Finite Group Databasebeta

← #46821129

Subgroups — #46821129

Order 34432.

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#31771210C211yesmaximal, characteristic, complemented
2#31771079C211yesmaximal, characteristic, complemented
3#31770930C212yesmaximal, complemented
4#31770906C212yesmaximal, complemented
5#31770801C212yesmaximal, complemented
6#31770741C212yesmaximal, complemented
7#31770718C212yesmaximal, complemented
8C4×D2152C212yesmaximal, complemented
9#433×C269C211yesmaximal, characteristic, complemented
10C22×D1076C2211yescharacteristic
11C2×D2152C2212yes—
12C2×D2152C2212yes—
13#22575450C2211yescharacteristic, complemented
14#22575445C2211yescharacteristic, complemented
15#22575438—22no—
16#22575427C2212yes—
17#22575426—22no—
18C4×D1076C2212yes—
19C4×D1076C2212yes—
20C4×D1076C2212yescomplemented
21#22575415—22no—
22#22575412C2211yescharacteristic
23C22⋊C4×D269—22no—
24#22575387C2212yescomplemented
25#22575385C2212yescomplemented
26#22575375C2212yes—
27#22575375C2212yes—
28#22575375C2212yescomplemented
29#22575375C2212yescomplemented
30#117×C269C2211yescharacteristic
31C4⋊C8×C269C2212yescomplemented
32C22⋊C8×C269C2212yes—
33#97×C269C2211yescharacteristic, complemented
34C4×C8×C269C2211yescharacteristic, complemented
35C23×D269—21no—
36C2×D1076—24no—
37C2×D1076—21no—
38C2×D1076—22no—
39C2×D1076C2312yes—
40C2×D1076C2312yes—
41C2×C22⋊D269—22no—
42C2×C4×D269—22no—
43C2×C4×D269—22no—
44C2×C4×D269—22no—
45D2152—24no—
46D2152—24no—
47C4⋊Dic269C2312yes—
48C4⋊Dic269C2312yes—
49#16864381—22no—
50C22⋊Dic269—21no—
51#16864379—22no—
52#16864379—22no—
53#16864379—22no—
54#16864379—22no—
55C4×Dic269—21no—
56C22×C4×C269C2311yescharacteristic
57C2×C8×C269C2312yes—
58C2×C8×C269C2312yes—
59C4⋊C4×C269D412yes—
60C22⋊C4×C269D412yes—
61C42×C269C2311yescharacteristic
62C42×C269C2311yescharacteristic
63C22×D269—22no—
64C22×D269—24no—
65C22×D269—22no—
66C22×D269—82no—
67D1076—24no—
68D1076—22no—
69D1076—22no—
70D1076—22no—
71D1076—82no—
72D1076#4114yes—
73C22⋊D269—82no—
74C2×Dic269—22no—
75C2×Dic269—22no—
76C4×D269—82no—
77C4×D269—82no—
78C4×D269—82no—
79C23×C269C2×D411yescharacteristic
80C2×C4×C269—22no—
81C2×C4×C269C2×D412yes—
82C2×C4×C269C2×D412yes—
83C2×C4×C269C2×D411yescharacteristic
84C2×C4×C269C2411yescharacteristic
85C8×C269—22no—
86C8×C269—22no—
87C22×C269—21no—
88C22×C269—22no—
89C22×C269C22×D411yescharacteristic
90C2×D269—24no—
91C2×D269—42no—
92C2×D269—42no—
93C2×D269—42no—
94C2×D269—42no—
95C2×D269—42no—
96C2×D269—84no—
97C4×C269—21no—
98C4×C269—22no—
99C4×C269—22no—
100C4×C269C2×#4112yes—
101Dic269—42no—
102Dic269—42no—
103C2×C269—41no—
104C2×C269#52511yescharacteristic
105C2×C269#57612yes—
106D269—44no—
107D269—82no—
108C269#312211yescharacteristic, complemented, Sylow
109#3122—2691nomaximal, Sylow
110#540—2691no—
111#518—2691no—
112#482—2692no—
113#478—2692no—
114#459—2692no—
115#447—2692no—
116#442—2692no—
117C4×D8—2692no—
118#433D26911yescharacteristic, complemented
119C22×D4—2691no—
120C2×D8—2692no—
121C2×D8—2692no—
122#127—2691no—
123#125—2691no—
124#123—5382no—
125#121—2692no—
126#121—5382no—
127C4×D4—2692no—
128C4×D4—2692no—
129C4×D4—2692no—
130C4×D4—5382no—
131#117—2691no—
132#117C2×D26911yescharacteristic
133C2×C22⋊C4—5382no—
134#107—2692no—
135#106—2692no—
136C4⋊C8C2×D26912yescomplemented
137#102—2692no—
138#102—2692no—
139#102—2692no—
140#102—2692no—
141C22⋊C8C2×D26912yes—
142#97C2×D26911yescharacteristic, complemented
143C4×C8C2×D26911yescharacteristic, complemented
144C24—5381no—
145C2×D4—2692no—
146C2×D4—2692no—
147C2×D4—5384no—
148C2×D4—5382no—
149C2×D4—5381no—
150C2×D4—5382no—
151C22×C4—5382no—
152C22×C4—5382no—
153C22×C4—5382no—
154C22×C4C22×D26911yescharacteristic
155D8—5384no—
156D8—5384no—
157C2×C8C22×D26912yes—
158C2×C8C22×D26912yes—
159C4⋊C4—2692no—
160C4⋊C4—2692no—
161C4⋊C4—5382no—
162C4⋊C4D107612yes—
163C22⋊C4—5381no—
164C22⋊C4—5382no—
165C22⋊C4—5382no—
166C22⋊C4—5382no—
167C22⋊C4—5382no—
168C22⋊C4D107612yes—
169C42—5381no—
170C42C22×D26911yescharacteristic
171C42C22×D26911yescharacteristic
172C23—5384no—
173C23—5382no—
174C23—5382no—
175C23—21522no—
176C23C2×D107611yescharacteristic
177D4—2694no—
178D4—5384no—
179D4—5382no—
180D4—5382no—
181D4—5382no—
182D4—21522no—
183D4—21522no—
184C2×C4—22no—
185C2×C4—5382no—
186C2×C4—5382no—
187C2×C4—21522no—
188C2×C4—21522no—
189C2×C4—21522no—
190C2×C4C2×D107611yescharacteristic
191C2×C4C2×D107612yes—
192C2×C4C2×D107612yes—
193C2×C4C23×D26911yescharacteristic
194C8—22no—
195C8—22no—
196C22—22no—
197C22—21no—
198C22—5384no—
199C22—10762no—
200C22—10762no—
201C22—10762no—
202C22—10762no—
203C22—10762no—
204C22—21524no—
205C22C22×D107611yescharacteristic
206C4—22no—
207C4—22no—
208C4—21no—
209C4—10762no—
210C4—10762no—
211C4#41×D26912yes—
212C2—41no—
213C2—10764no—
214C2—21522no—
215C2#3177111711yescharacteristic
216C2#3177141012yes—
subgroupG/H
centerC22C22×D1076
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#433×C269C2
socleC22×C269C22×D4
hypercenter#433D269
hypocenterC269#3122
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #31771210C2semidirect
2. #31771079C2semidirect
3. #31770930C2semidirect
4. #31770906C2semidirect
5. #31770801C2semidirect
6. #31770741C2semidirect
7. #31770718C2semidirect
8. C4×D2152C2semidirect
9. #433×C269C2semidirect
13. #22575450C22semidirect
14. #22575445C22semidirect
20. C4×D1076C22semidirect
24. #22575387C22semidirect
25. #22575385C22semidirect
28. #22575375C22semidirect
29. #22575375C22semidirect
31. C4⋊C8×C269C22semidirect
33. #97×C269C22semidirect
34. C4×C8×C269C22semidirect
108. C269#3122semidirect
118. #433D269semidirect
136. C4⋊C8C2×D269semidirect
142. #97C2×D269semidirect
143. C4×C8C2×D269semidirect

Maximal subgroups

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

subgroupindex
#317712102
#317710792
#317709302
#317709062
#317708012
#317707412
#317707182
C4×D21522
#433×C2692
#3122269