Finite Group Databasebeta

← #22620174

Subgroups — #22620174

Order 9344.

418 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 125 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#17989192C211yesmaximal, characteristic, complemented
2#17988911C212yesmaximal, complemented
3#17988887C212yesmaximal, complemented
4#17988782C212yesmaximal, complemented
5#17988721C212yesmaximal, complemented
6#17988697C212yesmaximal, complemented
7C4×#11924013C212yesmaximal, complemented
8#17988648C211yesmaximal, characteristic, complemented
9#518×C73C211yesmaximal, characteristic, complemented
10C2×#11924013C2212yes—
11C2×#11924013C2212yes—
12#14556588C2211yescharacteristic, complemented
13#14556583C2211yescharacteristic, complemented
14#14556576—22no—
15#14556565C2212yes—
16#14556564—22no—
17C4×D292C2212yescomplemented
18#14556524C2212yescomplemented
19#14556522C2212yescomplemented
20C4⋊#10596831C2212yescomplemented
21#14556512C2212yes—
22#14556512C2212yes—
23#14556511C2212yescomplemented
24#14556511C2212yescomplemented
25C22⋊#10596831C2212yes—
26#14556502C2211yescharacteristic, complemented
27C4×#10596831C2211yescharacteristic, complemented
28C22×D4×C73C2211yescharacteristic
29C4×D4×C73—22no—
30C4×D4×C73C2212yes—
31C4×D4×C73C2212yes—
32#117×C73C2211yescharacteristic
33#117×C73C2211yescharacteristic
34C2×C22⋊C4×C73—22no—
35C2×D292—22no—
36C2×D292C2312yes—
37C2×C22⋊D73—22no—
38C2×C4×D73—22no—
39#11924013—24no—
40#11924013—24no—
41C2×#10596831C2312yes—
42C2×#10596831C2312yes—
43C4⋊Dic73C2312yes—
44#11924007—22no—
45#11924005—22no—
46#11924005—22no—
47C24×C73—21no—
48C2×D4×C73—24no—
49C2×D4×C73—21no—
50C2×D4×C73C2312yes—
51C22×C4×C73—22no—
52C22×C4×C73—22no—
53C22×C4×C73C2311yescharacteristic
54C4⋊C4×C73D412yes—
55C4⋊C4×C73C2312yes—
56C22⋊C4×C73—21no—
57C22⋊C4×C73—22no—
58C22⋊C4×C73—22no—
59C22⋊C4×C73D412yes—
60C42×C73—21no—
61C42×C73C2311yescharacteristic
62C42×C73C2311yescharacteristic
63C23×C73—24no—
64C23×C73—22no—
65C23×C73—82no—
66C23×C73C2×D411yescharacteristic
67C22×D73—22no—
68D4×C73—24no—
69D4×C73—22no—
70D4×C73#4114yes—
71C2×C4×C73—22no—
72C2×C4×C73—22no—
73C2×C4×C73—82no—
74C2×C4×C73—82no—
75C2×C4×C73C2×D411yescharacteristic
76C2×C4×C73C2×D412yes—
77C2×C4×C73C2×D412yes—
78C2×C4×C73C2411yescharacteristic
79C22⋊D73—82no—
80C2×Dic73—22no—
81D292—22no—
82D292—22no—
83D292—82no—
84C4×D73—82no—
85#10596831—22no—
86#10596831—22no—
87C22×C73—21no—
88C22×C73—24no—
89C22×C73—22no—
90C22×C73—42no—
91C22×C73—42no—
92C22×C73—84no—
93C22×C73C22×D411yescharacteristic
94C2×D73—42no—
95C2×D73—42no—
96C2×D73—42no—
97C4×C73—21no—
98C4×C73—22no—
99C4×C73—22no—
100C4×C73—42no—
101C4×C73C2×#4112yes—
102Dic73—42no—
103C2×C73—41no—
104C2×C73—44no—
105C2×C73#52511yescharacteristic
106C2×C73#57612yes—
107D73—82no—
108#3122—731nomaximal, Sylow
109C73#312211yescharacteristic, complemented, Sylow
110#540—731no—
111#518D7311yescharacteristic, complemented
112#482—732no—
113#478—732no—
114#459—732no—
115#447—732no—
116#442—732no—
117C4×D8—732no—
118#433—731no—
119C22×D4C2×D7311yescharacteristic
120C2×D8—732no—
121C2×D8—732no—
122#127—731no—
123#125—731no—
124#123—1462no—
125#121—732no—
126#121—1462no—
127C4×D4—22no—
128C4×D4—732no—
129C4×D4C2×D7312yes—
130C4×D4C2×D7312yes—
131#117C2×D7311yescharacteristic
132#117C2×D7311yescharacteristic
133C2×C22⋊C4—22no—
134#107—732no—
135#106—732no—
136C4⋊C8—732no—
137#102—732no—
138#102—732no—
139#102—732no—
140#102—732no—
141C22⋊C8—732no—
142#97—731no—
143C4×C8—731no—
144C24—21no—
145C2×D4—24no—
146C2×D4—21no—
147C2×D4—732no—
148C2×D4—1462no—
149C2×D4—1462no—
150C2×D4C22×D7312yes—
151C22×C4—22no—
152C22×C4—22no—
153C22×C4—1462no—
154C22×C4C22×D7311yescharacteristic
155D8—1464no—
156D8—1464no—
157C2×C8—732no—
158C2×C8—732no—
159C4⋊C4—732no—
160C4⋊C4—1462no—
161C4⋊C4C22⋊D7312yes—
162C4⋊C4C22×D7312yes—
163C22⋊C4—21no—
164C22⋊C4—22no—
165C22⋊C4—22no—
166C22⋊C4—1462no—
167C22⋊C4—1462no—
168C22⋊C4C22⋊D7312yes—
169C42—21no—
170C42C22×D7311yescharacteristic
171C42C22×D7311yescharacteristic
172C23—24no—
173C23—22no—
174C23—82no—
175C23—1462no—
176C23C2×C22⋊D7311yescharacteristic
177D4—24no—
178D4—22no—
179D4—5842no—
180D4—5842no—
181D4—1462no—
182D4—1462no—
183D4#1192402814yes—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—82no—
187C2×C4—82no—
188C2×C4—5842no—
189C2×C4—1462no—
190C2×C4C2×C22⋊D7311yescharacteristic
191C2×C4C2×C22⋊D7312yes—
192C2×C4C2×C22⋊D7312yes—
193C2×C4C23×D7311yescharacteristic
194C8—1462no—
195C8—1462no—
196C22—22no—
197C22—21no—
198C22—24no—
199C22—42no—
200C22—42no—
201C22—84no—
202C22—2922no—
203C22—2922no—
204C22—2922no—
205C22C22×C22⋊D7311yescharacteristic
206C4—22no—
207C4—22no—
208C4—21no—
209C4—42no—
210C4—2922no—
211C4C2×#1192402812yes—
212C2—41no—
213C2—44no—
214C2—5842no—
215C2#1798909811yescharacteristic
216C2#1798939012yes—
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#518×C73C2
socleC22×C73C22×D4
hypercenter#518D73
hypocenterC73#3122
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
1. #17989192C2semidirect
2. #17988911C2semidirect
3. #17988887C2semidirect
4. #17988782C2semidirect
5. #17988721C2semidirect
6. #17988697C2semidirect
7. C4×#11924013C2semidirect
8. #17988648C2semidirect
9. #518×C73C2semidirect
12. #14556588C22semidirect
13. #14556583C22semidirect
17. C4×D292C22semidirect
18. #14556524C22semidirect
19. #14556522C22semidirect
20. C4⋊#10596831C22semidirect
23. #14556511C22semidirect
24. #14556511C22semidirect
26. #14556502C22semidirect
27. C4×#10596831C22semidirect
109. C73#3122semidirect
111. #518D73semidirect