Finite Group Databasebeta

← #22616939

Subgroups — #22616939

Order 9344.

492 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 137 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×#14556589C211yesmaximal, characteristic, complemented
2#17988510C212yesmaximal, complemented
3#17988501C212yesmaximal
4#17988499C212yesmaximal, complemented
5#17988494C211yesmaximal, characteristic, complemented
6#17988481C212yesmaximal, complemented
7#17988475C212yesmaximal, complemented
8#17988471C212yesmaximal, complemented
9C2×#124×C73C211yesmaximal, characteristic
10C22×Dic146C2211yescharacteristic
11#14556589—24no—
12C2×C4⋊Dic73C2211yescharacteristic
13C2×#11924007C2212yes—
14C2×#11924007C2212yes—
15C2×#11924007C2212yes—
16C2×C22⋊Dic73C2212yes—
17C2×C22⋊Dic73C2212yes—
18C2×C22⋊Dic73C2212yes—
19C2×C22⋊Dic73C2212yes—
20C2×C4×Dic73C2211yescharacteristic
21C2×C4×Dic73C2211yescharacteristic
22#14556498C2212yes—
23#14556498C2212yes—
24#14556498C2212yes—
25#14556498C2212yes—
26#14556498C2212yes—
27C22×Q8×C73C2211yescharacteristic
28C22×D4×C73C2211yescharacteristic
29#124×C73—24no—
30C2×C22⋊C4×C73C2212yes—
31C2×C22⋊C4×C73C2212yes—
32C2×C42×C73C2211yescharacteristic
33C2×Dic146—22no—
34C2×Dic146—41no—
35C2×Dic146—41no—
36C22×Dic73C2312yes—
37C22×Dic73C2312yes—
38C22×Dic73C2312yes—
39C22×Dic73C2312yes—
40C4⋊Dic73—41no—
41#11924007—24no—
42#11924007—24no—
43#11924007—24no—
44C22⋊Dic73—24no—
45C22⋊Dic73—24no—
46C22⋊Dic73—42no—
47C22⋊Dic73—42no—
48C4×Dic73—22no—
49C4×Dic73—41no—
50C24×C73C2312yes—
51C2×Q8×C73—41no—
52C2×Q8×C73—41no—
53C2×Q8×C73D414yes—
54C2×D4×C73—22no—
55C2×D4×C73—41no—
56C2×D4×C73—41no—
57C22×C4×C73C2312yes—
58C22×C4×C73C2311yescharacteristic
59C22×C4×C73C2311yescharacteristic
60C22×C4×C73C2311yescharacteristic
61C22⋊C4×C73—24no—
62C22⋊C4×C73—24no—
63C42×C73—22no—
64C23×C73—22no—
65C23×C73—22no—
66C23×C73—22no—
67C23×C73—22no—
68C23×C73—22no—
69C23×C73—22no—
70C23×C73—22no—
71C23×C73C2411yescharacteristic
72Q8×C73—44no—
73D4×C73—44no—
74C2×C4×C73—21no—
75C2×C4×C73—21no—
76C2×C4×C73—21no—
77C2×C4×C73—21no—
78C2×C4×C73—21no—
79C2×C4×C73—21no—
80C2×C4×C73—22no—
81C2×C4×C73—22no—
82C2×C4×C73—22no—
83C2×C4×C73C2×D412yes—
84C2×C4×C73C2×D412yes—
85C2×C4×C73C2×D412yes—
86C2×Dic73—22no—
87C2×Dic73—22no—
88C2×Dic73—22no—
89C2×Dic73—22no—
90C2×Dic73—22no—
91C2×Dic73—22no—
92C2×Dic73—22no—
93C2×Dic73—22no—
94C2×Dic73—22no—
95C2×Dic73—22no—
96C2×Dic73—22no—
97C2×Dic73#4114yes—
98Dic146—44no—
99C22×C73—42no—
100C22×C73—42no—
101C22×C73—42no—
102C22×C73—42no—
103C22×C73—42no—
104C22×C73—42no—
105C22×C73—42no—
106C22×C73C22×D411yescharacteristic
107C22×C73C2×#4112yes—
108C22×C73H(5,𝔽2)11yescharacteristic
109C22×C73H(5,𝔽2)11yescharacteristic
110C22×C732−1+412yes—
111C4×C73—22no—
112C4×C73—22no—
113C4×C73—22no—
114C4×C73—42no—
115Dic73—24no—
116Dic73—42no—
117Dic73—42no—
118Dic73—42no—
119C2×C73—82no—
120C2×C73#53411yescharacteristic
121C2×C73#54212yes—
122C2×C73#54812yes—
123C2×C73#55511yescharacteristic
124C2×C73#56311yescharacteristic
125#2731—731nomaximal, Sylow
126C73#273111yescharacteristic, complemented, Sylow
127C2×C4⋊Q8—731no—
128C2×#124D7311yescharacteristic
129#396—732no—
130#394—732no—
131#393—732no—
132#391—731no—
133#388—732no—
134#388—732no—
135#387—732no—
136C22×Q8—731no—
137C22×Q8C2×D7311yescharacteristic
138C22×D4C2×D7311yescharacteristic
139C4⋊Q8—1464no—
140#124—24no—
141C2×C4⋊C4—731no—
142C2×C4⋊C4—732no—
143C2×C4⋊C4—732no—
144C2×C4⋊C4—732no—
145C2×C22⋊C4—732no—
146C2×C22⋊C4—732no—
147C2×C22⋊C4—732no—
148C2×C22⋊C4—732no—
149C2×C22⋊C4C2×D7312yes—
150C2×C22⋊C4C2×D7312yes—
151C2×C42—731no—
152C2×C42—731no—
153C2×C42C2×D7311yescharacteristic
154#95—732no—
155#95—732no—
156#95—732no—
157#95—732no—
158#95—732no—
159C24C22×D7312yes—
160C2×Q8—41no—
161C2×Q8—41no—
162C2×Q8—2921no—
163C2×Q8—2921no—
164C2×Q8—1462no—
165C2×Q8C22⋊D7314yes—
166C2×D4—22no—
167C2×D4—41no—
168C2×D4—41no—
169C22×C4—732no—
170C22×C4—732no—
171C22×C4—732no—
172C22×C4—732no—
173C22×C4C22×D7312yes—
174C22×C4C22×D7311yescharacteristic
175C22×C4C22×D7311yescharacteristic
176C22×C4C22×D7311yescharacteristic
177C4⋊C4—2921no—
178C4⋊C4—1464no—
179C4⋊C4—1464no—
180C4⋊C4—1464no—
181C22⋊C4—24no—
182C22⋊C4—24no—
183C22⋊C4—2922no—
184C22⋊C4—2922no—
185C22⋊C4—1464no—
186C22⋊C4—1464no—
187C42—22no—
188C42—2921no—
189C42—1462no—
190C23—22no—
191C23—22no—
192C23—22no—
193C23—22no—
194C23—22no—
195C23—22no—
196C23—22no—
197C23C23×D7311yescharacteristic
198Q8—44no—
199Q8—2924no—
200D4—44no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—734no—
211C2×C4—1462no—
212C2×C4—1462no—
213C2×C4—1462no—
214C2×C4—1462no—
215C2×C4—1462no—
216C2×C4—1462no—
217C2×C4—1462no—
218C2×C4—1462no—
219C2×C4—1462no—
220C2×C4—1462no—
221C2×C4—1462no—
222C2×C4C2×C22⋊D7312yes—
223C2×C4C2×C22⋊D7312yes—
224C2×C4C2×C22⋊D7312yes—
225C22—42no—
226C22—42no—
227C22—42no—
228C22—42no—
229C22—42no—
230C22—42no—
231C22—42no—
232C22C22×C22⋊D7311yescharacteristic
233C22#41×D7312yes—
234C22#1455663611yescharacteristic
235C22#1455663611yescharacteristic
236C22#1455663812yes—
237C4—22no—
238C4—22no—
239C4—22no—
240C4—42no—
241C4—2922no—
242C4—2922no—
243C4—2922no—
244C4—1464no—
245C2—82no—
246C2#1798914611yescharacteristic
247C2#1798920112yes—
248C2#1798924412yes—
249C2#1798929911yescharacteristic
250C2#1798933711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
FittingC2×#124×C73C2
hypercenterC2×#124D73
hypocenterC73#2731
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#14556589C2semidirect
2. #17988510C2semidirect
4. #17988499C2semidirect
5. #17988494C2semidirect
6. #17988481C2semidirect
7. #17988475C2semidirect
8. #17988471C2semidirect
126. C73#2731semidirect