Finite Group Databasebeta

← #34056482

Subgroups — #34056482

Order 19072.

460 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750436C211yesmaximal, characteristic, complemented
2#23750433C211yesmaximal, characteristic, complemented
3#23750432C211yesmaximal, characteristic, complemented
4#23749996C211yesmaximal, characteristic, complemented
5#23749890C211yesmaximal, characteristic, complemented
6#23749888C211yesmaximal, characteristic, complemented
7#23749886C211yesmaximal, characteristic, complemented
8#23749885C211yesmaximal, characteristic, complemented
9#23749808C211yesmaximal, characteristic, complemented
10#23749806C211yesmaximal, characteristic, complemented
11#23749793C211yesmaximal, characteristic, complemented
12#23749791C211yesmaximal, characteristic, complemented
13#23749742C211yesmaximal, characteristic, complemented
14#23749740C211yesmaximal, characteristic, complemented
15#577×C149C211yesmaximal, characteristic, complemented
16#18011958C2211yescharacteristic
17#18011957C2211yescharacteristic, complemented
18#18011943—21no—
19#18011942—21no—
20#18011942C2211yescharacteristic, complemented
21#18011941—21no—
22#18011941C2211yescharacteristic, complemented
23#18011941C2211yescharacteristic, complemented
24#18011937—21no—
25#18011937C2211yescharacteristic
26#18011936—21no—
27#18011936C2211yescharacteristic
28#18011936C2211yescharacteristic
29#18011935—21no—
30#18011932—21no—
31#18011931—21no—
32#18011931—21no—
33#18011931C2211yescharacteristic
34C2×#14558725C2211yescharacteristic, complemented
35C2×#14558724—21no—
36C2×#14558724C2211yescharacteristic, complemented
37C2×#14558723—21no—
38C2×#14558723C2211yescharacteristic, complemented
39SD16×D149—21no—
40#18011918C2211yescharacteristic, complemented
41#18011918C2211yescharacteristic, complemented
42#18011917C2211yescharacteristic, complemented
43#18011909C2211yescharacteristic, complemented
44#18011907C2211yescharacteristic
45#18011847C2211yescharacteristic, complemented
46#18011846C2211yescharacteristic, complemented
47#18011838C2211yescharacteristic, complemented
48#18011838C2211yescharacteristic, complemented
49#18011838C2211yescharacteristic, complemented
50#18011837C2211yescharacteristic, complemented
51#18011830C2211yescharacteristic, complemented
52#18011829C2211yescharacteristic, complemented
53#18011828C2211yescharacteristic, complemented
54#18011827C2211yescharacteristic, complemented
55C8×Dic149C2211yescharacteristic, complemented
562−1+4×C149C2211yescharacteristic
57H(5,𝔽2)×C149C2211yescharacteristic, complemented
58#137×C149—21no—
59#137×C149C2211yescharacteristic, complemented
60AGL(1,ℤ/8)×C149—21no—
61AGL(1,ℤ/8)×C149C2211yescharacteristic
62#135×C149—21no—
63#135×C149C2211yescharacteristic
64C2×SD16×C149—21no—
65C2×SD16×C149C2211yescharacteristic, complemented
66#131×C149C2211yescharacteristic, complemented
67#14558737—21no—
68#14558736—21no—
69#14558736—21no—
70#14558736C2311yescharacteristic
71#14558735—21no—
72#14558735—41no—
73C2×Dic298—21no—
74C2×Dic298C2311yescharacteristic
75Q8×D149—21no—
76C2×D596—21no—
77C2×D596C2311yescharacteristic
78C2×C22⋊D149—41no—
79D4×D149—21no—
80D4×D149—41no—
81#14558726—21no—
82#14558726—21no—
83#14558726—21no—
84#14558726D411yescharacteristic, complemented
85#14558725—21no—
86#14558725—21no—
87#14558724—21no—
88#14558724—21no—
89#14558724—21no—
90#14558724—21no—
91#14558724—21no—
92#14558724D411yescharacteristic, complemented
93#14558723—21no—
94#14558723—21no—
95#14558723—21no—
96#14558723—21no—
97#14558723—21no—
98#14558723D411yescharacteristic, complemented
99#14558721—21no—
100#14558721—21no—
101#14558721—21no—
102#14558721D411yescharacteristic, complemented
103#14558720—21no—
104#14558720—21no—
105#14558720C2311yescharacteristic
106#14558720C2311yescharacteristic
107#14558720C2311yescharacteristic
108#14558719—21no—
109C2×#11924746—21no—
110C2×#11924746—21no—
111C2×#11924746C2311yescharacteristic
112C8×D149—21no—
113#14558715—41no—
114C4×Dic149C2311yescharacteristic
115#41×C149—21no—
116#41×C149—21no—
117#41×C149—21no—
118#41×C149—21no—
119#41×C149—41no—
120#41×C149C2311yescharacteristic
121#41×C149C2311yescharacteristic
122#41×C149C2311yescharacteristic
123C2×Q8×C149—21no—
124C2×Q8×C149—21no—
125C2×Q8×C149C2311yescharacteristic
126C2×D4×C149—21no—
127C2×D4×C149—21no—
128C2×D4×C149—41no—
129C2×D4×C149C2311yescharacteristic
130Q16×C149—21no—
131Q16×C149D411yescharacteristic, complemented
132SD16×C149—21no—
133SD16×C149—21no—
134SD16×C149—21no—
135SD16×C149—21no—
136SD16×C149D411yescharacteristic, complemented
137SD16×C149D411yescharacteristic, complemented
138D8×C149—21no—
139D8×C149D411yescharacteristic, complemented
140M16×C149—21no—
141M16×C149C2311yescharacteristic
142C2×C8×C149—21no—
143C2×C8×C149C2311yescharacteristic
144C22×D149—21no—
145C22×D149—41no—
146Dic298—21no—
147Dic298—21no—
148Dic298—41no—
149Dic298C2×D411yescharacteristic
150D596—21no—
151D596—21no—
152D596—41no—
153D596C2×D411yescharacteristic
154C22⋊D149—21no—
155C22⋊D149—41no—
156C22⋊D149—41no—
157C22⋊D149—82no—
158C2×Dic149—21no—
159C2×Dic149—21no—
160C2×Dic149—41no—
161C4×D149—21no—
162C4×D149—41no—
163C4×D149—41no—
164#11924746—21no—
165#11924746—21no—
166#11924746—21no—
167#11924746C2×D411yescharacteristic
168#11924746C2×D411yescharacteristic
169C23×C149—21no—
170C23×C149—41no—
171Q8×C149—21no—
172Q8×C149—21no—
173Q8×C149—41no—
174Q8×C149C2×D411yescharacteristic
175Q8×C149C2×D411yescharacteristic
176Q8×C149C2×D411yescharacteristic
177D4×C149—21no—
178D4×C149—21no—
179D4×C149—21no—
180D4×C149—21no—
181D4×C149—21no—
182D4×C149—41no—
183D4×C149—41no—
184D4×C149—41no—
185D4×C149C2×D411yescharacteristic
186D4×C149C2×D411yescharacteristic
187D4×C149C2×D411yescharacteristic
188C2×C4×C149—21no—
189C2×C4×C149—21no—
190C2×C4×C149—21no—
191C2×C4×C149—21no—
192C2×C4×C149—41no—
193C2×C4×C149—41no—
194C2×C4×C149—41no—
195C2×C4×C149C2411yescharacteristic
196C8×C149—21no—
197C8×C149C2×D411yescharacteristic
198C8×C149C2×D411yescharacteristic
199C22×C149—21no—
200C22×C149—21no—
201C22×C149—21no—
202C22×C149—41no—
203C22×C149—81no—
204C22×C149—161no—
205C22×C149H(5,𝔽2)11yescharacteristic
206C2×D149—21no—
207C2×D149—41no—
208C2×D149—81no—
209C2×D149—161no—
210C4×C149—21no—
211C4×C149—21no—
212C4×C149—21no—
213C4×C149—41no—
214C4×C149C22×D411yescharacteristic
215C4×C149C22×D411yescharacteristic
216Dic149—22no—
217Dic149—21no—
218Dic149—41no—
219C2×C149—21no—
220C2×C149—41no—
221C2×C149—41no—
222C2×C149—41no—
223C2×C149—81no—
224C2×C149D4211yescharacteristic
225D149—41no—
226D149—81no—
227C149#329111yescharacteristic, complemented, Sylow
228#3291—1491nomaximal, Sylow
229#577—1491no—
230#577—1491no—
231#577—1491no—
232#577D14911yescharacteristic, complemented
233#492—1491no—
234#471—1491no—
235#471—1491no—
236#471—1491no—
237#471—1491no—
238#456—1491no—
239#456—1491no—
240#453—1491no—
241#453—1491no—
242#443—1491no—
243#443—1491no—
2442−1+4—1491no—
2452−1+4C2×D14911yescharacteristic
246H(5,𝔽2)—1491no—
247H(5,𝔽2)C2×D14911yescharacteristic, complemented
248#137—21no—
249#137—2981no—
250#137—2981no—
251#137—2981no—
252#137—1491no—
253#137—1491no—
254#137—1491no—
255#137C2×D14911yescharacteristic, complemented
256AGL(1,ℤ/8)—21no—
257AGL(1,ℤ/8)—2981no—
258AGL(1,ℤ/8)—2981no—
259AGL(1,ℤ/8)—2981no—
260AGL(1,ℤ/8)—1491no—
261AGL(1,ℤ/8)—1491no—
262AGL(1,ℤ/8)—1491no—
263AGL(1,ℤ/8)C2×D14911yescharacteristic
264#135—21no—
265#135—2981no—
266#135—2981no—
267#135—2981no—
268#135—1491no—
269#135C2×D14911yescharacteristic
270C2×SD16—21no—
271C2×SD16—2981no—
272C2×SD16—2981no—
273C2×SD16—2981no—
274C2×SD16—1491no—
275C2×SD16—1491no—
276C2×SD16—1491no—
277C2×SD16C2×D14911yescharacteristic, complemented
278#131—1491no—
279#131—1491no—
280#131—1491no—
281#131C2×D14911yescharacteristic, complemented
282C4⋊Q8—1491no—
283#127—1491no—
284#108—1491no—
285#108—1491no—
286#104—1491no—
287#104—1491no—
288#104—1491no—
289#104—1491no—
290#101—1491no—
291#101—1491no—
292#100—1491no—
293#100—1491no—
294C4×C8—1491no—
295#41—21no—
296#41—21no—
297#41—21no—
298#41—21no—
299#41—41no—
300#41—2981no—
301#41—2981no—
302#41—2981no—
303#41—2981no—
304#41—5961no—
305#41—1491no—
306#41C22×D14911yescharacteristic
307#41C22×D14911yescharacteristic
308#41C22×D14911yescharacteristic
309C2×Q8—21no—
310C2×Q8—21no—
311C2×Q8—2981no—
312C2×Q8—2981no—
313C2×Q8—1491no—
314C2×Q8C22×D14911yescharacteristic
315C2×D4—21no—
316C2×D4—21no—
317C2×D4—41no—
318C2×D4—2981no—
319C2×D4—2981no—
320C2×D4—5961no—
321C2×D4—5961no—
322C2×D4—1491no—
323C2×D4C22×D14911yescharacteristic
324Q16—21no—
325Q16—2981no—
326Q16—2981no—
327Q16—2981no—
328Q16—1491no—
329Q16C22⋊D14911yescharacteristic, complemented
330SD16—21no—
331SD16—21no—
332SD16—21no—
333SD16—21no—
334SD16—2981no—
335SD16—2981no—
336SD16—2981no—
337SD16—2981no—
338SD16—2981no—
339SD16—2981no—
340SD16—2981no—
341SD16—2981no—
342SD16—2981no—
343SD16—2981no—
344SD16—2981no—
345SD16—2981no—
346SD16—1491no—
347SD16—1491no—
348SD16C22⋊D14911yescharacteristic, complemented
349SD16C22⋊D14911yescharacteristic, complemented
350D8—21no—
351D8—2981no—
352D8—2981no—
353D8—2981no—
354D8—1491no—
355D8C22⋊D14911yescharacteristic, complemented
356M16—21no—
357M16—2981no—
358M16—2981no—
359M16—2981no—
360M16—1491no—
361M16—1491no—
362M16—1491no—
363M16C22×D14911yescharacteristic
364C2×C8—21no—
365C2×C8—2981no—
366C2×C8—2981no—
367C2×C8—2981no—
368C2×C8—1491no—
369C2×C8C22×D14911yescharacteristic
370C4⋊C4—5961no—
371C42—1491no—
372C23—21no—
373C23—41no—
374C23—2981no—
375C23—5961no—
376Q8—21no—
377Q8—21no—
378Q8—41no—
379Q8—2981no—
380Q8—2981no—
381Q8—5961no—
382Q8—1491no—
383Q8D4×D14911yescharacteristic
384Q8C2×C22⋊D14911yescharacteristic
385Q8C2×C22⋊D14911yescharacteristic
386D4—21no—
387D4—21no—
388D4—21no—
389D4—21no—
390D4—21no—
391D4—41no—
392D4—41no—
393D4—41no—
394D4—2981no—
395D4—2981no—
396D4—2981no—
397D4—5961no—
398D4—5961no—
399D4—5961no—
400D4—1491no—
401D4—11922no—
402D4D4×D14911yescharacteristic
403D4C2×C22⋊D14911yescharacteristic
404D4C2×C22⋊D14911yescharacteristic
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—2981no—
413C2×C4—2981no—
414C2×C4—2981no—
415C2×C4—5961no—
416C2×C4—5961no—
417C2×C4—5961no—
418C2×C4C23×D14911yescharacteristic
419C8—21no—
420C8—2981no—
421C8—2981no—
422C8—2981no—
423C8—1491no—
424C8—1491no—
425C8C2×C22⋊D14911yescharacteristic
426C8C2×C22⋊D14911yescharacteristic
427C22—21no—
428C22—21no—
429C22—21no—
430C22—41no—
431C22—81no—
432C22—161no—
433C22—2981no—
434C22—23841no—
435C22—5961no—
436C22—11921no—
437C22#1801195611yescharacteristic
438C4—21no—
439C4—21no—
440C4—21no—
441C4—41no—
442C4—2982no—
443C4—2981no—
444C4—5961no—
445C4C2×D4×D14911yescharacteristic
446C4C22×C22⋊D14911yescharacteristic
447C2—21no—
448C2—41no—
449C2—41no—
450C2—41no—
451C2—81no—
452C2—5961no—
453C2—11921no—
454C2D4×C22⋊D14911yescharacteristic
subgroupG/H
centerC2D4×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#577×C149C2
socleC2×C149D42
hypercenter#577D149
hypocenterC149#3291
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C2×C4 ◁ #577

Complements

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

NH ≅ G/Ntype
1. #23750436C2semidirect
2. #23750433C2semidirect
3. #23750432C2semidirect
4. #23749996C2semidirect
5. #23749890C2semidirect
6. #23749888C2semidirect
7. #23749886C2semidirect
8. #23749885C2semidirect
9. #23749808C2semidirect
10. #23749806C2semidirect
11. #23749793C2semidirect
12. #23749791C2semidirect
13. #23749742C2semidirect
14. #23749740C2semidirect
15. #577×C149C2semidirect
17. #18011957C22semidirect
20. #18011942C22semidirect
22. #18011941C22semidirect
23. #18011941C22semidirect
34. C2×#14558725C22semidirect
36. C2×#14558724C22semidirect
38. C2×#14558723C22semidirect
40. #18011918C22semidirect
41. #18011918C22semidirect
42. #18011917C22semidirect
43. #18011909C22semidirect
45. #18011847C22semidirect
46. #18011846C22semidirect
47. #18011838C22semidirect
48. #18011838C22semidirect
49. #18011838C22semidirect
50. #18011837C22semidirect
51. #18011830C22semidirect
52. #18011829C22semidirect
53. #18011828C22semidirect
54. #18011827C22semidirect
55. C8×Dic149C22semidirect
57. H(5,𝔽2)×C149C22semidirect
59. #137×C149C22semidirect
65. C2×SD16×C149C22semidirect
66. #131×C149C22semidirect
84. #14558726D4semidirect
92. #14558724D4semidirect
98. #14558723D4semidirect
102. #14558721D4semidirect
131. Q16×C149D4semidirect
136. SD16×C149D4semidirect
137. SD16×C149D4semidirect
139. D8×C149D4semidirect
227. C149#3291semidirect
232. #577D149semidirect
247. H(5,𝔽2)C2×D149semidirect
255. #137C2×D149semidirect
277. C2×SD16C2×D149semidirect
281. #131C2×D149semidirect
329. Q16C22⋊D149semidirect
348. SD16C22⋊D149semidirect
349. SD16C22⋊D149semidirect
355. D8C22⋊D149semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237504362
#237504332
#237504322
#237499962
#237498902
#237498882
#237498862
#237498852
#237498082
#237498062
#237497932
#237497912
#237497422
#237497402
#577×C1492
#3291149