Finite Group Databasebeta

← #19136247

Subgroups — #19136247

Order 5504.

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#14583471C211yesmaximal, characteristic
2#14582880C211yesmaximal, characteristic
3#14582871C211yesmaximal, characteristic
4#14582690C211yesmaximal, characteristic, complemented
5#14582689C211yesmaximal, characteristic, complemented
6#14582688C211yesmaximal, characteristic, complemented
7C43×#352C211yesmaximal, characteristic, complemented
8C2×#10621900C2211yescharacteristic
9C22×Dic86C411yescharacteristic, complemented
10M16×D43—21no—
11#13063324—21no—
12#13063311—21no—
13#13063309C411yescharacteristic, complemented
14#13063308C411yescharacteristic, complemented
15#13063306C2211yescharacteristic
16#13063303—21no—
17#13063302—21no—
18#13063281—21no—
19#13063281C411yescharacteristic, complemented
20#13063243—21no—
21#13063242C2211yescharacteristic
22#13063240C2211yescharacteristic
23#13063239—21no—
24#123×C43C2211yescharacteristic
25#100×C43C2211yescharacteristic
26#99×C43C2211yescharacteristic
27C2×D4×C43C2311yescharacteristic
28C22×C4×C43C2×C411yescharacteristic
29C2×C22⋊D43C2×C411yescharacteristic
30C2×C22⋊D43D411yescharacteristic
31C22×Dic43C2×C411yescharacteristic
32C22×Dic43C2×C411yescharacteristic
33C22×Dic43D411yescharacteristic
34#10621900—41no—
35#10621900—41no—
36C2×C4×D43D411yescharacteristic
37C2×Dic86—21no—
38C2×Dic86—21no—
39C2×Dic86—41no—
40C2×Dic86—41no—
41C2×Dic86D411yescharacteristic
42M16×C43—21no—
43C4⋊C4×C43—21no—
44C22⋊C4×C43—21no—
45C22⋊C4×C43—21no—
46C22⋊C4×C43C2×C411yescharacteristic
47C22⋊Dic43—21no—
48C22⋊Dic43—21no—
49C22⋊Dic43C2×C411yescharacteristic
50(C2×D43)⋊C4—21no—
51(C2×D43)⋊C4—21no—
52C4⋊Dic43—21no—
53Dic43⋊C4—21no—
54Dic43⋊C4—21no—
55Dic43⋊C4—21no—
56Dic43⋊C4—41no—
57C4×Dic43—21no—
58C4×Dic43—41no—
59#10621877—21no—
60#10621872—41no—
61C8×D43—41no—
62C23×C43C22×C411yescharacteristic
63C23×C43C2×D411yescharacteristic
64C22×D43C22⋊C411yescharacteristic
65D4×C43—41no—
66C2×C4×C43—21no—
67C2×C4×C43—21no—
68C2×C4×C43—41no—
69C2×C4×C43—41no—
70C2×C4×C43C2×D411yescharacteristic
71C22⋊D43—41no—
72C22⋊D43—41no—
73C2×Dic43—21no—
74C2×Dic43—21no—
75C2×Dic43—21no—
76C2×Dic43—21no—
77C2×Dic43—21no—
78C2×Dic43—21no—
79C2×Dic43—41no—
80C2×Dic43—41no—
81C2×Dic43C22⋊C411yescharacteristic
82C2×Dic43C22⋊C411yescharacteristic
83C2×Dic43C22⋊C411yescharacteristic
84C4×D43—21no—
85C4×D43—21no—
86Dic86—41no—
87Dic86—42no—
88Dic86—41no—
89Dic86—41no—
90C8×C43—41no—
91C43⋊C8—41no—
92C22×C43—21no—
93C22×C43—21no—
94C22×C43—41no—
95C22×C43—41no—
96C22×C43C2×C22⋊C411yescharacteristic
97C2×D43—21no—
98C2×D43—41no—
99C4×C43—21no—
100C4×C43—41no—
101C4×C43—41no—
102C4×C43—81no—
103Dic43—21no—
104Dic43—21no—
105Dic43—41no—
106Dic43—41no—
107Dic43—81no—
108Dic43#9911yescharacteristic
109Dic43#9911yescharacteristic
110#2123—431nomaximal, Sylow
111C2×C43—21no—
112C2×C43—41no—
113C2×C43—41no—
114C2×C43C2×#9911yescharacteristic
115D43—41no—
116#536—431no—
117#413—431no—
118#410—431no—
119#352—431no—
120#352—431no—
121#352—431no—
122#352D4311yescharacteristic, complemented
123C43#212311yescharacteristic, complemented, Sylow
124C2×#41—431no—
125C22×Q8—431no—
126C2×M16—861no—
127C4⋊Q8—861no—
128#124—861no—
129#123—431no—
130#123—431no—
131#123—431no—
132#123C2×D4311yescharacteristic
133C22⋊Q8—861no—
134C22⋊Q8—861no—
135#117—431no—
136#117—861no—
137#101—861no—
138#100—431no—
139#100C2×D4311yescharacteristic
140#99—431no—
141#99—861no—
142#99C2×D4311yescharacteristic
143#41—1721no—
144#41—1721no—
145C2×Q8—431no—
146C2×Q8—861no—
147C2×Q8—861no—
148C2×Q8—1721no—
149C2×Q8—1721no—
150C2×D4—431no—
151C2×D4—431no—
152C2×D4C22×D4311yescharacteristic
153C22×C4—431no—
154C22×C4—431no—
155C22×C4—431no—
156C22×C4—431no—
157C22×C4C4×D4311yescharacteristic
158M16—21no—
159M16—861no—
160M16—1721no—
161C2×C8—1721no—
162C4⋊C4—21no—
163C4⋊C4—861no—
164C4⋊C4—861no—
165C4⋊C4—861no—
166C4⋊C4—861no—
167C4⋊C4—1721no—
168C22⋊C4—21no—
169C22⋊C4—21no—
170C22⋊C4—431no—
171C22⋊C4—861no—
172C22⋊C4—861no—
173C22⋊C4—861no—
174C22⋊C4—861no—
175C22⋊C4C4×D4311yescharacteristic
176C42—861no—
177C42—1721no—
178C23—431no—
179C23C2×C4×D4311yescharacteristic
180C23D4×D4311yescharacteristic
181Q8—1721no—
182Q8—1721no—
183Q8—1721no—
184Q8—1722no—
185D4—41no—
186D4—1721no—
187D4—1721no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—431no—
193C2×C4—431no—
194C2×C4—431no—
195C2×C4—861no—
196C2×C4—861no—
197C2×C4—861no—
198C2×C4—861no—
199C2×C4—861no—
200C2×C4—861no—
201C2×C4—861no—
202C2×C4—861no—
203C2×C4—1721no—
204C2×C4—1721no—
205C2×C4D4×D4311yescharacteristic
206C8—41no—
207C8—1721no—
208C22—21no—
209C22—21no—
210C22—41no—
211C22—41no—
212C22—861no—
213C22—1721no—
214C22C22⋊C4×D4311yescharacteristic
215C4—21no—
216C4—41no—
217C4—41no—
218C4—81no—
219C4—431no—
220C4—431no—
221C4—861no—
222C4—861no—
223C4—3441no—
224C4—1721no—
225C4—1721no—
226C2—21no—
227C2—41no—
228C2—41no—
229C2—1721no—
230C2#99×D4311yescharacteristic
subgroupG/H
centerC2#99×D43
commutatorC23×C43C22×C4
FrattiniC2×D4C22×D43
FittingC43×#352C2
socleC2×C43C2×#99
hypercenter#352D43
hypocenterC43#2123
LCSG ▷ C23×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #352

Complements

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

NH ≅ G/Ntype
4. #14582690C2semidirect
5. #14582689C2semidirect
6. #14582688C2semidirect
7. C43×#352C2semidirect
9. C22×Dic86C4semidirect
13. #13063309C4semidirect
14. #13063308C4semidirect
19. #13063281C4semidirect
122. #352D43semidirect
123. C43#2123semidirect