Finite Group Databasebeta

← #22625451

Subgroups — #22625451

Order 9344.

252 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 60 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#17989610C211yesmaximal, characteristic, complemented
2#17989588C211yesmaximal, characteristic, complemented
3#17989447C212yesmaximal, complemented
4#17989445C212yesmaximal, complemented
5#17989136C211yesmaximal, characteristic
6C2×#11924036—21no—
7#14556658C2212yes—
8#14556658C2212yes—
9C4⋊#10596833—21no—
10#14556648—21no—
11#14556646—21no—
12C2×#11924029C411yescharacteristic
13C2×#11924027C411yescharacteristic
14#14556589C2211yescharacteristic
15#14556587C2211yescharacteristic
16#14556579C411yescharacteristic
17#14556564—21no—
18#14556564—21no—
19#14556551—21no—
20#14556551—21no—
21C42×D73C2211yescharacteristic
22#124×C73C411yescharacteristic
23#11924036—42no—
24C2×#10596833—22no—
25C2×#10596833—22no—
26#11924029—42no—
27#11924027—42no—
28C2×Dic146C2×C411yescharacteristic
29C2×D292—21no—
30C2×D292C2×C411yescharacteristic
31C2×C22⋊D73—21no—
32C2×C22⋊D73—21no—
33C2×C22⋊D73—21no—
34C22×Dic73—21no—
35C2×C4×D73—21no—
36C2×C4×D73C2×C411yescharacteristic
37C2×C4×D73D411yescharacteristic
38C2×C4×D73D411yescharacteristic
39#11924007—21no—
40#11924007—21no—
41#11924005—21no—
42#11924005—21no—
43C4×Dic73D411yescharacteristic
44C4×Dic73D411yescharacteristic
45C4×Dic73C2311yescharacteristic
46C2×Q8×C73C2×C411yescharacteristic
47C2×D4×C73C2×C411yescharacteristic
48C22⋊C4×C73—21no—
49C22⋊C4×C73—21no—
50C42×C73C2×C411yescharacteristic
51C23×C73—21no—
52C22×D73—21no—
53C22×D73C22⋊C411yescharacteristic
54Q8×C73—41no—
55D4×C73—41no—
56C2×C4×C73—21no—
57C2×C4×C73C22⋊C411yescharacteristic
58C2×C4×C73C22⋊C411yescharacteristic
59C2×C4×C73C22×C411yescharacteristic
60C22⋊D73—42no—
61C22⋊D73—42no—
62C22⋊D73—41no—
63C22⋊D73—41no—
64C2×Dic73—21no—
65C2×Dic73—42no—
66C2×Dic73C22⋊C411yescharacteristic
67C2×Dic73C2×D411yescharacteristic
68C2×Dic73C2×D411yescharacteristic
69D292—41no—
70D292—42no—
71C4×D73—22no—
72C4×D73—22no—
73C4×D73—21no—
74C4×D73—21no—
75C4×D73—42no—
76Dic146—41no—
77#10596833—42no—
78#10596833—42no—
79C22×C73—41no—
80C22×C73—41no—
81C22×C73—41no—
82C22×C73C2×C22⋊C411yescharacteristic
83C2×D73—21no—
84C2×D73—21no—
85C2×D73—41no—
86C2×D73—41no—
87C2×D73—41no—
88C2×D73#10012yes—
89C4×C73—21no—
90C4×C73—21no—
91C4×C73—21no—
92C4×C73—41no—
93Dic73—21no—
94Dic73—41no—
95Dic73#13512yes—
96Dic73AGL(1,ℤ/8)11yescharacteristic
97Dic73#13711yescharacteristic
98C2×C73—81no—
99C2×C73C2×#10011yescharacteristic
100C2×C73#41611yescharacteristic
101C2×C73#41711yescharacteristic
102D73—22no—
103D73—81no—
104#1551—731nomaximal, Sylow
105C73#155111yescharacteristic, complemented, Sylow
106#532—731no—
107#432—731no—
108C2×C4⋊C8—731no—
109#333—732no—
110#331—732no—
111C2×#41—731no—
112C2×#41—731no—
113C22×C8—1461no—
114C4⋊Q8—731no—
115#127—731no—
116#124—731no—
117#124#6440811yescharacteristic
118#121—1461no—
119#121—1461no—
120C4×D4—1461no—
121C4×D4—1461no—
122C2×C42—731no—
123C4⋊C8—732no—
124C4⋊C8—732no—
125C4⋊C8—1461no—
126C22⋊C8—1461no—
127#97—1461no—
128#41—2922no—
129#41—2922no—
130C2×Q8—731no—
131C2×Q8C2×#6440811yescharacteristic
132C2×D4—731no—
133C2×D4—1461no—
134C2×D4—1461no—
135C2×D4—1461no—
136C2×D4—1461no—
137C2×D4C2×#6440811yescharacteristic
138C22×C4—731no—
139C22×C4—731no—
140C22×C4—731no—
141C22×C4—1461no—
142C22×C4—1461no—
143C2×C8—2922no—
144C2×C8—1462no—
145C2×C8—1462no—
146C4⋊C4—1461no—
147C4⋊C4—1461no—
148C22⋊C4—21no—
149C22⋊C4—21no—
150C22⋊C4—1461no—
151C22⋊C4—1461no—
152C42—731no—
153C42—731no—
154C42—731no—
155C42C2×#6440811yescharacteristic
156C23—21no—
157C23—731no—
158C23—1461no—
159Q8—41no—
160Q8—2921no—
161D4—41no—
162D4—2921no—
163D4—2922no—
164D4—2922no—
165D4—2922no—
166D4—2921no—
167D4—2921no—
168C2×C4—21no—
169C2×C4—2922no—
170C2×C4—2922no—
171C2×C4—731no—
172C2×C4—731no—
173C2×C4—731no—
174C2×C4—1461no—
175C2×C4—1462no—
176C2×C4—1461no—
177C2×C4—1462no—
178C2×C4—1461no—
179C2×C4C22⋊#6440811yescharacteristic
180C2×C4C22⋊#6440811yescharacteristic
181C2×C4C22×#6440811yescharacteristic
182C8—2922no—
183C8—2922no—
184C22—41no—
185C22—41no—
186C22—41no—
187C22—2921no—
188C22—2921no—
189C22—2921no—
190C22—732no—
191C22—1461no—
192C22—1461no—
193C22C2×C22⋊#6440811yescharacteristic
194C4—21no—
195C4—21no—
196C4—21no—
197C4—41no—
198C4—2921no—
199C4—732no—
200C4—731no—
201C4—731no—
202C4—1461no—
203C2—81no—
204C2—5841no—
205C2—1462no—
206C2D73⋊#10011yescharacteristic
207C2#1798957711yescharacteristic
208C2#1798957811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
Fitting#124×C73C4
socleC22×C73C2×C22⋊C4
hypercenter#124#64408
hypocenterC73#1551
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #17989610C2semidirect
2. #17989588C2semidirect
3. #17989447C2semidirect
4. #17989445C2semidirect
105. C73#1551semidirect