Finite Group Databasebeta

← #22625334

Subgroups — #22625334

Order 9344.

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

normal subgroups only

This group has 242 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
2C4×C4⋊#64408C211yesmaximal, characteristic, complemented
3#17989440C212yesmaximal, complemented
4#17989439C212yesmaximal
5#17989122C211yesmaximal, characteristic
6C2×C4⋊#64408—21no—
7C2×C4×#64408—21no—
8#14556658—21no—
9#14556648C2212yes—
10#14556646—21no—
11(C2×#64408)⋊C4C2212yes—
12#14556586—21no—
13#14556579C411yescharacteristic, complemented
14#14556576—21no—
15#14556571C2211yescharacteristic
16#14556566C2211yescharacteristic
17#14556556C411yescharacteristic, complemented
18#14556553—21no—
19#14556553C411yescharacteristic, complemented
20#14556549—21no—
21C42×D73C2211yescharacteristic
22#125×C73C411yescharacteristic, complemented
23C22×#64408—22no—
24C2×#10596833—22no—
25C4⋊#64408—24no—
26C4×#64408—42no—
27C2×Dic146C2×C411yescharacteristic
28C2×D292—21no—
29C2×D292C2×C411yescharacteristic
30C2×C4×D73—21no—
31C2×C4×D73D411yescharacteristic
32C2×C4×D73D411yescharacteristic
33C2×C4×D73C2311yescharacteristic
34C4⋊Dic73—21no—
35#11924007—21no—
36#11924005—21no—
37#11924005—21no—
38#11924005—21no—
39#11924005—21no—
40#11924005—21no—
41C4×Dic73—21no—
42C4×Dic73C2×C411yescharacteristic
43C4×Dic73D411yescharacteristic
44C4×Dic73D411yescharacteristic
45C4⋊C4×C73—21no—
46C4⋊C4×C73—21no—
47C4⋊C4×C73C2×C411yescharacteristic
48C4⋊C4×C73C2×C411yescharacteristic
49C42×C73C2×C411yescharacteristic
50C22×D73—21no—
51C22×D73C2×D411yescharacteristic
52C2×#64408—24no—
53C2×#64408—42no—
54C2×#64408—42no—
55C2×C4×C73—21no—
56C2×C4×C73—21no—
57C2×C4×C73C22⋊C411yescharacteristic
58C2×C4×C73C22⋊C411yescharacteristic
59C2×C4×C73C22×C411yescharacteristic
60C2×Dic73—21no—
61C2×Dic73C22⋊C411yescharacteristic
62C2×Dic73C22⋊C411yescharacteristic
63C2×Dic73C2×D411yescharacteristic
64D292—41no—
65D292—41no—
66D292—41no—
67C4×D73—21no—
68C4×D73—21no—
69C4×D73—22no—
70C4×D73—41no—
71C4×D73—42no—
72Dic146—41no—
73#10596833—42no—
74C22×C73C2×C22⋊C411yescharacteristic
75C2×D73—21no—
76C2×D73—21no—
77C2×D73—41no—
78C2×D73—41no—
79C2×D73—41no—
80C2×D73AGL(1,ℤ/8)11yescharacteristic
81C2×D73#13711yescharacteristic
82#64408—44no—
83C4×C73—21no—
84C4×C73—21no—
85C4×C73—21no—
86C4×C73—41no—
87C4×C73—41no—
88Dic73—21no—
89Dic73—21no—
90Dic73—41no—
91Dic73#10412yes—
92C2×C73#41011yescharacteristic
93C2×C73#41711yescharacteristic
94C2×C73C2×#10411yescharacteristic
95D73—21no—
96D73—21no—
97D73—81no—
98#1509—731nomaximal, Sylow
99C73#150911yescharacteristic, complemented, Sylow
100#529—731no—
101#432—731no—
102C4×C4⋊C4—731no—
103#328—732no—
104#327—732no—
105#126—1461no—
106#125#6440811yescharacteristic, complemented
107#124—731no—
108#123—1461no—
109C22⋊Q8—731no—
110#121—731no—
111C4×Q8—731no—
112C4×D4—731no—
113C4×D4—1461no—
114#117—1461no—
115C2×C4⋊C4—1461no—
116C2×C42—731no—
117C2×C42—1461no—
118C4⋊C8—1461no—
119C22⋊C8—732no—
120#97—1461no—
121#95—732no—
122C2×Q8—731no—
123C2×D4—731no—
124C2×D4—1461no—
125C22×C4—731no—
126C22×C4—731no—
127C22×C4—731no—
128C22×C4—1461no—
129C22×C4—1462no—
130C2×C8—1462no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—1461no—
134C4⋊C4—1461no—
135C4⋊C4—1464no—
136C4⋊C4C2×#6440811yescharacteristic
137C4⋊C4C2×#6440811yescharacteristic
138C22⋊C4—1461no—
139C22⋊C4—1461no—
140C22⋊C4—1461no—
141C22⋊C4—1461no—
142C22⋊C4—1461no—
143C42—2922no—
144C42—731no—
145C42—731no—
146C42—731no—
147C42—1461no—
148C42C2×#6440811yescharacteristic
149C23—731no—
150C23—1461no—
151Q8—2921no—
152D4—2921no—
153D4—2921no—
154D4—2921no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—2921no—
158C2×C4—2922no—
159C2×C4—2922no—
160C2×C4—2922no—
161C2×C4—731no—
162C2×C4—731no—
163C2×C4—731no—
164C2×C4—1462no—
165C2×C4—1461no—
166C2×C4—1461no—
167C2×C4—1464no—
168C2×C4—1461no—
169C2×C4C22⋊#6440811yescharacteristic
170C2×C4C22⋊#6440811yescharacteristic
171C2×C4C22×#6440811yescharacteristic
172C8—2922no—
173C22—2921no—
174C22—2921no—
175C22—2921no—
176C22—731no—
177C22—731no—
178C22—1461no—
179C22—1461no—
180C22C2×C22⋊#6440811yescharacteristic
181C4—21no—
182C4—21no—
183C4—21no—
184C4—41no—
185C4—41no—
186C4—2924no—
187C4—2921no—
188C4—732no—
189C4—1461no—
190C4—1461no—
191C2—5841no—
192C2—1461no—
193C2—1461no—
194C2#1798956811yescharacteristic
195C2#1798957811yescharacteristic
196C2D73⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
Fitting#125×C73C4
socleC22×C73C2×C22⋊C4
hypercenter#125#64408
hypocenterC73#1509
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
1. #17989610C2semidirect
2. C4×C4⋊#64408C2semidirect
3. #17989440C2semidirect
13. #14556579C4semidirect
17. #14556556C4semidirect
19. #14556553C4semidirect
22. #125×C73C4semidirect
99. C73#1509semidirect
106. #125#64408semidirect