Finite Group Databasebeta

← #22617195

Subgroups — #22617195

Order 9344.

484 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 121 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#17988523C211yesmaximal, characteristic, complemented
2#17988516C212yesmaximal, complemented
3#17988505C212yesmaximal, complemented
4#17988496C211yesmaximal, characteristic
5#17988487C212yesmaximal, complemented
6#17988479C212yesmaximal, complemented
7#17988469C212yesmaximal, complemented
8#17988466C212yesmaximal, complemented
9#381×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—
21C2×C4×Dic73C2212yes—
22#14556498C2212yes—
23#14556498C2212yes—
24#14556498C2211yescharacteristic
25#14556498C2211yescharacteristic
26C23×C4×C73C2211yescharacteristic
27C2×C22⋊C4×C73C2211yescharacteristic
28C2×C22⋊C4×C73C2211yescharacteristic
29#95×C73C2212yes—
30#95×C73C2212yes—
31C23×D73C2312yes—
32C2×D292—41no—
33C2×D292—42no—
34C2×C22⋊D73—24no—
35C2×C22⋊D73—24no—
36C2×C22⋊D73—42no—
37C22×Dic73C2312yes—
38C22×Dic73C2312yes—
39C22×Dic73C2312yes—
40C4⋊Dic73—41no—
41#11924007—24no—
42#11924007—42no—
43C22⋊Dic73—42no—
44#11924005—24no—
45#11924005—42no—
46#11924005—42no—
47#11924005—42no—
48#11924005—42no—
49C4×Dic73—42no—
50C24×C73C2311yescharacteristic
51C22×C4×C73—22no—
52C22×C4×C73—41no—
53C22×C4×C73—41no—
54C22×C4×C73C2311yescharacteristic
55C22×C4×C73C2311yescharacteristic
56C22×C4×C73C2312yes—
57C22×C4×C73C2312yes—
58C22⋊C4×C73—41no—
59C22⋊C4×C73—41no—
60C23×C73—22no—
61C23×C73—21no—
62C23×C73—21no—
63C23×C73—22no—
64C23×C73#4112yes—
65C23×C73C2411yescharacteristic
66C22×D73—22no—
67C22×D73—22no—
68C22×D73—22no—
69C22×D73—22no—
70C22×D73—22no—
71C22×D73—22no—
72C22×D73—22no—
73C2×C4×C73—22no—
74C2×C4×C73—22no—
75C2×C4×C73—22no—
76C2×C4×C73—22no—
77C2×C4×C73—21no—
78C2×C4×C73—21no—
79C2×C4×C73—22no—
80C2×C4×C73—22no—
81C2×C4×C73—22no—
82C2×C4×C73—22no—
83C2×C4×C73—44no—
84C22⋊D73—48no—
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×Dic73#4114yes—
94D292—44no—
95C22×C73—22no—
96C22×C73—24no—
97C22×C73—42no—
98C22×C73—41no—
99C22×C73—41no—
100C22×C73C2×#4112yes—
101C22×C73C2×#4111yescharacteristic
102C22×C73H(5,𝔽2)11yescharacteristic
103C22×C73H(5,𝔽2)11yescharacteristic
104C22×C73H(5,𝔽2)12yes—
105C2×D73—42no—
106C2×D73—42no—
107C2×D73—42no—
108C2×D73—42no—
109C2×D73—42no—
110C2×D73—42no—
111C2×D73—42no—
112C4×C73—42no—
113C4×C73—42no—
114C4×C73—41no—
115C4×C73—41no—
116Dic73—24no—
117Dic73—42no—
118Dic73—42no—
119C2×C73—42no—
120C2×C73#53811yescharacteristic
121C2×C73#54012yes—
122C2×C73#55112yes—
123C2×C73#55911yescharacteristic
124C2×C73#56011yescharacteristic
125D73—82no—
126#2752—731nomaximal, Sylow
127C73#275211yescharacteristic, complemented, Sylow
128#399—731no—
129#397—732no—
130#394—732no—
131#392—731no—
132#390—732no—
133#388—732no—
134#387—732no—
135#386—732no—
136#381D7311yescharacteristic, complemented
137C22×D4—732no—
138C22×D4—731no—
139C23×C4C2×D7311yescharacteristic
140C2×C4⋊C4—732no—
141C2×C4⋊C4—731no—
142C2×C4⋊C4—732no—
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
151C2×C42—732no—
152#95—732no—
153#95—732no—
154#95—731no—
155#95—731no—
156#95C2×D7312yes—
157#95C2×D7312yes—
158C24—732no—
159C24C22×D7311yescharacteristic
160C2×D4—2921no—
161C2×D4—2922no—
162C2×D4—2922no—
163C2×D4—1464no—
164C2×D4—1464no—
165C22×C4—22no—
166C22×C4—41no—
167C22×C4—41no—
168C22×C4—732no—
169C22×C4—732no—
170C22×C4—732no—
171C22×C4C22×D7312yes—
172C22×C4C22×D7311yescharacteristic
173C22×C4C22×D7311yescharacteristic
174C22×C4C22×D7312yes—
175C4⋊C4—2922no—
176C4⋊C4—2921no—
177C4⋊C4—1464no—
178C22⋊C4—41no—
179C22⋊C4—41no—
180C22⋊C4—2922no—
181C22⋊C4—2922no—
182C22⋊C4—2922no—
183C22⋊C4—2922no—
184C22⋊C4—2922no—
185C22⋊C4—1464no—
186C42—2922no—
187C23—22no—
188C23—21no—
189C23—21no—
190C23—22no—
191C23—1462no—
192C23—1462no—
193C23—1462no—
194C23—1462no—
195C23—1462no—
196C23—1462no—
197C23—1462no—
198C23#1192402812yes—
199C23C23×D7311yescharacteristic
200D4—2924no—
201D4—2928no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—44no—
213C2×C4—734no—
214C2×C4—1462no—
215C2×C4—1462no—
216C2×C4—1462no—
217C2×C4—1462no—
218C2×C4—1462no—
219C2×C4—1462no—
220C2×C4—1462no—
221C2×C4—1462no—
222C22—22no—
223C22—24no—
224C22—42no—
225C22—41no—
226C22—41no—
227C22—2922no—
228C22—2922no—
229C22—2922no—
230C22—2922no—
231C22—2922no—
232C22—2922no—
233C22—2922no—
234C22#41×D7312yes—
235C22C2×#1192402811yescharacteristic
236C22#1455663611yescharacteristic
237C22#1455663611yescharacteristic
238C22#1455663712yes—
239C4—42no—
240C4—42no—
241C4—41no—
242C4—41no—
243C4—2922no—
244C4—2922no—
245C4—1464no—
246C2—42no—
247C2—5842no—
248C2#1798917511yescharacteristic
249C2#1798918912yes—
250C2#1798926112yes—
251C2#1798932111yescharacteristic
252C2#1798932711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#381×C73C2
hypercenter#381D73
hypocenterC73#2752
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
1. #17988523C2semidirect
2. #17988516C2semidirect
3. #17988505C2semidirect
5. #17988487C2semidirect
6. #17988479C2semidirect
7. #17988469C2semidirect
8. #17988466C2semidirect
9. #381×C73C2semidirect
127. C73#2752semidirect
136. #381D73semidirect