Finite Group Databasebeta

← #46812896

Subgroups — #46812896

Order 34432.

226 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 41 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#31771358C211yesmaximal, characteristic, complemented
2#31770795C211yesmaximal, characteristic
3#31770783C211yesmaximal, characteristic
4#31770399C211yesmaximal, characteristic, complemented
5#31770395C211yesmaximal, characteristic, complemented
6#31770394C211yesmaximal, characteristic, complemented
7#458×C269C211yesmaximal, characteristic
8#22575483—21no—
9#22575452—21no—
10#22575446—21no—
11#22575446—21no—
12#22575443—21no—
13#22575440C2211yescharacteristic
14#22575434—21no—
15#22575434C2211yescharacteristic
16#22575432—21no—
17#22575430—21no—
18#22575380—21no—
19#22575370C2211yescharacteristic
20#22575368—21no—
21#22575368C2211yescharacteristic
22H(5,𝔽2)×C269C2211yescharacteristic
23#123×C269—21no—
24#123×C269C2211yescharacteristic
25#99×C269—21no—
26#99×C269C2211yescharacteristic
27C2×Dic538—21no—
28C2×Dic538D411yescharacteristic
29C22×Dic269D411yescharacteristic
30#16864392—41no—
31#16864390—41no—
32#16864386—21no—
33C4⋊Dic269—21no—
34C4⋊Dic269—21no—
35#16864381—21no—
36#16864381—21no—
37#16864381—21no—
38#16864381—21no—
39#16864381—21no—
40#16864381—41no—
41C22⋊Dic269—21no—
42C22⋊Dic269—21no—
43C22⋊Dic269—21no—
44C22⋊Dic269—21no—
45C22⋊Dic269—41no—
46C22⋊Dic269D411yescharacteristic
47C4×Dic269—21no—
48C4×Dic269D411yescharacteristic
49#41×C269—21no—
50#41×C269—41no—
51C2×D4×C269—21no—
52C2×D4×C269—21no—
53C2×D4×C269—41no—
54C2×D4×C269C2311yescharacteristic
55C22×C4×C269D411yescharacteristic
56C4⋊C4×C269—21no—
57C4⋊C4×C269—41no—
58C22⋊C4×C269—21no—
59C22⋊C4×C269—21no—
60C22⋊C4×C269—41no—
61C22⋊C4×C269D411yescharacteristic
62Dic538—41no—
63Dic538—81no—
64C2×Dic269—21no—
65C2×Dic269—21no—
66C2×Dic269—21no—
67C2×Dic269—21no—
68C2×Dic269—41no—
69C2×Dic269—41no—
70#14524130—41no—
71C23×C269—21no—
72C23×C269—21no—
73C23×C269C2×D411yescharacteristic
74C23×C269C2×D411yescharacteristic
75Q8×C269—21no—
76D4×C269—21no—
77D4×C269—41no—
78D4×C269—41no—
79D4×C269—41no—
80D4×C269—41no—
81C2×C4×C269—21no—
82C2×C4×C269—21no—
83C2×C4×C269—21no—
84C2×C4×C269—21no—
85C2×C4×C269—41no—
86C2×C4×C269—41no—
87C2×C4×C269—41no—
88C2×C4×C269C2×D411yescharacteristic
89C22×C269—21no—
90C22×C269—21no—
91C22×C269—41no—
92C22×C269—41no—
93C22×C269—41no—
94C22×C269—81no—
95C22×C269—81no—
96C22×C269#12011yescharacteristic
97C4×C269—21no—
98C4×C269—41no—
99C4×C269—41no—
100C4×C269—41no—
101C4×C269—81no—
102Dic269—41no—
103Dic269—41no—
104Dic269—41no—
105Dic269—41no—
106Dic269—81no—
107C2×C269—21no—
108C2×C269—41no—
109C2×C269—41no—
110C2×C269—81no—
111C2×C269B(4,𝔽2)11yescharacteristic
112C269#220111yescharacteristic, complemented, Sylow
113#2201—2691nomaximal, Sylow
114#563—2691no—
115#458—2691no—
116#458D26911yescharacteristic
117#455—2691no—
118#354—2691no—
119#352—2691no—
120#352—2691no—
121H(5,𝔽2)C2×D26911yescharacteristic
122#137—5381no—
123C4⋊Q8—5381no—
124#126—5381no—
125#126—5381no—
126#125—5381no—
127#124—2691no—
128#123—21no—
129#123—2691no—
130#123—5381no—
131#123C2×D26911yescharacteristic
132C22⋊Q8—5381no—
133C22⋊Q8—5381no—
134#104—5381no—
135#100—2691no—
136#99—21no—
137#99—2691no—
138#99—5381no—
139#99C2×D26911yescharacteristic
140#41—21no—
141#41—41no—
142C2×Q8—2691no—
143C2×Q8—5381no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—41no—
147C2×D4C22×D26911yescharacteristic
148C22×C4—2691no—
149C22×C4C22⋊D26911yescharacteristic
150Q16—10761no—
151SD16—10761no—
152M16—5381no—
153C4⋊C4—21no—
154C4⋊C4—41no—
155C4⋊C4—5381no—
156C4⋊C4—5381no—
157C4⋊C4—5381no—
158C4⋊C4—5381no—
159C4⋊C4—5381no—
160C4⋊C4—5381no—
161C4⋊C4—5381no—
162C4⋊C4—10761no—
163C22⋊C4—21no—
164C22⋊C4—21no—
165C22⋊C4—41no—
166C22⋊C4—2691no—
167C22⋊C4—5381no—
168C22⋊C4—5381no—
169C22⋊C4—5381no—
170C22⋊C4—5381no—
171C22⋊C4—10761no—
172C22⋊C4C22⋊D26911yescharacteristic
173C42—2691no—
174C42—5381no—
175C23—21no—
176C23—21no—
177C23D4×D26911yescharacteristic
178C23C2×C22⋊D26911yescharacteristic
179Q8—21no—
180Q8—10761no—
181Q8—21521no—
182D4—21no—
183D4—41no—
184D4—41no—
185D4—41no—
186D4—41no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—5381no—
195C2×C4—5381no—
196C2×C4—5381no—
197C2×C4—5381no—
198C2×C4—10761no—
199C2×C4—10761no—
200C2×C4D4×D26911yescharacteristic
201C8—10761no—
202C22—21no—
203C22—21no—
204C22—41no—
205C22—41no—
206C22—41no—
207C22—81no—
208C22—81no—
209C22#2257542111yescharacteristic
210C4—21no—
211C4—41no—
212C4—41no—
213C4—41no—
214C4—81no—
215C4—10761no—
216C4—10761no—
217C4—10761no—
218C4—10761no—
219C4—21521no—
220C2—21no—
221C2—41no—
222C2—41no—
223C2—81no—
224C2#3177079111yescharacteristic
subgroupG/H
centerC2#31770791
commutator, cosocleC2×D4×C269C23
FrattiniC2×D4C22×D269
Fitting#458×C269C2
socleC2×C269B(4,𝔽2)
prime radicalH(5,𝔽2)×C269C22
hypercenter#458D269
hypocenterC269#2201
LCSG ▷ C2×D4×C269 ▷ C22×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #458

Complements

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

NH ≅ G/Ntype
1. #31771358C2semidirect
4. #31770399C2semidirect
5. #31770395C2semidirect
6. #31770394C2semidirect
112. C269#2201semidirect

Maximal subgroups

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

subgroupindex
#317713582
#317707952
#317707832
#317703992
#317703952
#317703942
#458×C2692
#2201269