Finite Group Databasebeta

← #22625157

Subgroups — #22625157

Order 9344.

456 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 84 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#17989555C212yesmaximal, complemented
2#17989431C212yesmaximal, complemented
3#17989430C212yesmaximal, complemented
4C2×C22⋊C4×D73C211yesmaximal, characteristic
5C2×#11924036—22no—
6#14556648—22no—
7C22⋊#10596833C2214yescomplemented
8C24×D73C411yescharacteristic
9C22×C4×D73C411yescharacteristic
10C22×C4×D73C2211yescharacteristic
11C2×C22⋊Dic73C2211yescharacteristic
12C2×#11924005C411yescharacteristic
13C2×#11924005C2211yescharacteristic
14C22⋊C4×D73—22no—
15C22⋊C4×D73—22no—
16C2×C22⋊C4×C73C411yescharacteristic
17#11924036—44no—
18C2×#10596833—24no—
19C23×D73—21no—
20C23×D73—21no—
21C23×D73—22no—
22C23×D73—42no—
23C23×D73—42no—
24C23×D73C814yescomplemented
25C23×D73C2×C411yescharacteristic
26C23×D73C2×C411yescharacteristic
27C22×Dic73C2×C411yescharacteristic
28C22×Dic73C2311yescharacteristic
29C2×C4×D73—21no—
30C2×C4×D73—21no—
31C2×C4×D73—42no—
32C2×C4×D73—42no—
33C2×C4×D73D412yes—
34C2×C4×D73D412yes—
35C22⋊Dic73—22no—
36#11924005—22no—
37#11924005—22no—
38C24×C73C2×C411yescharacteristic
39C22×C4×C73C2×C411yescharacteristic
40C22×C4×C73C2×C411yescharacteristic
41C22⋊C4×C73—22no—
42C23×C73—21no—
43C23×C73—21no—
44C23×C73—41no—
45C23×C73—41no—
46C23×C73C2×C812yescomplemented
47C23×C73C22×C411yescharacteristic
48C22×D73—22no—
49C22×D73—22no—
50C22×D73—21no—
51C22×D73—21no—
52C22×D73—24no—
53C22×D73—24no—
54C22×D73—42no—
55C22×D73—42no—
56C22×D73—48no—
57C22×D73—48no—
58C22×D73—42no—
59C22×D73—42no—
60C22×D73—41no—
61C22×D73—41no—
62C22×D73C22⋊C411yescharacteristic
63C22×D73C22⋊C411yescharacteristic
64C22×D73C2×C812yes—
65C22×D73C2×C812yescomplemented
66C22×D73M1612yes—
67C2×C4×C73—21no—
68C2×C4×C73—41no—
69C2×C4×C73—41no—
70C2×C4×C73C22⋊C412yes—
71C2×Dic73—21no—
72C2×Dic73—41no—
73C2×Dic73—41no—
74C2×Dic73C2×D412yes—
75C4×D73—24no—
76C4×D73—42no—
77C4×D73—42no—
78C4×D73—42no—
79#10596833—44no—
80C22×C73—21no—
81C22×C73—21no—
82C22×C73—22no—
83C22×C73—42no—
84C22×C73—42no—
85C22×C73—41no—
86C22×C73—41no—
87C22×C73C2×C22⋊C411yescharacteristic
88C22×C73C22×C811yescharacteristic
89C22×C73C2×M1611yescharacteristic
90C2×D73—21no—
91C2×D73—21no—
92C2×D73—24no—
93C2×D73—24no—
94C2×D73—22no—
95C2×D73—48no—
96C2×D73—42no—
97C2×D73—41no—
98C2×D73—41no—
99C2×D73—48no—
100C2×D73—42no—
101C2×D73C22⋊C812yes—
102C2×D73C22⋊C812yes—
103C2×D73#9912yes—
104C2×D73#10012yes—
105C4×C73—22no—
106C4×C73—41no—
107Dic73—22no—
108Dic73—41no—
109C2×C73—21no—
110C2×C73—21no—
111C2×C73—42no—
112C2×C73C2×C22⋊C811yescharacteristic
113C2×C73C2×#9911yescharacteristic
114C2×C73C2×#10011yescharacteristic
115D73—22no—
116D73—42no—
117D73#32314yescomplemented
118C2×#323—731nomaximal, Sylow
119C73C2×#32311yescharacteristic, complemented, Sylow
120C22×C22⋊C4—731no—
121C2×C22⋊C8—732no—
122#323—732no—
123#323—732no—
124C25—731no—
125C23×C4—731no—
126C23×C4—731no—
127C22×C8—1462no—
128C2×C22⋊C4—731no—
129C2×C22⋊C4—731no—
130C2×C22⋊C4—731no—
131C2×C22⋊C4—1462no—
132C2×C22⋊C4—1462no—
133C2×C22⋊C4#6440811yescharacteristic
134C22⋊C8—734no—
135C22⋊C8—1462no—
136C24—2922no—
137C24—2922no—
138C24—734no—
139C24—731no—
140C24—731no—
141C24—1461no—
142C24—1461no—
143C24—1462no—
144C24C2×#6440811yescharacteristic
145C22×C4—2922no—
146C22×C4—2922no—
147C22×C4—731no—
148C22×C4—732no—
149C22×C4—731no—
150C22×C4—732no—
151C22×C4—1461no—
152C22×C4—1461no—
153C22×C4C2×#6440811yescharacteristic
154C22×C4C2×#6440811yescharacteristic
155C2×C8—2924no—
156C2×C8—1464no—
157C22⋊C4—22no—
158C22⋊C4—1462no—
159C22⋊C4—1462no—
160C22⋊C4—1462no—
161C23—21no—
162C23—21no—
163C23—41no—
164C23—41no—
165C23—2921no—
166C23—2921no—
167C23—2922no—
168C23—2922no—
169C23—2928no—
170C23—2922no—
171C23—2922no—
172C23—2928no—
173C23—732no—
174C23—731no—
175C23—732no—
176C23—732no—
177C23—731no—
178C23—1464no—
179C23—1464no—
180C23—1462no—
181C23—1462no—
182C23—1461no—
183C23—1461no—
184C23#1192403612yescomplemented
185C23C22×#6440811yescharacteristic
186C2×C4—21no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—2922no—
190C2×C4—2922no—
191C2×C4—2922no—
192C2×C4—2921no—
193C2×C4—2921no—
194C2×C4—732no—
195C2×C4—1464no—
196C2×C4—1461no—
197C2×C4C22⋊#6440812yes—
198C8—2924no—
199C22—21no—
200C22—21no—
201C22—22no—
202C22—42no—
203C22—42no—
204C22—41no—
205C22—41no—
206C22—2922no—
207C22—2922no—
208C22—2928no—
209C22—2928no—
210C22—2921no—
211C22—2921no—
212C22—732no—
213C22—732no—
214C22—732no—
215C22—732no—
216C22—1464no—
217C22—1464no—
218C22—1462no—
219C22—1461no—
220C22—1461no—
221C22C2×C22⋊#6440811yescharacteristic
222C22C2×#1192403611yescharacteristic
223C22D73⋊M1611yescharacteristic
224C4—22no—
225C4—41no—
226C4—2921no—
227C4—1462no—
228C2—21no—
229C2—21no—
230C2—42no—
231C2—2922no—
232C2—734no—
233C2—1462no—
234C2#1798955511yescharacteristic
235C2D73⋊#9911yescharacteristic
236C2D73⋊#10011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC22×C73C22×C8
FrattiniC23C22×#64408
FittingC2×C22⋊C4×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC2×C22⋊C4#64408
hypocenterC73C2×#323
LCSG ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #17989555C2semidirect
2. #17989431C2semidirect
3. #17989430C2semidirect
7. C22⋊#10596833C22semidirect
24. C23×D73C8semidirect
46. C23×C73C2×C8semidirect
65. C22×D73C2×C8semidirect
117. D73#323semidirect
119. C73C2×#323semidirect
184. C23#11924036semidirect