Finite Group Databasebeta

← #22616890

Subgroups — #22616890

Order 9344.

476 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14556584C212yesmaximal, complemented
2#17988523C212yesmaximal, complemented
3#17988510C212yesmaximal, complemented
4#17988501C212yesmaximal
5#17988485C211yesmaximal, characteristic, complemented
6#17988485C211yesmaximal, characteristic, complemented
7#17988482C212yesmaximal, complemented
8#17988480C212yesmaximal, complemented
9#390×C73C211yesmaximal, characteristic
10#14556584—28no—
11C2×C4⋊Dic73C2211yescharacteristic
12C2×C4⋊Dic73C2211yescharacteristic
13C2×C4⋊Dic73C2211yescharacteristic
14C2×C4⋊Dic73C2211yescharacteristic
15C2×#11924007C2212yes—
16C2×#11924007C2212yes—
17C2×#11924007C2212yes—
18C2×#11924007C2212yes—
19C2×C22⋊Dic73C2212yes—
20C2×C22⋊Dic73C2212yes—
21C2×C22⋊Dic73C2212yes—
22C2×C22⋊Dic73C2212yes—
23C2×C4×Dic73C2212yes—
24#14556498C2212yes—
25#14556498C2212yes—
26#14556498C2212yes—
27C22×D4×C73C2211yescharacteristic
28C2×C4⋊C4×C73C2211yescharacteristic
29C2×C22⋊C4×C73C2212yes—
30C2×C22⋊C4×C73C2212yes—
31C2×C42×C73C2211yescharacteristic
32C22×Dic73C2312yes—
33C22×Dic73C2312yes—
34C22×Dic73C2312yes—
35C22×Dic73C2312yes—
36C4⋊Dic73—22no—
37C4⋊Dic73—41no—
38C4⋊Dic73—41no—
39C4⋊Dic73D414yescomplemented
40#11924007—24no—
41#11924007—24no—
42#11924007—24no—
43#11924007—42no—
44C22⋊Dic73—24no—
45C22⋊Dic73—24no—
46C22⋊Dic73—42no—
47C22⋊Dic73—42no—
48C4×Dic73—24no—
49C24×C73C2312yes—
50C2×D4×C73—22no—
51C2×D4×C73—41no—
52C2×D4×C73—41no—
53C22×C4×C73C2312yes—
54C22×C4×C73C2311yescharacteristic
55C22×C4×C73C2311yescharacteristic
56C22×C4×C73C2311yescharacteristic
57C4⋊C4×C73—41no—
58C22⋊C4×C73—24no—
59C22⋊C4×C73—24no—
60C42×C73—41no—
61C23×C73—22no—
62C23×C73—22no—
63C23×C73—22no—
64C23×C73—22no—
65C23×C73—22no—
66C23×C73—22no—
67C23×C73—22no—
68C23×C73C2411yescharacteristic
69D4×C73—44no—
70C2×C4×C73—21no—
71C2×C4×C73—21no—
72C2×C4×C73—21no—
73C2×C4×C73—21no—
74C2×C4×C73—21no—
75C2×C4×C73—21no—
76C2×C4×C73—22no—
77C2×C4×C73—22no—
78C2×C4×C73—22no—
79C2×C4×C73C2×D412yes—
80C2×C4×C73#4112yes—
81C2×C4×C73#4112yes—
82C2×Dic73—22no—
83C2×Dic73—22no—
84C2×Dic73—22no—
85C2×Dic73—22no—
86C2×Dic73—22no—
87C2×Dic73—22no—
88C2×Dic73—22no—
89C2×Dic73—22no—
90C2×Dic73—22no—
91C2×Dic73—22no—
92C2×Dic73—22no—
93C2×Dic73C2×D414yes—
94C22×C73—42no—
95C22×C73—42no—
96C22×C73—42no—
97C22×C73—42no—
98C22×C73—42no—
99C22×C73—42no—
100C22×C73—42no—
101C22×C73C22×D411yescharacteristic
102C22×C73C2×#4111yescharacteristic
103C22×C73C2×#4111yescharacteristic
104C22×C73H(5,𝔽2)11yescharacteristic
105C22×C73H(5,𝔽2)11yescharacteristic
106C22×C732−1+411yescharacteristic
107C22×C732−1+411yescharacteristic
108C4×C73—22no—
109C4×C73—22no—
110C4×C73—22no—
111C4×C73—42no—
112Dic73—24no—
113Dic73—42no—
114Dic73—42no—
115Dic73—42no—
116C2×C73—82no—
117C2×C73#53711yescharacteristic
118C2×C73#53811yescharacteristic
119C2×C73#53911yescharacteristic
120C2×C73#54711yescharacteristic
121C2×C73#55011yescharacteristic
122C2×C73#55611yescharacteristic
123C2×C73#56311yescharacteristic
124#2727—731nomaximal, Sylow
125C73#272711yescharacteristic, complemented, Sylow
126C2×#126—732no—
127#399—732no—
128#396—732no—
129#394—732no—
130#390D7311yescharacteristic
131#389—732no—
132#389—731no—
133#389—731no—
134#388—732no—
135C22×D4C2×D7311yescharacteristic
136#126—1468no—
137C2×C4⋊C4—732no—
138C2×C4⋊C4—731no—
139C2×C4⋊C4—731no—
140C2×C4⋊C4—731no—
141C2×C4⋊C4—732no—
142C2×C4⋊C4—732no—
143C2×C4⋊C4—732no—
144C2×C4⋊C4—731no—
145C2×C4⋊C4C2×D7311yescharacteristic
146C2×C22⋊C4—732no—
147C2×C22⋊C4—732no—
148C2×C22⋊C4—732no—
149C2×C22⋊C4—732no—
150C2×C22⋊C4C2×D7312yes—
151C2×C22⋊C4C2×D7312yes—
152C2×C42—732no—
153C2×C42C2×D7311yescharacteristic
154#95—732no—
155#95—732no—
156#95—732no—
157C24C22×D7312yes—
158C2×D4—22no—
159C2×D4—41no—
160C2×D4—41no—
161C22×C4—732no—
162C22×C4—732no—
163C22×C4—732no—
164C22×C4—732no—
165C22×C4C22×D7312yes—
166C22×C4C22×D7311yescharacteristic
167C22×C4C22×D7311yescharacteristic
168C22×C4C22×D7311yescharacteristic
169C4⋊C4—41no—
170C4⋊C4—2922no—
171C4⋊C4—2921no—
172C4⋊C4—2921no—
173C4⋊C4—734no—
174C4⋊C4—1464no—
175C4⋊C4—1464no—
176C4⋊C4—1462no—
177C4⋊C4—1464no—
178C22⋊C4—24no—
179C22⋊C4—24no—
180C22⋊C4—2922no—
181C22⋊C4—2922no—
182C22⋊C4—1464no—
183C22⋊C4—1464no—
184C42—41no—
185C42—1464no—
186C23—22no—
187C23—22no—
188C23—22no—
189C23—22no—
190C23—22no—
191C23—22no—
192C23—22no—
193C23C23×D7311yescharacteristic
194D4—44no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—734no—
205C2×C4—1462no—
206C2×C4—1462no—
207C2×C4—1462no—
208C2×C4—1462no—
209C2×C4—1462no—
210C2×C4—1462no—
211C2×C4—1462no—
212C2×C4—1462no—
213C2×C4—1462no—
214C2×C4—1462no—
215C2×C4—1462no—
216C2×C4D4×D7312yes—
217C2×C4#1192402712yes—
218C2×C4#1192402812yes—
219C22—42no—
220C22—42no—
221C22—42no—
222C22—42no—
223C22—42no—
224C22—42no—
225C22—42no—
226C22C2×D4×D7311yescharacteristic
227C22C2×#1192402711yescharacteristic
228C22C2×#1192402811yescharacteristic
229C22#1455663611yescharacteristic
230C22#1455663611yescharacteristic
231C22#1455663811yescharacteristic
232C22#1455663811yescharacteristic
233C4—22no—
234C4—22no—
235C4—22no—
236C4—42no—
237C4—2922no—
238C4—2922no—
239C4—2922no—
240C4—1464no—
241C2—82no—
242C2#1798916411yescharacteristic
243C2#1798917511yescharacteristic
244C2#1798918211yescharacteristic
245C2#1798924211yescharacteristic
246C2#1798925711yescharacteristic
247C2#1798930711yescharacteristic
248C2#1798933711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#390×C73C2
hypercenter#390D73
hypocenterC73#2727
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#14556584C2semidirect
2. #17988523C2semidirect
3. #17988510C2semidirect
5. #17988485C2semidirect
6. #17988485C2semidirect
7. #17988482C2semidirect
8. #17988480C2semidirect
39. C4⋊Dic73D4semidirect
125. C73#2727semidirect