Finite Group Databasebeta

← #22620183

Subgroups — #22620183

Order 9344.

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

normal subgroups only

This group has 394 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#17989199C211yesmaximal, characteristic, complemented
2#17988928C212yesmaximal, complemented
3#17988887C212yesmaximal, complemented
4#17988792C212yesmaximal, complemented
5#17988738C212yesmaximal
6#17988687C212yesmaximal, complemented
7C4×#11924016C212yesmaximal, complemented
8#17988648C211yesmaximal, characteristic, complemented
9#518×C73C211yesmaximal, characteristic
10C2×#11924016C2212yes—
11C2×#11924016C2212yes—
12#14556591C2211yescharacteristic, complemented
13#14556584—22no—
14#14556583C2211yescharacteristic, complemented
15#14556581—22no—
16#14556570C2212yes—
17C4×Dic146C2212yescomplemented
18#14556524C2212yescomplemented
19#14556522C2212yescomplemented
20C4⋊#10596831C2212yescomplemented
21#14556514C2212yescomplemented
22#14556514C2212yescomplemented
23#14556512C2212yes—
24#14556512C2212yes—
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×Dic146C2312yes—
36#11924016—24no—
37#11924016—24no—
38C2×#10596831C2312yes—
39C2×#10596831C2312yes—
40C4⋊Dic73—22no—
41C4⋊Dic73C2312yes—
42#11924007—22no—
43#11924007—22no—
44#11924007—22no—
45C22⋊Dic73—22no—
46C4×Dic73—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
67D4×C73—24no—
68D4×C73—22no—
69D4×C73#4114yes—
70C2×C4×C73—22no—
71C2×C4×C73—22no—
72C2×C4×C73—82no—
73C2×C4×C73—82no—
74C2×C4×C73C2×D411yescharacteristic
75C2×C4×C73C2×D412yes—
76C2×C4×C73C2×D412yes—
77C2×C4×C73C2411yescharacteristic
78C2×Dic73—22no—
79C2×Dic73—22no—
80Dic146—22no—
81Dic146—22no—
82#10596831—22no—
83#10596831—22no—
84C22×C73—21no—
85C22×C73—24no—
86C22×C73—22no—
87C22×C73—42no—
88C22×C73—42no—
89C22×C73—84no—
90C22×C73C22×D411yescharacteristic
91C4×C73—21no—
92C4×C73—22no—
93C4×C73—22no—
94C4×C73—42no—
95C4×C73C2×#4112yes—
96Dic73—42no—
97Dic73—42no—
98C2×C73—41no—
99C2×C73—44no—
100C2×C73#52511yescharacteristic
101C2×C73#57712yes—
102#3123—731nomaximal, Sylow
103C73#312311yescharacteristic, complemented, Sylow
104#541—731no—
105#518D7311yescharacteristic
106#485—732no—
107#478—732no—
108#461—732no—
109#450—732no—
110#440—732no—
111C4×SD16—732no—
112#433—731no—
113C22×D4C2×D7311yescharacteristic
114C2×SD16—732no—
115C2×SD16—732no—
116C4⋊Q8—731no—
117#126—1462no—
118#125—731no—
119#125—1462no—
120C22⋊Q8—732no—
121C4×Q8—732no—
122C4×D4—22no—
123C4×D4C2×D7312yes—
124C4×D4C2×D7312yes—
125#117C2×D7311yescharacteristic
126#117C2×D7311yescharacteristic
127C2×C22⋊C4—22no—
128#107—732no—
129#106—732no—
130C4⋊C8—732no—
131#103—732no—
132#103—732no—
133#102—732no—
134#102—732no—
135C22⋊C8—732no—
136#97—731no—
137C4×C8—731no—
138C24—21no—
139C2×Q8—732no—
140C2×D4—24no—
141C2×D4—21no—
142C2×D4C22×D7312yes—
143C22×C4—22no—
144C22×C4—22no—
145C22×C4C22×D7311yescharacteristic
146SD16—1464no—
147SD16—1464no—
148C2×C8—732no—
149C2×C8—732no—
150C4⋊C4—732no—
151C4⋊C4—1462no—
152C4⋊C4—1462no—
153C4⋊C4—1462no—
154C4⋊C4—1462no—
155C4⋊C4C22⋊D7312yes—
156C4⋊C4C22×D7312yes—
157C22⋊C4—21no—
158C22⋊C4—22no—
159C22⋊C4—22no—
160C22⋊C4—1462no—
161C22⋊C4C22⋊D7312yes—
162C42—21no—
163C42—1462no—
164C42C22×D7311yescharacteristic
165C42C22×D7311yescharacteristic
166C23—24no—
167C23—22no—
168C23—82no—
169C23C2×C22⋊D7311yescharacteristic
170Q8—1462no—
171Q8—1462no—
172D4—24no—
173D4—22no—
174D4#1192402814yes—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—82no—
178C2×C4—82no—
179C2×C4—1462no—
180C2×C4—1462no—
181C2×C4C2×C22⋊D7311yescharacteristic
182C2×C4C2×C22⋊D7312yes—
183C2×C4C2×C22⋊D7312yes—
184C2×C4C23×D7311yescharacteristic
185C8—1462no—
186C8—1462no—
187C22—22no—
188C22—21no—
189C22—24no—
190C22—42no—
191C22—42no—
192C22—84no—
193C22C22×C22⋊D7311yescharacteristic
194C4—22no—
195C4—22no—
196C4—21no—
197C4—42no—
198C4—2922no—
199C4—2922no—
200C4C2×#1192402812yes—
201C2—41no—
202C2—44no—
203C2#1798909811yescharacteristic
204C2#1798939812yes—
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#518×C73C2
socleC22×C73C22×D4
hypercenter#518D73
hypocenterC73#3123
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. #17989199C2semidirect
2. #17988928C2semidirect
3. #17988887C2semidirect
4. #17988792C2semidirect
6. #17988687C2semidirect
7. C4×#11924016C2semidirect
8. #17988648C2semidirect
12. #14556591C22semidirect
14. #14556583C22semidirect
17. C4×Dic146C22semidirect
18. #14556524C22semidirect
19. #14556522C22semidirect
20. C4⋊#10596831C22semidirect
21. #14556514C22semidirect
22. #14556514C22semidirect
26. #14556502C22semidirect
27. C4×#10596831C22semidirect
103. C73#3123semidirect