Finite Group Databasebeta

← #46821209

Subgroups — #46821209

Order 34432.

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

normal subgroups only

This group has 400 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#31771160C211yesmaximal, characteristic, complemented
2#31771156C211yesmaximal, characteristic
3#31770961C214yesmaximal, complemented
4#31770955C211yesmaximal, characteristic, complemented
5#31770953C211yesmaximal, characteristic, complemented
6#31770952C211yesmaximal, characteristic, complemented
7#31770600C214yesmaximal, complemented
8C4×C8×D269C211yesmaximal, characteristic, complemented
9#487×C269C211yesmaximal, characteristic, complemented
10C2×#16864403C2212yes—
11C2×C8×D269C2212yes—
12#22575453C2211yescharacteristic
13#22575450C2211yescharacteristic
14#22575444C2212yes—
15#22575442C2212yes—
16#22575433—21no—
17#22575429—21no—
18#22575428—21no—
19#22575428—21no—
20Q8×Dic269—21no—
21#22575418—21no—
22#22575415—21no—
23#22575415—21no—
24#22575411C2212yes—
25C42×D269C2211yescharacteristic
26#22575377C2214yes—
27#22575375C2214yes—
28#22575373C2214yes—
29C4×#14524130C2211yescharacteristic
30C8×Dic269C2212yes—
31C4⋊Q8×C269C2211yescharacteristic
32C4⋊Q8×C269C2211yescharacteristic
33#103×C269C2214yes—
34C4×C8×C269C2211yescharacteristic
35#16864403—28no—
36C2×Dic538—21no—
37C2×D1076—22no—
38C2×D1076—21no—
39C2×D1076—21no—
40C2×D1076C2312yes—
41C2×C4×D269—22no—
42C2×C4×D269D411yescharacteristic
43C2×C4×D269D411yescharacteristic
44C2×C4×D269C2311yescharacteristic
45C2×#14524130C2312yes—
46C8×D269—24no—
47C4⋊Dic269—22no—
48C4⋊Dic269—21no—
49C4⋊Dic269C2312yes—
50#16864381—22no—
51#16864379—22no—
52#16864379—22no—
53#16864379—22no—
54C4×Dic269—22no—
55C4×Dic269D411yescharacteristic
56C4×Dic269D411yescharacteristic
57C4×Dic269C2311yescharacteristic
58C2×Q8×C269—21no—
59C2×Q8×C269C2312yes—
60C2×C8×C269C2312yes—
61C4⋊C4×C269—21no—
62C4⋊C4×C269—21no—
63C4⋊C4×C269—21no—
64C4⋊C4×C269C2312yes—
65C42×C269C2311yescharacteristic
66C22×D269—22no—
67C22×D269C2×D411yescharacteristic
68Dic538—42no—
69D1076—24no—
70D1076—44no—
71D1076—42no—
72D1076—42no—
73C2×Dic269—22no—
74C2×Dic269C2×D411yescharacteristic
75C2×Dic269C2×D411yescharacteristic
76C2×Dic269C2×D411yescharacteristic
77C4×D269—22no—
78C4×D269—22no—
79C4×D269—44no—
80C4×D269#4114yes—
81#14524130—22no—
82Q8×C269—24no—
83Q8×C269—42no—
84C2×C4×C269—22no—
85C2×C4×C269—22no—
86C2×C4×C269C2×D411yescharacteristic
87C2×C4×C269C2×D411yescharacteristic
88C2×C4×C269C2411yescharacteristic
89C8×C269—22no—
90C22×C269C22×D411yescharacteristic
91C2×D269—21no—
92C2×D269—21no—
93C2×D269—42no—
94C2×D269—42no—
95C2×D269—42no—
96C2×D269#12412yes—
97C4×C269—42no—
98C4×C269—42no—
99C4×C269#13512yes—
100C4×C269#13512yes—
101C4×C269C2×#4112yes—
102Dic269—21no—
103Dic269—21no—
104Dic269—42no—
105Dic269#12412yes—
106C2×C269C2×#12411yescharacteristic
107C2×C269C2×#13511yescharacteristic
108C2×C269C2×#13511yescharacteristic
109D269—22no—
110D269—82no—
111C269#313111yescharacteristic, complemented, Sylow
112#3131—2691nomaximal, Sylow
113#533—2691no—
114#532—2691no—
115#488—2694no—
116#487—2691no—
117#487D26911yescharacteristic, complemented
118#486—2691no—
119#486—2691no—
120#416—2694no—
121C2×C4×C8—2691no—
122C2×#41—2692no—
123C22×C8—2692no—
124C4⋊Q8—2691no—
125C4⋊Q8C2×D26911yescharacteristic
126C4⋊Q8C2×D26911yescharacteristic
127#127—2691no—
128#125—2692no—
129#124—2692no—
130C22⋊Q8—5381no—
131C22⋊Q8—5381no—
132#121—5381no—
133#121—5381no—
134C4×Q8—5381no—
135C4×Q8—5381no—
136C4×D4—5381no—
137C4×D4—5381no—
138#117—2692no—
139C2×C42—2691no—
140#103—2694no—
141#103C2×D26914yes—
142#102—2694no—
143#102—2694no—
144C4×C8—2692no—
145C4×C8—2691no—
146C4×C8C2×D26911yescharacteristic
147#41—5388no—
148C2×Q8—21no—
149C2×Q8—5381no—
150C2×Q8C22×D26912yes—
151C2×D4—2692no—
152C2×D4—5382no—
153C2×D4—5381no—
154C2×D4—5381no—
155C22×C4—2691no—
156C22×C4—2691no—
157C22×C4—2691no—
158C22×C4—5382no—
159C2×C8—2692no—
160C2×C8—5384no—
161C2×C8C22×D26912yes—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—21no—
165C4⋊C4—2692no—
166C4⋊C4—5382no—
167C4⋊C4—5382no—
168C4⋊C4—5381no—
169C4⋊C4C22×D26912yes—
170C22⋊C4—5382no—
171C22⋊C4—5382no—
172C22⋊C4—5382no—
173C42—2691no—
174C42—2691no—
175C42—2691no—
176C42—5382no—
177C42C22×D26911yescharacteristic
178C23—2691no—
179C23—5382no—
180Q8—24no—
181Q8—42no—
182Q8—10762no—
183D4—5384no—
184D4—10764no—
185D4—10762no—
186D4—10762no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—2691no—
190C2×C4—2694no—
191C2×C4—2691no—
192C2×C4—2691no—
193C2×C4—5382no—
194C2×C4—5382no—
195C2×C4—5382no—
196C2×C4—10764no—
197C2×C4D4×D26911yescharacteristic
198C2×C4D4×D26911yescharacteristic
199C2×C4C23×D26911yescharacteristic
200C8—22no—
201C8—5382no—
202C22—2692no—
203C22—5381no—
204C22—5381no—
205C22—10762no—
206C22—10762no—
207C22—10762no—
208C22C2×D4×D26911yescharacteristic
209C4—42no—
210C4—42no—
211C4—2692no—
212C4—5381no—
213C4—5381no—
214C4—10762no—
215C4#2257547412yes—
216C4#2257547612yes—
217C4#41×D26912yes—
218C2—5382no—
219C2—21522no—
220C2#124×D26911yescharacteristic
221C2C2×#2257547411yescharacteristic
222C2C2×#2257547611yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#487×C269C2
socleC22×C269C22×D4
prime radical#31771156C2
hypercenter#487D269
hypocenterC269#3131
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
1. #31771160C2semidirect
3. #31770961C2semidirect
4. #31770955C2semidirect
5. #31770953C2semidirect
6. #31770952C2semidirect
7. #31770600C2semidirect
8. C4×C8×D269C2semidirect
9. #487×C269C2semidirect
111. C269#3131semidirect
117. #487D269semidirect

Maximal subgroups

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

subgroupindex
#317711602
#317711562
#317709612
#317709552
#317709532
#317709522
#317706002
C4×C8×D2692
#487×C2692
#3131269