Finite Group Databasebeta

← #34080880

Subgroups — #34080880

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#23753027C211yesmaximal, characteristic, complemented
3#23753021C211yesmaximal, characteristic, complemented
4#23753020C211yesmaximal, characteristic, complemented
5#23752604C211yesmaximal, characteristic, complemented
6#23752486C211yesmaximal, characteristic, complemented
7#23752485C211yesmaximal, characteristic, complemented
8#23752478C211yesmaximal, characteristic, complemented
9#23752477C211yesmaximal, characteristic, complemented
10#23752394C211yesmaximal, characteristic, complemented
11#23752391C211yesmaximal, characteristic, complemented
12#23752386C211yesmaximal, characteristic, complemented
13#23752331C211yesmaximal, characteristic, complemented
14#23752331C211yesmaximal, characteristic, complemented
15#456×C151C211yesmaximal, characteristic, complemented
16#18012787C2211yescharacteristic
17#18012786C2211yescharacteristic, complemented
18#18012785C2211yescharacteristic
19#18012772C2211yescharacteristic
20#18012771—21no—
21#18012771—21no—
22#18012770—21no—
23#18012770—21no—
24#18012770C2211yescharacteristic
25#18012770C2211yescharacteristic, complemented
26#18012769—21no—
27#18012769C2211yescharacteristic
28#18012768—21no—
29#18012767C2211yescharacteristic
30#18012766—21no—
31#18012764—21no—
32#18012764C2211yescharacteristic
33#18012762—21no—
34#18012760—21no—
35#18012759—21no—
36#18012759—21no—
37#18012759C2211yescharacteristic
38#18012759C2211yescharacteristic
39C2×#14558994—21no—
40C2×#14558994C2211yescharacteristic, complemented
41C2×#14558994C2211yescharacteristic, complemented
42Q16×D151—21no—
43C2×#14558991—21no—
44C2×#14558991C2211yescharacteristic
45C2×#14558991C2211yescharacteristic
46SD16×D151—21no—
47#18012747C2211yescharacteristic
48#18012747C2211yescharacteristic, complemented
49#18012746C2211yescharacteristic
50#18012746C2211yescharacteristic, complemented
51#18012727C2211yescharacteristic
52#18012674C2211yescharacteristic, complemented
53#18012674C2211yescharacteristic, complemented
54#18012667C2211yescharacteristic
55#18012667C2211yescharacteristic, complemented
56#18012658C2211yescharacteristic, complemented
57#18012657C2211yescharacteristic, complemented
58#18012655C2211yescharacteristic
59#18012650C2211yescharacteristic, complemented
602−1+4×C151C2211yescharacteristic
61#137×C151C2211yescharacteristic
62#137×C151C2211yescharacteristic, complemented
63C4⋊Q8×C151C2211yescharacteristic, complemented
64#104×C151C2211yescharacteristic
65#104×C151C2211yescharacteristic, complemented
66#101×C151C2211yescharacteristic, complemented
67#14559005—21no—
68#14559005—21no—
69#14559005—21no—
70#14559004—21no—
71#14559004—21no—
72#14559004—41no—
73#14559004C2311yescharacteristic
74#14559004C2311yescharacteristic
75#14559003—21no—
76#14559003—41no—
77C2×Dic302—21no—
78C2×Dic302C2311yescharacteristic
79Q8×D151—21no—
80Q8×D151—21no—
81Q8×D151—21no—
82C2×D604—21no—
83C2×D604C2311yescharacteristic
84D4×D151—21no—
85D4×D151—41no—
86Dic604—21no—
87#14558994—21no—
88#14558994—21no—
89#14558994—21no—
90#14558994—21no—
91#14558994—21no—
92#14558994—21no—
93#14558994—21no—
94#14558994D411yescharacteristic
95#14558994D411yescharacteristic
96#14558993—21no—
97#14558993—21no—
98#14558992—21no—
99#14558992D411yescharacteristic
100#14558992D411yescharacteristic
101#14558991—21no—
102#14558991—21no—
103#14558991—21no—
104#14558991—21no—
105#14558991—21no—
106#14558991—21no—
107#14558991—21no—
108#14558991D411yescharacteristic
109#14558991D411yescharacteristic
110D1208—21no—
111#14558989—21no—
112#14558989D411yescharacteristic
113#14558989D411yescharacteristic
114#14558988—21no—
115#14558988—21no—
116#14558988C2311yescharacteristic
117#14558988C2311yescharacteristic
118#14558987—21no—
119#14558987—21no—
120C2×C151⋊C8—21no—
121C2×C151⋊C8—21no—
122C2×C151⋊C8C2311yescharacteristic
123C2×C151⋊C8C2311yescharacteristic
124C8×D151—21no—
125C8×D151—21no—
126(C2×D151)⋊C4—41no—
127#41×C151—21no—
128#41×C151—21no—
129#41×C151—41no—
130#41×C151C2311yescharacteristic
131#41×C151C2311yescharacteristic
132C2×Q8×C151—21no—
133C2×Q8×C151—21no—
134C2×Q8×C151C2311yescharacteristic
135C2×Q8×C151C2311yescharacteristic
136Q16×C151—21no—
137Q16×C151—21no—
138SD16×C151—21no—
139SD16×C151—21no—
140M16×C151C2311yescharacteristic
141M16×C151C2311yescharacteristic
142C4⋊C4×C151—41no—
143C42×C151C2311yescharacteristic
144C22×D151—21no—
145C22×D151—41no—
146Dic302—21no—
147Dic302—21no—
148Dic302—41no—
149Dic302—41no—
150Dic302C2×D411yescharacteristic
151Dic302C2×D411yescharacteristic
152D604—21no—
153D604—21no—
154D604—41no—
155D604—41no—
156D604C2×D411yescharacteristic
157D604C2×D411yescharacteristic
158C22⋊D151—21no—
159C22⋊D151—21no—
160C22⋊D151—41no—
161C22⋊D151—41no—
162C2×Dic151—21no—
163C2×Dic151—41no—
164C4×D151—21no—
165C4×D151—21no—
166C4×D151—41no—
167C4×D151—41no—
168C4×D151—41no—
169C4×D151—41no—
170C151⋊C8—21no—
171C151⋊C8—21no—
172C151⋊C8C2×D411yescharacteristic
173C151⋊C8C2×D411yescharacteristic
174C151⋊C8C2×D411yescharacteristic
175C151⋊C8C2×D411yescharacteristic
176Q8×C151—21no—
177Q8×C151—21no—
178Q8×C151—21no—
179Q8×C151—21no—
180Q8×C151—41no—
181Q8×C151C2×D411yescharacteristic
182Q8×C151C2×D411yescharacteristic
183D4×C151—21no—
184D4×C151—21no—
185D4×C151—41no—
186D4×C151C2×D411yescharacteristic
187D4×C151C2×D411yescharacteristic
188C2×C4×C151—21no—
189C2×C4×C151—21no—
190C2×C4×C151—21no—
191C2×C4×C151—21no—
192C2×C4×C151—21no—
193C2×C4×C151—41no—
194C2×C4×C151—41no—
195C2×C4×C151C2411yescharacteristic
196C8×C151—21no—
197C8×C151—21no—
198C22×C151—21no—
199C22×C151—21no—
200C22×C151H(5,𝔽2)11yescharacteristic
201C2×D151—21no—
202C2×D151—21no—
203C2×D151—41no—
204C2×D151—81no—
205C2×D151—161no—
206C4×C151—21no—
207C4×C151—21no—
208C4×C151—41no—
209C4×C151—41no—
210C4×C151—41no—
211C4×C151C22×D411yescharacteristic
212C4×C151C22×D411yescharacteristic
213Dic151—21no—
214Dic151—21no—
215Dic151—41no—
216C2×C151—21no—
217C2×C151—41no—
218C2×C151—41no—
219C2×C151D4211yescharacteristic
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#473—1511no—
232#471—1511no—
233#471—1511no—
234#456—1511no—
235#456D15111yescharacteristic, complemented
236#455—1511no—
237#454—1511no—
238#444—1511no—
239#444—1511no—
2402−1+4—1511no—
2412−1+4—1511no—
2422−1+4C2×D15111yescharacteristic
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, complemented
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×Q16—1511no—
270C2×SD16—3021no—
271C2×SD16—3021no—
272C2×SD16—1511no—
273C2×SD16—1511no—
274#131—1511no—
275#131—1511no—
276#131—1511no—
277#131—1511no—
278C4⋊Q8C2×D15111yescharacteristic, complemented
279#124—1511no—
280#108—1511no—
281#108—1511no—
282#104—1511no—
283#104—1511no—
284#104C2×D15111yescharacteristic
285#104C2×D15111yescharacteristic, complemented
286#101—1511no—
287#101—1511no—
288#101C2×D15111yescharacteristic, complemented
289#100—1511no—
290#97—1511no—
291#41—21no—
292#41—21no—
293#41—41no—
294#41—3021no—
295#41—3021no—
296#41—3021no—
297#41—3021no—
298#41—3021no—
299#41—3021no—
300#41—6041no—
301#41—6041no—
302#41—1511no—
303#41—1511no—
304#41C22×D15111yescharacteristic
305#41C22×D15111yescharacteristic
306C2×Q8—21no—
307C2×Q8—21no—
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—3021no—
322Q16—3021no—
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—3021no—
352M16—3021no—
353M16—3021no—
354M16—3021no—
355M16—1511no—
356M16—1511no—
357M16C22×D15111yescharacteristic
358M16C22×D15111yescharacteristic
359C2×C8—3021no—
360C2×C8—3021no—
361C2×C8—3021no—
362C2×C8—3021no—
363C2×C8—1511no—
364C2×C8—1511no—
365C4⋊C4—41no—
366C22⋊C4—6041no—
367C42C22×D15111yescharacteristic
368C23—3021no—
369C23—6041no—
370Q8—21no—
371Q8—21no—
372Q8—21no—
373Q8—21no—
374Q8—41no—
375Q8—3021no—
376Q8—3021no—
377Q8—6041no—
378Q8—6041no—
379Q8—1511no—
380Q8—1511no—
381Q8D4×D15111yescharacteristic
382Q8D4×D15111yescharacteristic
383D4—21no—
384D4—21no—
385D4—41no—
386D4—3021no—
387D4—3021no—
388D4—3021no—
389D4—3021no—
390D4—6041no—
391D4—6041no—
392D4—6041no—
393D4—6041no—
394D4—1511no—
395D4—1511no—
396D4D4×D15111yescharacteristic
397D4D4×D15111yescharacteristic
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—3021no—
406C2×C4—3021no—
407C2×C4—3021no—
408C2×C4—6041no—
409C2×C4—6041no—
410C2×C4—6041no—
411C2×C4—6041no—
412C2×C4—6041no—
413C2×C4C23×D15111yescharacteristic
414C8—21no—
415C8—21no—
416C8—3021no—
417C8—3021no—
418C8—1511no—
419C8—1511no—
420C8—1511no—
421C8—1511no—
422C22—21no—
423C22—21no—
424C22—3021no—
425C22—3021no—
426C22—6041no—
427C22—24161no—
428C22—12081no—
429C22#1801278411yescharacteristic
430C4—21no—
431C4—21no—
432C4—41no—
433C4—41no—
434C4—41no—
435C4—3021no—
436C4—3021no—
437C4—6041no—
438C4C2×D4×D15111yescharacteristic
439C4C2×D4×D15111yescharacteristic
440C2—21no—
441C2—41no—
442C2—41no—
443C2—6041no—
444C2—6041no—
445C2—12081no—
446C2#2375284411yescharacteristic
subgroupG/H
centerC2#23752844
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#456×C151C2
socleC2×C151D42
hypercenter#456D151
hypocenterC151#3289
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C2×C4 ◁ #456

Complements

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

NH ≅ G/Ntype
1. #23753028C2semidirect
2. #23753027C2semidirect
3. #23753021C2semidirect
4. #23753020C2semidirect
5. #23752604C2semidirect
6. #23752486C2semidirect
7. #23752485C2semidirect
8. #23752478C2semidirect
9. #23752477C2semidirect
10. #23752394C2semidirect
11. #23752391C2semidirect
12. #23752386C2semidirect
13. #23752331C2semidirect
14. #23752331C2semidirect
15. #456×C151C2semidirect
17. #18012786C22semidirect
25. #18012770C22semidirect
40. C2×#14558994C22semidirect
41. C2×#14558994C22semidirect
48. #18012747C22semidirect
50. #18012746C22semidirect
52. #18012674C22semidirect
53. #18012674C22semidirect
55. #18012667C22semidirect
56. #18012658C22semidirect
57. #18012657C22semidirect
59. #18012650C22semidirect
62. #137×C151C22semidirect
63. C4⋊Q8×C151C22semidirect
65. #104×C151C22semidirect
66. #101×C151C22semidirect
223. C151#3289semidirect
235. #456D151semidirect
255. #137C2×D151semidirect
278. C4⋊Q8C2×D151semidirect
285. #104C2×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
#237530272
#237530212
#237530202
#237526042
#237524862
#237524852
#237524782
#237524772
#237523942
#237523912
#237523862
#237523312
#456×C1512
#3289151