Finite Group Databasebeta

← #19145574

Subgroups — #19145574

Order 5504.

400 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583445C211yesmaximal, characteristic, complemented
2#14583435C211yesmaximal, characteristic, complemented
3#14583284C211yesmaximal, characteristic, complemented
4#14583280C211yesmaximal, characteristic, complemented
5#14583255C211yesmaximal, characteristic, complemented
6#14583252C211yesmaximal, characteristic, complemented
7#14583107C211yesmaximal, characteristic, complemented
8#14583103C211yesmaximal, characteristic, complemented
9#14583097C211yesmaximal, characteristic, complemented
10#14583093C211yesmaximal, characteristic, complemented
11#14583059C211yesmaximal, characteristic, complemented
12#14583046C211yesmaximal, characteristic, complemented
13#14583044C211yesmaximal, characteristic, complemented
14#14582949C211yesmaximal, characteristic, complemented
15C43×#452C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C2×#10621885C2211yescharacteristic
18C2×#10621873C2211yescharacteristic
19C2×#10621884C2211yescharacteristic
20C2×#10621884C2211yescharacteristic
21C2×D344C2211yescharacteristic
22C2×#10621882C2211yescharacteristic
23#13063323C2211yescharacteristic
24#13063321C2211yescharacteristic
25#13063320—21no—
26#13063316C2211yescharacteristic
27#13063314C2211yescharacteristic
28#13063314C2211yescharacteristic
29#13063312C2211yescharacteristic
30#13063309—21no—
31#13063299C2211yescharacteristic
32#13063297—21no—
33#13063297—21no—
34Q8×Dic43C2211yescharacteristic
35#13063287C2211yescharacteristic
36C4×C22⋊D43—21no—
37C4×C22⋊D43—21no—
38(C22⋊D43)⋊C4—21no—
39#13063283—21no—
40C2×C4×Dic43C2211yescharacteristic
41Dic43⋊C8C2211yescharacteristic
42Dic43⋊C8C2211yescharacteristic
43#13063250C2211yescharacteristic
44#13063249C2211yescharacteristic
45#13063248C2211yescharacteristic
46#13063247C2211yescharacteristic
47#13063246C2211yescharacteristic
48#13063245C2211yescharacteristic
49C22⋊(C43⋊C8)C2211yescharacteristic
50C8×Dic43C2211yescharacteristic
51C8×Dic43C2211yescharacteristic
52C2×#41×C43C2211yescharacteristic
53C2×Q16×C43C2211yescharacteristic
54C2×SD16×C43C2211yescharacteristic
55C22⋊Q8×C43C2211yescharacteristic
56#103×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58C22⋊C8×C43C2211yescharacteristic
59#41×C43—41no—
60#41×C43—41no—
61C2×Q8×C43C2311yescharacteristic
62C2×Q8×C43C2311yescharacteristic
63C2×D4×C43—21no—
64C2×D4×C43C2311yescharacteristic
65C22×C4×C43—21no—
66C22×C4×C43C2311yescharacteristic
67C2×C22⋊D43—21no—
68C2×C22⋊D43—21no—
69C2×C22⋊D43—21no—
70C2×C22⋊D43—21no—
71C22×Dic43D411yescharacteristic
72C22×Dic43D411yescharacteristic
73#10621898—41no—
74#10621898—41no—
75C2×D172C2311yescharacteristic
76C2×D172C2311yescharacteristic
77C2×C4×D43—21no—
78C2×C4×D43—21no—
79C2×Dic86C2311yescharacteristic
80Q16×C43—41no—
81SD16×C43—41no—
82C2×C8×C43C2311yescharacteristic
83C2×C8×C43C2311yescharacteristic
84C4⋊C4×C43—21no—
85C4⋊C4×C43C2311yescharacteristic
86C22⋊C4×C43—21no—
87C22⋊Dic43—21no—
88C22⋊Dic43—21no—
89#10621885—41no—
90#10621884—41no—
91#10621884—41no—
92#10621882—41no—
93(C2×D43)⋊C4—21no—
94(C2×D43)⋊C4—21no—
95(C2×D43)⋊C4—21no—
96(C2×D43)⋊C4—21no—
97(C2×D43)⋊C4—21no—
98(C2×D43)⋊C4—21no—
99C4⋊Dic43—21no—
100C4⋊Dic43—21no—
101C4⋊Dic43C2311yescharacteristic
102Dic43⋊C4—21no—
103Dic43⋊C4—21no—
104Dic43⋊C4—21no—
105C4×Dic43—21no—
106C4×Dic43D411yescharacteristic
107C4×Dic43D411yescharacteristic
108C4×Dic43C2311yescharacteristic
109C4×Dic43C2311yescharacteristic
110C2×C43⋊C8C2311yescharacteristic
111C2×C43⋊C8C2311yescharacteristic
112D344—41no—
113#10621873—41no—
114C23×C43—21no—
115C23×C43C2×D411yescharacteristic
116C22×D43—21no—
117C22×D43—21no—
118Q8×C43—21no—
119Q8×C43—21no—
120Q8×C43—21no—
121Q8×C43—21no—
122D4×C43—21no—
123D4×C43—21no—
124D4×C43—42no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—42no—
131C2×C4×C43C2×D411yescharacteristic
132C2×C4×C43C2411yescharacteristic
133C22⋊D43—42no—
134C22⋊D43—42no—
135C22⋊D43—42no—
136C22⋊D43—42no—
137C2×Dic43—22no—
138C2×Dic43—21no—
139C2×Dic43—21no—
140C2×Dic43—41no—
141C2×Dic43C2×D411yescharacteristic
142C2×Dic43C2×D411yescharacteristic
143C2×Dic43C2×D411yescharacteristic
144C2×Dic43C2×D411yescharacteristic
145D172—21no—
146D172—21no—
147D172—21no—
148D172—21no—
149C4×D43—42no—
150C4×D43—42no—
151Dic86—21no—
152Dic86—21no—
153C8×C43—21no—
154C8×C43—21no—
155C43⋊C8—21no—
156C43⋊C8—21no—
157C22×C43—21no—
158C22×C43—21no—
159C22×C43—21no—
160C22×C43—41no—
161C22×C43—41no—
162C22×C43—41no—
163C22×C43C22×D411yescharacteristic
164C2×D43—41no—
165C2×D43—41no—
166C2×D43—41no—
167C2×D43—41no—
168C2×D43—41no—
169C2×D43—41no—
170C4×C43—21no—
171C4×C43—41no—
172C4×C43—41no—
173C4×C43—41no—
174C4×C43H(5,𝔽2)11yescharacteristic
175C4×C43H(5,𝔽2)11yescharacteristic
176Dic43—21no—
177Dic43—21no—
178Dic43—21no—
179Dic43—41no—
180Dic43—41no—
181Dic43#13512yes—
182#3212—431nomaximal, Sylow
183C2×C43—41no—
184C2×C43—81no—
185C2×C43#53511yescharacteristic
186C2×C43C2×#13511yescharacteristic
187C2×C43#57511yescharacteristic
188D43—81no—
189D43—81no—
190#532—431no—
191#529—431no—
192#495—431no—
193#495—431no—
194#488—431no—
195#488—431no—
196#462—431no—
197#461—431no—
198#460—431no—
199#459—431no—
200#452—431no—
201#452D4311yescharacteristic, complemented
202#449—431no—
203#449—431no—
204#431—431no—
205C43#321211yescharacteristic, complemented, Sylow
206C2×#41—431no—
207C2×#41C2×D4311yescharacteristic
208C2×Q16—431no—
209C2×Q16C2×D4311yescharacteristic
210C2×SD16—431no—
211C2×SD16—431no—
212C2×SD16—431no—
213C2×SD16C2×D4311yescharacteristic
214C2×D8—431no—
215C2×D8—431no—
216C4⋊Q8—431no—
217#127—431no—
218#126—861no—
219#125—431no—
220#124—431no—
221#124—431no—
222#124—431no—
223#123—861no—
224C22⋊Q8C2×D4311yescharacteristic
225#121—431no—
226#121—861no—
227#121—861no—
228C4×Q8—431no—
229C4×D4—431no—
230C4×D4—861no—
231C4×D4—861no—
232C4×D4—861no—
233#117—861no—
234C2×C42—431no—
235C4⋊C8—431no—
236C4⋊C8—431no—
237#103—431no—
238#103—431no—
239#103—431no—
240#103C2×D4311yescharacteristic
241#102—431no—
242#102—431no—
243#102—431no—
244#102C2×D4311yescharacteristic
245C22⋊C8—431no—
246C22⋊C8C2×D4311yescharacteristic
247C4×C8—431no—
248C4×C8—431no—
249#41—41no—
250#41—41no—
251#41—1721no—
252#41—1721no—
253C2×Q8—431no—
254C2×Q8C22×D4311yescharacteristic
255C2×Q8C22×D4311yescharacteristic
256C2×D4—21no—
257C2×D4—431no—
258C2×D4—431no—
259C2×D4—861no—
260C2×D4—861no—
261C2×D4—861no—
262C2×D4—861no—
263C2×D4C22×D4311yescharacteristic
264C22×C4—21no—
265C22×C4—431no—
266C22×C4—431no—
267C22×C4—861no—
268C22×C4—861no—
269C22×C4C22×D4311yescharacteristic
270Q16—41no—
271Q16—1721no—
272SD16—41no—
273SD16—1721no—
274SD16—1721no—
275SD16—1721no—
276D8—1721no—
277D8—1721no—
278C2×C8—431no—
279C2×C8—431no—
280C2×C8C22×D4311yescharacteristic
281C2×C8C22×D4311yescharacteristic
282C4⋊C4—21no—
283C4⋊C4—431no—
284C4⋊C4—861no—
285C4⋊C4—861no—
286C4⋊C4—861no—
287C4⋊C4—861no—
288C4⋊C4—861no—
289C4⋊C4C22×D4311yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—861no—
292C22⋊C4—861no—
293C22⋊C4—861no—
294C22⋊C4—861no—
295C22⋊C4—861no—
296C22⋊C4—861no—
297C22⋊C4—861no—
298C22⋊C4—861no—
299C42—431no—
300C42—431no—
301C42—431no—
302C42—431no—
303C42—861no—
304C23—21no—
305C23—861no—
306C23—861no—
307C23D4×D4311yescharacteristic
308Q8—21no—
309Q8—21no—
310Q8—21no—
311Q8—21no—
312Q8—861no—
313Q8—861no—
314D4—21no—
315D4—21no—
316D4—42no—
317D4—861no—
318D4—861no—
319D4—861no—
320D4—861no—
321D4—1722no—
322D4—1722no—
323D4—1722no—
324D4—1722no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—42no—
331C2×C4—431no—
332C2×C4—431no—
333C2×C4—431no—
334C2×C4—431no—
335C2×C4—862no—
336C2×C4—861no—
337C2×C4—861no—
338C2×C4—1722no—
339C2×C4—1722no—
340C2×C4—1721no—
341C2×C4D4×D4311yescharacteristic
342C2×C4C23×D4311yescharacteristic
343C8—21no—
344C8—21no—
345C8—861no—
346C8—861no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—1721no—
354C22—1721no—
355C22—1721no—
356C22—1721no—
357C22—1721no—
358C22—1721no—
359C22C2×D4×D4311yescharacteristic
360C4—21no—
361C4—41no—
362C4—41no—
363C4—41no—
364C4—432no—
365C4—861no—
366C4—861no—
367C4—861no—
368C4—1721no—
369C4—1721no—
370C4#1306337011yescharacteristic
371C4#1306337011yescharacteristic
372C2—41no—
373C2—81no—
374C2—3441no—
375C2—3441no—
376C2#1458346411yescharacteristic
377C2#135×D4311yescharacteristic
378C2#1458369811yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#452C2
socleC22×C43C22×D4
hypercenter#452D43
hypocenterC43#3212
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. #14583445C2semidirect
2. #14583435C2semidirect
3. #14583284C2semidirect
4. #14583280C2semidirect
5. #14583255C2semidirect
6. #14583252C2semidirect
7. #14583107C2semidirect
8. #14583103C2semidirect
9. #14583097C2semidirect
10. #14583093C2semidirect
11. #14583059C2semidirect
12. #14583046C2semidirect
13. #14583044C2semidirect
14. #14582949C2semidirect
15. C43×#452C2semidirect
201. #452D43semidirect
205. C43#3212semidirect