Finite Group Databasebeta

← #22625271

Subgroups — #22625271

Order 9344.

316 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 68 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#17989609C211yesmaximal, characteristic, complemented
2C4×#11924038C211yesmaximal, characteristic, complemented
3#17989435C212yesmaximal, complemented
4D4⋊#10596833C212yesmaximal, complemented
5C4×D4×D73C211yesmaximal, characteristic
6C2×#11924038—21no—
7C4⋊#10596833C2212yescomplemented
8#14556648—21no—
9#14556646—21no—
10#14556646—21no—
11C4×#10596833C2212yescomplemented
12C2×D4×D73C411yescharacteristic
13C22×C4×D73—21no—
14C4×D292C411yescharacteristic
15D4×Dic73C2211yescharacteristic
16#14556553C2211yescharacteristic
17C4×C22⋊D73—21no—
18#14556551—21no—
19C4⋊C4×D73C411yescharacteristic
20C22⋊C4×D73—21no—
21C42×D73C2211yescharacteristic
22C4×D4×C73C411yescharacteristic
23#11924038—24no—
24C2×#10596833—22no—
25C2×#10596833—22no—
26C23×D73—21no—
27C2×D292C2×C411yescharacteristic
28C2×C22⋊D73—21no—
29D4×D73—22no—
30D4×D73—22no—
31C22×Dic73—21no—
32C2×C4×D73—21no—
33C2×C4×D73—21no—
34C2×C4×D73—21no—
35C2×C4×D73—44no—
36C2×C4×D73C2×C411yescharacteristic
37C2×C4×D73D411yescharacteristic
38C2×C4×D73D411yescharacteristic
39C4⋊Dic73C2×C411yescharacteristic
40#11924007—21no—
41C22⋊Dic73—21no—
42#11924005—21no—
43#11924005—21no—
44C4×Dic73D411yescharacteristic
45C4×Dic73D411yescharacteristic
46C4×Dic73C2311yescharacteristic
47C2×D4×C73C2×C411yescharacteristic
48C22×C4×C73—21no—
49C4⋊C4×C73C2×C411yescharacteristic
50C22⋊C4×C73—21no—
51C42×C73C2×C411yescharacteristic
52C23×C73—21no—
53C22×D73—24no—
54C22×D73—21no—
55C22×D73—42no—
56C22×D73—42no—
57C22×D73C22⋊C411yescharacteristic
58D4×C73—21no—
59D4×C73M1612yescomplemented
60C2×C4×C73—21no—
61C2×C4×C73—42no—
62C2×C4×C73C22⋊C411yescharacteristic
63C2×C4×C73C22⋊C411yescharacteristic
64C2×C4×C73C22×C411yescharacteristic
65C22⋊D73—24no—
66C2×Dic73—21no—
67C2×Dic73—42no—
68C2×Dic73C22⋊C411yescharacteristic
69C2×Dic73C2×D411yescharacteristic
70C2×Dic73C2×D411yescharacteristic
71D292—21no—
72D292M1612yescomplemented
73C4×D73—22no—
74C4×D73—21no—
75C4×D73—21no—
76C4×D73—22no—
77C4×D73—42no—
78C4×D73—42no—
79C4×D73—42no—
80#10596833—24no—
81#10596833—42no—
82C22×C73—22no—
83C22×C73—41no—
84C22×C73—41no—
85C22×C73C2×C22⋊C411yescharacteristic
86C2×D73—21no—
87C2×D73—21no—
88C2×D73—22no—
89C2×D73—48no—
90C2×D73—41no—
91C2×D73—41no—
92C2×D73#10412yes—
93C4×C73—21no—
94C4×C73—21no—
95C4×C73—41no—
96C4×C73C2×M1611yescharacteristic
97C4×C73C2×M1611yescharacteristic
98Dic73—21no—
99Dic73—21no—
100Dic73—41no—
101Dic73AGL(1,ℤ/8)12yes—
102C2×C73—42no—
103C2×C73#40711yescharacteristic
104C2×C73#41811yescharacteristic
105C2×C73C2×#10411yescharacteristic
106D73—22no—
107D73—42no—
108#1490—731nomaximal, Sylow
109C73#149011yescharacteristic, complemented, Sylow
110C2×C4×D4—731no—
111#432—731no—
112C4×M16—731no—
113D4⋊C8—732no—
114D4⋊C8—732no—
115C22×D4—731no—
116C23×C4—1461no—
117C2×M16—1461no—
118C4×D4—731no—
119C4×D4—731no—
120C4×D4—731no—
121C4×D4—1461no—
122C4×D4—1461no—
123C4×D4#6440811yescharacteristic
124C2×C4⋊C4—731no—
125C2×C22⋊C4—1461no—
126C2×C42—731no—
127C4⋊C8—732no—
128C22⋊C8—1461no—
129#97—1461no—
130#97—1461no—
131C4×C8—732no—
132C24—1461no—
133C2×D4—731no—
134C2×D4—1461no—
135C2×D4—1462no—
136C2×D4—1462no—
137C2×D4C2×#6440811yescharacteristic
138C22×C4—21no—
139C22×C4—2924no—
140C22×C4—731no—
141C22×C4—731no—
142C22×C4—731no—
143C22×C4—1461no—
144C22×C4—1461no—
145C22×C4—1461no—
146C22×C4—1461no—
147M16—1464no—
148C2×C8—1462no—
149C2×C8—1462no—
150C4⋊C4—731no—
151C4⋊C4—1461no—
152C4⋊C4C2×#6440811yescharacteristic
153C22⋊C4—21no—
154C22⋊C4—1461no—
155C22⋊C4—1461no—
156C22⋊C4—1461no—
157C42—731no—
158C42—731no—
159C42—731no—
160C42C2×#6440811yescharacteristic
161C23—21no—
162C23—2922no—
163C23—2922no—
164C23—731no—
165C23—1464no—
166C23—1461no—
167D4—21no—
168D4—732no—
169D4—1464no—
170D4—1461no—
171D4#1192403812yescomplemented
172C2×C4—21no—
173C2×C4—42no—
174C2×C4—2922no—
175C2×C4—2922no—
176C2×C4—2922no—
177C2×C4—2922no—
178C2×C4—731no—
179C2×C4—731no—
180C2×C4—731no—
181C2×C4—1462no—
182C2×C4—1462no—
183C2×C4—1461no—
184C2×C4—1461no—
185C2×C4—1461no—
186C2×C4C22⋊#6440811yescharacteristic
187C2×C4C22⋊#6440811yescharacteristic
188C2×C4C22×#6440811yescharacteristic
189C8—2922no—
190C8—1464no—
191C22—22no—
192C22—41no—
193C22—41no—
194C22—2928no—
195C22—2921no—
196C22—2921no—
197C22—732no—
198C22—1462no—
199C22—1461no—
200C22—1461no—
201C22C2×C22⋊#6440811yescharacteristic
202C4—21no—
203C4—21no—
204C4—41no—
205C4—2921no—
206C4—732no—
207C4—1461no—
208C4—1461no—
209C4D73⋊M1611yescharacteristic
210C4C2×#1192403811yescharacteristic
211C2—42no—
212C2—2922no—
213C2—1462no—
214C2#1798955811yescharacteristic
215C2#1798957911yescharacteristic
216C2D73⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC4×D4×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC4×D4#64408
hypocenterC73#1490
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #17989609C2semidirect
2. C4×#11924038C2semidirect
3. #17989435C2semidirect
4. D4⋊#10596833C2semidirect
7. C4⋊#10596833C22semidirect
11. C4×#10596833C22semidirect
59. D4×C73M16semidirect
72. D292M16semidirect
109. C73#1490semidirect
171. D4#11924038semidirect