Finite Group Databasebeta

← #21444739

Subgroups — #21444739

Order 7808.

368 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 53 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
1#16840324C211yesmaximal, characteristic, complemented
2#16839898C212yesmaximal, complemented
3#16839671C211yesmaximal, characteristic, complemented
4#16839497C212yesmaximal, complemented
5C61×#323C211yesmaximal, characteristic, complemented
6C22×D244C2211yescharacteristic, complemented
7C22×C22⋊D61—21no—
8C22×C22⋊D61—21no—
9C2×D488—22no—
10#14519761—22no—
11#14519751—21no—
12#14519751C2212yes—
13#14519747—22no—
14C2×#11758198—21no—
15#14519699—22no—
16#14519684C2211yescharacteristic, complemented
17C2×C22⋊C4×C61C2211yescharacteristic
18C22⋊C8×C61C2212yescomplemented
19C24×C61D411yescharacteristic
20C23×D61—21no—
21C23×D61—21no—
22C22×C4×C61D411yescharacteristic
23C22×C4×C61C2311yescharacteristic
24C2×C22⋊D61—22no—
25C2×C22⋊D61—22no—
26C2×C22⋊D61—42no—
27C2×C22⋊D61—42no—
28C2×C22⋊D61—42no—
29C2×C22⋊D61—42no—
30C2×C22⋊D61—42no—
31C22×Dic61—21no—
32C22×Dic61—21no—
33C2×D244—22no—
34C2×D244—21no—
35C2×D244—42no—
36C2×D244D412yescomplemented
37C2×C8×C61—22no—
38C22⋊C4×C61—22no—
39#11758198—22no—
40#11758198—22no—
41#11758198—42no—
42C4⋊Dic61—21no—
43C4⋊Dic61D412yescomplemented
44D488—44no—
45C23×C61—21no—
46C23×C61—21no—
47C23×C61—41no—
48C23×C61—41no—
49C23×C61D812yescomplemented
50C23×C61C2×D411yescharacteristic
51C22×D61—22no—
52C22×D61—22no—
53C22×D61—41no—
54C22×D61—41no—
55C22×D61—41no—
56C22×D61—42no—
57C22×D61—41no—
58C22×D61—41no—
59C22×D61—41no—
60C22×D61—81no—
61C22×D61—81no—
62C2×C4×C61—21no—
63C2×C4×C61—41no—
64C2×C4×C61—41no—
65C2×C4×C61C2×D412yes—
66C22⋊D61—44no—
67C22⋊D61—48no—
68C22⋊D61—42no—
69C22⋊D61—42no—
70C2×Dic61—22no—
71C2×Dic61—22no—
72C2×Dic61—41no—
73C2×Dic61—42no—
74C2×Dic61—41no—
75D244—24no—
76D244—42no—
77D244—42no—
78D244—81no—
79C8×C61—42no—
80C22×C61—21no—
81C22×C61—21no—
82C22×C61—22no—
83C22×C61—42no—
84C22×C61—41no—
85C22×C61—41no—
86C22×C61—81no—
87C22×C61#12011yescharacteristic
88C22×C61C2×D811yescharacteristic
89C22×C61AGL(1,ℤ/8)11yescharacteristic
90C2×D61—42no—
91C2×D61—42no—
92C2×D61—42no—
93C2×D61—42no—
94C2×D61—42no—
95C2×D61—42no—
96C2×D61—81no—
97C2×D61—81no—
98C2×D61—84no—
99C2×D61—81no—
100C2×D61—81no—
101C4×C61—22no—
102C4×C61—41no—
103Dic61—42no—
104Dic61—42no—
105#1595—611nomaximal, Sylow
106C2×C61—21no—
107C2×C61—21no—
108C2×C61—42no—
109C2×C61#44711yescharacteristic
110C2×C61#45311yescharacteristic
111C2×C61B(4,𝔽2)11yescharacteristic
112D61—82no—
113D61—82no—
114#534—611no—
115#447—612no—
116#392—611no—
117#327—612no—
118#323D6111yescharacteristic, complemented
119C61#159511yescharacteristic, complemented, Sylow
120C22×D4—611no—
121C22×D4—1221no—
122C22×D4—1221no—
123C2×D8—1222no—
124#123—1222no—
125#121—612no—
126#121—1221no—
127#120—1222no—
128C2×C22⋊C4—1221no—
129C2×C22⋊C4C2×D6111yescharacteristic
130#102—1222no—
131C22⋊C8C2×D6112yescomplemented
132#95—611no—
133C24—1221no—
134C24—1221no—
135C24D24411yescharacteristic
136C2×D4—612no—
137C2×D4—1221no—
138C2×D4—1222no—
139C2×D4—1222no—
140C2×D4—1222no—
141C2×D4—2442no—
142C2×D4—2442no—
143C2×D4—2442no—
144C2×D4—2442no—
145C2×D4—2442no—
146C2×D4—2442no—
147C22×C4—1221no—
148C22×C4—1221no—
149C22×C4D24411yescharacteristic
150C22×C4C22×D6111yescharacteristic
151D8—2444no—
152C2×C8—22no—
153C4⋊C4—612no—
154C4⋊C4—1221no—
155C22⋊C4—22no—
156C22⋊C4—1222no—
157C22⋊C4—1222no—
158C22⋊C4—2442no—
159C23—21no—
160C23—21no—
161C23—41no—
162C23—41no—
163C23—1222no—
164C23—1222no—
165C23—4881no—
166C23—4881no—
167C23—2441no—
168C23—2441no—
169C23—2441no—
170C23—2442no—
171C23—2441no—
172C23—2441no—
173C23—2441no—
174C23D48812yescomplemented
175C23C2×D24411yescharacteristic
176D4—1224no—
177D4—4881no—
178D4—2442no—
179D4—2442no—
180D4—2444no—
181D4—2448no—
182D4—2442no—
183D4—2442no—
184C2×C4—21no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—1222no—
188C2×C4—1222no—
189C2×C4—2441no—
190C2×C4—2442no—
191C2×C4—2441no—
192C2×C4D4×D6112yes—
193C8—42no—
194C22—21no—
195C22—21no—
196C22—22no—
197C22—42no—
198C22—41no—
199C22—41no—
200C22—81no—
201C22—4881no—
202C22—4881no—
203C22—4884no—
204C22—4881no—
205C22—4881no—
206C22—2442no—
207C22—2442no—
208C22—2442no—
209C22—2442no—
210C22—2442no—
211C22—2442no—
212C22#1451974711yescharacteristic
213C22C2×D48811yescharacteristic
214C22#1451980511yescharacteristic
215C4—22no—
216C4—41no—
217C4—2442no—
218C4—2442no—
219C2—21no—
220C2—21no—
221C2—42no—
222C2—4882no—
223C2—4882no—
224C2#1683989811yescharacteristic
225C2#1683993211yescharacteristic
226C2#1683995011yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#323C2
socleC22×C61#120
hypercenter#323D61
hypocenterC61#1595
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
1. #16840324C2semidirect
2. #16839898C2semidirect
3. #16839671C2semidirect
4. #16839497C2semidirect
5. C61×#323C2semidirect
6. C22×D244C22semidirect
16. #14519684C22semidirect
18. C22⋊C8×C61C22semidirect
36. C2×D244D4semidirect
43. C4⋊Dic61D4semidirect
49. C23×C61D8semidirect
118. #323D61semidirect
119. C61#1595semidirect
131. C22⋊C8C2×D61semidirect
174. C23D488semidirect