Finite Group Databasebeta

← #34056483

Subgroups — #34056483

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#23750437C211yesmaximal, characteristic, complemented
2#23750435C211yesmaximal, characteristic, complemented
3#23750434C211yesmaximal, characteristic, complemented
4#23750431C211yesmaximal, characteristic, complemented
5#23749996C211yesmaximal, characteristic, complemented
6#23749891C211yesmaximal, characteristic, complemented
7#23749889C211yesmaximal, characteristic, complemented
8#23749887C211yesmaximal, characteristic, complemented
9#23749810C211yesmaximal, characteristic, complemented
10#23749806C211yesmaximal, characteristic, complemented
11#23749795C211yesmaximal, characteristic, complemented
12#23749791C211yesmaximal, characteristic, complemented
13#23749741C211yesmaximal, characteristic, complemented
14#23749740C211yesmaximal, characteristic, complemented
15#471×C149C211yesmaximal, characteristic, complemented
16#18011959C2211yescharacteristic
17#18011958C2211yescharacteristic
18#18011957C2211yescharacteristic, complemented
19#18011956C2211yescharacteristic, complemented
20#18011944—21no—
21#18011944C2211yescharacteristic, complemented
22#18011944C2211yescharacteristic, complemented
23#18011943—21no—
24#18011942C2211yescharacteristic, complemented
25#18011940—21no—
26#18011940—21no—
27#18011939—21no—
28#18011939C2211yescharacteristic
29#18011939C2211yescharacteristic
30#18011938—21no—
31#18011938—21no—
32#18011937C2211yescharacteristic
33#18011935—21no—
34#18011934—21no—
35#18011933—21no—
36#18011933C2211yescharacteristic
37#18011932—21no—
38#18011931C2211yescharacteristic
39#18011930—21no—
40C2×#14558725—21no—
41C2×#14558725C2211yescharacteristic, complemented
42C2×#14558724C2211yescharacteristic, complemented
43C2×#14558723C2211yescharacteristic, complemented
44SD16×D149—21no—
45SD16×D149—21no—
46SD16×D149—21no—
47#18011919C2211yescharacteristic, complemented
48#18011919C2211yescharacteristic, complemented
49#18011917C2211yescharacteristic, complemented
50#18011909C2211yescharacteristic, complemented
51#18011907C2211yescharacteristic
52#18011846C2211yescharacteristic, complemented
53#18011838C2211yescharacteristic, complemented
54#18011837C2211yescharacteristic, complemented
55#18011837C2211yescharacteristic, complemented
56#18011837C2211yescharacteristic, complemented
57#18011829C2211yescharacteristic, complemented
58#18011827C2211yescharacteristic, complemented
59C8×Dic149C2211yescharacteristic, complemented
60#137×C149C2211yescharacteristic, complemented
61AGL(1,ℤ/8)×C149C2211yescharacteristic
62C2×SD16×C149C2211yescharacteristic, complemented
63#131×C149C2211yescharacteristic, complemented
64#108×C149C2211yescharacteristic, complemented
65#101×C149C2211yescharacteristic, complemented
66#100×C149C2211yescharacteristic, complemented
67#14558737—21no—
68#14558737—21no—
69#14558737—21no—
70#14558736—21no—
71#14558736—21no—
72#14558736—41no—
73#14558736C2311yescharacteristic
74#14558736C2311yescharacteristic
75#14558736C2311yescharacteristic
76#14558735—21no—
77#14558735—21no—
78#14558735—21no—
79#14558735—41no—
80C2×Dic298—21no—
81C2×Dic298C2311yescharacteristic
82Q8×D149—21no—
83Q8×D149—21no—
84Q8×D149—21no—
85C2×D596—21no—
86C2×D596C2311yescharacteristic
87C2×C22⋊D149—41no—
88C2×C22⋊D149—41no—
89D4×D149—21no—
90D4×D149—21no—
91D4×D149—21no—
92D4×D149—41no—
93Dic596—21no—
94Dic596—21no—
95Dic596D411yescharacteristic, complemented
96#14558726—21no—
97#14558726D411yescharacteristic, complemented
98#14558725—21no—
99#14558725—21no—
100#14558725—21no—
101#14558725—21no—
102#14558725—21no—
103#14558725—21no—
104#14558725D411yescharacteristic, complemented
105#14558725D411yescharacteristic, complemented
106#14558724—21no—
107#14558724—21no—
108#14558724—21no—
109#14558724D411yescharacteristic, complemented
110#14558723—21no—
111#14558723—21no—
112#14558723—21no—
113#14558723D411yescharacteristic, complemented
114D1192—21no—
115D1192—21no—
116D1192D411yescharacteristic, complemented
117#14558721—21no—
118#14558721D411yescharacteristic, complemented
119#14558720C2311yescharacteristic
120#14558719—21no—
121#14558719—21no—
122#14558719—21no—
123C2×#11924746C2311yescharacteristic
124C8×D149—21no—
125C8×D149—21no—
126C8×D149—21no—
127#14558715—41no—
128C4×Dic149C2311yescharacteristic
129#41×C149C2311yescharacteristic
130C2×Q8×C149C2311yescharacteristic
131C2×D4×C149C2311yescharacteristic
132Q16×C149—21no—
133SD16×C149—21no—
134SD16×C149—21no—
135SD16×C149—21no—
136SD16×C149—21no—
137D8×C149—21no—
138M16×C149—21no—
139M16×C149C2311yescharacteristic
140M16×C149C2311yescharacteristic
141M16×C149C2311yescharacteristic
142C2×C8×C149—21no—
143C2×C8×C149C2311yescharacteristic
144C22×D149—21no—
145C22×D149—41no—
146C22×D149—41no—
147Dic298—21no—
148Dic298—21no—
149Dic298—41no—
150Dic298—41no—
151Dic298C2×D411yescharacteristic
152Dic298C2×D411yescharacteristic
153Dic298C2×D411yescharacteristic
154D596—21no—
155D596—21no—
156D596—41no—
157D596—41no—
158D596C2×D411yescharacteristic
159D596C2×D411yescharacteristic
160D596C2×D411yescharacteristic
161C22⋊D149—21no—
162C22⋊D149—21no—
163C22⋊D149—21no—
164C22⋊D149—41no—
165C22⋊D149—41no—
166C22⋊D149—41no—
167C22⋊D149—41no—
168C22⋊D149—82no—
169C2×Dic149—21no—
170C2×Dic149—21no—
171C2×Dic149—41no—
172C2×Dic149—41no—
173C4×D149—21no—
174C4×D149—21no—
175C4×D149—21no—
176C4×D149—41no—
177C4×D149—41no—
178C4×D149—41no—
179C4×D149—41no—
180#11924746—21no—
181#11924746C2×D411yescharacteristic
182#11924746C2×D411yescharacteristic
183C23×C149—21no—
184Q8×C149—21no—
185Q8×C149—21no—
186Q8×C149C2×D411yescharacteristic
187D4×C149—21no—
188D4×C149—21no—
189D4×C149—21no—
190D4×C149C2×D411yescharacteristic
191C2×C4×C149—21no—
192C2×C4×C149—21no—
193C2×C4×C149C2411yescharacteristic
194C8×C149—21no—
195C8×C149—21no—
196C8×C149—21no—
197C8×C149C2×D411yescharacteristic
198C8×C149C2×D411yescharacteristic
199C22×C149—21no—
200C22×C149—41no—
201C22×C149—81no—
202C22×C149H(5,𝔽2)11yescharacteristic
203C2×D149—21no—
204C2×D149—21no—
205C2×D149—21no—
206C2×D149—41no—
207C2×D149—81no—
208C2×D149—161no—
209C2×D149—161no—
210C4×C149—21no—
211C4×C149—41no—
212C4×C149C22×D411yescharacteristic
213C4×C149C22×D411yescharacteristic
214Dic149—22no—
215Dic149—21no—
216Dic149—21no—
217Dic149—21no—
218Dic149—41no—
219C2×C149—21no—
220C2×C149—41no—
221C2×C149—81no—
222C2×C149D4211yescharacteristic
223D149—41no—
224D149—41no—
225D149—41no—
226D149—81no—
227C149#329111yescharacteristic, complemented, Sylow
228#3291—1491nomaximal, Sylow
229#577—1491no—
230#577—1491no—
231#577—1491no—
232#577—1491no—
233#492—1491no—
234#471—1491no—
235#471—1491no—
236#471—1491no—
237#471D14911yescharacteristic, complemented
238#456—1491no—
239#456—1491no—
240#453—1491no—
241#453—1491no—
242#443—1491no—
243#443—1491no—
2442−1+4—1491no—
2452−1+4—1491no—
246H(5,𝔽2)—1491no—
247H(5,𝔽2)—1491no—
248#137—2981no—
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)—2981no—
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—2981no—
265#135—2981no—
266#135—2981no—
267#135—2981no—
268#135—1491no—
269#135—1491no—
270C2×SD16—2981no—
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#108C2×D14911yescharacteristic, complemented
286#104—1491no—
287#104—1491no—
288#104—1491no—
289#104—1491no—
290#101—1491no—
291#101C2×D14911yescharacteristic, complemented
292#100—1491no—
293#100C2×D14911yescharacteristic, complemented
294C4×C8—1491no—
295#41—2981no—
296#41—2981no—
297#41—2981no—
298#41—2981no—
299#41—2981no—
300#41—2981no—
301#41—2981no—
302#41—2981no—
303#41—5961no—
304#41—5961no—
305#41—1491no—
306#41—1491no—
307#41—1491no—
308#41C22×D14911yescharacteristic
309C2×Q8—2981no—
310C2×Q8—2981no—
311C2×Q8—2981no—
312C2×Q8—2981no—
313C2×Q8—1491no—
314C2×Q8C22×D14911yescharacteristic
315C2×D4—2981no—
316C2×D4—2981no—
317C2×D4—2981no—
318C2×D4—2981no—
319C2×D4—5961no—
320C2×D4—5961no—
321C2×D4—5961no—
322C2×D4—1491no—
323C2×D4C22×D14911yescharacteristic
324Q16—21no—
325Q16—2981no—
326Q16—2981no—
327Q16—2981no—
328Q16—1491no—
329Q16—1491no—
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—
348SD16—1491no—
349SD16—1491no—
350D8—21no—
351D8—2981no—
352D8—2981no—
353D8—2981no—
354D8—1491no—
355D8—1491no—
356M16—21no—
357M16—2981no—
358M16—2981no—
359M16—2981no—
360M16—1491no—
361M16C22×D14911yescharacteristic
362M16C22×D14911yescharacteristic
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—2981no—
374C23—5961no—
375C23—5961no—
376Q8—21no—
377Q8—21no—
378Q8—2981no—
379Q8—2981no—
380Q8—5961no—
381Q8—5961no—
382Q8—1491no—
383Q8—1491no—
384Q8—1491no—
385Q8D4×D14911yescharacteristic
386D4—21no—
387D4—21no—
388D4—21no—
389D4—2981no—
390D4—2981no—
391D4—2981no—
392D4—2981no—
393D4—2981no—
394D4—5961no—
395D4—5961no—
396D4—5961no—
397D4—5961no—
398D4—5961no—
399D4—5961no—
400D4—1491no—
401D4—1491no—
402D4—1491no—
403D4—11922no—
404D4D4×D14911yescharacteristic
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—2981no—
408C2×C4—2981no—
409C2×C4—2981no—
410C2×C4—2981no—
411C2×C4—2981no—
412C2×C4—5961no—
413C2×C4—5961no—
414C2×C4—5961no—
415C2×C4—5961no—
416C2×C4—5961no—
417C2×C4—5961no—
418C2×C4C23×D14911yescharacteristic
419C8—21no—
420C8—21no—
421C8—21no—
422C8—2981no—
423C8—1491no—
424C8—1491no—
425C8D4×D14911yescharacteristic
426C8D4×D14911yescharacteristic
427C22—21no—
428C22—41no—
429C22—81no—
430C22—2981no—
431C22—2981no—
432C22—2981no—
433C22—23841no—
434C22—23841no—
435C22—5961no—
436C22—11921no—
437C22#1801195711yescharacteristic
438C4—21no—
439C4—41no—
440C4—2982no—
441C4—2981no—
442C4—2981no—
443C4—2981no—
444C4—5961no—
445C4C2×D4×D14911yescharacteristic
446C4C2×D4×D14911yescharacteristic
447C2—21no—
448C2—41no—
449C2—81no—
450C2—5961no—
451C2—5961no—
452C2—5961no—
453C2—11921no—
454C2#2375025911yescharacteristic
subgroupG/H
centerC2#23750259
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#471×C149C2
socleC2×C149D42
hypercenter#471D149
hypocenterC149#3291
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C2×C4 ◁ #471

Complements

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

NH ≅ G/Ntype
1. #23750437C2semidirect
2. #23750435C2semidirect
3. #23750434C2semidirect
4. #23750431C2semidirect
5. #23749996C2semidirect
6. #23749891C2semidirect
7. #23749889C2semidirect
8. #23749887C2semidirect
9. #23749810C2semidirect
10. #23749806C2semidirect
11. #23749795C2semidirect
12. #23749791C2semidirect
13. #23749741C2semidirect
14. #23749740C2semidirect
15. #471×C149C2semidirect
18. #18011957C22semidirect
19. #18011956C22semidirect
21. #18011944C22semidirect
22. #18011944C22semidirect
24. #18011942C22semidirect
41. C2×#14558725C22semidirect
42. C2×#14558724C22semidirect
43. C2×#14558723C22semidirect
47. #18011919C22semidirect
48. #18011919C22semidirect
49. #18011917C22semidirect
50. #18011909C22semidirect
52. #18011846C22semidirect
53. #18011838C22semidirect
54. #18011837C22semidirect
55. #18011837C22semidirect
56. #18011837C22semidirect
57. #18011829C22semidirect
58. #18011827C22semidirect
59. C8×Dic149C22semidirect
60. #137×C149C22semidirect
62. C2×SD16×C149C22semidirect
63. #131×C149C22semidirect
64. #108×C149C22semidirect
65. #101×C149C22semidirect
66. #100×C149C22semidirect
95. Dic596D4semidirect
97. #14558726D4semidirect
104. #14558725D4semidirect
105. #14558725D4semidirect
109. #14558724D4semidirect
113. #14558723D4semidirect
116. D1192D4semidirect
118. #14558721D4semidirect
227. C149#3291semidirect
237. #471D149semidirect
255. #137C2×D149semidirect
277. C2×SD16C2×D149semidirect
281. #131C2×D149semidirect
285. #108C2×D149semidirect
291. #101C2×D149semidirect
293. #100C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237504372
#237504352
#237504342
#237504312
#237499962
#237498912
#237498892
#237498872
#237498102
#237498062
#237497952
#237497912
#237497412
#237497402
#471×C1492
#3291149