Finite Group Databasebeta

← #22625321

Subgroups — #22625321

Order 9344.

272 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 58 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#17989523C211yesmaximal, characteristic, complemented
3#17989439C212yesmaximal, complemented
4#17989438C212yesmaximal, complemented
5#17989134C211yesmaximal, characteristic
6C2×C4×#64408—21no—
7#14556658—21no—
8#14556648C2212yes—
9#14556646—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—
25C4×#64408—24no—
26#11924028—44no—
27C2×Dic146—21no—
28C2×D292—21no—
29C2×D292C2×C411yescharacteristic
30C2×C22⋊D73—21no—
31C2×C22⋊D73—21no—
32C2×C22⋊D73—21no—
33C2×C4×D73—21no—
34C2×C4×D73D411yescharacteristic
35C2×C4×D73D411yescharacteristic
36C2×C4×D73C2311yescharacteristic
37C4⋊Dic73C2×C411yescharacteristic
38#11924007—21no—
39C22⋊Dic73—21no—
40#11924005—21no—
41#11924005—21no—
42C4×Dic73C2×C411yescharacteristic
43C4×Dic73D411yescharacteristic
44C4×Dic73D411yescharacteristic
45C2×D4×C73C2×C411yescharacteristic
46C22×C4×C73—21no—
47C4⋊C4×C73C2×C411yescharacteristic
48C22⋊C4×C73—21no—
49C42×C73C2×C411yescharacteristic
50C23×C73—21no—
51C22×D73—21no—
52C22×D73C2×D411yescharacteristic
53C2×#64408—24no—
54C2×#64408—42no—
55C2×#64408—42no—
56D4×C73—41no—
57C2×C4×C73—21no—
58C2×C4×C73—42no—
59C2×C4×C73C22⋊C411yescharacteristic
60C2×C4×C73C22⋊C411yescharacteristic
61C2×C4×C73C22×C411yescharacteristic
62C22⋊D73—42no—
63C22⋊D73—42no—
64C22⋊D73—42no—
65C2×Dic73—21no—
66C2×Dic73C22⋊C411yescharacteristic
67C2×Dic73C22⋊C411yescharacteristic
68C2×Dic73C2×D411yescharacteristic
69D292—41no—
70D292—42no—
71C4×D73—22no—
72C4×D73—22no—
73C4×D73—41no—
74C4×D73—42no—
75Dic146—42no—
76#10596833—42no—
77C22×C73—41no—
78C22×C73—41no—
79C22×C73—41no—
80C22×C73C2×C22⋊C411yescharacteristic
81C2×D73—21no—
82C2×D73—21no—
83C2×D73—41no—
84C2×D73—41no—
85C2×D73—41no—
86C2×D73AGL(1,ℤ/8)12yes—
87#64408—44no—
88C4×C73—21no—
89C4×C73—21no—
90C4×C73—21no—
91C4×C73—41no—
92Dic73—21no—
93Dic73—21no—
94Dic73—41no—
95Dic73#10412yes—
96C2×C73—81no—
97C2×C73#41011yescharacteristic
98C2×C73#41811yescharacteristic
99C2×C73C2×#10411yescharacteristic
100D73—22no—
101D73—81no—
102#1505—731nomaximal, Sylow
103C73#150511yescharacteristic, complemented, Sylow
104#532—731no—
105#432—731no—
106#376—731no—
107#327—732no—
108#327—732no—
109C2×#41—1461no—
110C4⋊Q8—731no—
111#127—731no—
112#124—1461no—
113#121—731no—
114#121—731no—
115#121—1461no—
116C4×D4—731no—
117C4×D4—1461no—
118C4×D4#6440811yescharacteristic, complemented
119C2×C42—731no—
120C2×C42—1461no—
121C4⋊C8—1461no—
122C22⋊C8—732no—
123#97—1461no—
124#95—732no—
125#95—1461no—
126#41—2924no—
127C2×Q8—1461no—
128C2×D4—731no—
129C2×D4—1461no—
130C2×D4—1461no—
131C2×D4—1461no—
132C2×D4—1461no—
133C2×D4C2×#6440811yescharacteristic
134C22×C4—21no—
135C22×C4—731no—
136C22×C4—731no—
137C22×C4—731no—
138C22×C4—1462no—
139C22×C4—1461no—
140C2×C8—1462no—
141C4⋊C4—731no—
142C4⋊C4—1461no—
143C4⋊C4C2×#6440811yescharacteristic
144C22⋊C4—21no—
145C22⋊C4—1461no—
146C22⋊C4—1461no—
147C22⋊C4—1461no—
148C42—731no—
149C42—731no—
150C42—731no—
151C42—1464no—
152C42C2×#6440811yescharacteristic
153C23—21no—
154C23—731no—
155C23—1461no—
156Q8—2922no—
157D4—41no—
158D4—2921no—
159D4—2922no—
160D4—2922no—
161D4—2922no—
162D4—2922no—
163C2×C4—21no—
164C2×C4—42no—
165C2×C4—2922no—
166C2×C4—2921no—
167C2×C4—2922no—
168C2×C4—2922no—
169C2×C4—731no—
170C2×C4—731no—
171C2×C4—731no—
172C2×C4—1462no—
173C2×C4—1462no—
174C2×C4—1464no—
175C2×C4—1461no—
176C2×C4C22⋊#6440811yescharacteristic
177C2×C4C22⋊#6440811yescharacteristic
178C2×C4C22×#6440811yescharacteristic
179C8—2922no—
180C22—41no—
181C22—41no—
182C22—41no—
183C22—2921no—
184C22—2921no—
185C22—2921no—
186C22—732no—
187C22—1461no—
188C22—1461no—
189C22C2×C22⋊#6440811yescharacteristic
190C4—21no—
191C4—21no—
192C4—21no—
193C4—41no—
194C4—2924no—
195C4—2921no—
196C4—732no—
197C4—1461no—
198C4—1461no—
199C2—81no—
200C2—5841no—
201C2—1462no—
202C2#1798956611yescharacteristic
203C2#1798957911yescharacteristic
204C2D73⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC4×D4×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC4×D4#64408
hypocenterC73#1505
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. #17989610C2semidirect
2. #17989523C2semidirect
3. #17989439C2semidirect
4. #17989438C2semidirect
13. #14556590C4semidirect
14. #14556587C4semidirect
19. C4×D292C4semidirect
22. C4×D4×C73C4semidirect
103. C73#1505semidirect
118. C4×D4#64408semidirect