Finite Group Databasebeta

← #22625208

Subgroups — #22625208

Order 9344.

322 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 64 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#17989558C211yesmaximal, characteristic, complemented
2#17989555C211yesmaximal, characteristic, complemented
3#17989431C214yesmaximal, complemented
4C2×#14556566C211yesmaximal, characteristic
5C2×#11924038—21no—
6C2×#11924036—21no—
7#14556648—21no—
8#14556648—21no—
9C22⋊#10596833C2212yes—
10C22⋊#10596833C2212yes—
11C22×D292C412yes—
12C22×D292C411yescharacteristic
13C22×C4×D73C2211yescharacteristic
14#14556566—21no—
15#14556566—21no—
16#14556566—21no—
17#14556566—21no—
18C2×#11924005C2212yes—
19C2×C4⋊C4×C73C411yescharacteristic
20#11924038—42no—
21#11924036—42no—
22C2×#10596833—22no—
23C2×#10596833—22no—
24C23×D73C2×C411yescharacteristic
25C23×D73C2×C412yes—
26C2×D292—22no—
27C2×D292—22no—
28C2×D292—21no—
29C2×D292—21no—
30C2×D292—42no—
31C2×D292—44no—
32C22×Dic73C2311yescharacteristic
33C2×C4×D73—42no—
34C2×C4×D73D411yescharacteristic
35C2×C4×D73D411yescharacteristic
36C2×C4×D73D411yescharacteristic
37C2×C4×D73D411yescharacteristic
38#11924005—22no—
39#11924005—22no—
40C22×C4×C73C2×C412yes—
41C22×C4×C73C2×C411yescharacteristic
42C4⋊C4×C73—21no—
43C4⋊C4×C73—21no—
44C23×C73C22×C411yescharacteristic
45C22×D73—22no—
46C22×D73—22no—
47C22×D73—22no—
48C22×D73—24no—
49C22×D73—41no—
50C22×D73—42no—
51C22×D73—42no—
52C22×D73C22⋊C411yescharacteristic
53C22×D73C22⋊C411yescharacteristic
54C2×C4×C73—22no—
55C2×C4×C73—22no—
56C2×C4×C73—42no—
57C2×C4×C73C22⋊C411yescharacteristic
58C2×C4×C73C22⋊C411yescharacteristic
59C2×Dic73—41no—
60C2×Dic73C2×D411yescharacteristic
61C2×Dic73C2×D411yescharacteristic
62D292—42no—
63D292—44no—
64D292—44no—
65D292—42no—
66C4×D73—22no—
67C4×D73—22no—
68C4×D73—41no—
69C4×D73—41no—
70#10596833—42no—
71#10596833—42no—
72C22×C73—21no—
73C22×C73—21no—
74C22×C73C2×C22⋊C411yescharacteristic
75C22×C73#13112yes—
76C2×D73—21no—
77C2×D73—21no—
78C2×D73—21no—
79C2×D73—21no—
80C2×D73—21no—
81C2×D73—44no—
82C2×D73—42no—
83C2×D73—42no—
84C2×D73—42no—
85C2×D73—84no—
86C2×D73#10012yes—
87C4×C73—21no—
88C4×C73—42no—
89C4×C73#9912yes—
90Dic73—21no—
91Dic73—21no—
92C2×C73—22no—
93C2×C73#40811yescharacteristic
94C2×C73C2×#9911yescharacteristic
95C2×C73C2×#10011yescharacteristic
96D73—22no—
97D73—41no—
98D73—82no—
99#1471—731nomaximal, Sylow
100C73#147111yescharacteristic, complemented, Sylow
101C2×#121—731no—
102#407—731no—
103C2×C22⋊C8—731no—
104#323—734no—
105C22×D4—732no—
106C22×D4—731no—
107C23×C4—731no—
108C2×M16—1461no—
109C22×C8—1461no—
110#121—1461no—
111#121—1461no—
112#121—1461no—
113#121—1461no—
114C2×C4⋊C4#6440811yescharacteristic
115C2×C22⋊C4—732no—
116C22⋊C8—732no—
117C22⋊C8—732no—
118C22⋊C8—1461no—
119C22⋊C8—1461no—
120C24—732no—
121C24—731no—
122C2×D4—2922no—
123C2×D4—2924no—
124C2×D4—1462no—
125C2×D4—1462no—
126C2×D4—1461no—
127C2×D4—1461no—
128C22×C4—2922no—
129C22×C4—731no—
130C22×C4—731no—
131C22×C4—731no—
132C22×C4—731no—
133C22×C4—731no—
134C22×C4C2×#6440812yes—
135C22×C4C2×#6440811yescharacteristic
136M16—2922no—
137C2×C8—2922no—
138C2×C8—1462no—
139C2×C8—1462no—
140C4⋊C4—21no—
141C4⋊C4—21no—
142C22⋊C4—1462no—
143C22⋊C4—1462no—
144C23—2921no—
145C23—2922no—
146C23—2922no—
147C23—731no—
148C23—731no—
149C23—1462no—
150C23—1462no—
151C23—1462no—
152C23—1464no—
153C23C22×#6440811yescharacteristic
154D4—2922no—
155D4—2924no—
156D4—2924no—
157D4—2922no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—42no—
161C2×C4—2921no—
162C2×C4—2921no—
163C2×C4—2921no—
164C2×C4—731no—
165C2×C4—731no—
166C2×C4—1462no—
167C2×C4—1462no—
168C2×C4C22⋊#6440811yescharacteristic
169C2×C4C22⋊#6440811yescharacteristic
170C8—2922no—
171C8—2922no—
172C22—21no—
173C22—21no—
174C22—2924no—
175C22—2922no—
176C22—2922no—
177C22—2922no—
178C22—5844no—
179C22—732no—
180C22—1461no—
181C22—1461no—
182C22—1461no—
183C22—1461no—
184C22—1461no—
185C22C2×C22⋊#6440811yescharacteristic
186C22#1455667912yes—
187C4—21no—
188C4—42no—
189C4—1461no—
190C4—1461no—
191C4#1455665012yes—
192C2—22no—
193C2—2921no—
194C2—5842no—
195C2—1462no—
196C2#1798956211yescharacteristic
197C2C2×#1455665011yescharacteristic
198C2D73⋊#10011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC23×C73C22×C4
FrattiniC23C22×#64408
FittingC2×C4⋊C4×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC2×C4⋊C4#64408
hypocenterC73#1471
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #17989558C2semidirect
2. #17989555C2semidirect
3. #17989431C2semidirect
100. C73#1471semidirect