Finite Group Databasebeta

← #19145477

Subgroups — #19145477

Order 5504.

390 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583477C211yesmaximal, characteristic
2#14583240C211yesmaximal, characteristic, complemented
3#14583232C211yesmaximal, characteristic, complemented
4#14583227C211yesmaximal, characteristic, complemented
5#14583223C211yesmaximal, characteristic, complemented
6#14583155C211yesmaximal, characteristic, complemented
7#14583147C211yesmaximal, characteristic, complemented
8#14583138C211yesmaximal, characteristic, complemented
9#14583130C211yesmaximal, characteristic, complemented
10#14583059C211yesmaximal, characteristic, complemented
11#14583059C211yesmaximal, characteristic, complemented
12#14583055C211yesmaximal, characteristic, complemented
13#14583038C211yesmaximal, characteristic, complemented
14#14582866C211yesmaximal, characteristic, complemented
15C43×#536C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C2×#10621885C2211yescharacteristic
18C2×#10621885C2211yescharacteristic
19C2×#10621884C2211yescharacteristic
20C2×#10621884C2211yescharacteristic
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#13063256C2211yescharacteristic
35#13063256C2211yescharacteristic
36#13063249C2211yescharacteristic
37#13063249C2211yescharacteristic
38#13063249C2211yescharacteristic
39#13063249C2211yescharacteristic
40#13063248C2211yescharacteristic
41#13063248C2211yescharacteristic
42#13063245C2211yescharacteristic
43#13063245C2211yescharacteristic
44C22⋊(C43⋊C8)C2211yescharacteristic
45C22⋊(C43⋊C8)C2211yescharacteristic
46C22⋊(C43⋊C8)C2211yescharacteristic
47C22⋊(C43⋊C8)C2211yescharacteristic
48C2×#41×C43C2211yescharacteristic
49C22×Q8×C43C2211yescharacteristic
50C4⋊Q8×C43—21no—
51#124×C43—21no—
52#123×C43—21no—
53#123×C43—21no—
54C22⋊Q8×C43C2211yescharacteristic
55C22⋊Q8×C43C2211yescharacteristic
56C22⋊Q8×C43C2211yescharacteristic
57C22⋊Q8×C43C2211yescharacteristic
58#117×C43C2211yescharacteristic
59#41×C43—41no—
60#41×C43—41no—
61C2×Q8×C43—21no—
62C2×Q8×C43—41no—
63C2×Q8×C43—41no—
64C2×Q8×C43D411yescharacteristic
65C2×Q8×C43C2311yescharacteristic
66C2×Q8×C43C2311yescharacteristic
67C2×D4×C43D411yescharacteristic
68C2×D4×C43D411yescharacteristic
69C2×D4×C43D411yescharacteristic
70C22×C4×C43—21no—
71C22×C4×C43C2311yescharacteristic
72C22×C4×C43C2311yescharacteristic
73C22×C4×C43C2311yescharacteristic
74C2×C22⋊D43—21no—
75C2×C22⋊D43—21no—
76C2×C22⋊D43—21no—
77C22×Dic43—21no—
78#10621898—41no—
79#10621898—41no—
80C2×D172C2311yescharacteristic
81C2×C4×D43—21no—
82C2×Dic86C2311yescharacteristic
83C4⋊C4×C43—21no—
84C4⋊C4×C43—21no—
85C4⋊C4×C43—21no—
86C4⋊C4×C43—21no—
87C4⋊C4×C43C2311yescharacteristic
88C4⋊C4×C43C2311yescharacteristic
89C22⋊C4×C43—21no—
90C22⋊C4×C43—21no—
91C22⋊C4×C43—21no—
92C22⋊C4×C43—21no—
93C22⋊C4×C43—21no—
94C42×C43—21no—
95C22⋊Dic43—21no—
96C22⋊Dic43—21no—
97#10621885—41no—
98#10621885—41no—
99#10621884—41no—
100#10621884—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×C43C2×D411yescharacteristic
115C23×C43C2×D411yescharacteristic
116C23×C43C2×D411yescharacteristic
117C22×D43—21no—
118Q8×C43—21no—
119Q8×C43—21no—
120Q8×C43—21no—
121Q8×C43—21no—
122Q8×C43—41no—
123Q8×C43—42no—
124D4×C43—41no—
125D4×C43—41no—
126D4×C43—41no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×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×C43—21no—
137C2×C4×C43—42no—
138C2×C4×C43C2×D411yescharacteristic
139C2×C4×C43C2×D411yescharacteristic
140C2×C4×C43C2×D411yescharacteristic
141C2×C4×C43C2411yescharacteristic
142C22⋊D43—42no—
143C22⋊D43—81no—
144C22⋊D43—81no—
145C2×Dic43—21no—
146C2×Dic43—21no—
147C2×Dic43—21no—
148C2×Dic43—81no—
149D172—21no—
150D172—21no—
151C4×D43—42no—
152Dic86—21no—
153Dic86—21no—
154C43⋊C8—21no—
155C43⋊C8—21no—
156C43⋊C8—21no—
157C43⋊C8—21no—
158C22×C43—21no—
159C22×C43—21no—
160C22×C43—21no—
161C22×C43—21no—
162C22×C43—21no—
163C22×C43—21no—
164C22×C43—21no—
165C22×C43—21no—
166C22×C43—21no—
167C22×C43C22×D411yescharacteristic
168C2×D43—41no—
169C2×D43—41no—
170C2×D43—41no—
171C4×C43—21no—
172C4×C43—21no—
173C4×C43—21no—
174C4×C43—41no—
175C4×C43—41no—
176C4×C43—41no—
177C4×C43—41no—
178C4×C43H(5,𝔽2)11yescharacteristic
179C4×C43H(5,𝔽2)11yescharacteristic
180Dic43—41no—
181Dic43—41no—
182Dic43—41no—
183#3201—431nomaximal, Sylow
184C2×C43—41no—
185C2×C43—41no—
186C2×C43—41no—
187C2×C43#53411yescharacteristic
188C2×C43#57711yescharacteristic
189C2×C43#57811yescharacteristic
190D43—81no—
191#537—431no—
192#536D4311yescharacteristic, complemented
193#485—431no—
194#484—431no—
195#483—431no—
196#482—431no—
197#470—431no—
198#468—431no—
199#467—431no—
200#465—431no—
201#452—431no—
202#452—431no—
203#451—431no—
204#448—431no—
205#408—431no—
206C43#320111yescharacteristic, complemented, Sylow
207C2×#41—431no—
208C2×#41C2×D4311yescharacteristic
209C22×Q8C2×D4311yescharacteristic
210C2×Q16—431no—
211C2×Q16—431no—
212C2×SD16—431no—
213C2×SD16—431no—
214C2×M16—431no—
215C22×C8—431no—
216C4⋊Q8—21no—
217#124—21no—
218#123—21no—
219#123—21no—
220C22⋊Q8—431no—
221C22⋊Q8—431no—
222C22⋊Q8—861no—
223C22⋊Q8C2×D4311yescharacteristic
224C22⋊Q8C2×D4311yescharacteristic
225C22⋊Q8C2×D4311yescharacteristic
226C22⋊Q8C2×D4311yescharacteristic
227#121—431no—
228#121—431no—
229#121—861no—
230#121—861no—
231#121—861no—
232#117C2×D4311yescharacteristic
233C2×C4⋊C4—431no—
234#107—431no—
235#107—431no—
236#106—431no—
237#106—431no—
238#103—431no—
239#103—431no—
240#103—431no—
241#103—431no—
242#103—431no—
243#103—431no—
244#102—431no—
245#102—431no—
246C22⋊C8—431no—
247C22⋊C8—431no—
248C22⋊C8—431no—
249C22⋊C8—431no—
250#41—41no—
251#41—41no—
252#41—1721no—
253#41—1721no—
254C2×Q8—21no—
255C2×Q8—41no—
256C2×Q8—41no—
257C2×Q8—431no—
258C2×Q8C22⋊D4311yescharacteristic
259C2×Q8C22×D4311yescharacteristic
260C2×Q8C22×D4311yescharacteristic
261C2×D4—431no—
262C2×D4—861no—
263C2×D4—861no—
264C2×D4—861no—
265C2×D4C22⋊D4311yescharacteristic
266C2×D4C22⋊D4311yescharacteristic
267C2×D4C22⋊D4311yescharacteristic
268C22×C4—21no—
269C22×C4—861no—
270C22×C4—861no—
271C22×C4C22×D4311yescharacteristic
272C22×C4C22×D4311yescharacteristic
273C22×C4C22×D4311yescharacteristic
274Q16—1721no—
275Q16—1721no—
276SD16—1721no—
277SD16—1721no—
278M16—1721no—
279C2×C8—431no—
280C2×C8—431no—
281C2×C8—431no—
282C2×C8—431no—
283C2×C8—1721no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—431no—
289C4⋊C4—431no—
290C4⋊C4—861no—
291C4⋊C4—861no—
292C4⋊C4—861no—
293C4⋊C4C22×D4311yescharacteristic
294C4⋊C4C22×D4311yescharacteristic
295C22⋊C4—21no—
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—861no—
301C22⋊C4—861no—
302C22⋊C4—861no—
303C22⋊C4—861no—
304C42—21no—
305C23—861no—
306C23C2×C22⋊D4311yescharacteristic
307C23C2×C22⋊D4311yescharacteristic
308C23C2×C22⋊D4311yescharacteristic
309Q8—21no—
310Q8—21no—
311Q8—21no—
312Q8—21no—
313Q8—41no—
314Q8—42no—
315Q8—861no—
316Q8—861no—
317D4—41no—
318D4—41no—
319D4—41no—
320D4—861no—
321D4—861no—
322D4—3441no—
323D4—3441no—
324D4—1722no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—42no—
336C2×C4—861no—
337C2×C4—861no—
338C2×C4—861no—
339C2×C4—3441no—
340C2×C4—1722no—
341C2×C4C2×C22⋊D4311yescharacteristic
342C2×C4C2×C22⋊D4311yescharacteristic
343C2×C4C2×C22⋊D4311yescharacteristic
344C2×C4C23×D4311yescharacteristic
345C8—861no—
346C8—861no—
347C8—861no—
348C8—861no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—1721no—
359C22—1721no—
360C22—1721no—
361C22C22×C22⋊D4311yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—1721no—
370C4—1721no—
371C4—1721no—
372C4#1306337011yescharacteristic
373C4#1306337011yescharacteristic
374C2—41no—
375C2—41no—
376C2—41no—
377C2—3441no—
378C2#1458345811yescharacteristic
379C2#1458370711yescharacteristic
380C2#1458371411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#536C2
socleC22×C43C22×D4
hypercenter#536D43
hypocenterC43#3201
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
2. #14583240C2semidirect
3. #14583232C2semidirect
4. #14583227C2semidirect
5. #14583223C2semidirect
6. #14583155C2semidirect
7. #14583147C2semidirect
8. #14583138C2semidirect
9. #14583130C2semidirect
10. #14583059C2semidirect
11. #14583059C2semidirect
12. #14583055C2semidirect
13. #14583038C2semidirect
14. #14582866C2semidirect
15. C43×#536C2semidirect
192. #536D43semidirect
206. C43#3201semidirect