Finite Group Databasebeta

← #11878838

Subgroups — #11878838

Order 1152.

1047 conjugacy classes of subgroups.

The subgroup lattice has 537 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5728C211yesmaximal, characteristic, complemented
2D3×#874C211yesmaximal, characteristic
3#10592784C211yesmaximal, characteristic, complemented
4C3×#5085C211yesmaximal, characteristic, complemented
5#10591651C214yesmaximal, complemented
6#10591617C214yesmaximal, complemented
7#10590281C211yesmaximal, characteristic, complemented
8#10590277C211yesmaximal, characteristic, complemented
9#10590261C211yesmaximal, characteristic, complemented
10#83355—31nomaximal
11#81766—31nomaximal
12C2×D3×D12—21no—
13C2×D3×D12—21no—
14C2×D3×D12C2212yes—
15C32×C4⋊Q8C2211yescharacteristic, complemented
16C2×#3755C2214yescomplemented
17#64083C2211yescharacteristic
18C3×#946C2212yes—
19C3×Q8×Dic3C2212yescomplemented
20C2×C3×#215C2214yescomplemented
21C3×#897—21no—
22C3×#892—21no—
23C3×#890—21no—
24C3×#887—21no—
25C3×#874C2211yescharacteristic
26C3×C42×D3C2211yescharacteristic
27C3×#869C2211yescharacteristic, complemented
28#63911—21no—
29#63911—21no—
30#63911C2212yes—
31C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
32C3×C4×C3⋊C8C2211yescharacteristic, complemented
33Dic3⋊(C3⋊C8)C2212yescomplemented
34#63564C2214yescomplemented
35#63562C2214yescomplemented
36(C2×D3)⋊(C3⋊C8)C2212yes—
37C3×#533—31no—
38#5728D311yescharacteristic, complemented
39D3×#127—31no—
40C2×#874—31no—
41C3×#492—31no—
42#5169—34no—
43#5163—34no—
44#5088—31no—
45#5088—31no—
46#5085—31no—
47#5085—31no—
48#5085—61no—
49#5085D311yescharacteristic, complemented
50#5070—31no—
51#5046—34no—
52#5027—34no—
53#4925—31no—
54#4694—31no—
55#4685—31no—
56C22×D32—22no—
57C2×C32×Q8C2312yes—
58C2×C4⋊(C3⋊D3)—21no—
59C2×C4⋊(C3⋊D3)—21no—
60C2×C4⋊(C3⋊D3)C2312yes—
61C2×C3×D12—21no—
62C2×C3×D12—21no—
63C2×C3×D12C2312yes—
64C2×C3×C4×D3D411yescharacteristic
65C2×C3×C4×D3D411yescharacteristic
66C2×C3×C4×D3C2311yescharacteristic
67C2×C3×Dic6—21no—
68C2×#626—22no—
69C2×#626—22no—
70C2×#626—22no—
71D3×D12—44no—
72D3×D12—44no—
73D3×D12—44no—
74C32×C4⋊C4—21no—
75C32×C4⋊C4—21no—
76C32×C42C2311yescharacteristic
77#3755—44no—
78C2×C3⋊(C3⋊C8)C2312yes—
79C3×#215—44no—
80C3×(C2×D3)⋊C4—22no—
81C3×C4⋊Dic3—21no—
82C3×C4⋊Dic3—22no—
83C3×C4⋊Dic3C2312yes—
84C3×Dic3⋊C4—22no—
85C3×C4×Dic3—22no—
86C3×C4×Dic3D411yescharacteristic
87C3×C4×Dic3D411yescharacteristic
88C3×C4×Dic3C2311yescharacteristic
89C2×C3×C3⋊C8C2312yes—
90#3208—91noSylow
91C2×D3×D4—32no—
92C2×D3×D4—61no—
93C2×D3×D4—61no—
94C22×D12—32no—
95C22×D12—61no—
96C22×D12—61no—
97C2×C3×SD16—34no—
98C3×C4⋊Q8—21no—
99C3×C4⋊Q8—31no—
100C3×C4⋊Q8C2×D311yescharacteristic, complemented
101C3×C4⋊Q8C2×D311yescharacteristic, complemented
102C3×#127—31no—
103C3×#125—61no—
104C3×C22⋊Q8—32no—
105C3×C22⋊Q8—61no—
106C3×C4×Q8—32no—
107C3×C4×Q8—61no—
108C3×#117—61no—
109C2×C3×C42—31no—
110#946C2×D312yes—
111Q8×Dic3C2×D312yescomplemented
112C2×#215—34no—
113C2×#215—34no—
114C2×#215—64no—
115C2×#215C2×D314yescomplemented
116#940—32no—
117#940—61no—
118#940—61no—
119#897—21no—
120#892—21no—
121#890—21no—
122#887—21no—
123#874—32no—
124#874—31no—
125#874—31no—
126#874—61no—
127#874—61no—
128#874—61no—
129#874C2×D311yescharacteristic
130C42×D3C2×D311yescharacteristic
131#869C2×D311yescharacteristic, complemented
132C3×C4×C8—31no—
133#832—34no—
134#830—32no—
135#821—34no—
136(C2×D3)⋊C8—32no—
137Dic3⋊C8—32no—
138#809—34no—
139#809—34no—
140C4⋊(C3⋊C8)—32no—
141C4×C3⋊C8—31no—
142C4×C3⋊C8—31no—
143C4×C3⋊C8—61no—
144C4×C3⋊C8C2×D311yescharacteristic, complemented
145C22×C3⋊D3—22no—
146C22×C3×D3—22no—
147C22×C3×D3C2×D411yescharacteristic
148C2×D32—44no—
149C2×D32—44no—
150C2×D32—44no—
151C32×Q8—24no—
152C2×C32×C4—22no—
153C2×C32×C4C2×D411yescharacteristic
154C2×C32×C4C2×D411yescharacteristic
155C2×C32×C4C2411yescharacteristic
156C4⋊(C3⋊D3)—24no—
157C4⋊(C3⋊D3)—42no—
158C4⋊(C3⋊D3)—42no—
159C2×C3×Dic3—22no—
160C2×C3×Dic3C2×D411yescharacteristic
161C2×C3×Dic3C2×D411yescharacteristic
162C2×C3×Dic3C2×D411yescharacteristic
163C3×D12—24no—
164C3×D12—42no—
165C3×D12—42no—
166C3×C4×D3—22no—
167C3×C4×D3—22no—
168C3×C4×D3SD1614yescomplemented
169C3×Dic6—42no—
170#626—44no—
171#626—44no—
172#626—44no—
173C3⋊(C3⋊C8)—22no—
174C3×C3⋊C8—22no—
175#533—31no—
176C2×#127—91no—
177#492—31no—
178#492—91no—
179#486—91no—
180#486—91no—
181#460—94no—
182#450—94no—
183#431—91no—
184C23×D3—62no—
185C23×D3—62no—
186C2×C3×Q8—22no—
187C2×C3×Q8—61no—
188C2×C3×Q8C22×D312yes—
189C2×C3×Q8C22×D312yes—
190C2×C3×D4—32no—
191C2×C3×D4—61no—
192C2×C3×D4—61no—
193C22×C3×C4—31no—
194C22×C3×C4—31no—
195C22×C3×C4—31no—
196C2×#67—62no—
197C2×#67—62no—
198C2×#67—62no—
199D3×D4—124no—
200D3×D4—124no—
201D3×D4—124no—
202C2×D12—21no—
203C2×D12—21no—
204C2×D12—32no—
205C2×D12—32no—
206C2×D12—62no—
207C2×D12—62no—
208C2×D12—62no—
209C2×D12—62no—
210C2×D12—61no—
211C2×D12—61no—
212C2×D12—61no—
213C2×D12—61no—
214C2×D12—121no—
215C2×D12—121no—
216C2×D12—124no—
217C2×D12—124no—
218C2×D12—124no—
219C2×D12C22×D312yes—
220C2×C4×D3#6711yescharacteristic
221C2×C4×D3#6711yescharacteristic
222C2×C4×D3C22×D311yescharacteristic
223C2×Dic6—21no—
224C3×SD16—124no—
225C2×C3×C8—32no—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4—21no—
229C3×C4⋊C4—21no—
230C3×C4⋊C4—32no—
231C3×C4⋊C4—41no—
232C3×C4⋊C4—41no—
233C3×C4⋊C4—62no—
234C3×C4⋊C4—62no—
235C3×C4⋊C4—61no—
236C3×C22⋊C4—62no—
237C3×C42—21no—
238C3×C42—31no—
239C3×C42—31no—
240C3×C42—31no—
241C3×C42—62no—
242C3×C42C22×D311yescharacteristic
243C3×C42C22×D311yescharacteristic
244#215—44no—
245#215—124no—
246#215—124no—
247#215—128no—
248(C2×D3)⋊C4—22no—
249C4⋊Dic3—21no—
250C4⋊Dic3—22no—
251C4⋊Dic3C22×D312yes—
252Dic3⋊C4—22no—
253C4×Dic3—22no—
254C4×Dic3#6711yescharacteristic
255C4×Dic3#6711yescharacteristic
256C4×Dic3C22×D311yescharacteristic
257C2×C3⋊C8—32no—
258C2×C3⋊C8—32no—
259C2×C3⋊C8—62no—
260C2×C3⋊C8C22×D312yes—
261C22×C32C22×D411yescharacteristic
262C2×C3⋊D3—42no—
263C2×C3⋊D3—42no—
264C2×C3⋊D3—42no—
265C2×C3×D3—21no—
266C2×C3×D3—21no—
267C2×C3×D3—42no—
268C2×C3×D3—42no—
269C2×C3×D3—42no—
270C2×C3×D3C2×SD1612yes—
271D32—88no—
272C32×C4—42no—
273C32×C4C2×SD1612yes—
274C32×C4AGL(1,ℤ/8)12yes—
275C32×C4H(5,𝔽2)12yes—
276C3×Dic3—21no—
277C3×Dic3—21no—
278C3×Dic3—42no—
279C3×Dic3C2×SD1612yes—
280C22×D4—92no—
281C22×D4—181no—
282C22×D4—181no—
283C2×SD16—34no—
284C2×SD16—94no—
285C4⋊Q8—31no—
286C4⋊Q8D3211yescharacteristic, complemented
287#127—31no—
288#127—92no—
289#127—91no—
290#127—181no—
291#127—181no—
292#125—61no—
293C22⋊Q8—32no—
294C22⋊Q8—61no—
295C4×Q8—32no—
296C4×Q8—61no—
297#117—61no—
298C2×C42—31no—
299C4⋊C8—92no—
300#102—94no—
301#102—94no—
302C22⋊C8—92no—
303C4×C8—31no—
304C4×C8—91no—
305C23×C3—31no—
306C23×C3—62no—
307C22×D3—22no—
308C22×D3—62no—
309C22×D3—62no—
310C22×D3—122no—
311C22×D3—124no—
312C22×D3—124no—
313C22×D3—124no—
314C22×D3—124no—
315C22×D3—124no—
316C22×D3—124no—
317C22×D3C2×#6711yescharacteristic
318C3×Q8—24no—
319C3×Q8—24no—
320C3×Q8—44no—
321C3×Q8—122no—
322C3×D4—64no—
323C3×D4—122no—
324C3×D4—122no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—31no—
331C2×C3×C4—34no—
332C2×C3×C4—31no—
333C2×C3×C4—31no—
334C2×C3×C4—42no—
335C2×C3×C4—62no—
336C2×C3×C4—62no—
337C2×C3×C4—62no—
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4D3×D411yescharacteristic
340C2×C3×C4C2×#6711yescharacteristic
341C2×C3×C4C2×#6711yescharacteristic
342C2×C3×C4C23×D311yescharacteristic
343C2×C3×C4C23×D311yescharacteristic
344#67—124no—
345#67—124no—
346#67—124no—
347C2×Dic3—22no—
348C2×Dic3C2×#6711yescharacteristic
349C2×Dic3C2×#6711yescharacteristic
350C2×Dic3C2×#6711yescharacteristic
351D12—24no—
352D12—42no—
353D12—42no—
354D12—64no—
355D12—64no—
356D12—124no—
357D12—124no—
358D12—124no—
359D12—124no—
360D12—122no—
361D12—122no—
362D12—122no—
363D12—122no—
364D12—242no—
365D12—242no—
366C4×D3—22no—
367C4×D3—22no—
368C4×D3#21514yescomplemented
369Dic6—42no—
370C3×C8—62no—
371C3⋊C8—22no—
372C3⋊C8—64no—
373C3⋊C8—62no—
374C3⋊C8—62no—
375C2×C32#53511yescharacteristic
376C2×C32C22×SD1611yescharacteristic
377C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
378C3⋊D3—82no—
379C3×D3—22no—
380C3×D3—82no—
381C24—182no—
382C2×Q8—61no—
383C2×Q8C2×D3212yes—
384C2×D4—32no—
385C2×D4—61no—
386C2×D4—61no—
387C2×D4—92no—
388C2×D4—182no—
389C2×D4—182no—
390C2×D4—182no—
391C2×D4—181no—
392C2×D4—181no—
393C2×D4—364no—
394C2×D4—364no—
395C2×D4—364no—
396C22×C4—31no—
397C22×C4—31no—
398C22×C4—31no—
399SD16—124no—
400SD16—364no—
401C2×C8—32no—
402C2×C8—92no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—32no—
406C4⋊C4—62no—
407C4⋊C4—62no—
408C4⋊C4—61no—
409C22⋊C4—62no—
410C42—31no—
411C42—31no—
412C42—31no—
413C42—62no—
414C42C2×D3211yescharacteristic
415C22×C3—21no—
416C22×C3—32no—
417C22×C3—61no—
418C22×C3—61no—
419C22×C3—122no—
420C22×C3—122no—
421C22×C3—122no—
422C22×C3C2×D3×D411yescharacteristic
423C22×C3C22×#6711yescharacteristic
424C2×D3—21no—
425C2×D3—21no—
426C2×D3—42no—
427C2×D3—42no—
428C2×D3—42no—
429C2×D3—122no—
430C2×D3—122no—
431C2×D3—122no—
432C2×D3—122no—
433C2×D3—122no—
434C2×D3—122no—
435C2×D3—242no—
436C2×D3—242no—
437C2×D3—242no—
438C2×D3—248no—
439C2×D3—248no—
440C2×D3C2×#21512yes—
441C3×C4—22no—
442C3×C4—22no—
443C3×C4—22no—
444C3×C4—32no—
445C3×C4—42no—
446C3×C4—42no—
447C3×C4—61no—
448C3×C4—61no—
449C3×C4—82no—
450C3×C4—122no—
451C3×C4D3×SD1612yes—
452C3×C4#91412yes—
453C3×C4C2×#21512yes—
454C3×C4#94912yes—
455C3×C4#100412yes—
456C3×C4#100912yes—
457Dic3—21no—
458Dic3—21no—
459Dic3—42no—
460Dic3C2×#21512yes—
461C32#320811yescharacteristic, complemented, Sylow
462C23—31no—
463C23—62no—
464C23—182no—
465C23—364no—
466C23—364no—
467C23—364no—
468Q8—24no—
469Q8—122no—
470D4—64no—
471D4—122no—
472D4—122no—
473D4—184no—
474D4—364no—
475D4—364no—
476D4—364no—
477D4—362no—
478D4—362no—
479C2×C4—22no—
480C2×C4—31no—
481C2×C4—34no—
482C2×C4—31no—
483C2×C4—31no—
484C2×C4—62no—
485C2×C4—62no—
486C2×C4—62no—
487C2×C4D3×#6711yescharacteristic
488C2×C4D3×#6711yescharacteristic
489C2×C4C22×D3211yescharacteristic
490C8—62no—
491C8—182no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—62no—
496C2×C3—242no—
497C2×C3#571511yescharacteristic
498C2×C3C2×D3×SD1611yescharacteristic
499C2×C3C2×#91411yescharacteristic
500C2×C3C22×#21511yescharacteristic
501C2×C3C2×#94911yescharacteristic
502C2×C3#583011yescharacteristic
503D3—22no—
504D3—82no—
505D3—242no—
506D3—242no—
507D3—482no—
508C22—32no—
509C22—61no—
510C22—61no—
511C22—122no—
512C22—122no—
513C22—122no—
514C22—362no—
515C22—362no—
516C22—362no—
517C22—728no—
518C22C2×D3×#6711yescharacteristic
519C4—32no—
520C4—42no—
521C4—61no—
522C4—61no—
523C4—122no—
524C4D3×#21512yes—
525C4#6393912yes—
526C4#6431412yes—
527C3—21no—
528C3#8176611yescharacteristic, complemented
529C3#8335511yescharacteristic, complemented
530C2—62no—
531C2—242no—
532C2—722no—
533C2#1059530311yescharacteristic
534C2C2×D3×#21511yescharacteristic
535C2C2×#6393911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalD3×#874C2
hypercenterC4⋊Q8D32
hypocenterC32#3208
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5728C2semidirect
3. #10592784C2semidirect
4. C3×#5085C2semidirect
5. #10591651C2semidirect
6. #10591617C2semidirect
7. #10590281C2semidirect
8. #10590277C2semidirect
9. #10590261C2semidirect
15. C32×C4⋊Q8C22semidirect
16. C2×#3755C22semidirect
19. C3×Q8×Dic3C22semidirect
20. C2×C3×#215C22semidirect
27. C3×#869C22semidirect
31. C4×C3⋊(C3⋊C8)C22semidirect
32. C3×C4×C3⋊C8C22semidirect
33. Dic3⋊(C3⋊C8)C22semidirect
34. #63564C22semidirect
35. #63562C22semidirect
38. #5728D3semidirect
49. #5085D3semidirect
100. C3×C4⋊Q8C2×D3semidirect
101. C3×C4⋊Q8C2×D3semidirect
111. Q8×Dic3C2×D3semidirect
115. C2×#215C2×D3semidirect
131. #869C2×D3semidirect
144. C4×C3⋊C8C2×D3semidirect
168. C3×C4×D3SD16semidirect
286. C4⋊Q8D32semidirect
368. C4×D3#215semidirect
461. C32#3208semidirect
528. C3#81766semidirect
529. C3#83355semidirect

Maximal subgroups

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

subgroupindex
C3×#57282
D3×#8742
#105927842
C3×#50852
#105916512
#105916172
#105902812
#105902772
#105902612
#833553
#817663