Finite Group Databasebeta

← #19147356

Subgroups — #19147356

Order 5504.

344 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583635C211yesmaximal, characteristic
2#14583625C211yesmaximal, characteristic, complemented
3#14583263C211yesmaximal, characteristic
4#14583257C211yesmaximal, characteristic, complemented
5#14583252C211yesmaximal, characteristic, complemented
6#14583207C211yesmaximal, characteristic, complemented
7#14583197C211yesmaximal, characteristic, complemented
8#14583187C211yesmaximal, characteristic, complemented
9#14583119C211yesmaximal, characteristic, complemented
10#14583119C211yesmaximal, characteristic, complemented
11#14583028C211yesmaximal, characteristic, complemented
12#14583004C211yesmaximal, characteristic, complemented
13#14583000C211yesmaximal, characteristic, complemented
14SD16×Dic43C211yesmaximal, characteristic, complemented
15C43×#460C211yesmaximal, characteristic
16C2×#10621885C2211yescharacteristic
17#13063324—21no—
18#13063324C2211yescharacteristic
19#13063317—21no—
20#13063317C2211yescharacteristic
21#13063316—21no—
22#13063316C2211yescharacteristic
23#13063312—21no—
24#13063312C2211yescharacteristic
25#13063312C2211yescharacteristic
26#13063306—21no—
27#13063306—21no—
28Q8×Dic43C2211yescharacteristic
29Q8×Dic43C2211yescharacteristic
30C4×Dic86—21no—
31C4×Dic86C2211yescharacteristic
32C4×Dic86C2211yescharacteristic
33D4×Dic43—21no—
34D4×Dic43C2211yescharacteristic
35D4×Dic43C2211yescharacteristic
36#13063259C2211yescharacteristic
37#13063257C2211yescharacteristic
38#13063256C2211yescharacteristic
39Dic43⋊C8C2211yescharacteristic
40Dic43⋊C8C2211yescharacteristic
41#13063250C2211yescharacteristic
42#13063250C2211yescharacteristic
43#13063249C2211yescharacteristic
44#13063248C2211yescharacteristic
45#13063246C2211yescharacteristic
46#13063246C2211yescharacteristic
47#13063246C2211yescharacteristic
48#13063246C2211yescharacteristic
49#13063236C2211yescharacteristic
50#13063235C2211yescharacteristic
51C8×Dic43C2211yescharacteristic
52C2×SD16×C43C2211yescharacteristic
53C2×SD16×C43C2211yescharacteristic
54#127×C43C2211yescharacteristic
55C4×Q8×C43C2211yescharacteristic
56C4⋊C8×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58#102×C43C2211yescharacteristic
59C2×Q8×C43C2311yescharacteristic
60C2×D4×C43—21no—
61C2×D4×C43—21no—
62C2×D4×C43C2311yescharacteristic
63C2×D4×C43C2311yescharacteristic
64C22×Dic43—21no—
65C22×Dic43—21no—
66C2×Dic86—21no—
67C2×Dic86D411yescharacteristic
68C2×Dic86C2311yescharacteristic
69SD16×C43—22no—
70SD16×C43—22no—
71C2×C8×C43C2311yescharacteristic
72C2×C8×C43C2311yescharacteristic
73C4⋊C4×C43—21no—
74C4⋊C4×C43C2311yescharacteristic
75C42×C43—21no—
76C42×C43C2311yescharacteristic
77C22⋊Dic43—21no—
78C22⋊Dic43—21no—
79C22⋊Dic43—21no—
80C22⋊Dic43—21no—
81C22⋊Dic43—21no—
82C22⋊Dic43—21no—
83#10621885—22no—
84C4⋊Dic43—21no—
85C4⋊Dic43—21no—
86C4⋊Dic43—21no—
87C4⋊Dic43D411yescharacteristic
88C4⋊Dic43C2311yescharacteristic
89C4⋊Dic43C2311yescharacteristic
90C4⋊Dic43C2311yescharacteristic
91Dic43⋊C4—21no—
92Dic43⋊C4—21no—
93Dic43⋊C4—21no—
94Dic43⋊C4—21no—
95Dic43⋊C4—21no—
96Dic43⋊C4D411yescharacteristic
97Dic43⋊C4D411yescharacteristic
98C4×Dic43—21no—
99C4×Dic43—21no—
100C4×Dic43—21no—
101C4×Dic43C2311yescharacteristic
102C4×Dic43C2311yescharacteristic
103C2×C43⋊C8C2311yescharacteristic
104C2×C43⋊C8C2311yescharacteristic
105C23×C43—21no—
106C23×C43—21no—
107Q8×C43—21no—
108Q8×C43#4112yes—
109D4×C43—21no—
110D4×C43—21no—
111D4×C43—21no—
112D4×C43—21no—
113D4×C43—42no—
114D4×C43—81no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43C2×D411yescharacteristic
118C2×C4×C43C2×D411yescharacteristic
119C2×C4×C43C2411yescharacteristic
120C2×Dic43—21no—
121C2×Dic43—21no—
122C2×Dic43—21no—
123C2×Dic43—21no—
124C2×Dic43—81no—
125C2×Dic43—81no—
126C2×Dic43C2×D411yescharacteristic
127C2×Dic43C2×D411yescharacteristic
128C2×Dic43C2×D411yescharacteristic
129C2×Dic43C2×D411yescharacteristic
130Dic86—21no—
131Dic86—21no—
132Dic86—41no—
133Dic86—42no—
134C8×C43—21no—
135C8×C43—21no—
136C43⋊C8—21no—
137C43⋊C8—21no—
138C22×C43—41no—
139C22×C43—41no—
140C22×C43—41no—
141C22×C43—41no—
142C22×C43—41no—
143C22×C43—41no—
144C22×C43C22×D411yescharacteristic
145C4×C43—22no—
146C4×C43—21no—
147C4×C43—21no—
148C4×C43—41no—
149C4×C43C2×#4111yescharacteristic
150C4×C432−1+411yescharacteristic
151Dic43—21no—
152Dic43—21no—
153Dic43—21no—
154Dic43—21no—
155Dic43—41no—
156Dic43—41no—
157Dic43—41no—
158Dic43—41no—
159#3371—431nomaximal, Sylow
160C2×C43—81no—
161C2×C43—81no—
162C2×C43#54811yescharacteristic
163C2×C43#57511yescharacteristic
164C2×C43#57711yescharacteristic
165#559—431no—
166#557—431no—
167#490—431no—
168#489—431no—
169#488—431no—
170#479—431no—
171#478—431no—
172#476—431no—
173#464—431no—
174#464—431no—
175#460D4311yescharacteristic
176#446—431no—
177#441—431no—
178#440—431no—
179C4×SD16—431no—
180C43#337111yescharacteristic, complemented, Sylow
181C2×Q16—431no—
182C2×SD16C2×D4311yescharacteristic
183C2×SD16C2×D4311yescharacteristic
184C4⋊Q8—431no—
185C4⋊Q8—861no—
186#127C2×D4311yescharacteristic
187#125—431no—
188#125—431no—
189#125—861no—
190#125—861no—
191#124—431no—
192#124—431no—
193#124—861no—
194#123—861no—
195#123—861no—
196C4×Q8—431no—
197C4×Q8—431no—
198C4×Q8—431no—
199C4×Q8—431no—
200C4×Q8—861no—
201C4×Q8C2×D4311yescharacteristic
202C4×D4—431no—
203C4×D4—431no—
204C4×D4—861no—
205#107—431no—
206#106—431no—
207#106—431no—
208C4⋊C8—431no—
209C4⋊C8—431no—
210C4⋊C8C2×D4311yescharacteristic
211#103—431no—
212#103—431no—
213#103—431no—
214#103—431no—
215#102—431no—
216#102—431no—
217#102—431no—
218#102—431no—
219#102C2×D4311yescharacteristic
220#102C2×D4311yescharacteristic
221#97—431no—
222#97—431no—
223C4×C8—431no—
224C2×Q8—431no—
225C2×Q8—431no—
226C2×Q8—861no—
227C2×Q8C22×D4311yescharacteristic
228C2×D4—21no—
229C2×D4—21no—
230C2×D4C22×D4311yescharacteristic
231C2×D4C22×D4311yescharacteristic
232C22×C4—861no—
233C22×C4—861no—
234Q16—862no—
235SD16—22no—
236SD16—22no—
237C2×C8—431no—
238C2×C8—431no—
239C2×C8C22×D4311yescharacteristic
240C2×C8C22×D4311yescharacteristic
241C4⋊C4—21no—
242C4⋊C4—431no—
243C4⋊C4—431no—
244C4⋊C4—431no—
245C4⋊C4—431no—
246C4⋊C4—431no—
247C4⋊C4—431no—
248C4⋊C4—861no—
249C4⋊C4—861no—
250C4⋊C4—861no—
251C4⋊C4—861no—
252C4⋊C4—861no—
253C4⋊C4—861no—
254C4⋊C4—861no—
255C4⋊C4—861no—
256C4⋊C4C22×D4311yescharacteristic
257C22⋊C4—861no—
258C22⋊C4—861no—
259C22⋊C4—861no—
260C22⋊C4—861no—
261C22⋊C4—861no—
262C22⋊C4—861no—
263C42—21no—
264C42—431no—
265C42—431no—
266C42—861no—
267C42—861no—
268C42—861no—
269C42C22×D4311yescharacteristic
270C23—21no—
271C23—21no—
272Q8—21no—
273Q8—861no—
274Q8—861no—
275Q8—1721no—
276Q8—1722no—
277Q8#1062190012yes—
278D4—21no—
279D4—21no—
280D4—21no—
281D4—21no—
282D4—42no—
283D4—81no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—431no—
287C2×C4—431no—
288C2×C4—431no—
289C2×C4—431no—
290C2×C4—861no—
291C2×C4—861no—
292C2×C4—861no—
293C2×C4—861no—
294C2×C4—3441no—
295C2×C4—3441no—
296C2×C4D4×D4311yescharacteristic
297C2×C4D4×D4311yescharacteristic
298C2×C4C23×D4311yescharacteristic
299C8—21no—
300C8—21no—
301C8—861no—
302C8—861no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22C2×D4×D4311yescharacteristic
310C4—22no—
311C4—21no—
312C4—21no—
313C4—41no—
314C4—861no—
315C4—861no—
316C4—861no—
317C4—861no—
318C4—1721no—
319C4—1721no—
320C4—1721no—
321C4—1721no—
322C4C2×#1062190011yescharacteristic
323C4#1306337211yescharacteristic
324C2—81no—
325C2—81no—
326C2#1458355511yescharacteristic
327C2#1458369511yescharacteristic
328C2#1458370511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#460C2
socleC22×C43C22×D4
hypercenter#460D43
hypocenterC43#3371
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
2. #14583625C2semidirect
4. #14583257C2semidirect
5. #14583252C2semidirect
6. #14583207C2semidirect
7. #14583197C2semidirect
8. #14583187C2semidirect
9. #14583119C2semidirect
10. #14583119C2semidirect
11. #14583028C2semidirect
12. #14583004C2semidirect
13. #14583000C2semidirect
14. SD16×Dic43C2semidirect
180. C43#3371semidirect