Finite Group Databasebeta

← #11860487

Subgroups — #11860487

Order 1152.

804 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596650C211yesmaximal, characteristic, complemented
2#10596642C211yesmaximal, characteristic, complemented
3C3⋊D3×AGL(1,ℤ/8)C211yesmaximal, characteristic
4#10593841C211yesmaximal, characteristic, complemented
5C2×#63782C211yesmaximal, characteristic, complemented
6#10593782C212yesmaximal, complemented
7SD16×#157C212yesmaximal, complemented
8#10593778C212yesmaximal, complemented
9D8×#157C212yesmaximal, complemented
10#10593775C211yesmaximal, characteristic, complemented
11#10593774C211yesmaximal, characteristic, complemented
12#41×C3⋊D3C2211yescharacteristic
13C2×D4×C3⋊D3C2211yescharacteristic
14C2×C22⋊#157—22no—
15Q8×#157C2212yescomplemented
16D4×#157—22no—
17D4×#157—21no—
18D4×#157—21no—
19D4×#157C2212yes—
20D4×#157C2212yes—
21D4×#157C2212yescomplemented
22#64286—21no—
23#64286C2211yescharacteristic
24#64286C2211yescharacteristic
25C2×C4⋊#157—21no—
26C2×C4⋊#157C2211yescharacteristic
27C2×#3787C2211yescharacteristic
28C32×AGL(1,ℤ/8)C411yescharacteristic, complemented
29#64158C411yescharacteristic, complemented
30#64141C411yescharacteristic, complemented
31#64123C412yescomplemented
32SD16×C3⋊D3C2212yes—
33#64120C412yescomplemented
34D8×C3⋊D3C2212yes—
35#64117C411yescharacteristic, complemented
36M16×C3⋊D3C2211yescharacteristic
37#63784C2211yescharacteristic, complemented
38#63784C2211yescharacteristic, complemented
39#63782C2212yes—
40#63782C2212yes—
41#63782C2211yescharacteristic, complemented
42#63782C2211yescharacteristic, complemented
43#63769C2212yescomplemented
44#63768C2212yescomplemented
45#63767C2212yescomplemented
46C8×#157C2212yescomplemented
47D3×AGL(1,ℤ/8)—62no—
48C23×C3⋊D3—21no—
49C22×#157—21no—
50C22×#157—22no—
51C22×#157—22no—
52C22×#157—22no—
53C32×#41C2×C411yescharacteristic, complemented
54C2×C32×D4C2×C411yescharacteristic, complemented
55C2×#638—21no—
56#3832C2×C411yescharacteristic, complemented
57Q8×C3⋊D3C2311yescharacteristic
58#3830—21no—
59#3830C2×C411yescharacteristic, complemented
60D4×C3⋊D3—21no—
61D4×C3⋊D3—21no—
62D4×C3⋊D3—21no—
63D4×C3⋊D3C2×C412yescomplemented
64D4×C3⋊D3C2312yes—
65D4×C3⋊D3C2311yescharacteristic
66#3828—21no—
67#3828C2×C411yescharacteristic, complemented
68C2×C4⋊(C3⋊D3)C2×C411yescharacteristic, complemented
69C2×C4×C3⋊D3—21no—
70C2×C4×C3⋊D3C2311yescharacteristic
71C22⋊#157—21no—
72C22⋊#157—22no—
73C22⋊#157—22no—
74C22⋊#157—22no—
75C22⋊#157D412yes—
76C2×#622—21no—
77C4⋊#157—22no—
78C4⋊#157—21no—
79C4⋊#157D411yescharacteristic
80C4⋊#157D411yescharacteristic
81C4⋊#157C2311yescharacteristic
82C4⋊#157C2312yes—
83C4⋊#157C2311yescharacteristic
84C4×#157—22no—
85C4×#157—21no—
86C4×#157C2312yes—
87#3787—21no—
88#3787C2311yescharacteristic
89#3787C2311yescharacteristic
90C32×SD16C2×C412yescomplemented
91C32×D8C2×C412yescomplemented
92C32×M16C2×C411yescharacteristic, complemented
93#3755C2×C412yescomplemented
94#3754C2×C412yescomplemented
95#3753C2×C412yescomplemented
96#3753C2×C412yescomplemented
97#3748C2×C411yescharacteristic, complemented
98#3745C2×C412yescomplemented
99#3744C2×C412yescomplemented
100#3743C2×C412yescomplemented
101C8×C3⋊D3C2312yes—
102#2946—91nomaximal, Sylow
103D3×#41—62no—
104C2×D3×D4—62no—
105C3×AGL(1,ℤ/8)—22no—
106#949—62no—
107#932—62no—
108#914—64no—
109D3×SD16—64no—
110#911—64no—
111D3×D8—64no—
112#908—62no—
113D3×M16—62no—
114C23×C32—21no—
115C22×C3⋊D3—21no—
116C22×C3⋊D3—22no—
117C22×C3⋊D3—21no—
118C22×C3⋊D3—22no—
119C22×C3⋊D3—81no—
120C22×C3⋊D3—81no—
121C22×C3⋊D3C2×D411yescharacteristic
122C2×#157—22no—
123C2×#157—21no—
124C2×#157—21no—
125C2×#157—82no—
126C2×#157—82no—
127C2×#157—82no—
128C2×#157—81no—
129C2×#157C2×D412yes—
130C2×#157C2×D412yes—
131C32×Q8C22×C411yescharacteristic
132C32×D4—21no—
133C32×D4—21no—
134C32×D4C22×C411yescharacteristic
135C32×D4C22×C412yes—
136C2×C32×C4—21no—
137C2×C32×C4C22×C411yescharacteristic
138#638—21no—
139#638—21no—
140#638—22no—
141#638—21no—
142#638—22no—
143C2×C3⋊Dic3—21no—
144C2×C3⋊Dic3#4111yescharacteristic
145C4⋊(C3⋊D3)—21no—
146C4⋊(C3⋊D3)—21no—
147C4⋊(C3⋊D3)C22×C412yes—
148C4⋊(C3⋊D3)C22×C411yescharacteristic
149C4×C3⋊D3—21no—
150C4×C3⋊D3—21no—
151C4×C3⋊D3—21no—
152C4×C3⋊D3C22×C411yescharacteristic
153C4×C3⋊D3C2×D411yescharacteristic
154C4×C3⋊D3#4111yescharacteristic
155C4×C3⋊D3C2411yescharacteristic
156#634—21no—
157#634C22×C411yescharacteristic
158#622—21no—
159#622—21no—
160C32×C8C22×C412yes—
161C3⋊(C3⋊C8)C22×C412yes—
162C2×AGL(1,ℤ/8)—91no—
163#520—91no—
164#518—91no—
165#442—92no—
166#440—92no—
167C4×SD16—92no—
168C4×D8—92no—
169#428—91no—
170#416—91no—
171C2×#102—91no—
172#405—91no—
173C23×D3—122no—
174C3×#41—22no—
175C2×C3×D4—22no—
176C2×#67—122no—
177#239—62no—
178D3×Q8—62no—
179#237—62no—
180#237—122no—
181D3×D4—62no—
182D3×D4—64no—
183D3×D4—64no—
184D3×D4—122no—
185D3×D4—122no—
186D3×D4—122no—
187#235—62no—
188#235—122no—
189C2×D12—62no—
190C2×C4×D3—62no—
191C2×C4×D3—122no—
192C3×SD16—24no—
193C3×D8—24no—
194C3×M16—22no—
195#215—64no—
196#214—64no—
197#213—64no—
198#213—64no—
199#208—62no—
200D24—64no—
201#204—64no—
202ΓL(1,𝔽25)—64no—
203D3×C8—64no—
204C22×C32—21no—
205C22×C32—22no—
206C22×C32—81no—
207C22×C32C4×D411yescharacteristic
208C2×C3⋊D3—21no—
209C2×C3⋊D3—21no—
210C2×C3⋊D3—21no—
211C2×C3⋊D3—22no—
212C2×C3⋊D3—41no—
213C2×C3⋊D3—42no—
214C2×C3⋊D3—42no—
215C2×C3⋊D3—41no—
216C2×C3⋊D3—82no—
217C2×C3⋊D3—81no—
218C2×C3⋊D3C4×D411yescharacteristic
219C2×C3⋊D3C22×D411yescharacteristic
220#157—22no—
221#157—22no—
222#157—42no—
223#157—41no—
224#157—41no—
225C32×C4—21no—
226C32×C4C4×D411yescharacteristic
227C32×C4C23×C411yescharacteristic
228C3⋊Dic3—21no—
229C3⋊Dic3C4×D411yescharacteristic
230C3⋊Dic3C2×#4111yescharacteristic
231C2×#41—91no—
232C22×D4—91no—
233AGL(1,ℤ/8)—91no—
234AGL(1,ℤ/8)—91no—
235AGL(1,ℤ/8)—92no—
236AGL(1,ℤ/8)—92no—
237AGL(1,ℤ/8)—91no—
238AGL(1,ℤ/8)#15711yescharacteristic, complemented
239C2×SD16—92no—
240C2×D8—92no—
241C2×M16—91no—
242C22×C8—91no—
243C4×Q8—92no—
244C4×D4—92no—
245C4×D4—92no—
246C4×D4—92no—
247C4×D4—182no—
248C4×D4—181no—
249C4×D4—181no—
250#117—91no—
251#117—91no—
252#117—181no—
253C2×C4⋊C4—91no—
254C2×C4⋊C4—181no—
255C2×C22⋊C4—182no—
256#107—92no—
257#106—92no—
258#103—91no—
259#103—91no—
260#102—92no—
261#102—92no—
262#102—91no—
263#102—91no—
264#97—92no—
265C4×C8—92no—
266C23×C3—42no—
267C22×D3—62no—
268C22×D3—122no—
269C22×D3—124no—
270C22×D3—124no—
271C22×D3—122no—
272C22×D3—244no—
273C22×D3—244no—
274C3×Q8—22no—
275C3×D4—22no—
276C3×D4—24no—
277C3×D4—42no—
278C3×D4—42no—
279C2×C3×C4—22no—
280C2×C3×C4—42no—
281#67—122no—
282#67—124no—
283#67—124no—
284#67—122no—
285#67—122no—
286C2×Dic3—62no—
287C2×Dic3—122no—
288D12—64no—
289D12—62no—
290D12—122no—
291D12—122no—
292C4×D3—62no—
293C4×D3—62no—
294C4×D3—62no—
295C4×D3—62no—
296C4×D3—122no—
297C4×D3—122no—
298C4×D3—122no—
299Dic6—62no—
300Dic6—122no—
301C3×C8—24no—
302C3⋊C8—64no—
303C2×C32—21no—
304C2×C32—42no—
305C2×C32—41no—
306C2×C32C2×C4×D411yescharacteristic
307C3⋊D3—21no—
308C3⋊D3—41no—
309C3⋊D3—42no—
310C3⋊D3#57611yescharacteristic
311C3⋊D3#57711yescharacteristic
312C24—181no—
313#41—91no—
314#41—91no—
315#41—91no—
316#41—181no—
317#41—181no—
318#41C2×#15711yescharacteristic, complemented
319C2×Q8—91no—
320C2×D4—91no—
321C2×D4—92no—
322C2×D4—92no—
323C2×D4—91no—
324C2×D4—181no—
325C2×D4—181no—
326C2×D4—181no—
327C2×D4—181no—
328C2×D4C2×#15711yescharacteristic, complemented
329C22×C4—91no—
330C22×C4—181no—
331C22×C4—182no—
332C22×C4—182no—
333C22×C4—182no—
334C22×C4—181no—
335SD16—92no—
336SD16—92no—
337SD16—92no—
338SD16C2×#15712yescomplemented
339D8—92no—
340D8—92no—
341D8—92no—
342D8C2×#15712yescomplemented
343M16—91no—
344M16—92no—
345M16C2×#15711yescharacteristic, complemented
346C2×C8—92no—
347C2×C8—91no—
348C2×C8—91no—
349C2×C8—181no—
350C2×C8—181no—
351C4⋊C4—91no—
352C4⋊C4—91no—
353C4⋊C4—92no—
354C4⋊C4—91no—
355C4⋊C4—91no—
356C4⋊C4—181no—
357C4⋊C4—182no—
358C22⋊C4—92no—
359C22⋊C4—182no—
360C22⋊C4—182no—
361C22⋊C4—182no—
362C22⋊C4—181no—
363C42—92no—
364C42—181no—
365C42—182no—
366C22×C3—22no—
367C22×C3—42no—
368C22×C3—44no—
369C22×C3—84no—
370C2×D3—62no—
371C2×D3—62no—
372C2×D3—122no—
373C2×D3—122no—
374C2×D3—122no—
375C2×D3—124no—
376C2×D3—244no—
377C2×D3—244no—
378C2×D3—242no—
379C2×D3—242no—
380C2×D3—248no—
381C2×D3—244no—
382C3×C4—22no—
383C3×C4—22no—
384C3×C4—42no—
385Dic3—62no—
386Dic3—62no—
387Dic3—122no—
388C32#294611yescharacteristic, complemented, Sylow
389C23—21no—
390C23—91no—
391C23—181no—
392C23—182no—
393C23—182no—
394C23—181no—
395C23—721no—
396C23—721no—
397Q8—91no—
398Q8—181no—
399Q8C22×#15711yescharacteristic
400D4—21no—
401D4—21no—
402D4—91no—
403D4—92no—
404D4—181no—
405D4—182no—
406D4—182no—
407D4—181no—
408D4—181no—
409D4—181no—
410D4—181no—
411D4C22×#15711yescharacteristic
412D4C22×#15712yes—
413C2×C4—21no—
414C2×C4—91no—
415C2×C4—91no—
416C2×C4—91no—
417C2×C4—91no—
418C2×C4—91no—
419C2×C4—92no—
420C2×C4—92no—
421C2×C4—181no—
422C2×C4—181no—
423C2×C4—181no—
424C2×C4—181no—
425C2×C4—181no—
426C2×C4—181no—
427C2×C4—182no—
428C2×C4—722no—
429C2×C4—722no—
430C2×C4—722no—
431C2×C4—721no—
432C2×C4C22×#15711yescharacteristic
433C8—92no—
434C8—181no—
435C8—181no—
436C8C22×#15712yes—
437C2×C3—22no—
438C2×C3—42no—
439C2×C3—84no—
440C2×C3—82no—
441D3—62no—
442D3—62no—
443D3—122no—
444D3—244no—
445D3—242no—
446C22—21no—
447C22—22no—
448C22—81no—
449C22—91no—
450C22—91no—
451C22—181no—
452C22—181no—
453C22—181no—
454C22—182no—
455C22—361no—
456C22—362no—
457C22—362no—
458C22—361no—
459C22—721no—
460C22—722no—
461C22D4×#15711yescharacteristic
462C4—21no—
463C4—91no—
464C4—91no—
465C4—182no—
466C4—182no—
467C4—181no—
468C4—361no—
469C4—362no—
470C4—361no—
471C4D4×#15711yescharacteristic
472C4C23×#15711yescharacteristic
473C3—22no—
474C2—21no—
475C2—42no—
476C2—41no—
477C2—91no—
478C2—91no—
479C2—181no—
480C2—362no—
481C2—361no—
482C2C2×D4×#15711yescharacteristic
subgroupG/H
centerC2C2×D4×#157
commutatorC32×C4C23×C4
FrattiniC4C23×#157
FittingC32×AGL(1,ℤ/8)C4
socleC2×C32C2×C4×D4
prime radicalC3⋊D3×AGL(1,ℤ/8)C2
cosocleC4×C3⋊D3C24
hypercenterAGL(1,ℤ/8)#157
hypocenterC32#2946
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #10596650C2semidirect
2. #10596642C2semidirect
4. #10593841C2semidirect
5. C2×#63782C2semidirect
6. #10593782C2semidirect
7. SD16×#157C2semidirect
8. #10593778C2semidirect
9. D8×#157C2semidirect
10. #10593775C2semidirect
11. #10593774C2semidirect
15. Q8×#157C22semidirect
21. D4×#157C22semidirect
28. C32×AGL(1,ℤ/8)C4semidirect
29. #64158C4semidirect
30. #64141C4semidirect
31. #64123C4semidirect
33. #64120C4semidirect
35. #64117C4semidirect
37. #63784C22semidirect
38. #63784C22semidirect
41. #63782C22semidirect
42. #63782C22semidirect
43. #63769C22semidirect
44. #63768C22semidirect
45. #63767C22semidirect
46. C8×#157C22semidirect
53. C32×#41C2×C4semidirect
54. C2×C32×D4C2×C4semidirect
56. #3832C2×C4semidirect
59. #3830C2×C4semidirect
63. D4×C3⋊D3C2×C4semidirect
67. #3828C2×C4semidirect
68. C2×C4⋊(C3⋊D3)C2×C4semidirect
90. C32×SD16C2×C4semidirect
91. C32×D8C2×C4semidirect
92. C32×M16C2×C4semidirect
93. #3755C2×C4semidirect
94. #3754C2×C4semidirect
95. #3753C2×C4semidirect
96. #3753C2×C4semidirect
97. #3748C2×C4semidirect
98. #3745C2×C4semidirect
99. #3744C2×C4semidirect
100. #3743C2×C4semidirect
238. AGL(1,ℤ/8)#157semidirect
318. #41C2×#157semidirect
328. C2×D4C2×#157semidirect
338. SD16C2×#157semidirect
342. D8C2×#157semidirect
345. M16C2×#157semidirect
388. C32#2946semidirect

Maximal subgroups

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

subgroupindex
#105966502
#105966422
C3⋊D3×AGL(1,ℤ/8)2
#105938412
C2×#637822
#105937822
SD16×#1572
#105937782
D8×#1572
#105937752
#105937742
#29469