Finite Group Databasebeta

← #11878842

Subgroups — #11878842

Order 1152.

1035 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#874C211yesmaximal, characteristic
2#10593859C211yesmaximal, characteristic, complemented
3#10592393C211yesmaximal, characteristic, complemented
4C3×#4693C211yesmaximal, characteristic, complemented
5C3×#4685C211yesmaximal, characteristic, complemented
6#10590942C214yesmaximal, complemented
7#10590799C214yesmaximal, complemented
8#10590373C211yesmaximal, characteristic, complemented
9#10590273C211yesmaximal, characteristic, complemented
10#81766—31nomaximal
11#79305—31nomaximal
12C2×D3×D12—21no—
13C2×D3×D12—21no—
14C2×D3×D12C2212yes—
15#64083C2211yescharacteristic
16#64078C2211yescharacteristic, complemented
17C2×C3×#204C2214yescomplemented
18C3×#874C2211yescharacteristic
19C3×C42×D3C2211yescharacteristic
20C3×#869C2211yescharacteristic, complemented
21#63911—21no—
22#63911—21no—
23#63911C2212yes—
24#63869—21no—
25#63857—21no—
26#63856C2212yes—
27#63844—21no—
28Dic3×Dic6C2212yescomplemented
29#63841—21no—
30C2×#3717C2214yescomplemented
31C32×C4×C8C2211yescharacteristic, complemented
32#63648C2214yescomplemented
33C3×(C2×D3)⋊C8C2212yes—
34C3×Dic3⋊C8C2212yescomplemented
35C3×C4×C3⋊C8C2211yescharacteristic, complemented
36#63563C2214yescomplemented
37#5728—31no—
38D3×#127—31no—
39C2×#874—31no—
40#5470—31no—
41C3×#492—31no—
42C3×#431—31no—
43#5169—34no—
44#5163—34no—
45#5085—31no—
46#5070—31no—
47#4848—34no—
48#4731—34no—
49#4694—31no—
50#4694—31no—
51#4694—31no—
52#4694—61no—
53#4693—31no—
54#4693D311yescharacteristic, complemented
55#4685D311yescharacteristic, complemented
56C22×D32—22no—
57C2×C4⋊(C3⋊D3)—21no—
58C2×C4⋊(C3⋊D3)—21no—
59C2×C4⋊(C3⋊D3)C2312yes—
60C2×#634—21no—
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×Dic6C2312yes—
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)C2312yes—
78C3×C4⋊Dic3—21no—
79C3×C4⋊Dic3—21no—
80C3×C4×Dic3D411yescharacteristic
81C3×C4×Dic3D411yescharacteristic
82C3×C4×Dic3C2311yescharacteristic
83C2×C3×C3⋊C8C2312yes—
84C3×#204—44no—
85#3724—22no—
86Dic3⋊Dic3—22no—
87(C2×D3)⋊Dic3—22no—
88Dic32—22no—
89#3717—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—
97C2×C3×SD16—34no—
98C3×C4⋊Q8—31no—
99C3×#127—31no—
100C2×C3×C42—31no—
101#946—32no—
102Q8×Dic3—32no—
103C2×#215—34no—
104#940—32no—
105#940—61no—
106#940—61no—
107#926—61no—
108#924—32no—
109#924—61no—
110C2×#204—34no—
111C2×#204C2×D314yescomplemented
112#897—61no—
113#892—61no—
114#890—61no—
115#887—61no—
116#874—32no—
117#874—31no—
118#874—31no—
119#874—61no—
120#874—61no—
121#874—61no—
122#874C2×D311yescharacteristic
123C42×D3C2×D311yescharacteristic
124#870—61no—
125#869—31no—
126#869—31no—
127#869—61no—
128#869C2×D311yescharacteristic, complemented
129C4×Dic6—32no—
130C4×Dic6—61no—
131C3×C4⋊C8—32no—
132C3×C22⋊C8—32no—
133C3×C4×C8—21no—
134C3×C4×C8—31no—
135C3×C4×C8C2×D311yescharacteristic, complemented
136C3×C4×C8C2×D311yescharacteristic, complemented
137#832—34no—
138#821—34no—
139#821—34no—
140#821—34no—
141#821—64no—
142(C2×D3)⋊C8C2×D312yes—
143Dic3⋊C8C2×D312yescomplemented
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—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—24no—
170#626—44no—
171#626—44no—
172#626—44no—
173C32×C8—22no—
174C3×C3⋊C8—22no—
175#533—91no—
176C2×#127—91no—
177#492—31no—
178#492—91no—
179#486—91no—
180#486—91no—
181#460—94no—
182#450—94no—
183#431—31no—
184C23×D3—62no—
185C23×D3—62no—
186C2×C3×Q8—32no—
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—61no—
221C2×Dic6—61no—
222C2×Dic6—121no—
223C2×Dic6C22×D312yes—
224C3×SD16—124no—
225C2×C3×C8—22no—
226C2×C3×C8—32no—
227C2×C3×C8C22×D312yes—
228C2×C3×C8C22×D312yes—
229C3×C4⋊C4—61no—
230C3×C4⋊C4—61no—
231C3×C42—21no—
232C3×C42—31no—
233C3×C42—31no—
234C3×C42—31no—
235C3×C42C22×D311yescharacteristic
236C3×C42C22×D311yescharacteristic
237#217—62no—
238#215—124no—
239(C2×D3)⋊C4—62no—
240C4⋊Dic3—21no—
241C4⋊Dic3—21no—
242C4⋊Dic3—32no—
243C4⋊Dic3—32no—
244C4⋊Dic3—62no—
245C4⋊Dic3—61no—
246C4⋊Dic3—61no—
247C4⋊Dic3—62no—
248C4⋊Dic3—121no—
249Dic3⋊C4—62no—
250Dic3⋊C4—62no—
251Dic3⋊C4—62no—
252C4×Dic3—62no—
253C4×Dic3—62no—
254C4×Dic3D1211yescharacteristic
255C4×Dic3D1211yescharacteristic
256C4×Dic3C22×D311yescharacteristic
257C2×C3⋊C8C22×D312yes—
258#204—44no—
259#204—124no—
260C22×C32C22×D411yescharacteristic
261C2×C3⋊D3—42no—
262C2×C3⋊D3—42no—
263C2×C3⋊D3—42no—
264C2×C3×D3—21no—
265C2×C3×D3—21no—
266C2×C3×D3—42no—
267C2×C3×D3—42no—
268C2×C3×D3—42no—
269C2×C3×D3C2×SD1612yes—
270D32—88no—
271C32×C4C2×SD1612yes—
272C32×C4AGL(1,ℤ/8)12yes—
273C32×C4H(5,𝔽2)12yes—
274C3⋊Dic3—42no—
275C3×Dic3—21no—
276C3×Dic3—21no—
277C3×Dic3—42no—
278C3×Dic3C2×SD1612yes—
279C22×D4—92no—
280C22×D4—181no—
281C22×D4—181no—
282C2×SD16—34no—
283C2×SD16—94no—
284C4⋊Q8—31no—
285C4⋊Q8—91no—
286#127—31no—
287#127—92no—
288#127—91no—
289#127—181no—
290#127—181no—
291#125—181no—
292C22⋊Q8—92no—
293C22⋊Q8—181no—
294C4×Q8—92no—
295C4×Q8—181no—
296#117—181no—
297C2×C42—31no—
298C4⋊C8—32no—
299#102—94no—
300#102—94no—
301C22⋊C8—32no—
302C4×C8—31no—
303C4×C8D3211yescharacteristic, complemented
304C23×C3—31no—
305C23×C3—62no—
306C22×D3—22no—
307C22×D3—62no—
308C22×D3—62no—
309C22×D3—122no—
310C22×D3—124no—
311C22×D3—124no—
312C22×D3—124no—
313C22×D3—124no—
314C22×D3—124no—
315C22×D3—124no—
316C22×D3C2×D1211yescharacteristic
317C3×Q8—64no—
318C3×D4—64no—
319C3×D4—122no—
320C3×D4—122no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—31no—
325C2×C3×C4—34no—
326C2×C3×C4—31no—
327C2×C3×C4—31no—
328C2×C3×C4—62no—
329C2×C3×C4—62no—
330C2×C3×C4—62no—
331C2×C3×C4C2×D1211yescharacteristic
332C2×C3×C4C2×D1211yescharacteristic
333C2×C3×C4D3×D411yescharacteristic
334C2×C3×C4D3×D411yescharacteristic
335C2×C3×C4C23×D311yescharacteristic
336C2×C3×C4C23×D311yescharacteristic
337#67—124no—
338#67—124no—
339#67—124no—
340C2×Dic3—22no—
341C2×Dic3—62no—
342C2×Dic3—62no—
343C2×Dic3—122no—
344C2×Dic3C2×D1211yescharacteristic
345C2×Dic3C2×D1211yescharacteristic
346C2×Dic3C2×D1211yescharacteristic
347D12—24no—
348D12—42no—
349D12—42no—
350D12—64no—
351D12—64no—
352D12—124no—
353D12—124no—
354D12—124no—
355D12—124no—
356D12—122no—
357D12—122no—
358D12—122no—
359D12—122no—
360D12—242no—
361D12—242no—
362C4×D3—22no—
363C4×D3—22no—
364C4×D3#20414yescomplemented
365Dic6—24no—
366Dic6—122no—
367Dic6—122no—
368Dic6—242no—
369C3×C8—22no—
370C3×C8—22no—
371C3×C8—42no—
372C3×C8—62no—
373C3⋊C8—22no—
374C2×C32#53511yescharacteristic
375C2×C32C22×SD1611yescharacteristic
376C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
377C3⋊D3—82no—
378C3×D3—22no—
379C3×D3—82no—
380C24—182no—
381C2×Q8—32no—
382C2×Q8—181no—
383C2×D4—32no—
384C2×D4—61no—
385C2×D4—61no—
386C2×D4—92no—
387C2×D4—182no—
388C2×D4—182no—
389C2×D4—182no—
390C2×D4—181no—
391C2×D4—181no—
392C2×D4—364no—
393C2×D4—364no—
394C2×D4—364no—
395C22×C4—31no—
396C22×C4—31no—
397C22×C4—31no—
398SD16—124no—
399SD16—364no—
400C2×C8—32no—
401C2×C8C2×D3212yes—
402C4⋊C4—61no—
403C4⋊C4—61no—
404C4⋊C4—92no—
405C4⋊C4—182no—
406C4⋊C4—182no—
407C4⋊C4—181no—
408C22⋊C4—182no—
409C42—31no—
410C42—31no—
411C42—31no—
412C42—182no—
413C42C2×D3211yescharacteristic
414C22×C3—21no—
415C22×C3—32no—
416C22×C3—61no—
417C22×C3—61no—
418C22×C3—122no—
419C22×C3—122no—
420C22×C3—122no—
421C22×C3C22×D1211yescharacteristic
422C22×C3C2×D3×D411yescharacteristic
423C2×D3—21no—
424C2×D3—21no—
425C2×D3—42no—
426C2×D3—42no—
427C2×D3—42no—
428C2×D3—122no—
429C2×D3—122no—
430C2×D3—122no—
431C2×D3—122no—
432C2×D3—122no—
433C2×D3—122no—
434C2×D3—242no—
435C2×D3—242no—
436C2×D3—242no—
437C2×D3—248no—
438C2×D3—248no—
439C2×D3C2×#20412yes—
440C3×C4—22no—
441C3×C4—22no—
442C3×C4—22no—
443C3×C4—32no—
444C3×C4—61no—
445C3×C4—61no—
446C3×C4—122no—
447C3×C4C2×#20412yes—
448C3×C4#90812yes—
449C3×C4D3×SD1612yes—
450C3×C4#91412yes—
451C3×C4#100412yes—
452C3×C4#100912yes—
453Dic3—21no—
454Dic3—21no—
455Dic3—42no—
456Dic3—122no—
457Dic3—122no—
458Dic3—242no—
459Dic3C2×#20412yes—
460C32#320811yescharacteristic, complemented, Sylow
461C23—31no—
462C23—62no—
463C23—182no—
464C23—364no—
465C23—364no—
466C23—364no—
467Q8—64no—
468Q8—362no—
469D4—64no—
470D4—122no—
471D4—122no—
472D4—184no—
473D4—364no—
474D4—364no—
475D4—364no—
476D4—362no—
477D4—362no—
478C2×C4—31no—
479C2×C4—34no—
480C2×C4—31no—
481C2×C4—31no—
482C2×C4—62no—
483C2×C4—62no—
484C2×C4—62no—
485C2×C4—182no—
486C2×C4D3×D1211yescharacteristic
487C2×C4D3×D1211yescharacteristic
488C2×C4C22×D3211yescharacteristic
489C8—22no—
490C8—62no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—62no—
495C2×C3—242no—
496C2×C3#552511yescharacteristic
497C2×C3#571511yescharacteristic
498C2×C3C22×#20411yescharacteristic
499C2×C3C2×#90811yescharacteristic
500C2×C3C2×D3×SD1611yescharacteristic
501C2×C3C2×#91411yescharacteristic
502D3—22no—
503D3—82no—
504D3—242no—
505D3—242no—
506D3—482no—
507C22—32no—
508C22—61no—
509C22—61no—
510C22—122no—
511C22—122no—
512C22—122no—
513C22—362no—
514C22—362no—
515C22—362no—
516C22—728no—
517C22C2×D3×D1211yescharacteristic
518C4—32no—
519C4—61no—
520C4—61no—
521C4—122no—
522C4—362no—
523C4D3×#20412yes—
524C4#6379412yes—
525C4#6430712yes—
526C3—21no—
527C3#7930511yescharacteristic, complemented
528C3#8176611yescharacteristic, complemented
529C2—62no—
530C2—242no—
531C2—722no—
532C2#1059400011yescharacteristic
533C2C2×D3×#20411yescharacteristic
534C2C2×#6379411yescharacteristic
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. #10592393C2semidirect
4. C3×#4693C2semidirect
5. C3×#4685C2semidirect
6. #10590942C2semidirect
7. #10590799C2semidirect
8. #10590373C2semidirect
9. #10590273C2semidirect
16. #64078C22semidirect
17. C2×C3×#204C22semidirect
20. C3×#869C22semidirect
28. Dic3×Dic6C22semidirect
30. C2×#3717C22semidirect
31. C32×C4×C8C22semidirect
32. #63648C22semidirect
34. C3×Dic3⋊C8C22semidirect
35. C3×C4×C3⋊C8C22semidirect
36. #63563C22semidirect
54. #4693D3semidirect
55. #4685D3semidirect
111. C2×#204C2×D3semidirect
128. #869C2×D3semidirect
135. C3×C4×C8C2×D3semidirect
136. C3×C4×C8C2×D3semidirect
143. Dic3⋊C8C2×D3semidirect
144. C4×C3⋊C8C2×D3semidirect
168. C3×C4×D3SD16semidirect
303. C4×C8D32semidirect
364. C4×D3#204semidirect
460. C32#3208semidirect
527. C3#79305semidirect
528. C3#81766semidirect

Maximal subgroups

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

subgroupindex
D3×#8742
#105938592
#105923932
C3×#46932
C3×#46852
#105909422
#105907992
#105903732
#105902732
#817663
#793053