Finite Group Databasebeta

← #19134702

Subgroups — #19134702

Order 5504.

296 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 73 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#14583372C211yesmaximal, characteristic
2C2×#13063239C211yesmaximal, characteristic
3C2×#13063239C211yesmaximal, characteristic
4#14582666C211yesmaximal, characteristic, complemented
5#14582665C211yesmaximal, characteristic, complemented
6#14582665C211yesmaximal, characteristic, complemented
7C43×#342C211yesmaximal, characteristic, complemented
8C22×C22⋊D43C2211yescharacteristic
9C4×C22⋊D43—22no—
10(C22⋊D43)⋊C4—22no—
11#13063281C412yescomplemented
12C2×C22⋊Dic43C2211yescharacteristic
13C2×C22⋊Dic43C2211yescharacteristic
14C2×C22⋊Dic43C2211yescharacteristic
15C22⋊C4×D43C412yescomplemented
16#13063239—22no—
17#13063239—22no—
18C2×C22⋊C4×C43C2211yescharacteristic
19C2×C22⋊C4×C43C2211yescharacteristic
20C2×C22⋊C4×C43C2211yescharacteristic
21C24×C43C2311yescharacteristic
22C23×D43C2×C411yescharacteristic
23C22×C4×C43—21no—
24C22×C4×C43—21no—
25C22×C4×C43—21no—
26C2×C22⋊D43—21no—
27C2×C22⋊D43—21no—
28C2×C22⋊D43—21no—
29C2×C22⋊D43—21no—
30C2×C22⋊D43D412yes—
31C2×C22⋊D43D412yes—
32C22×Dic43—21no—
33C22×Dic43—21no—
34C22×Dic43—21no—
35C22×Dic43C2×C411yescharacteristic
36C2×C4×D43—22no—
37C22⋊C4×C43—21no—
38C22⋊C4×C43—21no—
39C22⋊C4×C43—21no—
40C22⋊C4×C43—21no—
41C22⋊C4×C43—21no—
42C22⋊C4×C43C2×C412yes—
43C22⋊Dic43—21no—
44C22⋊Dic43—21no—
45C22⋊Dic43—21no—
46C22⋊Dic43—21no—
47C22⋊Dic43—21no—
48C22⋊Dic43C2×C412yes—
49(C2×D43)⋊C4—22no—
50Dic43⋊C4—22no—
51C4×Dic43—22no—
52C23×C43—81no—
53C23×C43C22×C411yescharacteristic
54C23×C43C2×D411yescharacteristic
55C23×C43C2×D411yescharacteristic
56C23×C43#4111yescharacteristic
57C23×C43#4111yescharacteristic
58C23×C43#4111yescharacteristic
59C23×C43#4111yescharacteristic
60C22×D43—21no—
61C22×D43—21no—
62C22×D43—81no—
63C22×D43C22⋊C412yes—
64C2×C4×C43—22no—
65C2×C4×C43—41no—
66C2×C4×C43—41no—
67C2×C4×C43—81no—
68C2×C4×C43—81no—
69C2×C4×C43—81no—
70C22⋊D43—22no—
71C22⋊D43—22no—
72C22⋊D43—22no—
73C22⋊D43—22no—
74C2×Dic43—21no—
75C2×Dic43—21no—
76C2×Dic43—22no—
77C2×Dic43—41no—
78C2×Dic43—41no—
79C2×Dic43—81no—
80C2×Dic43—81no—
81C2×Dic43—81no—
82C2×Dic43C22⋊C412yes—
83C4×D43—82no—
84C22×C43—41no—
85C22×C43—41no—
86C22×C43—41no—
87C22×C43—41no—
88C22×C43—41no—
89C22×C43—41no—
90C22×C43—41no—
91C22×C43C2×C22⋊C411yescharacteristic
92C22×C43#11711yescharacteristic
93C22×C43#11711yescharacteristic
94C22×C43#12311yescharacteristic
95C22×C43#12311yescharacteristic
96C22×C43#12311yescharacteristic
97C22×C43#12311yescharacteristic
98C2×D43—22no—
99C2×D43—42no—
100C2×D43—81no—
101C2×D43—81no—
102C4×C43—42no—
103C4×C43—81no—
104C4×C43—81no—
105Dic43—22no—
106Dic43—42no—
107Dic43—81no—
108Dic43—81no—
109#1828—431nomaximal, Sylow
110C2×C43—21no—
111C2×C43—21no—
112C2×C43—21no—
113C2×C43—21no—
114C2×C43—21no—
115C2×C43—21no—
116C2×C43—21no—
117C2×C43#38111yescharacteristic
118D43—42no—
119#518—431no—
120C2×#99—431no—
121C2×#99—431no—
122#342—431no—
123#342—431no—
124#342—431no—
125#342D4311yescharacteristic, complemented
126C43#182811yescharacteristic, complemented, Sylow
127C22×D4—431no—
128C4×D4—862no—
129C4×D4—862no—
130#117—432no—
131C2×C22⋊C4—431no—
132C2×C22⋊C4—432no—
133C2×C22⋊C4—431no—
134C2×C22⋊C4—431no—
135C2×C22⋊C4C2×D4311yescharacteristic
136C2×C22⋊C4C2×D4311yescharacteristic
137C2×C22⋊C4C2×D4311yescharacteristic
138#99—862no—
139#99—862no—
140C24—431no—
141C24C22×D4311yescharacteristic
142C2×D4—432no—
143C2×D4—432no—
144C2×D4—861no—
145C2×D4—861no—
146C2×D4—861no—
147C2×D4—861no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—21no—
151C22×C4—431no—
152C22×C4—862no—
153C22×C4—861no—
154C22×C4—861no—
155C22×C4—861no—
156C4⋊C4—862no—
157C22⋊C4—21no—
158C22⋊C4—21no—
159C22⋊C4—21no—
160C22⋊C4—21no—
161C22⋊C4—21no—
162C22⋊C4—432no—
163C22⋊C4—862no—
164C22⋊C4—861no—
165C22⋊C4—861no—
166C22⋊C4—861no—
167C22⋊C4—861no—
168C22⋊C4—861no—
169C22⋊C4C4×D4312yes—
170C42—862no—
171C23—81no—
172C23—432no—
173C23—861no—
174C23—861no—
175C23—3441no—
176C23C2×C4×D4311yescharacteristic
177C23#1062189811yescharacteristic
178C23#1062189811yescharacteristic
179C23D4×D4311yescharacteristic
180C23D4×D4311yescharacteristic
181C23#1062190011yescharacteristic
182C23#1062190211yescharacteristic
183D4—862no—
184D4—862no—
185D4—862no—
186D4—862no—
187C2×C4—22no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—81no—
191C2×C4—81no—
192C2×C4—81no—
193C2×C4—432no—
194C2×C4—861no—
195C2×C4—861no—
196C2×C4—862no—
197C2×C4—3442no—
198C2×C4—3441no—
199C2×C4—3441no—
200C2×C4—3441no—
201C2×C4—1721no—
202C2×C4—1721no—
203C22—41no—
204C22—41no—
205C22—41no—
206C22—41no—
207C22—41no—
208C22—41no—
209C22—41no—
210C22—862no—
211C22—3441no—
212C22—3441no—
213C22—1722no—
214C22C22⋊C4×D4311yescharacteristic
215C22#1306328211yescharacteristic
216C22#1306328311yescharacteristic
217C22#1306330711yescharacteristic
218C22#1306330711yescharacteristic
219C22#1306331011yescharacteristic
220C22#1306331011yescharacteristic
221C4—42no—
222C4—81no—
223C4—81no—
224C4—862no—
225C4—3441no—
226C4—3441no—
227C4—1722no—
228C2—21no—
229C2—21no—
230C2—21no—
231C2—21no—
232C2—21no—
233C2—21no—
234C2—21no—
235C2—1722no—
236C2#1458276111yescharacteristic
subgroupG/H
centerC2#14582761
commutatorC23×C43C22×C4
FrattiniC24C22×D43
FittingC43×#342C2
socleC2×C43#381
hypercenter#342D43
hypocenterC43#1828
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
4. #14582666C2semidirect
5. #14582665C2semidirect
6. #14582665C2semidirect
7. C43×#342C2semidirect
11. #13063281C4semidirect
15. C22⋊C4×D43C4semidirect
125. #342D43semidirect
126. C43#1828semidirect