Finite Group Databasebeta

← #46812537

Subgroups — #46812537

Order 34432.

234 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 55 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#31771177C211yesmaximal, characteristic
2#31770586C211yesmaximal, characteristic
3#31770577C211yesmaximal, characteristic
4#31770396C211yesmaximal, characteristic, complemented
5#31770395C211yesmaximal, characteristic, complemented
6#31770394C211yesmaximal, characteristic, complemented
7#352×C269C211yesmaximal, characteristic, complemented
8C2×#16864401C2211yescharacteristic
9C22×Dic538C411yescharacteristic, complemented
10M16×D269—21no—
11#22575452—21no—
12#22575439—21no—
13#22575437C411yescharacteristic, complemented
14#22575436C411yescharacteristic, complemented
15#22575434C2211yescharacteristic
16#22575431—21no—
17#22575430—21no—
18#22575409—21no—
19#22575409C411yescharacteristic, complemented
20#22575371—21no—
21#22575370C2211yescharacteristic
22#22575368C2211yescharacteristic
23#22575367—21no—
24#123×C269C2211yescharacteristic
25#100×C269C2211yescharacteristic
26#99×C269C2211yescharacteristic
27#16864401—41no—
28#16864401—41no—
29C2×Dic538—21no—
30C2×Dic538—21no—
31C2×Dic538—41no—
32C2×Dic538—41no—
33C2×Dic538D411yescharacteristic
34C2×C22⋊D269C2×C411yescharacteristic
35C2×C22⋊D269D411yescharacteristic
36C22×Dic269C2×C411yescharacteristic
37C22×Dic269C2×C411yescharacteristic
38C22×Dic269D411yescharacteristic
39C2×C4×D269D411yescharacteristic
40#16864386—21no—
41#16864385—41no—
42C8×D269—41no—
43C4⋊Dic269—21no—
44#16864381—21no—
45#16864381—21no—
46#16864381—21no—
47#16864381—41no—
48C22⋊Dic269—21no—
49C22⋊Dic269—21no—
50C22⋊Dic269C2×C411yescharacteristic
51#16864379—21no—
52#16864379—21no—
53C4×Dic269—21no—
54C4×Dic269—41no—
55C2×D4×C269C2311yescharacteristic
56C22×C4×C269C2×C411yescharacteristic
57M16×C269—21no—
58C4⋊C4×C269—21no—
59C22⋊C4×C269—21no—
60C22⋊C4×C269—21no—
61C22⋊C4×C269C2×C411yescharacteristic
62C22×D269C22⋊C411yescharacteristic
63Dic538—41no—
64Dic538—42no—
65Dic538—41no—
66Dic538—41no—
67C22⋊D269—41no—
68C22⋊D269—41no—
69C2×Dic269—21no—
70C2×Dic269—21no—
71C2×Dic269—21no—
72C2×Dic269—21no—
73C2×Dic269—21no—
74C2×Dic269—21no—
75C2×Dic269—41no—
76C2×Dic269—41no—
77C2×Dic269C22⋊C411yescharacteristic
78C2×Dic269C22⋊C411yescharacteristic
79C2×Dic269C22⋊C411yescharacteristic
80C4×D269—21no—
81C4×D269—21no—
82#14524130—41no—
83C23×C269C22×C411yescharacteristic
84C23×C269C2×D411yescharacteristic
85D4×C269—41no—
86C2×C4×C269—21no—
87C2×C4×C269—21no—
88C2×C4×C269—41no—
89C2×C4×C269—41no—
90C2×C4×C269C2×D411yescharacteristic
91C8×C269—41no—
92C22×C269—21no—
93C22×C269—21no—
94C22×C269—41no—
95C22×C269—41no—
96C22×C269C2×C22⋊C411yescharacteristic
97C2×D269—21no—
98C2×D269—41no—
99C4×C269—21no—
100C4×C269—41no—
101C4×C269—41no—
102C4×C269—81no—
103Dic269—21no—
104Dic269—21no—
105Dic269—41no—
106Dic269—41no—
107Dic269—81no—
108Dic269#9911yescharacteristic
109Dic269#9911yescharacteristic
110C2×C269—21no—
111C2×C269—41no—
112C2×C269—41no—
113C2×C269C2×#9911yescharacteristic
114D269—41no—
115C269#212311yescharacteristic, complemented, Sylow
116#2123—2691nomaximal, Sylow
117#536—2691no—
118#413—2691no—
119#410—2691no—
120#352—2691no—
121#352—2691no—
122#352—2691no—
123#352D26911yescharacteristic, complemented
124C2×#41—2691no—
125C22×Q8—2691no—
126C2×M16—5381no—
127C4⋊Q8—5381no—
128#124—5381no—
129#123—2691no—
130#123—2691no—
131#123—2691no—
132#123C2×D26911yescharacteristic
133C22⋊Q8—5381no—
134C22⋊Q8—5381no—
135#117—2691no—
136#117—5381no—
137#101—5381no—
138#100—2691no—
139#100C2×D26911yescharacteristic
140#99—2691no—
141#99—5381no—
142#99C2×D26911yescharacteristic
143#41—10761no—
144#41—10761no—
145C2×Q8—2691no—
146C2×Q8—5381no—
147C2×Q8—5381no—
148C2×Q8—10761no—
149C2×Q8—10761no—
150C2×D4—2691no—
151C2×D4—2691no—
152C2×D4C22×D26911yescharacteristic
153C22×C4—2691no—
154C22×C4—2691no—
155C22×C4—2691no—
156C22×C4—2691no—
157C22×C4C4×D26911yescharacteristic
158M16—21no—
159M16—5381no—
160M16—10761no—
161C2×C8—10761no—
162C4⋊C4—21no—
163C4⋊C4—5381no—
164C4⋊C4—5381no—
165C4⋊C4—5381no—
166C4⋊C4—5381no—
167C4⋊C4—10761no—
168C22⋊C4—21no—
169C22⋊C4—21no—
170C22⋊C4—2691no—
171C22⋊C4—5381no—
172C22⋊C4—5381no—
173C22⋊C4—5381no—
174C22⋊C4—5381no—
175C22⋊C4C4×D26911yescharacteristic
176C42—5381no—
177C42—10761no—
178C23—2691no—
179C23C2×C4×D26911yescharacteristic
180C23D4×D26911yescharacteristic
181Q8—10761no—
182Q8—10761no—
183Q8—10761no—
184Q8—10762no—
185D4—41no—
186D4—10761no—
187D4—10761no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—2691no—
193C2×C4—2691no—
194C2×C4—2691no—
195C2×C4—5381no—
196C2×C4—5381no—
197C2×C4—5381no—
198C2×C4—5381no—
199C2×C4—5381no—
200C2×C4—5381no—
201C2×C4—5381no—
202C2×C4—5381no—
203C2×C4—10761no—
204C2×C4—10761no—
205C2×C4D4×D26911yescharacteristic
206C8—41no—
207C8—10761no—
208C22—21no—
209C22—21no—
210C22—41no—
211C22—41no—
212C22—5381no—
213C22—10761no—
214C22C22⋊C4×D26911yescharacteristic
215C4—21no—
216C4—41no—
217C4—41no—
218C4—81no—
219C4—2691no—
220C4—2691no—
221C4—5381no—
222C4—5381no—
223C4—10761no—
224C4—10761no—
225C4—21521no—
226C2—21no—
227C2—41no—
228C2—41no—
229C2—10761no—
230C2#99×D26911yescharacteristic
subgroupG/H
centerC2#99×D269
commutatorC23×C269C22×C4
FrattiniC2×D4C22×D269
Fitting#352×C269C2
socleC2×C269C2×#99
prime radicalC2×#16864401C22
cosocleC2×D4×C269C23
hypercenter#352D269
hypocenterC269#2123
LCSG ▷ C23×C269 ▷ C22×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #352

Complements

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

NH ≅ G/Ntype
4. #31770396C2semidirect
5. #31770395C2semidirect
6. #31770394C2semidirect
7. #352×C269C2semidirect
9. C22×Dic538C4semidirect
13. #22575437C4semidirect
14. #22575436C4semidirect
19. #22575409C4semidirect
115. C269#2123semidirect
123. #352D269semidirect

Maximal subgroups

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

subgroupindex
#317711772
#317705862
#317705772
#317703962
#317703952
#317703942
#352×C2692
#2123269