Finite Group Databasebeta

← #19146541

Subgroups — #19146541

Order 5504.

408 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583612C211yesmaximal, characteristic, complemented
2#14583568C211yesmaximal, characteristic, complemented
3#14583244C211yesmaximal, characteristic, complemented
4#14583223C211yesmaximal, characteristic, complemented
5#14583221C211yesmaximal, characteristic, complemented
6#14583192C211yesmaximal, characteristic, complemented
7#14583135C211yesmaximal, characteristic, complemented
8#14583134C211yesmaximal, characteristic, complemented
9#14583093C211yesmaximal, characteristic, complemented
10#14583047C211yesmaximal, characteristic, complemented
11#14583044C211yesmaximal, characteristic, complemented
12#14582984C211yesmaximal, characteristic, complemented
13C8×C22⋊D43C211yesmaximal, characteristic, complemented
14#14582894C211yesmaximal, characteristic, complemented
15C43×#416C211yesmaximal, characteristic, complemented
16C2×#10621902C2211yescharacteristic
17C2×#10621884C2211yescharacteristic
18C2×D344C2211yescharacteristic
19C2×#10621882C2211yescharacteristic
20C2×C8×D43C2211yescharacteristic
21#13063324C2211yescharacteristic
22#13063321—21no—
23#13063321C2211yescharacteristic
24#13063313—21no—
25#13063311—21no—
26#13063300C2211yescharacteristic
27#13063299—21no—
28#13063299C2211yescharacteristic
29#13063299C2211yescharacteristic
30#13063298—21no—
31#13063296—21no—
32#13063296C2211yescharacteristic
33Q8×Dic43C2211yescharacteristic
34#13063287C2211yescharacteristic
35C4×C22⋊D43—21no—
36C4×C22⋊D43C2211yescharacteristic
37#13063283C2211yescharacteristic
38#13063282—21no—
39#13063259C2211yescharacteristic
40#13063258C2211yescharacteristic
41#13063256C2211yescharacteristic
42Dic43⋊C8C2211yescharacteristic
43#13063249C2211yescharacteristic
44#13063247C2211yescharacteristic
45#13063247C2211yescharacteristic
46#13063246C2211yescharacteristic
47#13063245C2211yescharacteristic
48#13063245C2211yescharacteristic
49C22⋊(C43⋊C8)C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51C8×Dic43C2211yescharacteristic
52C2×#41×C43C2211yescharacteristic
53C22×C8×C43C2211yescharacteristic
54#117×C43C2211yescharacteristic
55#103×C43C2211yescharacteristic
56#103×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58#102×C43C2211yescharacteristic
59#41×C43—22no—
60#41×C43—41no—
61C2×Q8×C43C2311yescharacteristic
62C2×D4×C43—21no—
63C2×D4×C43C2311yescharacteristic
64C22×C4×C43—21no—
65C22×C4×C43C2311yescharacteristic
66C2×C22⋊D43—21no—
67C2×C22⋊D43—21no—
68C2×C22⋊D43—21no—
69C2×C22⋊D43—21no—
70C2×C22⋊D43—21no—
71C2×C22⋊D43D411yescharacteristic
72#10621902—22no—
73#10621902—41no—
74C2×D172—21no—
75C2×D172—21no—
76C2×D172C2311yescharacteristic
77C2×D172C2311yescharacteristic
78C2×C4×D43—21no—
79C2×C4×D43—21no—
80C2×C4×D43C2311yescharacteristic
81C2×Dic86—21no—
82C2×C8×C43—41no—
83C2×C8×C43C2311yescharacteristic
84C2×C8×C43C2311yescharacteristic
85C4⋊C4×C43C2311yescharacteristic
86C4⋊C4×C43C2311yescharacteristic
87C22⋊C4×C43—21no—
88C42×C43—21no—
89C22⋊Dic43—21no—
90C22⋊Dic43D411yescharacteristic
91#10621884—22no—
92#10621882—41no—
93(C2×D43)⋊C4—21no—
94(C2×D43)⋊C4—21no—
95(C2×D43)⋊C4—21no—
96(C2×D43)⋊C4—21no—
97(C2×D43)⋊C4—21no—
98(C2×D43)⋊C4D411yescharacteristic
99C4⋊Dic43—21no—
100C4⋊Dic43C2311yescharacteristic
101C4⋊Dic43C2311yescharacteristic
102Dic43⋊C4—21no—
103Dic43⋊C4D411yescharacteristic
104C4×Dic43—21no—
105C4×Dic43—21no—
106C4×Dic43C2311yescharacteristic
107C2×C43⋊C8C2311yescharacteristic
108C2×C43⋊C8C2311yescharacteristic
109D344—41no—
110C8×D43—41no—
111C23×C43—21no—
112C23×C43C2×D411yescharacteristic
113C22×D43—21no—
114C22×D43—21no—
115C22×D43C2×D411yescharacteristic
116Q8×C43—21no—
117Q8×C43#4112yes—
118D4×C43—21no—
119D4×C43—21no—
120D4×C43—42no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—42no—
127C2×C4×C43C2×D411yescharacteristic
128C2×C4×C43C2411yescharacteristic
129C22⋊D43—22no—
130C22⋊D43—42no—
131C22⋊D43—81no—
132C22⋊D43—81no—
133C22⋊D43—81no—
134C22⋊D43—81no—
135C2×Dic43—21no—
136C2×Dic43—21no—
137C2×Dic43C2×D411yescharacteristic
138C2×Dic43C2×D411yescharacteristic
139C2×Dic43C2×D411yescharacteristic
140D172—21no—
141D172—21no—
142D172—21no—
143D172—21no—
144D172—42no—
145D172—81no—
146C4×D43—21no—
147C4×D43—21no—
148C4×D43—42no—
149C4×D43—42no—
150Dic86—81no—
151C8×C43—21no—
152C8×C43—21no—
153C43⋊C8—21no—
154C43⋊C8—21no—
155C22×C43—21no—
156C22×C43—21no—
157C22×C43—21no—
158C22×C43—41no—
159C22×C43—41no—
160C22×C43—41no—
161C22×C43C22×D411yescharacteristic
162C2×D43—21no—
163C2×D43—21no—
164C2×D43—21no—
165C2×D43—41no—
166C2×D43—41no—
167C2×D43—41no—
168C2×D43—41no—
169C2×D43—41no—
170C2×D43—41no—
171C4×C43—22no—
172C4×C43—21no—
173C4×C43—41no—
174C4×C43—41no—
175C4×C43C2×#4111yescharacteristic
176C4×C43H(5,𝔽2)11yescharacteristic
177Dic43—21no—
178Dic43—21no—
179Dic43—41no—
180Dic43—41no—
181Dic43#13512yes—
182#3305—431nomaximal, Sylow
183C2×C43—41no—
184C2×C43—81no—
185C2×C43#54611yescharacteristic
186C2×C43C2×#13511yescharacteristic
187C2×C43#57611yescharacteristic
188D43—41no—
189D43—81no—
190D43—81no—
191#555—431no—
192#550—431no—
193#486—431no—
194#482—431no—
195#482—431no—
196#477—431no—
197#466—431no—
198#466—431no—
199#459—431no—
200#449—431no—
201#449—431no—
202C4×SD16—431no—
203C8×D4—431no—
204#416—431no—
205#416D4311yescharacteristic, complemented
206C43#330511yescharacteristic, complemented, Sylow
207C2×#41—431no—
208C2×#41C2×D4311yescharacteristic
209C2×SD16—431no—
210C2×D8—431no—
211C2×D8—431no—
212C22×C8—431no—
213C22×C8C2×D4311yescharacteristic
214C4⋊Q8—431no—
215#127—431no—
216#127—861no—
217#124—861no—
218#124—861no—
219#121—431no—
220#121—431no—
221#121—431no—
222#121—431no—
223#121—861no—
224#121—861no—
225#121—861no—
226C4×Q8—431no—
227C4×D4—431no—
228C4×D4—431no—
229C4×D4—861no—
230#117—431no—
231#117—861no—
232#117C2×D4311yescharacteristic
233#107—431no—
234#107—431no—
235#106—431no—
236C4⋊C8—431no—
237#103—431no—
238#103C2×D4311yescharacteristic
239#103C2×D4311yescharacteristic
240#102—431no—
241#102—431no—
242#102—431no—
243#102—431no—
244#102—431no—
245#102C2×D4311yescharacteristic
246#102C2×D4311yescharacteristic
247C22⋊C8—431no—
248C22⋊C8—431no—
249C4×C8—431no—
250#41—22no—
251#41—41no—
252#41—862no—
253#41—1721no—
254C2×Q8—861no—
255C2×Q8C22×D4311yescharacteristic
256C2×D4—21no—
257C2×D4—431no—
258C2×D4—431no—
259C2×D4—431no—
260C2×D4—861no—
261C2×D4—861no—
262C2×D4—861no—
263C2×D4—861no—
264C2×D4—861no—
265C2×D4—861no—
266C2×D4—861no—
267C2×D4C22×D4311yescharacteristic
268C22×C4—21no—
269C22×C4—431no—
270C22×C4—861no—
271C22×C4—861no—
272C22×C4C22×D4311yescharacteristic
273SD16—862no—
274D8—1721no—
275D8—1721no—
276C2×C8—41no—
277C2×C8—431no—
278C2×C8—431no—
279C2×C8—1721no—
280C2×C8C22×D4311yescharacteristic
281C2×C8C22×D4311yescharacteristic
282C4⋊C4—431no—
283C4⋊C4—431no—
284C4⋊C4—431no—
285C4⋊C4—861no—
286C4⋊C4—861no—
287C4⋊C4C22×D4311yescharacteristic
288C4⋊C4C22×D4311yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—431no—
291C22⋊C4—431no—
292C22⋊C4—861no—
293C22⋊C4—861no—
294C22⋊C4—861no—
295C22⋊C4—861no—
296C22⋊C4—861no—
297C22⋊C4—861no—
298C42—21no—
299C42—431no—
300C42—861no—
301C42—861no—
302C23—21no—
303C23—431no—
304C23—861no—
305C23—861no—
306C23D4×D4311yescharacteristic
307Q8—21no—
308Q8—3441no—
309Q8#1062189812yes—
310D4—21no—
311D4—21no—
312D4—42no—
313D4—862no—
314D4—861no—
315D4—861no—
316D4—861no—
317D4—861no—
318D4—3441no—
319D4—3441no—
320D4—3441no—
321D4—3441no—
322D4—3441no—
323D4—1722no—
324D4—1722no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—42no—
331C2×C4—431no—
332C2×C4—431no—
333C2×C4—431no—
334C2×C4—861no—
335C2×C4—861no—
336C2×C4—861no—
337C2×C4—861no—
338C2×C4—1722no—
339C2×C4—1722no—
340C2×C4D4×D4311yescharacteristic
341C2×C4C23×D4311yescharacteristic
342C8—21no—
343C8—21no—
344C8—861no—
345C8—861no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—861no—
353C22—861no—
354C22—861no—
355C22—1721no—
356C22—1721no—
357C22—1721no—
358C22—1721no—
359C22—1721no—
360C22—1721no—
361C22C2×D4×D4311yescharacteristic
362C4—21no—
363C4—22no—
364C4—41no—
365C4—41no—
366C4—432no—
367C4—861no—
368C4—861no—
369C4—1721no—
370C4—1721no—
371C4C2×#1062189811yescharacteristic
372C4#1306337011yescharacteristic
373C2—41no—
374C2—81no—
375C2—3441no—
376C2—3441no—
377C2—1721no—
378C2#1458353911yescharacteristic
379C2#135×D4311yescharacteristic
380C2#1458370111yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#416C2
socleC22×C43C22×D4
hypercenter#416D43
hypocenterC43#3305
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. #14583612C2semidirect
2. #14583568C2semidirect
3. #14583244C2semidirect
4. #14583223C2semidirect
5. #14583221C2semidirect
6. #14583192C2semidirect
7. #14583135C2semidirect
8. #14583134C2semidirect
9. #14583093C2semidirect
10. #14583047C2semidirect
11. #14583044C2semidirect
12. #14582984C2semidirect
13. C8×C22⋊D43C2semidirect
14. #14582894C2semidirect
15. C43×#416C2semidirect
205. #416D43semidirect
206. C43#3305semidirect