Finite Group Databasebeta

← #34056475

Subgroups — #34056475

Order 19072.

454 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750441C211yesmaximal, characteristic, complemented
2#23750436C211yesmaximal, characteristic, complemented
3#23750434C211yesmaximal, characteristic, complemented
4#23750428C211yesmaximal, characteristic, complemented
5#23750007C211yesmaximal, characteristic, complemented
6#23749898C211yesmaximal, characteristic, complemented
7#23749894C211yesmaximal, characteristic, complemented
8#23749890C211yesmaximal, characteristic, complemented
9#23749887C211yesmaximal, characteristic, complemented
10#23749804C211yesmaximal, characteristic, complemented
11#23749799C211yesmaximal, characteristic, complemented
12#23749797C211yesmaximal, characteristic, complemented
13#23749739C211yesmaximal, characteristic, complemented
14#23749739C211yesmaximal, characteristic, complemented
15#455×C149C211yesmaximal, characteristic, complemented
16#18011959C2211yescharacteristic, complemented
17#18011958C2211yescharacteristic, complemented
18#18011957C2211yescharacteristic
19#18011944C2211yescharacteristic, complemented
20#18011943—21no—
21#18011943—21no—
22#18011941—21no—
23#18011941C2211yescharacteristic
24#18011940—21no—
25#18011939C2211yescharacteristic, complemented
26#18011938—21no—
27#18011937—21no—
28#18011937—21no—
29#18011937C2211yescharacteristic
30#18011937C2211yescharacteristic, complemented
31#18011936—21no—
32#18011936C2211yescharacteristic
33#18011934—21no—
34#18011932—21no—
35#18011931—21no—
36#18011931—21no—
37#18011931C2211yescharacteristic
38#18011931C2211yescharacteristic
39C2×#14558726C2211yescharacteristic, complemented
40Q16×D149—21no—
41C2×#14558724—21no—
42C2×#14558724C2211yescharacteristic, complemented
43C2×#14558723C2211yescharacteristic, complemented
44SD16×D149—21no—
45C2×#14558721—21no—
46C2×#14558721C2211yescharacteristic
47#18011919C2211yescharacteristic, complemented
48#18011919C2211yescharacteristic, complemented
49#18011918C2211yescharacteristic
50#18011918C2211yescharacteristic, complemented
51#18011899C2211yescharacteristic, complemented
52#18011846C2211yescharacteristic, complemented
53#18011846C2211yescharacteristic, complemented
54#18011839C2211yescharacteristic, complemented
55#18011839C2211yescharacteristic, complemented
56#18011830C2211yescharacteristic, complemented
57#18011829C2211yescharacteristic, complemented
58#18011827C2211yescharacteristic, complemented
59C4×#11924746C2211yescharacteristic, complemented
60H(5,𝔽2)×C149C2211yescharacteristic
61#137×C149C2211yescharacteristic
62#137×C149C2211yescharacteristic, complemented
63#124×C149C2211yescharacteristic, complemented
64#104×C149C2211yescharacteristic
65#104×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#14558735—21no—
76#14558735—41no—
77C2×Dic298—21no—
78C2×Dic298C2311yescharacteristic
79Q8×D149—21no—
80Q8×D149—21no—
81Q8×D149—21no—
82C2×D596—21no—
83C2×D596C2311yescharacteristic
84D4×D149—21no—
85D4×D149—41no—
86Dic596—21no—
87#14558726—21no—
88#14558726—21no—
89#14558726—21no—
90#14558726D411yescharacteristic
91#14558726D411yescharacteristic
92#14558725—21no—
93#14558725—21no—
94#14558724—21no—
95#14558724—21no—
96#14558724—21no—
97#14558724—21no—
98#14558724—21no—
99#14558724D411yescharacteristic
100#14558724D411yescharacteristic
101#14558723—21no—
102#14558723—21no—
103#14558723—21no—
104#14558723D411yescharacteristic
105#14558723D411yescharacteristic
106D1192—21no—
107#14558721—21no—
108#14558721—21no—
109#14558721—21no—
110#14558721—21no—
111#14558721—21no—
112#14558721D411yescharacteristic
113#14558721D411yescharacteristic
114#14558720—21no—
115#14558720—21no—
116#14558720C2311yescharacteristic
117#14558720C2311yescharacteristic
118#14558719—21no—
119#14558719—21no—
120C2×#11924746—21no—
121C2×#11924746—21no—
122C2×#11924746C2311yescharacteristic
123C2×#11924746C2311yescharacteristic
124C8×D149—21no—
125C8×D149—21no—
126#14558713—41no—
127#41×C149—21no—
128#41×C149—21no—
129#41×C149C2311yescharacteristic
130#41×C149C2311yescharacteristic
131C2×Q8×C149C2311yescharacteristic
132C2×D4×C149—21no—
133C2×D4×C149—21no—
134C2×D4×C149—41no—
135C2×D4×C149C2311yescharacteristic
136Q16×C149—21no—
137Q16×C149—21no—
138SD16×C149—21no—
139SD16×C149—21no—
140M16×C149C2311yescharacteristic
141M16×C149C2311yescharacteristic
142C22⋊C4×C149—41no—
143C42×C149C2311yescharacteristic
144C22×D149—21no—
145C22×D149—41no—
146Dic298—21no—
147Dic298—21no—
148Dic298—41no—
149Dic298—41no—
150Dic298C2×D411yescharacteristic
151Dic298C2×D411yescharacteristic
152D596—21no—
153D596—21no—
154D596—41no—
155D596—41no—
156D596C2×D411yescharacteristic
157D596C2×D411yescharacteristic
158C22⋊D149—21no—
159C22⋊D149—21no—
160C22⋊D149—41no—
161C22⋊D149—41no—
162C2×Dic149—21no—
163C2×Dic149—41no—
164C4×D149—21no—
165C4×D149—21no—
166C4×D149—41no—
167C4×D149—41no—
168C4×D149—41no—
169C4×D149—41no—
170#11924746—21no—
171#11924746—21no—
172#11924746C2×D411yescharacteristic
173#11924746C2×D411yescharacteristic
174#11924746C2×D411yescharacteristic
175#11924746C2×D411yescharacteristic
176C23×C149—21no—
177C23×C149—41no—
178Q8×C149—21no—
179Q8×C149—21no—
180Q8×C149C2×D411yescharacteristic
181Q8×C149C2×D411yescharacteristic
182D4×C149—21no—
183D4×C149—21no—
184D4×C149—21no—
185D4×C149—21no—
186D4×C149—41no—
187D4×C149—41no—
188D4×C149C2×D411yescharacteristic
189D4×C149C2×D411yescharacteristic
190C2×C4×C149—21no—
191C2×C4×C149—21no—
192C2×C4×C149—21no—
193C2×C4×C149—21no—
194C2×C4×C149—41no—
195C2×C4×C149C2411yescharacteristic
196C8×C149—21no—
197C8×C149—21no—
198C22×C149—21no—
199C22×C149—21no—
200C22×C149—41no—
201C22×C149—81no—
202C22×C149—161no—
203C22×C149H(5,𝔽2)11yescharacteristic
204C2×D149—21no—
205C2×D149—21no—
206C2×D149—41no—
207C2×D149—81no—
208C2×D149—161no—
209C4×C149—21no—
210C4×C149—21no—
211C4×C149—41no—
212C4×C149—41no—
213C4×C149C22×D411yescharacteristic
214C4×C149C22×D411yescharacteristic
215Dic149—21no—
216Dic149—21no—
217Dic149—41no—
218C2×C149—21no—
219C2×C149—41no—
220C2×C149—41no—
221C2×C149—81no—
222C2×C149D4211yescharacteristic
223D149—41no—
224D149—41no—
225D149—81no—
226C149#329011yescharacteristic, complemented, Sylow
227#3290—1491nomaximal, Sylow
228#578—1491no—
229#577—1491no—
230#577—1491no—
231#576—1491no—
232#495—1491no—
233#473—1491no—
234#472—1491no—
235#471—1491no—
236#471—1491no—
237#455—1491no—
238#455D14911yescharacteristic, complemented
239#454—1491no—
240#454—1491no—
241#443—1491no—
242#443—1491no—
2432−1+4—1491no—
2442−1+4—1491no—
245H(5,𝔽2)—1491no—
246H(5,𝔽2)C2×D14911yescharacteristic
247#137—2981no—
248#137—2981no—
249#137—2981no—
250#137—2981no—
251#137—1491no—
252#137—1491no—
253#137C2×D14911yescharacteristic
254#137C2×D14911yescharacteristic, complemented
255AGL(1,ℤ/8)—2981no—
256AGL(1,ℤ/8)—2981no—
257AGL(1,ℤ/8)—2981no—
258AGL(1,ℤ/8)—2981no—
259AGL(1,ℤ/8)—1491no—
260AGL(1,ℤ/8)—1491no—
261AGL(1,ℤ/8)—1491no—
262AGL(1,ℤ/8)—1491no—
263#135—2981no—
264#135—2981no—
265#135—2981no—
266#135—2981no—
267#135—1491no—
268#135—1491no—
269C2×Q16—2981no—
270C2×Q16—1491no—
271C2×SD16—2981no—
272C2×SD16—2981no—
273C2×SD16—1491no—
274C2×SD16—1491no—
275C2×D8—2981no—
276C2×D8—1491no—
277#131—1491no—
278#131—1491no—
279#131—1491no—
280#131—1491no—
281#124—1491no—
282#124C2×D14911yescharacteristic, complemented
283#108—1491no—
284#108—1491no—
285#104—1491no—
286#104—1491no—
287#104C2×D14911yescharacteristic
288#104C2×D14911yescharacteristic, complemented
289#101—1491no—
290#101—1491no—
291#100—1491no—
292#100C2×D14911yescharacteristic, complemented
293C4×C8—1491no—
294#41—21no—
295#41—21no—
296#41—2981no—
297#41—2981no—
298#41—2981no—
299#41—2981no—
300#41—2981no—
301#41—2981no—
302#41—5961no—
303#41—5961no—
304#41—1491no—
305#41—1491no—
306#41C22×D14911yescharacteristic
307#41C22×D14911yescharacteristic
308C2×Q8—2981no—
309C2×Q8—2981no—
310C2×Q8—2981no—
311C2×Q8—2981no—
312C2×Q8—1491no—
313C2×Q8C22×D14911yescharacteristic
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—41no—
317C2×D4—2981no—
318C2×D4—2981no—
319C2×D4—5961no—
320C2×D4—1491no—
321C2×D4C22×D14911yescharacteristic
322Q16—21no—
323Q16—21no—
324Q16—2981no—
325Q16—2981no—
326Q16—2981no—
327Q16—2981no—
328Q16—1491no—
329Q16—1491no—
330SD16—21no—
331SD16—21no—
332SD16—2981no—
333SD16—2981no—
334SD16—2981no—
335SD16—2981no—
336SD16—2981no—
337SD16—2981no—
338SD16—2981no—
339SD16—2981no—
340SD16—2981no—
341SD16—2981no—
342SD16—1491no—
343SD16—1491no—
344SD16—1491no—
345SD16—1491no—
346D8—2981no—
347D8—2981no—
348D8—2981no—
349D8—2981no—
350D8—2981no—
351D8—2981no—
352D8—1491no—
353D8—1491no—
354M16—2981no—
355M16—2981no—
356M16—2981no—
357M16—2981no—
358M16—1491no—
359M16—1491no—
360M16C22×D14911yescharacteristic
361M16C22×D14911yescharacteristic
362C2×C8—2981no—
363C2×C8—2981no—
364C2×C8—2981no—
365C2×C8—2981no—
366C2×C8—1491no—
367C2×C8—1491no—
368C22⋊C4—41no—
369C22⋊C4—5961no—
370C42C22×D14911yescharacteristic
371C23—21no—
372C23—41no—
373C23—2981no—
374C23—5961no—
375Q8—21no—
376Q8—21no—
377Q8—2981no—
378Q8—2981no—
379Q8—5961no—
380Q8—5961no—
381Q8—1491no—
382Q8—1491no—
383Q8D4×D14911yescharacteristic
384Q8D4×D14911yescharacteristic
385D4—21no—
386D4—21no—
387D4—21no—
388D4—21no—
389D4—41no—
390D4—41no—
391D4—2981no—
392D4—2981no—
393D4—2981no—
394D4—2981no—
395D4—5961no—
396D4—5961no—
397D4—5961no—
398D4—5961no—
399D4—1491no—
400D4—1491no—
401D4D4×D14911yescharacteristic
402D4D4×D14911yescharacteristic
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—41no—
408C2×C4—2981no—
409C2×C4—2981no—
410C2×C4—2981no—
411C2×C4—5961no—
412C2×C4—5961no—
413C2×C4—5961no—
414C2×C4—5961no—
415C2×C4—5961no—
416C2×C4C23×D14911yescharacteristic
417C8—21no—
418C8—21no—
419C8—2981no—
420C8—2981no—
421C8—1491no—
422C8—1491no—
423C8—1491no—
424C8—1491no—
425C22—21no—
426C22—21no—
427C22—41no—
428C22—81no—
429C22—161no—
430C22—2981no—
431C22—2981no—
432C22—23841no—
433C22—5961no—
434C22—11921no—
435C22#1801195611yescharacteristic
436C4—21no—
437C4—21no—
438C4—41no—
439C4—41no—
440C4—2981no—
441C4—2981no—
442C4—5961no—
443C4C2×D4×D14911yescharacteristic
444C4C2×D4×D14911yescharacteristic
445C2—21no—
446C2—41no—
447C2—41no—
448C2—81no—
449C2—5961no—
450C2—5961no—
451C2—11921no—
452C2#2375025711yescharacteristic
subgroupG/H
centerC2#23750257
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#455×C149C2
socleC2×C149D42
hypercenter#455D149
hypocenterC149#3290
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C2×C4 ◁ #455

Complements

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

NH ≅ G/Ntype
1. #23750441C2semidirect
2. #23750436C2semidirect
3. #23750434C2semidirect
4. #23750428C2semidirect
5. #23750007C2semidirect
6. #23749898C2semidirect
7. #23749894C2semidirect
8. #23749890C2semidirect
9. #23749887C2semidirect
10. #23749804C2semidirect
11. #23749799C2semidirect
12. #23749797C2semidirect
13. #23749739C2semidirect
14. #23749739C2semidirect
15. #455×C149C2semidirect
16. #18011959C22semidirect
17. #18011958C22semidirect
19. #18011944C22semidirect
25. #18011939C22semidirect
30. #18011937C22semidirect
39. C2×#14558726C22semidirect
42. C2×#14558724C22semidirect
43. C2×#14558723C22semidirect
47. #18011919C22semidirect
48. #18011919C22semidirect
50. #18011918C22semidirect
51. #18011899C22semidirect
52. #18011846C22semidirect
53. #18011846C22semidirect
54. #18011839C22semidirect
55. #18011839C22semidirect
56. #18011830C22semidirect
57. #18011829C22semidirect
58. #18011827C22semidirect
59. C4×#11924746C22semidirect
62. #137×C149C22semidirect
63. #124×C149C22semidirect
65. #104×C149C22semidirect
66. #100×C149C22semidirect
226. C149#3290semidirect
238. #455D149semidirect
254. #137C2×D149semidirect
282. #124C2×D149semidirect
288. #104C2×D149semidirect
292. #100C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237504412
#237504362
#237504342
#237504282
#237500072
#237498982
#237498942
#237498902
#237498872
#237498042
#237497992
#237497972
#237497392
#455×C1492
#3290149