Finite Group Databasebeta

← #46821128

Subgroups — #46821128

Order 34432.

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#31771210C211yesmaximal, characteristic, complemented
2#31770929C212yesmaximal, complemented
3#31770905C212yesmaximal, complemented
4#31770800C212yesmaximal, complemented
5#31770739C212yesmaximal, complemented
6#31770715C212yesmaximal, complemented
7C4×#16864387C212yesmaximal, complemented
8#31770666C211yesmaximal, characteristic, complemented
9#518×C269C211yesmaximal, characteristic, complemented
10C2×#16864387C2212yes—
11C2×#16864387C2212yes—
12#22575450C2211yescharacteristic, complemented
13#22575445C2211yescharacteristic, complemented
14#22575438—22no—
15#22575427C2212yes—
16#22575426—22no—
17C4×D1076C2212yescomplemented
18#22575386C2212yescomplemented
19#22575384C2212yescomplemented
20C4⋊#14524130C2212yescomplemented
21#22575374C2212yes—
22#22575374C2212yes—
23#22575373C2212yescomplemented
24#22575373C2212yescomplemented
25C22⋊#14524130C2212yes—
26#22575364C2211yescharacteristic, complemented
27C4×#14524130C2211yescharacteristic, complemented
28C22×D4×C269C2211yescharacteristic
29C4×D4×C269—22no—
30C4×D4×C269C2212yes—
31C4×D4×C269C2212yes—
32#117×C269C2211yescharacteristic
33#117×C269C2211yescharacteristic
34C2×C22⋊C4×C269—22no—
35C2×D1076—22no—
36C2×D1076C2312yes—
37C2×C22⋊D269—22no—
38C2×C4×D269—22no—
39#16864387—24no—
40#16864387—24no—
41C2×#14524130C2312yes—
42C2×#14524130C2312yes—
43C4⋊Dic269C2312yes—
44#16864381—22no—
45#16864379—22no—
46#16864379—22no—
47C24×C269—21no—
48C2×D4×C269—24no—
49C2×D4×C269—21no—
50C2×D4×C269C2312yes—
51C22×C4×C269—22no—
52C22×C4×C269—22no—
53C22×C4×C269C2311yescharacteristic
54C4⋊C4×C269D412yes—
55C4⋊C4×C269C2312yes—
56C22⋊C4×C269—21no—
57C22⋊C4×C269—22no—
58C22⋊C4×C269—22no—
59C22⋊C4×C269D412yes—
60C42×C269—21no—
61C42×C269C2311yescharacteristic
62C42×C269C2311yescharacteristic
63C22×D269—22no—
64D1076—22no—
65D1076—22no—
66D1076—82no—
67C22⋊D269—82no—
68C2×Dic269—22no—
69C4×D269—82no—
70#14524130—22no—
71#14524130—22no—
72C23×C269—24no—
73C23×C269—22no—
74C23×C269—82no—
75C23×C269C2×D411yescharacteristic
76D4×C269—24no—
77D4×C269—22no—
78D4×C269#4114yes—
79C2×C4×C269—22no—
80C2×C4×C269—22no—
81C2×C4×C269—82no—
82C2×C4×C269—82no—
83C2×C4×C269C2×D411yescharacteristic
84C2×C4×C269C2×D412yes—
85C2×C4×C269C2×D412yes—
86C2×C4×C269C2411yescharacteristic
87C22×C269—21no—
88C22×C269—24no—
89C22×C269—22no—
90C22×C269—42no—
91C22×C269—42no—
92C22×C269—84no—
93C22×C269C22×D411yescharacteristic
94C2×D269—42no—
95C2×D269—42no—
96C2×D269—42no—
97C4×C269—21no—
98C4×C269—22no—
99C4×C269—22no—
100C4×C269—42no—
101C4×C269C2×#4112yes—
102Dic269—42no—
103C2×C269—41no—
104C2×C269—44no—
105C2×C269#52511yescharacteristic
106C2×C269#57612yes—
107D269—82no—
108C269#312211yescharacteristic, complemented, Sylow
109#3122—2691nomaximal, Sylow
110#540—2691no—
111#518D26911yescharacteristic, complemented
112#482—2692no—
113#478—2692no—
114#459—2692no—
115#447—2692no—
116#442—2692no—
117C4×D8—2692no—
118#433—2691no—
119C22×D4C2×D26911yescharacteristic
120C2×D8—2692no—
121C2×D8—2692no—
122#127—2691no—
123#125—2691no—
124#123—5382no—
125#121—2692no—
126#121—5382no—
127C4×D4—22no—
128C4×D4—2692no—
129C4×D4C2×D26912yes—
130C4×D4C2×D26912yes—
131#117C2×D26911yescharacteristic
132#117C2×D26911yescharacteristic
133C2×C22⋊C4—22no—
134#107—2692no—
135#106—2692no—
136C4⋊C8—2692no—
137#102—2692no—
138#102—2692no—
139#102—2692no—
140#102—2692no—
141C22⋊C8—2692no—
142#97—2691no—
143C4×C8—2691no—
144C24—21no—
145C2×D4—24no—
146C2×D4—21no—
147C2×D4—2692no—
148C2×D4—5382no—
149C2×D4—5382no—
150C2×D4C22×D26912yes—
151C22×C4—22no—
152C22×C4—22no—
153C22×C4—5382no—
154C22×C4C22×D26911yescharacteristic
155D8—5384no—
156D8—5384no—
157C2×C8—2692no—
158C2×C8—2692no—
159C4⋊C4—2692no—
160C4⋊C4—5382no—
161C4⋊C4C22⋊D26912yes—
162C4⋊C4C22×D26912yes—
163C22⋊C4—21no—
164C22⋊C4—22no—
165C22⋊C4—22no—
166C22⋊C4—5382no—
167C22⋊C4—5382no—
168C22⋊C4C22⋊D26912yes—
169C42—21no—
170C42C22×D26911yescharacteristic
171C42C22×D26911yescharacteristic
172C23—24no—
173C23—22no—
174C23—82no—
175C23—5382no—
176C23C2×C22⋊D26911yescharacteristic
177D4—24no—
178D4—22no—
179D4—5382no—
180D4—5382no—
181D4—21522no—
182D4—21522no—
183D4#1686440214yes—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—82no—
187C2×C4—82no—
188C2×C4—5382no—
189C2×C4—21522no—
190C2×C4C2×C22⋊D26911yescharacteristic
191C2×C4C2×C22⋊D26912yes—
192C2×C4C2×C22⋊D26912yes—
193C2×C4C23×D26911yescharacteristic
194C8—5382no—
195C8—5382no—
196C22—22no—
197C22—21no—
198C22—24no—
199C22—42no—
200C22—42no—
201C22—84no—
202C22—10762no—
203C22—10762no—
204C22—10762no—
205C22C22×C22⋊D26911yescharacteristic
206C4—22no—
207C4—22no—
208C4—21no—
209C4—42no—
210C4—10762no—
211C4C2×#1686440212yes—
212C2—41no—
213C2—44no—
214C2—21522no—
215C2#3177111611yescharacteristic
216C2#3177140812yes—
subgroupG/H
centerC22C22×C22⋊D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#518×C269C2
socleC22×C269C22×D4
hypercenter#518D269
hypocenterC269#3122
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
1. #31771210C2semidirect
2. #31770929C2semidirect
3. #31770905C2semidirect
4. #31770800C2semidirect
5. #31770739C2semidirect
6. #31770715C2semidirect
7. C4×#16864387C2semidirect
8. #31770666C2semidirect
9. #518×C269C2semidirect
12. #22575450C22semidirect
13. #22575445C22semidirect
17. C4×D1076C22semidirect
18. #22575386C22semidirect
19. #22575384C22semidirect
20. C4⋊#14524130C22semidirect
23. #22575373C22semidirect
24. #22575373C22semidirect
26. #22575364C22semidirect
27. C4×#14524130C22semidirect
108. C269#3122semidirect
111. #518D269semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#317712102
#317709292
#317709052
#317708002
#317707392
#317707152
C4×#168643872
#317706662
#518×C2692
#3122269