Finite Group Databasebeta

← #22616246

Subgroups — #22616246

Order 9344.

544 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 157 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×#14556590C212yesmaximal, complemented
2C2×#14556570C212yesmaximal
3#17988523C211yesmaximal, characteristic
4#17988520C212yesmaximal, complemented
5#17988508C212yesmaximal, complemented
6#17988499C211yesmaximal, characteristic
7#17988480C212yesmaximal
8#17988474C212yesmaximal, complemented
9#385×C73C211yesmaximal, characteristic
10C22×Dic146C2211yescharacteristic
11C22×Dic146C2212yes—
12#14556590—28no—
13#14556570—28no—
14C2×C4⋊Dic73C2212yes—
15C2×C4⋊Dic73C2212yes—
16C2×C4⋊Dic73C2211yescharacteristic
17C2×#11924007C2212yes—
18C2×#11924007C2212yes—
19C2×#11924007C2212yes—
20C2×C22⋊Dic73C2212yes—
21C2×C22⋊Dic73C2212yes—
22C2×C4×Dic73C2212yes—
23#14556498C2211yescharacteristic
24#14556498C2212yes—
25#14556498C2212yes—
26#14556498C2212yes—
27#14556498C2211yescharacteristic
28C23×C4×C73C2211yescharacteristic
29C2×C4⋊C4×C73C2212yes—
30C2×C22⋊C4×C73C2211yescharacteristic
31C2×C22⋊C4×C73C2211yescharacteristic
32#95×C73C2212yes—
33C2×Dic146—24no—
34C2×Dic146—24no—
35C2×Dic146—24no—
36C2×Dic146—41no—
37C2×Dic146—42no—
38C22×Dic73C2312yes—
39C22×Dic73C2312yes—
40C22×Dic73C2312yes—
41C22×Dic73C2312yes—
42C4⋊Dic73—24no—
43C4⋊Dic73—24no—
44C4⋊Dic73—41no—
45#11924007—24no—
46#11924007—24no—
47#11924007D418yes—
48C22⋊Dic73—24no—
49C22⋊Dic73—24no—
50C4×Dic73—24no—
51C24×C73C2311yescharacteristic
52C22×C4×C73—24no—
53C22×C4×C73—41no—
54C22×C4×C73C2311yescharacteristic
55C22×C4×C73C2311yescharacteristic
56C22×C4×C73C2312yes—
57C22×C4×C73C2312yes—
58C4⋊C4×C73—24no—
59C22⋊C4×C73—41no—
60C22⋊C4×C73Q814yescomplemented
61C23×C73—22no—
62C23×C73—21no—
63C23×C73—22no—
64C23×C73—21no—
65C23×C73C2×Q812yes—
66C23×C73C2411yescharacteristic
67C2×C4×C73—22no—
68C2×C4×C73—22no—
69C2×C4×C73—22no—
70C2×C4×C73—22no—
71C2×C4×C73—22no—
72C2×C4×C73—21no—
73C2×C4×C73—21no—
74C2×C4×C73—22no—
75C2×C4×C73—44no—
76C2×C4×C73C2×D414yes—
77C2×C4×C73C2×Q814yes—
78C2×Dic73—22no—
79C2×Dic73—22no—
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—
89C2×Dic73C2×D414yes—
90Dic146—44no—
91Dic146—48no—
92C22×C73—22no—
93C22×C73—24no—
94C22×C73—42no—
95C22×C73—41no—
96C22×C73—41no—
97C22×C73C22×D412yes—
98C22×C73C22×Q811yescharacteristic
99C22×C73H(5,𝔽2)11yescharacteristic
100C22×C732−1+412yes—
101C22×C732−1+411yescharacteristic
102C4×C73—24no—
103C4×C73—24no—
104C4×C73—41no—
105C4×C73—41no—
106Dic73—24no—
107Dic73—24no—
108Dic73—42no—
109Dic73—42no—
110C2×C73—42no—
111C2×C73#53612yes—
112C2×C73#54411yescharacteristic
113C2×C73D4211yescharacteristic
114C2×C73D4×Q812yes—
115C2×C73#56311yescharacteristic
116#2677—731nomaximal, Sylow
117C73#267711yescharacteristic, complemented, Sylow
118C2×C4⋊Q8—732no—
119C2×C22⋊Q8—732no—
120#399—731no—
121#398—732no—
122#395—732no—
123#393—731no—
124#388—732no—
125#387—732no—
126#385D7311yescharacteristic
127C22×Q8—732no—
128C22×Q8—731no—
129C23×C4C2×D7311yescharacteristic
130C4⋊Q8—1468no—
131C22⋊Q8—1468no—
132C2×C4⋊C4—731no—
133C2×C4⋊C4—732no—
134C2×C4⋊C4—732no—
135C2×C4⋊C4—732no—
136C2×C4⋊C4—732no—
137C2×C4⋊C4—732no—
138C2×C4⋊C4C2×D7312yes—
139C2×C22⋊C4—732no—
140C2×C22⋊C4—732no—
141C2×C22⋊C4C2×D7311yescharacteristic
142C2×C22⋊C4C2×D7311yescharacteristic
143C2×C42—732no—
144#95—731no—
145#95—732no—
146#95—732no—
147#95—732no—
148#95—731no—
149#95C2×D7312yes—
150C24C22×D7311yescharacteristic
151C2×Q8—2922no—
152C2×Q8—2921no—
153C2×Q8—1464no—
154C2×Q8—1464no—
155C2×Q8—1464no—
156C22×C4—24no—
157C22×C4—41no—
158C22×C4—732no—
159C22×C4—732no—
160C22×C4—732no—
161C22×C4—732no—
162C22×C4C22×D7311yescharacteristic
163C22×C4C22×D7311yescharacteristic
164C22×C4C22×D7312yes—
165C22×C4C22×D7312yes—
166C4⋊C4—24no—
167C4⋊C4—2921no—
168C4⋊C4—738no—
169C4⋊C4—1464no—
170C4⋊C4—1464no—
171C4⋊C4—1464no—
172C4⋊C4—1464no—
173C22⋊C4—41no—
174C22⋊C4—1464no—
175C22⋊C4—1464no—
176C22⋊C4Dic14614yescomplemented
177C42—1464no—
178C23—22no—
179C23—21no—
180C23—22no—
181C23—21no—
182C23C2×Dic14612yes—
183C23C23×D7311yescharacteristic
184Q8—2928no—
185Q8—2924no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—22no—
194C2×C4—44no—
195C2×C4—734no—
196C2×C4—734no—
197C2×C4—1462no—
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×C4—1462no—
207C2×C4D4×D7314yes—
208C2×C4C2×Dic14614yes—
209C22—22no—
210C22—24no—
211C22—42no—
212C22—41no—
213C22—41no—
214C22C2×D4×D7312yes—
215C22C22×Dic14611yescharacteristic
216C22#1455663611yescharacteristic
217C22#1455663812yes—
218C22#1455663911yescharacteristic
219C4—24no—
220C4—24no—
221C4—41no—
222C4—41no—
223C4—2922no—
224C4—2922no—
225C4—1464no—
226C4—1464no—
227C2—42no—
228C2#1798916012yes—
229C2#1798921811yescharacteristic
230C2#1798921911yescharacteristic
231C2D4×Dic14612yes—
232C2#1798934011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#385×C73C2
hypercenter#385D73
hypocenterC73#2677
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. C2×#14556590C2semidirect
4. #17988520C2semidirect
5. #17988508C2semidirect
8. #17988474C2semidirect
60. C22⋊C4×C73Q8semidirect
117. C73#2677semidirect
176. C22⋊C4Dic146semidirect