Finite Group Databasebeta

← #19146103

Subgroups — #19146103

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×#13063355C211yesmaximal, characteristic, complemented
2C2×SD16×D43C211yesmaximal, characteristic, complemented
3#14583562C211yesmaximal, characteristic, complemented
4#14583537C211yesmaximal, characteristic
5#14583292C211yesmaximal, characteristic, complemented
6#14583147C211yesmaximal, characteristic, complemented
7#14583139C211yesmaximal, characteristic, complemented
8#14583124C211yesmaximal, characteristic, complemented
9#14583102C211yesmaximal, characteristic, complemented
10#14583053C211yesmaximal, characteristic, complemented
11#14583051C211yesmaximal, characteristic, complemented
12#14583040C211yesmaximal, characteristic, complemented
13#14582996C211yesmaximal, characteristic, complemented
14#14582973C211yesmaximal, characteristic, complemented
15C43×#452C211yesmaximal, characteristic, complemented
16C22×Dic86C2211yescharacteristic, complemented
17C2×Q8×D43C2211yescharacteristic
18C2×D4×D43C2211yescharacteristic
19#13063355—24no—
20C2×#10621885C2211yescharacteristic, complemented
21C2×#10621885C2211yescharacteristic, complemented
22C2×#10621873C2211yescharacteristic
23C2×#10621873C2211yescharacteristic
24C2×#10621883C2211yescharacteristic
25C2×#10621883C2211yescharacteristic
26C2×#10621884C2211yescharacteristic
27SD16×D43—24no—
28C2×#10621877C2211yescharacteristic, complemented
29C2×C8×D43C2211yescharacteristic
30#13063324—21no—
31#13063323C2211yescharacteristic, complemented
32#13063314C2211yescharacteristic
33#13063308—21no—
34#13063305C2211yescharacteristic
35#13063303—21no—
36#13063302—21no—
37#13063301C2211yescharacteristic
38#13063299C2211yescharacteristic
39#13063297—21no—
40#13063293—21no—
41#13063290C2211yescharacteristic, complemented
42D4×Dic43C2211yescharacteristic
43C4×C22⋊D43C2211yescharacteristic
44(C22⋊D43)⋊C4—21no—
45C2×(C2×D43)⋊C4—21no—
46#13063258C2211yescharacteristic, complemented
47Dic43⋊C8C2211yescharacteristic, complemented
48#13063250C2211yescharacteristic, complemented
49#13063250C2211yescharacteristic, complemented
50#13063249C2211yescharacteristic, complemented
51#13063245C2211yescharacteristic
52(C2×D43)⋊C8C2211yescharacteristic
53#13063235C2211yescharacteristic, complemented
54C2×#41×C43C2211yescharacteristic
55C2×Q16×C43C2211yescharacteristic, complemented
56C2×SD16×C43C2211yescharacteristic
57C22⋊Q8×C43C2211yescharacteristic, complemented
58#103×C43C2211yescharacteristic, complemented
59#102×C43C2211yescharacteristic
60C22⋊C8×C43C2211yescharacteristic, complemented
61C23×D43—21no—
62#41×C43—22no—
63#41×C43—41no—
64C2×Q8×C43C2311yescharacteristic
65C2×Q8×C43C2311yescharacteristic
66C2×D4×C43—21no—
67C2×D4×C43C2311yescharacteristic
68C22×C4×C43—21no—
69C22×C4×C43C2311yescharacteristic
70C2×C22⋊D43—21no—
71C2×C22⋊D43—21no—
72C2×C22⋊D43D411yescharacteristic
73C22×Dic43—21no—
74C22×Dic43—21no—
75Q8×D43—22no—
76Q8×D43—41no—
77D4×D43—22no—
78D4×D43—41no—
79C2×D172C2311yescharacteristic
80C2×C4×D43—21no—
81C2×C4×D43C2311yescharacteristic
82C2×Dic86—22no—
83C2×Dic86—21no—
84C2×Dic86—21no—
85C2×Dic86—41no—
86C2×Dic86C2311yescharacteristic
87C2×Dic86C2311yescharacteristic
88Q16×C43—41no—
89SD16×C43—22no—
90C2×C8×C43C2311yescharacteristic
91C2×C8×C43C2311yescharacteristic
92C4⋊C4×C43—21no—
93C4⋊C4×C43C2311yescharacteristic
94C22⋊C4×C43—21no—
95C22⋊Dic43—21no—
96C22⋊Dic43D411yescharacteristic
97#10621885—22no—
98#10621885—22no—
99#10621884—22no—
100#10621883—22no—
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)⋊C4D411yescharacteristic
108C4⋊Dic43—21no—
109C4⋊Dic43C2311yescharacteristic
110Dic43⋊C4—21no—
111Dic43⋊C4—21no—
112Dic43⋊C4—21no—
113Dic43⋊C4—21no—
114Dic43⋊C4D411yescharacteristic
115C4×Dic43—21no—
116C4×Dic43C2311yescharacteristic
117#10621877—22no—
118C2×C43⋊C8C2311yescharacteristic
119C2×C43⋊C8C2311yescharacteristic
120#10621873—22no—
121#10621873—41no—
122C8×D43—22no—
123C23×C43—21no—
124C23×C43C2×D411yescharacteristic
125C22×D43—21no—
126C22×D43—42no—
127C22×D43—42no—
128C22×D43—81no—
129C22×D43C2×D411yescharacteristic
130Q8×C43—21no—
131Q8×C43—21no—
132Q8×C43—21no—
133Q8×C43—21no—
134D4×C43—21no—
135D4×C43—42no—
136D4×C43C2×D412yes—
137C2×C4×C43—21no—
138C2×C4×C43—21no—
139C2×C4×C43—21no—
140C2×C4×C43—21no—
141C2×C4×C43—21no—
142C2×C4×C43—42no—
143C2×C4×C43C2×D411yescharacteristic
144C2×C4×C43C2411yescharacteristic
145C22⋊D43—22no—
146C22⋊D43—42no—
147C22⋊D43—81no—
148C2×Dic43—21no—
149C2×Dic43—21no—
150C2×Dic43—21no—
151C2×Dic43—42no—
152C2×Dic43—81no—
153C2×Dic43C2×D411yescharacteristic
154C2×Dic43C2×D411yescharacteristic
155C2×Dic43C2×D411yescharacteristic
156D172—21no—
157D172—21no—
158C4×D43—21no—
159C4×D43—21no—
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—21no—
173C22×C43—21no—
174C22×C43—21no—
175C22×C43—41no—
176C22×C43—41no—
177C22×C43C22×D411yescharacteristic
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—41no—
187C4×C43—41no—
188C4×C43—41no—
189C4×C43C22×D411yescharacteristic
190C4×C43H(5,𝔽2)11yescharacteristic
191Dic43—22no—
192Dic43—21no—
193Dic43—21no—
194Dic43—21no—
195Dic43—41no—
196Dic43—41no—
197#3266—431nomaximal, Sylow
198C2×C43—42no—
199C2×C43—41no—
200C2×C43D4211yescharacteristic
201C2×C43C2×#13711yescharacteristic
202C2×C43#57711yescharacteristic
203D43—22no—
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#461—431no—
214#452D4311yescharacteristic, complemented
215#451—431no—
216#450—431no—
217#448—431no—
218#440—431no—
219#435—431no—
220C43#326611yescharacteristic, complemented, Sylow
221C2×#41C2×D4311yescharacteristic
222C22×Q8—431no—
223C22×Q8—431no—
224C22×D4—431no—
225#137—864no—
226C2×Q16—431no—
227C2×Q16—431no—
228C2×Q16C2×D4311yescharacteristic, complemented
229C2×SD16—431no—
230C2×SD16—431no—
231C2×SD16—431no—
232C2×SD16—431no—
233C2×SD16—431no—
234C2×SD16—864no—
235C2×SD16C2×D4311yescharacteristic
236C2×M16—431no—
237C22×C8—431no—
238C4⋊Q8—431no—
239C4⋊Q8—861no—
240#124—431no—
241#123—861no—
242C22⋊Q8—431no—
243C22⋊Q8—431no—
244C22⋊Q8—861no—
245C22⋊Q8—861no—
246C22⋊Q8C2×D4311yescharacteristic, complemented
247#121—431no—
248#121—861no—
249#120—861no—
250C4×Q8—431no—
251C4×D4—431no—
252C4×D4—431no—
253C4×D4—861no—
254C2×C22⋊C4—861no—
255#107—431no—
256C4⋊C8—431no—
257#103—431no—
258#103—431no—
259#103—431no—
260#103C2×D4311yescharacteristic, complemented
261#102—431no—
262#102C2×D4311yescharacteristic
263C22⋊C8—431no—
264C22⋊C8C2×D4311yescharacteristic, complemented
265#97—431no—
266C24—861no—
267#41—22no—
268#41—41no—
269C2×Q8—431no—
270C2×Q8—431no—
271C2×Q8—861no—
272C2×Q8—862no—
273C2×Q8—861no—
274C2×Q8—862no—
275C2×Q8—1721no—
276C2×Q8—1721no—
277C2×Q8C22×D4311yescharacteristic
278C2×Q8C22×D4311yescharacteristic
279C2×D4—21no—
280C2×D4—431no—
281C2×D4—431no—
282C2×D4—861no—
283C2×D4—862no—
284C2×D4—861no—
285C2×D4—1721no—
286C2×D4C22×D4311yescharacteristic
287C22×C4—21no—
288C22×C4—431no—
289C22×C4—861no—
290C22×C4—861no—
291C22×C4—861no—
292C22×C4C22×D4311yescharacteristic
293Q16—41no—
294Q16—862no—
295Q16—862no—
296SD16—22no—
297SD16—434no—
298SD16—862no—
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—431no—
310C4⋊C4—431no—
311C4⋊C4—861no—
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—431no—
327C42—861no—
328C23—21no—
329C23—431no—
330C23—861no—
331C23—3441no—
332C23—1722no—
333C23—1722no—
334C23D4×D4311yescharacteristic
335Q8—21no—
336Q8—21no—
337Q8—21no—
338Q8—21no—
339Q8—432no—
340Q8—861no—
341Q8—861no—
342Q8—861no—
343Q8—1722no—
344Q8—1722no—
345D4—21no—
346D4—42no—
347D4—862no—
348D4—861no—
349D4—861no—
350D4—3441no—
351D4—1722no—
352D4D4×D4312yes—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—42no—
359C2×C4—431no—
360C2×C4—431no—
361C2×C4—431no—
362C2×C4—861no—
363C2×C4—861no—
364C2×C4—861no—
365C2×C4—861no—
366C2×C4—861no—
367C2×C4—3441no—
368C2×C4—1722no—
369C2×C4—1722no—
370C2×C4D4×D4311yescharacteristic
371C2×C4C23×D4311yescharacteristic
372C8—21no—
373C8—21no—
374C8—432no—
375C8—861no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—22no—
380C22—41no—
381C22—41no—
382C22—432no—
383C22—861no—
384C22—861no—
385C22—3444no—
386C22—1721no—
387C22—1721no—
388C22—1721no—
389C22C2×D4×D4311yescharacteristic
390C4—21no—
391C4—41no—
392C4—41no—
393C4—41no—
394C4—861no—
395C4—861no—
396C4—861no—
397C4—862no—
398C4—1721no—
399C4—1721no—
400C4C2×D4×D4311yescharacteristic
401C4#1306337011yescharacteristic
402C2—41no—
403C2—42no—
404C2—862no—
405C2—3441no—
406C2#1458353111yescharacteristic
407C2#137×D4311yescharacteristic
408C2#1458370611yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#452C2
socleC22×C43C22×D4
hypercenter#452D43
hypocenterC43#3266
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. C2×#13063355C2semidirect
2. C2×SD16×D43C2semidirect
3. #14583562C2semidirect
5. #14583292C2semidirect
6. #14583147C2semidirect
7. #14583139C2semidirect
8. #14583124C2semidirect
9. #14583102C2semidirect
10. #14583053C2semidirect
11. #14583051C2semidirect
12. #14583040C2semidirect
13. #14582996C2semidirect
14. #14582973C2semidirect
15. C43×#452C2semidirect
16. C22×Dic86C22semidirect
20. C2×#10621885C22semidirect
21. C2×#10621885C22semidirect
28. C2×#10621877C22semidirect
31. #13063323C22semidirect
41. #13063290C22semidirect
46. #13063258C22semidirect
47. Dic43⋊C8C22semidirect
48. #13063250C22semidirect
49. #13063250C22semidirect
50. #13063249C22semidirect
53. #13063235C22semidirect
55. C2×Q16×C43C22semidirect
57. C22⋊Q8×C43C22semidirect
58. #103×C43C22semidirect
60. C22⋊C8×C43C22semidirect
101. #10621883D4semidirect
184. C2×D43#137semidirect
214. #452D43semidirect
220. C43#3266semidirect
228. C2×Q16C2×D43semidirect
246. C22⋊Q8C2×D43semidirect
260. #103C2×D43semidirect
264. C22⋊C8C2×D43semidirect