Finite Group Databasebeta

← #22620982

Subgroups — #22620982

Order 9344.

420 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 109 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#17989193C211yesmaximal, characteristic, complemented
2#17989150C211yesmaximal, characteristic, complemented
3#17988976C211yesmaximal, characteristic, complemented
4#17988963C211yesmaximal, characteristic, complemented
5#17988944C211yesmaximal, characteristic, complemented
6#17988801C212yesmaximal, complemented
7#17988781C212yesmaximal, complemented
8#17988733C212yesmaximal, complemented
9#17988722C212yesmaximal, complemented
10#17988649C211yesmaximal, characteristic, complemented
11#490×C73C211yesmaximal, characteristic, complemented
12C2×#11924027C2211yescharacteristic
13C2×D4×D73C2211yescharacteristic
14C2×#11924017C2212yescomplemented
15C2×D584C2212yes—
16C2×#11924013C2212yes—
17C2×#11924013C2212yescomplemented
18#14556588C2211yescharacteristic, complemented
19#14556587C2211yescharacteristic
20#14556579C2211yescharacteristic
21#14556578C2211yescharacteristic
22#14556576—22no—
23#14556566—22no—
24#14556566C2212yes—
25#14556563—22no—
26#14556559—22no—
27#14556553C2212yescomplemented
28#14556548C2211yescharacteristic
29#14556520C2212yescomplemented
30#14556514C2212yescomplemented
31#14556511C2212yes—
32#14556503C2212yes—
33C4×#10596831C2211yescharacteristic, complemented
34#127×C73C2211yescharacteristic
35#125×C73C2211yescharacteristic, complemented
36#102×C73C2212yes—
37#102×C73C2212yescomplemented
38#97×C73C2211yescharacteristic, complemented
39C23×D73—21no—
40#11924027—42no—
41C2×Dic146C2311yescharacteristic
42C2×D292—22no—
43C2×D292—22no—
44C2×D292C2311yescharacteristic
45C2×D292C2312yes—
46C2×C22⋊D73—21no—
47C2×C22⋊D73—21no—
48C2×C22⋊D73—22no—
49D4×D73—42no—
50C22×Dic73—21no—
51C2×C4×D73—22no—
52C2×C4×D73C2311yescharacteristic
53#11924017—42no—
54D584—42no—
55#11924013—42no—
56#11924013—42no—
57C2×#10596831C2312yes—
58#11924007D412yes—
59C22⋊Dic73—22no—
60#11924005—22no—
61#11924005—22no—
62#11924005—22no—
63#11924005D412yes—
64C4×Dic73C2311yescharacteristic
65C2×D4×C73—22no—
66C2×D4×C73C2311yescharacteristic
67C2×D4×C73C2311yescharacteristic
68C2×C8×C73C2312yes—
69C4⋊C4×C73—22no—
70C4⋊C4×C73C2312yes—
71C42×C73C2311yescharacteristic
72C23×C73—21no—
73C23×C73—21no—
74C22×D73—22no—
75C22×D73—21no—
76C22×D73—42no—
77C22×D73—82no—
78C22×D73C2×D411yescharacteristic
79D4×C73—22no—
80D4×C73—22no—
81D4×C73—82no—
82C2×C4×C73—22no—
83C2×C4×C73C2×D412yes—
84C2×C4×C73C2411yescharacteristic
85C22⋊D73—42no—
86C22⋊D73—42no—
87C22⋊D73—82no—
88C2×Dic73—21no—
89C2×Dic73—42no—
90C2×Dic73C2×D412yes—
91C2×Dic73C2×D411yescharacteristic
92D292—22no—
93D292—22no—
94D292—22no—
95D292—82no—
96D292—82no—
97C4×D73—22no—
98C4×D73—82no—
99Dic146—22no—
100C8×C73—22no—
101#10596831—22no—
102C22×C73—41no—
103C22×C73—41no—
104C22×C73—42no—
105C22×C73—42no—
106C22×C73C22×D411yescharacteristic
107C2×D73—21no—
108C2×D73—22no—
109C2×D73—41no—
110C2×D73—42no—
111C2×D73—42no—
112C2×D73—42no—
113C2×D73—42no—
114C2×D73—84no—
115C4×C73—22no—
116C4×C73—42no—
117C4×C73H(5,𝔽2)12yes—
118Dic73—21no—
119Dic73—22no—
120Dic73—41no—
121C2×C73—81no—
122C2×C73—81no—
123C2×C73#53511yescharacteristic
124C2×C73#57612yes—
125D73—41no—
126D73—82no—
127D73—81no—
128#3220—731nomaximal, Sylow
129C73#322011yescharacteristic, complemented, Sylow
130#540—731no—
131#535—731no—
132#496—731no—
133#493—731no—
134#490D7311yescharacteristic, complemented
135#488—731no—
136#463—732no—
137#459—732no—
138#449—732no—
139#447—732no—
140#433—731no—
141C2×#41—731no—
142C22×D4—731no—
143C2×SD16—732no—
144C2×D8—732no—
145C2×D8—732no—
146C2×D8—732no—
147#127—731no—
148#127—731no—
149#127C2×D7311yescharacteristic
150#125C2×D7311yescharacteristic, complemented
151#124—731no—
152#124—731no—
153#123—1462no—
154#121—732no—
155#121—1462no—
156#121—1462no—
157#120—1462no—
158C4×D4—732no—
159#117—731no—
160C4⋊C8—732no—
161#103—732no—
162#102—732no—
163#102C2×D7312yes—
164#102C2×D7312yescomplemented
165C22⋊C8—732no—
166#97C2×D7311yescharacteristic, complemented
167C4×C8—731no—
168C24—1461no—
169#41—2922no—
170C2×Q8—731no—
171C2×D4—22no—
172C2×D4—2922no—
173C2×D4—731no—
174C2×D4—732no—
175C2×D4—1462no—
176C2×D4—1461no—
177C2×D4—1462no—
178C2×D4—1461no—
179C2×D4—1462no—
180C2×D4C22×D7311yescharacteristic
181C2×D4C22×D7311yescharacteristic
182C22×C4—731no—
183C22×C4—1462no—
184C22×C4—1461no—
185SD16—2922no—
186D8—2922no—
187D8—2922no—
188D8—2922no—
189C2×C8—732no—
190C2×C8C22×D7312yes—
191C4⋊C4—22no—
192C4⋊C4—732no—
193C4⋊C4C22×D7312yes—
194C22⋊C4—732no—
195C22⋊C4—1462no—
196C22⋊C4—1462no—
197C22⋊C4—1462no—
198C22⋊C4—1462no—
199C42—731no—
200C42C22×D7311yescharacteristic
201C23—21no—
202C23—21no—
203C23—2922no—
204C23—5842no—
205C23—731no—
206C23—1462no—
207C23—1461no—
208Q8—1462no—
209D4—22no—
210D4—22no—
211D4—82no—
212D4—2922no—
213D4—2922no—
214D4—5842no—
215D4—5842no—
216D4—5842no—
217D4—1462no—
218D4—1462no—
219D4—1462no—
220C2×C4—22no—
221C2×C4—2922no—
222C2×C4—5842no—
223C2×C4—732no—
224C2×C4—731no—
225C2×C4—1461no—
226C2×C4—1462no—
227C2×C4D4×D7312yes—
228C2×C4C23×D7311yescharacteristic
229C8—22no—
230C8—1462no—
231C22—42no—
232C22—42no—
233C22—41no—
234C22—41no—
235C22—2922no—
236C22—2922no—
237C22—2922no—
238C22—2921no—
239C22—2922no—
240C22—5844no—
241C22—1462no—
242C22—1461no—
243C22C2×D4×D7311yescharacteristic
244C4—22no—
245C4—42no—
246C4—2921no—
247C4—1462no—
248C4—1461no—
249C4#1455663712yes—
250C2—81no—
251C2—81no—
252C2—2921no—
253C2—5841no—
254C2—5842no—
255C2#1798915511yescharacteristic
256C2#1798939112yes—
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#490×C73C2
socleC22×C73C22×D4
hypercenter#490D73
hypocenterC73#3220
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #17989193C2semidirect
2. #17989150C2semidirect
3. #17988976C2semidirect
4. #17988963C2semidirect
5. #17988944C2semidirect
6. #17988801C2semidirect
7. #17988781C2semidirect
8. #17988733C2semidirect
9. #17988722C2semidirect
10. #17988649C2semidirect
11. #490×C73C2semidirect
14. C2×#11924017C22semidirect
17. C2×#11924013C22semidirect
18. #14556588C22semidirect
27. #14556553C22semidirect
29. #14556520C22semidirect
30. #14556514C22semidirect
33. C4×#10596831C22semidirect
35. #125×C73C22semidirect
37. #102×C73C22semidirect
38. #97×C73C22semidirect
129. C73#3220semidirect
134. #490D73semidirect
150. #125C2×D73semidirect
164. #102C2×D73semidirect
166. #97C2×D73semidirect