Finite Group Databasebeta

← #22608637

Subgroups — #22608637

Order 9344.

242 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 73 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#17988640C211yesmaximal, characteristic, complemented
3#17988332C212yesmaximal, complemented
4#17988330C212yesmaximal, complemented
5#432×C73C211yesmaximal, characteristic, complemented
6C2×#11924028—21no—
7#14556591C2211yescharacteristic
8#14556588C2211yescharacteristic
9#14556579—21no—
10#14556565—21no—
11#14556565C412yes—
12C4×D292—21no—
13C4×D292C412yes—
14C4⋊#10596831C2212yes—
15C22⋊#10596831—21no—
16C4×#10596831—21no—
17C2×C42×C73C2211yescharacteristic
18C4⋊C8×C73C2212yes—
19C22⋊C8×C73—21no—
20#97×C73—21no—
21#11924028—44no—
22C2×Dic146—21no—
23C2×D292—21no—
24C2×D292—21no—
25C2×D292C2×C412yes—
26C2×C22⋊D73—22no—
27C2×C4×D73—22no—
28C2×#10596831—22no—
29C4⋊Dic73—21no—
30C4⋊Dic73C2×C412yes—
31#11924005—22no—
32#11924005—22no—
33C22×C4×C73C2×C411yescharacteristic
34C22×C4×C73D411yescharacteristic
35C22×C4×C73D411yescharacteristic
36C2×C8×C73—22no—
37C42×C73C2×C411yescharacteristic
38C42×C73D411yescharacteristic
39C42×C73D411yescharacteristic
40C42×C73C2311yescharacteristic
41C23×C73C22⋊C411yescharacteristic
42C22×D73—22no—
43C2×C4×C73—22no—
44C2×C4×C73—22no—
45C2×C4×C73—41no—
46C2×C4×C73C22⋊C411yescharacteristic
47C2×C4×C73C22⋊C411yescharacteristic
48C2×C4×C73C22⋊C411yescharacteristic
49C2×C4×C73C22×C411yescharacteristic
50C2×C4×C73C2×D411yescharacteristic
51C2×C4×C73C2×D411yescharacteristic
52C22⋊D73—44no—
53C2×Dic73—22no—
54D292—42no—
55D292—42no—
56D292—42no—
57C4×D73—44no—
58Dic146—42no—
59C8×C73—42no—
60#10596831—42no—
61C22×C73—21no—
62C22×C73—21no—
63C22×C73—21no—
64C22×C73C2×C22⋊C411yescharacteristic
65C2×D73—42no—
66C2×D73—42no—
67C2×D73—42no—
68C4×C73—21no—
69C4×C73—21no—
70C4×C73—21no—
71C4×C73—21no—
72C4×C73#13512yes—
73C4×C73AGL(1,ℤ/8)12yes—
74Dic73—42no—
75C2×C73—41no—
76C2×C73#41311yescharacteristic
77C2×C73#41611yescharacteristic
78C2×C73#41811yescharacteristic
79D73—82no—
80#1553—731nomaximal, Sylow
81C73#155311yescharacteristic, complemented, Sylow
82#532—731no—
83#432D7311yescharacteristic, complemented
84#431—731no—
85#332—732no—
86#331—732no—
87C2×#41—1461no—
88C4⋊Q8—731no—
89#127—731no—
90#124—1461no—
91#121—732no—
92#121—1461no—
93C4×D4—732no—
94C4×D4—1461no—
95C2×C42C2×D7311yescharacteristic
96C4⋊C8—732no—
97C4⋊C8C2×D7312yes—
98C22⋊C8—21no—
99C22⋊C8—1461no—
100#97—21no—
101C4×C8—1461no—
102#41—2924no—
103C2×Q8—1461no—
104C2×D4—732no—
105C2×D4—1462no—
106C2×D4—1461no—
107C2×D4—1461no—
108C22×C4—1462no—
109C22×C4C4×D7311yescharacteristic
110C22×C4D29211yescharacteristic
111C22×C4C22⋊D7311yescharacteristic
112C2×C8—22no—
113C2×C8—1462no—
114C4⋊C4—732no—
115C4⋊C4—1461no—
116C22⋊C4—1462no—
117C22⋊C4—1462no—
118C42C4×D7311yescharacteristic
119C42D29211yescharacteristic
120C42C22⋊D7311yescharacteristic
121C42C22×D7311yescharacteristic
122C23—1462no—
123C23#1192400511yescharacteristic
124Q8—2922no—
125D4—2922no—
126D4—2924no—
127D4—2922no—
128D4—2922no—
129C2×C4—22no—
130C2×C4—22no—
131C2×C4—41no—
132C2×C4—2924no—
133C2×C4—1462no—
134C2×C4#1192400511yescharacteristic
135C2×C4#1192400511yescharacteristic
136C2×C4#1192400511yescharacteristic
137C2×C4C2×C4×D7311yescharacteristic
138C2×C4C2×C22⋊D7311yescharacteristic
139C2×C4C2×D29211yescharacteristic
140C8—42no—
141C8—2922no—
142C22—21no—
143C22—21no—
144C22—21no—
145C22—2922no—
146C22—2922no—
147C22—2922no—
148C22C2×#1192400511yescharacteristic
149C4—21no—
150C4—21no—
151C4—21no—
152C4—21no—
153C4—2922no—
154C4#1455661112yes—
155C4#1455661912yes—
156C2—41no—
157C2—5842no—
158C2#1798856911yescharacteristic
159C2#1798858111yescharacteristic
160C2#1798859311yescharacteristic
subgroupG/H
centerC22C2×#11924005
commutatorC2×C4×C73C22×C4
FrattiniC42C22×D73
Fitting#432×C73C2
socleC22×C73C2×C22⋊C4
hypercenter#432D73
hypocenterC73#1553
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. #17988640C2semidirect
3. #17988332C2semidirect
4. #17988330C2semidirect
5. #432×C73C2semidirect
81. C73#1553semidirect
83. #432D73semidirect