Finite Group Databasebeta

← #19146234

Subgroups — #19146234

Order 5504.

472 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063357C211yesmaximal, characteristic, complemented
2C2×#13063356C211yesmaximal, characteristic, complemented
3Q8×C22⋊D43C211yesmaximal, characteristic, complemented
4#14583551C211yesmaximal, characteristic
5#14583277C211yesmaximal, characteristic, complemented
6#14583156C211yesmaximal, characteristic, complemented
7#14583155C211yesmaximal, characteristic, complemented
8#14583107C211yesmaximal, characteristic, complemented
9#14583103C211yesmaximal, characteristic, complemented
10#14583063C211yesmaximal, characteristic, complemented
11#14583060C211yesmaximal, characteristic, complemented
12#14583056C211yesmaximal, characteristic, complemented
13#14582984C211yesmaximal, characteristic, complemented
14#14582974C211yesmaximal, characteristic, complemented
15C43×#451C211yesmaximal, characteristic, complemented
16C2×#10621902C2211yescharacteristic
17C2×#10621898C2211yescharacteristic
18C2×Q8×D43C2211yescharacteristic
19#13063357—24no—
20#13063356—24no—
21C2×Dic172C2211yescharacteristic
22C2×#10621885C2211yescharacteristic
23C2×#10621885C2211yescharacteristic
24C2×#10621885C2211yescharacteristic
25C2×#10621873C2211yescharacteristic
26C2×#10621884C2211yescharacteristic
27C2×#10621884C2211yescharacteristic
28C2×#10621877C2211yescharacteristic
29C2×#10621872C2211yescharacteristic
30#13063323—21no—
31#13063323C2211yescharacteristic
32#13063323C2211yescharacteristic
33#13063310—21no—
34#13063307—21no—
35#13063305C2211yescharacteristic
36#13063304—21no—
37#13063304C2211yescharacteristic
38#13063301—21no—
39#13063301C2211yescharacteristic
40#13063298—21no—
41Q8×Dic43C2211yescharacteristic
42#13063287C2211yescharacteristic
43C4×C22⋊D43—21no—
44C4×C22⋊D43C2211yescharacteristic
45C4⋊C4×D43—21no—
46#13063256C2211yescharacteristic
47Dic43⋊C8C2211yescharacteristic
48#13063250C2211yescharacteristic
49#13063249C2211yescharacteristic
50#13063248C2211yescharacteristic
51#13063247C2211yescharacteristic
52(C2×D43)⋊C8C2211yescharacteristic
53C8×Dic43C2211yescharacteristic
54C22×Q8×C43C2211yescharacteristic
55C2×Q16×C43C2211yescharacteristic
56C2×Q16×C43C2211yescharacteristic
57C22⋊Q8×C43C2211yescharacteristic
58#103×C43C2211yescharacteristic
59#103×C43C2211yescharacteristic
60C22⋊C8×C43C2211yescharacteristic
61C2×Q8×C43—21no—
62C2×Q8×C43—22no—
63C2×Q8×C43—41no—
64C2×Q8×C43C2311yescharacteristic
65C2×Q8×C43C2311yescharacteristic
66C2×Q8×C43C2311yescharacteristic
67C22×C4×C43—21no—
68C22×C4×C43C2311yescharacteristic
69C2×C22⋊D43—21no—
70C2×C22⋊D43D411yescharacteristic
71#10621902—22no—
72#10621902—41no—
73Q8×D43—22no—
74Q8×D43—41no—
75#10621898—22no—
76#10621898—41no—
77C2×D172—21no—
78C2×D172C2311yescharacteristic
79C2×C4×D43—21no—
80C2×C4×D43—21no—
81C2×C4×D43—21no—
82C2×C4×D43—21no—
83C2×C4×D43C2311yescharacteristic
84C2×Dic86—21no—
85C2×Dic86C2311yescharacteristic
86C2×Dic86C2311yescharacteristic
87Q16×C43—22no—
88Q16×C43—41no—
89C2×C8×C43C2311yescharacteristic
90C2×C8×C43C2311yescharacteristic
91C4⋊C4×C43—21no—
92C4⋊C4×C43C2311yescharacteristic
93C22⋊C4×C43—21no—
94C22⋊Dic43—21no—
95C22⋊Dic43D411yescharacteristic
96#10621885—22no—
97#10621885—22no—
98#10621885—22no—
99#10621884—22no—
100#10621884D414yescomplemented
101(C2×D43)⋊C4—21no—
102(C2×D43)⋊C4—21no—
103(C2×D43)⋊C4—21no—
104(C2×D43)⋊C4D411yescharacteristic
105C4⋊Dic43—21no—
106C4⋊Dic43—21no—
107C4⋊Dic43C2311yescharacteristic
108Dic43⋊C4—21no—
109Dic43⋊C4—21no—
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
120Dic172—41no—
121#10621873—22no—
122#10621872—22no—
123C23×C43C2×D411yescharacteristic
124C22×D43—21no—
125C22×D43C2×D411yescharacteristic
126Q8×C43—21no—
127Q8×C43—21no—
128Q8×C43—21no—
129Q8×C43—21no—
130Q8×C43—21no—
131Q8×C43—42no—
132Q8×C43C2×D412yes—
133C2×C4×C43—21no—
134C2×C4×C43—21no—
135C2×C4×C43—21no—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
138C2×C4×C43—21no—
139C2×C4×C43—42no—
140C2×C4×C43C2×D411yescharacteristic
141C2×C4×C43C2411yescharacteristic
142C22⋊D43—22no—
143C22⋊D43—42no—
144C2×Dic43—21no—
145C2×Dic43—21no—
146C2×Dic43—21no—
147C2×Dic43C2×D411yescharacteristic
148C2×Dic43C2×D411yescharacteristic
149C2×Dic43C2×D411yescharacteristic
150D172—21no—
151D172—42no—
152D172C2×D412yes—
153C4×D43—21no—
154C4×D43—21no—
155C4×D43—42no—
156C4×D43—42no—
157C4×D43—42no—
158C4×D43—42no—
159Dic86—21no—
160Dic86—21no—
161Dic86—21no—
162Dic86—21no—
163Dic86—42no—
164C8×C43—21no—
165C8×C43—21no—
166C43⋊C8—21no—
167C43⋊C8C2×D412yes—
168C22×C43—21no—
169C22×C43—21no—
170C22×C43—21no—
171C22×C43C22×D411yescharacteristic
172C2×D43—22no—
173C2×D43—21no—
174C2×D43—21no—
175C2×D43—21no—
176C2×D43—41no—
177C2×D43—41no—
178C4×C43—22no—
179C4×C43—21no—
180C4×C43—41no—
181C4×C43—41no—
182C4×C43—41no—
183C4×C43C22×D411yescharacteristic
184C4×C43H(5,𝔽2)11yescharacteristic
185Dic43—21no—
186Dic43—21no—
187Dic43—41no—
188Dic43—41no—
189Dic43—41no—
190Dic43#13712yescomplemented
191#3276—431nomaximal, Sylow
192C2×C43—41no—
193C2×C43D4211yescharacteristic
194C2×C43C2×#13711yescharacteristic
195C2×C43#57811yescharacteristic
196D43—41no—
197D43—42no—
198C2×#137—431no—
199C2×#137—431no—
200D4×Q8—431no—
201#547—431no—
202#494—431no—
203#470—431no—
204#470—431no—
205#462—431no—
206#461—431no—
207#452—431no—
208#452—431no—
209#451—431no—
210#451D4311yescharacteristic, complemented
211C4×SD16—431no—
212#436—431no—
213C43#327611yescharacteristic, complemented, Sylow
214C2×#41—431no—
215C2×#41—431no—
216C22×Q8—431no—
217C22×Q8C2×D4311yescharacteristic
218#137—864no—
219#137—864no—
220C2×Q16—431no—
221C2×Q16—431no—
222C2×Q16—431no—
223C2×Q16—431no—
224C2×Q16C2×D4311yescharacteristic
225C2×Q16C2×D4311yescharacteristic
226C2×SD16—431no—
227C2×SD16—431no—
228C2×SD16—431no—
229C2×M16—431no—
230C2×M16—431no—
231C4⋊Q8—431no—
232C4⋊Q8—431no—
233C4⋊Q8—861no—
234#123—861no—
235#123—861no—
236C22⋊Q8—431no—
237C22⋊Q8—431no—
238C22⋊Q8—431no—
239C22⋊Q8—861no—
240C22⋊Q8—861no—
241C22⋊Q8C2×D4311yescharacteristic
242#121—861no—
243C4×Q8—431no—
244C4×D4—431no—
245C4×D4—431no—
246C4×D4—861no—
247C2×C4⋊C4—861no—
248#106—431no—
249C4⋊C8—431no—
250#103—431no—
251#103—431no—
252#103—431no—
253#103C2×D4311yescharacteristic
254#103C2×D4311yescharacteristic
255#102—431no—
256C22⋊C8—431no—
257C22⋊C8C2×D4311yescharacteristic
258C4×C8—431no—
259#41—862no—
260#41—862no—
261#41—1721no—
262#41—1721no—
263C2×Q8—21no—
264C2×Q8—22no—
265C2×Q8—41no—
266C2×Q8—431no—
267C2×Q8—431no—
268C2×Q8—861no—
269C2×Q8—862no—
270C2×Q8—1721no—
271C2×Q8C22×D4311yescharacteristic
272C2×Q8C22×D4311yescharacteristic
273C2×Q8C22×D4311yescharacteristic
274C2×D4—431no—
275C2×D4—431no—
276C2×D4—861no—
277C2×D4—861no—
278C22×C4—21no—
279C22×C4—431no—
280C22×C4—861no—
281C22×C4—861no—
282C22×C4—861no—
283C22×C4—861no—
284C22×C4C22×D4311yescharacteristic
285Q16—22no—
286Q16—41no—
287Q16—862no—
288Q16—862no—
289Q16—862no—
290Q16—1721no—
291SD16—434no—
292SD16—862no—
293SD16—862no—
294M16—862no—
295M16—862no—
296C2×C8—431no—
297C2×C8—431no—
298C2×C8C22×D4311yescharacteristic
299C2×C8C22×D4311yescharacteristic
300C4⋊C4—21no—
301C4⋊C4—431no—
302C4⋊C4—431no—
303C4⋊C4—861no—
304C4⋊C4—861no—
305C4⋊C4—861no—
306C4⋊C4—861no—
307C4⋊C4—861no—
308C4⋊C4—861no—
309C4⋊C4—861no—
310C4⋊C4—861no—
311C4⋊C4C22×D4311yescharacteristic
312C22⋊C4—21no—
313C22⋊C4—431no—
314C22⋊C4—431no—
315C22⋊C4—861no—
316C22⋊C4—861no—
317C22⋊C4—861no—
318C22⋊C4—861no—
319C42—431no—
320C42—861no—
321C23—431no—
322C23—861no—
323C23D4×D4311yescharacteristic
324Q8—21no—
325Q8—21no—
326Q8—21no—
327Q8—21no—
328Q8—21no—
329Q8—42no—
330Q8—861no—
331Q8—861no—
332Q8—861no—
333Q8—861no—
334Q8—1722no—
335Q8D4×D4312yes—
336D4—432no—
337D4—862no—
338D4—861no—
339D4—1722no—
340D4—1722no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—42no—
348C2×C4—431no—
349C2×C4—431no—
350C2×C4—431no—
351C2×C4—861no—
352C2×C4—861no—
353C2×C4—861no—
354C2×C4—861no—
355C2×C4—861no—
356C2×C4—1722no—
357C2×C4—1722no—
358C2×C4—1722no—
359C2×C4—1722no—
360C2×C4D4×D4311yescharacteristic
361C2×C4C23×D4311yescharacteristic
362C8—21no—
363C8—21no—
364C8—432no—
365C8—861no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—861no—
370C22—861no—
371C22—861no—
372C22—862no—
373C22—1721no—
374C22—1721no—
375C22C2×D4×D4311yescharacteristic
376C4—21no—
377C4—22no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—432no—
382C4—861no—
383C4—861no—
384C4—1721no—
385C4—1721no—
386C4—1721no—
387C4C2×D4×D4311yescharacteristic
388C4#1306337011yescharacteristic
389C2—41no—
390C2—1721no—
391C2—1722no—
392C2#1458353111yescharacteristic
393C2#137×D4311yescharacteristic
394C2#1458371211yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#451C2
socleC22×C43C22×D4
hypercenter#451D43
hypocenterC43#3276
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
1. C2×#13063357C2semidirect
2. C2×#13063356C2semidirect
3. Q8×C22⋊D43C2semidirect
5. #14583277C2semidirect
6. #14583156C2semidirect
7. #14583155C2semidirect
8. #14583107C2semidirect
9. #14583103C2semidirect
10. #14583063C2semidirect
11. #14583060C2semidirect
12. #14583056C2semidirect
13. #14582984C2semidirect
14. #14582974C2semidirect
15. C43×#451C2semidirect
100. #10621884D4semidirect
190. Dic43#137semidirect
210. #451D43semidirect
213. C43#3276semidirect