Finite Group Databasebeta

← #22616837

Subgroups — #22616837

Order 9344.

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

normal subgroups only

This group has 448 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
1C2×#14556584C212yesmaximal
2#17988519C212yesmaximal, complemented
3#17988517C212yesmaximal, complemented
4#17988512C211yesmaximal, characteristic
5#17988512C211yesmaximal, characteristic
6#17988486C212yesmaximal, complemented
7#17988472C212yesmaximal, complemented
8#17988447C212yesmaximal
9#385×C73C211yesmaximal, characteristic
10#14556584—28no—
11C2×C4⋊Dic73C2212yes—
12C2×C4⋊Dic73C2212yes—
13C2×C4⋊Dic73C2212yes—
14C2×C4⋊Dic73C2211yescharacteristic
15C2×C4⋊Dic73C2211yescharacteristic
16C2×#11924007C2212yes—
17C2×#11924007C2212yes—
18C2×C22⋊Dic73C2212yes—
19C2×C22⋊Dic73C2212yes—
20C2×C4×Dic73C2212yes—
21#14556498C2212yes—
22#14556498C2212yes—
23#14556498C2211yescharacteristic
24#14556498C2212yes—
25#14556498C2212yes—
26#14556498C2211yescharacteristic
27C23×C4×C73C2211yescharacteristic
28C2×C4⋊C4×C73C2212yes—
29C2×C22⋊C4×C73C2211yescharacteristic
30C2×C22⋊C4×C73C2211yescharacteristic
31#95×C73C2212yes—
32C22×Dic73C2312yes—
33C22×Dic73C2312yes—
34C22×Dic73C2312yes—
35C22×Dic73C2312yes—
36C4⋊Dic73—24no—
37C4⋊Dic73—24no—
38C4⋊Dic73—42no—
39C4⋊Dic73—41no—
40C4⋊Dic73—41no—
41#11924007—24no—
42#11924007—24no—
43C22⋊Dic73—24no—
44C22⋊Dic73—24no—
45C4×Dic73—24no—
46C24×C73C2311yescharacteristic
47C22×C4×C73—24no—
48C22×C4×C73—41no—
49C22×C4×C73C2311yescharacteristic
50C22×C4×C73C2311yescharacteristic
51C22×C4×C73C2312yes—
52C22×C4×C73C2312yes—
53C4⋊C4×C73—24no—
54C22⋊C4×C73—41no—
55C22⋊C4×C73D414yes—
56C23×C73—22no—
57C23×C73—21no—
58C23×C73—22no—
59C23×C73—21no—
60C23×C73C2×D412yes—
61C23×C73C2411yescharacteristic
62C2×C4×C73—22no—
63C2×C4×C73—22no—
64C2×C4×C73—22no—
65C2×C4×C73—22no—
66C2×C4×C73—22no—
67C2×C4×C73—21no—
68C2×C4×C73—21no—
69C2×C4×C73—22no—
70C2×C4×C73—44no—
71C2×C4×C73C2×D414yes—
72C2×C4×C73#4114yes—
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—
84C2×Dic73—22no—
85C22×C73—22no—
86C22×C73—24no—
87C22×C73—42no—
88C22×C73—41no—
89C22×C73—41no—
90C22×C73C22×D411yescharacteristic
91C22×C73C2×#4112yes—
92C22×C73H(5,𝔽2)11yescharacteristic
93C22×C732−1+412yes—
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#53711yescharacteristic
105C2×C73#54112yes—
106C2×C73#54712yes—
107C2×C73#55111yescharacteristic
108C2×C73#56311yescharacteristic
109#2722—731nomaximal, Sylow
110C73#272211yescharacteristic, complemented, Sylow
111C2×#126—732no—
112#398—732no—
113#398—732no—
114#397—731no—
115#397—731no—
116#389—732no—
117#387—732no—
118#385D7311yescharacteristic
119#380—732no—
120C23×C4C2×D7311yescharacteristic
121#126—1468no—
122C2×C4⋊C4—732no—
123C2×C4⋊C4—731no—
124C2×C4⋊C4—731no—
125C2×C4⋊C4—732no—
126C2×C4⋊C4—732no—
127C2×C4⋊C4—732no—
128C2×C4⋊C4—732no—
129C2×C4⋊C4C2×D7312yes—
130C2×C22⋊C4—732no—
131C2×C22⋊C4—732no—
132C2×C22⋊C4C2×D7311yescharacteristic
133C2×C22⋊C4C2×D7311yescharacteristic
134C2×C42—732no—
135#95—732no—
136#95—732no—
137#95—731no—
138#95—732no—
139#95—732no—
140#95—731no—
141#95C2×D7312yes—
142C24C22×D7311yescharacteristic
143C22×C4—24no—
144C22×C4—41no—
145C22×C4—732no—
146C22×C4—732no—
147C22×C4—732no—
148C22×C4—732no—
149C22×C4C22×D7311yescharacteristic
150C22×C4C22×D7311yescharacteristic
151C22×C4C22×D7312yes—
152C22×C4C22×D7312yes—
153C4⋊C4—24no—
154C4⋊C4—2922no—
155C4⋊C4—2921no—
156C4⋊C4—2921no—
157C4⋊C4—1464no—
158C4⋊C4—1464no—
159C4⋊C4—1464no—
160C4⋊C4—1464no—
161C22⋊C4—41no—
162C22⋊C4—1464no—
163C22⋊C4—1464no—
164C22⋊C4D29214yes—
165C42—1464no—
166C23—22no—
167C23—21no—
168C23—22no—
169C23—21no—
170C23C2×D29212yes—
171C23C23×D7311yescharacteristic
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×D29214yes—
194C2×C4#1192402714yes—
195C22—22no—
196C22—24no—
197C22—42no—
198C22—41no—
199C22—41no—
200C22C22×D29211yescharacteristic
201C22C2×#1192402712yes—
202C22#1455663611yescharacteristic
203C22#1455663812yes—
204C22#1455663911yescharacteristic
205C4—24no—
206C4—24no—
207C4—41no—
208C4—41no—
209C4—2922no—
210C4—2922no—
211C4—2922no—
212C4—2922no—
213C2—42no—
214C2#1798916811yescharacteristic
215C2#1798919712yes—
216C2#1798924112yes—
217C2#1798926811yescharacteristic
218C2#1798934011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#385×C73C2
hypercenter#385D73
hypocenterC73#2722
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. #17988519C2semidirect
3. #17988517C2semidirect
6. #17988486C2semidirect
7. #17988472C2semidirect
110. C73#2722semidirect