Finite Group Databasebeta

← #21451406

Subgroups — #21451406

Order 7808.

604 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 141 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×C4×C22⋊D61C212yesmaximal, complemented
2#16839687C211yesmaximal, characteristic, complemented
3#16839678C212yesmaximal, complemented
4#16839671C211yesmaximal, characteristic
5#16839654C212yesmaximal, complemented
6#16839647C212yesmaximal, complemented
7#16839640C212yesmaximal, complemented
8#16839636C212yesmaximal, complemented
9C61×#381C211yesmaximal, characteristic, complemented
10C22×D244C2211yescharacteristic
11C22×C22⋊D61C2212yes—
12C22×C4×D61C2212yes—
13C4×C22⋊D61—28no—
14C2×C4⋊Dic61C2212yes—
15C2×C4⋊Dic61C2211yescharacteristic
16C2×#11758196C2212yes—
17C2×C22⋊Dic61C2212yes—
18C2×#11758198C2212yes—
19C2×#11758198C2212yes—
20C2×#11758198C2212yes—
21C2×#11758198C2212yes—
22C2×C4×Dic61C2212yes—
23#14519684C2212yes—
24#14519684C2211yescharacteristic
25#14519684C2212yes—
26#14519684C2211yescharacteristic
27C23×C4×C61C2211yescharacteristic
28C2×C22⋊C4×C61C2211yescharacteristic
29C2×C22⋊C4×C61C2211yescharacteristic
30#95×C61C2212yes—
31#95×C61C2212yes—
32C24×C61C2311yescharacteristic
33C23×D61C2312yes—
34C22×C4×C61—41no—
35C22×C4×C61—41no—
36C22×C4×C61D414yescomplemented
37C22×C4×C61C2311yescharacteristic
38C22×C4×C61C2312yes—
39C22×C4×C61C2311yescharacteristic
40C22×C4×C61C2312yes—
41C2×C22⋊D61—24no—
42C2×C22⋊D61—24no—
43C2×C22⋊D61—24no—
44C22×Dic61C2312yes—
45C22×Dic61C2312yes—
46C22×Dic61C2312yes—
47C2×D244—24no—
48C2×D244—41no—
49C2×C4×D61—24no—
50C2×C4×D61—42no—
51C2×C4×D61—42no—
52C22⋊C4×C61—41no—
53C22⋊C4×C61—41no—
54C22⋊Dic61—24no—
55#11758198—24no—
56#11758198—24no—
57#11758198—24no—
58#11758198—42no—
59C4⋊Dic61—24no—
60C4⋊Dic61—41no—
61#11758196—24no—
62C4×Dic61—24no—
63C23×C61—22no—
64C23×C61—22no—
65C23×C61—21no—
66C23×C61—21no—
67C23×C61C2×D412yes—
68C23×C61C2411yescharacteristic
69C22×D61—22no—
70C22×D61—22no—
71C22×D61—22no—
72C22×D61—22no—
73C22×D61—22no—
74C22×D61—22no—
75C22×D61#4114yes—
76C2×C4×C61—22no—
77C2×C4×C61—22no—
78C2×C4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61—22no—
81C2×C4×C61—22no—
82C2×C4×C61—21no—
83C2×C4×C61—22no—
84C2×C4×C61—21no—
85C2×C4×C61—44no—
86C2×C4×C61C2×D414yes—
87C22⋊D61—216no—
88C2×Dic61—22no—
89C2×Dic61—22no—
90C2×Dic61—22no—
91C2×Dic61—22no—
92C2×Dic61—22no—
93C2×Dic61—22no—
94C2×Dic61—22no—
95C2×Dic61—22no—
96C2×Dic61#4114yes—
97D244—44no—
98C4×D61—48no—
99C22×C61—24no—
100C22×C61—22no—
101C22×C61—41no—
102C22×C61—42no—
103C22×C61—41no—
104C22×C61C22×D411yescharacteristic
105C22×C61C2×#4112yes—
106C22×C61C2×#4112yes—
107C22×C61H(5,𝔽2)11yescharacteristic
108C22×C61H(5,𝔽2)11yescharacteristic
109C2×D61—24no—
110C2×D61—24no—
111C2×D61—24no—
112C2×D61—42no—
113C2×D61—42no—
114C2×D61—42no—
115C2×D61—42no—
116C4×C61—24no—
117C4×C61—41no—
118C4×C61—42no—
119C4×C61—41no—
120Dic61—24no—
121Dic61—42no—
122Dic61—42no—
123#2600—611nomaximal, Sylow
124C2×C61—42no—
125C2×C61#52512yes—
126C2×C61#53411yescharacteristic
127C2×C61#55111yescharacteristic
128C2×C61#55312yes—
129C2×C61#55911yescharacteristic
130D61—44no—
131C2×C4×D4—612no—
132#397—611no—
133#394—612no—
134#392—611no—
135#388—612no—
136#387—612no—
137#386—612no—
138#385—612no—
139#381D6111yescharacteristic, complemented
140C61#260011yescharacteristic, complemented, Sylow
141C22×D4—612no—
142C22×D4—611no—
143C23×C4—612no—
144C23×C4C2×D6111yescharacteristic
145C4×D4—1228no—
146C2×C4⋊C4—612no—
147C2×C4⋊C4—612no—
148C2×C4⋊C4—611no—
149C2×C22⋊C4—612no—
150C2×C22⋊C4—612no—
151C2×C22⋊C4—612no—
152C2×C22⋊C4—612no—
153C2×C22⋊C4—612no—
154C2×C22⋊C4C2×D6111yescharacteristic
155C2×C22⋊C4C2×D6111yescharacteristic
156C2×C42—612no—
157#95—612no—
158#95—612no—
159#95—611no—
160#95—611no—
161#95C2×D6112yes—
162#95C2×D6112yes—
163C24—612no—
164C24C22×D6111yescharacteristic
165C2×D4—1224no—
166C2×D4—1224no—
167C2×D4—1224no—
168C2×D4—1224no—
169C2×D4—2441no—
170C22×C4—41no—
171C22×C4—41no—
172C22×C4—612no—
173C22×C4—612no—
174C22×C4—612no—
175C22×C4—1224no—
176C22×C4—2442no—
177C22×C4—2442no—
178C22×C4D24414yescomplemented
179C22×C4C22×D6111yescharacteristic
180C22×C4C22×D6111yescharacteristic
181C22×C4C22×D6112yes—
182C22×C4C22×D6112yes—
183C4⋊C4—1224no—
184C4⋊C4—1224no—
185C4⋊C4—2441no—
186C22⋊C4—41no—
187C22⋊C4—41no—
188C22⋊C4—1224no—
189C22⋊C4—1224no—
190C22⋊C4—1224no—
191C22⋊C4—1224no—
192C22⋊C4—2442no—
193C42—1224no—
194C23—22no—
195C23—22no—
196C23—21no—
197C23—21no—
198C23—614no—
199C23—1222no—
200C23—1222no—
201C23—1222no—
202C23—1222no—
203C23—1222no—
204C23—1222no—
205C23C2×D24412yes—
206C23C23×D6111yescharacteristic
207D4—12216no—
208D4—2444no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—44no—
219C2×C4—614no—
220C2×C4—1222no—
221C2×C4—1222no—
222C2×C4—1222no—
223C2×C4—1222no—
224C2×C4—1222no—
225C2×C4—1222no—
226C2×C4—1222no—
227C2×C4—1222no—
228C2×C4—2448no—
229C2×C4C2×D24414yes—
230C22—24no—
231C22—22no—
232C22—42no—
233C22—41no—
234C22—41no—
235C22—1224no—
236C22—1224no—
237C22—1224no—
238C22—2442no—
239C22—2442no—
240C22—2442no—
241C22—2442no—
242C22C22×D24411yescharacteristic
243C22#41×D6112yes—
244C22#41×D6112yes—
245C22#1451982211yescharacteristic
246C22#1451982211yescharacteristic
247C4—24no—
248C4—42no—
249C4—41no—
250C4—41no—
251C4—1224no—
252C4—2442no—
253C4—2442no—
254C2—42no—
255C2—2444no—
256C2#1684027412yes—
257C2#1684032411yescharacteristic
258C2#1684044011yescharacteristic
259C2#1684045712yes—
260C2#1684049611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#381C2
hypercenter#381D61
hypocenterC61#2600
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
1. C2×C4×C22⋊D61C2semidirect
2. #16839687C2semidirect
3. #16839678C2semidirect
5. #16839654C2semidirect
6. #16839647C2semidirect
7. #16839640C2semidirect
8. #16839636C2semidirect
9. C61×#381C2semidirect
36. C22×C4×C61D4semidirect
139. #381D61semidirect
140. C61#2600semidirect
178. C22×C4D244semidirect