
57C4⋊Dic61—22no—
58C4⋊Dic61—28no—
59C23×C61C2411yescharacteristic
60C22×D61—22no—
61C22×D61—22no—
62C22×D61—22no—
63C22×D61—22no—
64C22×D61—22no—
65C22×D61—22no—
66C22×D61—22no—
67C22×D61—24no—
68C22×D61—24no—
69C22×D61—22no—
70C22×D61—22no—
71C22×D61#4114yes—
72C2×C4×C61—22no—
73C2×C4×C61—24no—
74C2×C4×C61—21no—
75C2×C4×C61—24no—
76C2×C4×C61—21no—
77C2×C4×C61C2×D412yes—
78C2×C4×C61C2×D418yes—
79C2×C4×C61C2×D412yes—
80C2×C4×C61C2×D412yes—
81C2×C4×C61C2×D414yes—
82C2×Dic61—22no—
83C2×Dic61—24no—
84C2×Dic61—22no—
85C2×Dic61—22no—
86C2×Dic61—22no—
87D244—28no—
88D244—416no—
89D244—44no—
90C4×D61—48no—
91Dic122—44no—
92C22×C61C22×D411yescharacteristic
93C22×C61C22×D412yes—
94C22×C61C2×#4112yes—
95C22×C61H(5,𝔽2)11yescharacteristic
96C22×C612−1+411yescharacteristic
97C2×D61—24no—
98C2×D61—24no—
99C2×D61—24no—
100C2×D61—42no—
101C2×D61—42no—
102C2×D61—42no—
103C2×D61—42no—
104C2×D61—42no—
105C2×D61—42no—
106C2×D61—42no—
107C2×D61—44no—
108C2×D61—44no—
109C4×C61—22no—
110C4×C61—22no—
111C4×C61—28no—
112C4×C61#12714yes—
113Dic61—42no—
114Dic61—42no—
115#2540—611nomaximal, Sylow
116C2×C61#52511yescharacteristic
117C2×C61C2×#12711yescharacteristic
118C2×C61#53711yescharacteristic
119C2×C61#54612yes—
120C2×C61#54812yes—
121D61—44no—
122D61—82no—
123C2×#124—611no—
124C2×C22⋊Q8—612no—
125C2×#121—612no—
126C2×C4×D4—611no—
127#399—612no—
128#392—612no—
129#390—614no—
130C4×C4⋊C4D6111yescharacteristic, complemented
131C61#254011yescharacteristic, complemented, Sylow
132C22×Q8—611no—
133C22×D4—611no—
134C22×D4—611no—
135C22×D4—614no—
136C23×C4—612no—
137#124—1224no—
138C22⋊Q8—1228no—
139#121—1228no—
140C4×D4—1224no—
141C2×C4⋊C4—611no—
142C2×C4⋊C4—614no—
143C2×C4⋊C4C2×D6112yes—
144C2×C22⋊C4—612no—
145C2×C22⋊C4—614no—
146C2×C22⋊C4—614no—
147C2×C22⋊C4—612no—
148C2×C22⋊C4—612no—
149C2×C42C2×D6112yes—
150C2×C42C2×D6111yescharacteristic
151#95C2×D6112yes—
152C24—612no—
153C24—612no—
154C2×Q8—1224no—
155C2×Q8—1222no—
156C2×D4—1224no—
157C2×D4—1228no—
158C2×D4—1222no—
159C2×D4—1228no—
160C2×D4—1224no—
161C2×D4—1222no—
162C2×D4—2444no—
163C22×C4—612no—
164C22×C4—612no—
165C22×C4—1224no—
166C22×C4—1224no—
167C22×C4—1224no—
168C22×C4C22×D6111yescharacteristic
169C22×C4C22×D6114yes—
170C22×C4C22×D6111yescharacteristic
171C22×C4C22×D6111yescharacteristic
172C4⋊C4—1222no—
173C4⋊C4—1228no—
174C4⋊C4D24418yescomplemented
175C22⋊C4—1224no—
176C22⋊C4—1228no—
177C22⋊C4—1228no—
178C22⋊C4—1224no—
179C22⋊C4—1224no—
180C42—42no—
181C42D24414yescomplemented
182C23—614no—
183C23—1222no—
184C23—1222no—
185C23—1222no—
186C23—1222no—
187C23—1222no—
188C23—1222no—
189C23—1222no—
190C23—1224no—
191C23—1224no—
192C23—1222no—
193C23—1222no—
194C23C23×D6111yescharacteristic
195Q8—2444no—
196D4—1228no—
197D4—24416no—
198D4—2444no—
199C2×C4—22no—
200C2×C4—24no—
201C2×C4—21no—
202C2×C4—24no—
203C2×C4—21no—
204C2×C4—1222no—
205C2×C4—1222no—
206C2×C4—1222no—
207C2×C4—1224no—
208C2×C4—1222no—
209C2×C4—2448no—
210C2×C4C2×D24412yes—
211C2×C4C2×D24412yes—
212C2×C4C2×D24418yes—
213C2×C4C2×D24412yes—
214C2×C4C2×D24414yes—
215C22—1224no—
216C22—1224no—
217C22—1224no—
218C22—2442no—
219C22—2442no—
220C22—2442no—
221C22—2444no—
222C22—2444no—
223C22—2442no—
224C22—2442no—
225C22—2442no—
226C22—2442no—
227C22C22×D24411yescharacteristic
228C22C22×D24412yes—
229C22#41×D6112yes—
230C22#1451982211yescharacteristic
231C22#1451982511yescharacteristic
232C4—22no—
233C4—22no—
234C4—28no—
235C4—2442no—
236C4—2442no—
237C4#1451977414yes—
238C2—4882no—
239C2—2444no—
240C2#1684027411yescharacteristic
241C2C2×#1451977411yescharacteristic
242C2#1684034311yescharacteristic
243C2#1684040712yes—
244C2#1684042412yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC4×C4⋊C4×C61C2
hypercenterC4×C4⋊C4D61
hypocenterC61#2540
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#14519765C2semidirect
2. C2×#14519757C2semidirect
3. C2×#14519752C2semidirect
4. C2×C4×D244C2semidirect
5. #16839699C2semidirect
6. #16839672C2semidirect
7. #16839664C2semidirect
8. C4×C4⋊C4×C61C2semidirect
49. C4⋊C4×C61D4semidirect
51. C42×C61D4semidirect
130. C4×C4⋊C4D61semidirect
131. C61#2540semidirect
174. C4⋊C4D244semidirect
181. C42D244semidirect