Finite Group Databasebeta

← #16857253

Subgroups — #16857253

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×#11758491C211yesmaximal, characteristic, complemented
2C2×#11758493C211yesmaximal, characteristic, complemented
3#14521721C211yesmaximal, characteristic, complemented
4#14521694C211yesmaximal, characteristic, complemented
5#14521438C211yesmaximal, characteristic, complemented
6#14521296C211yesmaximal, characteristic, complemented
7#14521286C211yesmaximal, characteristic, complemented
8#14521271C211yesmaximal, characteristic, complemented
9#14521244C211yesmaximal, characteristic, complemented
10#14521214C211yesmaximal, characteristic, complemented
11#14521197C211yesmaximal, characteristic, complemented
12#14521195C211yesmaximal, characteristic, complemented
13#14521184C211yesmaximal, characteristic, complemented
14#14521122C211yesmaximal, characteristic, complemented
15C31×#440C211yesmaximal, characteristic, complemented
16C2×#92499C2211yescharacteristic
17C2×#92499C2211yescharacteristic, complemented
18C2×#92497C2211yescharacteristic
19C2×D4×D31C2211yescharacteristic
20C2×SD16×C31C2211yescharacteristic
21C4×Q8×C31C2211yescharacteristic, complemented
22C4×D4×C31C2211yescharacteristic
23C2×#92482C2211yescharacteristic, complemented
24C2×#92481C2211yescharacteristic
25C2×#92479C2211yescharacteristic
26C2×#92479C2211yescharacteristic
27#11758507—21no—
28C2×(C2×D31)⋊C4—21no—
29#11758493—24no—
30#11758491—24no—
31C2×D248C2211yescharacteristic
32C2×D248C2211yescharacteristic
33C2×#92470C2211yescharacteristic, complemented
34C2×#92470C2211yescharacteristic, complemented
35C2×#92469C2211yescharacteristic
36C2×C8×D31C2211yescharacteristic, complemented
37#11758474C2211yescharacteristic
38#11758472—21no—
39#11758472—21no—
40#11758472C2211yescharacteristic
41#11758472C2211yescharacteristic
42#11758472C2211yescharacteristic, complemented
43#11758463—21no—
44#11758459—21no—
45#11758452C2211yescharacteristic
46#11758451—21no—
47#11758451C2211yescharacteristic, complemented
48C4×D124—21no—
49C4×D124C2211yescharacteristic
50C31×#107C2211yescharacteristic, complemented
51C31×#103C2211yescharacteristic, complemented
52C31×#102C2211yescharacteristic
53C31×#97C2211yescharacteristic, complemented
54(C2×D31)⋊C8C2211yescharacteristic
55(C2×D31)⋊C8C2211yescharacteristic, complemented
56#11758398C2211yescharacteristic, complemented
57#11758397C2211yescharacteristic
58#11758397C2211yescharacteristic, complemented
59#11758397C2211yescharacteristic, complemented
60C4⋊(C31⋊C8)C2211yescharacteristic, complemented
61C23×D31—21no—
62C2×Q8×C31C2311yescharacteristic
63C2×D4×C31C2311yescharacteristic
64C22×C4×C31—21no—
65C2×C22⋊D31—21no—
66C2×C22⋊D31—21no—
67C22×Dic31—21no—
68#92499—22no—
69#92499—22no—
70#92499—41no—
71#92499—41no—
72#92497—22no—
73#92497—41no—
74D4×D31—22no—
75D4×D31—41no—
76C2×D124—21no—
77C2×D124—21no—
78C2×D124—21no—
79C2×D124—21no—
80C2×D124—21no—
81C2×D124—21no—
82C2×D124—21no—
83C2×D124D411yescharacteristic
84C2×D124C2311yescharacteristic
85C2×D124C2311yescharacteristic
86C2×D124C2311yescharacteristic
87C2×C4×D31—21no—
88C2×C4×D31—21no—
89C2×C4×D31C2311yescharacteristic
90C2×C4×D31C2311yescharacteristic
91C2×Dic62C2311yescharacteristic
92SD16×C31D414yescomplemented
93C2×C8×C31C2311yescharacteristic
94C2×C8×C31C2311yescharacteristic
95C4⋊C4×C31—21no—
96C4⋊C4×C31C2311yescharacteristic
97C4⋊C4×C31C2311yescharacteristic
98C22⋊C4×C31—21no—
99C42×C31—21no—
100C42×C31C2311yescharacteristic
101#92482—22no—
102#92481—22no—
103#92479—22no—
104#92479—22no—
105(C2×D31)⋊C4—21no—
106(C2×D31)⋊C4—21no—
107(C2×D31)⋊C4—21no—
108(C2×D31)⋊C4—21no—
109(C2×D31)⋊C4—21no—
110(C2×D31)⋊C4—21no—
111(C2×D31)⋊C4D411yescharacteristic
112(C2×D31)⋊C4D411yescharacteristic
113C4⋊Dic31—21no—
114C4⋊Dic31D411yescharacteristic
115C2×C31⋊C8C2311yescharacteristic
116C2×C31⋊C8C2311yescharacteristic
117D248—22no—
118D248—41no—
119#92470—22no—
120#92470—41no—
121#92469—22no—
122C8×D31—22no—
123C23×C31—21no—
124C22×D31—21no—
125C22×D31—21no—
126C22×D31—21no—
127C22×D31—42no—
128C22×D31—42no—
129C22×D31—81no—
130C22×D31C2×D411yescharacteristic
131C22×D31C2×D411yescharacteristic
132Q8×C31—21no—
133Q8×C31C2×D412yes—
134D4×C31—21no—
135D4×C31C2×D412yes—
136C2×C4×C31—21no—
137C2×C4×C31—21no—
138C2×C4×C31—21no—
139C2×C4×C31—81no—
140C2×C4×C31C2×D411yescharacteristic
141C2×C4×C31C2×D411yescharacteristic
142C2×C4×C31C2411yescharacteristic
143C22⋊D31—42no—
144C22⋊D31—42no—
145C2×Dic31—21no—
146C2×Dic31—42no—
147C2×Dic31C2×D411yescharacteristic
148C2×Dic31C2×D411yescharacteristic
149D124—21no—
150D124—21no—
151D124—21no—
152D124—21no—
153D124—21no—
154D124—21no—
155D124—41no—
156D124—42no—
157D124—42no—
158D124—42no—
159D124—81no—
160D124—81no—
161D124—81no—
162D124—81no—
163C4×D31—21no—
164C4×D31—21no—
165C4×D31—21no—
166C4×D31—21no—
167C4×D31—42no—
168C4×D31—42no—
169Dic62—21no—
170Dic62—21no—
171C8×C31—21no—
172C8×C31C2×D412yes—
173C31⋊C8—21no—
174C31⋊C8—21no—
175#3268—311nomaximal, Sylow
176C22×C31—22no—
177C22×C31—41no—
178C22×C31—41no—
179C22×C31C22×D411yescharacteristic
180C2×D31—21no—
181C2×D31—21no—
182C2×D31—21no—
183C2×D31—21no—
184C2×D31—21no—
185C2×D31—21no—
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—22no—
197C4×C31—21no—
198C4×C31—21no—
199C4×C31—41no—
200C4×C31—41no—
201C4×C31C22×D411yescharacteristic
202C4×C31H(5,𝔽2)11yescharacteristic
203Dic31—21no—
204Dic31—21no—
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#440D3111yescharacteristic, complemented
220#435—311no—
221C2×C31—42no—
222C2×C31D4211yescharacteristic
223C2×C31#57511yescharacteristic
224C2×C31#57611yescharacteristic
225D31—41no—
226D31—41no—
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×SD16C2×D3111yescharacteristic
241C2×D8—311no—
242C2×D8—311no—
243C2×D8—311no—
244C2×D8—311no—
245C2×M16—311no—
246C22×C8—311no—
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×Q8C2×D3111yescharacteristic, complemented
260C4×D4—311no—
261C4×D4—621no—
262C4×D4C2×D3111yescharacteristic
263C2×C22⋊C4—621no—
264#107C2×D3111yescharacteristic, complemented
265C4⋊C8—311no—
266#103—311no—
267#103C2×D3111yescharacteristic, complemented
268#102—311no—
269#102—311no—
270#102—311no—
271#102C2×D3111yescharacteristic
272C22⋊C8—311no—
273C22⋊C8—311no—
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×Q8C22×D3111yescharacteristic
285C2×D4—311no—
286C2×D4—311no—
287C2×D4—311no—
288C2×D4—311no—
289C2×D4—621no—
290C2×D4—621no—
291C2×D4—621no—
292C2×D4—621no—
293C2×D4—621no—
294C2×D4—621no—
295C2×D4—622no—
296C2×D4—621no—
297C2×D4—621no—
298C2×D4—621no—
299C2×D4—1241no—
300C2×D4C22×D3111yescharacteristic
301C22×C4—21no—
302C22×C4—311no—
303C22×C4—311no—
304C22×C4—621no—
305C22×C4—621no—
306C22×C4—621no—
307Q16—622no—
308SD16—622no—
309SD16—622no—
310SD16—1241no—
311SD16D12414yescomplemented
312D8—622no—
313D8—622no—
314D8—622no—
315D8—1241no—
316M16—622no—
317C2×C8—311no—
318C2×C8—311no—
319C2×C8—622no—
320C2×C8C22×D3111yescharacteristic
321C2×C8C22×D3111yescharacteristic
322C4⋊C4—21no—
323C4⋊C4—311no—
324C4⋊C4—621no—
325C4⋊C4C22×D3111yescharacteristic
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—21no—
337C42C22×D3111yescharacteristic
338C23—21no—
339C23—311no—
340C23—311no—
341C23—621no—
342C23—621no—
343C23—621no—
344C23—1242no—
345C23—1242no—
346C23—2481no—
347Q8—21no—
348Q8—621no—
349Q8—621no—
350Q8C2×D12412yes—
351D4—21no—
352D4—621no—
353D4—621no—
354D4—621no—
355D4—621no—
356D4—621no—
357D4—621no—
358D4—1241no—
359D4—1242no—
360D4—1242no—
361D4—1242no—
362D4—1242no—
363D4—1242no—
364D4—2481no—
365D4—2481no—
366D4—2481no—
367D4—2481no—
368D4C2×D12412yes—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—81no—
373C2×C4—311no—
374C2×C4—311no—
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—621no—
388C8—621no—
389C8C2×D12412yes—
390C22—22no—
391C22—41no—
392C22—41no—
393C22—621no—
394C22—621no—
395C22—621no—
396C22—621no—
397C22—621no—
398C22—621no—
399C22—1241no—
400C22—1241no—
401C22—1241no—
402C22—1241no—
403C22—1241no—
404C22—1241no—
405C22—1241no—
406C22—1241no—
407C22—1241no—
408C22—2484no—
409C22C2×D4×D3111yescharacteristic
410C4—22no—
411C4—21no—
412C4—21no—
413C4—41no—
414C4—41no—
415C4—621no—
416C4—621no—
417C4—1241no—
418C4C22×D12411yescharacteristic
419C4#1175856611yescharacteristic
420C2—42no—
421C2—1241no—
422C2—1241no—
423C2—2481no—
424C2—2481no—
425C2—2481no—
426C2D4×D12411yescharacteristic
427C2#1452184811yescharacteristic
428C2#1452185311yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#440C2
socleC22×C31C22×D4
hypercenter#440D31
hypocenterC31#3268
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. C2×#11758491C2semidirect
2. C2×#11758493C2semidirect
3. #14521721C2semidirect
4. #14521694C2semidirect
5. #14521438C2semidirect
6. #14521296C2semidirect
7. #14521286C2semidirect
8. #14521271C2semidirect
9. #14521244C2semidirect
10. #14521214C2semidirect
11. #14521197C2semidirect
12. #14521195C2semidirect
13. #14521184C2semidirect
14. #14521122C2semidirect
15. C31×#440C2semidirect
17. C2×#92499C22semidirect
21. C4×Q8×C31C22semidirect
23. C2×#92482C22semidirect
33. C2×#92470C22semidirect
34. C2×#92470C22semidirect
36. C2×C8×D31C22semidirect
42. #11758472C22semidirect
47. #11758451C22semidirect
50. C31×#107C22semidirect
51. C31×#103C22semidirect
53. C31×#97C22semidirect
55. (C2×D31)⋊C8C22semidirect
56. #11758398C22semidirect
58. #11758397C22semidirect
59. #11758397C22semidirect
60. C4⋊(C31⋊C8)C22semidirect
92. SD16×C31D4semidirect
219. #440D31semidirect
259. C4×Q8C2×D31semidirect
264. #107C2×D31semidirect
267. #103C2×D31semidirect
274. #97C2×D31semidirect
275. C31#3268semidirect
311. SD16D124semidirect

Maximal subgroups

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

subgroupindex
C2×#117584912
C2×#117584932
#145217212
#145216942
#145214382
#145212962
#145212862
#145212712
#145212442
#145212142
#145211972
#145211952
#145211842
#145211222
C31×#4402
#326831