Finite Group Databasebeta

← #19146603

Subgroups — #19146603

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#14583570C211yesmaximal, characteristic, complemented
3#14583264C211yesmaximal, characteristic, complemented
4#14583224C211yesmaximal, characteristic, complemented
5#14583213C211yesmaximal, characteristic, complemented
6#14583207C211yesmaximal, characteristic, complemented
7#14583152C211yesmaximal, characteristic, complemented
8#14583135C211yesmaximal, characteristic, complemented
9#14583095C211yesmaximal, characteristic, complemented
10#14583046C211yesmaximal, characteristic, complemented
11#14583046C211yesmaximal, characteristic, complemented
12#14583001C211yesmaximal, characteristic, complemented
13#14582901C211yesmaximal, characteristic, complemented
14#14582896C211yesmaximal, characteristic, complemented
15C43×#435C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C2×#10621898C2211yescharacteristic
18C2×#10621873C2211yescharacteristic
19C2×D344C2211yescharacteristic
20C2×D344C2211yescharacteristic
21#13063322C2211yescharacteristic
22#13063321—21no—
23#13063320—21no—
24#13063317C2211yescharacteristic
25#13063307—21no—
26#13063299C2211yescharacteristic
27#13063299C2211yescharacteristic
28#13063299C2211yescharacteristic
29#13063299C2211yescharacteristic
30#13063298—21no—
31#13063298—21no—
32#13063297—21no—
33C4×Dic86C2211yescharacteristic
34C4×D172C2211yescharacteristic
35#13063287—21no—
36(C22⋊D43)⋊C4—21no—
37#13063284C2211yescharacteristic
38C2×C4⋊Dic43C2211yescharacteristic
39#13063259C2211yescharacteristic
40#13063259C2211yescharacteristic
41#13063257C2211yescharacteristic
42#13063250C2211yescharacteristic
43#13063250C2211yescharacteristic
44#13063250C2211yescharacteristic
45#13063247C2211yescharacteristic
46#13063247C2211yescharacteristic
47#13063247C2211yescharacteristic
48#13063247C2211yescharacteristic
49#13063247C2211yescharacteristic
50#13063247C2211yescharacteristic
51#13063247C2211yescharacteristic
52C2×M16×C43C2211yescharacteristic
53C22×C8×C43C2211yescharacteristic
54C4×D4×C43C2211yescharacteristic
55C4⋊C8×C43C2211yescharacteristic
56C22⋊C8×C43C2211yescharacteristic
57C22⋊C8×C43C2211yescharacteristic
58#97×C43C2211yescharacteristic
59C2×D4×C43D411yescharacteristic
60C22×C4×C43C2311yescharacteristic
61C22×C4×C43C2311yescharacteristic
62C2×C22⋊D43—21no—
63C2×C22⋊D43—21no—
64C2×C22⋊D43—21no—
65C2×C22⋊D43—21no—
66C2×C22⋊D43—21no—
67C2×C22⋊D43—21no—
68C22×Dic43—21no—
69#10621898—22no—
70#10621898—22no—
71#10621898—41no—
72#10621898—41no—
73C2×D172—21no—
74C2×D172—21no—
75C2×D172C2311yescharacteristic
76C2×D172C2311yescharacteristic
77C2×D172C2311yescharacteristic
78C2×C4×D43—21no—
79C2×C4×D43—21no—
80C2×C4×D43—21no—
81C2×Dic86C2311yescharacteristic
82M16×C43—41no—
83C2×C8×C43—41no—
84C2×C8×C43C2311yescharacteristic
85C2×C8×C43C2311yescharacteristic
86C2×C8×C43C2311yescharacteristic
87C2×C8×C43C2311yescharacteristic
88C4⋊C4×C43D411yescharacteristic
89C22⋊C4×C43D411yescharacteristic
90C22⋊C4×C43D411yescharacteristic
91C42×C43C2311yescharacteristic
92C22⋊Dic43—21no—
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—
98C4⋊Dic43—21no—
99C4⋊Dic43C2311yescharacteristic
100C4⋊Dic43C2311yescharacteristic
101C4⋊Dic43C2311yescharacteristic
102C4⋊Dic43C2311yescharacteristic
103Dic43⋊C4—21no—
104Dic43⋊C4—21no—
105Dic43⋊C4—21no—
106C4×Dic43—21no—
107C4×Dic43—21no—
108D344—41no—
109D344—41no—
110#10621873—22no—
111C23×C43C2×D411yescharacteristic
112C23×C43C2×D411yescharacteristic
113C22×D43—21no—
114C22×D43—21no—
115C22×D43—21no—
116D4×C43—41no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43C2×D411yescharacteristic
122C2×C4×C43C2×D411yescharacteristic
123C2×C4×C43C2×D411yescharacteristic
124C2×C4×C43C2×D411yescharacteristic
125C2×C4×C43C2411yescharacteristic
126C22⋊D43—42no—
127C22⋊D43—42no—
128C22⋊D43—42no—
129C22⋊D43—81no—
130C22⋊D43—81no—
131C22⋊D43—81no—
132C2×Dic43—21no—
133C2×Dic43—21no—
134C2×Dic43—21no—
135C2×Dic43—21no—
136C2×Dic43—21no—
137C2×Dic43—81no—
138D172—21no—
139D172—21no—
140D172—21no—
141D172—21no—
142D172—21no—
143D172—21no—
144D172—42no—
145D172—81no—
146C4×D43—42no—
147C4×D43—42no—
148C4×D43—81no—
149Dic86—21no—
150Dic86#4112yes—
151C8×C43—21no—
152C8×C43—21no—
153C8×C43—21no—
154C8×C43—21no—
155C22×C43—21no—
156C22×C43—21no—
157C22×C43—21no—
158C22×C43—21no—
159C22×C43—21no—
160C22×C43—21no—
161C22×C43C22×D411yescharacteristic
162C2×D43—41no—
163C2×D43—41no—
164C2×D43—41no—
165C2×D43—41no—
166C2×D43—41no—
167C2×D43—41no—
168C2×D43—41no—
169C2×D43—41no—
170C2×D43—41no—
171C4×C43—21no—
172C4×C43—21no—
173C4×C43—21no—
174C4×C43—21no—
175C4×C43C2×#4111yescharacteristic
176C4×C43H(5,𝔽2)11yescharacteristic
177Dic43—22no—
178Dic43—41no—
179Dic43—41no—
180Dic43—41no—
181Dic43—41no—
182#3309—431nomaximal, Sylow
183C2×C43—41no—
184C2×C43—41no—
185C2×C43#54611yescharacteristic
186C2×C43#57511yescharacteristic
187C2×C43#57611yescharacteristic
188D43—81no—
189D43—81no—
190D43—81no—
191#553—431no—
192#550—431no—
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#435D4311yescharacteristic, complemented
204#417—431no—
205#416—431no—
206C43#330911yescharacteristic, complemented, Sylow
207C2×#41—431no—
208C2×#41—431no—
209C2×SD16—431no—
210C2×D8—431no—
211C2×D8—431no—
212C2×M16C2×D4311yescharacteristic
213C22×C8C2×D4311yescharacteristic
214#127—431no—
215#127—861no—
216#126—861no—
217#125—431no—
218#123—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—861no—
229C4×D4—861no—
230C4×D4C2×D4311yescharacteristic
231#117—431no—
232C2×C4⋊C4—431no—
233#107—431no—
234#107—431no—
235#106—431no—
236C4⋊C8C2×D4311yescharacteristic
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⋊C8C2×D4311yescharacteristic
248C22⋊C8C2×D4311yescharacteristic
249#97C2×D4311yescharacteristic
250#41—862no—
251#41—862no—
252#41—1721no—
253#41—1721no—
254C2×Q8—431no—
255C2×D4—431no—
256C2×D4—431no—
257C2×D4—431no—
258C2×D4—861no—
259C2×D4—861no—
260C2×D4—861no—
261C2×D4—861no—
262C2×D4—861no—
263C2×D4—861no—
264C2×D4—861no—
265C2×D4—861no—
266C2×D4D17211yescharacteristic
267C22×C4—861no—
268C22×C4—861no—
269C22×C4—861no—
270C22×C4—861no—
271C22×C4C22×D4311yescharacteristic
272C22×C4C22×D4311yescharacteristic
273SD16—862no—
274D8—1721no—
275D8—1721no—
276M16—41no—
277C2×C8—41no—
278C2×C8C22×D4311yescharacteristic
279C2×C8C22×D4311yescharacteristic
280C2×C8C22×D4311yescharacteristic
281C2×C8C22×D4311yescharacteristic
282C4⋊C4—431no—
283C4⋊C4—431no—
284C4⋊C4—431no—
285C4⋊C4—431no—
286C4⋊C4—861no—
287C4⋊C4—861no—
288C4⋊C4—861no—
289C4⋊C4—861no—
290C4⋊C4D17211yescharacteristic
291C22⋊C4—861no—
292C22⋊C4—861no—
293C22⋊C4—861no—
294C22⋊C4—861no—
295C22⋊C4—861no—
296C22⋊C4—861no—
297C22⋊C4D17211yescharacteristic
298C22⋊C4D17211yescharacteristic
299C42—861no—
300C42—861no—
301C42C22×D4311yescharacteristic
302C23—861no—
303C23—861no—
304C23—861no—
305C23C2×D17211yescharacteristic
306C23C2×D17211yescharacteristic
307Q8—432no—
308Q8—861no—
309D4—41no—
310D4—861no—
311D4—861no—
312D4—861no—
313D4—861no—
314D4—861no—
315D4—861no—
316D4—3441no—
317D4—3441no—
318D4—3441no—
319D4—3441no—
320D4—1722no—
321D4—1722no—
322D4—1722no—
323D4—1722no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—861no—
329C2×C4—861no—
330C2×C4—861no—
331C2×C4—861no—
332C2×C4—861no—
333C2×C4—3441no—
334C2×C4—3441no—
335C2×C4—1722no—
336C2×C4—1722no—
337C2×C4C2×D17211yescharacteristic
338C2×C4C2×D17211yescharacteristic
339C2×C4C2×D17211yescharacteristic
340C2×C4C2×D17211yescharacteristic
341C2×C4C23×D4311yescharacteristic
342C8—21no—
343C8—21no—
344C8—21no—
345C8—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—1721no—
353C22—1721no—
354C22—1721no—
355C22—1721no—
356C22—1721no—
357C22—1721no—
358C22—1721no—
359C22—1721no—
360C22—1721no—
361C22C22×D17211yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—862no—
367C4—1721no—
368C4—1721no—
369C4—1721no—
370C4—1721no—
371C4#41×D4311yescharacteristic
372C4#1306337011yescharacteristic
373C2—41no—
374C2—41no—
375C2—3441no—
376C2—3441no—
377C2—3441no—
378C2#1458354411yescharacteristic
379C2#1458369911yescharacteristic
380C2#1458370411yescharacteristic
subgroupG/H
centerC22C22×D172
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#435C2
socleC22×C43C22×D4
hypercenter#435D43
hypocenterC43#3309
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #14583595C2semidirect
2. #14583570C2semidirect
3. #14583264C2semidirect
4. #14583224C2semidirect
5. #14583213C2semidirect
6. #14583207C2semidirect
7. #14583152C2semidirect
8. #14583135C2semidirect
9. #14583095C2semidirect
10. #14583046C2semidirect
11. #14583046C2semidirect
12. #14583001C2semidirect
13. #14582901C2semidirect
14. #14582896C2semidirect
15. C43×#435C2semidirect
203. #435D43semidirect
206. C43#3309semidirect