Finite Group Databasebeta

← #16857257

Subgroups — #16857257

Order 3968.

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×#11758488C211yesmaximal, characteristic, complemented
2C2×#11758489C211yesmaximal, characteristic, complemented
3#14521719C211yesmaximal, characteristic, complemented
4#14521694C211yesmaximal, characteristic, complemented
5#14521436C211yesmaximal, characteristic, complemented
6#14521294C211yesmaximal, characteristic, complemented
7#14521284C211yesmaximal, characteristic, complemented
8#14521272C211yesmaximal, characteristic, complemented
9#14521212C211yesmaximal, characteristic, complemented
10#14521195C211yesmaximal, characteristic, complemented
11#14521191C211yesmaximal, characteristic, complemented
12#14521181C211yesmaximal, characteristic, complemented
13#14521149C211yesmaximal, characteristic, complemented
14#14521119C211yesmaximal, characteristic, complemented
15C31×#459C211yesmaximal, characteristic, complemented
16C2×#92497C2211yescharacteristic
17C2×#92497C2211yescharacteristic
18C2×#92497C2211yescharacteristic, complemented
19C2×D4×D31C2211yescharacteristic
20C2×D8×C31C2211yescharacteristic
21C2×D8×C31C2211yescharacteristic
22C31×#127C2211yescharacteristic, complemented
23C4×D4×C31C2211yescharacteristic
24#11758517—21no—
25#11758516—21no—
26#11758516—21no—
27#11758515C2211yescharacteristic
28#11758515C2211yescharacteristic, complemented
29D4×Dic31—21no—
30C2×#92480C2211yescharacteristic
31C2×#92480C2211yescharacteristic, complemented
32C2×#92480C2211yescharacteristic, complemented
33C2×#92479C2211yescharacteristic
34C2×#92479C2211yescharacteristic
35#11758507—21no—
36C2×(C2×D31)⋊C4—21no—
37#11758489—24no—
38#11758488—24no—
39C2×Dic124C2211yescharacteristic, complemented
40C2×#92470C2211yescharacteristic
41C2×#92469C2211yescharacteristic
42C2×C8×D31C2211yescharacteristic, complemented
43#11758474C2211yescharacteristic
44#11758472C2211yescharacteristic
45#11758463—21no—
46#11758459—21no—
47#11758452C2211yescharacteristic
48C4×D124C2211yescharacteristic
49C4×Dic62C2211yescharacteristic, complemented
50C31×C4⋊C8C2211yescharacteristic, complemented
51C31×#102C2211yescharacteristic, complemented
52C31×#102C2211yescharacteristic, complemented
53#11758420C2211yescharacteristic
54#11758409C2211yescharacteristic
55(C2×D31)⋊C8C2211yescharacteristic
56(C2×D31)⋊C8C2211yescharacteristic, complemented
57#11758404C2211yescharacteristic, complemented
58#11758398C2211yescharacteristic, complemented
59#11758395C2211yescharacteristic, complemented
60#11758391C2211yescharacteristic, complemented
61C23×D31—21no—
62C2×D4×C31—21no—
63C2×D4×C31—21no—
64C2×D4×C31C2311yescharacteristic
65C2×D4×C31C2311yescharacteristic
66C2×D4×C31C2311yescharacteristic
67C22×C4×C31—21no—
68C2×C22⋊D31—21no—
69C2×C22⋊D31—21no—
70C2×C22⋊D31—21no—
71C2×C22⋊D31—21no—
72C2×C22⋊D31—21no—
73C2×C22⋊D31—21no—
74C22×Dic31—21no—
75C22×Dic31—21no—
76C22×Dic31—21no—
77#92497—22no—
78#92497—22no—
79#92497—22no—
80#92497—41no—
81#92497—41no—
82#92497—41no—
83D4×D31—22no—
84D4×D31—41no—
85C2×D124—21no—
86C2×D124D411yescharacteristic
87C2×D124C2311yescharacteristic
88C2×C4×D31C2311yescharacteristic
89C2×C4×D31C2311yescharacteristic
90C2×Dic62C2311yescharacteristic
91C2×Dic62C2311yescharacteristic
92D8×C31—22no—
93D8×C31—22no—
94C2×C8×C31C2311yescharacteristic
95C2×C8×C31C2311yescharacteristic
96C4⋊C4×C31C2311yescharacteristic
97C22⋊C4×C31—21no—
98C42×C31C2311yescharacteristic
99C22⋊Dic31—21no—
100C22⋊Dic31—21no—
101#92480—22no—
102#92480—41no—
103#92480D414yescomplemented
104#92479—22no—
105#92479—41no—
106(C2×D31)⋊C4—21no—
107(C2×D31)⋊C4—21no—
108(C2×D31)⋊C4—21no—
109(C2×D31)⋊C4—21no—
110(C2×D31)⋊C4D411yescharacteristic
111(C2×D31)⋊C4D411yescharacteristic
112C4⋊Dic31—21no—
113C4⋊Dic31D411yescharacteristic
114C4⋊Dic31C2311yescharacteristic
115Dic31⋊C4—21no—
116C4×Dic31—21no—
117C2×C31⋊C8C2311yescharacteristic
118C2×C31⋊C8C2311yescharacteristic
119Dic124—22no—
120#92470—22no—
121#92469—22no—
122C8×D31—22no—
123C23×C31—21no—
124C23×C31—21no—
125C23×C31—21no—
126C22×D31—21no—
127C22×D31—42no—
128C22×D31—42no—
129C22×D31—81no—
130C22×D31C2×D411yescharacteristic
131C22×D31C2×D411yescharacteristic
132D4×C31—21no—
133D4×C31—21no—
134D4×C31—21no—
135D4×C31—21no—
136D4×C31—21no—
137D4×C31—42no—
138D4×C31—81no—
139D4×C31C2×D412yes—
140C2×C4×C31—21no—
141C2×C4×C31—81no—
142C2×C4×C31C2×D411yescharacteristic
143C2×C4×C31C2×D411yescharacteristic
144C2×C4×C31C2411yescharacteristic
145C22⋊D31—42no—
146C22⋊D31—42no—
147C22⋊D31—42no—
148C22⋊D31—42no—
149C22⋊D31—81no—
150C22⋊D31—81no—
151C2×Dic31—21no—
152C2×Dic31—21no—
153C2×Dic31—21no—
154C2×Dic31—42no—
155C2×Dic31—42no—
156C2×Dic31—42no—
157C2×Dic31C2×D411yescharacteristic
158C2×Dic31C2×D411yescharacteristic
159D124—21no—
160D124—21no—
161D124—41no—
162D124—81no—
163C4×D31—21no—
164C4×D31—21no—
165C4×D31—21no—
166C4×D31—21no—
167Dic62—21no—
168Dic62—21no—
169Dic62—21no—
170Dic62C2×D412yes—
171C8×C31—21no—
172C8×C31—21no—
173C31⋊C8—21no—
174C31⋊C8C2×D412yes—
175#3268—311nomaximal, Sylow
176C22×C31—22no—
177C22×C31—41no—
178C22×C31—41no—
179C22×C31—41no—
180C22×C31—41no—
181C22×C31—41no—
182C22×C31—41no—
183C22×C31—41no—
184C22×C31—41no—
185C22×C31C22×D411yescharacteristic
186C2×D31—21no—
187C2×D31—21no—
188C2×D31—21no—
189C2×D31—21no—
190C2×D31—21no—
191C2×D31—21no—
192C2×D31—41no—
193C2×D31—41no—
194C2×D31—41no—
195C2×D31—84no—
196C4×C31—21no—
197C4×C31—21no—
198C4×C31—41no—
199C4×C31C22×D411yescharacteristic
200C4×C31H(5,𝔽2)11yescharacteristic
201Dic31—22no—
202Dic31—21no—
203Dic31—21no—
204Dic31—41no—
205Dic31—41no—
206C2×AGL(1,ℤ/8)—311no—
207C2×#135—311no—
208#550—311no—
209#546—311no—
210#496—311no—
211#468—311no—
212#466—311no—
213#464—311no—
214#459D3111yescharacteristic, complemented
215#452—311no—
216#449—311no—
217#449—311no—
218#447—311no—
219#440—311no—
220#435—311no—
221C2×C31—42no—
222C2×C31—81no—
223C2×C31—81no—
224C2×C31D4211yescharacteristic
225C2×C31#57511yescharacteristic
226C2×C31#57611yescharacteristic
227D31—41no—
228D31—41no—
229D31—81no—
230C2×#41—311no—
231C2×#41—311no—
232C2×#41—311no—
233C22×D4—311no—
234AGL(1,ℤ/8)—624no—
235#135—624no—
236C2×Q16—311no—
237C2×SD16—311no—
238C2×SD16—311no—
239C2×SD16—311no—
240C2×SD16—311no—
241C2×D8—311no—
242C2×D8—311no—
243C2×D8C2×D3111yescharacteristic
244C2×D8C2×D3111yescharacteristic
245C2×M16—311no—
246C22×C8—311no—
247#127—621no—
248#127C2×D3111yescharacteristic, complemented
249#124—311no—
250#123—621no—
251C22⋊Q8—311no—
252#121—311no—
253#121—311no—
254#121—311no—
255#121—621no—
256#121—621no—
257#121—621no—
258#120—621no—
259C4×Q8—311no—
260C4×D4—311no—
261C4×D4—621no—
262C4×D4C2×D3111yescharacteristic
263C2×C22⋊C4—621no—
264#107—311no—
265C4⋊C8C2×D3111yescharacteristic, complemented
266#103—311no—
267#103—311no—
268#102—311no—
269#102—311no—
270#102C2×D3111yescharacteristic, complemented
271#102C2×D3111yescharacteristic, complemented
272C22⋊C8—311no—
273C22⋊C8—311no—
274#97—311no—
275C31#326811yescharacteristic, complemented, Sylow
276C24—621no—
277#41—622no—
278#41—622no—
279#41—622no—
280#41—1241no—
281#41—1241no—
282#41—1241no—
283C2×Q8—311no—
284C2×Q8—311no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—311no—
288C2×D4—311no—
289C2×D4—621no—
290C2×D4—621no—
291C2×D4—622no—
292C2×D4—621no—
293C2×D4—621no—
294C2×D4—621no—
295C2×D4—621no—
296C2×D4—621no—
297C2×D4—1241no—
298C2×D4C22×D3111yescharacteristic
299C2×D4C22×D3111yescharacteristic
300C2×D4C22×D3111yescharacteristic
301C22×C4—21no—
302C22×C4—311no—
303C22×C4—311no—
304C22×C4—621no—
305C22×C4—621no—
306C22×C4—621no—
307Q16—622no—
308SD16—314no—
309SD16—622no—
310SD16—622no—
311SD16—1241no—
312D8—22no—
313D8—22no—
314D8—622no—
315D8—1241no—
316M16—622no—
317C2×C8—311no—
318C2×C8—311no—
319C2×C8—622no—
320C2×C8C22×D3111yescharacteristic
321C2×C8C22×D3111yescharacteristic
322C4⋊C4—311no—
323C4⋊C4—311no—
324C4⋊C4—621no—
325C4⋊C4—621no—
326C4⋊C4C22×D3111yescharacteristic
327C22⋊C4—21no—
328C22⋊C4—311no—
329C22⋊C4—311no—
330C22⋊C4—621no—
331C22⋊C4—621no—
332C22⋊C4—621no—
333C22⋊C4—621no—
334C22⋊C4—621no—
335C22⋊C4—621no—
336C42—621no—
337C42C22×D3111yescharacteristic
338C23—21no—
339C23—21no—
340C23—21no—
341C23—311no—
342C23—311no—
343C23—621no—
344C23—1242no—
345C23—1242no—
346C23—2481no—
347Q8—312no—
348Q8—621no—
349Q8—621no—
350Q8—621no—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—21no—
355D4—21no—
356D4—42no—
357D4—81no—
358D4—621no—
359D4—621no—
360D4—1241no—
361D4—1242no—
362D4—1242no—
363D4—1242no—
364D4—1242no—
365D4—2481no—
366D4—2481no—
367D4—2481no—
368D4D4×D3112yes—
369C2×C4—21no—
370C2×C4—81no—
371C2×C4—311no—
372C2×C4—311no—
373C2×C4—621no—
374C2×C4—621no—
375C2×C4—621no—
376C2×C4—621no—
377C2×C4—621no—
378C2×C4—621no—
379C2×C4—621no—
380C2×C4—1242no—
381C2×C4—1242no—
382C2×C4—1242no—
383C2×C4D4×D3111yescharacteristic
384C2×C4D4×D3111yescharacteristic
385C2×C4C23×D3111yescharacteristic
386C8—21no—
387C8—21no—
388C8—312no—
389C8—621no—
390C22—22no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—621no—
400C22—621no—
401C22—621no—
402C22—621no—
403C22—621no—
404C22—621no—
405C22—1241no—
406C22—1241no—
407C22—1241no—
408C22—2484no—
409C22C2×D4×D3111yescharacteristic
410C4—21no—
411C4—21no—
412C4—41no—
413C4—621no—
414C4—621no—
415C4—622no—
416C4—1241no—
417C4—1241no—
418C4C2×D4×D3111yescharacteristic
419C4#1175856611yescharacteristic
420C2—42no—
421C2—81no—
422C2—81no—
423C2—1241no—
424C2—1241no—
425C2—2481no—
426C2#1452168311yescharacteristic
427C2#1452184511yescharacteristic
428C2#1452185011yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#459C2
socleC22×C31C22×D4
hypercenter#459D31
hypocenterC31#3268
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×#11758488C2semidirect
2. C2×#11758489C2semidirect
3. #14521719C2semidirect
4. #14521694C2semidirect
5. #14521436C2semidirect
6. #14521294C2semidirect
7. #14521284C2semidirect
8. #14521272C2semidirect
9. #14521212C2semidirect
10. #14521195C2semidirect
11. #14521191C2semidirect
12. #14521181C2semidirect
13. #14521149C2semidirect
14. #14521119C2semidirect
15. C31×#459C2semidirect
18. C2×#92497C22semidirect
22. C31×#127C22semidirect
28. #11758515C22semidirect
31. C2×#92480C22semidirect
32. C2×#92480C22semidirect
39. C2×Dic124C22semidirect
42. C2×C8×D31C22semidirect
49. C4×Dic62C22semidirect
50. C31×C4⋊C8C22semidirect
51. C31×#102C22semidirect
52. C31×#102C22semidirect
56. (C2×D31)⋊C8C22semidirect
57. #11758404C22semidirect
58. #11758398C22semidirect
59. #11758395C22semidirect
60. #11758391C22semidirect
103. #92480D4semidirect
214. #459D31semidirect
248. #127C2×D31semidirect
265. C4⋊C8C2×D31semidirect
270. #102C2×D31semidirect
271. #102C2×D31semidirect
275. C31#3268semidirect

Maximal subgroups

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

subgroupindex
C2×#117584882
C2×#117584892
#145217192
#145216942
#145214362
#145212942
#145212842
#145212722
#145212122
#145211952
#145211912
#145211812
#145211492
#145211192
C31×#4592
#326831