Finite Group Databasebeta

← #22616513

Subgroups — #22616513

Order 9344.

612 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 129 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×#14556564C212yesmaximal, complemented
2#17988517C211yesmaximal, characteristic, complemented
3#17988503C212yesmaximal, complemented
4#17988495C212yesmaximal, complemented
5#17988488C211yesmaximal, characteristic, complemented
6#17988481C212yesmaximal, complemented
7#17988463C212yesmaximal, complemented
8#17988449C212yesmaximal, complemented
9#394×C73C211yesmaximal, characteristic, complemented
10C22×D292C2211yescharacteristic
11C22×C22⋊D73C2212yes—
12C22×C22⋊D73C2212yes—
13C22×C4×D73C2212yes—
14#14556564—28no—
15C2×C4⋊Dic73C2211yescharacteristic
16C2×#11924007C2212yes—
17C2×C22⋊Dic73C2212yes—
18C2×C22⋊Dic73C2212yes—
19C2×#11924005C2212yes—
20C2×#11924005C2212yes—
21C2×#11924005C2212yes—
22C2×C4×Dic73C2211yescharacteristic
23#14556498C2212yes—
24#14556498C2212yes—
25#14556498C2212yes—
26#14556498C2211yescharacteristic
27C22×D4×C73C2211yescharacteristic
28C2×C4⋊C4×C73C2211yescharacteristic
29C2×C22⋊C4×C73C2212yes—
30C2×C22⋊C4×C73C2212yes—
31#95×C73C2211yescharacteristic
32C23×D73C2312yes—
33C2×D292—41no—
34C2×D292—41no—
35C2×D292D414yescomplemented
36C2×C22⋊D73—24no—
37C2×C22⋊D73—24no—
38C2×C22⋊D73—24no—
39C2×C22⋊D73—42no—
40C2×C22⋊D73—42no—
41C2×C22⋊D73—42no—
42C22×Dic73C2312yes—
43C22×Dic73C2312yes—
44C22×Dic73C2312yes—
45C2×C4×D73—24no—
46C2×C4×D73—24no—
47C2×C4×D73—42no—
48C4⋊Dic73—41no—
49#11924007—24no—
50C22⋊Dic73—24no—
51C22⋊Dic73—42no—
52#11924005—24no—
53#11924005—42no—
54#11924005—42no—
55C4×Dic73—41no—
56C24×C73C2312yes—
57C2×D4×C73—41no—
58C2×D4×C73—42no—
59C22×C4×C73C2312yes—
60C22×C4×C73C2311yescharacteristic
61C22×C4×C73C2311yescharacteristic
62C22×C4×C73C2311yescharacteristic
63C4⋊C4×C73—41no—
64C22⋊C4×C73—24no—
65C22⋊C4×C73—42no—
66C23×C73—22no—
67C23×C73—22no—
68C23×C73—22no—
69C23×C73—22no—
70C23×C73—22no—
71C23×C73—22no—
72C23×C73—22no—
73C23×C73C2411yescharacteristic
74C22×D73—22no—
75C22×D73—22no—
76C22×D73—22no—
77C22×D73—22no—
78C22×D73—22no—
79C22×D73—22no—
80C22×D73C2×D414yes—
81D4×C73—44no—
82C2×C4×C73—21no—
83C2×C4×C73—21no—
84C2×C4×C73—22no—
85C2×C4×C73—22no—
86C2×C4×C73—22no—
87C2×C4×C73—22no—
88C2×C4×C73—21no—
89C2×C4×C73—21no—
90C2×C4×C73—22no—
91C2×C4×C73C2×D412yes—
92C22⋊D73—48no—
93C22⋊D73—48no—
94C2×Dic73—22no—
95C2×Dic73—22no—
96C2×Dic73—22no—
97C2×Dic73—22no—
98C2×Dic73—22no—
99C2×Dic73—22no—
100C2×Dic73—22no—
101C2×Dic73—22no—
102C2×Dic73#4114yes—
103D292—44no—
104C4×D73—48no—
105C22×C73—42no—
106C22×C73—42no—
107C22×C73—42no—
108C22×C73—42no—
109C22×C73—42no—
110C22×C73—42no—
111C22×C73—42no—
112C22×C73C22×D411yescharacteristic
113C22×C73C2×#4112yes—
114C22×C73H(5,𝔽2)11yescharacteristic
115C22×C73H(5,𝔽2)12yes—
116C22×C73H(5,𝔽2)11yescharacteristic
117C2×D73—24no—
118C2×D73—24no—
119C2×D73—24no—
120C2×D73—42no—
121C2×D73—42no—
122C2×D73—42no—
123C2×D73—42no—
124C4×C73—22no—
125C4×C73—42no—
126C4×C73—41no—
127C4×C73—41no—
128Dic73—24no—
129Dic73—42no—
130Dic73—42no—
131C2×C73—82no—
132C2×C73#53411yescharacteristic
133C2×C73#54012yes—
134C2×C73#54612yes—
135C2×C73#55511yescharacteristic
136C2×C73#56011yescharacteristic
137D73—44no—
138#2699—731nomaximal, Sylow
139C73#269911yescharacteristic, complemented, Sylow
140C2×#121—732no—
141#398—731no—
142#394—732no—
143#394D7311yescharacteristic, complemented
144#392—732no—
145#390—731no—
146#388—732no—
147#386—732no—
148#381—732no—
149C22×D4—732no—
150C22×D4—732no—
151C22×D4—731no—
152C22×D4C2×D7311yescharacteristic
153C23×C4—732no—
154#121—1468no—
155C2×C4⋊C4—731no—
156C2×C4⋊C4—732no—
157C2×C4⋊C4C2×D7311yescharacteristic
158C2×C22⋊C4—732no—
159C2×C22⋊C4—732no—
160C2×C22⋊C4—732no—
161C2×C22⋊C4—732no—
162C2×C22⋊C4—732no—
163C2×C22⋊C4C2×D7312yes—
164C2×C22⋊C4C2×D7312yes—
165C2×C42—731no—
166#95—732no—
167#95—732no—
168#95—732no—
169#95—731no—
170#95C2×D7311yescharacteristic
171C24—732no—
172C24C22×D7312yes—
173C2×D4—42no—
174C2×D4—41no—
175C2×D4—2921no—
176C2×D4—2921no—
177C2×D4—2922no—
178C2×D4—2922no—
179C2×D4—2922no—
180C2×D4—734no—
181C2×D4—1464no—
182C2×D4—1464no—
183C2×D4—1464no—
184C22×C4—2922no—
185C22×C4—732no—
186C22×C4—732no—
187C22×C4—732no—
188C22×C4—1464no—
189C22×C4—1464no—
190C22×C4C22×D7311yescharacteristic
191C22×C4C22×D7312yes—
192C22×C4C22×D7311yescharacteristic
193C22×C4C22×D7311yescharacteristic
194C4⋊C4—41no—
195C4⋊C4—2921no—
196C4⋊C4—1464no—
197C22⋊C4—24no—
198C22⋊C4—42no—
199C22⋊C4—2922no—
200C22⋊C4—2922no—
201C22⋊C4—2922no—
202C22⋊C4—1464no—
203C22⋊C4—1464no—
204C42—2921no—
205C23—22no—
206C23—22no—
207C23—22no—
208C23—22no—
209C23—22no—
210C23—22no—
211C23—22no—
212C23—734no—
213C23—1462no—
214C23—1462no—
215C23—1462no—
216C23—1462no—
217C23—1462no—
218C23—1462no—
219C23C23×D7311yescharacteristic
220D4—44no—
221D4—2924no—
222D4—2928no—
223D4—2928no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—2928no—
234C2×C4—734no—
235C2×C4—1462no—
236C2×C4—1462no—
237C2×C4—1462no—
238C2×C4—1462no—
239C2×C4—1462no—
240C2×C4—1462no—
241C2×C4—1462no—
242C2×C4—1462no—
243C2×C4D4×D7312yes—
244C22—42no—
245C22—42no—
246C22—42no—
247C22—42no—
248C22—42no—
249C22—42no—
250C22—42no—
251C22—2922no—
252C22—2922no—
253C22—2922no—
254C22—2922no—
255C22—1464no—
256C22—1464no—
257C22—1464no—
258C22C2×D4×D7311yescharacteristic
259C22#41×D7312yes—
260C22#1455663611yescharacteristic
261C22#1455663612yes—
262C22#1455663711yescharacteristic
263C4—22no—
264C4—42no—
265C4—41no—
266C4—41no—
267C4—2922no—
268C4—2922no—
269C4—1464no—
270C2—82no—
271C2—2924no—
272C2#1798914511yescharacteristic
273C2#1798918912yes—
274C2#1798923412yes—
275C2#1798929911yescharacteristic
276C2#1798932611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#394×C73C2
hypercenter#394D73
hypocenterC73#2699
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#14556564C2semidirect
2. #17988517C2semidirect
3. #17988503C2semidirect
4. #17988495C2semidirect
5. #17988488C2semidirect
6. #17988481C2semidirect
7. #17988463C2semidirect
8. #17988449C2semidirect
9. #394×C73C2semidirect
35. C2×D292D4semidirect
139. C73#2699semidirect
143. #394D73semidirect