Finite Group Databasebeta

← #22608664

Subgroups — #22608664

Order 9344.

254 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 77 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#17989137C211yesmaximal, characteristic
2#17988611C211yesmaximal, characteristic, complemented
3#17988335C212yesmaximal, complemented
4#17988330C212yesmaximal, complemented
5#423×C73C211yesmaximal, characteristic, complemented
6C2×#11924028C412yes—
7C2×#11924012—21no—
8#14556591C2211yescharacteristic
9#14556588C2211yescharacteristic
10#14556579C412yes—
11#14556565—21no—
12#14556565—21no—
13C4×D292—21no—
14C4×D292—21no—
15C4⋊#10596831—21no—
16C4⋊#10596831C2212yes—
17C2×M16×C73—21no—
18C2×C42×C73C2211yescharacteristic
19C4⋊C8×C73—21no—
20C4⋊C8×C73C2212yes—
21#11924028—44no—
22C2×Dic146C2×C412yes—
23C2×D292—21no—
24C2×D292—21no—
25C2×D292C2×C412yes—
26C2×C22⋊D73—22no—
27C2×C4×D73—22no—
28#11924012—42no—
29C2×#10596831—22no—
30C4⋊Dic73—21no—
31C4⋊Dic73—21no—
32#11924005—22no—
33#11924005—22no—
34C22×C4×C73C2×C411yescharacteristic
35C22×C4×C73D411yescharacteristic
36C22×C4×C73D411yescharacteristic
37M16×C73—42no—
38C2×C8×C73—22no—
39C42×C73C2×C411yescharacteristic
40C42×C73D411yescharacteristic
41C42×C73D411yescharacteristic
42C42×C73C2311yescharacteristic
43C23×C73C22⋊C411yescharacteristic
44C22×D73—22no—
45C2×C4×C73—22no—
46C2×C4×C73—21no—
47C2×C4×C73—21no—
48C2×C4×C73—21no—
49C2×C4×C73—21no—
50C2×C4×C73C22⋊C411yescharacteristic
51C2×C4×C73C22⋊C411yescharacteristic
52C2×C4×C73C22⋊C411yescharacteristic
53C2×C4×C73C22×C411yescharacteristic
54C2×C4×C73C2×D411yescharacteristic
55C2×C4×C73C2×D411yescharacteristic
56C22⋊D73—44no—
57C2×Dic73—22no—
58D292—42no—
59D292—41no—
60D292—41no—
61D292—41no—
62D292—41no—
63C4×D73—44no—
64Dic146—42no—
65C8×C73—42no—
66#10596831—42no—
67C22×C73—21no—
68C22×C73—21no—
69C22×C73—21no—
70C22×C73C2×C22⋊C411yescharacteristic
71C2×D73—42no—
72C2×D73—42no—
73C2×D73—42no—
74C4×C73—21no—
75C4×C73—21no—
76C4×C73—21no—
77C4×C73#10012yes—
78C4×C73AGL(1,ℤ/8)11yescharacteristic
79C4×C73AGL(1,ℤ/8)11yescharacteristic
80C4×C73#13711yescharacteristic
81C4×C73#13711yescharacteristic
82Dic73—42no—
83C2×C73—41no—
84C2×C73C2×#10011yescharacteristic
85C2×C73#41711yescharacteristic
86C2×C73#41711yescharacteristic
87D73—82no—
88#1560—731nomaximal, Sylow
89C73#156011yescharacteristic, complemented, Sylow
90#532—731no—
91#423—731no—
92#423D7311yescharacteristic, complemented
93#333—732no—
94#331—732no—
95C2×#41—732no—
96C2×M16—21no—
97C2×M16—1461no—
98C4⋊Q8—731no—
99#127—731no—
100#124—732no—
101#121—1461no—
102#121—1461no—
103C4×D4—1461no—
104C4×D4—1461no—
105C2×C42C2×D7311yescharacteristic
106C4⋊C8—21no—
107C4⋊C8—732no—
108C4⋊C8—1461no—
109C4⋊C8C2×D7312yes—
110#41—2924no—
111C2×Q8—732no—
112C2×D4—732no—
113C2×D4—1462no—
114C2×D4—1461no—
115C2×D4—1461no—
116C22×C4—1462no—
117C22×C4C4×D7311yescharacteristic
118C22×C4D29211yescharacteristic
119C22×C4C22⋊D7311yescharacteristic
120M16—42no—
121M16—2922no—
122C2×C8—22no—
123C2×C8—1462no—
124C4⋊C4—1461no—
125C4⋊C4—1461no—
126C22⋊C4—1462no—
127C22⋊C4—1462no—
128C42C4×D7311yescharacteristic
129C42D29211yescharacteristic
130C42C22⋊D7311yescharacteristic
131C42C22×D7311yescharacteristic
132C23—1462no—
133C23#1192400511yescharacteristic
134Q8—2922no—
135D4—2922no—
136D4—2924no—
137D4—2921no—
138D4—2921no—
139D4—2921no—
140D4—2921no—
141C2×C4—22no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—2924no—
147C2×C4—1462no—
148C2×C4#1192400511yescharacteristic
149C2×C4#1192400511yescharacteristic
150C2×C4#1192400511yescharacteristic
151C2×C4C2×C4×D7311yescharacteristic
152C2×C4C2×C22⋊D7311yescharacteristic
153C2×C4C2×D29211yescharacteristic
154C8—42no—
155C8—2922no—
156C22—21no—
157C22—21no—
158C22—21no—
159C22—2922no—
160C22—2922no—
161C22—2922no—
162C22C2×#1192400511yescharacteristic
163C4—21no—
164C4—21no—
165C4—21no—
166C4—2922no—
167C4#1455650712yes—
168C4#1455661711yescharacteristic
169C4#1455661911yescharacteristic
170C4#1455662211yescharacteristic
171C4#1455662411yescharacteristic
172C2—41no—
173C2—5842no—
174C2C2×#1455650711yescharacteristic
175C2#1798858611yescharacteristic
176C2#1798858911yescharacteristic
subgroupG/H
centerC22C2×#11924005
commutatorC2×C4×C73C22×C4
FrattiniC42C22×D73
Fitting#423×C73C2
socleC22×C73C2×C22⋊C4
hypercenter#423D73
hypocenterC73#1560
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
2. #17988611C2semidirect
3. #17988335C2semidirect
4. #17988330C2semidirect
5. #423×C73C2semidirect
89. C73#1560semidirect
92. #423D73semidirect