Finite Group Databasebeta

← #19146676

Subgroups — #19146676

Order 5504.

410 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583606C211yesmaximal, characteristic, complemented
2#14583258C211yesmaximal, characteristic, complemented
3#14583232C211yesmaximal, characteristic, complemented
4#14583210C211yesmaximal, characteristic, complemented
5#14583179C211yesmaximal, characteristic, complemented
6#14583143C211yesmaximal, characteristic, complemented
7#14583138C211yesmaximal, characteristic, complemented
8#14583118C211yesmaximal, characteristic, complemented
9#14583061C211yesmaximal, characteristic, complemented
10#14583050C211yesmaximal, characteristic, complemented
11#14582999C211yesmaximal, characteristic, complemented
12#14582971C211yesmaximal, characteristic, complemented
13#14582900C211yesmaximal, characteristic, complemented
14C2×#13063246C211yesmaximal, characteristic, complemented
15C43×#546C211yesmaximal, characteristic
16C2×#10621885C2211yescharacteristic, complemented
17C2×#10621883C2211yescharacteristic
18C2×#10621883C2211yescharacteristic
19C2×#10621877C2211yescharacteristic, complemented
20C22×C43⋊C8C2211yescharacteristic
21#13063325C2211yescharacteristic, complemented
22#13063316—21no—
23#13063304C2211yescharacteristic
24#13063304C2211yescharacteristic, complemented
25#13063302—21no—
26#13063302—21no—
27C4×Dic86C2211yescharacteristic, complemented
28D4×Dic43—21no—
29C2×C4⋊Dic43C2211yescharacteristic
30C2×C4⋊Dic43C2211yescharacteristic, complemented
31#13063258C2211yescharacteristic, complemented
32#13063258C2211yescharacteristic, complemented
33#13063258C2211yescharacteristic, complemented
34C4⋊(C43⋊C8)C2211yescharacteristic, complemented
35#13063249C2211yescharacteristic, complemented
36#13063249C2211yescharacteristic, complemented
37#13063249C2211yescharacteristic, complemented
38#13063248C2211yescharacteristic, complemented
39#13063246C2211yescharacteristic
40#13063246C2211yescharacteristic
41#13063246C2211yescharacteristic
42#13063246C2211yescharacteristic
43#13063246C2211yescharacteristic
44#13063246C2211yescharacteristic
45C22⋊(C43⋊C8)C2211yescharacteristic
46C22⋊(C43⋊C8)C2211yescharacteristic, complemented
47#13063236C2211yescharacteristic, complemented
48C2×#41×C43C2211yescharacteristic
49C22×D4×C43C2211yescharacteristic
50#124×C43C2211yescharacteristic
51#123×C43—21no—
52C22⋊Q8×C43C2211yescharacteristic
53#121×C43—21no—
54#121×C43C2211yescharacteristic
55#120×C43—21no—
56C4×D4×C43C2211yescharacteristic
57C4×D4×C43C2211yescharacteristic
58C2×C22⋊C4×C43—21no—
59C24×C43—21no—
60#41×C43—22no—
61#41×C43—41no—
62C2×Q8×C43C2311yescharacteristic
63C2×D4×C43—21no—
64C2×D4×C43—21no—
65C2×D4×C43—21no—
66C2×D4×C43—22no—
67C2×D4×C43—41no—
68C2×D4×C43D411yescharacteristic
69C2×D4×C43C2311yescharacteristic
70C2×D4×C43C2311yescharacteristic
71C22×C4×C43—21no—
72C22×C4×C43—21no—
73C22×C4×C43C2311yescharacteristic
74C22×C4×C43C2311yescharacteristic
75C22×Dic43—21no—
76C22×Dic43—21no—
77C2×Dic86—21no—
78C2×Dic86C2311yescharacteristic
79C4⋊C4×C43—21no—
80C4⋊C4×C43D411yescharacteristic
81C4⋊C4×C43C2311yescharacteristic
82C22⋊C4×C43—21no—
83C22⋊C4×C43—21no—
84C22⋊C4×C43—21no—
85C22⋊C4×C43—21no—
86C22⋊C4×C43—21no—
87C22⋊C4×C43D411yescharacteristic
88C22⋊C4×C43D411yescharacteristic
89C42×C43C2311yescharacteristic
90C22⋊Dic43—21no—
91C22⋊Dic43—21no—
92#10621885—41no—
93#10621883—22no—
94#10621883—41no—
95C4⋊Dic43—21no—
96C4⋊Dic43—21no—
97C4⋊Dic43—21no—
98C4⋊Dic43C2311yescharacteristic
99C4⋊Dic43C2311yescharacteristic
100C4⋊Dic43C2311yescharacteristic
101Dic43⋊C4—21no—
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×C43—42no—
114C23×C43—42no—
115C23×C43—81no—
116C23×C43C2×D411yescharacteristic
117C23×C43C2×D411yescharacteristic
118Q8×C43—21no—
119Q8×C43—21no—
120D4×C43—22no—
121D4×C43—21no—
122D4×C43—21no—
123D4×C43—21no—
124D4×C43—42no—
125D4×C43—42no—
126D4×C43—81no—
127D4×C43#4112yes—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43—42no—
135C2×C4×C43—81no—
136C2×C4×C43C2×D411yescharacteristic
137C2×C4×C43C2×D411yescharacteristic
138C2×C4×C43C2×D411yescharacteristic
139C2×C4×C43C2×D411yescharacteristic
140C2×C4×C43C2411yescharacteristic
141C2×Dic43—21no—
142C2×Dic43—21no—
143C2×Dic43—21no—
144C2×Dic43—21no—
145C2×Dic43—81no—
146C2×Dic43—81no—
147Dic86—21no—
148Dic86—21no—
149Dic86—81no—
150C43⋊C8—21no—
151C43⋊C8—21no—
152C43⋊C8—21no—
153C43⋊C8—21no—
154C22×C43—21no—
155C22×C43—21no—
156C22×C43—22no—
157C22×C43—21no—
158C22×C43—21no—
159C22×C43—21no—
160C22×C43—41no—
161C22×C43—41no—
162C22×C43—41no—
163C22×C43—41no—
164C22×C43—41no—
165C22×C43—84no—
166C22×C43#13712yes—
167C22×C43C22×D411yescharacteristic
168C4×C43—21no—
169C4×C43—21no—
170C4×C43—21no—
171C4×C43—21no—
172C4×C43—41no—
173C4×C43—41no—
174C4×C43C2×#4111yescharacteristic
175C4×C43H(5,𝔽2)11yescharacteristic
176Dic43—41no—
177Dic43—41no—
178Dic43—41no—
179Dic43—41no—
180#3314—431nomaximal, Sylow
181C2×C43—22no—
182C2×C43—41no—
183C2×C43—42no—
184C2×C43—81no—
185C2×C43#54611yescharacteristic
186C2×C43C2×#13711yescharacteristic
187C2×C43#57611yescharacteristic
188#554—431no—
189#546D4311yescharacteristic
190#489—431no—
191#484—431no—
192#480—431no—
193#474—431no—
194#468—431no—
195#467—431no—
196#464—431no—
197#452—431no—
198#450—431no—
199#440—431no—
200#435—431no—
201#417—431no—
202C2×#102—431no—
203C43#331411yescharacteristic, complemented, Sylow
204C2×#41C2×D4311yescharacteristic
205C22×D4C2×D4311yescharacteristic
206C2×Q16—431no—
207C2×SD16—431no—
208C2×SD16—431no—
209C2×M16—431no—
210C22×C8—431no—
211C4⋊Q8—431no—
212#125—861no—
213#124C2×D4311yescharacteristic
214#123—21no—
215C22⋊Q8—431no—
216C22⋊Q8—431no—
217C22⋊Q8—861no—
218C22⋊Q8—861no—
219C22⋊Q8C2×D4311yescharacteristic
220#121—21no—
221#121C2×D4311yescharacteristic
222#120—21no—
223C4×Q8—431no—
224C4×D4—861no—
225C4×D4C2×D4311yescharacteristic
226C4×D4C2×D4311yescharacteristic
227C2×C4⋊C4—431no—
228C2×C4⋊C4—431no—
229C2×C22⋊C4—21no—
230#107—431no—
231#107—431no—
232#107—431no—
233C4⋊C8—431no—
234#103—431no—
235#103—431no—
236#103—431no—
237#103—431no—
238#102—431no—
239#102—431no—
240#102—431no—
241#102—431no—
242#102—431no—
243#102—431no—
244C22⋊C8—431no—
245C22⋊C8—431no—
246#97—431no—
247C24—21no—
248#41—22no—
249#41—41no—
250C2×Q8—431no—
251C2×Q8—861no—
252C2×Q8C22×D4311yescharacteristic
253C2×D4—22no—
254C2×D4—21no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—41no—
258C2×D4C22⋊D4311yescharacteristic
259C2×D4C22×D4311yescharacteristic
260C2×D4C22×D4311yescharacteristic
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—861no—
264C22×C4—861no—
265C22×C4C22×D4311yescharacteristic
266C22×C4C22×D4311yescharacteristic
267Q16—1721no—
268SD16—862no—
269SD16—1721no—
270M16—1721no—
271C2×C8—431no—
272C2×C8—431no—
273C2×C8—431no—
274C2×C8—431no—
275C2×C8—1721no—
276C4⋊C4—21no—
277C4⋊C4—431no—
278C4⋊C4—431no—
279C4⋊C4—431no—
280C4⋊C4—861no—
281C4⋊C4—861no—
282C4⋊C4—861no—
283C4⋊C4—861no—
284C4⋊C4—861no—
285C4⋊C4—861no—
286C4⋊C4C22⋊D4311yescharacteristic
287C4⋊C4C22×D4311yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—861no—
294C22⋊C4—861no—
295C22⋊C4C22⋊D4311yescharacteristic
296C22⋊C4C22⋊D4311yescharacteristic
297C42—861no—
298C42C22×D4311yescharacteristic
299C23—21no—
300C23—21no—
301C23—42no—
302C23—42no—
303C23—81no—
304C23C2×C22⋊D4311yescharacteristic
305C23C2×C22⋊D4311yescharacteristic
306Q8—21no—
307Q8—21no—
308Q8—861no—
309Q8—861no—
310Q8—3441no—
311D4—22no—
312D4—21no—
313D4—21no—
314D4—21no—
315D4—42no—
316D4—42no—
317D4—81no—
318D4#1062190012yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—42no—
326C2×C4—81no—
327C2×C4—861no—
328C2×C4—861no—
329C2×C4—861no—
330C2×C4—861no—
331C2×C4—3441no—
332C2×C4—3441no—
333C2×C4C2×C22⋊D4311yescharacteristic
334C2×C4C2×C22⋊D4311yescharacteristic
335C2×C4C2×C22⋊D4311yescharacteristic
336C2×C4C2×C22⋊D4311yescharacteristic
337C2×C4C23×D4311yescharacteristic
338C8—861no—
339C8—861no—
340C8—861no—
341C8—861no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—22no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—84no—
354C22#1306335512yes—
355C22C22×C22⋊D4311yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—41no—
361C4—41no—
362C4—1721no—
363C4—1721no—
364C4—1721no—
365C4—1721no—
366C4C2×#1062190011yescharacteristic
367C4#1306337011yescharacteristic
368C2—22no—
369C2—41no—
370C2—42no—
371C2—81no—
372C2#1458354311yescharacteristic
373C2C2×#1306335511yescharacteristic
374C2#1458370211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#546C2
socleC22×C43C22×D4
hypercenter#546D43
hypocenterC43#3314
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #14583606C2semidirect
2. #14583258C2semidirect
3. #14583232C2semidirect
4. #14583210C2semidirect
5. #14583179C2semidirect
6. #14583143C2semidirect
7. #14583138C2semidirect
8. #14583118C2semidirect
9. #14583061C2semidirect
10. #14583050C2semidirect
11. #14582999C2semidirect
12. #14582971C2semidirect
13. #14582900C2semidirect
14. C2×#13063246C2semidirect
16. C2×#10621885C22semidirect
19. C2×#10621877C22semidirect
21. #13063325C22semidirect
24. #13063304C22semidirect
27. C4×Dic86C22semidirect
30. C2×C4⋊Dic43C22semidirect
31. #13063258C22semidirect
32. #13063258C22semidirect
33. #13063258C22semidirect
34. C4⋊(C43⋊C8)C22semidirect
35. #13063249C22semidirect
36. #13063249C22semidirect
37. #13063249C22semidirect
38. #13063248C22semidirect
46. C22⋊(C43⋊C8)C22semidirect
47. #13063236C22semidirect
203. C43#3314semidirect