Finite Group Databasebeta

← #22620169

Subgroups — #22620169

Order 9344.

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

normal subgroups only

This group has 418 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#17989061C211yesmaximal, characteristic, complemented
2#17988908C212yesmaximal, complemented
3#17988884C212yesmaximal, complemented
4#17988779C212yesmaximal, complemented
5#17988720C212yesmaximal, complemented
6#17988697C212yesmaximal, complemented
7C4×#11924013C212yesmaximal, complemented
8#17988648C211yesmaximal, characteristic, complemented
9#540×C73C211yesmaximal, characteristic, complemented
10C22×D292C2211yescharacteristic
11C2×#11924013C2212yes—
12C2×#11924013C2212yes—
13C4×D292C2212yes—
14C4×D292C2212yes—
15#14556553—22no—
16#14556550C2211yescharacteristic
17C22⋊C4×D73—22no—
18#14556524C2212yescomplemented
19#14556522C2212yescomplemented
20C4⋊#10596831C2212yescomplemented
21#14556512C2212yescomplemented
22#14556512C2212yescomplemented
23#14556511C2212yes—
24#14556511C2212yes—
25C22⋊#10596831C2212yes—
26#14556502C2211yescharacteristic, complemented
27C4×#10596831C2211yescharacteristic, complemented
28#127×C73C2211yescharacteristic, complemented
29#125×C73C2211yescharacteristic, complemented
30#123×C73—22no—
31#121×C73—22no—
32#121×C73C2212yes—
33C4×D4×C73C2212yescomplemented
34#117×C73C2211yescharacteristic
35C23×D73—21no—
36C2×D292—21no—
37C2×D292—24no—
38C2×D292C2312yes—
39C2×C4×D73—22no—
40C2×C4×D73—22no—
41#11924013—24no—
42#11924013—24no—
43C2×#10596831C2312yes—
44C2×#10596831C2312yes—
45C4⋊Dic73C2312yes—
46C22⋊Dic73—21no—
47#11924005—22no—
48#11924005—22no—
49C4×Dic73—21no—
50C2×D4×C73—22no—
51C2×D4×C73—22no—
52C2×D4×C73C2312yes—
53C22×C4×C73—22no—
54C22×C4×C73C2311yescharacteristic
55C4⋊C4×C73—22no—
56C4⋊C4×C73D412yes—
57C4⋊C4×C73C2312yes—
58C22⋊C4×C73—22no—
59C22⋊C4×C73—22no—
60C22⋊C4×C73D412yes—
61C42×C73C2311yescharacteristic
62C42×C73C2311yescharacteristic
63C23×C73—22no—
64C23×C73C2×D411yescharacteristic
65C22×D73—22no—
66C22×D73—24no—
67C22×D73—82no—
68D4×C73—22no—
69D4×C73—22no—
70D4×C73—82no—
71D4×C73—82no—
72C2×C4×C73—22no—
73C2×C4×C73—22no—
74C2×C4×C73—82no—
75C2×C4×C73C2×D412yes—
76C2×C4×C73C2×D412yes—
77C2×C4×C73C2×D411yescharacteristic
78C2×C4×C73C2411yescharacteristic
79C2×Dic73—22no—
80D292—24no—
81D292—22no—
82D292#4114yes—
83C4×D73—82no—
84C4×D73—82no—
85#10596831—22no—
86#10596831—22no—
87C22×C73—21no—
88C22×C73—22no—
89C22×C73—42no—
90C22×C73—42no—
91C22×C73—42no—
92C22×C73C22×D411yescharacteristic
93C2×D73—24no—
94C2×D73—42no—
95C2×D73—42no—
96C2×D73—84no—
97C4×C73—21no—
98C4×C73—22no—
99C4×C73—22no—
100C4×C73—42no—
101C4×C73C2×#4112yes—
102Dic73—42no—
103C2×C73—41no—
104C2×C73—82no—
105C2×C73#52511yescharacteristic
106C2×C73#57612yes—
107D73—44no—
108#3122—731nomaximal, Sylow
109C73#312211yescharacteristic, complemented, Sylow
110#540D7311yescharacteristic, complemented
111#518—731no—
112#482—732no—
113#478—732no—
114#459—732no—
115#447—732no—
116#442—732no—
117C4×D8—732no—
118#433—731no—
119C22×D4—731no—
120C2×D8—732no—
121C2×D8—732no—
122#127C2×D7311yescharacteristic, complemented
123#125C2×D7311yescharacteristic, complemented
124#123—22no—
125#121—22no—
126#121C2×D7312yes—
127C4×D4—732no—
128C4×D4—732no—
129C4×D4—1462no—
130C4×D4C2×D7312yescomplemented
131#117—731no—
132#117C2×D7311yescharacteristic
133C2×C22⋊C4—1462no—
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—1461no—
145C2×D4—22no—
146C2×D4—22no—
147C2×D4—732no—
148C2×D4—1464no—
149C2×D4—1461no—
150C2×D4C22×D7312yes—
151C22×C4—22no—
152C22×C4—1462no—
153C22×C4—1462no—
154C22×C4C22×D7311yescharacteristic
155D8—1464no—
156D8—1464no—
157C2×C8—732no—
158C2×C8—732no—
159C4⋊C4—22no—
160C4⋊C4—732no—
161C4⋊C4C22⋊D7312yes—
162C4⋊C4C22×D7312yes—
163C22⋊C4—22no—
164C22⋊C4—22no—
165C22⋊C4—1461no—
166C22⋊C4—1462no—
167C22⋊C4—1462no—
168C22⋊C4C22⋊D7312yes—
169C42—1461no—
170C42C22×D7311yescharacteristic
171C42C22×D7311yescharacteristic
172C23—22no—
173C23—5842no—
174C23—1464no—
175C23—1462no—
176C23C2×C22⋊D7311yescharacteristic
177D4—22no—
178D4—22no—
179D4—82no—
180D4—82no—
181D4—734no—
182D4—1464no—
183D4—1462no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—82no—
187C2×C4—5842no—
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—42no—
199C22—42no—
200C22—42no—
201C22—2922no—
202C22—2922no—
203C22—5844no—
204C22—1464no—
205C22C22×C22⋊D7311yescharacteristic
206C4—22no—
207C4—22no—
208C4—21no—
209C4—42no—
210C4—2922no—
211C4#41×D7312yes—
212C2—41no—
213C2—82no—
214C2—2924no—
215C2#1798909411yescharacteristic
216C2#1798939012yes—
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#540×C73C2
socleC22×C73C22×D4
hypercenter#540D73
hypocenterC73#3122
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #17989061C2semidirect
2. #17988908C2semidirect
3. #17988884C2semidirect
4. #17988779C2semidirect
5. #17988720C2semidirect
6. #17988697C2semidirect
7. C4×#11924013C2semidirect
8. #17988648C2semidirect
9. #540×C73C2semidirect
18. #14556524C22semidirect
19. #14556522C22semidirect
20. C4⋊#10596831C22semidirect
21. #14556512C22semidirect
22. #14556512C22semidirect
26. #14556502C22semidirect
27. C4×#10596831C22semidirect
28. #127×C73C22semidirect
29. #125×C73C22semidirect
33. C4×D4×C73C22semidirect
109. C73#3122semidirect
110. #540D73semidirect
122. #127C2×D73semidirect
123. #125C2×D73semidirect
130. C4×D4C2×D73semidirect