Finite Group Databasebeta

← #19136609

Subgroups — #19136609

Order 5504.

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#14583652C211yesmaximal, characteristic, complemented
2#14583090C211yesmaximal, characteristic
3#14583088C211yesmaximal, characteristic
4#14583079C211yesmaximal, characteristic
5#14582693C211yesmaximal, characteristic, complemented
6#14582690C211yesmaximal, characteristic, complemented
7C43×#352C211yesmaximal, characteristic, complemented
8#13063370C2211yescharacteristic
9#13063358—21no—
10#13063324—21no—
11#13063318—21no—
12#13063318—21no—
13#13063315—21no—
14#13063312C2211yescharacteristic
15#13063309—21no—
16#13063308—21no—
17#13063306C2211yescharacteristic
18#13063304—21no—
19#13063302—21no—
20#13063251—21no—
21#13063240C2211yescharacteristic
22#13063239—21no—
23#13063239—21no—
24#123×C43C2211yescharacteristic
25#100×C43C2211yescharacteristic
26#99×C43C2211yescharacteristic
27C2×D4×C43C2311yescharacteristic
28C22×C4×C43D411yescharacteristic
29C2×C22⋊D43—21no—
30C2×C22⋊D43—21no—
31C22×Dic43D411yescharacteristic
32#10621900—41no—
33D4×D43—41no—
34#10621898—21no—
35C2×Dic86—21no—
36C2×Dic86D411yescharacteristic
37M16×C43—21no—
38C4⋊C4×C43—21no—
39C22⋊C4×C43—21no—
40C22⋊C4×C43—21no—
41C22⋊C4×C43D411yescharacteristic
42C22⋊Dic43—21no—
43C22⋊Dic43—21no—
44C22⋊Dic43—21no—
45C22⋊Dic43—21no—
46C22⋊Dic43D411yescharacteristic
47(C2×D43)⋊C4—41no—
48(C2×D43)⋊C4—41no—
49C4⋊Dic43—21no—
50C4⋊Dic43—21no—
51C4⋊Dic43—41no—
52Dic43⋊C4—21no—
53Dic43⋊C4—21no—
54Dic43⋊C4—21no—
55Dic43⋊C4—21no—
56Dic43⋊C4—21no—
57Dic43⋊C4—41no—
58C4×Dic43—21no—
59C4×Dic43D411yescharacteristic
60Dic172—41no—
61#10621873—41no—
62C23×C43C2×D411yescharacteristic
63C23×C43C2×D411yescharacteristic
64C22×D43—21no—
65C22×D43—21no—
66D4×C43—41no—
67C2×C4×C43—21no—
68C2×C4×C43—21no—
69C2×C4×C43—41no—
70C2×C4×C43—41no—
71C2×C4×C43C2×D411yescharacteristic
72C22⋊D43—41no—
73C22⋊D43—41no—
74C22⋊D43—41no—
75C2×Dic43—21no—
76C2×Dic43—21no—
77C2×Dic43—21no—
78C2×Dic43—21no—
79C2×Dic43—21no—
80C2×Dic43—21no—
81C2×Dic43—41no—
82C2×Dic43—41no—
83D172—21no—
84C4×D43—41no—
85Dic86—21no—
86Dic86—41no—
87Dic86—81no—
88C8×C43—41no—
89C22×C43—21no—
90C22×C43—21no—
91C22×C43—41no—
92C22×C43—41no—
93C22×C43#12011yescharacteristic
94C2×D43—41no—
95C2×D43—81no—
96C2×D43—81no—
97C4×C43—21no—
98C4×C43—41no—
99C4×C43—41no—
100C4×C43—81no—
101Dic43—41no—
102Dic43—41no—
103Dic43—41no—
104Dic43—41no—
105Dic43—41no—
106Dic43—81no—
107#2201—431nomaximal, Sylow
108C2×C43—21no—
109C2×C43—41no—
110C2×C43—41no—
111C2×C43B(4,𝔽2)11yescharacteristic
112D43—81no—
113#563—431no—
114#458—431no—
115#458—431no—
116#455—431no—
117#354—431no—
118#352—431no—
119#352D4311yescharacteristic, complemented
120C43#220111yescharacteristic, complemented, Sylow
121H(5,𝔽2)—431no—
122#137—861no—
123C4⋊Q8—861no—
124#126—861no—
125#126—861no—
126#125—861no—
127#124—431no—
128#123—431no—
129#123—861no—
130#123—861no—
131#123C2×D4311yescharacteristic
132C22⋊Q8—861no—
133C22⋊Q8—861no—
134#104—861no—
135#100C2×D4311yescharacteristic
136#99—431no—
137#99—861no—
138#99—861no—
139#99C2×D4311yescharacteristic
140#41—861no—
141#41—1721no—
142C2×Q8—431no—
143C2×Q8—861no—
144C2×D4—861no—
145C2×D4—861no—
146C2×D4—1721no—
147C2×D4C22×D4311yescharacteristic
148C22×C4—431no—
149C22×C4D17211yescharacteristic
150Q16—1721no—
151SD16—1721no—
152M16—21no—
153C4⋊C4—21no—
154C4⋊C4—861no—
155C4⋊C4—861no—
156C4⋊C4—861no—
157C4⋊C4—861no—
158C4⋊C4—861no—
159C4⋊C4—861no—
160C4⋊C4—861no—
161C4⋊C4—1721no—
162C4⋊C4—1721no—
163C22⋊C4—21no—
164C22⋊C4—21no—
165C22⋊C4—431no—
166C22⋊C4—861no—
167C22⋊C4—861no—
168C22⋊C4—861no—
169C22⋊C4—861no—
170C22⋊C4—1721no—
171C22⋊C4—1721no—
172C22⋊C4D17211yescharacteristic
173C42—431no—
174C42—861no—
175C23—861no—
176C23—861no—
177C23C2×D17211yescharacteristic
178C23D4×D4311yescharacteristic
179Q8—861no—
180Q8—3441no—
181Q8—1721no—
182D4—41no—
183D4—861no—
184D4—1721no—
185D4—1721no—
186D4—1721no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—861no—
192C2×C4—861no—
193C2×C4—861no—
194C2×C4—861no—
195C2×C4—861no—
196C2×C4—861no—
197C2×C4—1721no—
198C2×C4—1721no—
199C2×C4—1721no—
200C2×C4D4×D4311yescharacteristic
201C8—41no—
202C22—21no—
203C22—21no—
204C22—41no—
205C22—41no—
206C22—3441no—
207C22—3441no—
208C22—1721no—
209C22#1306329511yescharacteristic
210C4—21no—
211C4—41no—
212C4—41no—
213C4—81no—
214C4—3441no—
215C4—1721no—
216C4—1721no—
217C4—1721no—
218C4—1721no—
219C4—1721no—
220C2—21no—
221C2—41no—
222C2—41no—
223C2—3441no—
224C2#1458308711yescharacteristic
subgroupG/H
centerC2#14583087
commutatorC2×D4×C43C23
FrattiniC2×D4C22×D43
FittingC43×#352C2
socleC2×C43B(4,𝔽2)
hypercenter#352D43
hypocenterC43#2201
LCSG ▷ C2×D4×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
1. #14583652C2semidirect
5. #14582693C2semidirect
6. #14582690C2semidirect
7. C43×#352C2semidirect
119. #352D43semidirect
120. C43#2201semidirect