Finite Group Databasebeta

← #22626190

Subgroups — #22626190

Order 9344.

266 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 54 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#17989573C211yesmaximal, characteristic, complemented
2#17989566C211yesmaximal, characteristic, complemented
3#17989487C214yesmaximal, complemented
4#17989154C211yesmaximal, characteristic
5D73⋊M16—21no—
6#14556670—21no—
7#14556652—21no—
8#14556651C2212yes—
9#14556650—21no—
10#14556649C2212yes—
11C2×#11924028C2211yescharacteristic
12#14556587—21no—
13#14556578—21no—
14#14556562—21no—
15#14556562—21no—
16#14556560C412yescomplemented
17#14556560C2212yes—
18#14556550C411yescharacteristic, complemented
19C22×D4×C73C411yescharacteristic, complemented
20#11924038—41no—
21#11924037—22no—
22#11924036—41no—
23C4⋊#64408—41no—
24C22⋊#64408—22no—
25C4×#64408—41no—
26#11924028—41no—
27#11924028—41no—
28C2×Dic146D411yescharacteristic
29C2×D292D411yescharacteristic
30C2×C22⋊D73—22no—
31C2×C22⋊D73—22no—
32C2×C22⋊D73C2×C411yescharacteristic
33C2×C22⋊D73C2311yescharacteristic
34C2×C4×D73D411yescharacteristic
35C2×C4×D73D411yescharacteristic
36C4⋊Dic73—21no—
37C22⋊Dic73—22no—
38C22⋊Dic73—22no—
39C22⋊Dic73C2×C412yes—
40C4×Dic73—21no—
41C24×C73C2×C412yes—
42C2×D4×C73—21no—
43C2×D4×C73—21no—
44C2×D4×C73—41no—
45C2×D4×C73—41no—
46C22×C4×C73C2×C411yescharacteristic
47C23×C73—22no—
48C23×C73—42no—
49C23×C73—82no—
50C23×C73C22×C411yescharacteristic
51C22×D73C22⋊C411yescharacteristic
52C22×D73C2×D411yescharacteristic
53C2×#64408—42no—
54D4×C73—42no—
55D4×C73—41no—
56D4×C73—41no—
57C2×C4×C73—21no—
58C2×C4×C73—21no—
59C2×C4×C73C22⋊C411yescharacteristic
60C2×C4×C73C22⋊C411yescharacteristic
61C22⋊D73—41no—
62C22⋊D73—41no—
63C22⋊D73—82no—
64C22⋊D73—82no—
65C2×Dic73—22no—
66C2×Dic73C22⋊C411yescharacteristic
67C2×Dic73C2×D411yescharacteristic
68D292—41no—
69C4×D73—21no—
70C4×D73—21no—
71C4×D73—21no—
72C4×D73—21no—
73Dic146—41no—
74#10596833—42no—
75C22×C73—21no—
76C22×C73—41no—
77C22×C73—42no—
78C22×C73—42no—
79C22×C73—42no—
80C22×C73—84no—
81C22×C73C2×C22⋊C411yescharacteristic
82C2×D73—21no—
83C2×D73—21no—
84C2×D73—41no—
85C2×D73—41no—
86#64408—82no—
87C4×C73—21no—
88C4×C73#9911yescharacteristic
89C4×C73#9911yescharacteristic
90Dic73—21no—
91Dic73—21no—
92Dic73—42no—
93C2×C73—21no—
94C2×C73—41no—
95C2×C73—82no—
96C2×C73C2×#9911yescharacteristic
97D73—41no—
98D73—41no—
99#2122—731nomaximal, Sylow
100C73#212211yescharacteristic, complemented, Sylow
101#535—731no—
102#413—731no—
103#410—731no—
104AΣL(1,𝔽16)—734no—
105C2×#41—731no—
106C22×D4#6440811yescharacteristic, complemented
107C2×M16—1461no—
108#127—1461no—
109#124—1461no—
110#121—1461no—
111#121—1461no—
112#120—732no—
113#120—732no—
114#117—731no—
115#117—1461no—
116#101—1461no—
117#100—732no—
118#99—732no—
119#99—1461no—
120C24C2×#6440812yes—
121#41—2921no—
122#41—2921no—
123C2×Q8—731no—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—41no—
127C2×D4—41no—
128C2×D4—731no—
129C2×D4—731no—
130C2×D4—731no—
131C2×D4—1462no—
132C2×D4—1462no—
133C22×C4—731no—
134C22×C4—731no—
135C22×C4C2×#6440811yescharacteristic
136M16—2921no—
137M16—1462no—
138C2×C8—2921no—
139C4⋊C4—2921no—
140C4⋊C4—1461no—
141C22⋊C4—732no—
142C22⋊C4—1462no—
143C22⋊C4—1462no—
144C22⋊C4—1462no—
145C42—2921no—
146C42—1461no—
147C23—22no—
148C23—42no—
149C23—82no—
150C23—731no—
151C23—731no—
152C23C22×#6440811yescharacteristic
153Q8—2921no—
154D4—42no—
155D4—41no—
156D4—41no—
157D4—2921no—
158D4—2921no—
159D4—2921no—
160D4—5842no—
161D4—5842no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—2922no—
165C2×C4—731no—
166C2×C4—731no—
167C2×C4—1462no—
168C2×C4—1461no—
169C2×C4—1461no—
170C2×C4—1461no—
171C2×C4—1461no—
172C2×C4C22⋊#6440811yescharacteristic
173C2×C4C22⋊#6440811yescharacteristic
174C8—2922no—
175C22—21no—
176C22—41no—
177C22—42no—
178C22—42no—
179C22—42no—
180C22—84no—
181C22—2921no—
182C22—2921no—
183C22—1461no—
184C22—1461no—
185C22C2×C22⋊#6440811yescharacteristic
186C4—21no—
187C4—2922no—
188C4—5842no—
189C4—1461no—
190C4—1461no—
191C4#1455664911yescharacteristic
192C4#1455664911yescharacteristic
193C2—21no—
194C2—41no—
195C2—82no—
196C2—2921no—
197C2—2921no—
198C2C2×#1455664911yescharacteristic
subgroupG/H
centerC2C2×#14556649
commutatorC23×C73C22×C4
FrattiniC23C22×#64408
FittingC22×D4×C73C4
socleC2×C73C2×#99
hypercenterC22×D4#64408
hypocenterC73#2122
LCSG ▷ C23×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #17989573C2semidirect
2. #17989566C2semidirect
3. #17989487C2semidirect
16. #14556560C4semidirect
18. #14556550C4semidirect
19. C22×D4×C73C4semidirect
100. C73#2122semidirect
106. C22×D4#64408semidirect