Finite Group Databasebeta

← #19146480

Subgroups — #19146480

Order 5504.

386 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583584C211yesmaximal, characteristic, complemented
2#14583555C211yesmaximal, characteristic
3#14583252C211yesmaximal, characteristic, complemented
4#14583242C211yesmaximal, characteristic, complemented
5#14583205C211yesmaximal, characteristic, complemented
6#14583141C211yesmaximal, characteristic, complemented
7#14583126C211yesmaximal, characteristic, complemented
8#14583120C211yesmaximal, characteristic, complemented
9#14583062C211yesmaximal, characteristic, complemented
10#14583057C211yesmaximal, characteristic, complemented
11#14582993C211yesmaximal, characteristic, complemented
12(C22⋊D43)⋊C8C211yesmaximal, characteristic, complemented
13#14582892C211yesmaximal, characteristic, complemented
14C2×#13063248C211yesmaximal, characteristic, complemented
15C43×#480C211yesmaximal, characteristic, complemented
16C2×#10621900C2211yescharacteristic
17C22×Dic86C2211yescharacteristic
18C2×Dic172C2211yescharacteristic
19C2×Dic172C2211yescharacteristic
20C2×#10621883C2211yescharacteristic
21C22×C43⋊C8C2211yescharacteristic
22C2×C8×D43C2211yescharacteristic
23#13063320—21no—
24#13063316C2211yescharacteristic
25#13063315—21no—
26#13063312C2211yescharacteristic
27#13063311—21no—
28#13063308—21no—
29#13063305C2211yescharacteristic
30#13063305C2211yescharacteristic
31#13063304C2211yescharacteristic
32#13063302—21no—
33#13063297—21no—
34#13063290C2211yescharacteristic
35#13063290C2211yescharacteristic
36D4×Dic43—21no—
37C4×C22⋊D43C2211yescharacteristic
38#13063284—21no—
39#13063283C2211yescharacteristic
40#13063256C2211yescharacteristic
41Dic43⋊C8C2211yescharacteristic
42#13063250C2211yescharacteristic
43#13063250C2211yescharacteristic
44#13063248C2211yescharacteristic
45#13063248C2211yescharacteristic
46#13063248C2211yescharacteristic
47#13063248C2211yescharacteristic
48#13063248C2211yescharacteristic
49#13063246C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51C8×Dic43C2211yescharacteristic
52#121×C43C2211yescharacteristic
53C2×C4⋊C4×C43C2211yescharacteristic
54#107×C43C2211yescharacteristic
55#107×C43C2211yescharacteristic
56#102×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58C22⋊C8×C43C2211yescharacteristic
59C2×D4×C43—21no—
60C2×D4×C43C2311yescharacteristic
61C22×C4×C43—21no—
62C22×C4×C43C2311yescharacteristic
63C2×C22⋊D43—21no—
64C2×C22⋊D43D411yescharacteristic
65C22×Dic43—21no—
66C22×Dic43—21no—
67#10621900—22no—
68#10621900—41no—
69C2×C4×D43C2311yescharacteristic
70C2×Dic86—22no—
71C2×Dic86—21no—
72C2×Dic86—41no—
73C2×Dic86C2311yescharacteristic
74C2×Dic86C2311yescharacteristic
75C2×Dic86C2311yescharacteristic
76C2×C8×C43C2311yescharacteristic
77C2×C8×C43C2311yescharacteristic
78C4⋊C4×C43—21no—
79C4⋊C4×C43C2311yescharacteristic
80C4⋊C4×C43C2311yescharacteristic
81C4⋊C4×C43C2311yescharacteristic
82C22⋊C4×C43—21no—
83C22⋊Dic43—21no—
84C22⋊Dic43—21no—
85C22⋊Dic43—21no—
86C22⋊Dic43D411yescharacteristic
87#10621883—41no—
88(C2×D43)⋊C4—21no—
89(C2×D43)⋊C4—21no—
90(C2×D43)⋊C4—21no—
91(C2×D43)⋊C4D411yescharacteristic
92C4⋊Dic43—21no—
93C4⋊Dic43—21no—
94C4⋊Dic43—21no—
95C4⋊Dic43C2311yescharacteristic
96Dic43⋊C4—21no—
97Dic43⋊C4—21no—
98Dic43⋊C4—21no—
99Dic43⋊C4—21no—
100Dic43⋊C4D411yescharacteristic
101C4×Dic43—21no—
102C4×Dic43—21no—
103C4×Dic43—21no—
104C4×Dic43C2311yescharacteristic
105C2×C43⋊C8—41no—
106C2×C43⋊C8C2311yescharacteristic
107C2×C43⋊C8C2311yescharacteristic
108Dic172—22no—
109Dic172—41no—
110C8×D43—41no—
111C23×C43—21no—
112C23×C43C2×D411yescharacteristic
113C22×D43C2×D411yescharacteristic
114D4×C43—21no—
115D4×C43—21no—
116D4×C43—42no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—42no—
123C2×C4×C43C2×D411yescharacteristic
124C2×C4×C43C2411yescharacteristic
125C22⋊D43—22no—
126C22⋊D43—42no—
127C2×Dic43—21no—
128C2×Dic43—21no—
129C2×Dic43—21no—
130C2×Dic43—21no—
131C2×Dic43—42no—
132C2×Dic43—42no—
133C2×Dic43C2×D411yescharacteristic
134C2×Dic43C2×D411yescharacteristic
135C2×Dic43C2×D411yescharacteristic
136C4×D43—21no—
137C4×D43—21no—
138Dic86—21no—
139Dic86—21no—
140Dic86—21no—
141Dic86—21no—
142Dic86—21no—
143Dic86—42no—
144Dic86#4112yes—
145C8×C43—21no—
146C8×C43—21no—
147C43⋊C8—21no—
148C43⋊C8—21no—
149C22×C43—21no—
150C22×C43—21no—
151C22×C43—41no—
152C22×C43—41no—
153C22×C43—41no—
154C22×C43#13512yes—
155C22×C43C22×D411yescharacteristic
156C2×D43—21no—
157C2×D43—21no—
158C2×D43—21no—
159C4×C43—21no—
160C4×C43—41no—
161C4×C43—41no—
162C4×C43—41no—
163C4×C43C2×#4111yescharacteristic
164C4×C43H(5,𝔽2)11yescharacteristic
165Dic43—22no—
166Dic43—21no—
167Dic43—21no—
168Dic43—21no—
169Dic43—41no—
170Dic43—41no—
171Dic43—41no—
172#3300—431nomaximal, Sylow
173C2×C43—22no—
174C2×C43—81no—
175C2×C43#54611yescharacteristic
176C2×C43C2×#13511yescharacteristic
177C2×C43#57811yescharacteristic
178D43—41no—
179#552—431no—
180#548—431no—
181#488—431no—
182#485—431no—
183#480D4311yescharacteristic, complemented
184#479—431no—
185#467—431no—
186#465—431no—
187#464—431no—
188#452—431no—
189#451—431no—
190C4×Q16—431no—
191C8×D4—431no—
192#416—431no—
193C2×#103—431no—
194C43#330011yescharacteristic, complemented, Sylow
195C2×#41—431no—
196C22×Q8—431no—
197C2×Q16—431no—
198C2×Q16—431no—
199C2×SD16—431no—
200C22×C8—431no—
201C22×C8—431no—
202#126—861no—
203#125—431no—
204#125—861no—
205#124—431no—
206#124—861no—
207#123—861no—
208C22⋊Q8—431no—
209C22⋊Q8—431no—
210C22⋊Q8—431no—
211C22⋊Q8—861no—
212#121—861no—
213#121C2×D4311yescharacteristic
214C4×Q8—431no—
215C4×Q8—431no—
216C4×D4—431no—
217C4×D4—861no—
218#117—431no—
219#117—861no—
220C2×C4⋊C4C2×D4311yescharacteristic
221#107C2×D4311yescharacteristic
222#107C2×D4311yescharacteristic
223#106—431no—
224C4⋊C8—431no—
225#103—431no—
226#103—431no—
227#103—431no—
228#103—431no—
229#103—431no—
230#103—431no—
231#103—431no—
232#102—431no—
233#102C2×D4311yescharacteristic
234#102C2×D4311yescharacteristic
235C22⋊C8—431no—
236C22⋊C8C2×D4311yescharacteristic
237C4×C8—431no—
238#41—862no—
239#41—1721no—
240C2×Q8—431no—
241C2×Q8—431no—
242C2×Q8—431no—
243C2×Q8—862no—
244C2×Q8—861no—
245C2×Q8—1721no—
246C2×D4—21no—
247C2×D4—431no—
248C2×D4—861no—
249C2×D4C22×D4311yescharacteristic
250C22×C4—21no—
251C22×C4—431no—
252C22×C4—861no—
253C22×C4—861no—
254C22×C4C22×D4311yescharacteristic
255Q16—862no—
256Q16—1721no—
257SD16—1721no—
258C2×C8—431no—
259C2×C8—431no—
260C2×C8—1721no—
261C2×C8—1721no—
262C2×C8C22×D4311yescharacteristic
263C2×C8C22×D4311yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—431no—
266C4⋊C4—431no—
267C4⋊C4—861no—
268C4⋊C4—861no—
269C4⋊C4—861no—
270C4⋊C4—861no—
271C4⋊C4—861no—
272C4⋊C4—861no—
273C4⋊C4—861no—
274C4⋊C4C22×D4311yescharacteristic
275C4⋊C4C22×D4311yescharacteristic
276C4⋊C4C22×D4311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—431no—
279C22⋊C4—431no—
280C22⋊C4—861no—
281C22⋊C4—861no—
282C22⋊C4—861no—
283C22⋊C4—861no—
284C22⋊C4—861no—
285C22⋊C4—861no—
286C42—431no—
287C42—861no—
288C42—861no—
289C42—861no—
290C23—21no—
291C23—431no—
292C23D4×D4311yescharacteristic
293Q8—432no—
294Q8—861no—
295Q8—861no—
296Q8—861no—
297Q8—861no—
298Q8—861no—
299Q8—1722no—
300D4—21no—
301D4—21no—
302D4—42no—
303D4—862no—
304D4—1722no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—42no—
311C2×C4—431no—
312C2×C4—431no—
313C2×C4—431no—
314C2×C4—861no—
315C2×C4—861no—
316C2×C4—861no—
317C2×C4—861no—
318C2×C4—861no—
319C2×C4—861no—
320C2×C4—1722no—
321C2×C4—1722no—
322C2×C4D4×D4311yescharacteristic
323C2×C4C23×D4311yescharacteristic
324C8—21no—
325C8—21no—
326C8—861no—
327C8—861no—
328C22—21no—
329C22—21no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—861no—
334C22—861no—
335C22—861no—
336C22#1306334412yes—
337C22C2×D4×D4311yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—861no—
343C4—861no—
344C4—861no—
345C4—862no—
346C4—1721no—
347C4—1721no—
348C4—1721no—
349C4#41×D4311yescharacteristic
350C4#1306337111yescharacteristic
351C2—22no—
352C2—81no—
353C2—1721no—
354C2#1458354111yescharacteristic
355C2C2×#1306334411yescharacteristic
356C2#1458371511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#480C2
socleC22×C43C22×D4
hypercenter#480D43
hypocenterC43#3300
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #14583584C2semidirect
3. #14583252C2semidirect
4. #14583242C2semidirect
5. #14583205C2semidirect
6. #14583141C2semidirect
7. #14583126C2semidirect
8. #14583120C2semidirect
9. #14583062C2semidirect
10. #14583057C2semidirect
11. #14582993C2semidirect
12. (C22⋊D43)⋊C8C2semidirect
13. #14582892C2semidirect
14. C2×#13063248C2semidirect
15. C43×#480C2semidirect
183. #480D43semidirect
194. C43#3300semidirect