Finite Group Databasebeta

← #22614209

Subgroups — #22614209

Order 9344.

700 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 700 conjugacy classes of subgroups — too many to draw. Only its 165 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
1C22×C22⋊Dic73C211yesmaximal, characteristic
2#17988515C214yesmaximal, complemented
3#17988460C212yesmaximal, complemented
4#17988459C212yesmaximal, complemented
5#17988450C212yesmaximal, complemented
6#17988448C212yesmaximal, complemented
7#17988443C211yesmaximal, characteristic
8C22×C22⋊C4×C73C211yesmaximal, characteristic
9C23×Dic73C2211yescharacteristic
10C23×Dic73C2211yescharacteristic
11C2×#11924007C2214yescomplemented
12C2×C22⋊Dic73—24no—
13C2×C22⋊Dic73C2212yes—
14C2×C22⋊Dic73C2212yes—
15C2×C22⋊Dic73C2212yes—
16C2×C22⋊Dic73C2212yes—
17C2×C22⋊Dic73C2212yes—
18#14556498C2214yescomplemented
19#14556498C2214yescomplemented
20#14556498C2214yescomplemented
21C25×C73C2211yescharacteristic
22C23×C4×C73C2211yescharacteristic
23C23×C4×C73C2211yescharacteristic
24C2×C22⋊C4×C73—24no—
25C2×C22⋊C4×C73C2212yes—
26C2×C22⋊C4×C73C2212yes—
27C22×Dic73—22no—
28C22×Dic73—22no—
29C22×Dic73—24no—
30C22×Dic73—42no—
31C22×Dic73C2312yes—
32C22×Dic73C2314yes—
33C22×Dic73C2312yes—
34#11924007—44no—
35C22⋊Dic73—24no—
36C22⋊Dic73—24no—
37C22⋊Dic73—24no—
38C22⋊Dic73—24no—
39C22⋊Dic73—42no—
40C24×C73—24no—
41C24×C73—24no—
42C24×C73—42no—
43C24×C73D414yes—
44C24×C73C2311yescharacteristic
45C24×C73C2311yescharacteristic
46C24×C73C2311yescharacteristic
47C22×C4×C73—22no—
48C22×C4×C73—22no—
49C22×C4×C73—24no—
50C22×C4×C73—42no—
51C22×C4×C73C2312yes—
52C22×C4×C73C2312yes—
53C22⋊C4×C73—24no—
54C22⋊C4×C73—24no—
55C23×C73—22no—
56C23×C73—22no—
57C23×C73—22no—
58C23×C73—22no—
59C23×C73—28no—
60C23×C73—28no—
61C23×C73—22no—
62C23×C73—22no—
63C23×C73—22no—
64C23×C73—44no—
65C23×C73—416no—
66C23×C73C2×D412yes—
67C23×C73C2×D412yes—
68C23×C73C2×D412yes—
69C23×C73#4114yes—
70C23×C73#4114yes—
71C23×C73C2411yescharacteristic
72C2×C4×C73—22no—
73C2×C4×C73—22no—
74C2×C4×C73—24no—
75C2×C4×C73—24no—
76C2×C4×C73—44no—
77C2×C4×C73—44no—
78C2×Dic73—22no—
79C2×Dic73—22no—
80C2×Dic73—24no—
81C2×Dic73—24no—
82C2×Dic73—24no—
83C2×Dic73—24no—
84C2×Dic73—24no—
85C2×Dic73—44no—
86C2×Dic73—44no—
87C22×C73—22no—
88C22×C73—22no—
89C22×C73—22no—
90C22×C73—22no—
91C22×C73—28no—
92C22×C73—28no—
93C22×C73—22no—
94C22×C73—22no—
95C22×C73—22no—
96C22×C73—416no—
97C22×C73—44no—
98C22×C73#12314yes—
99C22×C73#12314yes—
100C22×C73C22×D411yescharacteristic
101C22×C73C2×#4112yes—
102C22×C73C2×#4112yes—
103C22×C73H(5,𝔽2)12yes—
104C4×C73—42no—
105C4×C73—42no—
106Dic73—42no—
107Dic73—42no—
108Dic73—44no—
109C2×C73—24no—
110C2×C73—24no—
111C2×C73—42no—
112C2×C73C2×#12311yescharacteristic
113C2×C73C2×#12311yescharacteristic
114C2×C73#53411yescharacteristic
115C2×C73#55114yes—
116#2483—731nomaximal, Sylow
117C73#248311yescharacteristic, complemented, Sylow
118C22×C22⋊C4—731no—
119C22×C22⋊C4D7311yescharacteristic
120#397—734no—
121#385—732no—
122#385—732no—
123#381—732no—
124#381—732no—
125#379—731no—
126C25C2×D7311yescharacteristic
127C23×C4—731no—
128C23×C4—731no—
129C23×C4C2×D7311yescharacteristic
130C23×C4C2×D7311yescharacteristic
131C2×C4⋊C4—734no—
132C2×C22⋊C4—24no—
133C2×C22⋊C4—732no—
134C2×C22⋊C4—732no—
135C2×C22⋊C4—732no—
136C2×C22⋊C4—732no—
137C2×C22⋊C4—732no—
138C2×C22⋊C4—1464no—
139C2×C22⋊C4C2×D7312yes—
140C2×C22⋊C4C2×D7312yes—
141#95—734no—
142#95—734no—
143#95—734no—
144C24—24no—
145C24—24no—
146C24—42no—
147C24C22⋊D7314yes—
148C24C22×D7311yescharacteristic
149C24C22×D7311yescharacteristic
150C24C22×D7311yescharacteristic
151C22×C4—22no—
152C22×C4—22no—
153C22×C4—24no—
154C22×C4—42no—
155C22×C4—2922no—
156C22×C4—732no—
157C22×C4—734no—
158C22×C4—732no—
159C22×C4—1462no—
160C22×C4—1462no—
161C22×C4—1464no—
162C22×C4C22×D7312yes—
163C22×C4C22×D7312yes—
164C4⋊C4—2924no—
165C22⋊C4—24no—
166C22⋊C4—24no—
167C22⋊C4—2922no—
168C22⋊C4—1464no—
169C22⋊C4—1464no—
170C22⋊C4—1464no—
171C22⋊C4—1464no—
172C23—22no—
173C23—22no—
174C23—22no—
175C23—22no—
176C23—28no—
177C23—28no—
178C23—22no—
179C23—22no—
180C23—22no—
181C23—44no—
182C23—416no—
183C23C2×C22⋊D7312yes—
184C23C2×C22⋊D7312yes—
185C23C2×C22⋊D7312yes—
186C23#1192402714yes—
187C23#1192402814yes—
188C23C23×D7311yescharacteristic
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—24no—
192C2×C4—24no—
193C2×C4—44no—
194C2×C4—44no—
195C2×C4—2924no—
196C2×C4—2924no—
197C2×C4—1462no—
198C2×C4—1462no—
199C2×C4—1464no—
200C2×C4—1464no—
201C2×C4—1464no—
202C2×C4—1464no—
203C2×C4—1464no—
204C22—22no—
205C22—22no—
206C22—28no—
207C22—28no—
208C22—22no—
209C22—22no—
210C22—22no—
211C22—22no—
212C22—22no—
213C22—416no—
214C22—44no—
215C22#1455657214yes—
216C22#1455657414yes—
217C22C22×C22⋊D7311yescharacteristic
218C22C2×#1192402712yes—
219C22C2×#1192402812yes—
220C22#1455663612yes—
221C4—42no—
222C4—42no—
223C4—2922no—
224C4—2924no—
225C4—2922no—
226C2—24no—
227C2—24no—
228C2—42no—
229C2C2×#1455657211yescharacteristic
230C2C2×#1455657411yescharacteristic
231C2#1798914611yescharacteristic
232C2#1798926314yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
FittingC22×C22⋊C4×C73C2
hypercenterC22×C22⋊C4D73
hypocenterC73#2483
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #17988515C2semidirect
3. #17988460C2semidirect
4. #17988459C2semidirect
5. #17988450C2semidirect
6. #17988448C2semidirect
11. C2×#11924007C22semidirect
18. #14556498C22semidirect
19. #14556498C22semidirect
20. #14556498C22semidirect
117. C73#2483semidirect