Finite Group Databasebeta

← #22617060

Subgroups — #22617060

Order 9344.

416 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 141 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#17988526C212yesmaximal, complemented
2#17988523C211yesmaximal, characteristic
3#17988508C212yesmaximal, complemented
4#17988499C211yesmaximal, characteristic
5#17988486C212yesmaximal, complemented
6#17988480C212yesmaximal
7#17988470C212yesmaximal, complemented
8#17988447C212yesmaximal
9#385×C73C211yesmaximal, characteristic
10C22×Dic146C2211yescharacteristic
11C2×C4⋊Dic73C2212yes—
12C2×C4⋊Dic73C2212yes—
13C2×C4⋊Dic73C2212yes—
14C2×C4⋊Dic73C2211yescharacteristic
15C2×#11924007C2212yes—
16C2×C22⋊Dic73C2212yes—
17C2×C22⋊Dic73C2212yes—
18C2×C4×Dic73C2212yes—
19#14556498C2212yes—
20#14556498C2212yes—
21#14556498C2211yescharacteristic
22#14556498C2212yes—
23#14556498C2212yes—
24#14556498C2212yes—
25#14556498C2211yescharacteristic
26C23×C4×C73C2211yescharacteristic
27C2×C4⋊C4×C73C2212yes—
28C2×C22⋊C4×C73C2211yescharacteristic
29C2×C22⋊C4×C73C2211yescharacteristic
30#95×C73C2212yes—
31C2×Dic146—42no—
32C2×Dic146—41no—
33C22×Dic73C2312yes—
34C22×Dic73C2312yes—
35C22×Dic73C2312yes—
36C22×Dic73C2312yes—
37C4⋊Dic73—24no—
38C4⋊Dic73—42no—
39C4⋊Dic73—41no—
40C4⋊Dic73—42no—
41#11924007—42no—
42C22⋊Dic73—42no—
43C22⋊Dic73—42no—
44C4×Dic73—42no—
45C24×C73C2311yescharacteristic
46C22×C4×C73—24no—
47C22×C4×C73—41no—
48C22×C4×C73C2311yescharacteristic
49C22×C4×C73C2311yescharacteristic
50C22×C4×C73C2312yes—
51C22×C4×C73C2312yes—
52C4⋊C4×C73—24no—
53C22⋊C4×C73—41no—
54C22⋊C4×C73Q814yescomplemented
55C23×C73—22no—
56C23×C73—21no—
57C23×C73—22no—
58C23×C73—21no—
59C23×C73C2×Q812yes—
60C23×C73C2411yescharacteristic
61C2×C4×C73—22no—
62C2×C4×C73—22no—
63C2×C4×C73—22no—
64C2×C4×C73—22no—
65C2×C4×C73—22no—
66C2×C4×C73—21no—
67C2×C4×C73—21no—
68C2×C4×C73—22no—
69C2×C4×C73—44no—
70C2×C4×C73C2×Q814yes—
71C2×C4×C73#4114yes—
72C2×Dic73—22no—
73C2×Dic73—22no—
74C2×Dic73—22no—
75C2×Dic73—22no—
76C2×Dic73—22no—
77C2×Dic73—22no—
78C2×Dic73—22no—
79C2×Dic73—22no—
80C2×Dic73—22no—
81C2×Dic73—22no—
82C2×Dic73—22no—
83C2×Dic73—22no—
84Dic146—44no—
85C22×C73—22no—
86C22×C73—24no—
87C22×C73—42no—
88C22×C73—41no—
89C22×C73—41no—
90C22×C73C22×Q811yescharacteristic
91C22×C73C2×#4112yes—
92C22×C73H(5,𝔽2)11yescharacteristic
93C22×C73H(5,𝔽2)12yes—
94C22×C732−1+411yescharacteristic
95C4×C73—24no—
96C4×C73—24no—
97C4×C73—41no—
98C4×C73—41no—
99Dic73—42no—
100Dic73—42no—
101Dic73—42no—
102Dic73—42no—
103C2×C73—42no—
104C2×C73#54212yes—
105C2×C73#54411yescharacteristic
106C2×C73#55111yescharacteristic
107C2×C73#55412yes—
108C2×C73#56011yescharacteristic
109#2742—731nomaximal, Sylow
110C73#274211yescharacteristic, complemented, Sylow
111#400—732no—
112#399—731no—
113#395—732no—
114#393—731no—
115#389—732no—
116#388—732no—
117#387—732no—
118#385D7311yescharacteristic
119#380—732no—
120C22×Q8—731no—
121C23×C4C2×D7311yescharacteristic
122C2×C4⋊C4—732no—
123C2×C4⋊C4—732no—
124C2×C4⋊C4—732no—
125C2×C4⋊C4—731no—
126C2×C4⋊C4—732no—
127C2×C4⋊C4C2×D7312yes—
128C2×C22⋊C4—732no—
129C2×C22⋊C4—732no—
130C2×C22⋊C4C2×D7311yescharacteristic
131C2×C22⋊C4C2×D7311yescharacteristic
132C2×C42—732no—
133#95—732no—
134#95—732no—
135#95—731no—
136#95—732no—
137#95—732no—
138#95—732no—
139#95—731no—
140#95C2×D7312yes—
141C24C22×D7311yescharacteristic
142C2×Q8—2921no—
143C2×Q8—2922no—
144C22×C4—24no—
145C22×C4—41no—
146C22×C4—732no—
147C22×C4—732no—
148C22×C4—732no—
149C22×C4—732no—
150C22×C4C22×D7311yescharacteristic
151C22×C4C22×D7311yescharacteristic
152C22×C4C22×D7312yes—
153C22×C4C22×D7312yes—
154C4⋊C4—24no—
155C4⋊C4—2922no—
156C4⋊C4—2922no—
157C4⋊C4—2922no—
158C4⋊C4—2921no—
159C4⋊C4—1464no—
160C22⋊C4—41no—
161C22⋊C4—2922no—
162C22⋊C4—2922no—
163C22⋊C4Dic14614yescomplemented
164C42—2922no—
165C23—22no—
166C23—21no—
167C23—22no—
168C23—21no—
169C23C2×Dic14612yes—
170C23C23×D7311yescharacteristic
171Q8—2924no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—44no—
181C2×C4—1462no—
182C2×C4—1462no—
183C2×C4—1462no—
184C2×C4—1462no—
185C2×C4—1462no—
186C2×C4—1462no—
187C2×C4—1462no—
188C2×C4—1462no—
189C2×C4—1462no—
190C2×C4—1462no—
191C2×C4—1462no—
192C2×C4—1462no—
193C2×C4C2×Dic14614yes—
194C2×C4#1192402714yes—
195C22—22no—
196C22—24no—
197C22—42no—
198C22—41no—
199C22—41no—
200C22C22×Dic14611yescharacteristic
201C22C2×#1192402712yes—
202C22#1455663611yescharacteristic
203C22#1455663712yes—
204C22#1455663911yescharacteristic
205C4—24no—
206C4—24no—
207C4—41no—
208C4—41no—
209C4—2922no—
210C4—2922no—
211C4—2922no—
212C4—2922no—
213C2—42no—
214C2#1798921012yes—
215C2#1798921811yescharacteristic
216C2#1798926811yescharacteristic
217C2#1798929412yes—
218C2#1798932711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#385×C73C2
hypercenter#385D73
hypocenterC73#2742
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. #17988526C2semidirect
3. #17988508C2semidirect
5. #17988486C2semidirect
7. #17988470C2semidirect
54. C22⋊C4×C73Q8semidirect
110. C73#2742semidirect
163. C22⋊C4Dic146semidirect