Finite Group Databasebeta

← #19133126

Subgroups — #19133126

Order 5504.

274 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 63 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
1C22⋊Q8×D43C211yesmaximal, characteristic
2#14582861C211yesmaximal, characteristic
3#14582761C211yesmaximal, characteristic
4#14582637C211yesmaximal, characteristic, complemented
5#14582636C211yesmaximal, characteristic, complemented
6#14582635C211yesmaximal, characteristic, complemented
7C43×#328C211yesmaximal, characteristic, complemented
8C2×Q8×D43C411yescharacteristic, complemented
9C22×C4×D43C2211yescharacteristic
10C2×#10621872—21no—
11#13063305C411yescharacteristic, complemented
12#13063304C2211yescharacteristic
13#13063303—21no—
14#13063302—21no—
15#13063301C411yescharacteristic, complemented
16C4⋊C4×D43—21no—
17C4⋊C4×D43C411yescharacteristic, complemented
18C2×(C2×D43)⋊C4—21no—
19C22⋊C4×D43—21no—
20C22⋊(C43⋊C8)C2211yescharacteristic
21(C2×D43)⋊C8—21no—
22C43⋊#95—21no—
23C43⋊#95C2211yescharacteristic
24C22⋊Q8×C43C2211yescharacteristic
25C22⋊C8×C43C2211yescharacteristic
26#95×C43C2211yescharacteristic
27C23×D43D411yescharacteristic
28C2×Q8×C43C2×C411yescharacteristic
29C22×C4×C43—21no—
30C22×C4×C43C2311yescharacteristic
31C22×Dic43—21no—
32C22×Dic43D411yescharacteristic
33Q8×D43—42no—
34C2×C4×D43—21no—
35C2×C4×D43—21no—
36C2×C4×D43—42no—
37C2×C4×D43C2×C411yescharacteristic
38C2×C4×D43C2×C411yescharacteristic
39C2×C4×D43D411yescharacteristic
40C2×C4×D43D411yescharacteristic
41C2×Dic86—21no—
42C2×Dic86C2×C411yescharacteristic
43C2×C8×C43—21no—
44C4⋊C4×C43—21no—
45C4⋊C4×C43C2×C411yescharacteristic
46C22⋊C4×C43—21no—
47C22⋊Dic43—21no—
48(C2×D43)⋊C4—21no—
49(C2×D43)⋊C4—21no—
50(C2×D43)⋊C4—42no—
51C4⋊Dic43—21no—
52C4⋊Dic43C2×C411yescharacteristic
53Dic43⋊C4—21no—
54Dic43⋊C4—21no—
55Dic43⋊C4—21no—
56C2×C43⋊C8—21no—
57#10621872—42no—
58C23×C43C2×D411yescharacteristic
59C22×D43—21no—
60C22×D43—21no—
61C22×D43—22no—
62C22×D43—41no—
63C22×D43C22⋊C411yescharacteristic
64C22×D43C22⋊C411yescharacteristic
65Q8×C43—41no—
66C2×C4×C43—21no—
67C2×C4×C43—21no—
68C2×C4×C43—41no—
69C2×C4×C43—41no—
70C2×C4×C43—41no—
71C2×C4×C43—41no—
72C2×C4×C43C22×C411yescharacteristic
73C2×C4×C43C2×D411yescharacteristic
74C2×Dic43—21no—
75C2×Dic43—21no—
76C2×Dic43—41no—
77C2×Dic43—41no—
78C2×Dic43—41no—
79C2×Dic43—41no—
80C2×Dic43C22⋊C411yescharacteristic
81C2×Dic43C22⋊C411yescharacteristic
82C4×D43—22no—
83C4×D43—22no—
84C4×D43—41no—
85C4×D43—41no—
86C4×D43—42no—
87C4×D43—42no—
88Dic86—42no—
89Dic86—41no—
90C8×C43—41no—
91C43⋊C8—41no—
92C22×C43—21no—
93C22×C43—21no—
94C22×C43C2×C22⋊C411yescharacteristic
95C22×C43#13711yescharacteristic
96C22×C43#13711yescharacteristic
97C2×D43—21no—
98C2×D43—21no—
99C2×D43—21no—
100C2×D43—21no—
101C2×D43—21no—
102C2×D43—42no—
103C2×D43—42no—
104C2×D43#9912yes—
105C4×C43—21no—
106C4×C43—21no—
107C4×C43—41no—
108C4×C43—41no—
109C4×C43—81no—
110Dic43—21no—
111Dic43—21no—
112Dic43—41no—
113Dic43—41no—
114Dic43—81no—
115#1511—431nomaximal, Sylow
116C2×C43—21no—
117C2×C43—21no—
118C2×C43C2×#9911yescharacteristic
119C2×C43#41911yescharacteristic
120C2×C43#42111yescharacteristic
121D43—22no—
122D43—41no—
123C2×C22⋊Q8—431no—
124#407—431no—
125#381—431no—
126#328—431no—
127#328—431no—
128#328—431no—
129#328D4311yescharacteristic, complemented
130C43#151111yescharacteristic, complemented, Sylow
131C22×Q8—431no—
132C23×C4—431no—
133C2×M16—861no—
134C22⋊Q8—431no—
135C22⋊Q8—431no—
136C22⋊Q8—431no—
137C22⋊Q8—861no—
138C22⋊Q8—861no—
139C22⋊Q8C2×D4311yescharacteristic
140C2×C4⋊C4—431no—
141C2×C4⋊C4—861no—
142C2×C22⋊C4—861no—
143C2×C22⋊C4—861no—
144C22⋊C8—431no—
145C22⋊C8—861no—
146C22⋊C8C2×D4311yescharacteristic
147#95—431no—
148#95—861no—
149#95C2×D4311yescharacteristic
150C24—431no—
151C2×Q8—431no—
152C2×Q8—861no—
153C2×Q8—1722no—
154C2×Q8C4×D4311yescharacteristic
155C22×C4—21no—
156C22×C4—431no—
157C22×C4—431no—
158C22×C4—431no—
159C22×C4—431no—
160C22×C4—431no—
161C22×C4—861no—
162C22×C4—861no—
163C22×C4—861no—
164C22×C4—1722no—
165C22×C4C22×D4311yescharacteristic
166M16—1722no—
167C2×C8—21no—
168C2×C8—861no—
169C4⋊C4—21no—
170C4⋊C4—431no—
171C4⋊C4—861no—
172C4⋊C4—861no—
173C4⋊C4—861no—
174C4⋊C4—861no—
175C4⋊C4C4×D4311yescharacteristic
176C22⋊C4—21no—
177C22⋊C4—861no—
178C22⋊C4—861no—
179C22⋊C4—861no—
180C22⋊C4—1722no—
181C23—431no—
182C23—431no—
183C23—862no—
184C23—861no—
185C23—861no—
186C23—1721no—
187C23D4×D4311yescharacteristic
188Q8—41no—
189Q8—1721no—
190Q8—1722no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—431no—
198C2×C4—431no—
199C2×C4—862no—
200C2×C4—862no—
201C2×C4—861no—
202C2×C4—861no—
203C2×C4—1721no—
204C2×C4—1721no—
205C2×C4—1722no—
206C2×C4—1722no—
207C2×C4—1721no—
208C2×C4—1721no—
209C2×C4—1721no—
210C2×C4—1721no—
211C2×C4C2×C4×D4311yescharacteristic
212C2×C4D4×D4311yescharacteristic
213C8—41no—
214C8—1721no—
215C22—21no—
216C22—21no—
217C22—432no—
218C22—861no—
219C22—861no—
220C22—861no—
221C22—861no—
222C22—861no—
223C22—1722no—
224C22—1722no—
225C22C22⋊C4×D4311yescharacteristic
226C22#1306335411yescharacteristic
227C22#1306335711yescharacteristic
228C4—21no—
229C4—21no—
230C4—41no—
231C4—41no—
232C4—81no—
233C4—861no—
234C4—861no—
235C4—3441no—
236C4—1721no—
237C4—1721no—
238C2—21no—
239C2—21no—
240C2—862no—
241C2—1721no—
242C2#99×D4311yescharacteristic
243C2#1458290611yescharacteristic
244C2#1458291411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D43
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#328C2
socleC22×C43C2×C22⋊C4
hypercenter#328D43
hypocenterC43#1511
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
4. #14582637C2semidirect
5. #14582636C2semidirect
6. #14582635C2semidirect
7. C43×#328C2semidirect
8. C2×Q8×D43C4semidirect
11. #13063305C4semidirect
15. #13063301C4semidirect
17. C4⋊C4×D43C4semidirect
129. #328D43semidirect
130. C43#1511semidirect