Finite Group Databasebeta

← #19133165

Subgroups — #19133165

Order 5504.

288 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 71 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
2C22⋊C8×D43C211yesmaximal, characteristic
3#14582758C211yesmaximal, 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×C8×D43—21no—
11#13063305C411yescharacteristic, complemented
12#13063304C2211yescharacteristic
13#13063303—21no—
14#13063302—21no—
15#13063301C411yescharacteristic, complemented
16C2×Dic43⋊C4—21no—
17C4⋊C4×D43—21no—
18C4⋊C4×D43C411yescharacteristic, complemented
19C2×(C2×D43)⋊C4—21no—
20C22⋊C4×D43—21no—
21C22⋊(C43⋊C8)C2211yescharacteristic
22(C2×D43)⋊C8—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—
56Dic43⋊C4—42no—
57C2×C43⋊C8—21no—
58C8×D43—42no—
59C23×C43C2×D411yescharacteristic
60C22×D43—41no—
61C22×D43—41no—
62C22×D43C22⋊C411yescharacteristic
63C22×D43C22⋊C411yescharacteristic
64C22×D43SD1612yes—
65C22×D43Q1612yes—
66Q8×C43—41no—
67C2×C4×C43—21no—
68C2×C4×C43—21no—
69C2×C4×C43—41no—
70C2×C4×C43—41no—
71C2×C4×C43—41no—
72C2×C4×C43—41no—
73C2×C4×C43C22×C411yescharacteristic
74C2×C4×C43C2×D411yescharacteristic
75C2×Dic43—22no—
76C2×Dic43—21no—
77C2×Dic43—21no—
78C2×Dic43—41no—
79C2×Dic43—41no—
80C2×Dic43—41no—
81C2×Dic43C22⋊C411yescharacteristic
82C2×Dic43C22⋊C411yescharacteristic
83C4×D43—22no—
84C4×D43—22no—
85C4×D43—41no—
86C4×D43—41no—
87C4×D43—42no—
88C4×D43—42no—
89Dic86—42no—
90Dic86—41no—
91C8×C43—41no—
92C43⋊C8—41no—
93C22×C43—21no—
94C22×C43—21no—
95C22×C43C2×C22⋊C411yescharacteristic
96C22×C43C2×SD1611yescharacteristic
97C22×C43C2×Q1611yescharacteristic
98C2×D43—21no—
99C2×D43—21no—
100C2×D43—21no—
101C2×D43—21no—
102C2×D43—42no—
103C2×D43—42no—
104C2×D43#10312yes—
105C2×D43#10312yes—
106C4×C43—21no—
107C4×C43—21no—
108C4×C43—41no—
109C4×C43—41no—
110C4×C43—81no—
111Dic43—21no—
112Dic43—41no—
113Dic43—41no—
114Dic43—81no—
115Dic43#9912yes—
116#1520—431nomaximal, Sylow
117C2×C43—21no—
118C2×C43—21no—
119C2×C43C2×#9911yescharacteristic
120C2×C43C2×#10311yescharacteristic
121C2×C43#42111yescharacteristic
122D43—22no—
123D43—22no—
124C2×C22⋊Q8—431no—
125C2×C22⋊C8—431no—
126#380—431no—
127#328—431no—
128#328—431no—
129#328—431no—
130#328D4311yescharacteristic, complemented
131C43#152011yescharacteristic, complemented, Sylow
132C22×Q8—431no—
133C23×C4—431no—
134C22×C8—861no—
135C22⋊Q8—431no—
136C22⋊Q8—431no—
137C22⋊Q8—431no—
138C22⋊Q8—861no—
139C22⋊Q8—861no—
140C22⋊Q8C2×D4311yescharacteristic
141C2×C4⋊C4—431no—
142C2×C4⋊C4—861no—
143C2×C4⋊C4—861no—
144C2×C22⋊C4—861no—
145C2×C22⋊C4—861no—
146C22⋊C8—431no—
147C22⋊C8—861no—
148C22⋊C8C2×D4311yescharacteristic
149#95—431no—
150#95C2×D4311yescharacteristic
151C24—431no—
152C2×Q8—431no—
153C2×Q8—861no—
154C2×Q8—1722no—
155C2×Q8C4×D4311yescharacteristic
156C22×C4—21no—
157C22×C4—431no—
158C22×C4—431no—
159C22×C4—431no—
160C22×C4—431no—
161C22×C4—431no—
162C22×C4—861no—
163C22×C4—861no—
164C22×C4—861no—
165C22×C4—1722no—
166C22×C4C22×D4311yescharacteristic
167C2×C8—21no—
168C2×C8—861no—
169C2×C8—1722no—
170C4⋊C4—21no—
171C4⋊C4—431no—
172C4⋊C4—861no—
173C4⋊C4—861no—
174C4⋊C4—861no—
175C4⋊C4—861no—
176C4⋊C4—1722no—
177C4⋊C4C4×D4311yescharacteristic
178C22⋊C4—21no—
179C22⋊C4—861no—
180C22⋊C4—861no—
181C22⋊C4—861no—
182C22⋊C4—1722no—
183C23—431no—
184C23—431no—
185C23—432no—
186C23—432no—
187C23—1721no—
188C23—1721no—
189C23D4×D4311yescharacteristic
190Q8—41no—
191Q8—1721no—
192Q8—1722no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—431no—
200C2×C4—431no—
201C2×C4—862no—
202C2×C4—862no—
203C2×C4—862no—
204C2×C4—861no—
205C2×C4—861no—
206C2×C4—1721no—
207C2×C4—1721no—
208C2×C4—1722no—
209C2×C4—1722no—
210C2×C4—1721no—
211C2×C4—1721no—
212C2×C4—1721no—
213C2×C4C2×C4×D4311yescharacteristic
214C2×C4D4×D4311yescharacteristic
215C8—41no—
216C8—1721no—
217C22—21no—
218C22—21no—
219C22—432no—
220C22—432no—
221C22—861no—
222C22—861no—
223C22—861no—
224C22—861no—
225C22—1722no—
226C22—1722no—
227C22C22⋊C4×D4311yescharacteristic
228C22SD16×D4311yescharacteristic
229C22Q16×D4311yescharacteristic
230C4—21no—
231C4—21no—
232C4—41no—
233C4—41no—
234C4—81no—
235C4—432no—
236C4—861no—
237C4—3441no—
238C4—1721no—
239C4—1721no—
240C2—21no—
241C2—21no—
242C2—862no—
243C2—862no—
244C2#99×D4311yescharacteristic
245C2#103×D4311yescharacteristic
246C2#1458291411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D43
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#328C2
socleC22×C43C2×C22⋊C4
hypercenter#328D43
hypocenterC43#1520
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
18. C4⋊C4×D43C4semidirect
130. #328D43semidirect
131. C43#1520semidirect