Finite Group Databasebeta

← #21447255

Subgroups — #21447255

Order 7808.

256 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 83 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×#14519708C211yesmaximal, characteristic, complemented
2C2×C22⋊#92418C211yesmaximal, characteristic
3#16839622C211yesmaximal, characteristic
4#16839524C211yesmaximal, characteristic, complemented
5#16839524C211yesmaximal, characteristic, complemented
6#16839524C211yesmaximal, characteristic, complemented
7C61×#380C211yesmaximal, characteristic
8C22×#92418C2211yescharacteristic
9C22×#92418C2211yescharacteristic
10C2×C4⋊Dic61C2211yescharacteristic
11C2×C4⋊Dic61C2211yescharacteristic
12C2×C22⋊Dic61—21no—
13#14519708—22no—
14C22⋊#92418—22no—
15#14519684—21no—
16C23×C4×C61C2211yescharacteristic
17C2×C4⋊C4×C61C2211yescharacteristic
18C2×C4⋊C4×C61C2211yescharacteristic
19C2×C22⋊C4×C61—21no—
20#95×C61—21no—
21C24×C61D411yescharacteristic
22C22×C4×C61—21no—
23C22×C4×C61—21no—
24C22×C4×C61—21no—
25C22×C4×C61—21no—
26C22×C4×C61—21no—
27C22×C4×C61—21no—
28C22×C4×C61—21no—
29C22×C4×C61—21no—
30C22×C4×C61D411yescharacteristic
31C22×C4×C61C2311yescharacteristic
32C22×Dic61—21no—
33C22×Dic61—21no—
34C4⋊C4×C61—21no—
35C4⋊C4×C61—21no—
36C4⋊C4×C61—21no—
37C4⋊C4×C61—21no—
38C22⋊C4×C61—42no—
39C22⋊Dic61—42no—
40C4⋊Dic61—21no—
41C4⋊Dic61—21no—
42C4⋊Dic61—21no—
43C4⋊Dic61—21no—
44C2×#92418—21no—
45C2×#92418—21no—
46C2×#92418—21no—
47C2×#92418—21no—
48C2×#92418—21no—
49C2×#92418D412yes—
50C23×C61—21no—
51C23×C61—21no—
52C23×C61—21no—
53C23×C61—21no—
54C23×C61—21no—
55C23×C61—21no—
56C23×C61SD1612yes—
57C23×C61C2×D411yescharacteristic
58C2×C4×C61—21no—
59C2×C4×C61—21no—
60C2×C4×C61—21no—
61C2×C4×C61—41no—
62C2×C4×C61—41no—
63C2×C4×C61—41no—
64C2×C4×C61—41no—
65C2×C4×C61—41no—
66C2×C4×C61—41no—
67C2×C4×C61—41no—
68C2×C4×C61—41no—
69C2×C4×C61—41no—
70C2×C4×C61—41no—
71C2×C4×C61C2×D411yescharacteristic
72C2×C4×C61#4111yescharacteristic
73C2×C4×C61#4111yescharacteristic
74C2×C4×C61#4111yescharacteristic
75C2×C4×C61#4111yescharacteristic
76C2×C4×C61#4111yescharacteristic
77C2×Dic61—41no—
78C2×Dic61—41no—
79C2×Dic61—41no—
80C2×Dic61—41no—
81C2×Dic61—41no—
82C2×Dic61—41no—
83#92418—22no—
84#92418—41no—
85C22×C61—22no—
86C22×C61—22no—
87C22×C61—22no—
88C22×C61—41no—
89C22×C61—41no—
90C22×C61—41no—
91C22×C61—41no—
92C22×C61#12111yescharacteristic
93C22×C61#12311yescharacteristic
94C22×C61#12311yescharacteristic
95C22×C61C2×SD1611yescharacteristic
96C22×C61#13511yescharacteristic
97C22×C61AGL(1,ℤ/8)11yescharacteristic
98C22×C61#13711yescharacteristic
99C4×C61—41no—
100C4×C61—81no—
101C4×C61—81no—
102C4×C61#12311yescharacteristic
103C4×C61#12411yescharacteristic
104C4×C61#12611yescharacteristic
105C4×C61#12611yescharacteristic
106Dic61—81no—
107Dic61—81no—
108#2077—611nomaximal, Sylow
109C2×C61—42no—
110C2×C61#39711yescharacteristic
111C2×C61#46511yescharacteristic
112C2×C61#46811yescharacteristic
113C2×C61#48111yescharacteristic
114C2×C61#48211yescharacteristic
115C2×C61#48311yescharacteristic
116C2×C61#48511yescharacteristic
117C2×#106—611no—
118C2×C22⋊C8—611no—
119#380—611no—
120#380D6111yescharacteristic
121#340—611no—
122#340—611no—
123#340—611no—
124C61#207711yescharacteristic, complemented, Sylow
125C23×C4C2×D6111yescharacteristic
126C22×C8—611no—
127C22×C8—611no—
128C2×C4⋊C4—611no—
129C2×C4⋊C4—611no—
130C2×C4⋊C4C2×D6111yescharacteristic
131C2×C4⋊C4C2×D6111yescharacteristic
132C2×C22⋊C4—21no—
133C2×C22⋊C4—1221no—
134#106—1222no—
135C22⋊C8—1222no—
136#95—21no—
137#95—1221no—
138C24C22⋊D6111yescharacteristic
139C22×C4—21no—
140C22×C4—21no—
141C22×C4—21no—
142C22×C4—21no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—21no—
146C22×C4—21no—
147C22×C4—1221no—
148C22×C4—1221no—
149C22×C4C22⋊D6111yescharacteristic
150C22×C4C22×D6111yescharacteristic
151C2×C8—612no—
152C2×C8—1221no—
153C2×C8—1221no—
154C2×C8—1221no—
155C2×C8—1221no—
156C2×C8—1221no—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—1221no—
162C4⋊C4—1221no—
163C4⋊C4—1221no—
164C4⋊C4—1221no—
165C22⋊C4—42no—
166C22⋊C4—2442no—
167C23—21no—
168C23—21no—
169C23—21no—
170C23—21no—
171C23—21no—
172C23—21no—
173C23#1175820012yes—
174C23C2×C22⋊D6111yescharacteristic
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—2441no—
189C2×C4—2441no—
190C2×C4—2441no—
191C2×C4—2441no—
192C2×C4—2441no—
193C2×C4—2441no—
194C2×C4#1175822211yescharacteristic
195C2×C4#1175822211yescharacteristic
196C2×C4D4×D6111yescharacteristic
197C2×C4#1175822411yescharacteristic
198C2×C4#1175822411yescharacteristic
199C2×C4#1175822411yescharacteristic
200C8—1222no—
201C8—2441no—
202C22—22no—
203C22—22no—
204C22—22no—
205C22—41no—
206C22—41no—
207C22—41no—
208C22—41no—
209C22#1451974911yescharacteristic
210C22#1451975811yescharacteristic
211C22#1451976011yescharacteristic
212C22C2×#1175820011yescharacteristic
213C22#1451979711yescharacteristic
214C22#1451980211yescharacteristic
215C22#1451980811yescharacteristic
216C4—41no—
217C4—81no—
218C4—81no—
219C4—4881no—
220C4—4881no—
221C4#1451975911yescharacteristic
222C4#1451976311yescharacteristic
223C4#1451977011yescharacteristic
224C4#1451977011yescharacteristic
225C2—42no—
226C2#1683969011yescharacteristic
227C2#1683998911yescharacteristic
228C2#1684001011yescharacteristic
229C2#1684007811yescharacteristic
230C2#1684008611yescharacteristic
231C2#1684009211yescharacteristic
232C2#1684010011yescharacteristic
subgroupG/H
centerC23C2×C22⋊D61
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#380C2
socleC23×C61C2×D4
hypercenter#380D61
hypocenterC61#2077
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
1. C2×#14519708C2semidirect
4. #16839524C2semidirect
5. #16839524C2semidirect
6. #16839524C2semidirect
124. C61#2077semidirect