Finite Group Databasebeta

← #22625213

Subgroups — #22625213

Order 9344.

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

normal subgroups only

This group has 214 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#17989607C211yesmaximal, characteristic, complemented
2#17989603C211yesmaximal, characteristic, complemented
3#17989433C212yesmaximal, complemented
4#17989430C212yesmaximal
5C2×#14556584C211yesmaximal, characteristic
6#14556658—21no—
7C4⋊#10596833—21no—
8C22⋊#10596833C2212yes—
9C22⋊#10596833C2212yes—
10#14556646—21no—
11C4×#10596833—21no—
12#14556584—21no—
13#14556584—21no—
14#14556584—21no—
15#14556584—21no—
16C2×C4⋊Dic73C411yescharacteristic
17C2×#11924007C411yescharacteristic
18C2×#11924007C2211yescharacteristic
19C2×C22⋊Dic73C411yescharacteristic
20C2×C22⋊Dic73C2211yescharacteristic
21C2×C4×Dic73C2211yescharacteristic
22C2×C22⋊C4×C73C411yescharacteristic
23C2×#10596833—22no—
24C2×#10596833—22no—
25C22×Dic73C2×C411yescharacteristic
26C22×Dic73C2×C411yescharacteristic
27C22×Dic73C2×C411yescharacteristic
28C22×Dic73C2311yescharacteristic
29C4⋊Dic73—21no—
30C4⋊Dic73—21no—
31#11924007—21no—
32#11924007—21no—
33#11924007—21no—
34#11924007—21no—
35C22⋊Dic73—21no—
36C22⋊Dic73—21no—
37C22⋊Dic73—21no—
38C22⋊Dic73—21no—
39C4×Dic73D411yescharacteristic
40C4×Dic73D411yescharacteristic
41C4×Dic73D411yescharacteristic
42C4×Dic73D411yescharacteristic
43C24×C73C2×C411yescharacteristic
44C22×C4×C73C2×C411yescharacteristic
45C22×C4×C73C2×C411yescharacteristic
46C22⋊C4×C73—21no—
47C22⋊C4×C73—21no—
48C23×C73—21no—
49C23×C73—22no—
50C23×C73—41no—
51C23×C73—41no—
52C23×C73C22×C411yescharacteristic
53C2×C4×C73—22no—
54C2×C4×C73—21no—
55C2×C4×C73—41no—
56C2×C4×C73C22⋊C411yescharacteristic
57C2×C4×C73C22⋊C411yescharacteristic
58C2×Dic73—21no—
59C2×Dic73—21no—
60C2×Dic73—22no—
61C2×Dic73—41no—
62C2×Dic73—41no—
63C2×Dic73—41no—
64C2×Dic73C22⋊C411yescharacteristic
65C2×Dic73C22⋊C411yescharacteristic
66C2×Dic73C2×D411yescharacteristic
67C2×Dic73C2×D411yescharacteristic
68#10596833—42no—
69#10596833—42no—
70C22×C73—21no—
71C22×C73—21no—
72C22×C73—41no—
73C22×C73—41no—
74C22×C73—41no—
75C22×C73—82no—
76C22×C73C2×C22⋊C411yescharacteristic
77C22×C73#13112yes—
78C4×C73—21no—
79C4×C73—21no—
80C4×C73—41no—
81Dic73—21no—
82Dic73—21no—
83Dic73—21no—
84Dic73—21no—
85Dic73—41no—
86Dic73—41no—
87C2×C73—22no—
88C2×C73—81no—
89C2×C73#40811yescharacteristic
90C2×C73#41011yescharacteristic
91C2×C73#41311yescharacteristic
92#1473—731nomaximal, Sylow
93C73#147311yescharacteristic, complemented, Sylow
94C2×#126—731no—
95#432—731no—
96#431—731no—
97#324—732no—
98#323—732no—
99#126—1461no—
100#126—1461no—
101#126—1461no—
102#126—1461no—
103C2×C4⋊C4—731no—
104C2×C4⋊C4—731no—
105C2×C4⋊C4—731no—
106C2×C22⋊C4—731no—
107C2×C22⋊C4—731no—
108C2×C22⋊C4#6440811yescharacteristic
109C2×C42—731no—
110C4⋊C8—1461no—
111C4⋊C8—1461no—
112C22⋊C8—732no—
113C22⋊C8—732no—
114#97—1461no—
115C4×C8—1461no—
116C24C2×#6440811yescharacteristic
117C22×C4—731no—
118C22×C4—731no—
119C22×C4—731no—
120C22×C4—731no—
121C22×C4C2×#6440811yescharacteristic
122C22×C4C2×#6440811yescharacteristic
123C2×C8—1462no—
124C2×C8—1462no—
125C4⋊C4—1461no—
126C4⋊C4—1461no—
127C4⋊C4—1461no—
128C4⋊C4—1461no—
129C4⋊C4—1461no—
130C4⋊C4—1461no—
131C22⋊C4—21no—
132C22⋊C4—21no—
133C22⋊C4—1461no—
134C22⋊C4—1461no—
135C22⋊C4—1461no—
136C22⋊C4—1461no—
137C42—731no—
138C42—731no—
139C42—731no—
140C42—731no—
141C23—21no—
142C23—22no—
143C23—41no—
144C23—41no—
145C23C22×#6440811yescharacteristic
146C2×C4—22no—
147C2×C4—21no—
148C2×C4—41no—
149C2×C4—2921no—
150C2×C4—2921no—
151C2×C4—2921no—
152C2×C4—731no—
153C2×C4—731no—
154C2×C4—731no—
155C2×C4—731no—
156C2×C4—1462no—
157C2×C4—1461no—
158C2×C4—1461no—
159C2×C4C22⋊#6440811yescharacteristic
160C2×C4C22⋊#6440811yescharacteristic
161C8—2922no—
162C8—2922no—
163C22—21no—
164C22—21no—
165C22—41no—
166C22—41no—
167C22—41no—
168C22—82no—
169C22C2×C22⋊#6440811yescharacteristic
170C22#1455667812yes—
171C4—21no—
172C4—21no—
173C4—41no—
174C4—2921no—
175C4—2921no—
176C4—1461no—
177C4—1461no—
178C4—1461no—
179C4—1461no—
180C2—22no—
181C2—81no—
182C2#1798956011yescharacteristic
183C2#1798956711yescharacteristic
184C2#1798957311yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC23×C73C22×C4
FrattiniC23C22×#64408
FittingC2×C22⋊C4×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC2×C22⋊C4#64408
hypocenterC73#1473
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #17989607C2semidirect
2. #17989603C2semidirect
3. #17989433C2semidirect
93. C73#1473semidirect