Finite Group Databasebeta

← #22625200

Subgroups — #22625200

Order 9344.

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

normal subgroups only

This group has 256 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#17989607C211yesmaximal, characteristic, complemented
2#17989603C211yesmaximal, characteristic, complemented
3#17989431C212yesmaximal, complemented
4#17989430C212yesmaximal, complemented
5C2×#14556577C211yesmaximal, characteristic
6#14556658—21no—
7C4⋊#10596833—21no—
8C22⋊#10596833C2212yes—
9C22⋊#10596833C2212yes—
10#14556646—21no—
11C4×#10596833—21no—
12C22×Dic146C411yescharacteristic
13C22×C22⋊D73C411yescharacteristic
14#14556577—21no—
15#14556577—21no—
16#14556577—21no—
17#14556577—21no—
18C2×C22⋊Dic73C2211yescharacteristic
19C2×#11924005C411yescharacteristic
20C2×#11924005C2211yescharacteristic
21C2×C4×Dic73C2211yescharacteristic
22C2×C22⋊C4×C73C411yescharacteristic
23C2×#10596833—22no—
24C2×#10596833—22no—
25C23×D73C2×C411yescharacteristic
26C2×Dic146—21no—
27C2×Dic146—21no—
28C2×Dic146—42no—
29C2×C22⋊D73—21no—
30C2×C22⋊D73—21no—
31C2×C22⋊D73—42no—
32C22×Dic73C2×C411yescharacteristic
33C22×Dic73C2×C411yescharacteristic
34C22×Dic73C2311yescharacteristic
35C22⋊Dic73—21no—
36C22⋊Dic73—21no—
37#11924005—21no—
38#11924005—21no—
39#11924005—21no—
40#11924005—21no—
41C4×Dic73D411yescharacteristic
42C4×Dic73D411yescharacteristic
43C4×Dic73D411yescharacteristic
44C4×Dic73D411yescharacteristic
45C24×C73C2×C411yescharacteristic
46C22×C4×C73C2×C411yescharacteristic
47C22×C4×C73C2×C411yescharacteristic
48C22⋊C4×C73—21no—
49C22⋊C4×C73—21no—
50C23×C73—21no—
51C23×C73—22no—
52C23×C73—41no—
53C23×C73—41no—
54C23×C73C22×C411yescharacteristic
55C22×D73—21no—
56C22×D73—22no—
57C22×D73—41no—
58C22×D73—41no—
59C2×C4×C73—22no—
60C2×C4×C73—21no—
61C2×C4×C73—41no—
62C2×C4×C73C22⋊C411yescharacteristic
63C2×C4×C73C22⋊C411yescharacteristic
64C22⋊D73—42no—
65C22⋊D73—42no—
66C2×Dic73—22no—
67C2×Dic73—21no—
68C2×Dic73—41no—
69C2×Dic73—41no—
70C2×Dic73C22⋊C411yescharacteristic
71C2×Dic73C22⋊C411yescharacteristic
72C2×Dic73C2×D411yescharacteristic
73C2×Dic73C2×D411yescharacteristic
74Dic146—42no—
75Dic146—42no—
76#10596833—42no—
77#10596833—42no—
78C22×C73—21no—
79C22×C73—21no—
80C22×C73—41no—
81C22×C73—41no—
82C22×C73—41no—
83C22×C73—82no—
84C22×C73C2×C22⋊C411yescharacteristic
85C22×C73#13112yes—
86C2×D73—41no—
87C2×D73—41no—
88C2×D73—41no—
89C2×D73—82no—
90C4×C73—21no—
91C4×C73—21no—
92C4×C73—41no—
93Dic73—21no—
94Dic73—21no—
95Dic73—21no—
96Dic73—41no—
97Dic73#10012yes—
98C2×C73—22no—
99C2×C73—81no—
100C2×C73#40811yescharacteristic
101C2×C73#41011yescharacteristic
102C2×C73C2×#10011yescharacteristic
103D73—81no—
104#1469—731nomaximal, Sylow
105C73#146911yescharacteristic, complemented, Sylow
106C2×#124—731no—
107#432—731no—
108#431—731no—
109#323—732no—
110#323—732no—
111C22×Q8—731no—
112C22×D4—731no—
113#124—1461no—
114#124—1461no—
115#124—1461no—
116#124—1461no—
117C2×C22⋊C4—731no—
118C2×C22⋊C4—731no—
119C2×C22⋊C4—731no—
120C2×C22⋊C4#6440811yescharacteristic
121C2×C42—731no—
122C4⋊C8—1461no—
123C4⋊C8—1461no—
124C22⋊C8—732no—
125C22⋊C8—732no—
126#97—1461no—
127C4×C8—1461no—
128C24—731no—
129C24C2×#6440811yescharacteristic
130C2×Q8—2922no—
131C2×Q8—1461no—
132C2×Q8—1461no—
133C2×D4—2922no—
134C2×D4—1461no—
135C2×D4—1461no—
136C22×C4—731no—
137C22×C4—731no—
138C22×C4—731no—
139C22×C4C2×#6440811yescharacteristic
140C22×C4C2×#6440811yescharacteristic
141C2×C8—1462no—
142C2×C8—1462no—
143C22⋊C4—21no—
144C22⋊C4—21no—
145C22⋊C4—1461no—
146C22⋊C4—1461no—
147C22⋊C4—1461no—
148C22⋊C4—1461no—
149C22⋊C4—1461no—
150C22⋊C4—1461no—
151C42—731no—
152C42—731no—
153C42—731no—
154C42—731no—
155C23—21no—
156C23—22no—
157C23—41no—
158C23—41no—
159C23—2921no—
160C23—2921no—
161C23—1461no—
162C23—1462no—
163C23C22×#6440811yescharacteristic
164Q8—2922no—
165Q8—2922no—
166D4—2922no—
167D4—2922no—
168C2×C4—22no—
169C2×C4—21no—
170C2×C4—41no—
171C2×C4—2921no—
172C2×C4—2921no—
173C2×C4—731no—
174C2×C4—731no—
175C2×C4—731no—
176C2×C4—731no—
177C2×C4—1461no—
178C2×C4—1462no—
179C2×C4C22⋊#6440811yescharacteristic
180C2×C4C22⋊#6440811yescharacteristic
181C8—2922no—
182C8—2922no—
183C22—21no—
184C22—21no—
185C22—41no—
186C22—41no—
187C22—41no—
188C22—82no—
189C22—2921no—
190C22—2921no—
191C22—2921no—
192C22—5842no—
193C22C2×C22⋊#6440811yescharacteristic
194C22#1455667812yes—
195C4—21no—
196C4—21no—
197C4—41no—
198C4—2921no—
199C4—732no—
200C4—1461no—
201C4—1461no—
202C4—1461no—
203C2—22no—
204C2—81no—
205C2—5841no—
206C2#1798956011yescharacteristic
207C2#1798956611yescharacteristic
208C2D73⋊#10011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC23×C73C22×C4
FrattiniC23C22×#64408
FittingC2×C22⋊C4×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC2×C22⋊C4#64408
hypocenterC73#1469
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. #17989431C2semidirect
4. #17989430C2semidirect
105. C73#1469semidirect