Finite Group Databasebeta

← #16857256

Subgroups — #16857256

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×#11758485C211yesmaximal, characteristic, complemented
2C2×#11758481C211yesmaximal, characteristic, complemented
3#14521720C211yesmaximal, characteristic, complemented
4#14521695C211yesmaximal, characteristic, complemented
5#14521438C211yesmaximal, characteristic, complemented
6#14521295C211yesmaximal, characteristic, complemented
7#14521285C211yesmaximal, characteristic, complemented
8#14521272C211yesmaximal, characteristic, complemented
9#14521245C211yesmaximal, characteristic, complemented
10#14521213C211yesmaximal, characteristic, complemented
11#14521196C211yesmaximal, characteristic, complemented
12#14521196C211yesmaximal, characteristic, complemented
13#14521185C211yesmaximal, characteristic, complemented
14#14521151C211yesmaximal, characteristic, complemented
15C31×#435C211yesmaximal, characteristic, complemented
16C2×#92495C2211yescharacteristic
17C2×#92495C2211yescharacteristic
18C2×#92495C2211yescharacteristic, complemented
19C22×D124C2211yescharacteristic
20C2×M16×C31C2211yescharacteristic
21C22×C8×C31C2211yescharacteristic, complemented
22C4×D4×C31C2211yescharacteristic
23#11758517—21no—
24#11758514—21no—
25#11758507C2211yescharacteristic
26#11758507C2211yescharacteristic
27#11758507C2211yescharacteristic, complemented
28#11758501C2211yescharacteristic
29#11758485—24no—
30C2×Dic124C2211yescharacteristic, complemented
31#11758481—24no—
32C2×D248C2211yescharacteristic
33C2×D248C2211yescharacteristic
34C2×D248C2211yescharacteristic
35C2×D248C2211yescharacteristic
36C2×#92470C2211yescharacteristic
37C2×#92470C2211yescharacteristic
38C2×#92470C2211yescharacteristic, complemented
39C2×#92470C2211yescharacteristic, complemented
40#11758471—21no—
41#11758470—21no—
42#11758461—21no—
43#11758461—21no—
44#11758461—21no—
45C22⋊C4×D31—21no—
46#11758452C2211yescharacteristic
47#11758451C2211yescharacteristic, complemented
48C4×D124C2211yescharacteristic
49C4×Dic62C2211yescharacteristic, complemented
50C31×C4⋊C8C2211yescharacteristic, complemented
51C31×C22⋊C8C2211yescharacteristic
52C31×C22⋊C8C2211yescharacteristic, complemented
53C31×#97C2211yescharacteristic, complemented
54#11758409C2211yescharacteristic
55#11758409C2211yescharacteristic
56#11758409C2211yescharacteristic, complemented
57#11758409C2211yescharacteristic, complemented
58#11758406C2211yescharacteristic, complemented
59#11758404C2211yescharacteristic, complemented
60#11758404C2211yescharacteristic, complemented
61C23×D31—21no—
62C2×D4×C31D411yescharacteristic
63C22×C4×C31C2311yescharacteristic
64C22×C4×C31C2311yescharacteristic
65C2×C22⋊D31—21no—
66C2×C22⋊D31—21no—
67C2×C22⋊D31—21no—
68C2×C22⋊D31—21no—
69C2×C22⋊D31—21no—
70C2×C22⋊D31—21no—
71#92495—22no—
72#92495—22no—
73#92495—22no—
74#92495—41no—
75#92495—41no—
76#92495—41no—
77C2×D124—22no—
78C2×D124—21no—
79C2×D124—21no—
80C2×D124—21no—
81C2×D124—41no—
82C2×D124C2311yescharacteristic
83C2×D124C2311yescharacteristic
84C2×D124C2311yescharacteristic
85C2×D124C2311yescharacteristic
86C2×C4×D31—21no—
87C2×C4×D31—21no—
88C2×C4×D31—21no—
89C2×C4×D31—21no—
90C2×Dic62C2311yescharacteristic
91C2×Dic62C2311yescharacteristic
92M16×C31—22no—
93C2×C8×C31—22no—
94C2×C8×C31C2311yescharacteristic
95C2×C8×C31C2311yescharacteristic
96C2×C8×C31C2311yescharacteristic
97C2×C8×C31C2311yescharacteristic
98C4⋊C4×C31D411yescharacteristic
99C22⋊C4×C31D411yescharacteristic
100C22⋊C4×C31D411yescharacteristic
101C42×C31C2311yescharacteristic
102C22⋊Dic31—21no—
103(C2×D31)⋊C4—21no—
104(C2×D31)⋊C4—21no—
105(C2×D31)⋊C4—21no—
106(C2×D31)⋊C4—21no—
107(C2×D31)⋊C4—21no—
108(C2×D31)⋊C4—21no—
109C4⋊Dic31C2311yescharacteristic
110C4⋊Dic31C2311yescharacteristic
111Dic31⋊C4—21no—
112Dic31⋊C4—21no—
113C4×Dic31—21no—
114Dic124—22no—
115D248—22no—
116D248—22no—
117D248—22no—
118D248—41no—
119#92470—22no—
120#92470—22no—
121#92470—41no—
122#92470D414yescomplemented
123C23×C31C2×D411yescharacteristic
124C23×C31C2×D411yescharacteristic
125C22×D31—21no—
126C22×D31—21no—
127C22×D31—21no—
128C22×D31—21no—
129C22×D31—42no—
130C22×D31—42no—
131C22×D31—81no—
132D4×C31—41no—
133C2×C4×C31—21no—
134C2×C4×C31—21no—
135C2×C4×C31—21no—
136C2×C4×C31—21no—
137C2×C4×C31C2×D411yescharacteristic
138C2×C4×C31C2×D411yescharacteristic
139C2×C4×C31C2×D411yescharacteristic
140C2×C4×C31C2×D411yescharacteristic
141C2×C4×C31C2411yescharacteristic
142C22⋊D31—42no—
143C22⋊D31—42no—
144C22⋊D31—42no—
145C22⋊D31—81no—
146C22⋊D31—81no—
147C22⋊D31—81no—
148C2×Dic31—21no—
149C2×Dic31—21no—
150C2×Dic31—21no—
151C2×Dic31—21no—
152D124—21no—
153D124—21no—
154D124—21no—
155D124—21no—
156D124—21no—
157D124—21no—
158D124—21no—
159D124—42no—
160D124—42no—
161D124—81no—
162D124C2×D412yes—
163C4×D31—42no—
164C4×D31—42no—
165C4×D31—42no—
166C4×D31—81no—
167Dic62—21no—
168Dic62—21no—
169Dic62—21no—
170Dic62C2×D412yes—
171C8×C31—21no—
172C8×C31—21no—
173C8×C31—21no—
174C8×C31C2×D412yes—
175#3268—311nomaximal, Sylow
176C22×C31—21no—
177C22×C31—21no—
178C22×C31—21no—
179C22×C31—21no—
180C22×C31—21no—
181C22×C31—21no—
182C22×C31C22×D411yescharacteristic
183C2×D31—22no—
184C2×D31—41no—
185C2×D31—41no—
186C2×D31—41no—
187C2×D31—41no—
188C2×D31—41no—
189C2×D31—41no—
190C2×D31—41no—
191C2×D31—41no—
192C2×D31—41no—
193C2×D31—41no—
194C2×D31—41no—
195C2×D31—84no—
196C4×C31—21no—
197C4×C31—21no—
198C4×C31—21no—
199C4×C31—21no—
200C4×C31C22×D411yescharacteristic
201C4×C31H(5,𝔽2)11yescharacteristic
202Dic31—22no—
203Dic31—41no—
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#459—311no—
215#452—311no—
216#449—311no—
217#449—311no—
218#447—311no—
219#440—311no—
220#435D3111yescharacteristic, complemented
221C2×C31—41no—
222C2×C31—41no—
223C2×C31D4211yescharacteristic
224C2×C31#57511yescharacteristic
225C2×C31#57611yescharacteristic
226D31—42no—
227D31—81no—
228D31—81no—
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×D8—311no—
244C2×D8—311no—
245C2×M16C2×D3111yescharacteristic
246C22×C8C2×D3111yescharacteristic, complemented
247#127—311no—
248#127—621no—
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#102—311no—
271#102—311no—
272C22⋊C8C2×D3111yescharacteristic
273C22⋊C8C2×D3111yescharacteristic, complemented
274#97C2×D3111yescharacteristic, complemented
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—311no—
286C2×D4—311no—
287C2×D4—311no—
288C2×D4—311no—
289C2×D4—622no—
290C2×D4—621no—
291C2×D4—621no—
292C2×D4—621no—
293C2×D4—621no—
294C2×D4—621no—
295C2×D4—621no—
296C2×D4—621no—
297C2×D4—621no—
298C2×D4—621no—
299C2×D4—1241no—
300C2×D4D12411yescharacteristic
301C22×C4—621no—
302C22×C4—621no—
303C22×C4—621no—
304C22×C4—621no—
305C22×C4C22×D3111yescharacteristic
306C22×C4C22×D3111yescharacteristic
307Q16—622no—
308SD16—314no—
309SD16—622no—
310SD16—622no—
311SD16—1241no—
312D8—622no—
313D8—622no—
314D8—622no—
315D8—1241no—
316M16—22no—
317C2×C8—22no—
318C2×C8C22×D3111yescharacteristic
319C2×C8C22×D3111yescharacteristic
320C2×C8C22×D3111yescharacteristic
321C2×C8C22×D3111yescharacteristic
322C4⋊C4—311no—
323C4⋊C4—311no—
324C4⋊C4—621no—
325C4⋊C4—621no—
326C4⋊C4D12411yescharacteristic
327C22⋊C4—621no—
328C22⋊C4—621no—
329C22⋊C4—621no—
330C22⋊C4—621no—
331C22⋊C4—621no—
332C22⋊C4—621no—
333C22⋊C4—621no—
334C22⋊C4D12411yescharacteristic
335C22⋊C4D12411yescharacteristic
336C42—621no—
337C42C22×D3111yescharacteristic
338C23—621no—
339C23—621no—
340C23—621no—
341C23—621no—
342C23—1242no—
343C23—1242no—
344C23—2481no—
345C23C2×D12411yescharacteristic
346C23C2×D12411yescharacteristic
347Q8—312no—
348Q8—621no—
349Q8—621no—
350Q8—621no—
351D4—41no—
352D4—312no—
353D4—621no—
354D4—621no—
355D4—621no—
356D4—621no—
357D4—621no—
358D4—621no—
359D4—621no—
360D4—1242no—
361D4—1242no—
362D4—1242no—
363D4—1242no—
364D4—1242no—
365D4—2481no—
366D4—2481no—
367D4—2481no—
368D4—2481no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—621no—
374C2×C4—621no—
375C2×C4—621no—
376C2×C4—621no—
377C2×C4—1242no—
378C2×C4—1242no—
379C2×C4—1242no—
380C2×C4—2481no—
381C2×C4C2×D12411yescharacteristic
382C2×C4C2×D12411yescharacteristic
383C2×C4C2×D12411yescharacteristic
384C2×C4C2×D12411yescharacteristic
385C2×C4C23×D3111yescharacteristic
386C8—21no—
387C8—21no—
388C8—21no—
389C8D4×D3112yes—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—622no—
397C22—1241no—
398C22—1241no—
399C22—1241no—
400C22—1241no—
401C22—1241no—
402C22—1241no—
403C22—1241no—
404C22—1241no—
405C22—1241no—
406C22—1241no—
407C22—1241no—
408C22—2484no—
409C22C22×D12411yescharacteristic
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—622no—
415C4—1241no—
416C4—1241no—
417C4—1241no—
418C4C2×D4×D3111yescharacteristic
419C4#1175856611yescharacteristic
420C2—41no—
421C2—41no—
422C2—1242no—
423C2—2481no—
424C2—2481no—
425C2—2481no—
426C2D4×D12411yescharacteristic
427C2#1452184911yescharacteristic
428C2#1452185411yescharacteristic
subgroupG/H
centerC22C22×D124
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#435C2
socleC22×C31C22×D4
hypercenter#435D31
hypocenterC31#3268
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#11758485C2semidirect
2. C2×#11758481C2semidirect
3. #14521720C2semidirect
4. #14521695C2semidirect
5. #14521438C2semidirect
6. #14521295C2semidirect
7. #14521285C2semidirect
8. #14521272C2semidirect
9. #14521245C2semidirect
10. #14521213C2semidirect
11. #14521196C2semidirect
12. #14521196C2semidirect
13. #14521185C2semidirect
14. #14521151C2semidirect
15. C31×#435C2semidirect
18. C2×#92495C22semidirect
21. C22×C8×C31C22semidirect
27. #11758507C22semidirect
30. C2×Dic124C22semidirect
38. C2×#92470C22semidirect
39. C2×#92470C22semidirect
47. #11758451C22semidirect
49. C4×Dic62C22semidirect
50. C31×C4⋊C8C22semidirect
52. C31×C22⋊C8C22semidirect
53. C31×#97C22semidirect
56. #11758409C22semidirect
57. #11758409C22semidirect
58. #11758406C22semidirect
59. #11758404C22semidirect
60. #11758404C22semidirect
122. #92470D4semidirect
220. #435D31semidirect
246. C22×C8C2×D31semidirect
265. C4⋊C8C2×D31semidirect
273. C22⋊C8C2×D31semidirect
274. #97C2×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×#117584852
C2×#117584812
#145217202
#145216952
#145214382
#145212952
#145212852
#145212722
#145212452
#145212132
#145211962
#145211852
#145211512
C31×#4352
#326831