Finite Group Databasebeta

← #19146296

Subgroups — #19146296

Order 5504.

504 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D43C211yesmaximal, characteristic, complemented
2#14583556C211yesmaximal, characteristic, complemented
3#14583537C211yesmaximal, characteristic, complemented
4#14583280C211yesmaximal, characteristic, complemented
5#14583128C211yesmaximal, characteristic, complemented
6#14583125C211yesmaximal, characteristic, complemented
7#14583123C211yesmaximal, characteristic, complemented
8#14583112C211yesmaximal, characteristic, complemented
9#14583061C211yesmaximal, characteristic, complemented
10#14583053C211yesmaximal, characteristic, complemented
11#14583044C211yesmaximal, characteristic, complemented
12#14583031C211yesmaximal, characteristic, complemented
13SD16×Dic43C211yesmaximal, characteristic, complemented
14C8×C22⋊D43C211yesmaximal, characteristic, complemented
15C2×#135×C43C211yesmaximal, characteristic, complemented
16C2×Q8×D43C2211yescharacteristic
17C2×D4×D43C2211yescharacteristic
18C2×#10621885C2211yescharacteristic, complemented
19C2×#10621873C2211yescharacteristic
20C2×#10621883C2211yescharacteristic
21C2×#10621884C2211yescharacteristic
22SD16×D43—24no—
23C2×#10621882C2211yescharacteristic
24C2×C8×D43C2211yescharacteristic
25#13063314C2211yescharacteristic
26#13063312—21no—
27#13063312C2211yescharacteristic, complemented
28#13063308—21no—
29#13063304—21no—
30#13063304C2211yescharacteristic, complemented
31#13063301C2211yescharacteristic
32#13063299C2211yescharacteristic
33#13063297—21no—
34#13063296—21no—
35#13063296C2211yescharacteristic
36#13063293—21no—
37Q8×Dic43C2211yescharacteristic, complemented
38D4×Dic43C2211yescharacteristic
39C4×C22⋊D43—21no—
40C4×C22⋊D43C2211yescharacteristic
41C2×(C2×D43)⋊C4—21no—
42#13063257C2211yescharacteristic, complemented
43Dic43⋊C8C2211yescharacteristic, complemented
44#13063250C2211yescharacteristic, complemented
45#13063249C2211yescharacteristic, complemented
46#13063249C2211yescharacteristic, complemented
47#13063247C2211yescharacteristic
48#13063246C2211yescharacteristic
49#13063246C2211yescharacteristic, complemented
50C22⋊(C43⋊C8)C2211yescharacteristic, complemented
51(C2×D43)⋊C8C2211yescharacteristic
52C8×Dic43C2211yescharacteristic, complemented
53C2×#41×C43C2211yescharacteristic
54C2×#41×C43C2211yescharacteristic, complemented
55#135×C43—24no—
56C2×Q16×C43C2211yescharacteristic, complemented
57C2×SD16×C43C2211yescharacteristic
58C2×SD16×C43C2211yescharacteristic, complemented
59C2×D8×C43C2211yescharacteristic
60C22×C8×C43C2211yescharacteristic, complemented
61C23×D43—21no—
62#41×C43—22no—
63#41×C43—22no—
64#41×C43—41no—
65#41×C43—41no—
66C2×Q8×C43C2311yescharacteristic
67C2×Q8×C43C2311yescharacteristic
68C2×D4×C43—21no—
69C2×D4×C43—21no—
70C2×D4×C43C2311yescharacteristic
71C2×D4×C43C2311yescharacteristic
72C22×C4×C43—21no—
73C22×C4×C43—21no—
74C22×C4×C43C2311yescharacteristic
75C2×C22⋊D43—21no—
76C2×C22⋊D43—21no—
77C2×C22⋊D43—21no—
78C2×C22⋊D43D411yescharacteristic
79C22×Dic43—21no—
80Q8×D43—22no—
81Q8×D43—41no—
82D4×D43—22no—
83D4×D43—41no—
84C2×D172C2311yescharacteristic
85C2×C4×D43—21no—
86C2×C4×D43C2311yescharacteristic
87C2×Dic86—21no—
88C2×Dic86C2311yescharacteristic
89Q16×C43—22no—
90SD16×C43—22no—
91SD16×C43D414yescomplemented
92D8×C43—22no—
93C2×C8×C43—22no—
94C2×C8×C43C2311yescharacteristic
95C2×C8×C43C2311yescharacteristic
96C22⋊Dic43—21no—
97C22⋊Dic43—21no—
98C22⋊Dic43—21no—
99C22⋊Dic43—21no—
100C22⋊Dic43—21no—
101C22⋊Dic43D411yescharacteristic
102#10621885—41no—
103#10621884—22no—
104#10621883—22no—
105#10621882—41no—
106(C2×D43)⋊C4—21no—
107(C2×D43)⋊C4—21no—
108(C2×D43)⋊C4—21no—
109(C2×D43)⋊C4—21no—
110(C2×D43)⋊C4D411yescharacteristic
111C4⋊Dic43—21no—
112C4⋊Dic43C2311yescharacteristic
113C4⋊Dic43C2311yescharacteristic
114Dic43⋊C4—21no—
115Dic43⋊C4—21no—
116Dic43⋊C4D411yescharacteristic
117C4×Dic43—21no—
118C4×Dic43C2311yescharacteristic
119C2×C43⋊C8C2311yescharacteristic
120C2×C43⋊C8C2311yescharacteristic
121#10621873—22no—
122C8×D43—22no—
123C23×C43—21no—
124C23×C43—21no—
125C23×C43C2×D411yescharacteristic
126C22×D43—21no—
127C22×D43—42no—
128C22×D43—42no—
129C22×D43—81no—
130C22×D43C2×D411yescharacteristic
131Q8×C43—21no—
132Q8×C43—21no—
133Q8×C43—21no—
134Q8×C43C2×D412yes—
135D4×C43—21no—
136D4×C43—21no—
137D4×C43—21no—
138D4×C43—42no—
139D4×C43—42no—
140D4×C43C2×D412yes—
141C2×C4×C43—21no—
142C2×C4×C43—21no—
143C2×C4×C43—21no—
144C2×C4×C43—21no—
145C2×C4×C43—42no—
146C2×C4×C43—42no—
147C2×C4×C43C2×D411yescharacteristic
148C2×C4×C43C2411yescharacteristic
149C22⋊D43—22no—
150C22⋊D43—42no—
151C22⋊D43—42no—
152C22⋊D43—81no—
153C2×Dic43—21no—
154C2×Dic43—21no—
155C2×Dic43—21no—
156C2×Dic43—81no—
157C2×Dic43C2×D411yescharacteristic
158C2×Dic43C2×D411yescharacteristic
159C2×Dic43C2×D411yescharacteristic
160D172—21no—
161D172—21no—
162C4×D43—21no—
163C4×D43—21no—
164C4×D43—42no—
165Dic86—21no—
166Dic86—21no—
167Dic86—42no—
168C8×C43—21no—
169C8×C43C2×D412yes—
170C43⋊C8—21no—
171C43⋊C8—21no—
172C22×C43—22no—
173C22×C43—21no—
174C22×C43—21no—
175C22×C43—21no—
176C22×C43—41no—
177C22×C43—41no—
178C22×C43—41no—
179C22×C43—41no—
180C22×C43—41no—
181C22×C43C22×D411yescharacteristic
182C2×D43—21no—
183C2×D43—21no—
184C2×D43—41no—
185C2×D43—41no—
186C2×D43—41no—
187C2×D43—84no—
188C2×D43#13512yescomplemented
189C4×C43—22no—
190C4×C43—21no—
191C4×C43—41no—
192C4×C43C22×D411yescharacteristic
193C4×C43H(5,𝔽2)11yescharacteristic
194Dic43—21no—
195Dic43—21no—
196Dic43—21no—
197Dic43—41no—
198Dic43—41no—
199Dic43—41no—
200#3282—431nomaximal, Sylow
201C2×C43—42no—
202C2×C43—41no—
203C2×C43—81no—
204C2×C43D4211yescharacteristic
205C2×C43C2×#13511yescharacteristic
206C2×C43#57711yescharacteristic
207D43—22no—
208D43—81no—
209C2×#135D4311yescharacteristic, complemented
210C22×SD16—431no—
211#548—431no—
212#546—431no—
213#495—431no—
214#465—431no—
215#465—431no—
216#464—431no—
217#463—431no—
218#452—431no—
219#451—431no—
220#449—431no—
221#447—431no—
222C4×SD16—431no—
223C8×D4—431no—
224C43#328211yescharacteristic, complemented, Sylow
225C2×#41C2×D4311yescharacteristic
226C2×#41C2×D4311yescharacteristic, complemented
227C22×Q8—431no—
228C22×D4—431no—
229#135—24no—
230C2×Q16—431no—
231C2×Q16C2×D4311yescharacteristic, complemented
232C2×SD16—431no—
233C2×SD16—431no—
234C2×SD16—431no—
235C2×SD16—864no—
236C2×SD16C2×D4311yescharacteristic
237C2×SD16C2×D4311yescharacteristic, complemented
238C2×D8—431no—
239C2×D8C2×D4311yescharacteristic
240C22×C8—431no—
241C22×C8C2×D4311yescharacteristic, complemented
242#124—431no—
243#124—431no—
244#124—861no—
245#123—861no—
246C22⋊Q8—431no—
247C22⋊Q8—431no—
248C22⋊Q8—861no—
249#121—431no—
250#121—431no—
251#121—861no—
252#121—861no—
253#120—861no—
254C4×Q8—431no—
255C4×D4—431no—
256C4×D4—431no—
257C4×D4—861no—
258C2×C22⋊C4—861no—
259#106—431no—
260C4⋊C8—431no—
261#103—431no—
262#103—431no—
263#103—431no—
264#102—431no—
265#102—431no—
266#102—431no—
267C22⋊C8—431no—
268C22⋊C8—431no—
269C4×C8—431no—
270C24—861no—
271#41—22no—
272#41—22no—
273#41—41no—
274#41—41no—
275C2×Q8—431no—
276C2×Q8—861no—
277C2×Q8—862no—
278C2×Q8—1721no—
279C2×Q8C22×D4311yescharacteristic
280C2×Q8C22×D4311yescharacteristic
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—431no—
284C2×D4—431no—
285C2×D4—861no—
286C2×D4—862no—
287C2×D4—861no—
288C2×D4—861no—
289C2×D4—1721no—
290C2×D4C22×D4311yescharacteristic
291C2×D4C22×D4311yescharacteristic
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—431no—
295C22×C4—861no—
296C22×C4—861no—
297C22×C4C22×D4311yescharacteristic
298Q16—22no—
299Q16—1721no—
300SD16—22no—
301SD16—862no—
302SD16—862no—
303SD16—862no—
304SD16C22⋊D4314yescomplemented
305D8—22no—
306D8—1721no—
307C2×C8—22no—
308C2×C8—431no—
309C2×C8—431no—
310C2×C8—862no—
311C2×C8C22×D4311yescharacteristic
312C2×C8C22×D4311yescharacteristic
313C4⋊C4—431no—
314C4⋊C4—431no—
315C4⋊C4—431no—
316C4⋊C4—861no—
317C4⋊C4—861no—
318C4⋊C4—861no—
319C22⋊C4—431no—
320C22⋊C4—431no—
321C22⋊C4—861no—
322C22⋊C4—861no—
323C22⋊C4—861no—
324C22⋊C4—861no—
325C22⋊C4—861no—
326C22⋊C4—861no—
327C22⋊C4—861no—
328C22⋊C4—861no—
329C22⋊C4—861no—
330C42—431no—
331C42—861no—
332C23—21no—
333C23—21no—
334C23—431no—
335C23—861no—
336C23—3441no—
337C23—1722no—
338C23—1722no—
339C23D4×D4311yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—861no—
344Q8—861no—
345Q8—1722no—
346Q8C2×C22⋊D4312yes—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—42no—
351D4—42no—
352D4—862no—
353D4—861no—
354D4—861no—
355D4—3441no—
356D4—1722no—
357D4—1722no—
358D4C2×C22⋊D4312yes—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—431no—
366C2×C4—431no—
367C2×C4—431no—
368C2×C4—861no—
369C2×C4—861no—
370C2×C4—861no—
371C2×C4—861no—
372C2×C4—861no—
373C2×C4—3441no—
374C2×C4—1722no—
375C2×C4D4×D4311yescharacteristic
376C2×C4C23×D4311yescharacteristic
377C8—21no—
378C8—861no—
379C8—861no—
380C8C2×C22⋊D4312yes—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—22no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—432no—
391C22—861no—
392C22—861no—
393C22—3444no—
394C22—1721no—
395C22—1721no—
396C22—1721no—
397C22C2×D4×D4311yescharacteristic
398C4—21no—
399C4—22no—
400C4—41no—
401C4—861no—
402C4—861no—
403C4—861no—
404C4—1721no—
405C4—1721no—
406C4—1721no—
407C4C22×C22⋊D4311yescharacteristic
408C4#1306337011yescharacteristic
409C2—41no—
410C2—42no—
411C2—81no—
412C2—862no—
413C2—3441no—
414C2D4×C22⋊D4311yescharacteristic
415C2#135×D4311yescharacteristic
416C2#1458370611yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC2×#135×C43C2
socleC22×C43C22×D4
hypercenterC2×#135D43
hypocenterC43#3282
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D43C2semidirect
2. #14583556C2semidirect
3. #14583537C2semidirect
4. #14583280C2semidirect
5. #14583128C2semidirect
6. #14583125C2semidirect
7. #14583123C2semidirect
8. #14583112C2semidirect
9. #14583061C2semidirect
10. #14583053C2semidirect
11. #14583044C2semidirect
12. #14583031C2semidirect
13. SD16×Dic43C2semidirect
14. C8×C22⋊D43C2semidirect
15. C2×#135×C43C2semidirect
18. C2×#10621885C22semidirect
27. #13063312C22semidirect
30. #13063304C22semidirect
37. Q8×Dic43C22semidirect
42. #13063257C22semidirect
43. Dic43⋊C8C22semidirect
44. #13063250C22semidirect
45. #13063249C22semidirect
46. #13063249C22semidirect
49. #13063246C22semidirect
50. C22⋊(C43⋊C8)C22semidirect
52. C8×Dic43C22semidirect
54. C2×#41×C43C22semidirect
56. C2×Q16×C43C22semidirect
58. C2×SD16×C43C22semidirect
60. C22×C8×C43C22semidirect
91. SD16×C43D4semidirect
188. C2×D43#135semidirect
209. C2×#135D43semidirect
224. C43#3282semidirect
226. C2×#41C2×D43semidirect
231. C2×Q16C2×D43semidirect
237. C2×SD16C2×D43semidirect
241. C22×C8C2×D43semidirect
304. SD16C22⋊D43semidirect