Finite Group Databasebeta

← #22625350

Subgroups — #22625350

Order 9344.

252 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 56 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
2#17989532C211yesmaximal, characteristic, complemented
3#17989439C212yesmaximal, complemented
4#17989438C212yesmaximal, complemented
5#17989134C211yesmaximal, characteristic
6C4⋊#10596833—21no—
7#14556648C2212yes—
8#14556646—21no—
9(C2×#64408)⋊C4—21no—
10(C2×#64408)⋊C4—21no—
11(C2×#64408)⋊C4C2212yes—
12C2×#11924028—21no—
13#14556590C411yescharacteristic, complemented
14#14556587C411yescharacteristic, complemented
15#14556577—21no—
16#14556566C2211yescharacteristic
17#14556564—21no—
18#14556562C2211yescharacteristic
19C4×D292C411yescharacteristic, complemented
20C4×C22⋊D73—21no—
21C42×D73C2211yescharacteristic
22C4×D4×C73C411yescharacteristic, complemented
23C22×#64408—22no—
24C2×#10596833—22no—
25#11924028—44no—
26C2×Dic146—21no—
27C2×D292—21no—
28C2×D292C2×C411yescharacteristic
29C2×C22⋊D73—21no—
30C2×C22⋊D73—21no—
31C2×C22⋊D73—21no—
32C2×C4×D73—21no—
33C2×C4×D73D411yescharacteristic
34C2×C4×D73D411yescharacteristic
35C2×C4×D73C2311yescharacteristic
36C4⋊Dic73C2×C411yescharacteristic
37#11924007—21no—
38C22⋊Dic73—21no—
39#11924005—21no—
40#11924005—21no—
41C4×Dic73C2×C411yescharacteristic
42C4×Dic73D411yescharacteristic
43C4×Dic73D411yescharacteristic
44C2×D4×C73C2×C411yescharacteristic
45C22×C4×C73—21no—
46C4⋊C4×C73C2×C411yescharacteristic
47C22⋊C4×C73—21no—
48C42×C73C2×C411yescharacteristic
49C23×C73—21no—
50C22×D73—21no—
51C22×D73C2×D411yescharacteristic
52C2×#64408—42no—
53C2×#64408—42no—
54C2×#64408—42no—
55D4×C73—41no—
56C2×C4×C73—21no—
57C2×C4×C73—42no—
58C2×C4×C73C22⋊C411yescharacteristic
59C2×C4×C73C22⋊C411yescharacteristic
60C2×C4×C73C22×C411yescharacteristic
61C22⋊D73—42no—
62C22⋊D73—42no—
63C22⋊D73—42no—
64C2×Dic73—21no—
65C2×Dic73C22⋊C411yescharacteristic
66C2×Dic73C22⋊C411yescharacteristic
67C2×Dic73C2×D411yescharacteristic
68D292—41no—
69D292—42no—
70C4×D73—22no—
71C4×D73—41no—
72C4×D73—41no—
73C4×D73—42no—
74Dic146—42no—
75#10596833—42no—
76C22×C73—41no—
77C22×C73—41no—
78C22×C73—41no—
79C22×C73C2×C22⋊C411yescharacteristic
80C2×D73—21no—
81C2×D73—21no—
82C2×D73—41no—
83C2×D73—41no—
84C2×D73—41no—
85C2×D73AGL(1,ℤ/8)12yes—
86#64408—82no—
87C4×C73—21no—
88C4×C73—21no—
89C4×C73—21no—
90C4×C73—41no—
91Dic73—21no—
92Dic73—21no—
93Dic73—21no—
94Dic73—41no—
95C2×C73—81no—
96C2×C73#41011yescharacteristic
97C2×C73#41811yescharacteristic
98C2×C73#42111yescharacteristic
99D73—22no—
100D73—81no—
101#1514—731nomaximal, Sylow
102C73#151411yescharacteristic, complemented, Sylow
103#532—731no—
104#432—731no—
105#383—731no—
106#327—732no—
107#327—732no—
108C2×#41—1461no—
109C4⋊Q8—731no—
110#127—731no—
111#124—1461no—
112#121—731no—
113#121—731no—
114#121—1461no—
115C4×D4—731no—
116C4×D4—1461no—
117C4×D4#6440811yescharacteristic, complemented
118C2×C42—731no—
119C4⋊C8—1461no—
120C22⋊C8—732no—
121#97—1461no—
122#95—732no—
123#95—1461no—
124#95—1461no—
125#41—2924no—
126C2×Q8—1461no—
127C2×D4—731no—
128C2×D4—1461no—
129C2×D4—1461no—
130C2×D4—1461no—
131C2×D4—1461no—
132C2×D4C2×#6440811yescharacteristic
133C22×C4—21no—
134C22×C4—731no—
135C22×C4—731no—
136C22×C4—731no—
137C22×C4—1462no—
138C22×C4—1461no—
139C2×C8—1462no—
140C4⋊C4—731no—
141C4⋊C4—1461no—
142C4⋊C4C2×#6440811yescharacteristic
143C22⋊C4—21no—
144C22⋊C4—1461no—
145C22⋊C4—1461no—
146C22⋊C4—1461no—
147C42—731no—
148C42—731no—
149C42—731no—
150C42C2×#6440811yescharacteristic
151C23—21no—
152C23—731no—
153C23—1461no—
154Q8—2922no—
155D4—41no—
156D4—2921no—
157D4—2922no—
158D4—2922no—
159D4—2922no—
160D4—2922no—
161C2×C4—21no—
162C2×C4—42no—
163C2×C4—2922no—
164C2×C4—2921no—
165C2×C4—2921no—
166C2×C4—2922no—
167C2×C4—2922no—
168C2×C4—2922no—
169C2×C4—731no—
170C2×C4—731no—
171C2×C4—731no—
172C2×C4—1462no—
173C2×C4—1461no—
174C2×C4C22⋊#6440811yescharacteristic
175C2×C4C22⋊#6440811yescharacteristic
176C2×C4C22×#6440811yescharacteristic
177C8—2922no—
178C22—41no—
179C22—41no—
180C22—41no—
181C22—2921no—
182C22—2921no—
183C22—2921no—
184C22—732no—
185C22—1461no—
186C22—1461no—
187C22C2×C22⋊#6440811yescharacteristic
188C4—21no—
189C4—21no—
190C4—21no—
191C4—41no—
192C4—2921no—
193C4—5842no—
194C4—1461no—
195C4—1461no—
196C4—1461no—
197C2—81no—
198C2—5841no—
199C2—1462no—
200C2#1798956611yescharacteristic
201C2#1798957911yescharacteristic
202C2#1798958411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC4×D4×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC4×D4#64408
hypocenterC73#1514
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #17989609C2semidirect
2. #17989532C2semidirect
3. #17989439C2semidirect
4. #17989438C2semidirect
13. #14556590C4semidirect
14. #14556587C4semidirect
19. C4×D292C4semidirect
22. C4×D4×C73C4semidirect
102. C73#1514semidirect
117. C4×D4#64408semidirect