Finite Group Databasebeta

← #22618006

Subgroups — #22618006

Order 9344.

456 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 125 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×#14556586C212yesmaximal, complemented
2#17988521C212yesmaximal, complemented
3#17988511C212yesmaximal, complemented
4#17988509C212yesmaximal, complemented
5#17988509C212yesmaximal, complemented
6#17988505C212yesmaximal
7#17988504C211yesmaximal, characteristic
8#17988456C211yesmaximal, characteristic, complemented
9#398×C73C211yesmaximal, characteristic, complemented
10C22×D292C2211yescharacteristic
11#14556586—28no—
12C2×C4⋊Dic73C2212yes—
13C2×C4⋊Dic73C2211yescharacteristic
14C2×#11924007C2212yes—
15C2×#11924007C2212yes—
16C2×#11924007C2212yes—
17C2×#11924007C2212yes—
18C2×#11924005C2212yes—
19C2×#11924005C2212yes—
20C2×#11924005C2212yes—
21C2×#11924005C2212yes—
22C2×#11924005C2212yes—
23C2×#11924005C2212yes—
24C2×C4×Dic73C2211yescharacteristic
25#14556498C2211yescharacteristic
26#14556498C2212yes—
27C2×C4⋊C4×C73C2212yes—
28C2×C4⋊C4×C73C2211yescharacteristic
29C2×C4⋊C4×C73C2211yescharacteristic
30#95×C73C2212yes—
31#95×C73C2211yescharacteristic
32C23×D73C2312yes—
33C2×D292—41no—
34C2×D292—42no—
35C22×Dic73C2312yes—
36C22×Dic73C2312yes—
37C22×Dic73C2312yes—
38C4⋊Dic73—24no—
39C4⋊Dic73—41no—
40#11924007—24no—
41#11924007—42no—
42#11924007—42no—
43#11924007—42no—
44#11924005—24no—
45#11924005—24no—
46#11924005—24no—
47#11924005—42no—
48#11924005—42no—
49#11924005—42no—
50C4×Dic73D414yescomplemented
51C22×C4×C73C2311yescharacteristic
52C22×C4×C73C2312yes—
53C22×C4×C73C2312yes—
54C22×C4×C73C2311yescharacteristic
55C22×C4×C73C2311yescharacteristic
56C4⋊C4×C73—24no—
57C4⋊C4×C73—41no—
58C4⋊C4×C73—41no—
59C23×C73C2411yescharacteristic
60C22×D73—22no—
61C22×D73—22no—
62C22×D73—22no—
63C22×D73—22no—
64C22×D73—22no—
65C22×D73—22no—
66C22×D73—22no—
67C2×C4×C73—21no—
68C2×C4×C73—21no—
69C2×C4×C73—22no—
70C2×C4×C73—22no—
71C2×C4×C73—21no—
72C2×C4×C73—22no—
73C2×C4×C73—21no—
74C2×C4×C73—22no—
75C2×C4×C73—22no—
76C2×C4×C73—22no—
77C2×C4×C73—22no—
78C2×C4×C73—22no—
79C2×C4×C73C2×D412yes—
80C2×Dic73—22no—
81C2×Dic73—22no—
82C2×Dic73—22no—
83C2×Dic73—22no—
84C2×Dic73—22no—
85C2×Dic73—22no—
86C2×Dic73—22no—
87C2×Dic73—22no—
88C2×Dic73C2×D414yes—
89D292—44no—
90C22×C73C22×D411yescharacteristic
91C22×C73H(5,𝔽2)11yescharacteristic
92C22×C73H(5,𝔽2)12yes—
93C22×C732−1+411yescharacteristic
94C22×C732−1+412yes—
95C2×D73—42no—
96C2×D73—42no—
97C2×D73—42no—
98C2×D73—42no—
99C2×D73—42no—
100C2×D73—42no—
101C2×D73—42no—
102C4×C73—22no—
103C4×C73—42no—
104C4×C73—42no—
105C4×C73—41no—
106C4×C73—41no—
107Dic73—24no—
108Dic73—42no—
109Dic73—42no—
110C2×C73#53711yescharacteristic
111C2×C73#53712yes—
112C2×C73#56011yescharacteristic
113C2×C73#56311yescharacteristic
114C2×C73#56312yes—
115D73—82no—
116#2823—731nomaximal, Sylow
117C73#282311yescharacteristic, complemented, Sylow
118C2×#126—732no—
119#398—732no—
120#398D7311yescharacteristic, complemented
121#396—732no—
122#396—732no—
123#396—732no—
124#394—731no—
125#394—732no—
126#384—731no—
127C22×D4—731no—
128#126—1468no—
129C2×C4⋊C4—732no—
130C2×C4⋊C4—732no—
131C2×C4⋊C4—731no—
132C2×C4⋊C4—732no—
133C2×C4⋊C4—732no—
134C2×C4⋊C4—732no—
135C2×C4⋊C4C2×D7312yes—
136C2×C4⋊C4C2×D7311yescharacteristic
137C2×C4⋊C4C2×D7311yescharacteristic
138C2×C22⋊C4—732no—
139C2×C22⋊C4—732no—
140C2×C22⋊C4—732no—
141C2×C22⋊C4—732no—
142C2×C22⋊C4—732no—
143C2×C22⋊C4—732no—
144C2×C42—731no—
145#95—731no—
146#95—732no—
147#95C2×D7312yes—
148#95C2×D7311yescharacteristic
149C24—732no—
150C2×D4—2921no—
151C2×D4—2922no—
152C22×C4—732no—
153C22×C4—732no—
154C22×C4—732no—
155C22×C4C22×D7311yescharacteristic
156C22×C4C22×D7312yes—
157C22×C4C22×D7312yes—
158C22×C4C22×D7311yescharacteristic
159C22×C4C22×D7311yescharacteristic
160C4⋊C4—24no—
161C4⋊C4—41no—
162C4⋊C4—41no—
163C4⋊C4—2922no—
164C4⋊C4—2922no—
165C4⋊C4—2922no—
166C4⋊C4—2921no—
167C4⋊C4—1464no—
168C4⋊C4—1464no—
169C22⋊C4—2922no—
170C22⋊C4—2922no—
171C22⋊C4—2922no—
172C22⋊C4—1464no—
173C22⋊C4—1464no—
174C22⋊C4—1464no—
175C42—734no—
176C23—1462no—
177C23—1462no—
178C23—1462no—
179C23—1462no—
180C23—1462no—
181C23—1462no—
182C23—1462no—
183C23C23×D7311yescharacteristic
184D4—2924no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—734no—
198C2×C4—1462no—
199C2×C4—1462no—
200C2×C4—1462no—
201C2×C4—1462no—
202C2×C4—1462no—
203C2×C4—1462no—
204C2×C4—1462no—
205C2×C4—1462no—
206C2×C4D4×D7312yes—
207C22—2922no—
208C22—2922no—
209C22—2922no—
210C22—2922no—
211C22—2922no—
212C22—2922no—
213C22—2922no—
214C22C2×D4×D7311yescharacteristic
215C22#1455663611yescharacteristic
216C22#1455663712yes—
217C22#1455663811yescharacteristic
218C22#1455663912yes—
219C4—22no—
220C4—42no—
221C4—42no—
222C4—41no—
223C4—41no—
224C4—2922no—
225C4—2922no—
226C4—1464no—
227C2—5842no—
228C2#1798916411yescharacteristic
229C2#1798916712yes—
230C2#1798932711yescharacteristic
231C2#1798933611yescharacteristic
232C2#1798934112yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#398×C73C2
hypercenter#398D73
hypocenterC73#2823
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#14556586C2semidirect
2. #17988521C2semidirect
3. #17988511C2semidirect
4. #17988509C2semidirect
5. #17988509C2semidirect
8. #17988456C2semidirect
9. #398×C73C2semidirect
50. C4×Dic73D4semidirect
117. C73#2823semidirect
120. #398D73semidirect