Finite Group Databasebeta

← #11868983

Subgroups — #11868983

Order 1152.

891 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5798C211yesmaximal, characteristic
2#10595051C211yesmaximal, characteristic, complemented
3#10592914C211yesmaximal, characteristic
4C2×C3×#832C211yesmaximal, characteristic
5#10591411C212yesmaximal, complemented
6#10591410C212yesmaximal, complemented
7#10591409C212yesmaximal, complemented
8#10591408C212yesmaximal, complemented
9#10591139C211yesmaximal, characteristic, complemented
10#10591122C211yesmaximal, characteristic, complemented
11#10591116C211yesmaximal, characteristic, complemented
12#82539—31nomaximal
13#78731—31nomaximal
14C22×C32×D4C2211yescharacteristic
15#64135C2211yescharacteristic
16C2×#3748C2211yescharacteristic
17C2×C3×#217—22no—
18C3×D4×Dic3—21no—
19C3×D4×Dic3—21no—
20C3×D4×Dic3C2212yes—
21C3×D4×Dic3C2212yes—
22C3×#926C2211yescharacteristic
23C3×#926C2211yescharacteristic
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26#63964—22no—
27#63919—21no—
28#63918C2212yescomplemented
29#63872—21no—
30#63869C2212yescomplemented
31#63659C2212yes—
32#63659C2212yes—
33C3×#832C2212yes—
34C3×#832C2212yes—
35#63576C2212yescomplemented
36#63575C2211yescharacteristic, complemented
37#63575C2211yescharacteristic, complemented
38#63574C2212yescomplemented
39#63573C2211yescharacteristic, complemented
40#63573C2211yescharacteristic, complemented
41Dic3⋊(C3⋊C8)C2212yescomplemented
42Dic3⋊(C3⋊C8)C2212yescomplemented
43C3×#518—31no—
44#5798D311yescharacteristic
45#5519—31no—
46#5500—31no—
47C2×C3×#102—31no—
48#5215—31no—
49#5215—31no—
50#5215—61no—
51C2×#832D311yescharacteristic
52#5106—31no—
53#5102—31no—
54#5009—32no—
55#5009—32no—
56#5008—32no—
57#5007—32no—
58#4999—31no—
59#4998—31no—
60#4995—31no—
61#4964—31no—
62#4766—32no—
63#4763—32no—
64#4761—32no—
65#4759—32no—
66C24×C32—21no—
67C2×C32×D4—21no—
68C2×C32×D4—22no—
69C2×C32×D4Q814yescomplemented
70C2×C32×D4C2312yes—
71C22×C32×C4C2311yescharacteristic
72C22×C3×Dic3—21no—
73C22×C3×Dic3—22no—
74C22×C3×Dic3—22no—
75C2×#627—22no—
76#3757—21no—
77C4⋊(C3⋊Dic3)C2311yescharacteristic
78C4⋊(C3⋊Dic3)C2311yescharacteristic
79C4×C3⋊Dic3—21no—
80#3748—22no—
81C2×C3⋊(C3⋊C8)C2312yes—
82C3×#217—21no—
83C3×#217—22no—
84C3×#217—22no—
85C3×#217D412yes—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3D411yescharacteristic
88C3×C4⋊Dic3D411yescharacteristic
89C3×C4⋊Dic3C2312yes—
90C3×C4⋊Dic3C2311yescharacteristic
91C3×C4⋊Dic3C2311yescharacteristic
92C3×C4×Dic3—21no—
93C3×C4×Dic3C2312yes—
94C2×C3×C3⋊C8—22no—
95C2×C3×C3⋊C8C2311yescharacteristic
96C2×C3×C3⋊C8C2311yescharacteristic
97#3724—22no—
98Dic3⋊Dic3—22no—
99Dic3⋊Dic3—22no—
100#3081—91noSylow
101C22×C3×D4—21no—
102C22×C3×D4C2×D311yescharacteristic
103C22×C3×D4C2×D311yescharacteristic
104C22×C3×C8—31no—
105C3×C4×D4—32no—
106C3×C4×D4—32no—
107C3×C4×D4—61no—
108C3×C4×D4—61no—
109C3×#117—31no—
110C3×#117—31no—
111C2×C3×C4⋊C4—31no—
112C2×C3×C22⋊C4—62no—
113C2×#217—22no—
114D4×Dic3—21no—
115D4×Dic3—21no—
116D4×Dic3C2×D312yes—
117D4×Dic3C2×D312yes—
118#926—31no—
119#926—31no—
120#926—61no—
121#926C2×D311yescharacteristic
122#926C2×D311yescharacteristic
123C2×C4⋊Dic3C2×D311yescharacteristic
124#924—62no—
125C2×#208—31no—
126C2×#208—31no—
127C2×#208—61no—
128C22×C3⋊C8C2×D311yescharacteristic
129#890—32no—
130#890—61no—
131#890—61no—
132#888—32no—
133#888—61no—
134#888—61no—
135#878—62no—
136#870—32no—
137#869—32no—
138C3×#102—32no—
139C3×#102—32no—
140#832—32no—
141#832—32no—
142#832—32no—
143#832—32no—
144#832—62no—
145#832—62no—
146#832C2×D312yes—
147#832C2×D312yes—
148#818—31no—
149#818—31no—
150#817—31no—
151#817—31no—
152Dic3⋊C8—32no—
153Dic3⋊C8—32no—
154#808—32no—
155#808—32no—
156#808—31no—
157#808—31no—
158#807—32no—
159#807—32no—
160#807—31no—
161#807—31no—
162C4⋊(C3⋊C8)—32no—
163C4⋊(C3⋊C8)—32no—
164C23×C32—22no—
165C23×C32—24no—
166C23×C32—81no—
167C23×C32—81no—
168C23×C32C2×D411yescharacteristic
169C32×D4—24no—
170C32×D4—22no—
171C32×D4C2×Q814yes—
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2×Q812yes—
174C2×C32×C4#4112yes—
175C2×C32×C4C2411yescharacteristic
176C2×C3⋊Dic3—21no—
177C2×C3⋊Dic3—21no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—21no—
180C2×C3×Dic3—21no—
181C2×C3×Dic3—82no—
182C2×C3×Dic3—82no—
183C2×C3×Dic3—81no—
184C2×C3×Dic3C2×D412yes—
185C2×C3×Dic3C2×D412yes—
186#627—82no—
187C3⋊(C3⋊C8)—22no—
188C3×C3⋊C8—21no—
189C3×C3⋊C8—21no—
190#544—91no—
191#518—31no—
192#478—92no—
193#478—92no—
194#476—92no—
195#474—92no—
196#428—91no—
197#427—91no—
198#424—91no—
199#418—91no—
200C2×#102—31no—
201C24×C3—21no—
202C24×C3—21no—
203C24×C3—41no—
204C2×C3×D4—22no—
205C2×C3×D4—21no—
206C2×C3×D4—22no—
207C2×C3×D4—21no—
208C2×C3×D4—24no—
209C2×C3×D4—22no—
210C2×C3×D4—42no—
211C2×C3×D4—41no—
212C2×C3×D4Dic614yescomplemented
213C2×C3×D4Dic614yescomplemented
214C2×C3×D4C22×D312yes—
215C2×C3×D4C22×D312yes—
216C22×C3×C4—21no—
217C22×C3×C4—62no—
218C22×C3×C4—62no—
219C22×C3×C4—61no—
220C22×C3×C4C22×D311yescharacteristic
221C22×C3×C4C22×D311yescharacteristic
222C22×Dic3—21no—
223C22×Dic3—22no—
224C22×Dic3—22no—
225C2×Dic6—62no—
226C2×Dic6—62no—
227C2×C3×C8—31no—
228C2×C3×C8—31no—
229C2×C3×C8—62no—
230C3×C4⋊C4—31no—
231C3×C4⋊C4—31no—
232C3×C4⋊C4—31no—
233C3×C4⋊C4—31no—
234C3×C4⋊C4—32no—
235C3×C4⋊C4—61no—
236C3×C22⋊C4—32no—
237C3×C22⋊C4—62no—
238C3×C22⋊C4—62no—
239C3×C22⋊C4—61no—
240C3×C42—32no—
241C3×C42—61no—
242#217—21no—
243#217—22no—
244#217—22no—
245#217—61no—
246#217—61no—
247#217—121no—
248#217#6712yes—
249C4⋊Dic3—21no—
250C4⋊Dic3—31no—
251C4⋊Dic3—31no—
252C4⋊Dic3—31no—
253C4⋊Dic3—31no—
254C4⋊Dic3—61no—
255C4⋊Dic3—61no—
256C4⋊Dic3—62no—
257C4⋊Dic3—62no—
258C4⋊Dic3#6711yescharacteristic
259C4⋊Dic3#6711yescharacteristic
260C4⋊Dic3C22×D311yescharacteristic
261C4⋊Dic3C22×D312yes—
262C4⋊Dic3C22×D311yescharacteristic
263Dic3⋊C4—62no—
264Dic3⋊C4—62no—
265Dic3⋊C4—62no—
266Dic3⋊C4—62no—
267C4×Dic3—21no—
268C4×Dic3—61no—
269C4×Dic3—61no—
270C4×Dic3—121no—
271C4×Dic3C22×D312yes—
272#208—62no—
273#208—62no—
274#208—122no—
275C2×C3⋊C8—22no—
276C2×C3⋊C8—32no—
277C2×C3⋊C8—32no—
278C2×C3⋊C8—62no—
279C2×C3⋊C8C22×D311yescharacteristic
280C2×C3⋊C8C22×D311yescharacteristic
281C22×C32—21no—
282C22×C32—21no—
283C22×C32—24no—
284C22×C32—42no—
285C22×C32—42no—
286C22×C32—84no—
287C22×C32C22⋊Q812yes—
288C22×C32C22×D411yescharacteristic
289C32×C4C22⋊Q812yes—
290C32×C4C22×Q811yescharacteristic
291C32×C4C2×#4111yescharacteristic
292C3⋊Dic3—41no—
293C3⋊Dic3—41no—
294C3×Dic3—22no—
295C3×Dic3—22no—
296C3×Dic3—42no—
297C3×Dic3—41no—
298C3×Dic3—41no—
299C22×D4D3211yescharacteristic
300C2×M16—91no—
301C22×C8—31no—
302C4⋊Q8—92no—
303C4⋊Q8—181no—
304#125—92no—
305#125—181no—
306C22⋊Q8—182no—
307C4×D4—32no—
308C4×D4—32no—
309C4×D4—61no—
310C4×D4—61no—
311#117—31no—
312#117—31no—
313#117—91no—
314C2×C4⋊C4—31no—
315C2×C22⋊C4—62no—
316#107—92no—
317#107—91no—
318#107—91no—
319#106—92no—
320#106—91no—
321#106—91no—
322C4⋊C8—92no—
323C4⋊C8—92no—
324#102—32no—
325#102—32no—
326#102—92no—
327#102—92no—
328C23×C3—22no—
329C23×C3—22no—
330C23×C3—24no—
331C23×C3—24no—
332C23×C3—21no—
333C23×C3—42no—
334C23×C3—44no—
335C23×C3—81no—
336C23×C3—81no—
337C23×C3—81no—
338C23×C3—81no—
339C23×C3—82no—
340C23×C3—82no—
341C23×C3D3×D411yescharacteristic
342C23×C3C2×#6711yescharacteristic
343C3×D4—24no—
344C3×D4—24no—
345C3×D4—22no—
346C3×D4—22no—
347C3×D4—24no—
348C3×D4—42no—
349C3×D4—44no—
350C3×D4C2×Dic614yes—
351C3×D4C2×Dic614yes—
352C2×C3×C4—21no—
353C2×C3×C4—22no—
354C2×C3×C4—22no—
355C2×C3×C4—21no—
356C2×C3×C4—32no—
357C2×C3×C4—32no—
358C2×C3×C4—61no—
359C2×C3×C4—61no—
360C2×C3×C4—62no—
361C2×C3×C4—242no—
362C2×C3×C4—242no—
363C2×C3×C4—241no—
364C2×C3×C4C2×Dic612yes—
365C2×C3×C4C2×Dic612yes—
366C2×C3×C4#23512yes—
367C2×C3×C4D3×D411yescharacteristic
368C2×C3×C4#23712yes—
369C2×C3×C4C2×#6711yescharacteristic
370C2×C3×C4C23×D311yescharacteristic
371C2×C3×C4C23×D311yescharacteristic
372C2×Dic3—22no—
373C2×Dic3—21no—
374C2×Dic3—21no—
375C2×Dic3—61no—
376C2×Dic3—61no—
377C2×Dic3—61no—
378C2×Dic3—61no—
379C2×Dic3—82no—
380C2×Dic3—82no—
381C2×Dic3—81no—
382C2×Dic3—121no—
383C2×Dic3—121no—
384C2×Dic3C2×#6712yes—
385C2×Dic3C2×#6712yes—
386Dic6—242no—
387Dic6—242no—
388C3×C8—61no—
389C3×C8—61no—
390C3⋊C8—21no—
391C3⋊C8—21no—
392C3⋊C8—62no—
393C3⋊C8—62no—
394C3⋊C8—122no—
395C2×C32—22no—
396C2×C32—44no—
397C2×C32C2×C22⋊Q811yescharacteristic
398C2×C32#57611yescharacteristic
399C2×C32#57711yescharacteristic
400C24—21no—
401C2×Q8—182no—
402C2×D4—22no—
403C2×D4—21no—
404C2×D4#62714yescomplemented
405C2×D4C2×D3212yes—
406C22×C4—62no—
407C22×C4—62no—
408C22×C4—61no—
409C22×C4C2×D3211yescharacteristic
410M16—182no—
411C2×C8—31no—
412C2×C8—31no—
413C2×C8—62no—
414C2×C8—92no—
415C4⋊C4—31no—
416C4⋊C4—31no—
417C4⋊C4—32no—
418C4⋊C4—31no—
419C4⋊C4—31no—
420C4⋊C4—61no—
421C4⋊C4—91no—
422C4⋊C4—91no—
423C4⋊C4—182no—
424C4⋊C4—182no—
425C4⋊C4—182no—
426C22⋊C4—32no—
427C22⋊C4—62no—
428C22⋊C4—62no—
429C22⋊C4—61no—
430C22⋊C4—181no—
431C42—32no—
432C42—61no—
433C42—181no—
434C22×C3—21no—
435C22×C3—21no—
436C22×C3—21no—
437C22×C3—21no—
438C22×C3—24no—
439C22×C3—24no—
440C22×C3—21no—
441C22×C3—22no—
442C22×C3—41no—
443C22×C3—41no—
444C22×C3—44no—
445C22×C3—42no—
446C22×C3—42no—
447C22×C3—42no—
448C22×C3—42no—
449C22×C3—82no—
450C22×C3—82no—
451C22×C3—84no—
452C22×C3—84no—
453C22×C3—88no—
454C22×C3#87812yes—
455C22×C3#92412yes—
456C22×C3C2×D3×D411yescharacteristic
457C22×C3C22×#6711yescharacteristic
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—22no—
461C3×C4—62no—
462C3×C4—62no—
463C3×C4—121no—
464C3×C4—121no—
465C3×C4—122no—
466C3×C4#87812yes—
467C3×C4#92412yes—
468C3×C4C22×Dic611yescharacteristic
469C3×C4C22×Dic611yescharacteristic
470C3×C4C2×#23511yescharacteristic
471C3×C4C2×#23711yescharacteristic
472Dic3—22no—
473Dic3—22no—
474Dic3—42no—
475Dic3—41no—
476Dic3—41no—
477Dic3—121no—
478Dic3—121no—
479Dic3—121no—
480Dic3—121no—
481Dic3—241no—
482Dic3—241no—
483C32#308111yescharacteristic, complemented, Sylow
484C23—22no—
485C23—24no—
486C23—81no—
487C23—81no—
488C23D3×#6711yescharacteristic
489Q8—722no—
490D4—22no—
491D4—24no—
492D4C2×#62714yes—
493C2×C4—32no—
494C2×C4—32no—
495C2×C4—61no—
496C2×C4—61no—
497C2×C4—62no—
498C2×C4—181no—
499C2×C4—181no—
500C2×C4—242no—
501C2×C4—242no—
502C2×C4—241no—
503C2×C4#380412yes—
504C2×C4C2×#62712yes—
505C2×C4D3×#6711yescharacteristic
506C2×C4C22×D3211yescharacteristic
507C8—61no—
508C8—61no—
509C8—182no—
510C2×C3—22no—
511C2×C3—22no—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3—42no—
516C2×C3—44no—
517C2×C3—44no—
518C2×C3—84no—
519C2×C3C2×#87811yescharacteristic
520C2×C3#575711yescharacteristic
521C2×C3#576211yescharacteristic
522C2×C3C2×#92411yescharacteristic
523C2×C3#583511yescharacteristic
524C2×C3#583611yescharacteristic
525C22—21no—
526C22—21no—
527C22—24no—
528C22—42no—
529C22—42no—
530C22—84no—
531C22#6396412yes—
532C22C2×D3×#6711yescharacteristic
533C4—62no—
534C4—62no—
535C4—121no—
536C4—122no—
537C4—121no—
538C4—361no—
539C4—361no—
540C4#6396412yes—
541C4C2×#380411yescharacteristic
542C4C22×#62711yescharacteristic
543C3—21no—
544C3#7873111yescharacteristic, complemented
545C3#8253911yescharacteristic, complemented
546C2—22no—
547C2—44no—
548C2#1059509611yescharacteristic
549C2#1059510511yescharacteristic
550C2C2×#6396411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
Fitting, prime radicalC22×C32×D4C22
socleC22×C32C22×D4
hypercenterC22×D4D32
hypocenterC32#3081
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. #10595051C2semidirect
5. #10591411C2semidirect
6. #10591410C2semidirect
7. #10591409C2semidirect
8. #10591408C2semidirect
9. #10591139C2semidirect
10. #10591122C2semidirect
11. #10591116C2semidirect
28. #63918C22semidirect
30. #63869C22semidirect
35. #63576C22semidirect
36. #63575C22semidirect
37. #63575C22semidirect
38. #63574C22semidirect
39. #63573C22semidirect
40. #63573C22semidirect
41. Dic3⋊(C3⋊C8)C22semidirect
42. Dic3⋊(C3⋊C8)C22semidirect
69. C2×C32×D4Q8semidirect
212. C2×C3×D4Dic6semidirect
213. C2×C3×D4Dic6semidirect
404. C2×D4#627semidirect
483. C32#3081semidirect
544. C3#78731semidirect
545. C3#82539semidirect

Maximal subgroups

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

subgroupindex
C3×#57982
#105950512
#105929142
C2×C3×#8322
#105914112
#105914102
#105914092
#105914082
#105911392
#105911222
#105911162
#825393
#787313