Finite Group Databasebeta

← #19146172

Subgroups — #19146172

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×#13063358C211yesmaximal, characteristic, complemented
2C2×Q16×D43C211yesmaximal, characteristic, complemented
3#14583562C211yesmaximal, characteristic, complemented
4#14583559C211yesmaximal, characteristic
5#14583292C211yesmaximal, characteristic, complemented
6#14583129C211yesmaximal, characteristic, complemented
7#14583124C211yesmaximal, characteristic, complemented
8#14583108C211yesmaximal, characteristic, complemented
9#14583059C211yesmaximal, characteristic, complemented
10#14583056C211yesmaximal, characteristic, complemented
11#14583054C211yesmaximal, characteristic, complemented
12#14583039C211yesmaximal, characteristic, complemented
13#14583005C211yesmaximal, characteristic, complemented
14#14582968C211yesmaximal, characteristic, complemented
15C43×#470C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C22×Dic86C2211yescharacteristic
18C2×Q8×D43C2211yescharacteristic
19C2×Q8×D43C2211yescharacteristic
20#13063358—24no—
21C2×Dic172C2211yescharacteristic
22C2×Dic172C2211yescharacteristic
23C2×#10621885C2211yescharacteristic
24C2×#10621885C2211yescharacteristic
25C2×#10621885C2211yescharacteristic
26Q16×D43—24no—
27C2×#10621873C2211yescharacteristic
28C2×#10621873C2211yescharacteristic
29C2×#10621884C2211yescharacteristic
30C2×C8×D43C2211yescharacteristic
31#13063324—21no—
32#13063323C2211yescharacteristic
33#13063314C2211yescharacteristic
34#13063311—21no—
35#13063305C2211yescharacteristic
36#13063303—21no—
37#13063303—21no—
38#13063302—21no—
39#13063300C2211yescharacteristic
40#13063298—21no—
41#13063290C2211yescharacteristic
42#13063290C2211yescharacteristic
43#13063287—21no—
44C4×C22⋊D43C2211yescharacteristic
45(C22⋊D43)⋊C4—21no—
46Dic43⋊C8C2211yescharacteristic
47#13063248C2211yescharacteristic
48#13063248C2211yescharacteristic
49#13063248C2211yescharacteristic
50#13063245C2211yescharacteristic
51C22⋊(C43⋊C8)C2211yescharacteristic
52(C2×D43)⋊C8C2211yescharacteristic
53#13063235C2211yescharacteristic
54C2×Q16×C43C2211yescharacteristic
55C2×M16×C43C2211yescharacteristic
56C22⋊Q8×C43C2211yescharacteristic
57C22⋊Q8×C43C2211yescharacteristic
58#106×C43C2211yescharacteristic
59#103×C43C2211yescharacteristic
60#103×C43C2211yescharacteristic
61C2×Q8×C43C2311yescharacteristic
62C2×Q8×C43C2311yescharacteristic
63C22×C4×C43C2311yescharacteristic
64C2×C22⋊D43—21no—
65C2×C22⋊D43D411yescharacteristic
66C22×Dic43—21no—
67Q8×D43—22no—
68Q8×D43—22no—
69Q8×D43—41no—
70Q8×D43—41no—
71#10621898—22no—
72#10621898—41no—
73C2×D172—21no—
74C2×D172C2311yescharacteristic
75C2×C4×D43—21no—
76C2×C4×D43—21no—
77C2×C4×D43—21no—
78C2×C4×D43C2311yescharacteristic
79C2×Dic86—22no—
80C2×Dic86—21no—
81C2×Dic86—21no—
82C2×Dic86—21no—
83C2×Dic86—41no—
84C2×Dic86C2311yescharacteristic
85C2×Dic86C2311yescharacteristic
86C2×Dic86C2311yescharacteristic
87Q16×C43—22no—
88M16×C43—22no—
89C2×C8×C43C2311yescharacteristic
90C2×C8×C43C2311yescharacteristic
91C4⋊C4×C43—21no—
92C4⋊C4×C43—21no—
93C4⋊C4×C43C2311yescharacteristic
94C4⋊C4×C43C2311yescharacteristic
95C22⋊C4×C43—21no—
96C22⋊C4×C43—21no—
97C22⋊Dic43D411yescharacteristic
98#10621885—22no—
99#10621885—22no—
100#10621885—41no—
101#10621884—41no—
102(C2×D43)⋊C4—21no—
103(C2×D43)⋊C4—21no—
104(C2×D43)⋊C4—21no—
105(C2×D43)⋊C4—21no—
106(C2×D43)⋊C4D411yescharacteristic
107C4⋊Dic43—21no—
108Dic43⋊C4—21no—
109Dic43⋊C4—21no—
110Dic43⋊C4—21no—
111Dic43⋊C4—21no—
112Dic43⋊C4D411yescharacteristic
113C4×Dic43—21no—
114C4×Dic43—21no—
115C4×Dic43C2311yescharacteristic
116C2×C43⋊C8C2311yescharacteristic
117C2×C43⋊C8C2311yescharacteristic
118Dic172—22no—
119Dic172D414yescomplemented
120#10621873—22no—
121#10621873—22no—
122C8×D43—22no—
123C23×C43C2×D411yescharacteristic
124C22×D43—21no—
125C22×D43C2×D411yescharacteristic
126Q8×C43—21no—
127Q8×C43—21no—
128Q8×C43—21no—
129Q8×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43—21no—
135C2×C4×C43—21no—
136C2×C4×C43C2×D411yescharacteristic
137C2×C4×C43C2411yescharacteristic
138C22⋊D43—22no—
139C22⋊D43—42no—
140C2×Dic43—21no—
141C2×Dic43—21no—
142C2×Dic43—21no—
143C2×Dic43—42no—
144C2×Dic43C2×D411yescharacteristic
145C2×Dic43C2×D411yescharacteristic
146C2×Dic43C2×D411yescharacteristic
147D172—21no—
148D172—21no—
149D172—42no—
150C4×D43—21no—
151C4×D43—21no—
152C4×D43—42no—
153C4×D43—42no—
154C4×D43—42no—
155Dic86—21no—
156Dic86—21no—
157Dic86—21no—
158Dic86—21no—
159Dic86—42no—
160Dic86—42no—
161Dic86—42no—
162Dic86C2×D412yes—
163Dic86C2×D412yes—
164C8×C43—21no—
165C8×C43C2×D412yes—
166C43⋊C8—21no—
167C43⋊C8—21no—
168C22×C43—21no—
169C22×C43—21no—
170C22×C43—21no—
171C22×C43C22×D411yescharacteristic
172C2×D43—21no—
173C2×D43—21no—
174C2×D43—41no—
175C2×D43—41no—
176C2×D43—41no—
177C2×D43#13712yescomplemented
178C4×C43—21no—
179C4×C43—41no—
180C4×C43—41no—
181C4×C43—41no—
182C4×C43—41no—
183C4×C43C22×D411yescharacteristic
184C4×C43H(5,𝔽2)11yescharacteristic
185Dic43—22no—
186Dic43—22no—
187Dic43—21no—
188Dic43—21no—
189Dic43—21no—
190Dic43—41no—
191#3270—431nomaximal, Sylow
192C2×C43—41no—
193C2×C43D4211yescharacteristic
194C2×C43C2×#13711yescharacteristic
195C2×C43#57811yescharacteristic
196D43—22no—
197D43—81no—
198C2×#137—431no—
199C22×Q16—431no—
200D4×Q8—431no—
201#548—431no—
202#497—431no—
203#470D4311yescharacteristic, complemented
204#465—431no—
205#464—431no—
206#462—431no—
207#452—431no—
208#451—431no—
209#451—431no—
210#448—431no—
211#441—431no—
212#435—431no—
213C43#327011yescharacteristic, complemented, Sylow
214C2×#41—431no—
215C22×Q8—431no—
216C22×Q8—431no—
217C22×Q8—431no—
218#137—864no—
219C2×Q16—431no—
220C2×Q16—431no—
221C2×Q16—431no—
222C2×Q16—431no—
223C2×Q16—431no—
224C2×Q16—864no—
225C2×Q16C2×D4311yescharacteristic
226C2×SD16—431no—
227C2×SD16—431no—
228C2×SD16—431no—
229C2×M16C2×D4311yescharacteristic
230C22×C8—431no—
231C4⋊Q8—431no—
232C4⋊Q8—861no—
233#124—431no—
234#124—861no—
235C22⋊Q8—431no—
236C22⋊Q8—861no—
237C22⋊Q8—861no—
238C22⋊Q8—861no—
239C22⋊Q8C2×D4311yescharacteristic
240C22⋊Q8C2×D4311yescharacteristic
241#121—431no—
242#121—861no—
243C4×Q8—431no—
244C4×Q8—431no—
245C4×D4—431no—
246C4×D4—861no—
247C4×D4—861no—
248#106C2×D4311yescharacteristic
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⋊C8—431no—
258#97—431no—
259#41—862no—
260#41—1721no—
261C2×Q8—431no—
262C2×Q8—431no—
263C2×Q8—431no—
264C2×Q8—861no—
265C2×Q8—861no—
266C2×Q8—862no—
267C2×Q8—861no—
268C2×Q8—862no—
269C2×Q8—862no—
270C2×Q8—1721no—
271C2×Q8—1721no—
272C2×Q8—1721no—
273C2×Q8C22×D4311yescharacteristic
274C2×Q8C22×D4311yescharacteristic
275C2×D4—431no—
276C2×D4—431no—
277C2×D4—861no—
278C2×D4—861no—
279C22×C4—431no—
280C22×C4—861no—
281C22×C4—861no—
282C22×C4—861no—
283C22×C4—861no—
284C22×C4C22×D4311yescharacteristic
285Q16—22no—
286Q16—434no—
287Q16—862no—
288Q16—862no—
289Q16—862no—
290Q16—1721no—
291SD16—862no—
292SD16—862no—
293SD16—1721no—
294M16—22no—
295C2×C8—431no—
296C2×C8—431no—
297C2×C8—862no—
298C2×C8C22×D4311yescharacteristic
299C2×C8C22×D4311yescharacteristic
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—431no—
303C4⋊C4—861no—
304C4⋊C4—861no—
305C4⋊C4—861no—
306C4⋊C4—861no—
307C4⋊C4—861no—
308C4⋊C4C22×D4311yescharacteristic
309C4⋊C4C22×D4311yescharacteristic
310C22⋊C4—21no—
311C22⋊C4—21no—
312C22⋊C4—431no—
313C22⋊C4—431no—
314C22⋊C4—861no—
315C22⋊C4—861no—
316C22⋊C4—861no—
317C22⋊C4—861no—
318C42—431no—
319C42—861no—
320C42—861no—
321C23—431no—
322C23—861no—
323C23D4×D4311yescharacteristic
324Q8—21no—
325Q8—21no—
326Q8—21no—
327Q8—21no—
328Q8—432no—
329Q8—432no—
330Q8—861no—
331Q8—861no—
332Q8—861no—
333Q8—861no—
334Q8—1722no—
335Q8—1722no—
336Q8—1722no—
337D4—862no—
338D4—861no—
339D4—861no—
340D4—1722no—
341D4—1722no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
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—861no—
364C8—861no—
365C8D4×D4312yes—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—432no—
370C22—861no—
371C22—861no—
372C22—1721no—
373C22—1721no—
374C22—1721no—
375C22C2×D4×D4311yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—861no—
382C4—861no—
383C4—861no—
384C4—862no—
385C4—862no—
386C4—1721no—
387C4C2×D4×D4311yescharacteristic
388C4#1306337111yescharacteristic
389C2—41no—
390C2—862no—
391C2—3441no—
392C2#1458353311yescharacteristic
393C2#137×D4311yescharacteristic
394C2#1458371511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#470C2
socleC22×C43C22×D4
hypercenter#470D43
hypocenterC43#3270
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. C2×#13063358C2semidirect
2. C2×Q16×D43C2semidirect
3. #14583562C2semidirect
5. #14583292C2semidirect
6. #14583129C2semidirect
7. #14583124C2semidirect
8. #14583108C2semidirect
9. #14583059C2semidirect
10. #14583056C2semidirect
11. #14583054C2semidirect
12. #14583039C2semidirect
13. #14583005C2semidirect
14. #14582968C2semidirect
15. C43×#470C2semidirect
119. Dic172D4semidirect
177. C2×D43#137semidirect
203. #470D43semidirect
213. C43#3270semidirect