Finite Group Databasebeta

← #19133148

Subgroups — #19133148

Order 5504.

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

normal subgroups only

This group has 284 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
1#14583409C211yesmaximal, characteristic
2C22⋊C8×D43C211yesmaximal, characteristic, complemented
3#14582761C211yesmaximal, characteristic, complemented
4#14582637C211yesmaximal, characteristic, complemented
5#14582635C211yesmaximal, characteristic, complemented
6#14582633C211yesmaximal, characteristic, complemented
7C43×#327C211yesmaximal, characteristic, complemented
8C2×#10621900C411yescharacteristic, complemented
9C22×C4×D43C2211yescharacteristic
10C2×C8×D43—21no—
11#13063307—21no—
12#13063305C411yescharacteristic, complemented
13#13063304C2211yescharacteristic
14#13063296C411yescharacteristic, complemented
15#13063293—21no—
16D4×Dic43—21no—
17(C22⋊D43)⋊C4—21no—
18#13063283C411yescharacteristic, complemented
19C2×(C2×D43)⋊C4—21no—
20C22⋊(C43⋊C8)C2211yescharacteristic
21(C2×D43)⋊C8—21no—
22C43⋊#95—21no—
23C43⋊#95C2211yescharacteristic
24#121×C43C2211yescharacteristic
25C22⋊C8×C43C2211yescharacteristic
26#95×C43C2211yescharacteristic
27C23×D43D411yescharacteristic
28C2×D4×C43—21no—
29C2×D4×C43C2×C411yescharacteristic
30C22×C4×C43—21no—
31C22×C4×C43C2311yescharacteristic
32C2×C22⋊D43—21no—
33C2×C22⋊D43—21no—
34C22×Dic43—21no—
35C22×Dic43—21no—
36C22×Dic43D411yescharacteristic
37#10621900—42no—
38C2×C4×D43—42no—
39C2×C4×D43C2×C411yescharacteristic
40C2×C4×D43C2×C411yescharacteristic
41C2×C4×D43D411yescharacteristic
42C2×C4×D43D411yescharacteristic
43C2×Dic86C2×C411yescharacteristic
44C2×C8×C43—21no—
45C4⋊C4×C43C2×C411yescharacteristic
46C22⋊C4×C43—21no—
47C22⋊Dic43—21no—
48C22⋊Dic43—21no—
49(C2×D43)⋊C4—21no—
50(C2×D43)⋊C4—21no—
51(C2×D43)⋊C4—42no—
52C4⋊Dic43—21no—
53C4⋊Dic43C2×C411yescharacteristic
54Dic43⋊C4—21no—
55C4×Dic43—21no—
56C2×C43⋊C8—21no—
57C8×D43—42no—
58C23×C43—21no—
59C23×C43C2×D411yescharacteristic
60C22×D43—21no—
61C22×D43—21no—
62C22×D43—22no—
63C22×D43—41no—
64C22×D43C22⋊C411yescharacteristic
65C22×D43C22⋊C411yescharacteristic
66D4×C43—41no—
67D4×C43—41no—
68D4×C43—41no—
69C2×C4×C43—21no—
70C2×C4×C43—41no—
71C2×C4×C43—41no—
72C2×C4×C43—41no—
73C2×C4×C43—41no—
74C2×C4×C43C22×C411yescharacteristic
75C2×C4×C43C2×D411yescharacteristic
76C22⋊D43—42no—
77C22⋊D43—42no—
78C2×Dic43—21no—
79C2×Dic43—21no—
80C2×Dic43—41no—
81C2×Dic43—42no—
82C2×Dic43—41no—
83C2×Dic43—41no—
84C2×Dic43—41no—
85C2×Dic43C22⋊C411yescharacteristic
86C2×Dic43C22⋊C411yescharacteristic
87C4×D43—22no—
88C4×D43—22no—
89C4×D43—41no—
90C4×D43—41no—
91Dic86—41no—
92C8×C43—41no—
93C43⋊C8—41no—
94C22×C43—21no—
95C22×C43—21no—
96C22×C43—41no—
97C22×C43—41no—
98C22×C43—41no—
99C22×C43C2×C22⋊C411yescharacteristic
100C22×C43#13511yescharacteristic
101C22×C43#13511yescharacteristic
102C2×D43—21no—
103C2×D43—21no—
104C2×D43—21no—
105C2×D43—21no—
106C2×D43—21no—
107C2×D43—42no—
108C2×D43—42no—
109C2×D43#9912yes—
110C4×C43—21no—
111C4×C43—21no—
112C4×C43—41no—
113C4×C43—81no—
114Dic43—21no—
115Dic43—21no—
116Dic43—41no—
117Dic43—41no—
118Dic43—81no—
119#1516—431nomaximal, Sylow
120C2×C43—21no—
121C2×C43—21no—
122C2×C43—81no—
123C2×C43C2×#9911yescharacteristic
124C2×C43#41611yescharacteristic
125C2×C43#42111yescharacteristic
126D43—22no—
127D43—41no—
128#525—431no—
129C2×C22⋊C8—431no—
130#381—431no—
131#328—431no—
132#328—431no—
133#327—431no—
134#327D4311yescharacteristic, complemented
135C43#151611yescharacteristic, complemented, Sylow
136C2×#41—431no—
137C23×C4—431no—
138C22×C8—861no—
139#123—861no—
140C22⋊Q8—431no—
141C22⋊Q8—431no—
142#121—431no—
143#121C2×D4311yescharacteristic
144#120—861no—
145C4×D4—861no—
146C4×D4—861no—
147#117—431no—
148C2×C22⋊C4—861no—
149C22⋊C8—431no—
150C22⋊C8—861no—
151C22⋊C8C2×D4311yescharacteristic
152#95—431no—
153#95—861no—
154#95C2×D4311yescharacteristic
155C24—431no—
156#41—1722no—
157C2×Q8—431no—
158C2×D4—21no—
159C2×D4—861no—
160C2×D4—861no—
161C2×D4C4×D4311yescharacteristic
162C22×C4—21no—
163C22×C4—431no—
164C22×C4—431no—
165C22×C4—431no—
166C22×C4—431no—
167C22×C4—431no—
168C22×C4—861no—
169C22×C4—861no—
170C22×C4—1722no—
171C22×C4C22×D4311yescharacteristic
172C2×C8—21no—
173C2×C8—861no—
174C2×C8—1722no—
175C4⋊C4—431no—
176C4⋊C4—861no—
177C4⋊C4—861no—
178C4⋊C4C4×D4311yescharacteristic
179C22⋊C4—21no—
180C22⋊C4—861no—
181C22⋊C4—861no—
182C22⋊C4—861no—
183C22⋊C4—861no—
184C22⋊C4—1722no—
185C42—861no—
186C23—21no—
187C23—431no—
188C23—431no—
189C23—862no—
190C23—861no—
191C23—861no—
192C23—1721no—
193C23D4×D4311yescharacteristic
194Q8—1721no—
195D4—41no—
196D4—41no—
197D4—41no—
198D4—1722no—
199D4—1722no—
200C2×C4—21no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—431no—
206C2×C4—431no—
207C2×C4—862no—
208C2×C4—862no—
209C2×C4—861no—
210C2×C4—861no—
211C2×C4—1721no—
212C2×C4—1721no—
213C2×C4—1721no—
214C2×C4—1722no—
215C2×C4—1721no—
216C2×C4—1721no—
217C2×C4—1721no—
218C2×C4C2×C4×D4311yescharacteristic
219C2×C4D4×D4311yescharacteristic
220C8—41no—
221C8—1721no—
222C22—21no—
223C22—21no—
224C22—41no—
225C22—41no—
226C22—41no—
227C22—432no—
228C22—861no—
229C22—861no—
230C22—861no—
231C22—861no—
232C22—861no—
233C22—1722no—
234C22—1722no—
235C22C22⋊C4×D4311yescharacteristic
236C22#1306334411yescharacteristic
237C22#1306334611yescharacteristic
238C4—21no—
239C4—21no—
240C4—41no—
241C4—81no—
242C4—861no—
243C4—861no—
244C4—3441no—
245C4—1721no—
246C4—1721no—
247C2—21no—
248C2—21no—
249C2—81no—
250C2—862no—
251C2—1721no—
252C2#99×D4311yescharacteristic
253C2#1458289211yescharacteristic
254C2#1458291411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D43
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#327C2
socleC22×C43C2×C22⋊C4
hypercenter#327D43
hypocenterC43#1516
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. C22⋊C8×D43C2semidirect
3. #14582761C2semidirect
4. #14582637C2semidirect
5. #14582635C2semidirect
6. #14582633C2semidirect
7. C43×#327C2semidirect
8. C2×#10621900C4semidirect
12. #13063305C4semidirect
14. #13063296C4semidirect
18. #13063283C4semidirect
134. #327D43semidirect
135. C43#1516semidirect