Finite Group Databasebeta

← #22618024

Subgroups — #22618024

Order 9344.

464 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 117 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
1#17988528C212yesmaximal, complemented
2#17988523C211yesmaximal, characteristic, complemented
3#17988513C212yesmaximal, complemented
4#17988509C212yesmaximal, complemented
5#17988505C212yesmaximal, complemented
6#17988502C212yesmaximal, complemented
7#17988496C211yesmaximal, characteristic
8#17988466C212yesmaximal, complemented
9#385×C73C211yesmaximal, characteristic, complemented
10C22×D292C2211yescharacteristic
11C22×C22⋊D73C2212yes—
12C2×C4⋊Dic73C2211yescharacteristic
13C2×#11924007C2212yes—
14C2×#11924007C2212yes—
15C2×C22⋊Dic73C2212yes—
16C2×#11924005C2212yes—
17C2×#11924005C2212yes—
18C2×#11924005C2212yes—
19C2×#11924005C2212yes—
20C2×#11924005C2212yes—
21#14556498C2212yes—
22#14556498C2212yes—
23#14556498C2211yescharacteristic
24#14556498C2212yes—
25#14556498C2211yescharacteristic
26C23×C4×C73C2211yescharacteristic
27C2×C4⋊C4×C73C2212yes—
28C2×C22⋊C4×C73C2211yescharacteristic
29C2×C22⋊C4×C73C2211yescharacteristic
30#95×C73C2212yes—
31C23×D73C2312yes—
32C2×D292—41no—
33C2×D292—42no—
34C2×C22⋊D73—24no—
35C2×C22⋊D73—42no—
36C2×C22⋊D73—42no—
37C22×Dic73C2312yes—
38C22×Dic73C2312yes—
39C22×Dic73C2312yes—
40C4⋊Dic73—41no—
41#11924007—42no—
42#11924007—42no—
43C22⋊Dic73—42no—
44#11924005—42no—
45#11924005—42no—
46#11924005—42no—
47#11924005—42no—
48#11924005—42no—
49C24×C73C2311yescharacteristic
50C22×C4×C73—42no—
51C22×C4×C73—41no—
52C22×C4×C73C2311yescharacteristic
53C22×C4×C73C2312yes—
54C22×C4×C73C2312yes—
55C22×C4×C73C2311yescharacteristic
56C4⋊C4×C73—42no—
57C22⋊C4×C73—22no—
58C22⋊C4×C73—41no—
59C23×C73—21no—
60C23×C73—22no—
61C23×C73—22no—
62C23×C73—21no—
63C23×C73#4112yes—
64C23×C73C2411yescharacteristic
65C22×D73—22no—
66C22×D73—22no—
67C22×D73—22no—
68C22×D73—22no—
69C22×D73—22no—
70C22×D73—22no—
71C22×D73—22no—
72C2×C4×C73—22no—
73C2×C4×C73—21no—
74C2×C4×C73—21no—
75C2×C4×C73—22no—
76C2×C4×C73—22no—
77C2×C4×C73—22no—
78C2×C4×C73—22no—
79C2×C4×C73—22no—
80C2×C4×C73—22no—
81C2×C4×C73—22no—
82C2×C4×C73—44no—
83C22⋊D73—48no—
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—
93D292—44no—
94C22×C73—24no—
95C22×C73—22no—
96C22×C73—41no—
97C22×C73—41no—
98C22×C73—42no—
99C22×C73C2×#4111yescharacteristic
100C22×C73H(5,𝔽2)12yes—
101C22×C73H(5,𝔽2)11yescharacteristic
102C22×C73H(5,𝔽2)12yes—
103C22×C732−1+411yescharacteristic
104C2×D73—42no—
105C2×D73—42no—
106C2×D73—42no—
107C2×D73—42no—
108C2×D73—42no—
109C2×D73—42no—
110C2×D73—42no—
111C4×C73—42no—
112C4×C73—41no—
113C4×C73—41no—
114C4×C73—42no—
115Dic73—42no—
116Dic73—42no—
117Dic73—42no—
118C2×C73—42no—
119C2×C73#53812yes—
120C2×C73#53911yescharacteristic
121C2×C73#56011yescharacteristic
122C2×C73#56011yescharacteristic
123C2×C73#56212yes—
124D73—82no—
125#2826—731nomaximal, Sylow
126C73#282611yescharacteristic, complemented, Sylow
127#400—732no—
128#399—731no—
129#397—732no—
130#396—732no—
131#394—732no—
132#394—732no—
133#392—731no—
134#386—732no—
135#385D7311yescharacteristic, complemented
136C22×D4—732no—
137C22×D4—731no—
138C23×C4C2×D7311yescharacteristic
139C2×C4⋊C4—732no—
140C2×C4⋊C4—732no—
141C2×C4⋊C4—731no—
142C2×C4⋊C4C2×D7312yes—
143C2×C22⋊C4—732no—
144C2×C22⋊C4—732no—
145C2×C22⋊C4—732no—
146C2×C22⋊C4—732no—
147C2×C22⋊C4—732no—
148C2×C22⋊C4—732no—
149C2×C22⋊C4C2×D7311yescharacteristic
150C2×C22⋊C4C2×D7311yescharacteristic
151#95—732no—
152#95—732no—
153#95—731no—
154#95—732no—
155#95—731no—
156#95C2×D7312yes—
157C24—732no—
158C24C22×D7311yescharacteristic
159C2×D4—2921no—
160C2×D4—2922no—
161C2×D4—2922no—
162C2×D4—2922no—
163C2×D4—1464no—
164C22×C4—41no—
165C22×C4—42no—
166C22×C4—732no—
167C22×C4—732no—
168C22×C4—732no—
169C22×C4C22×D7312yes—
170C22×C4C22×D7311yescharacteristic
171C22×C4C22×D7312yes—
172C22×C4C22×D7311yescharacteristic
173C4⋊C4—42no—
174C4⋊C4—2922no—
175C4⋊C4—2922no—
176C4⋊C4—2921no—
177C22⋊C4—22no—
178C22⋊C4—41no—
179C22⋊C4—2922no—
180C22⋊C4—2922no—
181C22⋊C4—2922no—
182C22⋊C4—2922no—
183C22⋊C4—2922no—
184C22⋊C4—2922no—
185C23—21no—
186C23—22no—
187C23—22no—
188C23—21no—
189C23—1462no—
190C23—1462no—
191C23—1462no—
192C23—1462no—
193C23—1462no—
194C23—1462no—
195C23—1462no—
196C23#1192402812yes—
197C23C23×D7311yescharacteristic
198D4—2924no—
199D4—2928no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—44no—
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—
220C22—24no—
221C22—22no—
222C22—41no—
223C22—41no—
224C22—42no—
225C22—2922no—
226C22—2922no—
227C22—2922no—
228C22—2922no—
229C22—2922no—
230C22—2922no—
231C22—2922no—
232C22C2×#1192402811yescharacteristic
233C22#1455663612yes—
234C22#1455663611yescharacteristic
235C22#1455663712yes—
236C22#1455663911yescharacteristic
237C4—42no—
238C4—42no—
239C4—41no—
240C4—41no—
241C4—2922no—
242C4—2922no—
243C4—2922no—
244C2—42no—
245C2—5842no—
246C2#1798917012yes—
247C2#1798918411yescharacteristic
248C2#1798932611yescharacteristic
249C2#1798932711yescharacteristic
250C2#1798933312yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#385×C73C2
hypercenter#385D73
hypocenterC73#2826
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. #17988528C2semidirect
2. #17988523C2semidirect
3. #17988513C2semidirect
4. #17988509C2semidirect
5. #17988505C2semidirect
6. #17988502C2semidirect
8. #17988466C2semidirect
9. #385×C73C2semidirect
126. C73#2826semidirect
135. #385D73semidirect