Finite Group Databasebeta

← #22625401

Subgroups — #22625401

Order 9344.

256 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 60 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#17989546C211yesmaximal, characteristic, complemented
3#17989442C214yesmaximal, complemented
4#17989135C211yesmaximal, characteristic
5C2×#11924036—21no—
6C4⋊#10596833—21no—
7#14556648—21no—
8#14556646—21no—
9#14556646C2212yes—
10#14556646C2212yes—
11C2×#11924027C412yes—
12#14556591C411yescharacteristic
13#14556578C2212yes—
14#14556562—21no—
15#14556562—21no—
16D4×Dic73—21no—
17D4×Dic73—21no—
18C42×D73C2211yescharacteristic
19#127×C73C411yescharacteristic
20#11924036—24no—
21C2×#10596833—22no—
22C2×#10596833—22no—
23#11924027—44no—
24C2×Dic146C2×C412yes—
25C2×C22⋊D73—22no—
26C22×Dic73—22no—
27C2×C4×D73C2×C411yescharacteristic
28C2×C4×D73D411yescharacteristic
29C2×C4×D73D411yescharacteristic
30C4⋊Dic73—21no—
31C4⋊Dic73—21no—
32C22⋊Dic73—22no—
33C22⋊Dic73—22no—
34C4×Dic73D411yescharacteristic
35C4×Dic73D411yescharacteristic
36C4×Dic73C2311yescharacteristic
37C2×D4×C73—21no—
38C2×D4×C73—21no—
39C2×D4×C73C2×C412yes—
40C42×C73C2×C411yescharacteristic
41C23×C73—22no—
42C22×D73C22⋊C411yescharacteristic
43D4×C73—42no—
44D4×C73—42no—
45D4×C73—42no—
46C2×C4×C73C22⋊C411yescharacteristic
47C2×C4×C73C22⋊C411yescharacteristic
48C2×C4×C73C22×C411yescharacteristic
49C22⋊D73—44no—
50C2×Dic73—22no—
51C2×Dic73—44no—
52C2×Dic73C22⋊C411yescharacteristic
53C2×Dic73C2×D411yescharacteristic
54C2×Dic73C2×D411yescharacteristic
55C4×D73—22no—
56C4×D73—22no—
57C4×D73—41no—
58Dic146—42no—
59#10596833—24no—
60#10596833—42no—
61C22×C73—42no—
62C22×C73—42no—
63C22×C73—42no—
64C22×C73C2×C22⋊C411yescharacteristic
65C2×D73—21no—
66C2×D73—21no—
67C2×D73#10012yes—
68C4×C73—21no—
69C4×C73—21no—
70C4×C73#10412yes—
71Dic73—21no—
72Dic73—21no—
73Dic73—21no—
74Dic73—42no—
75C2×C73—82no—
76C2×C73C2×#10011yescharacteristic
77C2×C73C2×#10411yescharacteristic
78C2×C73#42111yescharacteristic
79D73—22no—
80#1530—731nomaximal, Sylow
81C73#153011yescharacteristic, complemented, Sylow
82#532—731no—
83#432—731no—
84C2×#97—731no—
85#329—734no—
86C2×#41—732no—
87C22×C8—1461no—
88C4⋊Q8—731no—
89#127#6440811yescharacteristic
90#124—732no—
91#121—1461no—
92#121—1461no—
93C4×D4—1461no—
94C4×D4—1461no—
95C2×C42—731no—
96C4⋊C8—1461no—
97C22⋊C8—1461no—
98#97—732no—
99#97—732no—
100#97—1461no—
101#41—2924no—
102C2×Q8—732no—
103C2×D4—21no—
104C2×D4—21no—
105C2×D4—1462no—
106C2×D4C2×#6440812yes—
107C22×C4—731no—
108C22×C4—731no—
109C22×C4—731no—
110C22×C4—1462no—
111C2×C8—1462no—
112C2×C8—1462no—
113C2×C8—1464no—
114C4⋊C4—1461no—
115C4⋊C4—1461no—
116C22⋊C4—1462no—
117C22⋊C4—1462no—
118C42—731no—
119C42—731no—
120C42—731no—
121C42C2×#6440811yescharacteristic
122C23—22no—
123C23—731no—
124Q8—2922no—
125D4—42no—
126D4—42no—
127D4—42no—
128D4—2924no—
129C2×C4—2921no—
130C2×C4—2924no—
131C2×C4—731no—
132C2×C4—731no—
133C2×C4—731no—
134C2×C4—1462no—
135C2×C4—1462no—
136C2×C4—1462no—
137C2×C4C22⋊#6440811yescharacteristic
138C2×C4C22⋊#6440811yescharacteristic
139C2×C4C22×#6440811yescharacteristic
140C8—2922no—
141C8—1464no—
142C22—42no—
143C22—42no—
144C22—42no—
145C22—732no—
146C22—1461no—
147C22—1461no—
148C22C2×C22⋊#6440811yescharacteristic
149C4—21no—
150C4—21no—
151C4—2922no—
152C4—1461no—
153C4—1461no—
154C4—1461no—
155C4#1455665512yes—
156C2—82no—
157C2—1462no—
158C2D73⋊#10011yescharacteristic
159C2C2×#1455665511yescharacteristic
160C2#1798958511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
Fitting#127×C73C4
socleC22×C73C2×C22⋊C4
hypercenter#127#64408
hypocenterC73#1530
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #17989609C2semidirect
2. #17989546C2semidirect
3. #17989442C2semidirect
81. C73#1530semidirect