Finite Group Databasebeta

← #11895416

Subgroups — #11895416

Order 1152.

848 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5718C211yesmaximal, characteristic
2#10593856C211yesmaximal, characteristic, complemented
3#10592774C211yesmaximal, characteristic, complemented
4C3×#5070C211yesmaximal, characteristic, complemented
5#10591487C212yesmaximal, complemented
6#10591439C212yesmaximal, complemented
7#10591408C212yesmaximal, complemented
8#10591401C212yesmaximal, complemented
9C4×#3716C211yesmaximal, characteristic, complemented
10#10590266C211yesmaximal, characteristic, complemented
11C3⋊C8×Dic6C211yesmaximal, characteristic, complemented
12#83586—31nomaximal
13#81588—31nomaximal
14C2×C3×#237—21no—
15C32×#127C2211yescharacteristic
16C2×#3754C2212yes—
17C4×#634C2211yescharacteristic
18C3×#940C2212yes—
19C3×#939—22no—
20C3×#938—21no—
21C3×D4×Dic3C2212yes—
22C3×C4×D12C2211yescharacteristic
23C3×#869C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63919—21no—
26#63918C2212yes—
27#63844C2212yes—
28#63843—21no—
29#63839—22no—
30C2×#3716C2211yescharacteristic
31#63659C2212yes—
32C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
33C3×#832C2212yes—
34C3×#832C2212yes—
35C3×C4×C3⋊C8C2211yescharacteristic
36#63574C2212yes—
37#63573C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2212yes—
39#63567C2211yescharacteristic
40#63563C2211yescharacteristic
41#63562C2212yes—
42Dic3×C3⋊C8C2212yes—
43C3×#550—31no—
44#5722—31no—
45#5718D311yescharacteristic
46Q8×Dic6—31no—
47C3×#486—31no—
48#5084—31no—
49#5075—31no—
50#5075—31no—
51#5075—32no—
52#5075—61no—
53#5070—32no—
54#5070D311yescharacteristic, complemented
55Q8×C3⋊C8—31no—
56C4×#214—32no—
57C4×#214—31no—
58#5008—31no—
59#5008—32no—
60#4762—32no—
61#4761—32no—
62#4760—32no—
63#4758—32no—
64C4×#204—31no—
65C8×Dic6—31no—
66C2×C32×D4—21no—
67C2×C32×D4—21no—
68C2×C32×D4C2312yes—
69C2×#634C2311yescharacteristic
70C2×C3×#67—22no—
71C2×C3×#67—22no—
72C22×C3×Dic3—22no—
73C3×#237—44no—
74C2×C3×D12C2311yescharacteristic
75C2×C3×C4×D3—21no—
76C2×C3×Dic6—21no—
77C2×C3×Dic6D411yescharacteristic
78C2×#627—22no—
79C32×C42C2311yescharacteristic
80#3754—24no—
81C4⋊(C3⋊Dic3)C2311yescharacteristic
82#3750—21no—
83C4×C3⋊Dic3—21no—
84C2×C3⋊(C3⋊C8)C2312yes—
85C3×#217—22no—
86C3×(C2×D3)⋊C4—21no—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3D411yescharacteristic
89C3×C4⋊Dic3C2311yescharacteristic
90C3×C4⋊Dic3C2312yes—
91C3×Dic3⋊C4D412yes—
92C3×C4×Dic3C2312yes—
93C2×C3×C3⋊C8C2311yescharacteristic
94C2×C3×C3⋊C8C2311yescharacteristic
95#3724—22no—
96Dic3⋊Dic3—22no—
97Dic32—22no—
98#3716—22no—
99#3362—91noSylow
100C2×C3×#41—61no—
101C2×#237—21no—
102C3×C4⋊Q8—31no—
103C3×#127—21no—
104C3×#127—32no—
105C3×#127C2×D311yescharacteristic
106C3×#127C2×D311yescharacteristic
107C3×#121—61no—
108C3×#121—62no—
109C3×C4×Q8—31no—
110C3×C4×D4—32no—
111C3×C4×D4—31no—
112Q8×Dic3—61no—
113#944—62no—
114#940C2×D312yes—
115#939—22no—
116#938—21no—
117D4×Dic3C2×D312yes—
118C2×#214—32no—
119C2×#214—32no—
120C2×#214—31no—
121C2×#214—62no—
122C2×#204—31no—
123#888—32no—
124#888—61no—
125#888—62no—
126#888—61no—
127#887—32no—
128#887—61no—
129C4×D12C2×D311yescharacteristic
130#869—32no—
131#869C2×D311yescharacteristic
132C4×Dic6—31no—
133C4×Dic6—31no—
134C4×Dic6—32no—
135C4×Dic6—61no—
136C4×Dic6C2×D311yescharacteristic
137C3×#102—32no—
138C3×#102—32no—
139C3×C4×C8—31no—
140#832—32no—
141#832—32no—
142#832—32no—
143#832—31no—
144#832—62no—
145#832C2×D312yes—
146#832C2×D312yes—
147#821—31no—
148#817—31no—
149#816—31no—
150Dic3⋊C8—32no—
151C8×Dic3—32no—
152#810—31no—
153#809—32no—
154#808—32no—
155#808—32no—
156#808—31no—
157C4⋊(C3⋊C8)—31no—
158C4⋊(C3⋊C8)—31no—
159C4⋊(C3⋊C8)—32no—
160C4⋊(C3⋊C8)—61no—
161C4×C3⋊C8—32no—
162C4×C3⋊C8C2×D311yescharacteristic
163C23×C32—22no—
164C22×C3×D3—21no—
165C32×D4—22no—
166C32×D4—22no—
167C32×D4—42no—
168C32×D4—81no—
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2411yescharacteristic
172C2×C3⋊Dic3—21no—
173C2×C3⋊Dic3—21no—
174#634—21no—
175#634#4112yescomplemented
176C3×#67—44no—
177C3×#67—82no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—21no—
180C2×C3×Dic3—44no—
181C2×C3×Dic3C2×D412yes—
182C2×C3×Dic3C2×D412yes—
183C3×D12—21no—
184C3×D12—21no—
185C3×C4×D3—42no—
186C3×Dic6—81no—
187C3×Dic6SD1614yescomplemented
188#627—82no—
189C3⋊(C3⋊C8)—22no—
190C3×C3⋊C8—21no—
191C3×C3⋊C8—21no—
192Q82—91no—
193#550—31no—
194#486—31no—
195#486—92no—
196#476—92no—
197#476—91no—
198#460—92no—
199#460—91no—
200C8×Q8—91no—
201C4×SD16—91no—
202C4×SD16—92no—
203C3×#41—124no—
204C2×C3×Q8—31no—
205C2×C3×Q8—61no—
206C2×C3×D4—21no—
207C2×C3×D4—21no—
208C2×C3×D4—21no—
209C2×C3×D4—21no—
210C2×C3×D4—22no—
211C2×C3×D4—31no—
212C2×C3×D4—41no—
213C2×C3×D4—41no—
214C2×C3×D4—62no—
215C2×C3×D4—62no—
216C2×C3×D4C22×D312yes—
217C2×C3×D4C22×D312yes—
218C22×C3×C4—62no—
219C22×C3×C4—61no—
220C2×#67—22no—
221C2×#67—22no—
222C22×Dic3—22no—
223#237—44no—
224C2×D12C22×D311yescharacteristic
225C2×C4×D3—21no—
226C2×Dic6—21no—
227C2×Dic6—31no—
228C2×Dic6—31no—
229C2×Dic6—61no—
230C2×Dic6—62no—
231C2×Dic6—62no—
232C2×Dic6#6711yescharacteristic
233C2×C3×C8—31no—
234C2×C3×C8—31no—
235C3×C4⋊C4—32no—
236C3×C4⋊C4—31no—
237C3×C4⋊C4—31no—
238C3×C4⋊C4—32no—
239C3×C4⋊C4—61no—
240C3×C22⋊C4—62no—
241C3×C22⋊C4—61no—
242C3×C42—21no—
243C3×C42—32no—
244C3×C42C22×D311yescharacteristic
245C3×C42C22×D311yescharacteristic
246#217—22no—
247#214—62no—
248#214—64no—
249#214—64no—
250#214—124no—
251(C2×D3)⋊C4—21no—
252C4⋊Dic3—21no—
253C4⋊Dic3—31no—
254C4⋊Dic3—31no—
255C4⋊Dic3—61no—
256C4⋊Dic3—62no—
257C4⋊Dic3#6711yescharacteristic
258C4⋊Dic3C22×D311yescharacteristic
259C4⋊Dic3C22×D312yes—
260Dic3⋊C4—62no—
261Dic3⋊C4—61no—
262Dic3⋊C4—61no—
263Dic3⋊C4—62no—
264Dic3⋊C4—62no—
265Dic3⋊C4—121no—
266Dic3⋊C4#6712yes—
267C4×Dic3—62no—
268C4×Dic3—61no—
269C4×Dic3—61no—
270C4×Dic3—62no—
271C4×Dic3—121no—
272C4×Dic3C22×D312yes—
273C2×C3⋊C8—32no—
274C2×C3⋊C8—32no—
275C2×C3⋊C8—62no—
276C2×C3⋊C8C22×D311yescharacteristic
277C2×C3⋊C8C22×D311yescharacteristic
278#204—62no—
279C22×C32—42no—
280C22×C32—42no—
281C22×C32—42no—
282C22×C32C22×D411yescharacteristic
283C2×C3×D3—41no—
284C2×C3×D3—41no—
285C2×C3×D3—41no—
286C32×C4—21no—
287C32×C4C2×SD1612yes—
288C32×C4C2×#4111yescharacteristic
289C32×C42−1+411yescharacteristic
290C3⋊Dic3—22no—
291C3⋊Dic3—41no—
292C3×Dic3—22no—
293C3×Dic3—41no—
294C3×Dic3—42no—
295C3×Dic3C2×SD1614yes—
296C2×#41—61no—
297C2×SD16—91no—
298C2×SD16—92no—
299C4⋊Q8—31no—
300C4⋊Q8—92no—
301C4⋊Q8—181no—
302C4⋊Q8—182no—
303#127—32no—
304#127D3211yescharacteristic
305#121—61no—
306#121—62no—
307C4×Q8—31no—
308C4×Q8—92no—
309C4×Q8—91no—
310C4×Q8—181no—
311C4×D4—32no—
312C4×D4—31no—
313#106—92no—
314#106—91no—
315C4⋊C8—92no—
316C4⋊C8—91no—
317#103—91no—
318#102—32no—
319#102—32no—
320#102—92no—
321#102—91no—
322#102—92no—
323C4×C8—31no—
324C4×C8—92no—
325C23×C3—22no—
326C23×C3—22no—
327C23×C3—42no—
328C23×C3—61no—
329C22×D3—21no—
330C3×Q8—34no—
331C3×Q8—241no—
332C3×D4—22no—
333C3×D4—22no—
334C3×D4—22no—
335C3×D4—22no—
336C3×D4—42no—
337C3×D4—42no—
338C3×D4—42no—
339C3×D4—42no—
340C3×D4—61no—
341C3×D4—61no—
342C3×D4—82no—
343C3×D4—81no—
344C3×D4—81no—
345C3×D4—82no—
346C3×D4—124no—
347C3×D4—242no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—32no—
352C2×C3×C4—32no—
353C2×C3×C4—61no—
354C2×C3×C4—62no—
355C2×C3×C4—124no—
356C2×C3×C4—122no—
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4C2×#6711yescharacteristic
360C2×C3×C4C2×#6711yescharacteristic
361C2×C3×C4C23×D311yescharacteristic
362C2×C3×C4C23×D311yescharacteristic
363#67—44no—
364#67—82no—
365C2×Dic3—22no—
366C2×Dic3—21no—
367C2×Dic3—44no—
368C2×Dic3—61no—
369C2×Dic3—61no—
370C2×Dic3—61no—
371C2×Dic3—61no—
372C2×Dic3—121no—
373C2×Dic3—121no—
374C2×Dic3C2×#6712yes—
375C2×Dic3C2×#6712yes—
376D12—21no—
377D12—21no—
378C4×D3—42no—
379Dic6—32no—
380Dic6—32no—
381Dic6—62no—
382Dic6—61no—
383Dic6—61no—
384Dic6—81no—
385Dic6—121no—
386Dic6—242no—
387Dic6—242no—
388Dic6#21414yescomplemented
389C3×C8—61no—
390C3×C8—61no—
391C3⋊C8—21no—
392C3⋊C8—21no—
393C3⋊C8—62no—
394C3⋊C8—62no—
395C3⋊C8—122no—
396C2×C32—82no—
397C2×C32#54811yescharacteristic
398C2×C32C22×SD1611yescharacteristic
399C2×C32#57611yescharacteristic
400C3×D3—81no—
401#41—124no—
402C2×Q8—31no—
403C2×Q8—61no—
404C2×Q8—91no—
405C2×Q8—182no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—31no—
409C2×D4—62no—
410C2×D4—62no—
411C2×D4C2×D3212yes—
412C22×C4—62no—
413C22×C4—61no—
414SD16—182no—
415SD16—184no—
416C2×C8—31no—
417C2×C8—31no—
418C2×C8—92no—
419C4⋊C4—32no—
420C4⋊C4—31no—
421C4⋊C4—32no—
422C4⋊C4—31no—
423C4⋊C4—61no—
424C4⋊C4—91no—
425C4⋊C4—182no—
426C4⋊C4—182no—
427C4⋊C4—181no—
428C22⋊C4—62no—
429C22⋊C4—61no—
430C42—32no—
431C42—182no—
432C42—181no—
433C42C2×D3211yescharacteristic
434C22×C3—21no—
435C22×C3—42no—
436C22×C3—42no—
437C22×C3—42no—
438C22×C3—42no—
439C22×C3—42no—
440C22×C3—42no—
441C22×C3—82no—
442C22×C3—82no—
443C22×C3—82no—
444C22×C3—121no—
445C22×C3—121no—
446C22×C3—121no—
447C22×C3C2×D3×D411yescharacteristic
448C22×C3C22×#6711yescharacteristic
449C2×D3—41no—
450C2×D3—41no—
451C2×D3—41no—
452C3×C4—21no—
453C3×C4—21no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—22no—
457C3×C4—34no—
458C3×C4—41no—
459C3×C4—62no—
460C3×C4—121no—
461C3×C4—122no—
462C3×C4D3×SD1612yes—
463C3×C4C2×#21412yes—
464C3×C4D3×#4111yescharacteristic
465C3×C4D3×#4111yescharacteristic
466C3×C4#101011yescharacteristic
467C3×C4#101011yescharacteristic
468Dic3—22no—
469Dic3—42no—
470Dic3—41no—
471Dic3—62no—
472Dic3—62no—
473Dic3—122no—
474Dic3—121no—
475Dic3—121no—
476Dic3—241no—
477Dic3C2×#21414yes—
478C32#336211yescharacteristic, complemented, Sylow
479C23—22no—
480C23—61no—
481Q8—34no—
482Q8—92no—
483Q8—181no—
484Q8—241no—
485Q8—722no—
486D4—22no—
487D4—22no—
488D4—42no—
489D4—61no—
490D4—61no—
491D4—81no—
492D4—124no—
493D4—242no—
494C2×C4—32no—
495C2×C4—32no—
496C2×C4—62no—
497C2×C4—61no—
498C2×C4—124no—
499C2×C4—122no—
500C2×C4—181no—
501C2×C4—181no—
502C2×C4D3×#6711yescharacteristic
503C2×C4D3×#6711yescharacteristic
504C2×C4C22×D3211yescharacteristic
505C8—61no—
506C8—61no—
507C8—182no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—82no—
512C2×C3—82no—
513C2×C3—162no—
514C2×C3—241no—
515C2×C3#567711yescharacteristic
516C2×C3#575711yescharacteristic
517C2×C3C2×D3×SD1611yescharacteristic
518C2×C3C22×#21411yescharacteristic
519C2×C3#583111yescharacteristic
520C2×C3#583511yescharacteristic
521D3—81no—
522C22—42no—
523C22—42no—
524C22—42no—
525C22—121no—
526C22—121no—
527C22—121no—
528C22C2×D3×#6711yescharacteristic
529C4—21no—
530C4—34no—
531C4—62no—
532C4—122no—
533C4—121no—
534C4—182no—
535C4—361no—
536C4D3×#21412yes—
537C4#6430911yescharacteristic
538C4#6431211yescharacteristic
539C3—21no—
540C3#8158811yescharacteristic, complemented
541C3#8358611yescharacteristic, complemented
542C2—82no—
543C2—241no—
544C2#1059509611yescharacteristic
545C2C2×D3×#21411yescharacteristic
546C2#1059523711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#127C22
socleC22×C32C22×D4
prime radicalC3×#5718C2
hypercenter#127D32
hypocenterC32#3362
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
2. #10593856C2semidirect
3. #10592774C2semidirect
4. C3×#5070C2semidirect
5. #10591487C2semidirect
6. #10591439C2semidirect
7. #10591408C2semidirect
8. #10591401C2semidirect
9. C4×#3716C2semidirect
10. #10590266C2semidirect
11. C3⋊C8×Dic6C2semidirect
54. #5070D3semidirect
175. #634#41semidirect
187. C3×Dic6SD16semidirect
388. Dic6#214semidirect
478. C32#3362semidirect
540. C3#81588semidirect
541. C3#83586semidirect

Maximal subgroups

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

subgroupindex
C3×#57182
#105938562
#105927742
C3×#50702
#105914872
#105914392
#105914082
#105914012
C4×#37162
#105902662
C3⋊C8×Dic62
#835863
#815883