Finite Group Databasebeta

← #22625196

Subgroups — #22625196

Order 9344.

280 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 62 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#17989557C211yesmaximal, characteristic, complemented
2C2×C22⋊#10596833C211yesmaximal, characteristic, complemented
3#17989433C212yesmaximal, complemented
4#17989430C212yesmaximal, complemented
5C2×#14556572C211yesmaximal, characteristic
6C2×#11924037—21no—
7C22×#10596833—21no—
8C22⋊#10596833—21no—
9C22⋊#10596833—21no—
10C22⋊#10596833C2212yes—
11C22⋊#10596833C2212yes—
12C23×Dic73C2211yescharacteristic
13#14556572—21no—
14#14556572—21no—
15#14556572—21no—
16#14556572—21no—
17C2×#11924007C411yescharacteristic
18C2×#11924007C2211yescharacteristic
19C2×C22⋊Dic73C411yescharacteristic
20C2×C22⋊Dic73C411yescharacteristic
21C2×C22⋊Dic73C2211yescharacteristic
22C22×D4×C73C411yescharacteristic
23#11924037—42no—
24C2×#10596833—22no—
25C2×#10596833—22no—
26C2×#10596833—42no—
27C22×Dic73—42no—
28C22×Dic73C2×C411yescharacteristic
29C22×Dic73C2×C411yescharacteristic
30C22×Dic73C2×C411yescharacteristic
31C22×Dic73D411yescharacteristic
32C22×Dic73D411yescharacteristic
33C22×Dic73D411yescharacteristic
34C22×Dic73D411yescharacteristic
35C22×Dic73C2311yescharacteristic
36#11924007—21no—
37#11924007—21no—
38#11924007—21no—
39#11924007—21no—
40C22⋊Dic73—21no—
41C22⋊Dic73—21no—
42C22⋊Dic73—21no—
43C22⋊Dic73—21no—
44C22⋊Dic73—21no—
45C22⋊Dic73—21no—
46C24×C73C2×C411yescharacteristic
47C24×C73C2×C411yescharacteristic
48C2×D4×C73—21no—
49C2×D4×C73—21no—
50C2×D4×C73—42no—
51C22×C4×C73C2×C411yescharacteristic
52C23×C73—22no—
53C23×C73—22no—
54C23×C73—21no—
55C23×C73—22no—
56C23×C73—41no—
57C23×C73—41no—
58C23×C73—41no—
59C23×C73C22⋊C411yescharacteristic
60C23×C73C22⋊C411yescharacteristic
61C23×C73C22×C411yescharacteristic
62D4×C73—42no—
63D4×C73—42no—
64C2×C4×C73—21no—
65C2×C4×C73—41no—
66C2×Dic73—22no—
67C2×Dic73—22no—
68C2×Dic73—21no—
69C2×Dic73—21no—
70C2×Dic73—22no—
71C2×Dic73—41no—
72C2×Dic73—41no—
73C2×Dic73—41no—
74C2×Dic73—41no—
75C2×Dic73—41no—
76C2×Dic73C22⋊C411yescharacteristic
77C2×Dic73C22⋊C411yescharacteristic
78C2×Dic73C2×D411yescharacteristic
79C2×Dic73C2×D411yescharacteristic
80#10596833—42no—
81#10596833—42no—
82C22×C73—21no—
83C22×C73—21no—
84C22×C73—21no—
85C22×C73—21no—
86C22×C73—21no—
87C22×C73—21no—
88C22×C73—21no—
89C22×C73—44no—
90C22×C73—41no—
91C22×C73—41no—
92C22×C73—41no—
93C22×C73—82no—
94C22×C73#9912yes—
95C22×C73C2×C22⋊C411yescharacteristic
96C22×C73#13112yes—
97C4×C73—41no—
98Dic73—21no—
99Dic73—21no—
100Dic73—21no—
101Dic73—21no—
102Dic73—41no—
103Dic73—41no—
104C2×C73—22no—
105C2×C73—22no—
106C2×C73—41no—
107C2×C73—81no—
108C2×C73#40811yescharacteristic
109C2×C73C2×#9911yescharacteristic
110C2×C73#41311yescharacteristic
111#1468—731nomaximal, Sylow
112C73#146811yescharacteristic, complemented, Sylow
113C2×#123—731no—
114#407—731no—
115C2×C22⋊C8—731no—
116#324—732no—
117#323—732no—
118C22×D4#6440811yescharacteristic
119C23×C4—731no—
120C2×M16—1461no—
121C22×C8—1461no—
122#123—1461no—
123#123—1461no—
124#123—1461no—
125#123—1461no—
126C2×C4⋊C4—731no—
127C2×C4⋊C4—731no—
128C2×C22⋊C4—731no—
129C2×C22⋊C4—731no—
130C2×C22⋊C4—731no—
131C22⋊C8—732no—
132C22⋊C8—732no—
133C22⋊C8—1461no—
134C22⋊C8—1461no—
135C24C2×#6440811yescharacteristic
136C24C2×#6440811yescharacteristic
137C2×D4—21no—
138C2×D4—21no—
139C2×D4—42no—
140C22×C4—2922no—
141C22×C4—731no—
142C22×C4—731no—
143C22×C4—731no—
144C22×C4—731no—
145C22×C4—731no—
146C22×C4—731no—
147C22×C4—731no—
148C22×C4—731no—
149C22×C4C2×#6440811yescharacteristic
150M16—2922no—
151C2×C8—2922no—
152C2×C8—1462no—
153C2×C8—1462no—
154C4⋊C4—1461no—
155C4⋊C4—1461no—
156C4⋊C4—1461no—
157C4⋊C4—1461no—
158C22⋊C4—1461no—
159C22⋊C4—1461no—
160C22⋊C4—1461no—
161C22⋊C4—1461no—
162C22⋊C4—1461no—
163C22⋊C4—1461no—
164C23—22no—
165C23—22no—
166C23—21no—
167C23—22no—
168C23—41no—
169C23—41no—
170C23—41no—
171C23C22⋊#6440811yescharacteristic
172C23C22⋊#6440811yescharacteristic
173C23C22×#6440811yescharacteristic
174D4—42no—
175D4—42no—
176C2×C4—21no—
177C2×C4—41no—
178C2×C4—2921no—
179C2×C4—2921no—
180C2×C4—2921no—
181C2×C4—2921no—
182C2×C4—2921no—
183C2×C4—731no—
184C2×C4—731no—
185C2×C4—731no—
186C2×C4—731no—
187C2×C4—1462no—
188C2×C4—1461no—
189C2×C4—1461no—
190C2×C4—1462no—
191C2×C4—1462no—
192C8—2922no—
193C8—2922no—
194C22—21no—
195C22—21no—
196C22—21no—
197C22—21no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—44no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—82no—
206C22#1455664912yes—
207C22C2×C22⋊#6440811yescharacteristic
208C22#1455667812yes—
209C4—41no—
210C4—2921no—
211C4—2921no—
212C4—1461no—
213C4—1461no—
214C4—1461no—
215C4—1461no—
216C2—22no—
217C2—22no—
218C2—41no—
219C2—81no—
220C2#1798956011yescharacteristic
221C2C2×#1455664911yescharacteristic
222C2#1798957411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC23×C73C22×C4
FrattiniC23C22×#64408
FittingC22×D4×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC22×D4#64408
hypocenterC73#1468
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #17989557C2semidirect
2. C2×C22⋊#10596833C2semidirect
3. #17989433C2semidirect
4. #17989430C2semidirect
112. C73#1468semidirect