Finite Group Databasebeta

← #19146159

Subgroups — #19146159

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×Q16×D43C211yesmaximal, characteristic, complemented
2Q8×C22⋊D43C211yesmaximal, characteristic, complemented
3#14583556C211yesmaximal, characteristic
4#14583290C211yesmaximal, characteristic, complemented
5#14583157C211yesmaximal, characteristic, complemented
6#14583125C211yesmaximal, characteristic, complemented
7#14583119C211yesmaximal, characteristic, complemented
8#14583107C211yesmaximal, characteristic, complemented
9#14583061C211yesmaximal, characteristic, complemented
10#14583055C211yesmaximal, characteristic, complemented
11#14583053C211yesmaximal, characteristic, complemented
12#14583036C211yesmaximal, characteristic, complemented
13#14583006C211yesmaximal, characteristic, complemented
14#14582968C211yesmaximal, characteristic, complemented
15C2×#137×C43C211yesmaximal, characteristic, complemented
16C2×Q8×D43C2211yescharacteristic
17C2×Q8×D43C2211yescharacteristic
18C2×Dic172C2211yescharacteristic
19C2×#10621885C2211yescharacteristic
20C2×#10621885C2211yescharacteristic
21C2×#10621885C2211yescharacteristic
22Q16×D43—24no—
23C2×#10621883C2211yescharacteristic
24C2×C8×D43C2211yescharacteristic
25#13063323—21no—
26#13063323C2211yescharacteristic
27#13063312—21no—
28#13063312C2211yescharacteristic
29#13063304—21no—
30#13063304—21no—
31#13063304C2211yescharacteristic
32#13063304C2211yescharacteristic
33#13063301—21no—
34#13063301C2211yescharacteristic
35#13063296—21no—
36#13063296C2211yescharacteristic
37Q8×Dic43C2211yescharacteristic
38Q8×Dic43C2211yescharacteristic
39C4×C22⋊D43—21no—
40C4×C22⋊D43—21no—
41C4×C22⋊D43C2211yescharacteristic
42#13063257C2211yescharacteristic
43Dic43⋊C8C2211yescharacteristic
44#13063250C2211yescharacteristic
45#13063250C2211yescharacteristic
46#13063249C2211yescharacteristic
47#13063249C2211yescharacteristic
48#13063249C2211yescharacteristic
49#13063246C2211yescharacteristic
50C22⋊(C43⋊C8)C2211yescharacteristic
51(C2×D43)⋊C8C2211yescharacteristic
52#13063235C2211yescharacteristic
53C2×#41×C43C2211yescharacteristic
54C22×Q8×C43C2211yescharacteristic
55#137×C43—24no—
56C2×Q16×C43C2211yescharacteristic
57C2×Q16×C43C2211yescharacteristic
58C2×SD16×C43C2211yescharacteristic
59C2×SD16×C43C2211yescharacteristic
60C2×M16×C43C2211yescharacteristic
61#41×C43—22no—
62#41×C43—41no—
63C2×Q8×C43—21no—
64C2×Q8×C43—22no—
65C2×Q8×C43—41no—
66C2×Q8×C43C2311yescharacteristic
67C2×Q8×C43C2311yescharacteristic
68C2×Q8×C43C2311yescharacteristic
69C2×D4×C43—21no—
70C2×D4×C43C2311yescharacteristic
71C22×C4×C43—21no—
72C22×C4×C43—21no—
73C22×C4×C43C2311yescharacteristic
74C2×C22⋊D43—21no—
75C2×C22⋊D43D411yescharacteristic
76Q8×D43—22no—
77Q8×D43—22no—
78Q8×D43—41no—
79Q8×D43—41no—
80C2×C4×D43—21no—
81C2×C4×D43—21no—
82C2×C4×D43C2311yescharacteristic
83C2×Dic86—21no—
84C2×Dic86—21no—
85C2×Dic86C2311yescharacteristic
86C2×Dic86C2311yescharacteristic
87Q16×C43—22no—
88Q16×C43D414yescomplemented
89SD16×C43—22no—
90SD16×C43—22no—
91M16×C43—22no—
92C2×C8×C43C2311yescharacteristic
93C2×C8×C43C2311yescharacteristic
94C22⋊Dic43—21no—
95C22⋊Dic43—21no—
96C22⋊Dic43—21no—
97C22⋊Dic43—21no—
98C22⋊Dic43—21no—
99C22⋊Dic43D411yescharacteristic
100#10621885—22no—
101#10621885—22no—
102#10621885—41no—
103#10621883—41no—
104(C2×D43)⋊C4—21no—
105(C2×D43)⋊C4D411yescharacteristic
106C4⋊Dic43—21no—
107C4⋊Dic43—21no—
108C4⋊Dic43C2311yescharacteristic
109C4⋊Dic43C2311yescharacteristic
110Dic43⋊C4—21no—
111Dic43⋊C4—21no—
112Dic43⋊C4—21no—
113Dic43⋊C4—21no—
114Dic43⋊C4—21no—
115Dic43⋊C4D411yescharacteristic
116C4×Dic43—21no—
117C4×Dic43—21no—
118C4×Dic43C2311yescharacteristic
119C2×C43⋊C8C2311yescharacteristic
120C2×C43⋊C8C2311yescharacteristic
121Dic172—22no—
122C8×D43—22no—
123C23×C43—21no—
124C23×C43C2×D411yescharacteristic
125C22×D43C2×D411yescharacteristic
126Q8×C43—21no—
127Q8×C43—21no—
128Q8×C43—21no—
129Q8×C43—21no—
130Q8×C43—42no—
131Q8×C43C2×D412yes—
132Q8×C43C2×D412yes—
133D4×C43—21no—
134D4×C43—21no—
135D4×C43—42no—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
138C2×C4×C43—21no—
139C2×C4×C43—21no—
140C2×C4×C43—21no—
141C2×C4×C43—42no—
142C2×C4×C43—42no—
143C2×C4×C43C2×D411yescharacteristic
144C2×C4×C43C2411yescharacteristic
145C22⋊D43—22no—
146C22⋊D43—42no—
147C2×Dic43—21no—
148C2×Dic43—21no—
149C2×Dic43—21no—
150C2×Dic43—21no—
151C2×Dic43C2×D411yescharacteristic
152C2×Dic43C2×D411yescharacteristic
153C2×Dic43C2×D411yescharacteristic
154C4×D43—21no—
155C4×D43—21no—
156C4×D43—42no—
157C4×D43—42no—
158Dic86—21no—
159Dic86—21no—
160Dic86—21no—
161Dic86—21no—
162Dic86—42no—
163Dic86—42no—
164C8×C43—21no—
165C8×C43C2×D412yes—
166C43⋊C8—21no—
167C43⋊C8—21no—
168C22×C43—21no—
169C22×C43—21no—
170C22×C43—21no—
171C22×C43—41no—
172C22×C43—41no—
173C22×C43—41no—
174C22×C43C22×D411yescharacteristic
175C2×D43—21no—
176C2×D43—21no—
177C2×D43#13712yescomplemented
178C4×C43—22no—
179C4×C43—22no—
180C4×C43—21no—
181C4×C43—41no—
182C4×C43C22×D411yescharacteristic
183C4×C43H(5,𝔽2)11yescharacteristic
184Dic43—21no—
185Dic43—21no—
186Dic43—21no—
187Dic43—41no—
188Dic43—41no—
189Dic43—41no—
190Dic43—41no—
191#3270—431nomaximal, Sylow
192C2×C43—41no—
193C2×C43—81no—
194C2×C43D4211yescharacteristic
195C2×C43C2×#13711yescharacteristic
196C2×C43#57811yescharacteristic
197D43—22no—
198C2×#137D4311yescharacteristic, complemented
199C22×Q16—431no—
200D4×Q8—431no—
201#548—431no—
202#497—431no—
203#470—431no—
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×#41C2×D4311yescharacteristic
215C22×Q8—431no—
216C22×Q8—431no—
217C22×Q8C2×D4311yescharacteristic
218#137—24no—
219C2×Q16—431no—
220C2×Q16—431no—
221C2×Q16—431no—
222C2×Q16—431no—
223C2×Q16—864no—
224C2×Q16C2×D4311yescharacteristic
225C2×Q16C2×D4311yescharacteristic
226C2×SD16—431no—
227C2×SD16C2×D4311yescharacteristic
228C2×SD16C2×D4311yescharacteristic
229C2×M16C2×D4311yescharacteristic
230C22×C8—431no—
231C4⋊Q8—431no—
232C4⋊Q8—861no—
233#124—431no—
234#124—861no—
235C22⋊Q8—431no—
236C22⋊Q8—431no—
237C22⋊Q8—431no—
238C22⋊Q8—861no—
239C22⋊Q8—861no—
240C22⋊Q8—861no—
241#121—431no—
242#121—861no—
243C4×Q8—431no—
244C4×Q8—431no—
245C4×D4—431no—
246C4×D4—861no—
247C4×D4—861no—
248#106—431no—
249C4⋊C8—431no—
250#103—431no—
251#103—431no—
252#103—431no—
253#103—431no—
254#103—431no—
255#102—431no—
256C22⋊C8—431no—
257C22⋊C8—431no—
258#97—431no—
259#41—22no—
260#41—41no—
261C2×Q8—21no—
262C2×Q8—22no—
263C2×Q8—41no—
264C2×Q8—431no—
265C2×Q8—431no—
266C2×Q8—861no—
267C2×Q8—861no—
268C2×Q8—862no—
269C2×Q8—862no—
270C2×Q8—1721no—
271C2×Q8—1721no—
272C2×Q8C22×D4311yescharacteristic
273C2×Q8C22×D4311yescharacteristic
274C2×Q8C22×D4311yescharacteristic
275C2×D4—21no—
276C2×D4—431no—
277C2×D4—861no—
278C2×D4C22×D4311yescharacteristic
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—431no—
282C22×C4—861no—
283C22×C4—861no—
284C22×C4C22×D4311yescharacteristic
285Q16—22no—
286Q16—862no—
287Q16—862no—
288Q16—862no—
289Q16—1721no—
290Q16C22⋊D4314yescomplemented
291SD16—22no—
292SD16—22no—
293SD16—1721no—
294M16—22no—
295C2×C8—431no—
296C2×C8—431no—
297C2×C8—862no—
298C2×C8C22×D4311yescharacteristic
299C2×C8C22×D4311yescharacteristic
300C4⋊C4—431no—
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—
310C22⋊C4—431no—
311C22⋊C4—431no—
312C22⋊C4—861no—
313C22⋊C4—861no—
314C22⋊C4—861no—
315C22⋊C4—861no—
316C22⋊C4—861no—
317C22⋊C4—861no—
318C42—431no—
319C42—861no—
320C42—861no—
321C23—21no—
322C23—431no—
323C23D4×D4311yescharacteristic
324Q8—21no—
325Q8—21no—
326Q8—21no—
327Q8—21no—
328Q8—42no—
329Q8—861no—
330Q8—861no—
331Q8—861no—
332Q8—861no—
333Q8—1722no—
334Q8—1722no—
335Q8C2×C22⋊D4312yes—
336Q8C2×C22⋊D4312yes—
337D4—21no—
338D4—21no—
339D4—42no—
340D4—862no—
341D4—1722no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—431no—
350C2×C4—431no—
351C2×C4—431no—
352C2×C4—861no—
353C2×C4—861no—
354C2×C4—861no—
355C2×C4—861no—
356C2×C4—861no—
357C2×C4—861no—
358C2×C4—1722no—
359C2×C4—1722no—
360C2×C4D4×D4311yescharacteristic
361C2×C4C23×D4311yescharacteristic
362C8—21no—
363C8—861no—
364C8—861no—
365C8C2×C22⋊D4312yes—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—432no—
373C22—861no—
374C22—861no—
375C22C2×D4×D4311yescharacteristic
376C4—21no—
377C4—22no—
378C4—22no—
379C4—41no—
380C4—861no—
381C4—861no—
382C4—861no—
383C4—1721no—
384C4—1721no—
385C4—1721no—
386C4—1721no—
387C4C22×C22⋊D4311yescharacteristic
388C4#1306337011yescharacteristic
389C2—41no—
390C2—81no—
391C2—862no—
392C2D4×C22⋊D4311yescharacteristic
393C2#137×D4311yescharacteristic
394C2#1458371511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC2×#137×C43C2
socleC22×C43C22×D4
hypercenterC2×#137D43
hypocenterC43#3270
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×Q16×D43C2semidirect
2. Q8×C22⋊D43C2semidirect
4. #14583290C2semidirect
5. #14583157C2semidirect
6. #14583125C2semidirect
7. #14583119C2semidirect
8. #14583107C2semidirect
9. #14583061C2semidirect
10. #14583055C2semidirect
11. #14583053C2semidirect
12. #14583036C2semidirect
13. #14583006C2semidirect
14. #14582968C2semidirect
15. C2×#137×C43C2semidirect
88. Q16×C43D4semidirect
177. C2×D43#137semidirect
198. C2×#137D43semidirect
213. C43#3270semidirect
290. Q16C22⋊D43semidirect