Finite Group Databasebeta

← #19146366

Subgroups — #19146366

Order 5504.

448 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583714C211yesmaximal, characteristic, complemented
2#14583707C211yesmaximal, characteristic, complemented
3#14583706C211yesmaximal, characteristic, complemented
4#14583292C211yesmaximal, characteristic, complemented
5#14583172C211yesmaximal, characteristic, complemented
6#14583171C211yesmaximal, characteristic, complemented
7#14583164C211yesmaximal, characteristic, complemented
8#14583162C211yesmaximal, characteristic, complemented
9#14583082C211yesmaximal, characteristic, complemented
10#14583080C211yesmaximal, characteristic, complemented
11#14583075C211yesmaximal, characteristic, complemented
12#14583072C211yesmaximal, characteristic, complemented
13#14583021C211yesmaximal, characteristic, complemented
14#14583019C211yesmaximal, characteristic, complemented
15C43×#578C211yesmaximal, characteristic, complemented
16#13063372C2211yescharacteristic
17#13063371C2211yescharacteristic
18#13063357—21no—
19#13063356—21no—
20#13063356—21no—
21#13063356C2211yescharacteristic
22#13063356C2211yescharacteristic
23#13063355—21no—
24#13063355C2211yescharacteristic
25#13063355C2211yescharacteristic, complemented
26#13063350—21no—
27#13063350C2211yescharacteristic
28#13063350C2211yescharacteristic
29#13063349—21no—
30#13063346—21no—
31#13063345—21no—
32#13063345—21no—
33#13063345C2211yescharacteristic
34C2×#10621885—21no—
35C2×#10621885C2211yescharacteristic, complemented
36C2×#10621873C2211yescharacteristic
37C2×#10621884—21no—
38C2×#10621884C2211yescharacteristic
39SD16×D43—21no—
40#13063332C2211yescharacteristic
41#13063332C2211yescharacteristic, complemented
42#13063331C2211yescharacteristic
43#13063323C2211yescharacteristic, complemented
44#13063314C2211yescharacteristic
45#13063261C2211yescharacteristic, complemented
46#13063260C2211yescharacteristic, complemented
47#13063252C2211yescharacteristic
48#13063252C2211yescharacteristic, complemented
49#13063252C2211yescharacteristic, complemented
50#13063251C2211yescharacteristic
51#13063244C2211yescharacteristic, complemented
52#13063244C2211yescharacteristic, complemented
53#13063243C2211yescharacteristic, complemented
54#13063241C2211yescharacteristic
55#13063235C2211yescharacteristic, complemented
562−1+4×C43C2211yescharacteristic
572−1+4×C43C2211yescharacteristic, complemented
58#137×C43—21no—
59#137×C43—21no—
60#137×C43C2211yescharacteristic
61#137×C43C2211yescharacteristic, complemented
62#135×C43—21no—
63#135×C43C2211yescharacteristic
64C2×Q16×C43—21no—
65C2×Q16×C43C2211yescharacteristic, complemented
66#131×C43C2211yescharacteristic, complemented
67#41×C43—21no—
68#41×C43—21no—
69#41×C43—21no—
70#41×C43—21no—
71#41×C43—41no—
72#41×C43—41no—
73#41×C43C2311yescharacteristic
74#41×C43C2311yescharacteristic
75#41×C43C2311yescharacteristic
76C2×Q8×C43—21no—
77C2×Q8×C43—21no—
78C2×Q8×C43—21no—
79C2×Q8×C43—21no—
80C2×Q8×C43C2311yescharacteristic
81C2×Q8×C43C2311yescharacteristic
82#10621902—21no—
83Q8×D43—21no—
84#10621900—21no—
85#10621900—41no—
86D4×D43—21no—
87D4×D43—41no—
88#10621898—21no—
89#10621898—21no—
90#10621898C2311yescharacteristic
91C2×D172—21no—
92C2×D172C2311yescharacteristic
93C2×Dic86—21no—
94C2×Dic86C2311yescharacteristic
95Q16×C43—21no—
96Q16×C43—21no—
97Q16×C43—21no—
98Q16×C43—21no—
99Q16×C43D411yescharacteristic
100SD16×C43—21no—
101SD16×C43—21no—
102SD16×C43D411yescharacteristic
103SD16×C43D411yescharacteristic
104D8×C43D411yescharacteristic
105M16×C43—21no—
106M16×C43C2311yescharacteristic
107C2×C8×C43—21no—
108C2×C8×C43C2311yescharacteristic
109#10621885—21no—
110#10621885—21no—
111#10621885—21no—
112#10621885—21no—
113#10621885—21no—
114#10621885—21no—
115#10621885D411yescharacteristic
116#10621884—21no—
117#10621884—21no—
118#10621884—21no—
119#10621884—21no—
120#10621884—21no—
121#10621884—21no—
122#10621884D411yescharacteristic
123#10621883—21no—
124#10621883—21no—
125#10621883D411yescharacteristic
126#10621882—21no—
127#10621882—21no—
128#10621882D411yescharacteristic
129(C2×D43)⋊C4—41no—
130Dic43⋊C4—41no—
131C4×Dic43C2311yescharacteristic
132#10621877—21no—
133#10621877—21no—
134#10621877C2311yescharacteristic
135#10621877C2311yescharacteristic
136#10621877C2311yescharacteristic
137C2×C43⋊C8—21no—
138C2×C43⋊C8—21no—
139C2×C43⋊C8C2311yescharacteristic
140#10621873—21no—
141#10621873—21no—
142#10621872—21no—
143C8×D43—21no—
144C22×D43—21no—
145C22×D43—41no—
146Q8×C43—21no—
147Q8×C43—21no—
148Q8×C43—21no—
149Q8×C43—21no—
150Q8×C43—41no—
151Q8×C43—41no—
152Q8×C43C2×D411yescharacteristic
153Q8×C43C2×D411yescharacteristic
154Q8×C43C2×D411yescharacteristic
155D4×C43—21no—
156D4×C43—21no—
157D4×C43—21no—
158D4×C43—41no—
159D4×C43—41no—
160D4×C43C2×D411yescharacteristic
161D4×C43C2×D411yescharacteristic
162D4×C43C2×D411yescharacteristic
163C2×C4×C43—21no—
164C2×C4×C43—21no—
165C2×C4×C43—21no—
166C2×C4×C43—21no—
167C2×C4×C43—21no—
168C2×C4×C43—41no—
169C2×C4×C43—41no—
170C2×C4×C43—41no—
171C2×C4×C43—41no—
172C2×C4×C43C2411yescharacteristic
173C22⋊D43—21no—
174C22⋊D43—41no—
175C22⋊D43—41no—
176C2×Dic43—21no—
177C2×Dic43—21no—
178C2×Dic43—41no—
179D172—21no—
180D172—21no—
181D172—41no—
182D172C2×D411yescharacteristic
183C4×D43—21no—
184C4×D43—41no—
185C4×D43—41no—
186Dic86—21no—
187Dic86—21no—
188Dic86—41no—
189Dic86C2×D411yescharacteristic
190C8×C43—21no—
191C8×C43C2×D411yescharacteristic
192C8×C43C2×D411yescharacteristic
193C43⋊C8—21no—
194C43⋊C8—21no—
195C43⋊C8—21no—
196C43⋊C8C2×D411yescharacteristic
197C43⋊C8C2×D411yescharacteristic
198C22×C43—21no—
199C22×C43—21no—
200C22×C43—21no—
201C22×C43H(5,𝔽2)11yescharacteristic
202C2×D43—21no—
203C2×D43—41no—
204C2×D43—81no—
205C2×D43—161no—
206C4×C43—21no—
207C4×C43—21no—
208C4×C43—21no—
209C4×C43—41no—
210C4×C43—41no—
211C4×C43C22×D411yescharacteristic
212C4×C43C22×D411yescharacteristic
213Dic43—21no—
214Dic43—41no—
215Dic43—41no—
216#3289—431nomaximal, Sylow
217C2×C43—21no—
218C2×C43—41no—
219C2×C43—41no—
220C2×C43—41no—
221C2×C43D4211yescharacteristic
222D43—41no—
223D43—81no—
224#578—431no—
225#578D4311yescharacteristic, complemented
226#577—431no—
227#577—431no—
228#497—431no—
229#473—431no—
230#473—431no—
231#471—431no—
232#471—431no—
233#456—431no—
234#456—431no—
235#455—431no—
236#454—431no—
237#444—431no—
238#444—431no—
239C43#328911yescharacteristic, complemented, Sylow
2402−1+4—431no—
2412−1+4C2×D4311yescharacteristic
2422−1+4C2×D4311yescharacteristic, complemented
243H(5,𝔽2)—431no—
244#137—21no—
245#137—21no—
246#137—431no—
247#137—431no—
248#137—431no—
249#137—431no—
250#137—861no—
251#137—861no—
252#137—861no—
253#137—861no—
254#137C2×D4311yescharacteristic
255#137C2×D4311yescharacteristic, complemented
256AGL(1,ℤ/8)—431no—
257AGL(1,ℤ/8)—431no—
258AGL(1,ℤ/8)—861no—
259AGL(1,ℤ/8)—861no—
260#135—21no—
261#135—431no—
262#135—861no—
263#135—861no—
264#135—861no—
265#135C2×D4311yescharacteristic
266C2×Q16—21no—
267C2×Q16—431no—
268C2×Q16—861no—
269C2×Q16C2×D4311yescharacteristic, complemented
270C2×SD16—431no—
271C2×SD16—431no—
272C2×SD16—861no—
273C2×SD16—861no—
274#131—431no—
275#131—431no—
276#131—431no—
277#131C2×D4311yescharacteristic, complemented
278C4⋊Q8—431no—
279#124—431no—
280#108—431no—
281#108—431no—
282#104—431no—
283#104—431no—
284#104—431no—
285#104—431no—
286#101—431no—
287#101—431no—
288#101—431no—
289#100—431no—
290#97—431no—
291#41—21no—
292#41—21no—
293#41—21no—
294#41—21no—
295#41—41no—
296#41—41no—
297#41—431no—
298#41—861no—
299#41—861no—
300#41—861no—
301#41—861no—
302#41—1721no—
303#41C22×D4311yescharacteristic
304#41C22×D4311yescharacteristic
305#41C22×D4311yescharacteristic
306C2×Q8—21no—
307C2×Q8—21no—
308C2×Q8—21no—
309C2×Q8—21no—
310C2×Q8—431no—
311C2×Q8—861no—
312C2×Q8—861no—
313C2×Q8C22×D4311yescharacteristic
314C2×Q8C22×D4311yescharacteristic
315C2×D4—431no—
316C2×D4—861no—
317C2×D4—861no—
318C2×D4—1721no—
319Q16—21no—
320Q16—21no—
321Q16—21no—
322Q16—21no—
323Q16—431no—
324Q16—861no—
325Q16—861no—
326Q16—861no—
327Q16—861no—
328Q16—861no—
329Q16—861no—
330Q16C22⋊D4311yescharacteristic
331SD16—21no—
332SD16—21no—
333SD16—431no—
334SD16—431no—
335SD16—861no—
336SD16—861no—
337SD16—861no—
338SD16—861no—
339SD16—861no—
340SD16—861no—
341SD16—861no—
342SD16—861no—
343SD16—861no—
344SD16—861no—
345SD16C22⋊D4311yescharacteristic
346SD16C22⋊D4311yescharacteristic
347D8—431no—
348D8—861no—
349D8—861no—
350D8C22⋊D4311yescharacteristic
351M16—21no—
352M16—431no—
353M16—431no—
354M16—431no—
355M16—861no—
356M16—861no—
357M16—861no—
358M16C22×D4311yescharacteristic
359C2×C8—21no—
360C2×C8—431no—
361C2×C8—861no—
362C2×C8—861no—
363C2×C8—861no—
364C2×C8C22×D4311yescharacteristic
365C4⋊C4—1721no—
366C22⋊C4—1721no—
367C42—431no—
368C23—861no—
369C23—1721no—
370Q8—21no—
371Q8—21no—
372Q8—21no—
373Q8—21no—
374Q8—41no—
375Q8—41no—
376Q8—431no—
377Q8—861no—
378Q8—861no—
379Q8—1721no—
380Q8D4×D4311yescharacteristic
381Q8C2×C22⋊D4311yescharacteristic
382Q8C2×C22⋊D4311yescharacteristic
383D4—21no—
384D4—21no—
385D4—21no—
386D4—41no—
387D4—41no—
388D4—431no—
389D4—861no—
390D4—861no—
391D4—861no—
392D4—1721no—
393D4—1721no—
394D4—1721no—
395D4D4×D4311yescharacteristic
396D4C2×C22⋊D4311yescharacteristic
397D4C2×C22⋊D4311yescharacteristic
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—861no—
408C2×C4—861no—
409C2×C4—861no—
410C2×C4—1721no—
411C2×C4—1721no—
412C2×C4—1721no—
413C2×C4C23×D4311yescharacteristic
414C8—21no—
415C8—431no—
416C8—431no—
417C8—861no—
418C8—861no—
419C8—861no—
420C8C2×C22⋊D4311yescharacteristic
421C8C2×C22⋊D4311yescharacteristic
422C22—21no—
423C22—21no—
424C22—21no—
425C22—861no—
426C22—3441no—
427C22—1721no—
428C22—6881no—
429C22#1306337011yescharacteristic
430C4—21no—
431C4—21no—
432C4—21no—
433C4—41no—
434C4—41no—
435C4—861no—
436C4—1721no—
437C4—1721no—
438C4C2×D4×D4311yescharacteristic
439C4C22×C22⋊D4311yescharacteristic
440C2—21no—
441C2—41no—
442C2—41no—
443C2—41no—
444C2—3441no—
445C2—1721no—
446C2D4×C22⋊D4311yescharacteristic
subgroupG/H
centerC2D4×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#578C2
socleC2×C43D42
hypercenter#578D43
hypocenterC43#3289
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ #578

Complements

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

NH ≅ G/Ntype
1. #14583714C2semidirect
2. #14583707C2semidirect
3. #14583706C2semidirect
4. #14583292C2semidirect
5. #14583172C2semidirect
6. #14583171C2semidirect
7. #14583164C2semidirect
8. #14583162C2semidirect
9. #14583082C2semidirect
10. #14583080C2semidirect
11. #14583075C2semidirect
12. #14583072C2semidirect
13. #14583021C2semidirect
14. #14583019C2semidirect
15. C43×#578C2semidirect
25. #13063355C22semidirect
35. C2×#10621885C22semidirect
41. #13063332C22semidirect
43. #13063323C22semidirect
45. #13063261C22semidirect
46. #13063260C22semidirect
48. #13063252C22semidirect
49. #13063252C22semidirect
51. #13063244C22semidirect
52. #13063244C22semidirect
53. #13063243C22semidirect
55. #13063235C22semidirect
57. 2−1+4×C43C22semidirect
61. #137×C43C22semidirect
65. C2×Q16×C43C22semidirect
66. #131×C43C22semidirect
225. #578D43semidirect
239. C43#3289semidirect
242. 2−1+4C2×D43semidirect
255. #137C2×D43semidirect
269. C2×Q16C2×D43semidirect
277. #131C2×D43semidirect