Finite Group Databasebeta

← #19146601

Subgroups — #19146601

Order 5504.

404 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#14583595C211yesmaximal, characteristic, complemented
2#14583263C211yesmaximal, characteristic, complemented
3#14583220C211yesmaximal, characteristic, complemented
4#14583210C211yesmaximal, characteristic, complemented
5#14583206C211yesmaximal, characteristic, complemented
6#14583150C211yesmaximal, characteristic, complemented
7#14583133C211yesmaximal, characteristic, complemented
8#14583091C211yesmaximal, characteristic, complemented
9#14583044C211yesmaximal, characteristic, complemented
10#14583044C211yesmaximal, characteristic, complemented
11#14582997C211yesmaximal, characteristic, complemented
12#14582971C211yesmaximal, characteristic, complemented
13#14582900C211yesmaximal, characteristic, complemented
14#14582895C211yesmaximal, characteristic, complemented
15C43×#550C211yesmaximal, characteristic, complemented
16C2×#10621884C2211yescharacteristic
17C2×#10621882C2211yescharacteristic
18C2×#10621882C2211yescharacteristic
19C2×#10621877C2211yescharacteristic
20C22×C43⋊C8C2211yescharacteristic
21#13063320—21no—
22#13063317C2211yescharacteristic
23#13063307—21no—
24#13063299C2211yescharacteristic
25#13063299C2211yescharacteristic
26#13063297—21no—
27C4×D172C2211yescharacteristic
28(C22⋊D43)⋊C4—21no—
29#13063284C2211yescharacteristic
30C2×C4⋊Dic43C2211yescharacteristic
31#13063258C2211yescharacteristic
32#13063258C2211yescharacteristic
33#13063256C2211yescharacteristic
34C4⋊(C43⋊C8)C2211yescharacteristic
35#13063249C2211yescharacteristic
36#13063249C2211yescharacteristic
37#13063249C2211yescharacteristic
38#13063246C2211yescharacteristic
39#13063246C2211yescharacteristic
40#13063246C2211yescharacteristic
41#13063246C2211yescharacteristic
42#13063246C2211yescharacteristic
43#13063246C2211yescharacteristic
44#13063245C2211yescharacteristic
45C22⋊(C43⋊C8)C2211yescharacteristic
46C22⋊(C43⋊C8)C2211yescharacteristic
47#13063236C2211yescharacteristic
48C2×#41×C43C2211yescharacteristic
49C2×#41×C43C2211yescharacteristic
50#127×C43—21no—
51#127×C43C2211yescharacteristic
52#121×C43—21no—
53#121×C43—21no—
54#121×C43C2211yescharacteristic
55#121×C43C2211yescharacteristic
56C4×Q8×C43C2211yescharacteristic
57C4×D4×C43—21no—
58C4×D4×C43C2211yescharacteristic
59#41×C43—22no—
60#41×C43—22no—
61#41×C43—41no—
62#41×C43—41no—
63C2×Q8×C43C2311yescharacteristic
64C2×D4×C43—21no—
65C2×D4×C43—21no—
66C2×D4×C43—21no—
67C2×D4×C43—21no—
68C2×D4×C43—21no—
69C2×D4×C43—21no—
70C2×D4×C43D411yescharacteristic
71C2×D4×C43C2311yescharacteristic
72C2×D4×C43C2311yescharacteristic
73C22×C4×C43—21no—
74C22×C4×C43—21no—
75C22×C4×C43C2311yescharacteristic
76C22×C4×C43C2311yescharacteristic
77C2×C22⋊D43—21no—
78C2×C22⋊D43—21no—
79C22×Dic43—21no—
80C2×D172C2311yescharacteristic
81C2×C4×D43—21no—
82C4⋊C4×C43—21no—
83C4⋊C4×C43D411yescharacteristic
84C4⋊C4×C43C2311yescharacteristic
85C22⋊C4×C43—21no—
86C22⋊C4×C43—21no—
87C22⋊C4×C43D411yescharacteristic
88C22⋊C4×C43D411yescharacteristic
89C42×C43—21no—
90C42×C43C2311yescharacteristic
91C22⋊Dic43—21no—
92#10621884—22no—
93#10621882—41no—
94#10621882—41no—
95(C2×D43)⋊C4—21no—
96(C2×D43)⋊C4—21no—
97(C2×D43)⋊C4—21no—
98C4⋊Dic43—21no—
99C4⋊Dic43C2311yescharacteristic
100C4⋊Dic43C2311yescharacteristic
101C4⋊Dic43C2311yescharacteristic
102Dic43⋊C4—21no—
103Dic43⋊C4—21no—
104C4×Dic43—21no—
105#10621877—41no—
106C2×C43⋊C8—41no—
107C2×C43⋊C8C2311yescharacteristic
108C2×C43⋊C8C2311yescharacteristic
109C2×C43⋊C8C2311yescharacteristic
110C2×C43⋊C8C2311yescharacteristic
111C23×C43—21no—
112C23×C43—21no—
113C23×C43C2×D411yescharacteristic
114C23×C43C2×D411yescharacteristic
115C22×D43—21no—
116Q8×C43—21no—
117Q8×C43#4112yes—
118D4×C43—21no—
119D4×C43—21no—
120D4×C43—21no—
121D4×C43—21no—
122D4×C43—41no—
123D4×C43—42no—
124D4×C43—42no—
125D4×C43—42no—
126D4×C43—81no—
127D4×C43—81no—
128D4×C43—81no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43—21no—
135C2×C4×C43—42no—
136C2×C4×C43—42no—
137C2×C4×C43C2×D411yescharacteristic
138C2×C4×C43C2×D411yescharacteristic
139C2×C4×C43C2×D411yescharacteristic
140C2×C4×C43C2×D411yescharacteristic
141C2×C4×C43C2411yescharacteristic
142C22⋊D43—42no—
143C22⋊D43—81no—
144C2×Dic43—21no—
145C2×Dic43—21no—
146C2×Dic43—21no—
147C2×Dic43—81no—
148D172—21no—
149D172—21no—
150C4×D43—81no—
151C43⋊C8—21no—
152C43⋊C8—21no—
153C43⋊C8—21no—
154C43⋊C8—21no—
155C22×C43—21no—
156C22×C43—21no—
157C22×C43—21no—
158C22×C43—21no—
159C22×C43—21no—
160C22×C43—21no—
161C22×C43—41no—
162C22×C43—41no—
163C22×C43—41no—
164C22×C43—41no—
165C22×C43—41no—
166C22×C43—41no—
167C22×C43C22×D411yescharacteristic
168C2×D43—41no—
169C2×D43—41no—
170C2×D43—41no—
171C4×C43—21no—
172C4×C43—21no—
173C4×C43—22no—
174C4×C43—21no—
175C4×C43—21no—
176C4×C43—41no—
177C4×C43C2×#4111yescharacteristic
178C4×C43H(5,𝔽2)11yescharacteristic
179Dic43—41no—
180Dic43—41no—
181Dic43—41no—
182#3309—431nomaximal, Sylow
183C2×C43—41no—
184C2×C43—41no—
185C2×C43—81no—
186C2×C43—81no—
187C2×C43#54611yescharacteristic
188C2×C43#57511yescharacteristic
189C2×C43#57611yescharacteristic
190D43—81no—
191#553—431no—
192#550D4311yescharacteristic, complemented
193#490—431no—
194#482—431no—
195#480—431no—
196#479—431no—
197#469—431no—
198#466—431no—
199#459—431no—
200#449—431no—
201#449—431no—
202#440—431no—
203#435—431no—
204#417—431no—
205#416—431no—
206C43#330911yescharacteristic, complemented, Sylow
207C2×#41C2×D4311yescharacteristic
208C2×#41C2×D4311yescharacteristic
209C2×SD16—431no—
210C2×D8—431no—
211C2×D8—431no—
212C2×M16—431no—
213C22×C8—431no—
214#127—21no—
215#127C2×D4311yescharacteristic
216#126—861no—
217#125—431no—
218#123—861no—
219#121—21no—
220#121—21no—
221#121—431no—
222#121—431no—
223#121—861no—
224#121C2×D4311yescharacteristic
225#121C2×D4311yescharacteristic
226C4×Q8C2×D4311yescharacteristic
227C4×D4—21no—
228C4×D4—431no—
229C4×D4—861no—
230C4×D4C2×D4311yescharacteristic
231#117—431no—
232C2×C4⋊C4—431no—
233#107—431no—
234#107—431no—
235#106—431no—
236C4⋊C8—431no—
237#103—431no—
238#103—431no—
239#103—431no—
240#102—431no—
241#102—431no—
242#102—431no—
243#102—431no—
244#102—431no—
245#102—431no—
246#102—431no—
247C22⋊C8—431no—
248C22⋊C8—431no—
249#97—431no—
250#41—22no—
251#41—22no—
252#41—41no—
253#41—41no—
254C2×Q8C22×D4311yescharacteristic
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—431no—
262C2×D4—861no—
263C2×D4—861no—
264C2×D4C22⋊D4311yescharacteristic
265C2×D4C22×D4311yescharacteristic
266C2×D4C22×D4311yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—861no—
270C22×C4—861no—
271C22×C4C22×D4311yescharacteristic
272C22×C4C22×D4311yescharacteristic
273SD16—862no—
274D8—1721no—
275D8—1721no—
276M16—1721no—
277C2×C8—431no—
278C2×C8—431no—
279C2×C8—431no—
280C2×C8—431no—
281C2×C8—1721no—
282C4⋊C4—21no—
283C4⋊C4—431no—
284C4⋊C4—431no—
285C4⋊C4—431no—
286C4⋊C4—861no—
287C4⋊C4—861no—
288C4⋊C4—861no—
289C4⋊C4C22⋊D4311yescharacteristic
290C4⋊C4C22×D4311yescharacteristic
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—861no—
294C22⋊C4—861no—
295C22⋊C4—861no—
296C22⋊C4—861no—
297C22⋊C4C22⋊D4311yescharacteristic
298C22⋊C4C22⋊D4311yescharacteristic
299C42—21no—
300C42—861no—
301C42C22×D4311yescharacteristic
302C23—21no—
303C23—21no—
304C23—861no—
305C23C2×C22⋊D4311yescharacteristic
306C23C2×C22⋊D4311yescharacteristic
307Q8—21no—
308Q8#1062190012yes—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—21no—
313D4—41no—
314D4—42no—
315D4—42no—
316D4—42no—
317D4—81no—
318D4—81no—
319D4—81no—
320D4—861no—
321D4—861no—
322D4—3441no—
323D4—1722no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—861no—
333C2×C4—861no—
334C2×C4—861no—
335C2×C4—3441no—
336C2×C4—3441no—
337C2×C4C2×C22⋊D4311yescharacteristic
338C2×C4C2×C22⋊D4311yescharacteristic
339C2×C4C2×C22⋊D4311yescharacteristic
340C2×C4C2×C22⋊D4311yescharacteristic
341C2×C4C23×D4311yescharacteristic
342C8—861no—
343C8—861no—
344C8—861no—
345C8—861no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—1721no—
359C22—1721no—
360C22—1721no—
361C22C22×C22⋊D4311yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—22no—
367C4—41no—
368C4—1721no—
369C4—1721no—
370C4—1721no—
371C4C2×#1062190011yescharacteristic
372C4#1306337011yescharacteristic
373C2—41no—
374C2—41no—
375C2—81no—
376C2—81no—
377C2—3441no—
378C2#1458354311yescharacteristic
379C2#1458369711yescharacteristic
380C2#1458370211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#550C2
socleC22×C43C22×D4
hypercenter#550D43
hypocenterC43#3309
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ #550

Complements

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

NH ≅ G/Ntype
1. #14583595C2semidirect
2. #14583263C2semidirect
3. #14583220C2semidirect
4. #14583210C2semidirect
5. #14583206C2semidirect
6. #14583150C2semidirect
7. #14583133C2semidirect
8. #14583091C2semidirect
9. #14583044C2semidirect
10. #14583044C2semidirect
11. #14582997C2semidirect
12. #14582971C2semidirect
13. #14582900C2semidirect
14. #14582895C2semidirect
15. C43×#550C2semidirect
192. #550D43semidirect
206. C43#3309semidirect