Finite Group Databasebeta

← #21451671

Subgroups — #21451671

Order 7808.

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

normal subgroups only

This group has 628 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×#14519765C211yesmaximal, characteristic, complemented
2#16839688C212yesmaximal, complemented
3#16839674C212yesmaximal, complemented
4#16839671C212yesmaximal, complemented
5#16839670C212yesmaximal, complemented
6#16839641C214yesmaximal, complemented
7#16839630C211yesmaximal, characteristic, complemented
8C2×C4×D4×C61C211yesmaximal, characteristic, complemented
9C22×Dic122C2211yescharacteristic
10C22×D244C2211yescharacteristic
11C22×C22⋊D61C2214yes—
12#14519765—24no—
13C2×C22⋊Dic61C2214yes—
14C2×#11758198C2212yes—
15C2×#11758198C2212yes—
16C2×#11758198C2214yes—
17#14519684C2212yes—
18#14519684C2214yes—
19#14519684C2212yes—
20#14519684C2212yes—
21C22×D4×C61C2211yescharacteristic
22C23×C4×C61C2212yes—
23C4×D4×C61—24no—
24C2×C4⋊C4×C61C2211yescharacteristic
25C2×C22⋊C4×C61C2212yes—
26C2×C42×C61C2211yescharacteristic
27C24×C61C2312yes—
28C23×D61C2312yes—
29C2×D4×C61—24no—
30C2×D4×C61—22no—
31C22×C4×C61—24no—
32C22×C4×C61—44no—
33C22×C4×C61C2312yes—
34C22×C4×C61C2311yescharacteristic
35C22×C4×C61C2311yescharacteristic
36C22×C4×C61C2311yescharacteristic
37C2×C22⋊D61—28no—
38C2×C22⋊D61—44no—
39C2×C22⋊D61—44no—
40C22×Dic61C2314yes—
41C22×Dic61C2312yes—
42C2×D244—22no—
43C2×D244—42no—
44C2×Dic122—22no—
45C2×Dic122—42no—
46C4⋊C4×C61—22no—
47C22⋊C4×C61—24no—
48C42×C61D414yescomplemented
49C22⋊Dic61—44no—
50#11758198—24no—
51#11758198—24no—
52#11758198—44no—
53C23×C61—22no—
54C23×C61—22no—
55C23×C61—24no—
56C23×C61—24no—
57C23×C61#4114yes—
58C23×C61C2411yescharacteristic
59C22×D61—22no—
60C22×D61—24no—
61C22×D61—22no—
62C22×D61—24no—
63C22×D61—22no—
64D4×C61—28no—
65C2×C4×C61—22no—
66C2×C4×C61—22no—
67C2×C4×C61—22no—
68C2×C4×C61—22no—
69C2×C4×C61—24no—
70C2×C4×C61—48no—
71C2×C4×C61C2×D412yes—
72C2×C4×C61C2×D412yes—
73C2×C4×C61C2×D412yes—
74C22⋊D61—416no—
75C2×Dic61—22no—
76C2×Dic61—24no—
77C2×Dic61—24no—
78C2×Dic61—24no—
79C2×Dic61—24no—
80D244—44no—
81Dic122—44no—
82C22×C61—24no—
83C22×C61—28no—
84C22×C61—42no—
85C22×C61—42no—
86C22×C61—44no—
87C22×C61C22×D411yescharacteristic
88C22×C61C2×#4112yes—
89C22×C61H(5,𝔽2)12yes—
90C22×C61H(5,𝔽2)12yes—
91C2×D61—42no—
92C2×D61—42no—
93C2×D61—42no—
94C2×D61—44no—
95C2×D61—44no—
96C4×C61—22no—
97C4×C61—22no—
98C4×C61—22no—
99C4×C61—42no—
100Dic61—42no—
101Dic61—44no—
102#2631—611nomaximal, Sylow
103C2×C61—44no—
104C2×C61#52511yescharacteristic
105C2×C61#53511yescharacteristic
106C2×C61#53511yescharacteristic
107C2×C61#53814yes—
108D61—82no—
109C2×#124—611no—
110C2×C4×D4D6111yescharacteristic, complemented
111#397—612no—
112#393—612no—
113#392—612no—
114#392—612no—
115#386—614no—
116#383—611no—
117C61#263111yescharacteristic, complemented, Sylow
118C22×Q8—611no—
119C22×D4—614no—
120C22×D4—611no—
121C22×D4C2×D6111yescharacteristic
122C23×C4C2×D6112yes—
123#124—1224no—
124C4×D4—24no—
125C2×C4⋊C4C2×D6111yescharacteristic
126C2×C22⋊C4—612no—
127C2×C22⋊C4—612no—
128C2×C22⋊C4—614no—
129C2×C22⋊C4—614no—
130C2×C22⋊C4C2×D6112yes—
131C2×C42C2×D6111yescharacteristic
132#95—612no—
133#95—612no—
134#95—612no—
135#95—614no—
136C24—612no—
137C24C22×D6112yes—
138C2×Q8—1222no—
139C2×Q8—2442no—
140C2×D4—24no—
141C2×D4—22no—
142C2×D4—1228no—
143C2×D4—1222no—
144C2×D4—2442no—
145C2×D4—2444no—
146C2×D4—2444no—
147C22×C4—24no—
148C22×C4—44no—
149C22×C4—614no—
150C22×C4—612no—
151C22×C4C22×D6112yes—
152C22×C4C22×D6111yescharacteristic
153C22×C4C22×D6111yescharacteristic
154C22×C4C22×D6111yescharacteristic
155C4⋊C4—22no—
156C22⋊C4—24no—
157C22⋊C4—1224no—
158C22⋊C4—1224no—
159C22⋊C4—2444no—
160C22⋊C4—2444no—
161C42C22⋊D6114yescomplemented
162C23—22no—
163C23—22no—
164C23—24no—
165C23—24no—
166C23—1222no—
167C23—1224no—
168C23—1222no—
169C23—1222no—
170C23—1224no—
171C23#1175822214yes—
172C23C23×D6111yescharacteristic
173Q8—2444no—
174D4—28no—
175D4—2444no—
176D4—24416no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—24no—
182C2×C4—48no—
183C2×C4—1222no—
184C2×C4—1224no—
185C2×C4—1224no—
186C2×C4—1224no—
187C2×C4—1224no—
188C2×C4C2×C22⋊D6112yes—
189C2×C4C2×C22⋊D6112yes—
190C2×C4C2×C22⋊D6112yes—
191C22—24no—
192C22—28no—
193C22—42no—
194C22—42no—
195C22—44no—
196C22—2442no—
197C22—2442no—
198C22—2442no—
199C22—2444no—
200C22—2444no—
201C22C22×C22⋊D6111yescharacteristic
202C22C2×#1175822212yes—
203C22#1451982212yes—
204C22#1451982312yes—
205C4—22no—
206C4—22no—
207C4—22no—
208C4—42no—
209C4—2442no—
210C4—2444no—
211C2—44no—
212C2—4882no—
213C2#1684027311yescharacteristic
214C2#1684032611yescharacteristic
215C2#1684032911yescharacteristic
216C2#1684034514yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×C4×D4×C61C2
hypercenterC2×C4×D4D61
hypocenterC61#2631
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. #16839688C2semidirect
3. #16839674C2semidirect
4. #16839671C2semidirect
5. #16839670C2semidirect
6. #16839641C2semidirect
7. #16839630C2semidirect
8. C2×C4×D4×C61C2semidirect
48. C42×C61D4semidirect
110. C2×C4×D4D61semidirect
117. C61#2631semidirect
161. C42C22⋊D61semidirect