Finite Group Databasebeta

← #22611367

Subgroups — #22611367

Order 9344.

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×#14556522C211yesmaximal, characteristic, complemented
2C2×C22⋊#10596831C211yesmaximal, characteristic
3#17988447C211yesmaximal, characteristic
4#17988349C211yesmaximal, characteristic, complemented
5#17988349C211yesmaximal, characteristic, complemented
6#17988349C211yesmaximal, characteristic, complemented
7#380×C73C211yesmaximal, characteristic
8C22×#10596831C2211yescharacteristic
9C22×#10596831C2211yescharacteristic
10C2×C4⋊Dic73C2211yescharacteristic
11C2×C4⋊Dic73C2211yescharacteristic
12C2×C22⋊Dic73—21no—
13#14556522—22no—
14C22⋊#10596831—22no—
15#14556498—21no—
16C23×C4×C73C2211yescharacteristic
17C2×C4⋊C4×C73C2211yescharacteristic
18C2×C4⋊C4×C73C2211yescharacteristic
19C2×C22⋊C4×C73—21no—
20#95×C73—21no—
21C22×Dic73—21no—
22C22×Dic73—21no—
23C2×#10596831—21no—
24C2×#10596831—21no—
25C2×#10596831—21no—
26C2×#10596831—21no—
27C2×#10596831—21no—
28C2×#10596831D412yes—
29C4⋊Dic73—21no—
30C4⋊Dic73—21no—
31C4⋊Dic73—21no—
32C4⋊Dic73—21no—
33C22⋊Dic73—42no—
34C24×C73D411yescharacteristic
35C22×C4×C73—21no—
36C22×C4×C73—21no—
37C22×C4×C73—21no—
38C22×C4×C73—21no—
39C22×C4×C73—21no—
40C22×C4×C73—21no—
41C22×C4×C73—21no—
42C22×C4×C73—21no—
43C22×C4×C73D411yescharacteristic
44C22×C4×C73C2311yescharacteristic
45C4⋊C4×C73—21no—
46C4⋊C4×C73—21no—
47C4⋊C4×C73—21no—
48C4⋊C4×C73—21no—
49C22⋊C4×C73—42no—
50C23×C73—21no—
51C23×C73—21no—
52C23×C73—21no—
53C23×C73—21no—
54C23×C73—21no—
55C23×C73—21no—
56C23×C73SD1612yes—
57C23×C73C2×D411yescharacteristic
58C2×C4×C73—21no—
59C2×C4×C73—21no—
60C2×C4×C73—21no—
61C2×C4×C73—41no—
62C2×C4×C73—41no—
63C2×C4×C73—41no—
64C2×C4×C73—41no—
65C2×C4×C73—41no—
66C2×C4×C73—41no—
67C2×C4×C73—41no—
68C2×C4×C73—41no—
69C2×C4×C73—41no—
70C2×C4×C73—41no—
71C2×C4×C73C2×D411yescharacteristic
72C2×C4×C73#4111yescharacteristic
73C2×C4×C73#4111yescharacteristic
74C2×C4×C73#4111yescharacteristic
75C2×C4×C73#4111yescharacteristic
76C2×C4×C73#4111yescharacteristic
77C2×Dic73—41no—
78C2×Dic73—41no—
79C2×Dic73—41no—
80C2×Dic73—41no—
81C2×Dic73—41no—
82C2×Dic73—41no—
83#10596831—22no—
84#10596831—41no—
85C22×C73—22no—
86C22×C73—22no—
87C22×C73—22no—
88C22×C73—41no—
89C22×C73—41no—
90C22×C73—41no—
91C22×C73—41no—
92C22×C73#12111yescharacteristic
93C22×C73#12311yescharacteristic
94C22×C73#12311yescharacteristic
95C22×C73C2×SD1611yescharacteristic
96C22×C73#13511yescharacteristic
97C22×C73AGL(1,ℤ/8)11yescharacteristic
98C22×C73#13711yescharacteristic
99C4×C73—41no—
100C4×C73—81no—
101C4×C73—81no—
102C4×C73#12311yescharacteristic
103C4×C73#12411yescharacteristic
104C4×C73#12611yescharacteristic
105C4×C73#12611yescharacteristic
106Dic73—81no—
107Dic73—81no—
108C2×C73—42no—
109C2×C73#39711yescharacteristic
110C2×C73#46511yescharacteristic
111C2×C73#46811yescharacteristic
112C2×C73#48111yescharacteristic
113C2×C73#48211yescharacteristic
114C2×C73#48311yescharacteristic
115C2×C73#48511yescharacteristic
116#2077—731nomaximal, Sylow
117C73#207711yescharacteristic, complemented, Sylow
118C2×#106—731no—
119C2×C22⋊C8—731no—
120#380—731no—
121#380D7311yescharacteristic
122#340—731no—
123#340—731no—
124#340—731no—
125C23×C4C2×D7311yescharacteristic
126C22×C8—731no—
127C22×C8—731no—
128C2×C4⋊C4—731no—
129C2×C4⋊C4—731no—
130C2×C4⋊C4C2×D7311yescharacteristic
131C2×C4⋊C4C2×D7311yescharacteristic
132C2×C22⋊C4—21no—
133C2×C22⋊C4—1461no—
134#106—1462no—
135C22⋊C8—1462no—
136#95—21no—
137#95—1461no—
138C24C22⋊D7311yescharacteristic
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—1461no—
148C22×C4—1461no—
149C22×C4C22⋊D7311yescharacteristic
150C22×C4C22×D7311yescharacteristic
151C2×C8—732no—
152C2×C8—1461no—
153C2×C8—1461no—
154C2×C8—1461no—
155C2×C8—1461no—
156C2×C8—1461no—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—1461no—
162C4⋊C4—1461no—
163C4⋊C4—1461no—
164C4⋊C4—1461no—
165C22⋊C4—42no—
166C22⋊C4—2922no—
167C23—21no—
168C23—21no—
169C23—21no—
170C23—21no—
171C23—21no—
172C23—21no—
173C23#1192401612yes—
174C23C2×C22⋊D7311yescharacteristic
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—2921no—
189C2×C4—2921no—
190C2×C4—2921no—
191C2×C4—2921no—
192C2×C4—2921no—
193C2×C4—2921no—
194C2×C4D4×D7311yescharacteristic
195C2×C4#1192402711yescharacteristic
196C2×C4#1192402711yescharacteristic
197C2×C4#1192402711yescharacteristic
198C2×C4#1192402811yescharacteristic
199C2×C4#1192402811yescharacteristic
200C8—2921no—
201C8—1462no—
202C22—22no—
203C22—22no—
204C22—22no—
205C22—41no—
206C22—41no—
207C22—41no—
208C22—41no—
209C22#1455656311yescharacteristic
210C22#1455657211yescharacteristic
211C22#1455657411yescharacteristic
212C22C2×#1192401611yescharacteristic
213C22#1455661111yescharacteristic
214C22#1455661611yescharacteristic
215C22#1455662211yescharacteristic
216C4—41no—
217C4—81no—
218C4—81no—
219C4—5841no—
220C4—5841no—
221C4#1455657311yescharacteristic
222C4#1455657711yescharacteristic
223C4#1455658411yescharacteristic
224C4#1455658411yescharacteristic
225C2—42no—
226C2#1798851511yescharacteristic
227C2#1798881411yescharacteristic
228C2#1798883511yescharacteristic
229C2#1798890311yescharacteristic
230C2#1798891111yescharacteristic
231C2#1798891711yescharacteristic
232C2#1798892511yescharacteristic
subgroupG/H
centerC23C2×C22⋊D73
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
Fitting#380×C73C2
socleC23×C73C2×D4
hypercenter#380D73
hypocenterC73#2077
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
1. C2×#14556522C2semidirect
4. #17988349C2semidirect
5. #17988349C2semidirect
6. #17988349C2semidirect
117. C73#2077semidirect