Finite Group Databasebeta

← #19147089

Subgroups — #19147089

Order 5504.

360 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583614C211yesmaximal, characteristic, complemented
2#14583309C211yesmaximal, characteristic, complemented
3#14583223C211yesmaximal, characteristic, complemented
4#14583220C211yesmaximal, characteristic, complemented
5#14583220C211yesmaximal, characteristic, complemented
6#14583212C211yesmaximal, characteristic, complemented
7#14583196C211yesmaximal, characteristic, complemented
8#14583179C211yesmaximal, characteristic, complemented
9#14583150C211yesmaximal, characteristic, complemented
10#14583133C211yesmaximal, characteristic, complemented
11#14583009C211yesmaximal, characteristic, complemented
12#14582971C211yesmaximal, characteristic, complemented
13#14582939C211yesmaximal, characteristic, complemented
14#14582935C211yesmaximal, characteristic, complemented
15C43×#553C211yesmaximal, characteristic, complemented
16C2×#10621882C2211yescharacteristic
17C2×#10621877C2211yescharacteristic
18C22×C43⋊C8C2211yescharacteristic
19#13063325C2211yescharacteristic
20#13063311—21no—
21#13063311—21no—
22#13063299C2211yescharacteristic
23#13063299C2211yescharacteristic
24#13063296—21no—
25C4×D172C2211yescharacteristic
26#13063284C2211yescharacteristic
27#13063284C2211yescharacteristic
28#13063283—21no—
29#13063258C2211yescharacteristic
30#13063258C2211yescharacteristic
31#13063258C2211yescharacteristic
32#13063258C2211yescharacteristic
33#13063258C2211yescharacteristic
34#13063256C2211yescharacteristic
35#13063256C2211yescharacteristic
36#13063256C2211yescharacteristic
37#13063256C2211yescharacteristic
38C4⋊(C43⋊C8)C2211yescharacteristic
39#13063246C2211yescharacteristic
40#13063246C2211yescharacteristic
41#13063246C2211yescharacteristic
42#13063245C2211yescharacteristic
43#13063245C2211yescharacteristic
44#13063245C2211yescharacteristic
45C22⋊(C43⋊C8)C2211yescharacteristic
46C22⋊(C43⋊C8)C2211yescharacteristic
47#13063236C2211yescharacteristic
48#126×C43—21no—
49#125×C43C2211yescharacteristic
50#123×C43—21no—
51#121×C43—21no—
52#121×C43C2211yescharacteristic
53#121×C43C2211yescharacteristic
54C4×D4×C43—21no—
55C4×D4×C43C2211yescharacteristic
56C4×D4×C43C2211yescharacteristic
57#117×C43C2211yescharacteristic
58C2×C4⋊C4×C43C2211yescharacteristic
59C2×D4×C43—21no—
60C2×D4×C43—21no—
61C2×D4×C43D411yescharacteristic
62C2×D4×C43C2311yescharacteristic
63C22×C4×C43—21no—
64C22×C4×C43—21no—
65C22×C4×C43C2311yescharacteristic
66C22×C4×C43C2311yescharacteristic
67C2×C22⋊D43—21no—
68C2×C22⋊D43—21no—
69C2×D172C2311yescharacteristic
70C2×C4×D43—21no—
71C2×Dic86—21no—
72C4⋊C4×C43—21no—
73C4⋊C4×C43—21no—
74C4⋊C4×C43—21no—
75C4⋊C4×C43D411yescharacteristic
76C4⋊C4×C43C2311yescharacteristic
77C4⋊C4×C43C2311yescharacteristic
78C4⋊C4×C43C2311yescharacteristic
79C22⋊C4×C43—21no—
80C22⋊C4×C43—21no—
81C22⋊C4×C43—21no—
82C22⋊C4×C43—21no—
83C22⋊C4×C43D411yescharacteristic
84C22⋊C4×C43D411yescharacteristic
85C42×C43—21no—
86C42×C43C2311yescharacteristic
87C22⋊Dic43—21no—
88C22⋊Dic43—21no—
89#10621882—22no—
90(C2×D43)⋊C4—21no—
91(C2×D43)⋊C4—21no—
92(C2×D43)⋊C4—21no—
93C4⋊Dic43—21no—
94C4⋊Dic43C2311yescharacteristic
95C4⋊Dic43C2311yescharacteristic
96C4⋊Dic43C2311yescharacteristic
97C4×Dic43—21no—
98C4×Dic43—21no—
99#10621877—22no—
100C2×C43⋊C8—22no—
101C2×C43⋊C8C2311yescharacteristic
102C2×C43⋊C8C2311yescharacteristic
103C2×C43⋊C8C2311yescharacteristic
104C2×C43⋊C8C2311yescharacteristic
105C23×C43—21no—
106C23×C43C2×D411yescharacteristic
107C23×C43C2×D411yescharacteristic
108C22×D43—21no—
109D4×C43—21no—
110D4×C43—21no—
111D4×C43—41no—
112D4×C43—42no—
113D4×C43—81no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—81no—
122C2×C4×C43—81no—
123C2×C4×C43C2×D411yescharacteristic
124C2×C4×C43C2×D411yescharacteristic
125C2×C4×C43C2×D411yescharacteristic
126C2×C4×C43C2×D411yescharacteristic
127C2×C4×C43C2411yescharacteristic
128C22⋊D43—81no—
129C22⋊D43—81no—
130C2×Dic43—21no—
131C2×Dic43—21no—
132C2×Dic43—21no—
133D172—21no—
134D172—21no—
135C4×D43—42no—
136Dic86—81no—
137C43⋊C8—21no—
138C43⋊C8—21no—
139C43⋊C8—21no—
140C43⋊C8#4112yes—
141C22×C43—21no—
142C22×C43—21no—
143C22×C43—21no—
144C22×C43—21no—
145C22×C43—21no—
146C22×C43—21no—
147C22×C43—41no—
148C22×C43—41no—
149C22×C43—41no—
150C22×C43C22×D411yescharacteristic
151C2×D43—41no—
152C2×D43—41no—
153C2×D43—41no—
154C4×C43—21no—
155C4×C43—21no—
156C4×C43—21no—
157C4×C43—21no—
158C4×C43—41no—
159C4×C43—41no—
160C4×C43—41no—
161C4×C43C2×#4111yescharacteristic
162C4×C432−1+411yescharacteristic
163Dic43—41no—
164Dic43—41no—
165Dic43—41no—
166#3347—431nomaximal, Sylow
167C2×C43—41no—
168C2×C43—41no—
169C2×C43—81no—
170C2×C43#54711yescharacteristic
171C2×C43#57511yescharacteristic
172C2×C43#57611yescharacteristic
173D43—81no—
174#555—431no—
175#553D4311yescharacteristic, complemented
176#501—431no—
177#482—431no—
178#482—431no—
179#482—431no—
180#480—431no—
181#478—431no—
182#474—431no—
183#469—431no—
184#466—431no—
185#442—431no—
186#435—431no—
187#428—431no—
188#427—431no—
189C43#334711yescharacteristic, complemented, Sylow
190C2×D8—431no—
191C2×M16—431no—
192C22×C8—431no—
193C4⋊Q8—431no—
194#126—21no—
195#125C2×D4311yescharacteristic
196#124—861no—
197#124—861no—
198#123—21no—
199#121—21no—
200#121—431no—
201#121—431no—
202#121—861no—
203#121C2×D4311yescharacteristic
204#121C2×D4311yescharacteristic
205C4×D4—21no—
206C4×D4—431no—
207C4×D4C2×D4311yescharacteristic
208C4×D4C2×D4311yescharacteristic
209#117—431no—
210#117—431no—
211#117—861no—
212#117C2×D4311yescharacteristic
213C2×C4⋊C4C2×D4311yescharacteristic
214#107—431no—
215#107—431no—
216#107—431no—
217#107—431no—
218#107—431no—
219#106—431no—
220#106—431no—
221#106—431no—
222#106—431no—
223C4⋊C8—431no—
224#102—431no—
225#102—431no—
226#102—431no—
227#102—431no—
228#102—431no—
229#102—431no—
230C22⋊C8—431no—
231C22⋊C8—431no—
232#97—431no—
233C2×Q8—861no—
234C2×D4—21no—
235C2×D4—21no—
236C2×D4—431no—
237C2×D4—861no—
238C2×D4—861no—
239C2×D4C22⋊D4311yescharacteristic
240C2×D4C22×D4311yescharacteristic
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—861no—
244C22×C4C22×D4311yescharacteristic
245C22×C4C22×D4311yescharacteristic
246D8—862no—
247M16—862no—
248C2×C8—431no—
249C2×C8—431no—
250C2×C8—431no—
251C2×C8—431no—
252C2×C8—862no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—431no—
257C4⋊C4—431no—
258C4⋊C4—431no—
259C4⋊C4—861no—
260C4⋊C4C22⋊D4311yescharacteristic
261C4⋊C4C22×D4311yescharacteristic
262C4⋊C4C22×D4311yescharacteristic
263C4⋊C4C22×D4311yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—861no—
269C22⋊C4—861no—
270C22⋊C4—861no—
271C22⋊C4—861no—
272C22⋊C4—861no—
273C22⋊C4C22⋊D4311yescharacteristic
274C22⋊C4C22⋊D4311yescharacteristic
275C42—21no—
276C42—861no—
277C42—861no—
278C42C22×D4311yescharacteristic
279C23—21no—
280C23—861no—
281C23C2×C22⋊D4311yescharacteristic
282C23C2×C22⋊D4311yescharacteristic
283Q8—3441no—
284D4—21no—
285D4—21no—
286D4—41no—
287D4—42no—
288D4—81no—
289D4—861no—
290D4—861no—
291D4—3441no—
292D4—3441no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—861no—
303C2×C4—861no—
304C2×C4—861no—
305C2×C4—1722no—
306C2×C4C2×C22⋊D4311yescharacteristic
307C2×C4C2×C22⋊D4311yescharacteristic
308C2×C4C2×C22⋊D4311yescharacteristic
309C2×C4C2×C22⋊D4311yescharacteristic
310C2×C4C23×D4311yescharacteristic
311C8—432no—
312C8—861no—
313C8—861no—
314C8—861no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—1721no—
325C22—1721no—
326C22—1721no—
327C22C22×C22⋊D4311yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—1721no—
336C4—1721no—
337C4—1721no—
338C4#41×D4311yescharacteristic
339C4#1306337211yescharacteristic
340C2—41no—
341C2—41no—
342C2—81no—
343C2—3441no—
344C2#1458354811yescharacteristic
345C2#1458369711yescharacteristic
346C2#1458370211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#553C2
socleC22×C43C22×D4
hypercenter#553D43
hypocenterC43#3347
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #14583614C2semidirect
2. #14583309C2semidirect
3. #14583223C2semidirect
4. #14583220C2semidirect
5. #14583220C2semidirect
6. #14583212C2semidirect
7. #14583196C2semidirect
8. #14583179C2semidirect
9. #14583150C2semidirect
10. #14583133C2semidirect
11. #14583009C2semidirect
12. #14582971C2semidirect
13. #14582939C2semidirect
14. #14582935C2semidirect
15. C43×#553C2semidirect
175. #553D43semidirect
189. C43#3347semidirect