Finite Group Databasebeta

← #19146887

Subgroups — #19146887

Order 5504.

386 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583612C211yesmaximal, characteristic
2#14583562C211yesmaximal, characteristic, complemented
3#14583248C211yesmaximal, characteristic, complemented
4#14583243C211yesmaximal, characteristic, complemented
5#14583193C211yesmaximal, characteristic, complemented
6#14583147C211yesmaximal, characteristic, complemented
7#14583146C211yesmaximal, characteristic, complemented
8#14583103C211yesmaximal, characteristic, complemented
9#14583040C211yesmaximal, characteristic, complemented
10#14583039C211yesmaximal, characteristic, complemented
11#14582986C211yesmaximal, characteristic, complemented
12#14582974C211yesmaximal, characteristic, complemented
13#14582907C211yesmaximal, characteristic, complemented
14#14582906C211yesmaximal, characteristic, complemented
15C43×#485C211yesmaximal, characteristic, complemented
16C22×Dic86C2211yescharacteristic
17C2×Q8×D43C2211yescharacteristic
18C2×#10621873C2211yescharacteristic
19C2×#10621873C2211yescharacteristic
20C2×#10621884C2211yescharacteristic
21C2×#10621877C2211yescharacteristic
22C2×#10621872C2211yescharacteristic
23#13063324—21no—
24#13063324C2211yescharacteristic
25#13063323C2211yescharacteristic
26#13063313—21no—
27#13063311—21no—
28#13063305C2211yescharacteristic
29#13063303—21no—
30#13063302—21no—
31#13063300C2211yescharacteristic
32#13063299C2211yescharacteristic
33#13063298—21no—
34#13063290C2211yescharacteristic
35#13063287C2211yescharacteristic
36C4×C22⋊D43C2211yescharacteristic
37(C22⋊D43)⋊C4—21no—
38#13063283C2211yescharacteristic
39#13063282—21no—
40#13063258C2211yescharacteristic
41Dic43⋊C8C2211yescharacteristic
42#13063250C2211yescharacteristic
43#13063250C2211yescharacteristic
44#13063249C2211yescharacteristic
45#13063248C2211yescharacteristic
46#13063248C2211yescharacteristic
47#13063248C2211yescharacteristic
48#13063248C2211yescharacteristic
49#13063245C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51C8×Dic43C2211yescharacteristic
52C22⋊Q8×C43C2211yescharacteristic
53#117×C43C2211yescharacteristic
54#107×C43C2211yescharacteristic
55#106×C43C2211yescharacteristic
56#103×C43C2211yescharacteristic
57#103×C43C2211yescharacteristic
58C22⋊C8×C43C2211yescharacteristic
59C2×Q8×C43C2311yescharacteristic
60C22×C4×C43C2311yescharacteristic
61C2×C22⋊D43—21no—
62C2×C22⋊D43D411yescharacteristic
63C22×Dic43—21no—
64Q8×D43—22no—
65Q8×D43—41no—
66C2×D172—21no—
67C2×D172C2311yescharacteristic
68C2×C4×D43—21no—
69C2×C4×D43—21no—
70C2×C4×D43C2311yescharacteristic
71C2×Dic86—22no—
72C2×Dic86—21no—
73C2×Dic86—21no—
74C2×Dic86—21no—
75C2×Dic86—41no—
76C2×Dic86C2311yescharacteristic
77C2×Dic86C2311yescharacteristic
78C2×C8×C43C2311yescharacteristic
79C2×C8×C43C2311yescharacteristic
80C4⋊C4×C43—21no—
81C4⋊C4×C43C2311yescharacteristic
82C4⋊C4×C43C2311yescharacteristic
83C4⋊C4×C43C2311yescharacteristic
84C22⋊C4×C43—21no—
85C22⋊C4×C43—21no—
86C42×C43—21no—
87C22⋊Dic43D411yescharacteristic
88#10621884—41no—
89(C2×D43)⋊C4—21no—
90(C2×D43)⋊C4—21no—
91(C2×D43)⋊C4—21no—
92(C2×D43)⋊C4—21no—
93(C2×D43)⋊C4—21no—
94(C2×D43)⋊C4D411yescharacteristic
95C4⋊Dic43—21no—
96C4⋊Dic43C2311yescharacteristic
97Dic43⋊C4—21no—
98Dic43⋊C4—21no—
99Dic43⋊C4—21no—
100Dic43⋊C4—21no—
101Dic43⋊C4D411yescharacteristic
102C4×Dic43—21no—
103C4×Dic43—21no—
104C4×Dic43C2311yescharacteristic
105#10621877—41no—
106C2×C43⋊C8C2311yescharacteristic
107C2×C43⋊C8C2311yescharacteristic
108#10621873—22no—
109#10621873—41no—
110#10621872—41no—
111C23×C43C2×D411yescharacteristic
112C22×D43—21no—
113C22×D43C2×D411yescharacteristic
114Q8×C43—21no—
115Q8×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—21no—
122C2×C4×C43C2×D411yescharacteristic
123C2×C4×C43C2411yescharacteristic
124C22⋊D43—22no—
125C22⋊D43—81no—
126C2×Dic43—21no—
127C2×Dic43—21no—
128C2×Dic43—21no—
129C2×Dic43—42no—
130C2×Dic43C2×D411yescharacteristic
131C2×Dic43C2×D411yescharacteristic
132C2×Dic43C2×D411yescharacteristic
133D172—21no—
134D172—21no—
135D172—81no—
136C4×D43—21no—
137C4×D43—21no—
138C4×D43—42no—
139C4×D43—42no—
140Dic86—21no—
141Dic86—21no—
142Dic86—21no—
143Dic86—42no—
144Dic86—42no—
145Dic86—81no—
146Dic86#4112yes—
147C8×C43—21no—
148C8×C43—21no—
149C43⋊C8—21no—
150C43⋊C8—21no—
151C22×C43—21no—
152C22×C43—21no—
153C22×C43—21no—
154C22×C43C22×D411yescharacteristic
155C2×D43—21no—
156C2×D43—21no—
157C2×D43—21no—
158C2×D43—41no—
159C2×D43—41no—
160C2×D43—41no—
161C4×C43—21no—
162C4×C43—41no—
163C4×C43—41no—
164C4×C43—41no—
165C4×C43—41no—
166C4×C43C2×#4111yescharacteristic
167C4×C43H(5,𝔽2)11yescharacteristic
168Dic43—22no—
169Dic43—21no—
170Dic43—21no—
171Dic43—41no—
172Dic43—41no—
173Dic43#13712yes—
174#3329—431nomaximal, Sylow
175C2×C43—41no—
176C2×C43#54611yescharacteristic
177C2×C43C2×#13711yescharacteristic
178C2×C43#57711yescharacteristic
179D43—41no—
180D43—81no—
181#555—431no—
182D4×Q8—431no—
183#487—431no—
184#485—431no—
185#485D4311yescharacteristic, complemented
186#477—431no—
187#468—431no—
188#468—431no—
189#461—431no—
190#448—431no—
191#448—431no—
192C4×SD16—431no—
193#436—431no—
194#419—431no—
195#419—431no—
196C43#332911yescharacteristic, complemented, Sylow
197C22×Q8—431no—
198C22×Q8—431no—
199C2×SD16—431no—
200C2×SD16—431no—
201C2×SD16—431no—
202C2×M16—431no—
203C2×M16—431no—
204C4⋊Q8—431no—
205C4⋊Q8—431no—
206C4⋊Q8—861no—
207#124—861no—
208#124—861no—
209C22⋊Q8—431no—
210C22⋊Q8—861no—
211C22⋊Q8—861no—
212C22⋊Q8C2×D4311yescharacteristic
213#121—431no—
214#121—431no—
215#121—861no—
216C4×Q8—431no—
217C4×D4—431no—
218C4×D4—431no—
219C4×D4—861no—
220#117—431no—
221#117—861no—
222#117C2×D4311yescharacteristic
223#107—431no—
224#107C2×D4311yescharacteristic
225#106C2×D4311yescharacteristic
226C4⋊C8—431no—
227#103—431no—
228#103—431no—
229#103—431no—
230#103—431no—
231#103—431no—
232#103—431no—
233#103—431no—
234#103C2×D4311yescharacteristic
235#103C2×D4311yescharacteristic
236#102—431no—
237C22⋊C8—431no—
238C22⋊C8C2×D4311yescharacteristic
239C4×C8—431no—
240C2×Q8—431no—
241C2×Q8—431no—
242C2×Q8—861no—
243C2×Q8—861no—
244C2×Q8—862no—
245C2×Q8—861no—
246C2×Q8—862no—
247C2×Q8—1721no—
248C2×Q8—1721no—
249C2×Q8C22×D4311yescharacteristic
250C2×D4—431no—
251C2×D4—431no—
252C2×D4—861no—
253C2×D4—861no—
254C22×C4—431no—
255C22×C4—861no—
256C22×C4—861no—
257C22×C4—861no—
258C22×C4C22×D4311yescharacteristic
259SD16—862no—
260SD16—1721no—
261SD16—1721no—
262M16—1721no—
263M16—1721no—
264C2×C8—431no—
265C2×C8—431no—
266C2×C8C22×D4311yescharacteristic
267C2×C8C22×D4311yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—431no—
270C4⋊C4—431no—
271C4⋊C4—861no—
272C4⋊C4—861no—
273C4⋊C4—861no—
274C4⋊C4—861no—
275C4⋊C4—861no—
276C4⋊C4C22×D4311yescharacteristic
277C4⋊C4C22×D4311yescharacteristic
278C4⋊C4C22×D4311yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—431no—
282C22⋊C4—431no—
283C22⋊C4—861no—
284C22⋊C4—861no—
285C22⋊C4—861no—
286C22⋊C4—861no—
287C22⋊C4—861no—
288C42—21no—
289C42—431no—
290C42—861no—
291C42—861no—
292C23—431no—
293C23—861no—
294C23D4×D4311yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—432no—
298Q8—861no—
299Q8—861no—
300Q8—861no—
301Q8—3441no—
302Q8—1722no—
303Q8—1722no—
304D4—862no—
305D4—861no—
306D4—861no—
307D4—3441no—
308D4—3441no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—431no—
316C2×C4—431no—
317C2×C4—431no—
318C2×C4—861no—
319C2×C4—861no—
320C2×C4—861no—
321C2×C4—861no—
322C2×C4—861no—
323C2×C4—1722no—
324C2×C4—1722no—
325C2×C4—1722no—
326C2×C4D4×D4311yescharacteristic
327C2×C4C23×D4311yescharacteristic
328C8—21no—
329C8—21no—
330C8—861no—
331C8—861no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—861no—
336C22—861no—
337C22—861no—
338C22—1721no—
339C22—1721no—
340C22—1721no—
341C22C2×D4×D4311yescharacteristic
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—432no—
348C4—861no—
349C4—861no—
350C4—862no—
351C4—1721no—
352C4—1721no—
353C4#41×D4311yescharacteristic
354C4#1306337111yescharacteristic
355C2—41no—
356C2—3441no—
357C2—1721no—
358C2#1458354111yescharacteristic
359C2#137×D4311yescharacteristic
360C2#1458370611yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#485C2
socleC22×C43C22×D4
hypercenter#485D43
hypocenterC43#3329
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
2. #14583562C2semidirect
3. #14583248C2semidirect
4. #14583243C2semidirect
5. #14583193C2semidirect
6. #14583147C2semidirect
7. #14583146C2semidirect
8. #14583103C2semidirect
9. #14583040C2semidirect
10. #14583039C2semidirect
11. #14582986C2semidirect
12. #14582974C2semidirect
13. #14582907C2semidirect
14. #14582906C2semidirect
15. C43×#485C2semidirect
185. #485D43semidirect
196. C43#3329semidirect