Finite Group Databasebeta

← #19145492

Subgroups — #19145492

Order 5504.

402 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583477C211yesmaximal, characteristic, complemented
2#14583234C211yesmaximal, characteristic, complemented
3#14583232C211yesmaximal, characteristic, complemented
4#14583212C211yesmaximal, characteristic, complemented
5#14583210C211yesmaximal, characteristic, complemented
6#14583147C211yesmaximal, characteristic, complemented
7#14583143C211yesmaximal, characteristic, complemented
8#14583138C211yesmaximal, characteristic, complemented
9#14583133C211yesmaximal, characteristic, complemented
10#14583061C211yesmaximal, characteristic, complemented
11#14583059C211yesmaximal, characteristic, complemented
12#14583044C211yesmaximal, characteristic, complemented
13#14583042C211yesmaximal, characteristic, complemented
14#14582866C211yesmaximal, characteristic, complemented
15C43×#537C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C2×#10621885C2211yescharacteristic
18C2×#10621883C2211yescharacteristic
19C2×#10621884C2211yescharacteristic
20C2×#10621882C2211yescharacteristic
21C2×#10621877C2211yescharacteristic
22C22×C43⋊C8C2211yescharacteristic
23#13063304C2211yescharacteristic
24#13063304C2211yescharacteristic
25#13063301—21no—
26#13063299C2211yescharacteristic
27#13063299C2211yescharacteristic
28#13063297—21no—
29#13063297—21no—
30#13063296—21no—
31C2×C4⋊Dic43C2211yescharacteristic
32#13063258C2211yescharacteristic
33#13063258C2211yescharacteristic
34#13063258C2211yescharacteristic
35#13063258C2211yescharacteristic
36#13063249C2211yescharacteristic
37#13063249C2211yescharacteristic
38#13063248C2211yescharacteristic
39#13063248C2211yescharacteristic
40#13063246C2211yescharacteristic
41#13063246C2211yescharacteristic
42#13063245C2211yescharacteristic
43#13063245C2211yescharacteristic
44C22⋊(C43⋊C8)C2211yescharacteristic
45C22⋊(C43⋊C8)C2211yescharacteristic
46C22⋊(C43⋊C8)C2211yescharacteristic
47C22⋊(C43⋊C8)C2211yescharacteristic
48C2×#41×C43C2211yescharacteristic
49C2×#41×C43C2211yescharacteristic
50C22⋊Q8×C43—21no—
51C22⋊Q8×C43C2211yescharacteristic
52C22⋊Q8×C43C2211yescharacteristic
53#121×C43—21no—
54#121×C43—21no—
55#121×C43—21no—
56#121×C43C2211yescharacteristic
57#121×C43C2211yescharacteristic
58C2×C4⋊C4×C43C2211yescharacteristic
59#41×C43—41no—
60#41×C43—41no—
61#41×C43—41no—
62#41×C43—41no—
63C2×Q8×C43D411yescharacteristic
64C2×Q8×C43C2311yescharacteristic
65C2×D4×C43—21no—
66C2×D4×C43—21no—
67C2×D4×C43—21no—
68C2×D4×C43D411yescharacteristic
69C2×D4×C43D411yescharacteristic
70C2×D4×C43D411yescharacteristic
71C2×D4×C43C2311yescharacteristic
72C22×C4×C43—21no—
73C22×C4×C43—21no—
74C22×C4×C43C2311yescharacteristic
75C22×C4×C43C2311yescharacteristic
76C22×C4×C43C2311yescharacteristic
77C2×C22⋊D43—21no—
78C2×C22⋊D43—21no—
79C2×C22⋊D43—21no—
80C22×Dic43—21no—
81#10621898—41no—
82#10621898—41no—
83C2×D172C2311yescharacteristic
84C2×C4×D43—21no—
85C2×Dic86C2311yescharacteristic
86C4⋊C4×C43—21no—
87C4⋊C4×C43—21no—
88C4⋊C4×C43—21no—
89C4⋊C4×C43C2311yescharacteristic
90C4⋊C4×C43C2311yescharacteristic
91C22⋊C4×C43—21no—
92C22⋊C4×C43—21no—
93C22⋊C4×C43—21no—
94C22⋊C4×C43—21no—
95C22⋊Dic43—21no—
96C22⋊Dic43—21no—
97#10621885—41no—
98#10621884—41no—
99#10621883—41no—
100#10621882—41no—
101(C2×D43)⋊C4—21no—
102(C2×D43)⋊C4—21no—
103C4⋊Dic43—21no—
104C4⋊Dic43C2311yescharacteristic
105C4⋊Dic43C2311yescharacteristic
106Dic43⋊C4—21no—
107Dic43⋊C4—21no—
108#10621877—41no—
109C2×C43⋊C8—41no—
110C2×C43⋊C8C2311yescharacteristic
111C2×C43⋊C8C2311yescharacteristic
112C2×C43⋊C8C2311yescharacteristic
113C2×C43⋊C8C2311yescharacteristic
114C23×C43—21no—
115C23×C43C2×D411yescharacteristic
116C23×C43C2×D411yescharacteristic
117C23×C43C2×D411yescharacteristic
118C22×D43—21no—
119Q8×C43—21no—
120Q8×C43—21no—
121Q8×C43—41no—
122D4×C43—21no—
123D4×C43—21no—
124D4×C43—41no—
125D4×C43—41no—
126D4×C43—41no—
127D4×C43—42no—
128D4×C43—81no—
129D4×C43—81no—
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×C43—21no—
137C2×C4×C43—21no—
138C2×C4×C43—21no—
139C2×C4×C43—42no—
140C2×C4×C43—81no—
141C2×C4×C43C2×D411yescharacteristic
142C2×C4×C43C2×D411yescharacteristic
143C2×C4×C43C2×D411yescharacteristic
144C2×C4×C43C2411yescharacteristic
145C22⋊D43—42no—
146C22⋊D43—81no—
147C22⋊D43—81no—
148C2×Dic43—21no—
149C2×Dic43—21no—
150C2×Dic43—21no—
151C2×Dic43—81no—
152D172—21no—
153D172—21no—
154C4×D43—42no—
155Dic86—21no—
156Dic86—21no—
157C43⋊C8—21no—
158C43⋊C8—21no—
159C43⋊C8—21no—
160C43⋊C8—21no—
161C22×C43—21no—
162C22×C43—21no—
163C22×C43—21no—
164C22×C43—21no—
165C22×C43—21no—
166C22×C43—21no—
167C22×C43—21no—
168C22×C43—21no—
169C22×C43—21no—
170C22×C43—41no—
171C22×C43—41no—
172C22×C43—41no—
173C22×C43C22×D411yescharacteristic
174C2×D43—41no—
175C2×D43—41no—
176C2×D43—41no—
177C4×C43—21no—
178C4×C43—21no—
179C4×C43—21no—
180C4×C43—41no—
181C4×C43—41no—
182C4×C43—41no—
183C4×C43H(5,𝔽2)11yescharacteristic
184C4×C43H(5,𝔽2)11yescharacteristic
185Dic43—41no—
186Dic43—41no—
187Dic43—41no—
188#3203—431nomaximal, Sylow
189C2×C43—41no—
190C2×C43—41no—
191C2×C43—41no—
192C2×C43—81no—
193C2×C43#53411yescharacteristic
194C2×C43#57611yescharacteristic
195C2×C43#57811yescharacteristic
196D43—81no—
197#537—431no—
198#537D4311yescharacteristic, complemented
199#484—431no—
200#484—431no—
201#480—431no—
202#480—431no—
203#468—431no—
204#468—431no—
205#467—431no—
206#466—431no—
207#452—431no—
208#452—431no—
209#449—431no—
210#449—431no—
211#408—431no—
212C43#320311yescharacteristic, complemented, Sylow
213C2×#41—431no—
214C2×#41C2×D4311yescharacteristic
215C2×#41C2×D4311yescharacteristic
216C2×Q16—431no—
217C2×SD16—431no—
218C2×SD16—431no—
219C2×D8—431no—
220C2×M16—431no—
221C22×C8—431no—
222C22⋊Q8—21no—
223C22⋊Q8—431no—
224C22⋊Q8—431no—
225C22⋊Q8—861no—
226C22⋊Q8C2×D4311yescharacteristic
227C22⋊Q8C2×D4311yescharacteristic
228#121—21no—
229#121—21no—
230#121—21no—
231#121—431no—
232#121—431no—
233#121—861no—
234#121—861no—
235#121—861no—
236#121C2×D4311yescharacteristic
237#121C2×D4311yescharacteristic
238C2×C4⋊C4—431no—
239C2×C4⋊C4C2×D4311yescharacteristic
240#107—431no—
241#107—431no—
242#107—431no—
243#107—431no—
244#103—431no—
245#103—431no—
246#103—431no—
247#103—431no—
248#102—431no—
249#102—431no—
250#102—431no—
251#102—431no—
252C22⋊C8—431no—
253C22⋊C8—431no—
254C22⋊C8—431no—
255C22⋊C8—431no—
256#41—41no—
257#41—41no—
258#41—41no—
259#41—41no—
260#41—1721no—
261#41—1721no—
262C2×Q8—431no—
263C2×Q8C22⋊D4311yescharacteristic
264C2×Q8C22×D4311yescharacteristic
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—431no—
269C2×D4—861no—
270C2×D4—861no—
271C2×D4—861no—
272C2×D4C22⋊D4311yescharacteristic
273C2×D4C22⋊D4311yescharacteristic
274C2×D4C22⋊D4311yescharacteristic
275C2×D4C22×D4311yescharacteristic
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—861no—
279C22×C4—861no—
280C22×C4C22×D4311yescharacteristic
281C22×C4C22×D4311yescharacteristic
282C22×C4C22×D4311yescharacteristic
283Q16—1721no—
284SD16—1721no—
285SD16—1721no—
286D8—1721no—
287M16—1721no—
288C2×C8—431no—
289C2×C8—431no—
290C2×C8—431no—
291C2×C8—431no—
292C2×C8—1721no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—431no—
297C4⋊C4—431no—
298C4⋊C4—861no—
299C4⋊C4—861no—
300C4⋊C4—861no—
301C4⋊C4C22×D4311yescharacteristic
302C4⋊C4C22×D4311yescharacteristic
303C22⋊C4—21no—
304C22⋊C4—21no—
305C22⋊C4—21no—
306C22⋊C4—21no—
307C22⋊C4—861no—
308C22⋊C4—861no—
309C22⋊C4—861no—
310C22⋊C4—861no—
311C23—21no—
312C23—861no—
313C23C2×C22⋊D4311yescharacteristic
314C23C2×C22⋊D4311yescharacteristic
315C23C2×C22⋊D4311yescharacteristic
316Q8—21no—
317Q8—21no—
318Q8—41no—
319Q8—861no—
320Q8—861no—
321D4—21no—
322D4—21no—
323D4—41no—
324D4—41no—
325D4—41no—
326D4—42no—
327D4—81no—
328D4—81no—
329D4—861no—
330D4—861no—
331D4—3441no—
332D4—3441no—
333D4—1722no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—42no—
344C2×C4—81no—
345C2×C4—861no—
346C2×C4—861no—
347C2×C4—861no—
348C2×C4—3441no—
349C2×C4—1722no—
350C2×C4C2×C22⋊D4311yescharacteristic
351C2×C4C2×C22⋊D4311yescharacteristic
352C2×C4C2×C22⋊D4311yescharacteristic
353C2×C4C23×D4311yescharacteristic
354C8—861no—
355C8—861no—
356C8—861no—
357C8—861no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—1721no—
371C22—1721no—
372C22—1721no—
373C22C22×C22⋊D4311yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—1721no—
381C4—1721no—
382C4—1721no—
383C4#1306337011yescharacteristic
384C4#1306337011yescharacteristic
385C2—41no—
386C2—41no—
387C2—41no—
388C2—81no—
389C2—3441no—
390C2#1458345811yescharacteristic
391C2#1458370211yescharacteristic
392C2#1458371411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#537C2
socleC22×C43C22×D4
hypercenter#537D43
hypocenterC43#3203
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#41 ◁ #537

Complements

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

NH ≅ G/Ntype
1. #14583477C2semidirect
2. #14583234C2semidirect
3. #14583232C2semidirect
4. #14583212C2semidirect
5. #14583210C2semidirect
6. #14583147C2semidirect
7. #14583143C2semidirect
8. #14583138C2semidirect
9. #14583133C2semidirect
10. #14583061C2semidirect
11. #14583059C2semidirect
12. #14583044C2semidirect
13. #14583042C2semidirect
14. #14582866C2semidirect
15. C43×#537C2semidirect
198. #537D43semidirect
212. C43#3203semidirect