Finite Group Databasebeta

← #19135578

Subgroups — #19135578

Order 5504.

324 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 85 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
1C2×#13063302C211yesmaximal, characteristic
2#14582757C211yesmaximal, characteristic
3C22⋊C4×Dic43C211yesmaximal, characteristic
4#14582666C211yesmaximal, characteristic
5#14582665C211yesmaximal, characteristic
6#14582665C211yesmaximal, characteristic
7C43×#342C211yesmaximal, characteristic
8C22×Dic86C411yescharacteristic, complemented
9C23×Dic43C2211yescharacteristic
10#13063302—21no—
11#13063302—21no—
12#13063302—21no—
13#13063302—21no—
14C2×C4⋊Dic43C411yescharacteristic, complemented
15C2×Dic43⋊C4—21no—
16C2×Dic43⋊C4C411yescharacteristic, complemented
17C2×Dic43⋊C4C411yescharacteristic, complemented
18C2×C22⋊Dic43C2211yescharacteristic
19C2×C22⋊Dic43C2211yescharacteristic
20C2×C22⋊Dic43C2211yescharacteristic
21C2×C4×Dic43—21no—
22C43⋊#95—21no—
23C43⋊#95—21no—
24C2×C22⋊C4×C43C2211yescharacteristic
25C2×C22⋊C4×C43C2211yescharacteristic
26C2×C22⋊C4×C43C2211yescharacteristic
27C24×C43C2311yescharacteristic
28C22×C4×C43—21no—
29C22×C4×C43—21no—
30C22×C4×C43C2×C411yescharacteristic
31C22×C4×C43C2×C411yescharacteristic
32C22×Dic43—21no—
33C22×Dic43—21no—
34C22×Dic43—42no—
35C22×Dic43C2×C411yescharacteristic
36C22×Dic43C2×C411yescharacteristic
37C22×Dic43C2×C411yescharacteristic
38C22×Dic43C2×C411yescharacteristic
39C22×Dic43D411yescharacteristic
40C22×Dic43D411yescharacteristic
41C22×Dic43D411yescharacteristic
42C22×Dic43D411yescharacteristic
43C2×Dic86—21no—
44C2×Dic86—21no—
45C2×Dic86—42no—
46C22⋊C4×C43—21no—
47C22⋊C4×C43—21no—
48C22⋊C4×C43—21no—
49C22⋊C4×C43—21no—
50C22⋊C4×C43—21no—
51C22⋊C4×C43Q812yescomplemented
52C22⋊Dic43—21no—
53C22⋊Dic43—21no—
54C22⋊Dic43—21no—
55C22⋊Dic43—21no—
56C22⋊Dic43—21no—
57C22⋊Dic43Q812yescomplemented
58C4⋊Dic43—21no—
59C4⋊Dic43—21no—
60Dic43⋊C4—21no—
61Dic43⋊C4—21no—
62Dic43⋊C4—21no—
63Dic43⋊C4—21no—
64Dic43⋊C4—42no—
65C4×Dic43—42no—
66C23×C43—41no—
67C23×C43—41no—
68C23×C43C22×C411yescharacteristic
69C23×C43C2×D411yescharacteristic
70C23×C43C2×D411yescharacteristic
71C23×C43C2×Q811yescharacteristic
72C23×C43C2×Q811yescharacteristic
73C23×C43#4111yescharacteristic
74C23×C43#4111yescharacteristic
75C2×C4×C43—21no—
76C2×C4×C43—21no—
77C2×C4×C43—22no—
78C2×C4×C43—41no—
79C2×C4×C43—41no—
80C2×C4×C43—41no—
81C2×C4×C43—41no—
82C2×C4×C43—41no—
83C2×C4×C43—41no—
84C2×C4×C43—41no—
85C2×Dic43—22no—
86C2×Dic43—22no—
87C2×Dic43—22no—
88C2×Dic43—21no—
89C2×Dic43—21no—
90C2×Dic43—22no—
91C2×Dic43—41no—
92C2×Dic43—41no—
93C2×Dic43—41no—
94C2×Dic43—41no—
95C2×Dic43—41no—
96C2×Dic43—41no—
97C2×Dic43—41no—
98C2×Dic43—41no—
99C2×Dic43—41no—
100C2×Dic43—41no—
101C2×Dic43C22⋊C411yescharacteristic
102C2×Dic43C22⋊C411yescharacteristic
103C2×Dic43C22⋊C411yescharacteristic
104C2×Dic43C22⋊C411yescharacteristic
105Dic86—42no—
106Dic86—42no—
107C22×C43—21no—
108C22×C43—21no—
109C22×C43—21no—
110C22×C43—21no—
111C22×C43—21no—
112C22×C43—21no—
113C22×C43—41no—
114C22×C43—41no—
115C22×C43—41no—
116C22×C43—41no—
117C22×C43C2×C22⋊C411yescharacteristic
118C22×C43C4×Q811yescharacteristic
119C22×C43C4×Q811yescharacteristic
120C22×C43C22⋊Q811yescharacteristic
121C22×C43C22⋊Q811yescharacteristic
122C22×C43#12411yescharacteristic
123C22×C43C4⋊Q811yescharacteristic
124C4×C43—42no—
125C4×C43—41no—
126C4×C43—41no—
127C4×C43—81no—
128Dic43—21no—
129Dic43—21no—
130Dic43—21no—
131Dic43—42no—
132Dic43—41no—
133Dic43—41no—
134Dic43—81no—
135Dic43#9912yes—
136#1996—431nomaximal, Sylow
137C2×C43—21no—
138C2×C43—21no—
139C2×C43—21no—
140C2×C43—21no—
141C2×C43—21no—
142C2×C43—21no—
143C2×C43#39111yescharacteristic
144C2×C43C2×#9911yescharacteristic
145C2×C43#41011yescharacteristic
146C2×C22⋊Q8—431no—
147#380—431no—
148C4×C22⋊C4—431no—
149#342—431no—
150#342—431no—
151#342—431no—
152#342D4311yescharacteristic
153C43#199611yescharacteristic, complemented, Sylow
154C22×Q8—431no—
155C23×C4—431no—
156C22⋊Q8—861no—
157C22⋊Q8—861no—
158C22⋊Q8—861no—
159C22⋊Q8—861no—
160C2×C4⋊C4—431no—
161C2×C4⋊C4—431no—
162C2×C4⋊C4—431no—
163C2×C4⋊C4—861no—
164C2×C22⋊C4—431no—
165C2×C22⋊C4—431no—
166C2×C22⋊C4—431no—
167C2×C22⋊C4C2×D4311yescharacteristic
168C2×C22⋊C4C2×D4311yescharacteristic
169C2×C22⋊C4C2×D4311yescharacteristic
170C2×C42—861no—
171#95—861no—
172#95—861no—
173C24C22×D4311yescharacteristic
174C2×Q8—861no—
175C2×Q8—861no—
176C2×Q8—1722no—
177C22×C4—21no—
178C22×C4—21no—
179C22×C4—431no—
180C22×C4—431no—
181C22×C4—431no—
182C22×C4—431no—
183C22×C4—431no—
184C22×C4—431no—
185C22×C4—431no—
186C22×C4—431no—
187C22×C4—861no—
188C22×C4—861no—
189C22×C4—1722no—
190C22×C4C4×D4311yescharacteristic
191C22×C4C4×D4311yescharacteristic
192C4⋊C4—861no—
193C4⋊C4—861no—
194C4⋊C4—861no—
195C4⋊C4—861no—
196C4⋊C4—861no—
197C4⋊C4—861no—
198C4⋊C4—1722no—
199C22⋊C4—21no—
200C22⋊C4—21no—
201C22⋊C4—21no—
202C22⋊C4—21no—
203C22⋊C4—21no—
204C22⋊C4—432no—
205C22⋊C4—861no—
206C22⋊C4—861no—
207C22⋊C4—861no—
208C22⋊C4—861no—
209C22⋊C4—861no—
210C22⋊C4Dic8612yescomplemented
211C42—1722no—
212C23—41no—
213C23—41no—
214C23C2×Dic8611yescharacteristic
215C23C2×C4×D4311yescharacteristic
216C23#1062189811yescharacteristic
217C23D4×D4311yescharacteristic
218C23D4×D4311yescharacteristic
219C23#1062190011yescharacteristic
220C23Q8×D4311yescharacteristic
221Q8—1722no—
222Q8—1722no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—431no—
234C2×C4—431no—
235C2×C4—431no—
236C2×C4—431no—
237C2×C4—862no—
238C2×C4—862no—
239C2×C4—862no—
240C2×C4—861no—
241C2×C4—861no—
242C2×C4—862no—
243C2×C4—1721no—
244C2×C4—1721no—
245C2×C4—1721no—
246C2×C4—1721no—
247C2×C4—1721no—
248C2×C4—1721no—
249C2×C4—1721no—
250C2×C4—1721no—
251C2×C4—1721no—
252C2×C4—1721no—
253C22—21no—
254C22—21no—
255C22—21no—
256C22—21no—
257C22—21no—
258C22—21no—
259C22—41no—
260C22—41no—
261C22—41no—
262C22—41no—
263C22C22⋊C4×D4311yescharacteristic
264C22#1306329011yescharacteristic
265C22C4×Dic8611yescharacteristic
266C22#1306330211yescharacteristic
267C22#1306330311yescharacteristic
268C22#1306331111yescharacteristic
269C22#1306332411yescharacteristic
270C4—42no—
271C4—41no—
272C4—41no—
273C4—81no—
274C4—432no—
275C4—861no—
276C4—861no—
277C4—861no—
278C4—3441no—
279C4—1722no—
280C4—1721no—
281C4—1721no—
282C2—21no—
283C2—21no—
284C2—21no—
285C2—21no—
286C2—21no—
287C2—21no—
288C2#1458280311yescharacteristic
289C2#99×D4311yescharacteristic
290C2#1458287111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D43
commutatorC23×C43C22×C4
FrattiniC24C22×D43
FittingC43×#342C2
socleC22×C43C2×C22⋊C4
hypercenter#342D43
hypocenterC43#1996
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
8. C22×Dic86C4semidirect
14. C2×C4⋊Dic43C4semidirect
16. C2×Dic43⋊C4C4semidirect
17. C2×Dic43⋊C4C4semidirect
51. C22⋊C4×C43Q8semidirect
57. C22⋊Dic43Q8semidirect
153. C43#1996semidirect
210. C22⋊C4Dic86semidirect