Finite Group Databasebeta

← #22614201

Subgroups — #22614201

Order 9344.

672 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 153 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×#11924005C211yesmaximal, characteristic
2#17988522C212yesmaximal, complemented
3#17988513C212yesmaximal, complemented
4#17988478C214yesmaximal, complemented
5#17988459C212yesmaximal, complemented
6#17988450C211yesmaximal, characteristic, complemented
7#17988442C212yesmaximal
8C2×#117×C73C211yesmaximal, characteristic, complemented
9C24×D73C2211yescharacteristic
10C23×Dic73C2211yescharacteristic
11C2×#11924007C2214yescomplemented
12C2×C22⋊Dic73C2212yes—
13C2×#11924005—24no—
14C2×#11924005C2214yes—
15C2×#11924005C2212yes—
16C2×#11924005C2212yes—
17C2×#11924005C2214yes—
18#14556498C2212yescomplemented
19#14556498C2212yescomplemented
20#14556498C2214yescomplemented
21C23×C4×C73C2211yescharacteristic
22#117×C73—24no—
23C2×C4⋊C4×C73C2211yescharacteristic, complemented
24C2×C4⋊C4×C73C2211yescharacteristic, complemented
25C2×C22⋊C4×C73C2212yes—
26C2×C42×C73C2212yescomplemented
27C23×D73—22no—
28C23×D73—24no—
29C23×D73—24no—
30C23×D73—42no—
31C23×D73C2312yes—
32C22×Dic73—22no—
33C22×Dic73—42no—
34C22×Dic73C2314yes—
35C22×Dic73C2312yes—
36#11924007—44no—
37C22⋊Dic73—24no—
38#11924005—28no—
39#11924005—24no—
40#11924005—24no—
41#11924005—44no—
42C24×C73C2311yescharacteristic
43C22×C4×C73—24no—
44C22×C4×C73D414yes—
45C22×C4×C73C2312yes—
46C22×C4×C73C2312yes—
47C22×C4×C73C2311yescharacteristic
48C22×C4×C73C2311yescharacteristic
49C4⋊C4×C73—22no—
50C4⋊C4×C73—22no—
51C22⋊C4×C73—24no—
52C42×C73—24no—
53C23×C73—22no—
54C23×C73—22no—
55C23×C73C2×D412yes—
56C23×C73#4114yes—
57C23×C73C2411yescharacteristic
58C22×D73—28no—
59C22×D73—22no—
60C22×D73—22no—
61C22×D73—24no—
62C22×D73—24no—
63C22×D73—416no—
64C22×D73—44no—
65C22×D73—44no—
66C22×D73#4114yes—
67C2×C4×C73—28no—
68C2×C4×C73—22no—
69C2×C4×C73—22no—
70C2×C4×C73—22no—
71C2×C4×C73—22no—
72C2×C4×C73—24no—
73C2×C4×C73—24no—
74C2×C4×C73C2×D412yes—
75C2×C4×C73C2×D412yes—
76C2×Dic73—22no—
77C2×Dic73—24no—
78C2×Dic73—24no—
79C2×Dic73—24no—
80C2×Dic73—24no—
81C2×Dic73—44no—
82C22×C73—22no—
83C22×C73—22no—
84C22×C73—28no—
85C22×C73#12314yes—
86C22×C73C22×D411yescharacteristic
87C22×C73C2×#4112yes—
88C22×C73C2×#4112yes—
89C22×C73H(5,𝔽2)12yes—
90C2×D73—24no—
91C2×D73—28no—
92C2×D73—416no—
93C2×D73—42no—
94C2×D73—42no—
95C2×D73—44no—
96C4×C73—22no—
97C4×C73—22no—
98C4×C73—42no—
99C4×C73—42no—
100Dic73—42no—
101Dic73—44no—
102C2×C73—24no—
103C2×C73C2×#12311yescharacteristic
104C2×C73#52511yescharacteristic
105C2×C73#53511yescharacteristic
106C2×C73#55114yes—
107D73—44no—
108#2482—731nomaximal, Sylow
109C73#248211yescharacteristic, complemented, Sylow
110C2×#117D7311yescharacteristic, complemented
111C22×C22⋊C4—731no—
112#399—732no—
113#397—732no—
114#388—734no—
115#385—732no—
116#381—731no—
117#379—732no—
118C25—731no—
119C23×C4—731no—
120C23×C4C2×D7311yescharacteristic
121#117—24no—
122C2×C4⋊C4—734no—
123C2×C4⋊C4C2×D7311yescharacteristic, complemented
124C2×C4⋊C4C2×D7311yescharacteristic, complemented
125C2×C22⋊C4—734no—
126C2×C22⋊C4—732no—
127C2×C22⋊C4—732no—
128C2×C22⋊C4—732no—
129C2×C22⋊C4—734no—
130C2×C22⋊C4—1464no—
131C2×C22⋊C4C2×D7312yes—
132C2×C42C2×D7312yescomplemented
133#95—732no—
134#95—732no—
135#95—734no—
136C24—2922no—
137C24—732no—
138C24—1464no—
139C24—1464no—
140C24—1462no—
141C24C22×D7311yescharacteristic
142C22×C4—24no—
143C22×C4—2922no—
144C22×C4—734no—
145C22×C4—732no—
146C22×C4—1462no—
147C22×C4C22⋊D7314yes—
148C22×C4C22×D7312yes—
149C22×C4C22×D7312yes—
150C22×C4C22×D7311yescharacteristic
151C22×C4C22×D7311yescharacteristic
152C4⋊C4—22no—
153C4⋊C4—22no—
154C4⋊C4—2924no—
155C22⋊C4—24no—
156C22⋊C4—2924no—
157C22⋊C4—1468no—
158C22⋊C4—1464no—
159C22⋊C4—1464no—
160C22⋊C4—1464no—
161C42—24no—
162C23—22no—
163C23—22no—
164C23—2924no—
165C23—29216no—
166C23—2924no—
167C23—734no—
168C23—1468no—
169C23—1462no—
170C23—1462no—
171C23—1464no—
172C23—1464no—
173C23C2×C22⋊D7312yes—
174C23#1192402814yes—
175C23C23×D7311yescharacteristic
176C2×C4—28no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—24no—
182C2×C4—24no—
183C2×C4—2924no—
184C2×C4—1462no—
185C2×C4—1464no—
186C2×C4—1464no—
187C2×C4—1464no—
188C2×C4—1464no—
189C2×C4C2×C22⋊D7312yes—
190C2×C4C2×C22⋊D7312yes—
191C22—22no—
192C22—28no—
193C22—22no—
194C22—29216no—
195C22—2922no—
196C22—2924no—
197C22—2922no—
198C22—1468no—
199C22—1464no—
200C22#1455657414yes—
201C22C22×C22⋊D7311yescharacteristic
202C22#41×D7312yes—
203C22C2×#1192402812yes—
204C22#1455663712yes—
205C4—22no—
206C4—22no—
207C4—42no—
208C4—42no—
209C4—2922no—
210C4—2924no—
211C2—24no—
212C2—2924no—
213C2C2×#1455657411yescharacteristic
214C2#1798909411yescharacteristic
215C2#1798915111yescharacteristic
216C2#1798926114yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
FittingC2×#117×C73C2
hypercenterC2×#117D73
hypocenterC73#2482
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #17988522C2semidirect
3. #17988513C2semidirect
4. #17988478C2semidirect
5. #17988459C2semidirect
6. #17988450C2semidirect
8. C2×#117×C73C2semidirect
11. C2×#11924007C22semidirect
18. #14556498C22semidirect
19. #14556498C22semidirect
20. #14556498C22semidirect
23. C2×C4⋊C4×C73C22semidirect
24. C2×C4⋊C4×C73C22semidirect
26. C2×C42×C73C22semidirect
109. C73#2482semidirect
110. C2×#117D73semidirect
123. C2×C4⋊C4C2×D73semidirect
124. C2×C4⋊C4C2×D73semidirect
132. C2×C42C2×D73semidirect