Finite Group Databasebeta

← #21450758

Subgroups — #21450758

Order 7808.

760 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 760 conjugacy classes of subgroups — too many to draw. Only its 173 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×#14519756C212yesmaximal, complemented
3C2×#14519751C212yesmaximal, complemented
4#16839697C212yesmaximal, complemented
5#16839670C212yesmaximal, complemented
6#16839662C214yesmaximal, complemented
7C4×C4⋊Dic61C211yesmaximal, characteristic, complemented
8C2×C4×D4×C61C211yesmaximal, characteristic, complemented
9C22×Dic122C2211yescharacteristic
10C22×D244C2211yescharacteristic
11C22×C22⋊D61C2214yes—
12#14519765—24no—
13#14519756—28no—
14#14519751—28no—
15C2×C4⋊Dic61C2212yes—
16C2×#11758196C2214yes—
17C2×C22⋊Dic61C2214yes—
18C2×#11758198C2214yes—
19C2×#11758198C2212yes—
20C2×#11758198C2212yes—
21C2×C4×Dic61C2212yes—
22#14519684C2212yes—
23C22×D4×C61C2211yescharacteristic
24C23×C4×C61C2212yes—
25C4×D4×C61—24no—
26C2×C4⋊C4×C61C2211yescharacteristic
27C2×C22⋊C4×C61C2212yes—
28C2×C42×C61C2211yescharacteristic
29C24×C61C2312yes—
30C23×D61C2312yes—
31C2×D4×C61—24no—
32C2×D4×C61—22no—
33C22×C4×C61—24no—
34C22×C4×C61—24no—
35C22×C4×C61—24no—
36C22×C4×C61C2312yes—
37C22×C4×C61C2311yescharacteristic
38C22×C4×C61C2311yescharacteristic
39C22×C4×C61C2311yescharacteristic
40C2×C22⋊D61—28no—
41C2×C22⋊D61—28no—
42C2×C22⋊D61—44no—
43C22×Dic61C2312yes—
44C22×Dic61C2314yes—
45C2×D244—24no—
46C2×D244—22no—
47C2×Dic122—24no—
48C2×Dic122—22no—
49C4⋊C4×C61—22no—
50C22⋊C4×C61—24no—
51C42×C61D414yescomplemented
52C22⋊Dic61—28no—
53#11758198—24no—
54#11758198—24no—
55#11758198—28no—
56C4⋊Dic61D418yescomplemented
57#11758196—28no—
58C4×Dic61—42no—
59C23×C61—22no—
60C23×C61—22no—
61C23×C61—22no—
62C23×C61—22no—
63C23×C61—22no—
64C23×C61—22no—
65C23×C61#4114yes—
66C23×C61C2411yescharacteristic
67C22×D61—22no—
68C22×D61—24no—
69C22×D61—24no—
70C22×D61—22no—
71C22×D61—22no—
72D4×C61—28no—
73C2×C4×C61—22no—
74C2×C4×C61—21no—
75C2×C4×C61—21no—
76C2×C4×C61—22no—
77C2×C4×C61—22no—
78C2×C4×C61—22no—
79C2×C4×C61—48no—
80C2×C4×C61C2×D412yes—
81C2×C4×C61C2×D412yes—
82C2×C4×C61C2×D414yes—
83C2×C4×C61C2×D412yes—
84C22⋊D61—416no—
85C2×Dic61—24no—
86C2×Dic61—24no—
87C2×Dic61—24no—
88C2×Dic61—22no—
89C2×Dic61C2×D418yes—
90D244—44no—
91Dic122—44no—
92C22×C61—24no—
93C22×C61—24no—
94C22×C61—24no—
95C22×C61—42no—
96C22×C61—42no—
97C22×C61—42no—
98C22×C61—42no—
99C22×C61C22×D412yes—
100C22×C61C22×D411yescharacteristic
101C22×C61C2×#4112yes—
102C22×C61H(5,𝔽2)11yescharacteristic
103C22×C612−1+411yescharacteristic
104C2×D61—42no—
105C2×D61—42no—
106C2×D61—42no—
107C2×D61—44no—
108C2×D61—44no—
109C4×C61—22no—
110C4×C61—22no—
111C4×C61—42no—
112C4×C61#12714yes—
113Dic61—28no—
114Dic61—42no—
115#2540—611nomaximal, Sylow
116C2×C61—44no—
117C2×C61#52511yescharacteristic
118C2×C61C2×#12711yescharacteristic
119C2×C61#53711yescharacteristic
120C2×C61#54612yes—
121C2×C61#54812yes—
122D61—82no—
123C2×#124—611no—
124C2×C22⋊Q8—612no—
125C2×#121—612no—
126C2×C4×D4D6111yescharacteristic, complemented
127#399—612no—
128#392—612no—
129#390—614no—
130C4×C4⋊C4—611no—
131C61#254011yescharacteristic, complemented, Sylow
132C22×Q8—611no—
133C22×D4—614no—
134C22×D4—611no—
135C22×D4C2×D6111yescharacteristic
136C23×C4C2×D6112yes—
137#124—1224no—
138C22⋊Q8—1228no—
139#121—1228no—
140C4×D4—24no—
141C2×C4⋊C4—612no—
142C2×C4⋊C4—614no—
143C2×C4⋊C4C2×D6111yescharacteristic
144C2×C22⋊C4—614no—
145C2×C22⋊C4—614no—
146C2×C22⋊C4—612no—
147C2×C22⋊C4—612no—
148C2×C22⋊C4C2×D6112yes—
149C2×C42—612no—
150C2×C42C2×D6111yescharacteristic
151#95—612no—
152C24—612no—
153C24C22×D6112yes—
154C2×Q8—1224no—
155C2×Q8—1222no—
156C2×D4—24no—
157C2×D4—22no—
158C2×D4—1228no—
159C2×D4—1228no—
160C2×D4—1224no—
161C2×D4—1222no—
162C2×D4—2444no—
163C22×C4—24no—
164C22×C4—24no—
165C22×C4—24no—
166C22×C4—614no—
167C22×C4—612no—
168C22×C4C22×D6112yes—
169C22×C4C22×D6111yescharacteristic
170C22×C4C22×D6111yescharacteristic
171C22×C4C22×D6111yescharacteristic
172C4⋊C4—22no—
173C4⋊C4—618no—
174C4⋊C4—1228no—
175C22⋊C4—24no—
176C22⋊C4—1228no—
177C22⋊C4—1228no—
178C22⋊C4—1224no—
179C22⋊C4—1224no—
180C42—2442no—
181C42C22⋊D6114yescomplemented
182C23—22no—
183C23—22no—
184C23—22no—
185C23—22no—
186C23—22no—
187C23—22no—
188C23—1224no—
189C23—1222no—
190C23—1224no—
191C23—1222no—
192C23—1222no—
193C23#1175822214yes—
194C23C23×D6111yescharacteristic
195Q8—2444no—
196D4—28no—
197D4—24416no—
198D4—2444no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—48no—
206C2×C4—618no—
207C2×C4—1224no—
208C2×C4—1224no—
209C2×C4—1224no—
210C2×C4—1222no—
211C2×C4D4×D6114yes—
212C2×C4C2×C22⋊D6112yes—
213C2×C4C2×C22⋊D6112yes—
214C2×C4C2×C22⋊D6112yes—
215C22—24no—
216C22—24no—
217C22—24no—
218C22—42no—
219C22—42no—
220C22—42no—
221C22—42no—
222C22—2442no—
223C22—2442no—
224C22—2442no—
225C22—2444no—
226C22—2444no—
227C22C2×D4×D6112yes—
228C22C22×C22⋊D6111yescharacteristic
229C22C2×#1175822212yes—
230C22#1451982311yescharacteristic
231C22#1451982411yescharacteristic
232C4—22no—
233C4—22no—
234C4—42no—
235C4—1228no—
236C4—2442no—
237C4#1451977314yes—
238C2—44no—
239C2—4882no—
240C2#1684027311yescharacteristic
241C2C2×#1451977311yescharacteristic
242C2#1684034011yescharacteristic
243C2#1684040812yes—
244C2#1684042112yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×C4×D4×C61C2
hypercenterC2×C4×D4D61
hypocenterC61#2540
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#14519765C2semidirect
2. C2×#14519756C2semidirect
3. C2×#14519751C2semidirect
4. #16839697C2semidirect
5. #16839670C2semidirect
6. #16839662C2semidirect
7. C4×C4⋊Dic61C2semidirect
8. C2×C4×D4×C61C2semidirect
51. C42×C61D4semidirect
56. C4⋊Dic61D4semidirect
126. C2×C4×D4D61semidirect
131. C61#2540semidirect
181. C42C22⋊D61semidirect