Finite Group Databasebeta

← #46820416

Subgroups — #46820416

Order 34432.

458 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C2×#22575486C211yesmaximal, characteristic
2C22×Dic1076C211yesmaximal, characteristic, complemented
3#31771181C211yesmaximal, characteristic
4#31771082C211yesmaximal, characteristic, complemented
5#31770828C214yesmaximal, complemented
6#31770816C214yesmaximal, complemented
7#31770615C211yesmaximal, characteristic, complemented
8#31770602C211yesmaximal, characteristic
9#424×C269C211yesmaximal, characteristic, complemented
10C2×#16864402C2211yescharacteristic
11C22×Dic538C2211yescharacteristic
12C22×Dic538C2211yescharacteristic
13#22575486—24no—
14C2×Dic1076—24no—
15C2×Dic1076C2212yes—
16C2×Dic1076C2214yes—
17C2×#16864391C2212yes—
18#22575453C2212yes—
19#22575441C2212yes—
20#22575437—22no—
21#22575433—22no—
22C4×Dic538C2214yes—
23#22575418—22no—
24#22575412C2211yescharacteristic
25#22575409—22no—
26#22575378C2212yes—
27#22575378C2214yes—
28#22575375C2212yes—
29C2×M16×C269C2211yescharacteristic
30C22×C8×C269C2211yescharacteristic
31#117×C269C2211yescharacteristic
32C4⋊C8×C269C2214yes—
33#16864402—22no—
34#16864402—22no—
35C2×Dic538—21no—
36C2×Dic538—21no—
37C2×Dic538—22no—
38C2×Dic538—22no—
39C2×Dic538—22no—
40C2×Dic538D414yes—
41C2×Dic538C2312yes—
42C2×Dic538C2311yescharacteristic
43C2×Dic538C2312yes—
44C2×D1076C2311yescharacteristic
45C2×C22⋊D269—21no—
46C22×Dic269—21no—
47C22×Dic269—21no—
48C2×C4×D269—21no—
49Dic1076—28no—
50Dic1076—24no—
51#16864391—24no—
52C4⋊Dic269—24no—
53C4⋊Dic269C2312yes—
54#16864381—24no—
55C22⋊Dic269—21no—
56#16864379—24no—
57C4×Dic269—24no—
58C4×Dic269—21no—
59C22×C4×C269C2311yescharacteristic
60M16×C269—22no—
61C2×C8×C269—22no—
62C2×C8×C269C2312yes—
63C2×C8×C269C2312yes—
64C4⋊C4×C269D412yes—
65C22⋊C4×C269D412yes—
66C42×C269C2312yes—
67C22×D269—21no—
68Dic538—24no—
69Dic538—22no—
70Dic538—22no—
71Dic538—21no—
72Dic538—22no—
73Dic538—21no—
74Dic538—42no—
75Dic538C2×D414yes—
76D1076—21no—
77D1076—21no—
78C22⋊D269—42no—
79C2×Dic269—24no—
80C2×Dic269—22no—
81C2×Dic269—22no—
82C2×Dic269—22no—
83C2×Dic269—21no—
84C2×Dic269—42no—
85C4×D269—42no—
86C23×C269C2×D411yescharacteristic
87C2×C4×C269C2×D412yes—
88C2×C4×C269C2×D414yes—
89C2×C4×C269C2×D411yescharacteristic
90C2×C4×C269#4112yes—
91C2×C4×C269C2411yescharacteristic
92C8×C269—22no—
93C8×C269—22no—
94C22×C269—22no—
95C22×C269#12112yes—
96C22×C269C22×D411yescharacteristic
97C2×D269—41no—
98C2×D269—42no—
99C4×C269—24no—
100C4×C269#12112yes—
101C4×C269C22×D411yescharacteristic
102C4×C269C2×#4111yescharacteristic
103Dic269—24no—
104Dic269—41no—
105Dic269—42no—
106Dic269—42no—
107C2×C269—22no—
108C2×C269C2×#12111yescharacteristic
109C2×C269#57812yes—
110D269—81no—
111C269#304411yescharacteristic, complemented, Sylow
112#3044—2691nomaximal, Sylow
113C2×#137—2691no—
114C22×Q16—2691no—
115#536—2691no—
116#519—2691no—
117#464—2694no—
118#462—2694no—
119#424D26911yescharacteristic, complemented
120#419—2691no—
121#416—2691no—
122C2×#41—2691no—
123C22×Q8—2691no—
124C22×Q8—2691no—
125#137—5384no—
126C2×Q16—2694no—
127C2×Q16—2692no—
128C2×Q16—5384no—
129C2×SD16—2692no—
130C2×M16C2×D26911yescharacteristic
131C22×C8C2×D26911yescharacteristic
132C4⋊Q8—2692no—
133#124—2692no—
134#123—5382no—
135C22⋊Q8—5382no—
136C4×Q8—2694no—
137C4×Q8—5382no—
138#117—2691no—
139#117—5382no—
140#117C2×D26911yescharacteristic
141C4⋊C8C2×D26914yes—
142#103—2692no—
143#103—2694no—
144#102—2692no—
145#41—5382no—
146#41—5382no—
147C2×Q8—2694no—
148C2×Q8—2692no—
149C2×Q8—2692no—
150C2×Q8—2691no—
151C2×Q8—5381no—
152C2×Q8—5381no—
153C2×Q8—5382no—
154C2×Q8—5382no—
155C2×Q8—5382no—
156C2×D4—2691no—
157C2×D4—5381no—
158C22×C4—5381no—
159C22×C4—5381no—
160C22×C4—5381no—
161C22×C4C22×D26911yescharacteristic
162Q16—5388no—
163Q16—5384no—
164SD16—5384no—
165M16—22no—
166C2×C8—22no—
167C2×C8C22×D26912yes—
168C2×C8C22×D26912yes—
169C4⋊C4—2692no—
170C4⋊C4—5384no—
171C4⋊C4—5384no—
172C4⋊C4D107612yes—
173C22⋊C4—5381no—
174C22⋊C4—5384no—
175C22⋊C4D107612yes—
176C42—5381no—
177C42—5384no—
178C42C22×D26912yes—
179C23—5381no—
180C23C2×D107611yescharacteristic
181Q8—2694no—
182Q8—5384no—
183Q8—5382no—
184Q8—5382no—
185Q8—5381no—
186Q8—5382no—
187Q8—5381no—
188Q8—10762no—
189D4—5381no—
190D4—5381no—
191D4—10762no—
192C2×C4—5384no—
193C2×C4—5382no—
194C2×C4—5382no—
195C2×C4—5382no—
196C2×C4—5381no—
197C2×C4—10762no—
198C2×C4—10762no—
199C2×C4D4×D26912yes—
200C2×C4C2×D107614yes—
201C2×C4C2×D107611yescharacteristic
202C2×C4#1686440312yes—
203C2×C4C23×D26911yescharacteristic
204C8—22no—
205C8—22no—
206C22—22no—
207C22—10762no—
208C22—10761no—
209C22#2257542812yes—
210C22C22×D107611yescharacteristic
211C4—24no—
212C4—5384no—
213C4—10762no—
214C4—10761no—
215C4—10762no—
216C4#2257542812yes—
217C4C2×D4×D26911yescharacteristic
218C4C2×#1686440311yescharacteristic
219C2—22no—
220C2—21521no—
221C2C2×#2257542811yescharacteristic
222C2#3177142212yes—
subgroupG/H
centerC22C22×D1076
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#424×C269C2
socleC22×C269C22×D4
prime radicalC2×#16864402C22
hypercenter#424D269
hypocenterC269#3044
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
2. C22×Dic1076C2semidirect
4. #31771082C2semidirect
5. #31770828C2semidirect
6. #31770816C2semidirect
7. #31770615C2semidirect
9. #424×C269C2semidirect
111. C269#3044semidirect
119. #424D269semidirect

Maximal subgroups

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

subgroupindex
C2×#225754862
C22×Dic10762
#317711812
#317710822
#317708282
#317708162
#317706152
#317706022
#424×C2692
#3044269