Finite Group Databasebeta

← #19146669

Subgroups — #19146669

Order 5504.

410 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583607C211yesmaximal, characteristic, complemented
2#14583537C211yesmaximal, characteristic
3#14583260C211yesmaximal, characteristic, complemented
4#14583233C211yesmaximal, characteristic, complemented
5#14583213C211yesmaximal, characteristic, complemented
6#14583177C211yesmaximal, characteristic, complemented
7#14583147C211yesmaximal, characteristic, complemented
8#14583137C211yesmaximal, characteristic, complemented
9#14583123C211yesmaximal, characteristic, complemented
10#14583048C211yesmaximal, characteristic, complemented
11#14583000C211yesmaximal, characteristic, complemented
12#14582973C211yesmaximal, characteristic, complemented
13#14582900C211yesmaximal, characteristic, complemented
14#102×D43C211yesmaximal, characteristic, complemented
15C43×#452C211yesmaximal, characteristic, complemented
16C2×D4×D43C2211yescharacteristic
17C2×#10621884C2211yescharacteristic
18C2×#10621877C2211yescharacteristic, complemented
19C2×C8×D43C2211yescharacteristic
20#13063324C2211yescharacteristic, complemented
21#13063315—21no—
22#13063314C2211yescharacteristic
23#13063308—21no—
24#13063305—21no—
25#13063302—21no—
26#13063301C2211yescharacteristic
27#13063301C2211yescharacteristic
28#13063299C2211yescharacteristic
29#13063297—21no—
30#13063293—21no—
31Q8×Dic43C2211yescharacteristic, complemented
32D4×Dic43C2211yescharacteristic
33C4×C22⋊D43C2211yescharacteristic
34(C22⋊D43)⋊C4—21no—
35C2×C4⋊Dic43C2211yescharacteristic, complemented
36C4⋊C4×D43C2211yescharacteristic
37C2×(C2×D43)⋊C4—21no—
38#13063259C2211yescharacteristic, complemented
39#13063259C2211yescharacteristic, complemented
40#13063258C2211yescharacteristic, complemented
41Dic43⋊C8C2211yescharacteristic, complemented
42#13063249C2211yescharacteristic, complemented
43#13063249C2211yescharacteristic, complemented
44#13063249C2211yescharacteristic, complemented
45#13063247C2211yescharacteristic
46#13063247C2211yescharacteristic
47#13063246C2211yescharacteristic
48#13063246C2211yescharacteristic
49#13063245C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51#13063235C2211yescharacteristic, complemented
52C2×#41×C43C2211yescharacteristic
53C2×Q16×C43C2211yescharacteristic, complemented
54C2×SD16×C43C2211yescharacteristic
55C22⋊Q8×C43C2211yescharacteristic, complemented
56#103×C43C2211yescharacteristic, complemented
57#102×C43C2211yescharacteristic
58C22⋊C8×C43C2211yescharacteristic, complemented
59C23×D43—21no—
60#41×C43—22no—
61#41×C43—41no—
62C2×Q8×C43C2311yescharacteristic
63C2×Q8×C43C2311yescharacteristic
64C2×D4×C43—21no—
65C2×D4×C43C2311yescharacteristic
66C22×C4×C43—21no—
67C22×C4×C43C2311yescharacteristic
68C2×C22⋊D43—21no—
69C2×C22⋊D43—21no—
70C2×C22⋊D43D411yescharacteristic
71C22×Dic43—21no—
72C22×Dic43—21no—
73D4×D43—22no—
74D4×D43—41no—
75C2×D172C2311yescharacteristic
76C2×C4×D43—21no—
77C2×C4×D43C2311yescharacteristic
78C2×Dic86—21no—
79Q16×C43—41no—
80SD16×C43—22no—
81C2×C8×C43C2311yescharacteristic
82C2×C8×C43C2311yescharacteristic
83C4⋊C4×C43—21no—
84C4⋊C4×C43C2311yescharacteristic
85C22⋊C4×C43—21no—
86C22⋊Dic43—21no—
87C22⋊Dic43D411yescharacteristic
88#10621884—41no—
89(C2×D43)⋊C4—21no—
90(C2×D43)⋊C4—21no—
91(C2×D43)⋊C4—21no—
92(C2×D43)⋊C4—21no—
93(C2×D43)⋊C4—21no—
94(C2×D43)⋊C4D411yescharacteristic
95C4⋊Dic43—21no—
96C4⋊Dic43—21no—
97C4⋊Dic43C2311yescharacteristic
98C4⋊Dic43C2311yescharacteristic
99C4⋊Dic43C2311yescharacteristic
100Dic43⋊C4—21no—
101Dic43⋊C4—21no—
102Dic43⋊C4—21no—
103Dic43⋊C4—21no—
104Dic43⋊C4D411yescharacteristic
105C4×Dic43—21no—
106C4×Dic43C2311yescharacteristic
107#10621877—41no—
108C2×C43⋊C8C2311yescharacteristic
109C2×C43⋊C8C2311yescharacteristic
110C8×D43—41no—
111C23×C43—21no—
112C23×C43C2×D411yescharacteristic
113C22×D43—21no—
114C22×D43—42no—
115C22×D43—42no—
116C22×D43—81no—
117C22×D43C2×D411yescharacteristic
118Q8×C43—21no—
119Q8×C43—21no—
120Q8×C43—21no—
121Q8×C43—21no—
122D4×C43—21no—
123D4×C43—42no—
124D4×C43#4112yes—
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—22no—
134C22⋊D43—42no—
135C22⋊D43—81no—
136C2×Dic43—21no—
137C2×Dic43—21no—
138C2×Dic43—21no—
139C2×Dic43—81no—
140C2×Dic43—81no—
141C2×Dic43C2×D411yescharacteristic
142C2×Dic43C2×D411yescharacteristic
143C2×Dic43C2×D411yescharacteristic
144D172—21no—
145D172—21no—
146C4×D43—21no—
147C4×D43—21no—
148C4×D43—81no—
149Dic86—81no—
150C8×C43—21no—
151C8×C43—21no—
152C43⋊C8—21no—
153C43⋊C8—21no—
154C22×C43—22no—
155C22×C43—21no—
156C22×C43—21no—
157C22×C43—21no—
158C22×C43—41no—
159C22×C43—41no—
160C22×C43C22×D411yescharacteristic
161C2×D43—21no—
162C2×D43—21no—
163C2×D43—41no—
164C2×D43—41no—
165C2×D43—41no—
166C2×D43—84no—
167C2×D43#13712yes—
168C4×C43—21no—
169C4×C43—41no—
170C4×C43—41no—
171C4×C43—41no—
172C4×C43C2×#4111yescharacteristic
173C4×C43H(5,𝔽2)11yescharacteristic
174Dic43—21no—
175Dic43—21no—
176Dic43—21no—
177Dic43—41no—
178Dic43—41no—
179Dic43—41no—
180#3314—431nomaximal, Sylow
181C2×C43—42no—
182C2×C43—41no—
183C2×C43#54611yescharacteristic
184C2×C43C2×#13711yescharacteristic
185C2×C43#57611yescharacteristic
186D43—22no—
187D43—81no—
188#554—431no—
189#546—431no—
190#489—431no—
191#484—431no—
192#480—431no—
193#474—431no—
194#468—431no—
195#467—431no—
196#464—431no—
197#452D4311yescharacteristic, complemented
198#450—431no—
199#440—431no—
200#435—431no—
201#417—431no—
202C2×#102—431no—
203C43#331411yescharacteristic, complemented, Sylow
204C2×#41C2×D4311yescharacteristic
205C22×D4—431no—
206C2×Q16C2×D4311yescharacteristic, complemented
207C2×SD16—431no—
208C2×SD16C2×D4311yescharacteristic
209C2×M16—431no—
210C22×C8—431no—
211C4⋊Q8—431no—
212#125—861no—
213#124—431no—
214#123—861no—
215C22⋊Q8—431no—
216C22⋊Q8—431no—
217C22⋊Q8—861no—
218C22⋊Q8—861no—
219C22⋊Q8C2×D4311yescharacteristic, complemented
220#121—431no—
221#121—861no—
222#120—861no—
223C4×Q8—431no—
224C4×D4—431no—
225C4×D4—431no—
226C4×D4—861no—
227C2×C4⋊C4—431no—
228C2×C4⋊C4—431no—
229C2×C22⋊C4—861no—
230#107—431no—
231#107—431no—
232#107—431no—
233C4⋊C8—431no—
234#103—431no—
235#103—431no—
236#103—431no—
237#103C2×D4311yescharacteristic, complemented
238#102—431no—
239#102—431no—
240#102—431no—
241#102—431no—
242#102—431no—
243#102C2×D4311yescharacteristic
244C22⋊C8—431no—
245C22⋊C8C2×D4311yescharacteristic, complemented
246#97—431no—
247C24—861no—
248#41—22no—
249#41—41no—
250C2×Q8—861no—
251C2×Q8C22×D4311yescharacteristic
252C2×Q8C22×D4311yescharacteristic
253C2×D4—21no—
254C2×D4—431no—
255C2×D4—431no—
256C2×D4—861no—
257C2×D4—862no—
258C2×D4—861no—
259C2×D4—1721no—
260C2×D4C22×D4311yescharacteristic
261C22×C4—21no—
262C22×C4—431no—
263C22×C4—861no—
264C22×C4—861no—
265C22×C4—861no—
266C22×C4C22×D4311yescharacteristic
267Q16—41no—
268SD16—22no—
269SD16—1721no—
270M16—1721no—
271C2×C8—431no—
272C2×C8—431no—
273C2×C8—1721no—
274C2×C8C22×D4311yescharacteristic
275C2×C8C22×D4311yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—431no—
278C4⋊C4—431no—
279C4⋊C4—431no—
280C4⋊C4—431no—
281C4⋊C4—861no—
282C4⋊C4—861no—
283C4⋊C4—861no—
284C4⋊C4—861no—
285C4⋊C4—861no—
286C4⋊C4—861no—
287C4⋊C4C22×D4311yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—431no—
290C22⋊C4—431no—
291C22⋊C4—861no—
292C22⋊C4—861no—
293C22⋊C4—861no—
294C22⋊C4—861no—
295C22⋊C4—861no—
296C22⋊C4—861no—
297C42—431no—
298C42—861no—
299C23—21no—
300C23—431no—
301C23—861no—
302C23—3441no—
303C23—1722no—
304C23—1722no—
305C23D4×D4311yescharacteristic
306Q8—21no—
307Q8—21no—
308Q8—21no—
309Q8—21no—
310Q8—3441no—
311D4—21no—
312D4—42no—
313D4—862no—
314D4—861no—
315D4—861no—
316D4—3441no—
317D4—1722no—
318D4#1062190012yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—42no—
325C2×C4—431no—
326C2×C4—431no—
327C2×C4—431no—
328C2×C4—861no—
329C2×C4—861no—
330C2×C4—861no—
331C2×C4—861no—
332C2×C4—861no—
333C2×C4—3441no—
334C2×C4—3441no—
335C2×C4—3441no—
336C2×C4D4×D4311yescharacteristic
337C2×C4C23×D4311yescharacteristic
338C8—21no—
339C8—21no—
340C8—861no—
341C8—861no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—22no—
346C22—41no—
347C22—41no—
348C22—432no—
349C22—861no—
350C22—861no—
351C22—3444no—
352C22—1721no—
353C22—1721no—
354C22—1721no—
355C22C2×D4×D4311yescharacteristic
356C4—21no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—861no—
361C4—861no—
362C4—861no—
363C4—1721no—
364C4—1721no—
365C4—1721no—
366C4C2×#1062190011yescharacteristic
367C4#1306337011yescharacteristic
368C2—41no—
369C2—42no—
370C2—862no—
371C2—3441no—
372C2#1458353611yescharacteristic
373C2#137×D4311yescharacteristic
374C2#1458370111yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#452C2
socleC22×C43C22×D4
hypercenter#452D43
hypocenterC43#3314
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. #14583607C2semidirect
3. #14583260C2semidirect
4. #14583233C2semidirect
5. #14583213C2semidirect
6. #14583177C2semidirect
7. #14583147C2semidirect
8. #14583137C2semidirect
9. #14583123C2semidirect
10. #14583048C2semidirect
11. #14583000C2semidirect
12. #14582973C2semidirect
13. #14582900C2semidirect
14. #102×D43C2semidirect
15. C43×#452C2semidirect
18. C2×#10621877C22semidirect
20. #13063324C22semidirect
31. Q8×Dic43C22semidirect
35. C2×C4⋊Dic43C22semidirect
38. #13063259C22semidirect
39. #13063259C22semidirect
40. #13063258C22semidirect
41. Dic43⋊C8C22semidirect
42. #13063249C22semidirect
43. #13063249C22semidirect
44. #13063249C22semidirect
51. #13063235C22semidirect
53. C2×Q16×C43C22semidirect
55. C22⋊Q8×C43C22semidirect
56. #103×C43C22semidirect
58. C22⋊C8×C43C22semidirect
197. #452D43semidirect
203. C43#3314semidirect
206. C2×Q16C2×D43semidirect
219. C22⋊Q8C2×D43semidirect
237. #103C2×D43semidirect
245. C22⋊C8C2×D43semidirect