Finite Group Databasebeta

← #19144857

Subgroups — #19144857

Order 5504.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583520C211yesmaximal, characteristic, complemented
2#14583234C211yesmaximal, characteristic, complemented
3#14583212C211yesmaximal, characteristic, complemented
4#14583194C211yesmaximal, characteristic, complemented
5#14583179C211yesmaximal, characteristic, complemented
6#14583121C211yesmaximal, characteristic, complemented
7#14583114C211yesmaximal, characteristic, complemented
8#14583061C211yesmaximal, characteristic, complemented
9#14583044C211yesmaximal, characteristic
10#14582999C211yesmaximal, characteristic, complemented
11#14582997C211yesmaximal, characteristic, complemented
12C4×#10621885C211yesmaximal, characteristic, complemented
13C4×#10621882C211yesmaximal, characteristic, complemented
14#14582960C211yesmaximal, characteristic, complemented
15C43×#520C211yesmaximal, characteristic, complemented
16C2×#10621885C2211yescharacteristic
17C2×#10621883C2211yescharacteristic
18C2×#10621884C2211yescharacteristic
19C2×#10621882C2211yescharacteristic
20#13063325C2211yescharacteristic
21#13063320—21no—
22#13063313C2211yescharacteristic
23#13063311—21no—
24#13063307—21no—
25#13063304C2211yescharacteristic
26#13063303—21no—
27#13063299C2211yescharacteristic
28C4×Dic86C2211yescharacteristic
29C4×D172C2211yescharacteristic
30#13063258C2211yescharacteristic
31#13063258C2211yescharacteristic
32#13063258C2211yescharacteristic
33#13063258C2211yescharacteristic
34C4⋊(C43⋊C8)C2211yescharacteristic
35C4⋊(C43⋊C8)C2211yescharacteristic
36#13063249C2211yescharacteristic
37#13063249C2211yescharacteristic
38#13063248C2211yescharacteristic
39#13063248C2211yescharacteristic
40#13063246C2211yescharacteristic
41#13063246C2211yescharacteristic
42#13063245C2211yescharacteristic
43#13063245C2211yescharacteristic
44C22⋊(C43⋊C8)C2211yescharacteristic
45C22⋊(C43⋊C8)C2211yescharacteristic
46#13063236C2211yescharacteristic
47C4×C43⋊C8C2211yescharacteristic
48C2×#41×C43C2211yescharacteristic
49C4×Q8×C43C2211yescharacteristic
50C4×Q8×C43C2211yescharacteristic
51C4×D4×C43—21no—
52C4×D4×C43—21no—
53C4×D4×C43C2211yescharacteristic
54C4×D4×C43C2211yescharacteristic
55#117×C43—21no—
56#117×C43C2211yescharacteristic
57C2×C4⋊C4×C43—21no—
58C2×C4⋊C4×C43C2211yescharacteristic
59#41×C43—22no—
60#41×C43—22no—
61C2×Q8×C43C2311yescharacteristic
62C2×D4×C43—21no—
63C2×D4×C43C2311yescharacteristic
64C22×C4×C43—21no—
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43—21no—
68C22×C4×C43C2311yescharacteristic
69C2×C22⋊D43—21no—
70C2×D172C2311yescharacteristic
71C2×C4×D43—21no—
72C2×Dic86—21no—
73C2×Dic86C2311yescharacteristic
74C4⋊C4×C43—21no—
75C4⋊C4×C43—21no—
76C4⋊C4×C43—21no—
77C4⋊C4×C43D411yescharacteristic
78C4⋊C4×C43D411yescharacteristic
79C4⋊C4×C43C2311yescharacteristic
80C4⋊C4×C43C2311yescharacteristic
81C22⋊C4×C43—21no—
82C22⋊C4×C43—21no—
83C22⋊C4×C43D411yescharacteristic
84C22⋊C4×C43D411yescharacteristic
85C42×C43—21no—
86C42×C43—21no—
87C42×C43C2311yescharacteristic
88C42×C43C2311yescharacteristic
89C22⋊Dic43—21no—
90#10621885—22no—
91#10621884—22no—
92#10621883—22no—
93#10621882—22no—
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
101Dic43⋊C4—21no—
102Dic43⋊C4—21no—
103C4×Dic43—21no—
104C2×C43⋊C8C2311yescharacteristic
105C2×C43⋊C8C2311yescharacteristic
106C2×C43⋊C8C2311yescharacteristic
107C2×C43⋊C8C2311yescharacteristic
108C23×C43—21no—
109C23×C43C2×D411yescharacteristic
110C22×D43—21no—
111Q8×C43—21no—
112Q8×C43#4112yes—
113D4×C43—24no—
114D4×C43—21no—
115D4×C43#4112yes—
116C2×C4×C43—24no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—81no—
123C2×C4×C43—81no—
124C2×C4×C43—81no—
125C2×C4×C43C2×D411yescharacteristic
126C2×C4×C43C2×D411yescharacteristic
127C2×C4×C43C2×D411yescharacteristic
128C2×C4×C43C2×D411yescharacteristic
129C2×C4×C43C2×D411yescharacteristic
130C2×C4×C43C2411yescharacteristic
131C22⋊D43—81no—
132C2×Dic43—21no—
133C2×Dic43—21no—
134C2×Dic43—21no—
135D172—21no—
136D172—21no—
137C4×D43—81no—
138Dic86—21no—
139Dic86—21no—
140Dic86—81no—
141C43⋊C8—21no—
142C43⋊C8—21no—
143C43⋊C8—21no—
144C43⋊C8—21no—
145C22×C43—22no—
146C22×C43—21no—
147C22×C43—21no—
148C22×C43—21no—
149C22×C43—41no—
150C22×C43—41no—
151C22×C43C22×D411yescharacteristic
152C2×D43—41no—
153C2×D43—41no—
154C2×D43—41no—
155C4×C43—21no—
156C4×C43—22no—
157C4×C43—21no—
158C4×C43—21no—
159C4×C43—21no—
160C4×C43—21no—
161C4×C43—41no—
162C4×C43—41no—
163C4×C43C2×#4111yescharacteristic
164C4×C43C2×#4111yescharacteristic
165Dic43—41no—
166Dic43—41no—
167Dic43—41no—
168#3124—431nomaximal, Sylow
169C2×C43—41no—
170C2×C43—42no—
171C2×C43#52511yescharacteristic
172C2×C43#57611yescharacteristic
173C2×C43#57811yescharacteristic
174D43—81no—
175#542—431no—
176#520D4311yescharacteristic, complemented
177#484—431no—
178#480—431no—
179#477—431no—
180#474—431no—
181#464—431no—
182#463—431no—
183#452—431no—
184#449—431no—
185#440—431no—
186#440—431no—
187C4×Q16—431no—
188C4×D8—431no—
189#433—431no—
190C43#312411yescharacteristic, complemented, Sylow
191C2×#41C2×D4311yescharacteristic
192C2×Q16—431no—
193C2×SD16—431no—
194C2×SD16—431no—
195C2×D8—431no—
196C4⋊Q8—431no—
197#126—861no—
198#124—431no—
199#124—861no—
200#123—861no—
201C22⋊Q8—431no—
202C22⋊Q8—861no—
203#121—431no—
204C4×Q8—431no—
205C4×Q8C2×D4311yescharacteristic
206C4×Q8C2×D4311yescharacteristic
207C4×D4—21no—
208C4×D4—21no—
209C4×D4—431no—
210C4×D4C2×D4311yescharacteristic
211C4×D4C2×D4311yescharacteristic
212#117—21no—
213#117C2×D4311yescharacteristic
214C2×C4⋊C4—21no—
215C2×C4⋊C4C2×D4311yescharacteristic
216#107—431no—
217#107—431no—
218#107—431no—
219#107—431no—
220C4⋊C8—431no—
221C4⋊C8—431no—
222#103—431no—
223#103—431no—
224#103—431no—
225#103—431no—
226#102—431no—
227#102—431no—
228#102—431no—
229#102—431no—
230C22⋊C8—431no—
231C22⋊C8—431no—
232#97—431no—
233C4×C8—431no—
234#41—22no—
235#41—22no—
236C2×Q8—431no—
237C2×Q8—861no—
238C2×Q8C22×D4311yescharacteristic
239C2×D4—21no—
240C2×D4—431no—
241C2×D4—861no—
242C2×D4C22×D4311yescharacteristic
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—861no—
248C22×C4C22×D4311yescharacteristic
249Q16—862no—
250SD16—862no—
251SD16—862no—
252D8—862no—
253C2×C8—431no—
254C2×C8—431no—
255C2×C8—431no—
256C2×C8—431no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—431no—
261C4⋊C4—431no—
262C4⋊C4—861no—
263C4⋊C4—861no—
264C4⋊C4—861no—
265C4⋊C4C22⋊D4311yescharacteristic
266C4⋊C4C22⋊D4311yescharacteristic
267C4⋊C4C22×D4311yescharacteristic
268C4⋊C4C22×D4311yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—861no—
272C22⋊C4—861no—
273C22⋊C4—861no—
274C22⋊C4—861no—
275C22⋊C4—861no—
276C22⋊C4C22⋊D4311yescharacteristic
277C22⋊C4C22⋊D4311yescharacteristic
278C42—21no—
279C42—21no—
280C42—861no—
281C42C22×D4311yescharacteristic
282C42C22×D4311yescharacteristic
283C23—21no—
284C23—861no—
285C23C2×C22⋊D4311yescharacteristic
286Q8—21no—
287Q8—861no—
288Q8—861no—
289Q8—3441no—
290Q8#1062189812yes—
291D4—24no—
292D4—21no—
293D4—861no—
294D4—861no—
295D4—3441no—
296D4#1062189812yes—
297C2×C4—24no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—861no—
307C2×C4—861no—
308C2×C4—861no—
309C2×C4—3441no—
310C2×C4C2×C22⋊D4311yescharacteristic
311C2×C4C2×C22⋊D4311yescharacteristic
312C2×C4C2×C22⋊D4311yescharacteristic
313C2×C4C2×C22⋊D4311yescharacteristic
314C2×C4C2×C22⋊D4311yescharacteristic
315C2×C4C23×D4311yescharacteristic
316C8—861no—
317C8—861no—
318C8—861no—
319C8—861no—
320C22—21no—
321C22—22no—
322C22—21no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—1721no—
327C22—1721no—
328C22—1721no—
329C22C22×C22⋊D4311yescharacteristic
330C4—21no—
331C4—22no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—41no—
337C4—41no—
338C4—1721no—
339C4—1721no—
340C4—1721no—
341C4C2×#1062189811yescharacteristic
342C4C2×#1062189811yescharacteristic
343C2—41no—
344C2—42no—
345C2—3441no—
346C2#1458341011yescharacteristic
347C2#1458370211yescharacteristic
348C2#1458371411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#520C2
socleC22×C43C22×D4
hypercenter#520D43
hypocenterC43#3124
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #117 ◁ #520

Complements

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

NH ≅ G/Ntype
1. #14583520C2semidirect
2. #14583234C2semidirect
3. #14583212C2semidirect
4. #14583194C2semidirect
5. #14583179C2semidirect
6. #14583121C2semidirect
7. #14583114C2semidirect
8. #14583061C2semidirect
10. #14582999C2semidirect
11. #14582997C2semidirect
12. C4×#10621885C2semidirect
13. C4×#10621882C2semidirect
14. #14582960C2semidirect
15. C43×#520C2semidirect
176. #520D43semidirect
190. C43#3124semidirect