Finite Group Databasebeta

← #19146111

Subgroups — #19146111

Order 5504.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063354C211yesmaximal, characteristic, complemented
2C2×SD16×D43C211yesmaximal, characteristic, complemented
3#14583564C211yesmaximal, characteristic, complemented
4#14583544C211yesmaximal, characteristic
5#14583291C211yesmaximal, characteristic, complemented
6#14583148C211yesmaximal, characteristic, complemented
7#14583139C211yesmaximal, characteristic, complemented
8#14583122C211yesmaximal, characteristic, complemented
9#14583058C211yesmaximal, characteristic, complemented
10#14583056C211yesmaximal, characteristic, complemented
11#14583048C211yesmaximal, characteristic, complemented
12#14583039C211yesmaximal, characteristic, complemented
13#14582999C211yesmaximal, characteristic, complemented
14#14582969C211yesmaximal, characteristic, complemented
15C43×#461C211yesmaximal, characteristic, complemented
16C2×#10621900C2211yescharacteristic
17C2×Q8×D43C2211yescharacteristic
18C2×Q8×D43C2211yescharacteristic, complemented
19C2×D4×D43C2211yescharacteristic
20#13063354—24no—
21C2×Dic172C2211yescharacteristic, complemented
22C2×#10621885C2211yescharacteristic, complemented
23C2×#10621885C2211yescharacteristic, complemented
24C2×#10621873C2211yescharacteristic
25C2×#10621883C2211yescharacteristic
26C2×#10621884C2211yescharacteristic
27C2×#10621884C2211yescharacteristic
28SD16×D43—24no—
29C2×#10621872C2211yescharacteristic, complemented
30C2×C8×D43C2211yescharacteristic
31#13063324—21no—
32#13063313C2211yescharacteristic
33#13063309—21no—
34#13063305C2211yescharacteristic
35#13063303—21no—
36#13063303—21no—
37#13063301C2211yescharacteristic
38#13063301C2211yescharacteristic, complemented
39#13063300C2211yescharacteristic
40#13063299—21no—
41#13063295—21no—
42C4×Dic86C2211yescharacteristic, complemented
43C4×D172C2211yescharacteristic
44#13063287—21no—
45C2×(C2×D43)⋊C4—21no—
46#13063258C2211yescharacteristic, complemented
47#13063250C2211yescharacteristic, complemented
48#13063248C2211yescharacteristic, complemented
49#13063247C2211yescharacteristic
50#13063246C2211yescharacteristic
51(C2×D43)⋊C8C2211yescharacteristic
52(C2×D43)⋊C8C2211yescharacteristic, complemented
53#13063236C2211yescharacteristic, complemented
54C2×SD16×C43C2211yescharacteristic
55C2×SD16×C43C2211yescharacteristic
56C4⋊Q8×C43C2211yescharacteristic, complemented
57C4×D4×C43C2211yescharacteristic
58C4⋊C8×C43C2211yescharacteristic, complemented
59#103×C43C2211yescharacteristic, complemented
60#103×C43C2211yescharacteristic, complemented
61C23×D43—21no—
62C2×Q8×C43C2311yescharacteristic
63C2×Q8×C43C2311yescharacteristic
64C2×D4×C43C2311yescharacteristic
65C22×C4×C43—21no—
66C2×C22⋊D43—21no—
67C2×C22⋊D43—21no—
68C22×Dic43—21no—
69Q8×D43—22no—
70Q8×D43—22no—
71Q8×D43—41no—
72Q8×D43—41no—
73#10621900—22no—
74#10621900—41no—
75D4×D43—22no—
76D4×D43—41no—
77C2×D172—21no—
78C2×D172D411yescharacteristic
79C2×D172C2311yescharacteristic
80C2×C4×D43—21no—
81C2×C4×D43—21no—
82C2×C4×D43C2311yescharacteristic
83C2×C4×D43C2311yescharacteristic
84C2×Dic86—21no—
85C2×Dic86—21no—
86C2×Dic86C2311yescharacteristic
87C2×Dic86C2311yescharacteristic
88SD16×C43—22no—
89SD16×C43—22no—
90C2×C8×C43C2311yescharacteristic
91C2×C8×C43C2311yescharacteristic
92C4⋊C4×C43—21no—
93C4⋊C4×C43—21no—
94C4⋊C4×C43C2311yescharacteristic
95C22⋊C4×C43—21no—
96C42×C43C2311yescharacteristic
97#10621885—22no—
98#10621885—41no—
99#10621884—22no—
100#10621884—41no—
101#10621883D414yescomplemented
102(C2×D43)⋊C4—21no—
103(C2×D43)⋊C4—21no—
104(C2×D43)⋊C4—21no—
105(C2×D43)⋊C4—21no—
106(C2×D43)⋊C4—21no—
107(C2×D43)⋊C4—21no—
108(C2×D43)⋊C4D411yescharacteristic
109(C2×D43)⋊C4D411yescharacteristic
110C4⋊Dic43—21no—
111C4⋊Dic43D411yescharacteristic
112C4⋊Dic43C2311yescharacteristic
113Dic43⋊C4—21no—
114Dic43⋊C4—21no—
115Dic43⋊C4—21no—
116C4×Dic43—21no—
117C2×C43⋊C8C2311yescharacteristic
118C2×C43⋊C8C2311yescharacteristic
119Dic172—22no—
120#10621873—22no—
121#10621872—22no—
122C8×D43—22no—
123C23×C43—21no—
124C22×D43—21no—
125C22×D43—42no—
126C22×D43—42no—
127C22×D43—81no—
128C22×D43C2×D411yescharacteristic
129C22×D43C2×D411yescharacteristic
130Q8×C43—21no—
131Q8×C43—21no—
132Q8×C43—21no—
133Q8×C43—21no—
134D4×C43—21no—
135D4×C43C2×D412yes—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
138C2×C4×C43—21no—
139C2×C4×C43—81no—
140C2×C4×C43C2×D411yescharacteristic
141C2×C4×C43C2×D411yescharacteristic
142C2×C4×C43C2411yescharacteristic
143C22⋊D43—42no—
144C22⋊D43—42no—
145C2×Dic43—21no—
146C2×Dic43—21no—
147C2×Dic43—21no—
148C2×Dic43—42no—
149C2×Dic43C2×D411yescharacteristic
150C2×Dic43C2×D411yescharacteristic
151D172—22no—
152D172—21no—
153D172—21no—
154D172—81no—
155C4×D43—21no—
156C4×D43—21no—
157C4×D43—21no—
158C4×D43—21no—
159C4×D43—42no—
160C4×D43—42no—
161Dic86—21no—
162Dic86—21no—
163Dic86—21no—
164Dic86—42no—
165Dic86—42no—
166Dic86C2×D412yes—
167C8×C43—21no—
168C8×C43—21no—
169C43⋊C8—21no—
170C43⋊C8C2×D412yes—
171C22×C43—22no—
172C22×C43—41no—
173C22×C43—41no—
174C22×C43C22×D411yescharacteristic
175C2×D43—21no—
176C2×D43—21no—
177C2×D43—21no—
178C2×D43—21no—
179C2×D43—21no—
180C2×D43—41no—
181C2×D43—41no—
182C2×D43—41no—
183C2×D43—84no—
184C2×D43#13712yescomplemented
185C4×C43—21no—
186C4×C43—21no—
187C4×C43—41no—
188C4×C43—41no—
189C4×C43—41no—
190C4×C43C22×D411yescharacteristic
191C4×C43H(5,𝔽2)11yescharacteristic
192Dic43—22no—
193Dic43—21no—
194Dic43—21no—
195Dic43—41no—
196Dic43—41no—
197#3266—431nomaximal, Sylow
198C2×C43—42no—
199C2×C43D4211yescharacteristic
200C2×C43C2×#13711yescharacteristic
201C2×C43#57711yescharacteristic
202D43—22no—
203D43—41no—
204D43—81no—
205C2×#137—431no—
206C22×SD16—431no—
207D4×Q8—431no—
208#546—431no—
209#497—431no—
210#468—431no—
211#467—431no—
212#464—431no—
213#461D4311yescharacteristic, complemented
214#452—431no—
215#451—431no—
216#450—431no—
217#448—431no—
218#440—431no—
219#435—431no—
220C43#326611yescharacteristic, complemented, Sylow
221C2×#41—431no—
222C22×Q8—431no—
223C22×Q8—431no—
224C22×D4—431no—
225#137—864no—
226C2×Q16—431no—
227C2×Q16—431no—
228C2×Q16—431no—
229C2×SD16—431no—
230C2×SD16—431no—
231C2×SD16—431no—
232C2×SD16—431no—
233C2×SD16—864no—
234C2×SD16C2×D4311yescharacteristic
235C2×SD16C2×D4311yescharacteristic
236C2×M16—431no—
237C22×C8—431no—
238C4⋊Q8—861no—
239C4⋊Q8C2×D4311yescharacteristic, complemented
240#124—431no—
241#123—861no—
242C22⋊Q8—431no—
243C22⋊Q8—431no—
244C22⋊Q8—431no—
245C22⋊Q8—861no—
246C22⋊Q8—861no—
247#121—431no—
248#121—861no—
249#120—861no—
250C4×Q8—431no—
251C4×D4—431no—
252C4×D4—861no—
253C4×D4C2×D4311yescharacteristic
254C2×C22⋊C4—861no—
255#107—431no—
256C4⋊C8C2×D4311yescharacteristic, complemented
257#103—431no—
258#103—431no—
259#103C2×D4311yescharacteristic, complemented
260#103C2×D4311yescharacteristic, complemented
261#102—431no—
262#102—431no—
263C22⋊C8—431no—
264C22⋊C8—431no—
265#97—431no—
266C24—861no—
267#41—862no—
268#41—1721no—
269C2×Q8—431no—
270C2×Q8—431no—
271C2×Q8—861no—
272C2×Q8—861no—
273C2×Q8—862no—
274C2×Q8—862no—
275C2×Q8—1721no—
276C2×Q8—1721no—
277C2×Q8C22×D4311yescharacteristic
278C2×Q8C22×D4311yescharacteristic
279C2×D4—431no—
280C2×D4—431no—
281C2×D4—861no—
282C2×D4—861no—
283C2×D4—862no—
284C2×D4—861no—
285C2×D4—1721no—
286C2×D4C22×D4311yescharacteristic
287C22×C4—21no—
288C22×C4—431no—
289C22×C4—431no—
290C22×C4—861no—
291C22×C4—861no—
292C22×C4—861no—
293Q16—862no—
294Q16—862no—
295Q16—1721no—
296SD16—22no—
297SD16—22no—
298SD16—434no—
299SD16—862no—
300SD16—862no—
301SD16—1721no—
302M16—862no—
303C2×C8—431no—
304C2×C8—431no—
305C2×C8—862no—
306C2×C8C22×D4311yescharacteristic
307C2×C8C22×D4311yescharacteristic
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—431no—
311C4⋊C4—431no—
312C4⋊C4—861no—
313C4⋊C4—861no—
314C4⋊C4—861no—
315C4⋊C4—861no—
316C4⋊C4C22×D4311yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—431no—
319C22⋊C4—431no—
320C22⋊C4—861no—
321C22⋊C4—861no—
322C22⋊C4—861no—
323C22⋊C4—861no—
324C22⋊C4—861no—
325C22⋊C4—861no—
326C42—861no—
327C42C22×D4311yescharacteristic
328C23—21no—
329C23—431no—
330C23—431no—
331C23—861no—
332C23—3441no—
333C23—1722no—
334C23—1722no—
335Q8—21no—
336Q8—21no—
337Q8—21no—
338Q8—21no—
339Q8—432no—
340Q8—861no—
341Q8—861no—
342Q8—861no—
343Q8—1722no—
344Q8—1722no—
345D4—21no—
346D4—862no—
347D4—861no—
348D4—861no—
349D4—3441no—
350D4—1722no—
351D4—1722no—
352D4D4×D4312yes—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—81no—
357C2×C4—431no—
358C2×C4—431no—
359C2×C4—861no—
360C2×C4—861no—
361C2×C4—861no—
362C2×C4—861no—
363C2×C4—861no—
364C2×C4—861no—
365C2×C4—861no—
366C2×C4—1722no—
367C2×C4—1722no—
368C2×C4—1722no—
369C2×C4D4×D4311yescharacteristic
370C2×C4D4×D4311yescharacteristic
371C2×C4C23×D4311yescharacteristic
372C8—21no—
373C8—21no—
374C8—432no—
375C8—861no—
376C22—22no—
377C22—41no—
378C22—41no—
379C22—432no—
380C22—861no—
381C22—861no—
382C22—861no—
383C22—861no—
384C22—861no—
385C22—3444no—
386C22—1721no—
387C22—1721no—
388C22—1721no—
389C22C2×D4×D4311yescharacteristic
390C4—21no—
391C4—21no—
392C4—41no—
393C4—41no—
394C4—41no—
395C4—861no—
396C4—861no—
397C4—862no—
398C4—1721no—
399C4—1721no—
400C4C2×D4×D4311yescharacteristic
401C4#1306337111yescharacteristic
402C2—42no—
403C2—862no—
404C2—3441no—
405C2—1721no—
406C2#1458353311yescharacteristic
407C2#137×D4311yescharacteristic
408C2#1458370511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#461C2
socleC22×C43C22×D4
hypercenter#461D43
hypocenterC43#3266
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. C2×#13063354C2semidirect
2. C2×SD16×D43C2semidirect
3. #14583564C2semidirect
5. #14583291C2semidirect
6. #14583148C2semidirect
7. #14583139C2semidirect
8. #14583122C2semidirect
9. #14583058C2semidirect
10. #14583056C2semidirect
11. #14583048C2semidirect
12. #14583039C2semidirect
13. #14582999C2semidirect
14. #14582969C2semidirect
15. C43×#461C2semidirect
18. C2×Q8×D43C22semidirect
21. C2×Dic172C22semidirect
22. C2×#10621885C22semidirect
23. C2×#10621885C22semidirect
29. C2×#10621872C22semidirect
38. #13063301C22semidirect
42. C4×Dic86C22semidirect
46. #13063258C22semidirect
47. #13063250C22semidirect
48. #13063248C22semidirect
52. (C2×D43)⋊C8C22semidirect
53. #13063236C22semidirect
56. C4⋊Q8×C43C22semidirect
58. C4⋊C8×C43C22semidirect
59. #103×C43C22semidirect
60. #103×C43C22semidirect
101. #10621883D4semidirect
184. C2×D43#137semidirect
213. #461D43semidirect
220. C43#3266semidirect
239. C4⋊Q8C2×D43semidirect
256. C4⋊C8C2×D43semidirect
259. #103C2×D43semidirect
260. #103C2×D43semidirect