Finite Group Databasebeta

← #19144851

Subgroups — #19144851

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#14583379C211yesmaximal, characteristic, complemented
2#14583232C211yesmaximal, characteristic, complemented
3#14583210C211yesmaximal, characteristic, complemented
4#14583191C211yesmaximal, characteristic, complemented
5#14583176C211yesmaximal, characteristic, complemented
6#14583118C211yesmaximal, characteristic, complemented
7#14583111C211yesmaximal, characteristic, complemented
8#14583059C211yesmaximal, characteristic, complemented
9#14583042C211yesmaximal, characteristic
10#14582999C211yesmaximal, characteristic, complemented
11#14582997C211yesmaximal, characteristic, complemented
12C4×#10621885C211yesmaximal, characteristic, complemented
13C4×#10621882C211yesmaximal, characteristic, complemented
14#14582960C211yesmaximal, characteristic, complemented
15C43×#542C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C2×#10621885C2211yescharacteristic
18C2×#10621883C2211yescharacteristic
19C2×#10621884C2211yescharacteristic
20C2×#10621882C2211yescharacteristic
21C4×Dic86C2211yescharacteristic
22C4×Dic86C2211yescharacteristic
23C4×D172C2211yescharacteristic
24C4×D172C2211yescharacteristic
25(C22⋊D43)⋊C4—21no—
26(C22⋊D43)⋊C4—21no—
27#13063283—21no—
28C2×C4⋊Dic43C2211yescharacteristic
29C4⋊C4×D43—21no—
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
48C4⋊Q8×C43C2211yescharacteristic
49#126×C43—21no—
50#124×C43—21no—
51#124×C43C2211yescharacteristic
52#123×C43—21no—
53C22⋊Q8×C43—21no—
54C22⋊Q8×C43C2211yescharacteristic
55#121×C43C2211yescharacteristic
56C4×Q8×C43C2211yescharacteristic
57C4×D4×C43C2211yescharacteristic
58#117×C43C2211yescharacteristic
59C2×Q8×C43—21no—
60C2×Q8×C43C2311yescharacteristic
61C2×D4×C43—21no—
62C2×D4×C43C2311yescharacteristic
63C22×C4×C43—21no—
64C22×C4×C43C2311yescharacteristic
65C2×C22⋊D43—21no—
66C22×Dic43—21no—
67#10621898—22no—
68#10621898—22no—
69C2×D172C2311yescharacteristic
70C2×C4×D43—21no—
71C2×C4×D43—21no—
72C2×C4×D43—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×C43—21no—
84C22⋊C4×C43—21no—
85C22⋊C4×C43—21no—
86C22⋊C4×C43D411yescharacteristic
87C22⋊C4×C43D411yescharacteristic
88C42×C43—21no—
89C42×C43C2311yescharacteristic
90C42×C43C2311yescharacteristic
91#10621885—22no—
92#10621884—22no—
93#10621883—22no—
94#10621882—22no—
95(C2×D43)⋊C4—21no—
96(C2×D43)⋊C4—21no—
97C4⋊Dic43—21no—
98C4⋊Dic43C2311yescharacteristic
99C4⋊Dic43C2311yescharacteristic
100Dic43⋊C4—21no—
101Dic43⋊C4—21no—
102C4×Dic43—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—21no—
113Q8×C43—81no—
114D4×C43—21no—
115D4×C43—21no—
116D4×C43—81no—
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×C43C2×D411yescharacteristic
124C2×C4×C43C2×D411yescharacteristic
125C2×C4×C43C2×D411yescharacteristic
126C2×C4×C43C2×D411yescharacteristic
127C2×C4×C43C2×D411yescharacteristic
128C2×C4×C43C2411yescharacteristic
129C22⋊D43—24no—
130C2×Dic43—21no—
131C2×Dic43—21no—
132C2×Dic43—21no—
133C2×Dic43—81no—
134D172—21no—
135D172#4112yes—
136C4×D43—24no—
137C4×D43—81no—
138C4×D43—81no—
139Dic86—21no—
140Dic86#4112yes—
141C43⋊C8—21no—
142C43⋊C8—21no—
143C43⋊C8—21no—
144C43⋊C8—21no—
145C22×C43—21no—
146C22×C43—21no—
147C22×C43—21no—
148C22×C43—41no—
149C22×C43—41no—
150C22×C43—41no—
151C22×C43C22×D411yescharacteristic
152C2×D43—22no—
153C2×D43—41no—
154C2×D43—41no—
155C4×C43—21no—
156C4×C43—21no—
157C4×C43—21no—
158C4×C43—21no—
159C4×C43—21no—
160C4×C43—41no—
161C4×C43—41no—
162C4×C43—41no—
163C4×C43C2×#4111yescharacteristic
164C4×C43C2×#4111yescharacteristic
165Dic43—22no—
166Dic43—41no—
167Dic43—41no—
168#3124—431nomaximal, Sylow
169C2×C43—41no—
170C2×C43—81no—
171C2×C43#52511yescharacteristic
172C2×C43#57611yescharacteristic
173C2×C43#57811yescharacteristic
174D43—42no—
175#542D4311yescharacteristic, complemented
176#520—431no—
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×#41—431no—
192C2×Q16—431no—
193C2×SD16—431no—
194C2×SD16—431no—
195C2×D8—431no—
196C4⋊Q8C2×D4311yescharacteristic
197#126—21no—
198#124—21no—
199#124C2×D4311yescharacteristic
200#123—21no—
201C22⋊Q8—21no—
202C22⋊Q8C2×D4311yescharacteristic
203#121C2×D4311yescharacteristic
204C4×Q8—431no—
205C4×Q8—431no—
206C4×Q8C2×D4311yescharacteristic
207C4×D4—431no—
208C4×D4—431no—
209C4×D4—861no—
210C4×D4—861no—
211C4×D4C2×D4311yescharacteristic
212#117—861no—
213#117C2×D4311yescharacteristic
214C2×C4⋊C4—431no—
215C2×C4⋊C4—861no—
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—862no—
235#41—862no—
236C2×Q8—21no—
237C2×Q8—431no—
238C2×Q8C22×D4311yescharacteristic
239C2×D4—21no—
240C2×D4—431no—
241C2×D4—861no—
242C2×D4C22×D4311yescharacteristic
243C22×C4—21no—
244C22×C4—861no—
245C22×C4—861no—
246C22×C4—861no—
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—21no—
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—861no—
275C22⋊C4—861no—
276C22⋊C4C22⋊D4311yescharacteristic
277C22⋊C4C22⋊D4311yescharacteristic
278C42—21no—
279C42—861no—
280C42—861no—
281C42C22×D4311yescharacteristic
282C42C22×D4311yescharacteristic
283C23—21no—
284C23—861no—
285C23C2×C22⋊D4311yescharacteristic
286Q8—21no—
287Q8—21no—
288Q8—81no—
289Q8—432no—
290Q8—861no—
291D4—21no—
292D4—21no—
293D4—81no—
294D4—432no—
295D4—864no—
296D4—861no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—81no—
303C2×C4—864no—
304C2×C4—861no—
305C2×C4—861no—
306C2×C4—861no—
307C2×C4—3441no—
308C2×C4—3441no—
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—21no—
322C22—21no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—862no—
327C22—1721no—
328C22—1721no—
329C22C22×C22⋊D4311yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—862no—
339C4—1721no—
340C4—1721no—
341C4#41×D4311yescharacteristic
342C4#41×D4311yescharacteristic
343C2—41no—
344C2—81no—
345C2—1722no—
346C2#1458340611yescharacteristic
347C2#1458370211yescharacteristic
348C2#1458371411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#542C2
socleC22×C43C22×D4
hypercenter#542D43
hypocenterC43#3124
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #14583379C2semidirect
2. #14583232C2semidirect
3. #14583210C2semidirect
4. #14583191C2semidirect
5. #14583176C2semidirect
6. #14583118C2semidirect
7. #14583111C2semidirect
8. #14583059C2semidirect
10. #14582999C2semidirect
11. #14582997C2semidirect
12. C4×#10621885C2semidirect
13. C4×#10621882C2semidirect
14. #14582960C2semidirect
15. C43×#542C2semidirect
175. #542D43semidirect
190. C43#3124semidirect