Finite Group Databasebeta

← #22626073

Subgroups — #22626073

Order 9344.

396 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 76 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#17989590C211yesmaximal, characteristic, complemented
2C2×#14556651C214yesmaximal, complemented
3C4×#11924037C211yesmaximal, characteristic, complemented
4C2×#14556587C211yesmaximal, characteristic
5C2×#11924037C2212yes—
6C2×#11924037C2212yes—
7#14556658—21no—
8C4⋊#10596833—21no—
9#14556651—28no—
10#14556646—21no—
11C4×#10596833—21no—
12C22×D292C411yescharacteristic
13C22×C22⋊D73C412yes—
14C22×C22⋊D73C2212yes—
15#14556587—21no—
16#14556587—21no—
17#14556587—21no—
18#14556587—21no—
19C2×C4×Dic73C2211yescharacteristic
20C22×D4×C73C411yescharacteristic
21#11924037—22no—
22#11924037—24no—
23#11924037D414yescomplemented
24C2×#10596833—22no—
25C2×#10596833—22no—
26C23×D73C2×C412yes—
27C2×D292—21no—
28C2×D292—21no—
29C2×D292—42no—
30C2×C22⋊D73—22no—
31C2×C22⋊D73—22no—
32C2×C22⋊D73—22no—
33C2×C22⋊D73—22no—
34C2×C22⋊D73—24no—
35C2×C22⋊D73—24no—
36C2×C22⋊D73—44no—
37C22×Dic73C2×C411yescharacteristic
38C22×Dic73C2311yescharacteristic
39C4×Dic73D411yescharacteristic
40C4×Dic73D411yescharacteristic
41C4×Dic73D411yescharacteristic
42C4×Dic73D411yescharacteristic
43C24×C73C2×C412yes—
44C2×D4×C73—21no—
45C2×D4×C73—21no—
46C2×D4×C73—42no—
47C22×C4×C73C2×C411yescharacteristic
48C23×C73—22no—
49C23×C73—24no—
50C23×C73—42no—
51C23×C73—42no—
52C23×C73C22×C411yescharacteristic
53C22×D73—22no—
54C22×D73—24no—
55C22×D73—42no—
56C22×D73—42no—
57D4×C73—42no—
58D4×C73—42no—
59C2×C4×C73—22no—
60C2×C4×C73C22⋊C411yescharacteristic
61C2×C4×C73C22⋊C411yescharacteristic
62C22⋊D73—44no—
63C22⋊D73—44no—
64C22⋊D73—44no—
65C22⋊D73—42no—
66C22⋊D73—42no—
67C2×Dic73—22no—
68C2×Dic73C22⋊C411yescharacteristic
69C2×Dic73C22⋊C411yescharacteristic
70C2×Dic73C2×D411yescharacteristic
71C2×Dic73C2×D412yes—
72C2×Dic73C2×D411yescharacteristic
73C2×Dic73#4112yes—
74D292—42no—
75D292—42no—
76#10596833—24no—
77#10596833—42no—
78C22×C73—21no—
79C22×C73—21no—
80C22×C73—42no—
81C22×C73—42no—
82C22×C73—42no—
83C22×C73—84no—
84C22×C73C2×C22⋊C411yescharacteristic
85C22×C73C4×D412yes—
86C2×D73—42no—
87C2×D73—42no—
88C2×D73—42no—
89C2×D73—84no—
90C4×C73—21no—
91C4×C73#10012yescomplemented
92Dic73—21no—
93Dic73#10012yescomplemented
94Dic73#12112yes—
95Dic73#12411yescharacteristic
96Dic73#12711yescharacteristic
97C2×C73—22no—
98C2×C73—82no—
99C2×C73#39011yescharacteristic
100C2×C73C2×#10011yescharacteristic
101C2×C73C2×#10011yescharacteristic
102D73—82no—
103#1965—731nomaximal, Sylow
104C73#196511yescharacteristic, complemented, Sylow
105C2×#127—731no—
106#423—731no—
107C2×#100—734no—
108C4×M16—731no—
109C22×D4—732no—
110C22×D4—732no—
111C22×D4—731no—
112C22×D4#6440811yescharacteristic
113C2×M16—732no—
114C2×M16—732no—
115#127—1461no—
116#127—1461no—
117#127—1461no—
118#127—1461no—
119C2×C42—731no—
120C4⋊C8—1461no—
121C4⋊C8—1461no—
122#100—1468no—
123#97—1461no—
124C4×C8—1461no—
125C24—732no—
126C24C2×#6440812yes—
127C2×D4—21no—
128C2×D4—21no—
129C2×D4—42no—
130C2×D4—2922no—
131C2×D4—2924no—
132C2×D4—1464no—
133C2×D4—1462no—
134C2×D4—1462no—
135C2×D4—1462no—
136C2×D4—1462no—
137C2×D4—1464no—
138C2×D4—1461no—
139C2×D4—1461no—
140C22×C4—731no—
141C22×C4—731no—
142C22×C4C2×#6440811yescharacteristic
143M16—734no—
144M16—1464no—
145M16—1462no—
146C2×C8—1462no—
147C2×C8—1462no—
148C42—731no—
149C42—731no—
150C42—731no—
151C42—731no—
152C23—22no—
153C23—24no—
154C23—42no—
155C23—42no—
156C23—2922no—
157C23—2922no—
158C23—1462no—
159C23—1464no—
160C23C22×#6440811yescharacteristic
161D4—42no—
162D4—42no—
163D4—2922no—
164D4—2924no—
165D4—2922no—
166D4—2924no—
167D4—2922no—
168D4—2924no—
169D4—2922no—
170C2×C4—22no—
171C2×C4—731no—
172C2×C4—731no—
173C2×C4—731no—
174C2×C4—732no—
175C2×C4—732no—
176C2×C4—731no—
177C2×C4—1462no—
178C2×C4C22⋊#6440811yescharacteristic
179C2×C4C22⋊#6440811yescharacteristic
180C8—2922no—
181C8—1464no—
182C22—21no—
183C22—21no—
184C22—42no—
185C22—42no—
186C22—42no—
187C22—84no—
188C22—2922no—
189C22—2922no—
190C22—2922no—
191C22—5844no—
192C22C2×C22⋊#6440811yescharacteristic
193C22D4×#6440812yes—
194C4—21no—
195C4—731no—
196C4—732no—
197C4—731no—
198C4—732no—
199C4—1461no—
200C4#1455665112yescomplemented
201C2—22no—
202C2—82no—
203C2—5842no—
204C2#1798953911yescharacteristic
205C2C2×#1455665111yescharacteristic
206C2D73⋊#10011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC23×C73C22×C4
FrattiniC23C22×#64408
FittingC22×D4×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC22×D4#64408
hypocenterC73#1965
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #17989590C2semidirect
2. C2×#14556651C2semidirect
3. C4×#11924037C2semidirect
23. #11924037D4semidirect
91. C4×C73#100semidirect
93. Dic73#100semidirect
104. C73#1965semidirect
200. C4#14556651semidirect