Finite Group Databasebeta

← #34080877

Subgroups — #34080877

Order 19328.

464 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23753024C211yesmaximal, characteristic, complemented
2#23753019C211yesmaximal, characteristic, complemented
3#23753017C211yesmaximal, characteristic, complemented
4#23753014C211yesmaximal, characteristic, complemented
5#23752601C211yesmaximal, characteristic, complemented
6#23752483C211yesmaximal, characteristic, complemented
7#23752482C211yesmaximal, characteristic, complemented
8#23752476C211yesmaximal, characteristic, complemented
9#23752475C211yesmaximal, characteristic, complemented
10#23752391C211yesmaximal, characteristic, complemented
11#23752386C211yesmaximal, characteristic, complemented
12#23752381C211yesmaximal, characteristic, complemented
13#23752381C211yesmaximal, characteristic, complemented
14#23752335C211yesmaximal, characteristic, complemented
15#444×C151C211yesmaximal, characteristic, complemented
16#18012786C2211yescharacteristic, complemented
17#18012785C2211yescharacteristic
18#18012785C2211yescharacteristic, complemented
19#18012785C2211yescharacteristic, complemented
20#18012772—21no—
21#18012772C2211yescharacteristic, complemented
22#18012771—21no—
23#18012769C2211yescharacteristic, complemented
24#18012767—21no—
25#18012767—21no—
26#18012767—21no—
27#18012767C2211yescharacteristic
28#18012767C2211yescharacteristic, complemented
29#18012767C2211yescharacteristic, complemented
30#18012766—21no—
31#18012766—21no—
32#18012764C2211yescharacteristic
33#18012764C2211yescharacteristic, complemented
34#18012764C2211yescharacteristic, complemented
35#18012763—21no—
36#18012762—21no—
37#18012761—21no—
38#18012761—21no—
39#18012761C2211yescharacteristic
40#18012760—21no—
41C2×#14558993—21no—
42C2×#14558993C2211yescharacteristic, complemented
43C2×#14558993C2211yescharacteristic, complemented
44SD16×D151—21no—
45C2×D1208—21no—
46C2×D1208C2211yescharacteristic, complemented
47C2×D1208C2211yescharacteristic, complemented
48D8×D151—21no—
49#18012745C2211yescharacteristic, complemented
50#18012745C2211yescharacteristic, complemented
51#18012736C2211yescharacteristic, complemented
52#18012727C2211yescharacteristic, complemented
53#18012675C2211yescharacteristic, complemented
54#18012667C2211yescharacteristic, complemented
55#18012667C2211yescharacteristic, complemented
56#18012657C2211yescharacteristic, complemented
57#18012655C2211yescharacteristic, complemented
58#18012655C2211yescharacteristic, complemented
59#18012655C2211yescharacteristic, complemented
60#135×C151C2211yescharacteristic
61#131×C151C2211yescharacteristic, complemented
62#131×C151C2211yescharacteristic, complemented
63#108×C151C2211yescharacteristic, complemented
64#104×C151C2211yescharacteristic, complemented
65#104×C151C2211yescharacteristic, complemented
66#97×C151C2211yescharacteristic, complemented
67#14559005—21no—
68#14559005—21no—
69#14559005—21no—
70#14559004—21no—
71#14559004—21no—
72#14559004—21no—
73#14559004—21no—
74#14559004C2311yescharacteristic
75#14559004C2311yescharacteristic
76#14559003—21no—
77#14559003—41no—
78C2×Dic302—21no—
79C2×Dic302C2311yescharacteristic
80Q8×D151—21no—
81C2×D604—21no—
82C2×D604—21no—
83C2×D604—21no—
84C2×D604—41no—
85C2×D604C2311yescharacteristic
86C2×D604C2311yescharacteristic
87C2×D604C2311yescharacteristic
88D4×D151—21no—
89D4×D151—21no—
90D4×D151—21no—
91D4×D151—41no—
92D4×D151—41no—
93D4×D151—41no—
94Dic604—21no—
95Dic604D411yescharacteristic, complemented
96#14558994—21no—
97#14558993—21no—
98#14558993—21no—
99#14558993—21no—
100#14558993—21no—
101#14558993—21no—
102#14558993—21no—
103#14558993—21no—
104#14558993—21no—
105#14558993D411yescharacteristic, complemented
106#14558993D411yescharacteristic, complemented
107#14558992—21no—
108#14558991—21no—
109#14558991—21no—
110#14558991—21no—
111D1208—21no—
112D1208—21no—
113D1208—21no—
114D1208—21no—
115D1208—21no—
116D1208—21no—
117D1208—21no—
118D1208D411yescharacteristic, complemented
119#14558989—21no—
120#14558989—21no—
121#14558989—21no—
122#14558988C2311yescharacteristic
123#14558988C2311yescharacteristic
124#14558987—21no—
125#14558987—21no—
126C8×D151—21no—
127C8×D151—21no—
128(C2×D151)⋊C4—41no—
129#41×C151C2311yescharacteristic
130#41×C151C2311yescharacteristic
131Q16×C151D411yescharacteristic, complemented
132SD16×C151D411yescharacteristic, complemented
133SD16×C151D411yescharacteristic, complemented
134D8×C151D411yescharacteristic, complemented
135M16×C151—21no—
136M16×C151—21no—
137M16×C151C2311yescharacteristic
138M16×C151C2311yescharacteristic
139C2×C8×C151—21no—
140C2×C8×C151—21no—
141C2×C8×C151C2311yescharacteristic
142C2×C8×C151C2311yescharacteristic
143C42×C151C2311yescharacteristic
144C22×D151—21no—
145C22×D151—21no—
146C22×D151—21no—
147C22×D151—41no—
148C22×D151—41no—
149C22×D151—41no—
150Dic302—21no—
151Dic302—21no—
152Dic302—41no—
153Dic302C2×D411yescharacteristic
154Dic302C2×D411yescharacteristic
155D604—21no—
156D604—21no—
157D604—21no—
158D604—21no—
159D604—21no—
160D604—21no—
161D604—41no—
162D604—41no—
163D604—41no—
164D604—82no—
165D604C2×D411yescharacteristic
166D604C2×D411yescharacteristic
167C22⋊D151—21no—
168C22⋊D151—21no—
169C22⋊D151—41no—
170C22⋊D151—41no—
171C22⋊D151—41no—
172C22⋊D151—41no—
173C2×Dic151—21no—
174C2×Dic151—41no—
175C4×D151—21no—
176C4×D151—21no—
177C4×D151—41no—
178C4×D151—41no—
179C4×D151—41no—
180C4×D151—41no—
181C151⋊C8—21no—
182C151⋊C8—21no—
183Q8×C151C2×D411yescharacteristic
184Q8×C151C2×D411yescharacteristic
185D4×C151—21no—
186D4×C151—21no—
187D4×C151C2×D411yescharacteristic
188D4×C151C2×D411yescharacteristic
189C2×C4×C151—21no—
190C2×C4×C151—21no—
191C2×C4×C151—21no—
192C2×C4×C151C2411yescharacteristic
193C8×C151—21no—
194C8×C151—21no—
195C8×C151C2×D411yescharacteristic
196C8×C151C2×D411yescharacteristic
197C8×C151C2×D411yescharacteristic
198C8×C151C2×D411yescharacteristic
199C22×C151—21no—
200C22×C151—21no—
201C22×C151H(5,𝔽2)11yescharacteristic
202C2×D151—21no—
203C2×D151—21no—
204C2×D151—41no—
205C2×D151—41no—
206C2×D151—41no—
207C2×D151—81no—
208C2×D151—81no—
209C2×D151—81no—
210C2×D151—161no—
211C2×D151—161no—
212C2×D151—161no—
213C4×C151—21no—
214C4×C151—21no—
215C4×C151—41no—
216C4×C151C22×D411yescharacteristic
217C4×C151C22×D411yescharacteristic
218Dic151—21no—
219Dic151—21no—
220Dic151—41no—
221C2×C151—21no—
222C2×C151—41no—
223C2×C151—41no—
224C2×C151D4211yescharacteristic
225D151—41no—
226D151—41no—
227D151—81no—
228D151—81no—
229D151—81no—
230C151#328811yescharacteristic, complemented, Sylow
231#3288—1511nomaximal, Sylow
232#577—1511no—
233#577—1511no—
234#576—1511no—
235#576—1511no—
236#496—1511no—
237#472—1511no—
238#472—1511no—
239#471—1511no—
240#471—1511no—
241#455—1511no—
242#454—1511no—
243#453—1511no—
244#453—1511no—
245#444—1511no—
246#444D15111yescharacteristic, complemented
2472−1+4—1511no—
248H(5,𝔽2)—1511no—
249H(5,𝔽2)—1511no—
250H(5,𝔽2)—1511no—
251#137—3021no—
252#137—3021no—
253#137—1511no—
254#137—1511no—
255AGL(1,ℤ/8)—3021no—
256AGL(1,ℤ/8)—3021no—
257AGL(1,ℤ/8)—3021no—
258AGL(1,ℤ/8)—3021no—
259AGL(1,ℤ/8)—3021no—
260AGL(1,ℤ/8)—3021no—
261AGL(1,ℤ/8)—1511no—
262AGL(1,ℤ/8)—1511no—
263AGL(1,ℤ/8)—1511no—
264AGL(1,ℤ/8)—1511no—
265AGL(1,ℤ/8)—1511no—
266AGL(1,ℤ/8)—1511no—
267#135—3021no—
268#135—3021no—
269#135—3021no—
270#135—3021no—
271#135—1511no—
272#135C2×D15111yescharacteristic
273C2×SD16—3021no—
274C2×SD16—3021no—
275C2×SD16—1511no—
276C2×SD16—1511no—
277C2×D8—3021no—
278C2×D8—3021no—
279C2×D8—1511no—
280C2×D8—1511no—
281#131—1511no—
282#131—1511no—
283#131C2×D15111yescharacteristic, complemented
284#131C2×D15111yescharacteristic, complemented
285#127—1511no—
286#124—1511no—
287#108—1511no—
288#108C2×D15111yescharacteristic, complemented
289#104—1511no—
290#104—1511no—
291#104C2×D15111yescharacteristic, complemented
292#104C2×D15111yescharacteristic, complemented
293#101—1511no—
294#100—1511no—
295#100—1511no—
296#100—1511no—
297#97C2×D15111yescharacteristic, complemented
298#41—3021no—
299#41—3021no—
300#41—3021no—
301#41—3021no—
302#41—3021no—
303#41—3021no—
304#41—3021no—
305#41—3021no—
306#41—6041no—
307#41—1511no—
308#41—1511no—
309#41C22×D15111yescharacteristic
310#41C22×D15111yescharacteristic
311C2×Q8—3021no—
312C2×Q8—3021no—
313C2×Q8—1511no—
314C2×D4—3021no—
315C2×D4—3021no—
316C2×D4—3021no—
317C2×D4—3021no—
318C2×D4—3021no—
319C2×D4—3021no—
320C2×D4—6041no—
321C2×D4—6041no—
322C2×D4—6041no—
323C2×D4—6041no—
324C2×D4—1511no—
325C2×D4—1511no—
326C2×D4—1511no—
327Q16—3021no—
328Q16—3021no—
329Q16—1511no—
330Q16D60411yescharacteristic, complemented
331SD16—3021no—
332SD16—3021no—
333SD16—3021no—
334SD16—3021no—
335SD16—3021no—
336SD16—3021no—
337SD16—3021no—
338SD16—3021no—
339SD16—3021no—
340SD16—3021no—
341SD16—3021no—
342SD16—3021no—
343SD16—1511no—
344SD16—1511no—
345SD16D60411yescharacteristic, complemented
346SD16D60411yescharacteristic, complemented
347D8—3021no—
348D8—3021no—
349D8—3021no—
350D8—3021no—
351D8—3021no—
352D8—3021no—
353D8—3021no—
354D8—3021no—
355D8—3021no—
356D8—3021no—
357D8—1511no—
358D8D60411yescharacteristic, complemented
359M16—21no—
360M16—21no—
361M16—3021no—
362M16—3021no—
363M16—1511no—
364M16—1511no—
365M16C22×D15111yescharacteristic
366M16C22×D15111yescharacteristic
367C2×C8—21no—
368C2×C8—21no—
369C2×C8—3021no—
370C2×C8—3021no—
371C2×C8C22×D15111yescharacteristic
372C2×C8C22×D15111yescharacteristic
373C22⋊C4—6041no—
374C42C22×D15111yescharacteristic
375C23—3021no—
376C23—3021no—
377C23—3021no—
378C23—6041no—
379C23—6041no—
380C23—6041no—
381Q8—3021no—
382Q8—3021no—
383Q8—6041no—
384Q8—1511no—
385Q8—1511no—
386Q8C2×D60411yescharacteristic
387Q8C2×D60411yescharacteristic
388D4—21no—
389D4—21no—
390D4—3021no—
391D4—3021no—
392D4—3021no—
393D4—3021no—
394D4—3021no—
395D4—3021no—
396D4—3021no—
397D4—3021no—
398D4—6041no—
399D4—6041no—
400D4—6041no—
401D4—6041no—
402D4—6041no—
403D4—6041no—
404D4—6041no—
405D4—1511no—
406D4—1511no—
407D4—12082no—
408D4C2×D60411yescharacteristic
409D4C2×D60411yescharacteristic
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—3021no—
414C2×C4—3021no—
415C2×C4—3021no—
416C2×C4—6041no—
417C2×C4—6041no—
418C2×C4—6041no—
419C2×C4—6041no—
420C2×C4—6041no—
421C2×C4C23×D15111yescharacteristic
422C8—21no—
423C8—21no—
424C8—3021no—
425C8—3021no—
426C8D4×D15111yescharacteristic
427C8D4×D15111yescharacteristic
428C8C2×D60411yescharacteristic
429C8C2×D60411yescharacteristic
430C22—21no—
431C22—21no—
432C22—3021no—
433C22—3021no—
434C22—6041no—
435C22—6041no—
436C22—6041no—
437C22—24161no—
438C22—24161no—
439C22—24161no—
440C22—12081no—
441C22—12081no—
442C22—12081no—
443C22#1801278511yescharacteristic
444C4—21no—
445C4—21no—
446C4—41no—
447C4—3021no—
448C4—3021no—
449C4—6041no—
450C4C2×D4×D15111yescharacteristic
451C4C22×D60411yescharacteristic
452C2—21no—
453C2—41no—
454C2—41no—
455C2—6041no—
456C2—6041no—
457C2—12081no—
458C2—12081no—
459C2—12081no—
460C2D4×D60411yescharacteristic
subgroupG/H
centerC2D4×D604
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#444×C151C2
socleC2×C151D42
hypercenter#444D151
hypocenterC151#3288
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C2×C4 ◁ #444

Complements

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

NH ≅ G/Ntype
1. #23753024C2semidirect
2. #23753019C2semidirect
3. #23753017C2semidirect
4. #23753014C2semidirect
5. #23752601C2semidirect
6. #23752483C2semidirect
7. #23752482C2semidirect
8. #23752476C2semidirect
9. #23752475C2semidirect
10. #23752391C2semidirect
11. #23752386C2semidirect
12. #23752381C2semidirect
13. #23752381C2semidirect
14. #23752335C2semidirect
15. #444×C151C2semidirect
16. #18012786C22semidirect
18. #18012785C22semidirect
19. #18012785C22semidirect
21. #18012772C22semidirect
23. #18012769C22semidirect
28. #18012767C22semidirect
29. #18012767C22semidirect
33. #18012764C22semidirect
34. #18012764C22semidirect
42. C2×#14558993C22semidirect
43. C2×#14558993C22semidirect
46. C2×D1208C22semidirect
47. C2×D1208C22semidirect
49. #18012745C22semidirect
50. #18012745C22semidirect
51. #18012736C22semidirect
52. #18012727C22semidirect
53. #18012675C22semidirect
54. #18012667C22semidirect
55. #18012667C22semidirect
56. #18012657C22semidirect
57. #18012655C22semidirect
58. #18012655C22semidirect
59. #18012655C22semidirect
61. #131×C151C22semidirect
62. #131×C151C22semidirect
63. #108×C151C22semidirect
64. #104×C151C22semidirect
65. #104×C151C22semidirect
66. #97×C151C22semidirect
95. Dic604D4semidirect
105. #14558993D4semidirect
106. #14558993D4semidirect
118. D1208D4semidirect
131. Q16×C151D4semidirect
132. SD16×C151D4semidirect
133. SD16×C151D4semidirect
134. D8×C151D4semidirect
230. C151#3288semidirect
246. #444D151semidirect
283. #131C2×D151semidirect
284. #131C2×D151semidirect
288. #108C2×D151semidirect
291. #104C2×D151semidirect
292. #104C2×D151semidirect
297. #97C2×D151semidirect
330. Q16D604semidirect
345. SD16D604semidirect
346. SD16D604semidirect
358. D8D604semidirect

Maximal subgroups

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

subgroupindex
#237530242
#237530192
#237530172
#237530142
#237526012
#237524832
#237524822
#237524762
#237524752
#237523912
#237523862
#237523812
#237523352
#444×C1512
#3288151