Finite Group Databasebeta

← #34080652

Subgroups — #34080652

Order 19328.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012766C211yesmaximal, characteristic, complemented
2C2×#18012760C211yesmaximal, characteristic, complemented
3#23752884C211yesmaximal, characteristic, complemented
4#23752857C211yesmaximal, characteristic, complemented
5#23752601C211yesmaximal, characteristic, complemented
6#23752459C211yesmaximal, characteristic, complemented
7#23752449C211yesmaximal, characteristic, complemented
8#23752434C211yesmaximal, characteristic, complemented
9#23752407C211yesmaximal, characteristic, complemented
10#23752377C211yesmaximal, characteristic, complemented
11#23752360C211yesmaximal, characteristic, complemented
12#23752358C211yesmaximal, characteristic, complemented
13#23752347C211yesmaximal, characteristic, complemented
14#23752285C211yesmaximal, characteristic, complemented
15#440×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×#14559005C2211yescharacteristic, complemented
18C2×#14559003C2211yescharacteristic
19C2×D4×D151C2211yescharacteristic
20#18012766—24no—
21#18012760—24no—
22C2×#14558994C2211yescharacteristic, complemented
23C2×#14558993C2211yescharacteristic, complemented
24C2×#14558993C2211yescharacteristic, complemented
25C2×#14558991C2211yescharacteristic
26C2×D1208C2211yescharacteristic
27C2×D1208C2211yescharacteristic
28C2×#14558989C2211yescharacteristic
29C2×#14558989C2211yescharacteristic
30C2×#14558987C2211yescharacteristic
31C2×C8×D151C2211yescharacteristic, complemented
32#18012736—21no—
33#18012736C2211yescharacteristic, complemented
34#18012727C2211yescharacteristic
35#18012723—21no—
36#18012719C2211yescharacteristic
37#18012714—21no—
38#18012714—21no—
39#18012714C2211yescharacteristic
40#18012714C2211yescharacteristic
41#18012714C2211yescharacteristic, complemented
42#18012713—21no—
43#18012709—21no—
44C4×D604—21no—
45C4×D604C2211yescharacteristic
46C2×(C2×D151)⋊C4—21no—
47C4⋊(C151⋊C8)C2211yescharacteristic, complemented
48#18012662C2211yescharacteristic, complemented
49#18012659C2211yescharacteristic
50#18012659C2211yescharacteristic, complemented
51#18012659C2211yescharacteristic, complemented
52(C2×D151)⋊C8C2211yescharacteristic
53(C2×D151)⋊C8C2211yescharacteristic, complemented
54C2×SD16×C151C2211yescharacteristic
55C4×Q8×C151C2211yescharacteristic, complemented
56C4×D4×C151C2211yescharacteristic
57#107×C151C2211yescharacteristic, complemented
58#103×C151C2211yescharacteristic, complemented
59#102×C151C2211yescharacteristic
60#97×C151C2211yescharacteristic, complemented
61C23×D151—21no—
62#14559005—22no—
63#14559005—22no—
64#14559005—41no—
65#14559005—41no—
66#14559003—22no—
67#14559003—41no—
68C2×Dic302C2311yescharacteristic
69C2×D604—21no—
70C2×D604—21no—
71C2×D604—21no—
72C2×D604—21no—
73C2×D604—21no—
74C2×D604—21no—
75C2×D604—21no—
76C2×D604D411yescharacteristic
77C2×D604C2311yescharacteristic
78C2×D604C2311yescharacteristic
79C2×D604C2311yescharacteristic
80C2×C22⋊D151—21no—
81C2×C22⋊D151—21no—
82D4×D151—22no—
83D4×D151—41no—
84C22×Dic151—21no—
85C2×C4×D151—21no—
86C2×C4×D151—21no—
87C2×C4×D151C2311yescharacteristic
88C2×C4×D151C2311yescharacteristic
89#14558994—22no—
90#14558993—22no—
91#14558993—41no—
92#14558991—22no—
93D1208—22no—
94D1208—41no—
95#14558989—22no—
96#14558989—22no—
97#14558987—22no—
98C2×C151⋊C8C2311yescharacteristic
99C2×C151⋊C8C2311yescharacteristic
100C8×D151—22no—
101C4⋊Dic151—21no—
102C4⋊Dic151D411yescharacteristic
103(C2×D151)⋊C4—21no—
104(C2×D151)⋊C4—21no—
105(C2×D151)⋊C4—21no—
106(C2×D151)⋊C4—21no—
107(C2×D151)⋊C4—21no—
108(C2×D151)⋊C4—21no—
109(C2×D151)⋊C4D411yescharacteristic
110(C2×D151)⋊C4D411yescharacteristic
111C2×Q8×C151C2311yescharacteristic
112C2×D4×C151C2311yescharacteristic
113C22×C4×C151—21no—
114SD16×C151D414yescomplemented
115C2×C8×C151C2311yescharacteristic
116C2×C8×C151C2311yescharacteristic
117C4⋊C4×C151—21no—
118C4⋊C4×C151C2311yescharacteristic
119C4⋊C4×C151C2311yescharacteristic
120C22⋊C4×C151—21no—
121C42×C151—21no—
122C42×C151C2311yescharacteristic
123C22×D151—21no—
124C22×D151—21no—
125C22×D151—21no—
126C22×D151—42no—
127C22×D151—42no—
128C22×D151—81no—
129C22×D151C2×D411yescharacteristic
130C22×D151C2×D411yescharacteristic
131Dic302—21no—
132Dic302—21no—
133D604—21no—
134D604—21no—
135D604—21no—
136D604—21no—
137D604—21no—
138D604—21no—
139D604—41no—
140D604—42no—
141D604—42no—
142D604—42no—
143D604—81no—
144D604—81no—
145D604—81no—
146D604—81no—
147C22⋊D151—42no—
148C22⋊D151—42no—
149C2×Dic151—21no—
150C2×Dic151—42no—
151C2×Dic151C2×D411yescharacteristic
152C2×Dic151C2×D411yescharacteristic
153C4×D151—21no—
154C4×D151—21no—
155C4×D151—21no—
156C4×D151—21no—
157C4×D151—42no—
158C4×D151—42no—
159C151⋊C8—21no—
160C151⋊C8—21no—
161C23×C151—21no—
162Q8×C151—21no—
163Q8×C151C2×D412yes—
164D4×C151—21no—
165D4×C151C2×D412yes—
166C2×C4×C151—21no—
167C2×C4×C151—21no—
168C2×C4×C151—21no—
169C2×C4×C151—81no—
170C2×C4×C151C2×D411yescharacteristic
171C2×C4×C151C2×D411yescharacteristic
172C2×C4×C151C2411yescharacteristic
173C8×C151—21no—
174C8×C151C2×D412yes—
175C22×C151—22no—
176C22×C151—41no—
177C22×C151—41no—
178C22×C151C22×D411yescharacteristic
179C2×D151—21no—
180C2×D151—21no—
181C2×D151—21no—
182C2×D151—21no—
183C2×D151—21no—
184C2×D151—21no—
185C2×D151—41no—
186C2×D151—41no—
187C2×D151—41no—
188C2×D151—41no—
189C2×D151—41no—
190C2×D151—41no—
191C2×D151—41no—
192C2×D151—41no—
193C2×D151—41no—
194C2×D151—84no—
195C4×C151—22no—
196C4×C151—21no—
197C4×C151—21no—
198C4×C151—41no—
199C4×C151—41no—
200C4×C151C22×D411yescharacteristic
201C4×C151H(5,𝔽2)11yescharacteristic
202Dic151—21no—
203Dic151—21no—
204Dic151—41no—
205C2×C151—42no—
206C2×C151D4211yescharacteristic
207C2×C151#57511yescharacteristic
208C2×C151#57611yescharacteristic
209D151—41no—
210D151—41no—
211D151—81no—
212D151—81no—
213D151—81no—
214C151#326811yescharacteristic, complemented, Sylow
215#3268—1511nomaximal, Sylow
216C2×AGL(1,ℤ/8)—1511no—
217C2×#135—1511no—
218#550—1511no—
219#546—1511no—
220#496—1511no—
221#468—1511no—
222#466—1511no—
223#464—1511no—
224#459—1511no—
225#452—1511no—
226#449—1511no—
227#449—1511no—
228#447—1511no—
229#440D15111yescharacteristic, complemented
230#435—1511no—
231C2×#41—1511no—
232C2×#41—1511no—
233C2×#41—1511no—
234C22×D4—1511no—
235AGL(1,ℤ/8)—3024no—
236#135—3024no—
237C2×Q16—1511no—
238C2×SD16—1511no—
239C2×SD16—1511no—
240C2×SD16—1511no—
241C2×SD16C2×D15111yescharacteristic
242C2×D8—1511no—
243C2×D8—1511no—
244C2×D8—1511no—
245C2×D8—1511no—
246C2×M16—1511no—
247C22×C8—1511no—
248#127—3021no—
249#127—1511no—
250#124—1511no—
251#123—3021no—
252C22⋊Q8—1511no—
253#121—3021no—
254#121—3021no—
255#121—3021no—
256#121—1511no—
257#121—1511no—
258#121—1511no—
259#120—3021no—
260C4×Q8C2×D15111yescharacteristic, complemented
261C4×D4—3021no—
262C4×D4—1511no—
263C4×D4C2×D15111yescharacteristic
264C2×C22⋊C4—3021no—
265#107C2×D15111yescharacteristic, complemented
266C4⋊C8—1511no—
267#103—1511no—
268#103C2×D15111yescharacteristic, complemented
269#102—1511no—
270#102—1511no—
271#102—1511no—
272#102C2×D15111yescharacteristic
273C22⋊C8—1511no—
274C22⋊C8—1511no—
275#97C2×D15111yescharacteristic, complemented
276C24—3021no—
277#41—3022no—
278#41—3022no—
279#41—3022no—
280#41—6041no—
281#41—6041no—
282#41—6041no—
283C2×Q8—1511no—
284C2×Q8C22×D15111yescharacteristic
285C2×D4—3021no—
286C2×D4—3021no—
287C2×D4—3021no—
288C2×D4—3021no—
289C2×D4—3021no—
290C2×D4—3022no—
291C2×D4—3021no—
292C2×D4—3021no—
293C2×D4—3021no—
294C2×D4—3021no—
295C2×D4—6041no—
296C2×D4—1511no—
297C2×D4—1511no—
298C2×D4—1511no—
299C2×D4—1511no—
300C2×D4C22×D15111yescharacteristic
301C22×C4—21no—
302C22×C4—3021no—
303C22×C4—3021no—
304C22×C4—3021no—
305C22×C4—1511no—
306C22×C4—1511no—
307Q16—3022no—
308SD16—3022no—
309SD16—3022no—
310SD16—6041no—
311SD16D60414yescomplemented
312D8—3022no—
313D8—3022no—
314D8—3022no—
315D8—6041no—
316M16—3022no—
317C2×C8—3022no—
318C2×C8—1511no—
319C2×C8—1511no—
320C2×C8C22×D15111yescharacteristic
321C2×C8C22×D15111yescharacteristic
322C4⋊C4—21no—
323C4⋊C4—3021no—
324C4⋊C4—1511no—
325C4⋊C4C22×D15111yescharacteristic
326C4⋊C4C22×D15111yescharacteristic
327C22⋊C4—21no—
328C22⋊C4—3021no—
329C22⋊C4—3021no—
330C22⋊C4—3021no—
331C22⋊C4—3021no—
332C22⋊C4—3021no—
333C22⋊C4—3021no—
334C22⋊C4—1511no—
335C22⋊C4—1511no—
336C42—21no—
337C42C22×D15111yescharacteristic
338C23—21no—
339C23—3021no—
340C23—3021no—
341C23—3021no—
342C23—6042no—
343C23—6042no—
344C23—1511no—
345C23—1511no—
346C23—12081no—
347Q8—21no—
348Q8—3021no—
349Q8—3021no—
350Q8C2×D60412yes—
351D4—21no—
352D4—3021no—
353D4—3021no—
354D4—3021no—
355D4—3021no—
356D4—3021no—
357D4—3021no—
358D4—6041no—
359D4—6042no—
360D4—6042no—
361D4—6042no—
362D4—6042no—
363D4—6042no—
364D4—12081no—
365D4—12081no—
366D4—12081no—
367D4—12081no—
368D4C2×D60412yes—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—81no—
373C2×C4—3021no—
374C2×C4—3021no—
375C2×C4—3021no—
376C2×C4—3021no—
377C2×C4—3021no—
378C2×C4—6042no—
379C2×C4—6042no—
380C2×C4—6042no—
381C2×C4—1511no—
382C2×C4—1511no—
383C2×C4D4×D15111yescharacteristic
384C2×C4D4×D15111yescharacteristic
385C2×C4C23×D15111yescharacteristic
386C8—21no—
387C8—3021no—
388C8—3021no—
389C8C2×D60412yes—
390C22—22no—
391C22—41no—
392C22—41no—
393C22—3021no—
394C22—3021no—
395C22—3021no—
396C22—3021no—
397C22—3021no—
398C22—3021no—
399C22—6041no—
400C22—6041no—
401C22—6041no—
402C22—6041no—
403C22—6041no—
404C22—6041no—
405C22—6041no—
406C22—6041no—
407C22—6041no—
408C22—12084no—
409C22C2×D4×D15111yescharacteristic
410C4—21no—
411C4—21no—
412C4—22no—
413C4—41no—
414C4—41no—
415C4—3021no—
416C4—3021no—
417C4—6041no—
418C4C22×D60411yescharacteristic
419C4#1801278511yescharacteristic
420C2—42no—
421C2—6041no—
422C2—6041no—
423C2—12081no—
424C2—12081no—
425C2—12081no—
426C2D4×D60411yescharacteristic
427C2#2375301111yescharacteristic
428C2#2375301611yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#440×C151C2
socleC22×C151C22×D4
hypercenter#440D151
hypocenterC151#3268
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. C2×#18012766C2semidirect
2. C2×#18012760C2semidirect
3. #23752884C2semidirect
4. #23752857C2semidirect
5. #23752601C2semidirect
6. #23752459C2semidirect
7. #23752449C2semidirect
8. #23752434C2semidirect
9. #23752407C2semidirect
10. #23752377C2semidirect
11. #23752360C2semidirect
12. #23752358C2semidirect
13. #23752347C2semidirect
14. #23752285C2semidirect
15. #440×C151C2semidirect
17. C2×#14559005C22semidirect
22. C2×#14558994C22semidirect
23. C2×#14558993C22semidirect
24. C2×#14558993C22semidirect
31. C2×C8×D151C22semidirect
33. #18012736C22semidirect
41. #18012714C22semidirect
47. C4⋊(C151⋊C8)C22semidirect
48. #18012662C22semidirect
50. #18012659C22semidirect
51. #18012659C22semidirect
53. (C2×D151)⋊C8C22semidirect
55. C4×Q8×C151C22semidirect
57. #107×C151C22semidirect
58. #103×C151C22semidirect
60. #97×C151C22semidirect
114. SD16×C151D4semidirect
214. C151#3268semidirect
229. #440D151semidirect
260. C4×Q8C2×D151semidirect
265. #107C2×D151semidirect
268. #103C2×D151semidirect
275. #97C2×D151semidirect
311. SD16D604semidirect

Maximal subgroups

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

subgroupindex
C2×#180127662
C2×#180127602
#237528842
#237528572
#237526012
#237524592
#237524492
#237524342
#237524072
#237523772
#237523602
#237523582
#237523472
#237522852
#440×C1512
#3268151