Finite Group Databasebeta

← #22625429

Subgroups — #22625429

Order 9344.

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

normal subgroups only

This group has 256 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#17989604C211yesmaximal, characteristic, complemented
2C2×#14556658C211yesmaximal, characteristic, complemented
3#17989446C212yesmaximal, complemented
4#17989445C212yesmaximal, complemented
5#17989132C211yesmaximal, characteristic
6C22×#10596833—21no—
7#14556658—21no—
8#14556658C2212yes—
9#14556658C2212yes—
10C22⋊#10596833—21no—
11C4×#10596833—21no—
12C2×#11924027—21no—
13#14556590C2211yescharacteristic
14#14556587C2211yescharacteristic
15#14556577—21no—
16#14556565C411yescharacteristic
17#14556563—21no—
18D4×Dic73C411yescharacteristic
19#14556553C411yescharacteristic
20#14556551—21no—
21C2×C4×Dic73C2211yescharacteristic
22#121×C73C411yescharacteristic
23C2×#10596833—22no—
24C2×#10596833—22no—
25C2×#10596833—42no—
26#11924027—42no—
27#11924027—42no—
28C2×Dic146—21no—
29C2×D292C2×C411yescharacteristic
30C2×C22⋊D73—21no—
31C2×C22⋊D73—21no—
32C2×C22⋊D73—21no—
33C22×Dic73—21no—
34C22×Dic73D411yescharacteristic
35C22×Dic73D411yescharacteristic
36C2×C4×D73—21no—
37C4⋊Dic73C2×C411yescharacteristic
38#11924007—21no—
39C22⋊Dic73—21no—
40#11924005—21no—
41#11924005—21no—
42C4×Dic73C2×C411yescharacteristic
43C4×Dic73D411yescharacteristic
44C4×Dic73D411yescharacteristic
45C4×Dic73C2311yescharacteristic
46C2×D4×C73—21no—
47C2×D4×C73C2×C411yescharacteristic
48C22×C4×C73C2×C411yescharacteristic
49C4⋊C4×C73C2×C411yescharacteristic
50C22⋊C4×C73—21no—
51C23×C73—21no—
52C23×C73C22⋊C411yescharacteristic
53C22×D73—21no—
54D4×C73—41no—
55D4×C73—42no—
56C2×C4×C73—21no—
57C2×C4×C73—41no—
58C2×C4×C73C22⋊C411yescharacteristic
59C2×C4×C73C22×C411yescharacteristic
60C22⋊D73—42no—
61C22⋊D73—41no—
62C22⋊D73—41no—
63C22⋊D73—42no—
64C2×Dic73—22no—
65C2×Dic73—21no—
66C2×Dic73—42no—
67C2×Dic73C22⋊C411yescharacteristic
68C2×Dic73C22⋊C411yescharacteristic
69C2×Dic73D812yes—
70C2×Dic73SD1612yes—
71C2×Dic73C2×D411yescharacteristic
72C2×Dic73C2×D411yescharacteristic
73D292—41no—
74C4×D73—42no—
75Dic146—41no—
76Dic146—41no—
77#10596833—42no—
78#10596833—42no—
79C22×C73—21no—
80C22×C73—21no—
81C22×C73—41no—
82C22×C73—41no—
83C22×C73—41no—
84C22×C73#10212yes—
85C22×C73C2×C22⋊C411yescharacteristic
86C2×D73—41no—
87C2×D73—41no—
88C2×D73—41no—
89C4×C73—21no—
90C4×C73—21no—
91C4×C73—41no—
92Dic73—21no—
93Dic73—41no—
94Dic73#10212yes—
95Dic73C2×D811yescharacteristic
96Dic73C2×SD1611yescharacteristic
97Dic73#13512yes—
98C2×C73—22no—
99C2×C73—81no—
100C2×C73#41311yescharacteristic
101C2×C73C2×#10211yescharacteristic
102C2×C73#41611yescharacteristic
103D73—81no—
104#1540—731nomaximal, Sylow
105C73#154011yescharacteristic, complemented, Sylow
106#532—731no—
107#431—731no—
108C2×C4⋊C8—731no—
109#332—732no—
110#331—732no—
111C2×#41—1461no—
112C22×C8—1461no—
113C4⋊Q8—731no—
114#127—731no—
115#124—1461no—
116#121—731no—
117#121—1461no—
118#121#6440811yescharacteristic
119C4×D4—731no—
120C4×D4—731no—
121C4×D4—1461no—
122C2×C42—731no—
123C4⋊C8—732no—
124C4⋊C8—732no—
125C4⋊C8—1461no—
126C22⋊C8—1461no—
127C4×C8—1461no—
128#41—2922no—
129#41—2922no—
130C2×Q8—1461no—
131C2×D4—21no—
132C2×D4—731no—
133C2×D4—1461no—
134C2×D4—1461no—
135C2×D4—1461no—
136C2×D4C2×#6440811yescharacteristic
137C22×C4—731no—
138C22×C4—731no—
139C22×C4—1461no—
140C22×C4—1461no—
141C22×C4C2×#6440811yescharacteristic
142C2×C8—2922no—
143C2×C8—1462no—
144C2×C8—1462no—
145C4⋊C4—731no—
146C4⋊C4—1461no—
147C4⋊C4C2×#6440811yescharacteristic
148C22⋊C4—21no—
149C22⋊C4—1461no—
150C22⋊C4—1461no—
151C22⋊C4—1461no—
152C42—731no—
153C42—731no—
154C42—731no—
155C42—731no—
156C23—21no—
157C23—1461no—
158C23C22⋊#6440811yescharacteristic
159Q8—2921no—
160Q8—2921no—
161D4—41no—
162D4—42no—
163D4—2921no—
164D4—2922no—
165D4—2921no—
166D4—2921no—
167D4—2922no—
168C2×C4—21no—
169C2×C4—41no—
170C2×C4—2922no—
171C2×C4—2922no—
172C2×C4—732no—
173C2×C4—732no—
174C2×C4—731no—
175C2×C4—731no—
176C2×C4—731no—
177C2×C4—731no—
178C2×C4—1461no—
179C2×C4—1462no—
180C2×C4C22⋊#6440811yescharacteristic
181C2×C4C22×#6440811yescharacteristic
182C8—2922no—
183C8—2922no—
184C22—21no—
185C22—21no—
186C22—41no—
187C22—41no—
188C22—41no—
189C22—2921no—
190C22—2921no—
191C22—2921no—
192C22#1455665312yes—
193C22C2×C22⋊#6440811yescharacteristic
194C4—21no—
195C4—21no—
196C4—41no—
197C4—2921no—
198C4—731no—
199C4—732no—
200C4—731no—
201C4—732no—
202C4—1461no—
203C2—22no—
204C2—81no—
205C2—5841no—
206C2#1798957411yescharacteristic
207C2C2×#1455665311yescharacteristic
208C2#1798957711yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
Fitting#121×C73C4
socleC22×C73C2×C22⋊C4
hypercenter#121#64408
hypocenterC73#1540
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #17989604C2semidirect
2. C2×#14556658C2semidirect
3. #17989446C2semidirect
4. #17989445C2semidirect
105. C73#1540semidirect