Finite Group Databasebeta

← #22614937

Subgroups — #22614937

Order 9344.

544 conjugacy classes of subgroups; only the 185 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 185 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×#14556568C212yesmaximal
2#17988519C212yesmaximal, complemented
3#17988508C212yesmaximal, complemented
4#17988493C212yesmaximal, complemented
5#17988485C212yesmaximal, complemented
6#17988462C212yesmaximal
7#17988447C211yesmaximal, characteristic
8C2×#14556498C211yesmaximal, characteristic
9C4×C22⋊C4×C73C211yesmaximal, characteristic
10C22×Dic146C2212yes—
11C23×Dic73C2212yes—
12#14556568—28no—
13C2×C4⋊Dic73C2212yes—
14C2×C4⋊Dic73C2212yes—
15C2×C4⋊Dic73C2212yes—
16C2×C4⋊Dic73C2212yes—
17C2×#11924007C2212yes—
18C2×#11924007C2212yes—
19C2×C22⋊Dic73C2212yes—
20#14556498C2212yes—
21#14556498C2211yescharacteristic
22#14556498C2211yescharacteristic
23#14556498C2211yescharacteristic
24#14556498C2211yescharacteristic
25#14556498C2212yes—
26#14556498C2212yes—
27C23×C4×C73C2211yescharacteristic
28C2×C22⋊C4×C73C2211yescharacteristic
29C2×C22⋊C4×C73C2211yescharacteristic
30C2×C42×C73C2212yes—
31#95×C73C2212yes—
32C2×Dic146—24no—
33C2×Dic146—24no—
34C2×Dic146—42no—
35C22×Dic73—24no—
36C22×Dic73—24no—
37C22×Dic73—42no—
38C22×Dic73C2312yes—
39C22×Dic73C2312yes—
40C22×Dic73C2312yes—
41C22×Dic73C2312yes—
42C4⋊Dic73—24no—
43C4⋊Dic73—24no—
44C4⋊Dic73—42no—
45C4⋊Dic73—42no—
46#11924007—24no—
47#11924007—24no—
48C22⋊Dic73—24no—
49C24×C73C2311yescharacteristic
50C22×C4×C73—42no—
51C22×C4×C73Q814yescomplemented
52C22×C4×C73C2312yes—
53C22×C4×C73C2311yescharacteristic
54C22×C4×C73C2312yes—
55C22×C4×C73C2311yescharacteristic
56C22⋊C4×C73D414yes—
57C22⋊C4×C73Q814yescomplemented
58C42×C73—42no—
59C23×C73—22no—
60C23×C73—22no—
61C23×C73C2×D412yes—
62C23×C73C2×Q812yes—
63C23×C73C2×Q812yes—
64C23×C73C2411yescharacteristic
65C2×C4×C73—22no—
66C2×C4×C73—22no—
67C2×C4×C73—22no—
68C2×C4×C73—22no—
69C2×C4×C73—22no—
70C2×C4×C73—22no—
71C2×C4×C73—44no—
72C2×C4×C73C2×D414yes—
73C2×C4×C73C2×Q814yes—
74C2×C4×C73C2×Q812yes—
75C2×C4×C73C2×Q812yes—
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—
85C2×Dic73—22no—
86C2×Dic73—22no—
87C2×Dic73—48no—
88C2×Dic73#4114yes—
89Dic146—48no—
90C22×C73—22no—
91C22×C73—22no—
92C22×C73—24no—
93C22×C73—24no—
94C22×C73C4⋊Q814yes—
95C22×C73C22×D411yescharacteristic
96C22×C73C22×Q811yescharacteristic
97C22×C73C22×Q811yescharacteristic
98C22×C73C2×#4112yes—
99C22×C73H(5,𝔽2)12yes—
100C4×C73—22no—
101C4×C73—22no—
102C4×C73—24no—
103C4×C73—24no—
104Dic73—24no—
105Dic73—42no—
106Dic73—42no—
107Dic73—42no—
108C2×C73—24no—
109C2×C73C2×C4⋊Q811yescharacteristic
110C2×C73#53311yescharacteristic
111C2×C73#54311yescharacteristic
112C2×C73#54612yes—
113C2×C73#55412yes—
114#2549—731nomaximal, Sylow
115C73#254911yescharacteristic, complemented, Sylow
116C2×C22⋊Q8—732no—
117#398—732no—
118#395—732no—
119#391—732no—
120#389—732no—
121#385—732no—
122#380—731no—
123C4×C22⋊C4D7311yescharacteristic
124C2×#95—731no—
125C22×Q8—732no—
126C23×C4—732no—
127C23×C4C2×D7311yescharacteristic
128C22⋊Q8—1468no—
129C2×C4⋊C4—732no—
130C2×C4⋊C4—732no—
131C2×C4⋊C4—732no—
132C2×C4⋊C4—732no—
133C2×C4⋊C4—732no—
134C2×C4⋊C4—732no—
135C2×C22⋊C4—732no—
136C2×C22⋊C4C2×D7311yescharacteristic
137C2×C22⋊C4C2×D7311yescharacteristic
138C2×C42C2×D7312yes—
139#95—732no—
140#95—731no—
141#95—731no—
142#95—731no—
143#95—731no—
144#95—732no—
145#95—732no—
146#95C2×D7312yes—
147C24C22×D7311yescharacteristic
148C2×Q8—2922no—
149C2×Q8—1464no—
150C2×Q8—1464no—
151C22×C4—42no—
152C22×C4—2922no—
153C22×C4—732no—
154C22×C4—732no—
155C22×C4—732no—
156C22×C4—732no—
157C22×C4—1464no—
158C22×C4—1464no—
159C22×C4Dic14614yescomplemented
160C22×C4C22×D7312yes—
161C22×C4C22×D7311yescharacteristic
162C22×C4C22×D7311yescharacteristic
163C22×C4C22×D7312yes—
164C4⋊C4—2922no—
165C4⋊C4—2922no—
166C4⋊C4—1464no—
167C4⋊C4—1464no—
168C4⋊C4—1464no—
169C4⋊C4—1464no—
170C22⋊C4—1464no—
171C22⋊C4Dic14614yescomplemented
172C22⋊C4D29214yes—
173C42—42no—
174C23—22no—
175C23—22no—
176C23C2×D29212yes—
177C23C2×Dic14612yes—
178C23C2×Dic14612yes—
179C23C23×D7311yescharacteristic
180Q8—2928no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—44no—
188C2×C4—2928no—
189C2×C4—734no—
190C2×C4—1462no—
191C2×C4—1462no—
192C2×C4—1462no—
193C2×C4—1462no—
194C2×C4—1462no—
195C2×C4—1462no—
196C2×C4—1462no—
197C2×C4—1462no—
198C2×C4—1462no—
199C2×C4—1462no—
200C2×C4—1462no—
201C2×C4C2×D29214yes—
202C2×C4C2×Dic14614yes—
203C2×C4C2×Dic14612yes—
204C2×C4C2×Dic14612yes—
205C22—22no—
206C22—22no—
207C22—24no—
208C22—24no—
209C22#1455659114yes—
210C22C22×D29211yescharacteristic
211C22C22×Dic14611yescharacteristic
212C22C22×Dic14611yescharacteristic
213C22#41×D7312yes—
214C22#1455663612yes—
215C4—22no—
216C4—22no—
217C4—24no—
218C4—24no—
219C4—2922no—
220C4—2922no—
221C4—2922no—
222C4—1464no—
223C2—24no—
224C2C2×#1455659111yescharacteristic
225C2#1798914011yescharacteristic
226C2#1798921311yescharacteristic
227C2#1798923212yes—
228C2#1798929612yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
FittingC4×C22⋊C4×C73C2
hypercenterC4×C22⋊C4D73
hypocenterC73#2549
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #17988519C2semidirect
3. #17988508C2semidirect
4. #17988493C2semidirect
5. #17988485C2semidirect
51. C22×C4×C73Q8semidirect
57. C22⋊C4×C73Q8semidirect
115. C73#2549semidirect
159. C22×C4Dic146semidirect
171. C22⋊C4Dic146semidirect