Finite Group Databasebeta

← #22625469

Subgroups — #22625469

Order 9344.

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

normal subgroups only

This group has 254 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#17989592C212yesmaximal, complemented
2#17989447C212yesmaximal, complemented
3#17989445C212yesmaximal, complemented
4#17989136C211yesmaximal, characteristic
5C2×#11924038—22no—
6#14556658—22no—
7#14556658C2214yes—
8C2×#11924029C411yescharacteristic
9C2×#11924027C411yescharacteristic
10#14556589C2211yescharacteristic
11#14556587C2211yescharacteristic
12#14556579C411yescharacteristic
13#14556564—22no—
14#14556551—22no—
15C42×D73C2211yescharacteristic
16#124×C73C411yescharacteristic
17#11924038—44no—
18C2×#10596833—24no—
19#11924029—42no—
20#11924027—42no—
21C2×Dic146C2×C411yescharacteristic
22C2×D292—21no—
23C2×D292C2×C411yescharacteristic
24C2×C22⋊D73—21no—
25C2×C22⋊D73—22no—
26C22×Dic73—21no—
27C2×C4×D73—21no—
28C2×C4×D73C2×C411yescharacteristic
29C2×C4×D73D412yes—
30#11924007—22no—
31#11924005—22no—
32C4×Dic73D412yes—
33C4×Dic73C2311yescharacteristic
34C2×Q8×C73C2×C411yescharacteristic
35C2×D4×C73C2×C411yescharacteristic
36C22⋊C4×C73—22no—
37C42×C73C2×C411yescharacteristic
38C23×C73—21no—
39C22×D73—21no—
40C22×D73C22⋊C411yescharacteristic
41Q8×C73—41no—
42D4×C73—41no—
43C2×C4×C73—21no—
44C2×C4×C73C22⋊C412yes—
45C2×C4×C73C22×C411yescharacteristic
46C22⋊D73—42no—
47C22⋊D73—42no—
48C22⋊D73—42no—
49C2×Dic73—21no—
50C2×Dic73—42no—
51C2×Dic73C22⋊C411yescharacteristic
52C2×Dic73C2×D412yes—
53D292—41no—
54D292—42no—
55C4×D73—22no—
56C4×D73—22no—
57C4×D73—22no—
58C4×D73—42no—
59Dic146—41no—
60#10596833—44no—
61C22×C73—41no—
62C22×C73—42no—
63C22×C73C2×C22⋊C411yescharacteristic
64C2×D73—21no—
65C2×D73—22no—
66C2×D73—41no—
67C2×D73—42no—
68C4×C73—21no—
69C4×C73—22no—
70C4×C73—41no—
71Dic73—41no—
72Dic73#10012yes—
73Dic73AGL(1,ℤ/8)12yes—
74Dic73#13712yes—
75C2×C73—81no—
76C2×C73C2×#10011yescharacteristic
77C2×C73#41712yes—
78D73—41no—
79D73—81no—
80#1560—731nomaximal, Sylow
81C73#156011yescharacteristic, complemented, Sylow
82#532—731no—
83#423—732no—
84#333—732no—
85#331—732no—
86C2×#41—731no—
87C2×#41—731no—
88C2×M16—1462no—
89C4⋊Q8—731no—
90#127—731no—
91#124—731no—
92#124#6440811yescharacteristic
93#121—1462no—
94C4×D4—1462no—
95C2×C42—731no—
96C4⋊C8—734no—
97C4⋊C8—1462no—
98#41—2922no—
99#41—2922no—
100C2×Q8—731no—
101C2×Q8C2×#6440811yescharacteristic
102C2×D4—731no—
103C2×D4—1461no—
104C2×D4—1462no—
105C2×D4—1461no—
106C2×D4C2×#6440811yescharacteristic
107C22×C4—732no—
108C22×C4—731no—
109C22×C4—1461no—
110C22×C4—1461no—
111M16—2924no—
112C2×C8—1464no—
113C4⋊C4—1462no—
114C22⋊C4—22no—
115C22⋊C4—1462no—
116C42—732no—
117C42—731no—
118C42C2×#6440811yescharacteristic
119C23—21no—
120C23—731no—
121C23—1461no—
122Q8—41no—
123Q8—2921no—
124D4—41no—
125D4—2921no—
126D4—2922no—
127D4—2922no—
128D4—2922no—
129D4—2922no—
130C2×C4—21no—
131C2×C4—2922no—
132C2×C4—2922no—
133C2×C4—732no—
134C2×C4—731no—
135C2×C4—1462no—
136C2×C4—1462no—
137C2×C4—1462no—
138C2×C4—1461no—
139C2×C4C22⋊#6440812yes—
140C2×C4C22×#6440811yescharacteristic
141C8—2924no—
142C22—41no—
143C22—42no—
144C22—2921no—
145C22—2922no—
146C22—1461no—
147C22—1462no—
148C22C2×C22⋊#6440811yescharacteristic
149C4—21no—
150C4—22no—
151C4—41no—
152C4—2921no—
153C4—732no—
154C4—732no—
155C4—732no—
156C2—81no—
157C2—2921no—
158C2—5841no—
159C2D73⋊#10011yescharacteristic
160C2#1798957812yes—
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
Fitting#124×C73C4
socleC22×C73C2×C22⋊C4
hypercenter#124#64408
hypocenterC73#1560
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #17989592C2semidirect
2. #17989447C2semidirect
3. #17989445C2semidirect
81. C73#1560semidirect