Finite Group Databasebeta

← #34080884

Subgroups — #34080884

Order 19328.

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#23753028C211yesmaximal, characteristic, complemented
2#23753025C211yesmaximal, characteristic, complemented
3#23753024C211yesmaximal, characteristic, complemented
4#23753021C211yesmaximal, characteristic, complemented
5#23752605C211yesmaximal, characteristic, complemented
6#23752486C211yesmaximal, characteristic, complemented
7#23752478C211yesmaximal, characteristic, complemented
8#23752476C211yesmaximal, characteristic, complemented
9#23752397C211yesmaximal, characteristic, complemented
10#23752393C211yesmaximal, characteristic, complemented
11#23752388C211yesmaximal, characteristic, complemented
12#23752387C211yesmaximal, characteristic, complemented
13#23752333C211yesmaximal, characteristic, complemented
14#23752332C211yesmaximal, characteristic, complemented
15#473×C151C211yesmaximal, characteristic, complemented
16#18012787C2211yescharacteristic
17#18012787C2211yescharacteristic, complemented
18#18012786C2211yescharacteristic
19#18012785C2211yescharacteristic
20#18012772—21no—
21#18012772C2211yescharacteristic
22#18012772C2211yescharacteristic, complemented
23#18012771—21no—
24#18012771—21no—
25#18012771—21no—
26#18012771—21no—
27#18012770C2211yescharacteristic
28#18012770C2211yescharacteristic, complemented
29#18012768—21no—
30#18012767—21no—
31#18012767C2211yescharacteristic
32#18012767C2211yescharacteristic
33#18012766—21no—
34#18012762—21no—
35#18012762—21no—
36#18012761—21no—
37#18012761C2211yescharacteristic
38#18012760—21no—
39#18012759C2211yescharacteristic
40C2×#14558994C2211yescharacteristic, complemented
41Q16×D151—21no—
42Q16×D151—21no—
43C2×#14558993—21no—
44C2×#14558993C2211yescharacteristic
45C2×#14558991C2211yescharacteristic
46SD16×D151—21no—
47#18012747C2211yescharacteristic
48#18012747C2211yescharacteristic, complemented
49#18012745C2211yescharacteristic, complemented
50#18012737C2211yescharacteristic, complemented
51#18012728C2211yescharacteristic
52#18012674C2211yescharacteristic, complemented
53#18012666C2211yescharacteristic
54#18012665C2211yescharacteristic
55#18012665C2211yescharacteristic, complemented
56#18012665C2211yescharacteristic, complemented
57#18012657C2211yescharacteristic, complemented
58#18012655C2211yescharacteristic
59#18012649C2211yescharacteristic, complemented
60#137×C151C2211yescharacteristic
61#137×C151C2211yescharacteristic
62C2×Q16×C151C2211yescharacteristic, complemented
63#131×C151C2211yescharacteristic
64#108×C151C2211yescharacteristic, complemented
65#101×C151C2211yescharacteristic, complemented
66#101×C151C2211yescharacteristic, complemented
67#14559005—21no—
68#14559005—21no—
69#14559005—21no—
70#14559005—21no—
71#14559005—21no—
72#14559004—21no—
73#14559004—21no—
74#14559004—41no—
75#14559004—41no—
76#14559004C2311yescharacteristic
77#14559004C2311yescharacteristic
78#14559004C2311yescharacteristic
79#14559003—21no—
80#14559003—41no—
81C2×Dic302—21no—
82C2×Dic302C2311yescharacteristic
83Q8×D151—21no—
84Q8×D151—21no—
85Q8×D151—21no—
86Q8×D151—21no—
87Q8×D151—21no—
88C2×D604—21no—
89C2×D604C2311yescharacteristic
90D4×D151—21no—
91D4×D151—41no—
92Dic604—21no—
93Dic604—21no—
94Dic604D411yescharacteristic
95#14558994—21no—
96#14558994—21no—
97#14558994—21no—
98#14558994—21no—
99#14558994D411yescharacteristic
100#14558993—21no—
101#14558993—21no—
102#14558993—21no—
103#14558993—21no—
104#14558993—21no—
105#14558993—21no—
106#14558993D411yescharacteristic
107#14558993D411yescharacteristic
108#14558992D411yescharacteristic
109#14558991—21no—
110#14558991—21no—
111#14558991—21no—
112#14558991—21no—
113#14558991D411yescharacteristic
114D1208—21no—
115D1208—21no—
116D1208D411yescharacteristic
117#14558989D411yescharacteristic
118#14558988C2311yescharacteristic
119#14558987—21no—
120#14558987—21no—
121#14558987—21no—
122C2×C151⋊C8C2311yescharacteristic
123C8×D151—21no—
124C8×D151—21no—
125C8×D151—21no—
126Dic151⋊C4—41no—
127(C2×D151)⋊C4—41no—
128C4×Dic151C2311yescharacteristic
129#41×C151C2311yescharacteristic
130C2×Q8×C151C2311yescharacteristic
131C2×Q8×C151C2311yescharacteristic
132Q16×C151—21no—
133Q16×C151—21no—
134Q16×C151—21no—
135Q16×C151—21no—
136SD16×C151—21no—
137SD16×C151—21no—
138M16×C151—21no—
139M16×C151C2311yescharacteristic
140M16×C151C2311yescharacteristic
141M16×C151C2311yescharacteristic
142C2×C8×C151—21no—
143C2×C8×C151C2311yescharacteristic
144C22×D151—21no—
145C22×D151—41no—
146Dic302—21no—
147Dic302—21no—
148Dic302—41no—
149Dic302—41no—
150Dic302—41no—
151Dic302C2×D411yescharacteristic
152Dic302C2×D411yescharacteristic
153Dic302C2×D411yescharacteristic
154D604—21no—
155D604—21no—
156D604—41no—
157D604—41no—
158D604—41no—
159D604C2×D411yescharacteristic
160D604C2×D411yescharacteristic
161D604C2×D411yescharacteristic
162C22⋊D151—21no—
163C22⋊D151—21no—
164C22⋊D151—21no—
165C22⋊D151—41no—
166C22⋊D151—41no—
167C2×Dic151—21no—
168C2×Dic151—21no—
169C2×Dic151—41no—
170C4×D151—21no—
171C4×D151—21no—
172C4×D151—21no—
173C4×D151—41no—
174C4×D151—41no—
175C4×D151—41no—
176C4×D151—41no—
177C4×D151—41no—
178C4×D151—41no—
179C151⋊C8—21no—
180C151⋊C8C2×D411yescharacteristic
181C151⋊C8C2×D411yescharacteristic
182Q8×C151—21no—
183Q8×C151—21no—
184Q8×C151—21no—
185Q8×C151—21no—
186Q8×C151C2×D411yescharacteristic
187D4×C151—21no—
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×C151—21no—
196C8×C151C2×D411yescharacteristic
197C8×C151C2×D411yescharacteristic
198C22×C151—21no—
199C22×C151H(5,𝔽2)11yescharacteristic
200C2×D151—21no—
201C2×D151—21no—
202C2×D151—21no—
203C2×D151—41no—
204C2×D151—81no—
205C2×D151—161no—
206C4×C151—21no—
207C4×C151—41no—
208C4×C151—41no—
209C4×C151C22×D411yescharacteristic
210C4×C151C22×D411yescharacteristic
211Dic151—21no—
212Dic151—21no—
213Dic151—21no—
214Dic151—41no—
215Dic151—41no—
216C2×C151—21no—
217C2×C151—41no—
218C2×C151D4211yescharacteristic
219D151—41no—
220D151—41no—
221D151—41no—
222D151—81no—
223C151#328911yescharacteristic, complemented, Sylow
224#3289—1511nomaximal, Sylow
225#578—1511no—
226#578—1511no—
227#577—1511no—
228#577—1511no—
229#497—1511no—
230#473—1511no—
231#473D15111yescharacteristic, complemented
232#471—1511no—
233#471—1511no—
234#456—1511no—
235#456—1511no—
236#455—1511no—
237#454—1511no—
238#444—1511no—
239#444—1511no—
2402−1+4—1511no—
2412−1+4—1511no—
2422−1+4—1511no—
243H(5,𝔽2)—1511no—
244#137—3021no—
245#137—3021no—
246#137—3021no—
247#137—3021no—
248#137—3021no—
249#137—3021no—
250#137—1511no—
251#137—1511no—
252#137—1511no—
253#137—1511no—
254#137C2×D15111yescharacteristic
255#137C2×D15111yescharacteristic
256AGL(1,ℤ/8)—3021no—
257AGL(1,ℤ/8)—3021no—
258AGL(1,ℤ/8)—1511no—
259AGL(1,ℤ/8)—1511no—
260#135—3021no—
261#135—3021no—
262#135—3021no—
263#135—3021no—
264#135—1511no—
265#135—1511no—
266C2×Q16—3021no—
267C2×Q16—3021no—
268C2×Q16—1511no—
269C2×Q16C2×D15111yescharacteristic, complemented
270C2×SD16—3021no—
271C2×SD16—3021no—
272C2×SD16—1511no—
273C2×SD16—1511no—
274#131—1511no—
275#131—1511no—
276#131—1511no—
277#131C2×D15111yescharacteristic
278C4⋊Q8—1511no—
279#124—1511no—
280#108—1511no—
281#108C2×D15111yescharacteristic, complemented
282#104—1511no—
283#104—1511no—
284#104—1511no—
285#104—1511no—
286#101—1511no—
287#101C2×D15111yescharacteristic, complemented
288#101C2×D15111yescharacteristic, complemented
289#100—1511no—
290#97—1511no—
291#41—3021no—
292#41—3021no—
293#41—3021no—
294#41—3021no—
295#41—3021no—
296#41—3021no—
297#41—3021no—
298#41—3021no—
299#41—6041no—
300#41—6041no—
301#41—6041no—
302#41—1511no—
303#41—1511no—
304#41—1511no—
305#41C22×D15111yescharacteristic
306C2×Q8—3021no—
307C2×Q8—3021no—
308C2×Q8—3021no—
309C2×Q8—3021no—
310C2×Q8—3021no—
311C2×Q8—3021no—
312C2×Q8—1511no—
313C2×Q8C22×D15111yescharacteristic
314C2×Q8C22×D15111yescharacteristic
315C2×D4—3021no—
316C2×D4—3021no—
317C2×D4—6041no—
318C2×D4—1511no—
319Q16—21no—
320Q16—21no—
321Q16—21no—
322Q16—21no—
323Q16—3021no—
324Q16—3021no—
325Q16—3021no—
326Q16—3021no—
327Q16—3021no—
328Q16—3021no—
329Q16—1511no—
330Q16—1511no—
331SD16—21no—
332SD16—21no—
333SD16—3021no—
334SD16—3021no—
335SD16—3021no—
336SD16—3021no—
337SD16—3021no—
338SD16—3021no—
339SD16—3021no—
340SD16—3021no—
341SD16—3021no—
342SD16—3021no—
343SD16—1511no—
344SD16—1511no—
345SD16—1511no—
346SD16—1511no—
347D8—3021no—
348D8—3021no—
349D8—1511no—
350D8—1511no—
351M16—21no—
352M16—3021no—
353M16—3021no—
354M16—3021no—
355M16—1511no—
356M16C22×D15111yescharacteristic
357M16C22×D15111yescharacteristic
358M16C22×D15111yescharacteristic
359C2×C8—21no—
360C2×C8—3021no—
361C2×C8—3021no—
362C2×C8—3021no—
363C2×C8—1511no—
364C2×C8C22×D15111yescharacteristic
365C4⋊C4—6041no—
366C22⋊C4—6041no—
367C42—1511no—
368C23—3021no—
369C23—6041no—
370Q8—21no—
371Q8—21no—
372Q8—21no—
373Q8—21no—
374Q8—3021no—
375Q8—3021no—
376Q8—6041no—
377Q8—6041no—
378Q8—6041no—
379Q8—1511no—
380Q8—1511no—
381Q8—1511no—
382Q8D4×D15111yescharacteristic
383D4—21no—
384D4—3021no—
385D4—3021no—
386D4—3021no—
387D4—3021no—
388D4—3021no—
389D4—6041no—
390D4—6041no—
391D4—6041no—
392D4—6041no—
393D4—6041no—
394D4—1511no—
395D4—1511no—
396D4—1511no—
397D4D4×D15111yescharacteristic
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—3021no—
402C2×C4—3021no—
403C2×C4—3021no—
404C2×C4—3021no—
405C2×C4—3021no—
406C2×C4—6041no—
407C2×C4—6041no—
408C2×C4—6041no—
409C2×C4—6041no—
410C2×C4—6041no—
411C2×C4—6041no—
412C2×C4—6041no—
413C2×C4C23×D15111yescharacteristic
414C8—21no—
415C8—21no—
416C8—21no—
417C8—3021no—
418C8—1511no—
419C8—1511no—
420C8D4×D15111yescharacteristic
421C8D4×D15111yescharacteristic
422C22—21no—
423C22—3021no—
424C22—3021no—
425C22—3021no—
426C22—6041no—
427C22—24161no—
428C22—12081no—
429C22#1801278511yescharacteristic
430C4—21no—
431C4—41no—
432C4—41no—
433C4—3021no—
434C4—3021no—
435C4—3021no—
436C4—6041no—
437C4—6041no—
438C4C2×D4×D15111yescharacteristic
439C4C2×D4×D15111yescharacteristic
440C2—21no—
441C2—41no—
442C2—6041no—
443C2—6041no—
444C2—6041no—
445C2—12081no—
446C2#2375284611yescharacteristic
subgroupG/H
centerC2#23752846
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#473×C151C2
socleC2×C151D42
hypercenter#473D151
hypocenterC151#3289
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C2×C4 ◁ #473

Complements

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

NH ≅ G/Ntype
1. #23753028C2semidirect
2. #23753025C2semidirect
3. #23753024C2semidirect
4. #23753021C2semidirect
5. #23752605C2semidirect
6. #23752486C2semidirect
7. #23752478C2semidirect
8. #23752476C2semidirect
9. #23752397C2semidirect
10. #23752393C2semidirect
11. #23752388C2semidirect
12. #23752387C2semidirect
13. #23752333C2semidirect
14. #23752332C2semidirect
15. #473×C151C2semidirect
17. #18012787C22semidirect
22. #18012772C22semidirect
28. #18012770C22semidirect
40. C2×#14558994C22semidirect
48. #18012747C22semidirect
49. #18012745C22semidirect
50. #18012737C22semidirect
52. #18012674C22semidirect
55. #18012665C22semidirect
56. #18012665C22semidirect
57. #18012657C22semidirect
59. #18012649C22semidirect
62. C2×Q16×C151C22semidirect
64. #108×C151C22semidirect
65. #101×C151C22semidirect
66. #101×C151C22semidirect
223. C151#3289semidirect
231. #473D151semidirect
269. C2×Q16C2×D151semidirect
281. #108C2×D151semidirect
287. #101C2×D151semidirect
288. #101C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237530282
#237530252
#237530242
#237530212
#237526052
#237524862
#237524782
#237524762
#237523972
#237523932
#237523882
#237523872
#237523332
#237523322
#473×C1512
#3289151