Finite Group Databasebeta

← #11878840

Subgroups — #11878840

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
1D3×#874C211yesmaximal, characteristic
2#10593859C211yesmaximal, characteristic, complemented
3#10592392C211yesmaximal, characteristic, complemented
4C3×#4694C211yesmaximal, characteristic, complemented
5C3×#4685C211yesmaximal, characteristic, complemented
6#10590946C214yesmaximal, complemented
7#10590879C214yesmaximal, complemented
8#10590369C211yesmaximal, characteristic, complemented
9#10590281C211yesmaximal, characteristic, complemented
10#81568—31nomaximal
11#79305—31nomaximal
12C2×D3×D12—21no—
13C2×D3×D12—21no—
14C2×D3×D12C2212yes—
15C2×#3744C2214yescomplemented
16#64083C2211yescharacteristic
17#64078C2211yescharacteristic, complemented
18C3×#874C2211yescharacteristic
19C3×C42×D3C2211yescharacteristic
20C3×#869C2211yescharacteristic, complemented
21#63911—21no—
22#63911—21no—
23#63911C2212yes—
24#63869—21no—
25#63857C2212yes—
26#63856—21no—
27#63844C2212yescomplemented
28Dic3×Dic6—21no—
29#63841—21no—
30C2×#3716C2214yescomplemented
31C32×C4×C8C2211yescharacteristic, complemented
32C3×#821C2214yescomplemented
33C3×(C2×D3)⋊C8C2212yes—
34C3×Dic3⋊C8C2212yescomplemented
35C3×C4×C3⋊C8C2211yescharacteristic, complemented
36#63564C2214yescomplemented
37#5728—31no—
38D3×#127—31no—
39C2×#874—31no—
40#5470—31no—
41C3×#486—31no—
42C3×#431—31no—
43#5088—31no—
44#5076—31no—
45#4848—34no—
46#4776—34no—
47#4762—34no—
48#4731—34no—
49#4694—31no—
50#4694D311yescharacteristic, complemented
51#4693—31no—
52#4693—31no—
53#4693—31no—
54#4693—61no—
55#4685D311yescharacteristic, complemented
56C22×D32—22no—
57C2×C4⋊(C3⋊D3)—21no—
58C2×C4⋊(C3⋊D3)—21no—
59C2×C4⋊(C3⋊D3)C2312yes—
60C2×#634C2312yes—
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—
74C2×C32×C8C2312yes—
75C32×C42C2311yescharacteristic
76C4⋊(C3⋊Dic3)—21no—
77C4⋊(C3⋊Dic3)—21no—
78#3744—44no—
79C3×C4⋊Dic3—21no—
80C3×C4⋊Dic3C2312yes—
81C3×C4×Dic3D411yescharacteristic
82C3×C4×Dic3D411yescharacteristic
83C3×C4×Dic3C2311yescharacteristic
84C2×C3×C3⋊C8C2312yes—
85#3724—22no—
86Dic3⋊Dic3—22no—
87(C2×D3)⋊Dic3—22no—
88Dic32—22no—
89#3716—44no—
90#3208—91noSylow
91C2×D3×D4—32no—
92C2×D3×D4—61no—
93C2×D3×D4—61no—
94C22×D12—32no—
95C22×D12—61no—
96C22×D12—61no—
97C3×C4⋊Q8—31no—
98C3×#127—31no—
99C2×C3×C42—31no—
100#946—61no—
101Q8×Dic3—61no—
102#940—32no—
103#940—61no—
104#940—61no—
105C2×#214—34no—
106#926—61no—
107#924—32no—
108#924—61no—
109C2×#204—34no—
110C2×#204—34no—
111C2×#204—34no—
112C2×#204—64no—
113#897—32no—
114#892—61no—
115#890—61no—
116#887—32no—
117#874—32no—
118#874—31no—
119#874—31no—
120#874—61no—
121#874—61no—
122#874—61no—
123#874C2×D311yescharacteristic
124C42×D3C2×D311yescharacteristic
125#870—61no—
126#869—31no—
127#869—31no—
128#869—61no—
129#869C2×D311yescharacteristic, complemented
130C4×Dic6—32no—
131C4×Dic6—61no—
132C3×C4⋊C8—32no—
133C3×#102—34no—
134C3×C22⋊C8—32no—
135C3×C4×C8—21no—
136C3×C4×C8—31no—
137C3×C4×C8C2×D311yescharacteristic, complemented
138C3×C4×C8C2×D311yescharacteristic, complemented
139#821—34no—
140#821C2×D314yescomplemented
141(C2×D3)⋊C8C2×D312yes—
142Dic3⋊C8C2×D312yescomplemented
143#809—34no—
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—
151C2×C32×C4C2×D411yescharacteristic
152C2×C32×C4C2×D411yescharacteristic
153C2×C32×C4C2411yescharacteristic
154C2×C3⋊Dic3—22no—
155C4⋊(C3⋊D3)—24no—
156C4⋊(C3⋊D3)—42no—
157C4⋊(C3⋊D3)—42no—
158#634—24no—
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—
173C32×C8—22no—
174C3×C3⋊C8—22no—
175#533—91no—
176C2×#127—91no—
177#492—91no—
178#492—91no—
179#486—31no—
180#486—91no—
181#460—94no—
182#450—94no—
183#431—31no—
184C23×D3—62no—
185C23×D3—62no—
186C2×C3×Q8—61no—
187C2×C3×D4—32no—
188C2×C3×D4—61no—
189C2×C3×D4—61no—
190C22×C3×C4—31no—
191C22×C3×C4—31no—
192C22×C3×C4—31no—
193C2×#67—62no—
194C2×#67—62no—
195C2×#67—62no—
196D3×D4—124no—
197D3×D4—124no—
198D3×D4—124no—
199C2×D12—21no—
200C2×D12—21no—
201C2×D12—32no—
202C2×D12—32no—
203C2×D12—62no—
204C2×D12—62no—
205C2×D12—62no—
206C2×D12—62no—
207C2×D12—61no—
208C2×D12—61no—
209C2×D12—61no—
210C2×D12—61no—
211C2×D12—121no—
212C2×D12—121no—
213C2×D12—124no—
214C2×D12—124no—
215C2×D12—124no—
216C2×D12C22×D312yes—
217C2×C4×D3D1211yescharacteristic
218C2×C4×D3D1211yescharacteristic
219C2×C4×D3C22×D311yescharacteristic
220C2×Dic6—21no—
221C2×Dic6—32no—
222C2×Dic6—32no—
223C2×Dic6—62no—
224C2×C3×C8—22no—
225C2×C3×C8—32no—
226C2×C3×C8C22×D312yes—
227C2×C3×C8C22×D312yes—
228C3×C4⋊C4—32no—
229C3×C4⋊C4—61no—
230C3×C42—21no—
231C3×C42—31no—
232C3×C42—31no—
233C3×C42—31no—
234C3×C42C22×D311yescharacteristic
235C3×C42C22×D311yescharacteristic
236#217—62no—
237#214—124no—
238(C2×D3)⋊C4—62no—
239C4⋊Dic3—21no—
240C4⋊Dic3—61no—
241C4⋊Dic3—61no—
242C4⋊Dic3—61no—
243C4⋊Dic3—61no—
244C4⋊Dic3—62no—
245C4⋊Dic3—121no—
246C4⋊Dic3—121no—
247C4⋊Dic3C22×D312yes—
248Dic3⋊C4—62no—
249Dic3⋊C4—62no—
250Dic3⋊C4—62no—
251C4×Dic3—62no—
252C4×Dic3—62no—
253C4×Dic3D1211yescharacteristic
254C4×Dic3D1211yescharacteristic
255C4×Dic3C22×D311yescharacteristic
256C2×C3⋊C8C22×D312yes—
257#204—124no—
258#204—124no—
259#204—128no—
260#204—124no—
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×C4C2×SD1612yes—
273C32×C4AGL(1,ℤ/8)12yes—
274C32×C4H(5,𝔽2)12yes—
275C3⋊Dic3—42no—
276C3×Dic3—21no—
277C3×Dic3—21no—
278C3×Dic3—42no—
279C3×Dic3C2×SD1612yes—
280C22×D4—92no—
281C22×D4—181no—
282C22×D4—181no—
283C2×SD16—94no—
284C2×SD16—94no—
285C4⋊Q8—31no—
286C4⋊Q8—91no—
287#127—31no—
288#127—92no—
289#127—91no—
290#127—181no—
291#127—181no—
292#125—181no—
293C22⋊Q8—92no—
294C22⋊Q8—181no—
295C4×Q8—92no—
296C4×Q8—181no—
297#117—181no—
298C2×C42—31no—
299C4⋊C8—32no—
300#102—34no—
301#102—94no—
302C22⋊C8—32no—
303C4×C8—31no—
304C4×C8D3211yescharacteristic, complemented
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×D1211yescharacteristic
318C3×Q8—122no—
319C3×D4—64no—
320C3×D4—122no—
321C3×D4—122no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—31no—
326C2×C3×C4—34no—
327C2×C3×C4—31no—
328C2×C3×C4—31no—
329C2×C3×C4—62no—
330C2×C3×C4—62no—
331C2×C3×C4—62no—
332C2×C3×C4C2×D1211yescharacteristic
333C2×C3×C4C2×D1211yescharacteristic
334C2×C3×C4D3×D411yescharacteristic
335C2×C3×C4D3×D411yescharacteristic
336C2×C3×C4C23×D311yescharacteristic
337C2×C3×C4C23×D311yescharacteristic
338#67—124no—
339#67—124no—
340#67—124no—
341C2×Dic3—22no—
342C2×Dic3—62no—
343C2×Dic3—62no—
344C2×Dic3—122no—
345C2×Dic3C2×D1211yescharacteristic
346C2×Dic3C2×D1211yescharacteristic
347C2×Dic3C2×D1211yescharacteristic
348D12—24no—
349D12—42no—
350D12—42no—
351D12—64no—
352D12—64no—
353D12—124no—
354D12—124no—
355D12—124no—
356D12—124no—
357D12—122no—
358D12—122no—
359D12—122no—
360D12—122no—
361D12—242no—
362D12—242no—
363C4×D3—22no—
364C4×D3—22no—
365C4×D3#20414yescomplemented
366Dic6—42no—
367Dic6—64no—
368Dic6—64no—
369Dic6—124no—
370C3×C8—24no—
371C3×C8—22no—
372C3×C8—22no—
373C3×C8—62no—
374C3⋊C8—22no—
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×Q8—92no—
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—364no—
400SD16—364no—
401C2×C8—32no—
402C2×C8C2×D3212yes—
403C4⋊C4—32no—
404C4⋊C4—61no—
405C4⋊C4—182no—
406C4⋊C4—182no—
407C4⋊C4—181no—
408C4⋊C4—181no—
409C22⋊C4—182no—
410C42—31no—
411C42—31no—
412C42—31no—
413C42—182no—
414C42C2×D3211yescharacteristic
415C22×C3—21no—
416C22×C3—32no—
417C22×C3—61no—
418C22×C3—61no—
419C22×C3—122no—
420C22×C3—122no—
421C22×C3—122no—
422C22×C3C22×D1211yescharacteristic
423C22×C3C2×D3×D411yescharacteristic
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×#20412yes—
441C3×C4—22no—
442C3×C4—22no—
443C3×C4—22no—
444C3×C4—32no—
445C3×C4—61no—
446C3×C4—61no—
447C3×C4—122no—
448C3×C4C2×#20412yes—
449C3×C4#90812yes—
450C3×C4#91112yes—
451C3×C4D3×SD1612yes—
452C3×C4#100912yes—
453C3×C4#100912yes—
454Dic3—21no—
455Dic3—21no—
456Dic3—42no—
457Dic3—122no—
458Dic3—122no—
459Dic3—242no—
460Dic3C2×#20412yes—
461C32#320811yescharacteristic, complemented, Sylow
462C23—31no—
463C23—62no—
464C23—182no—
465C23—364no—
466C23—364no—
467C23—364no—
468Q8—122no—
469Q8—184no—
470D4—64no—
471D4—122no—
472D4—122no—
473D4—184no—
474D4—364no—
475D4—364no—
476D4—364no—
477D4—362no—
478D4—362no—
479C2×C4—31no—
480C2×C4—34no—
481C2×C4—31no—
482C2×C4—31no—
483C2×C4—62no—
484C2×C4—62no—
485C2×C4—62no—
486C2×C4—182no—
487C2×C4D3×D1211yescharacteristic
488C2×C4D3×D1211yescharacteristic
489C2×C4C22×D3211yescharacteristic
490C8—22no—
491C8—62no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—62no—
496C2×C3—242no—
497C2×C3#552511yescharacteristic
498C2×C3#567411yescharacteristic
499C2×C3C22×#20411yescharacteristic
500C2×C3C2×#90811yescharacteristic
501C2×C3C2×#91111yescharacteristic
502C2×C3C2×D3×SD1611yescharacteristic
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×D1211yescharacteristic
519C4—32no—
520C4—61no—
521C4—61no—
522C4—122no—
523C4—362no—
524C4D3×#20412yes—
525C4#6379512yes—
526C4#6430812yes—
527C3—21no—
528C3#7930511yescharacteristic, complemented
529C3#8156811yescharacteristic, complemented
530C2—62no—
531C2—242no—
532C2—722no—
533C2#1059400111yescharacteristic
534C2C2×D3×#20411yescharacteristic
535C2C2×#6379511yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radicalD3×#874C2
hypercenterC4×C8D32
hypocenterC32#3208
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. #10593859C2semidirect
3. #10592392C2semidirect
4. C3×#4694C2semidirect
5. C3×#4685C2semidirect
6. #10590946C2semidirect
7. #10590879C2semidirect
8. #10590369C2semidirect
9. #10590281C2semidirect
15. C2×#3744C22semidirect
17. #64078C22semidirect
20. C3×#869C22semidirect
27. #63844C22semidirect
30. C2×#3716C22semidirect
31. C32×C4×C8C22semidirect
32. C3×#821C22semidirect
34. C3×Dic3⋊C8C22semidirect
35. C3×C4×C3⋊C8C22semidirect
36. #63564C22semidirect
50. #4694D3semidirect
55. #4685D3semidirect
129. #869C2×D3semidirect
137. C3×C4×C8C2×D3semidirect
138. C3×C4×C8C2×D3semidirect
140. #821C2×D3semidirect
142. Dic3⋊C8C2×D3semidirect
144. C4×C3⋊C8C2×D3semidirect
168. C3×C4×D3SD16semidirect
304. C4×C8D32semidirect
365. C4×D3#204semidirect
461. C32#3208semidirect
528. C3#79305semidirect
529. C3#81568semidirect

Maximal subgroups

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

subgroupindex
D3×#8742
#105938592
#105923922
C3×#46942
C3×#46852
#105909462
#105908792
#105903692
#105902812
#815683
#793053