Finite Group Databasebeta

← #11787743

Subgroups — #11787743

Order 1152.

825 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594990C211yesmaximal, characteristic, complemented
2C2×#63830C211yesmaximal, characteristic
3C2×#63632C211yesmaximal, characteristic, complemented
4C3×#4939C211yesmaximal, characteristic, complemented
5#10591085C211yesmaximal, characteristic, complemented
6C3×#4523C211yesmaximal, characteristic, complemented
7#10589167C211yesmaximal, characteristic, complemented
8#69663—31nomaximal
9#68776—31nomaximal
10C2×#3828C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×C3×(C2×D3)⋊C4—22no—
15C3×#926C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×#208C2211yescharacteristic
18#63952—22no—
19#63900—21no—
20#63894—21no—
21#63849—21no—
22#63844—21no—
23#63830—22no—
24#63830C414yescomplemented
25C2×#3716—21no—
26C2×#3714—21no—
27#63632—22no—
28#63562—21no—
29#63562—21no—
30C2×#932—31no—
31C2×#908—31no—
32#5523—31no—
33#5504—31no—
34C3×#390—31no—
35#5215—31no—
36#5001—31no—
37#4939D311yescharacteristic, complemented
38C2×#805—31no—
39C2×#805—31no—
40C2×#805—61no—
41C3×#339—31no—
42#4554—31no—
43#4530—31no—
44#4523D311yescharacteristic, complemented
45C23×C3×D3—21no—
46C22×C32×C4—21no—
47C22×C32×C4C2311yescharacteristic
48C2×#638—21no—
49#3828—21no—
50#3828—21no—
51#3828C2×C412yes—
52#3828D412yes—
53C2×C4⋊(C3⋊D3)D411yescharacteristic
54C2×C4×C3⋊D3—21no—
55C2×#634D411yescharacteristic
56C22×C3×Dic3D412yes—
57C2×C3×D12—21no—
58C2×C3×D12—21no—
59C2×C3×D12—21no—
60C2×C3×D12—21no—
61C2×C3×D12—21no—
62C2×C3×D12C2×C412yescomplemented
63C2×#624—22no—
64C32×C42—21no—
65C32×C42—21no—
66#3748—21no—
67#3748—21no—
68C2×C3⋊(C3⋊C8)—21no—
69C3×#217—21no—
70C3×(C2×D3)⋊C4—44no—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3—21no—
73C3×C4⋊Dic3D411yescharacteristic
74C3×C4⋊Dic3D411yescharacteristic
75C3×C4×Dic3—21no—
76C3×#208—21no—
77C3×#208C2×C412yescomplemented
78C2×C3×C3⋊C8—21no—
79#3724—22no—
80#3722—22no—
81Dic32—22no—
82#3716—24no—
83#3714—24no—
84#1883—91noSylow
85C22×C3×D4—31no—
86C2×#235—31no—
87C2×#235—31no—
88C2×#235—61no—
89C22×D12C2×D311yescharacteristic
90C2×C3×M16—31no—
91C3×#117—31no—
92C2×C3×C4⋊C4—31no—
93C2×C3×C22⋊C4—62no—
94C2×C3×C42—21no—
95C2×C3×C42C2×D311yescharacteristic
96C2×C3×C42C2×D311yescharacteristic
97C2×#214—61no—
98#932—34no—
99#932—62no—
100C2×#213—61no—
101C4×#67—62no—
102C2×(C2×D3)⋊C4—22no—
103#926C2×D311yescharacteristic
104C2×C4⋊Dic3C2×D311yescharacteristic
105C2×#208—31no—
106C2×#208—31no—
107C2×#208—61no—
108C2×#208C2×D311yescharacteristic
109#908—34no—
110#908—62no—
111C2×D24—61no—
112C2×#204—61no—
113#893—61no—
114#892—61no—
115#892—61no—
116D3×C4⋊C4—61no—
117D3×C4⋊C4—61no—
118#887—61no—
119#67⋊C4—62no—
120C4×D12—61no—
121C4×Dic6—61no—
122#832—61no—
123#832—61no—
124#809—61no—
125#809—61no—
126#805—62no—
127#805—62no—
128#805—64no—
129C23×C32C2×D411yescharacteristic
130C22×C3⋊D3—21no—
131C22×C3×D3—22no—
132C22×C3×D3—42no—
133C22×C3×D3—42no—
134C22×C3×D3—41no—
135C22×C3×D3—41no—
136C2×C32×C4—22no—
137C2×C32×C4—41no—
138C2×C32×C4—41no—
139C2×C32×C4C22×C411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4#4111yescharacteristic
144C2×C32×C4#4111yescharacteristic
145#638—22no—
146#638—22no—
147C2×C3⋊Dic3—21no—
148C4⋊(C3⋊D3)—21no—
149C4⋊(C3⋊D3)C22⋊C412yescomplemented
150C4×C3⋊D3—22no—
151C4×C3⋊D3—22no—
152#634—21no—
153#634C22⋊C412yescomplemented
154C2×C3×Dic3—21no—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—21no—
157C2×C3×Dic3—42no—
158C3×D12—22no—
159C3×D12—22no—
160C3×D12—41no—
161C3×D12—41no—
162#624—82no—
163C3⋊(C3⋊C8)—41no—
164C3×C3⋊C8—22no—
165C2×AGL(1,ℤ/8)—91no—
166#520—91no—
167C2×#104—91no—
168#418—91no—
169#390—31no—
170#343—91no—
171#339—31no—
172C24×C3—61no—
173C23×D3—21no—
174C2×C3×D4—32no—
175C2×C3×D4—61no—
176C2×C3×D4—61no—
177C2×C3×D4—61no—
178C2×C3×D4—61no—
179C2×C3×D4—61no—
180C22×C3×C4—21no—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—32no—
184C22×C3×C4—41no—
185C22×C3×C4C22×D311yescharacteristic
186C22×C3×C4C22×D311yescharacteristic
187C2×#67—61no—
188C2×#67—61no—
189C2×#67—121no—
190C22×Dic3#6712yes—
191#235—32no—
192#235—32no—
193#235—32no—
194#235—32no—
195#235—62no—
196#235—62no—
197#235—61no—
198#235—61no—
199#235—61no—
200#235—61no—
201#235—121no—
202#235—121no—
203C2×D12—21no—
204C2×D12—21no—
205C2×D12—21no—
206C2×D12—21no—
207C2×D12—21no—
208C2×D12—31no—
209C2×D12—31no—
210C2×D12—61no—
211C2×D12C4×D312yescomplemented
212C2×C4×D3—61no—
213C2×C4×D3—61no—
214C2×C4×D3—62no—
215C2×C4×D3—62no—
216C2×C4×D3—121no—
217C2×Dic6—31no—
218C2×Dic6—31no—
219C2×Dic6—61no—
220C3×M16—32no—
221C3×M16—61no—
222C2×C3×C8—61no—
223C3×C4⋊C4—31no—
224C3×C4⋊C4—31no—
225C3×C4⋊C4—61no—
226C3×C4⋊C4—61no—
227C3×C22⋊C4—61no—
228C3×C22⋊C4—124no—
229C3×C42—22no—
230C3×C42—21no—
231C3×C42—21no—
232C3×C42—21no—
233C3×C42—21no—
234C3×C42—41no—
235C3×C42—61no—
236#217—21no—
237#214—64no—
238#213—64no—
239(C2×D3)⋊C4—44no—
240(C2×D3)⋊C4—62no—
241(C2×D3)⋊C4—62no—
242C4⋊Dic3—21no—
243C4⋊Dic3—21no—
244C4⋊Dic3D1211yescharacteristic
245C4⋊Dic3D1211yescharacteristic
246Dic3⋊C4—62no—
247Dic3⋊C4—62no—
248C4×Dic3—21no—
249C4×Dic3—62no—
250C4×Dic3—62no—
251#208—21no—
252#208—62no—
253#208—61no—
254#208—61no—
255#208—61no—
256#208—61no—
257#208—121no—
258#208C4×D312yescomplemented
259C2×C3⋊C8—21no—
260C2×C3⋊C8—61no—
261C2×C3⋊C8—61no—
262C2×C3⋊C8—121no—
263D24—64no—
264#204—64no—
265C22×C32—21no—
266C22×C32—21no—
267C22×C32C4×D411yescharacteristic
268C22×C32#12011yescharacteristic
269C22×C32#12111yescharacteristic
270C2×C3⋊D3—22no—
271C2×C3⋊D3—41no—
272C2×C3⋊D3—41no—
273C2×C3×D3—44no—
274C2×C3×D3—42no—
275C2×C3×D3—82no—
276C2×C3×D3—81no—
277C2×C3×D3—81no—
278C32×C4—42no—
279C32×C4C2×C22⋊C411yescharacteristic
280C32×C4C4×D411yescharacteristic
281C32×C4#12111yescharacteristic
282C32×C4#12311yescharacteristic
283C3⋊Dic3—22no—
284C3×Dic3—41no—
285C3×Dic3—42no—
286C3×Dic3—41no—
287C2×#41—91no—
288C22×D4—31no—
289AGL(1,ℤ/8)—94no—
290AGL(1,ℤ/8)—182no—
291C2×SD16—181no—
292C2×D8—181no—
293C2×M16—31no—
294C2×M16—91no—
295C4×Q8—181no—
296C4×D4—181no—
297C4×D4—182no—
298#117—31no—
299#117—181no—
300C2×C4⋊C4—31no—
301C2×C4⋊C4—181no—
302C2×C22⋊C4—62no—
303C2×C42D3211yescharacteristic
304#104—182no—
305#102—181no—
306#102—181no—
307C23×C3—21no—
308C23×C3—62no—
309C23×C3—122no—
310C23×C3—122no—
311C23×C3—121no—
312C23×C3—121no—
313C23×C3D3×D411yescharacteristic
314C23×C3C2×#6711yescharacteristic
315C22×D3—22no—
316C22×D3—42no—
317C22×D3—42no—
318C22×D3—41no—
319C22×D3—41no—
320C22×D3—61no—
321C22×D3—61no—
322C22×D3—121no—
323C3×D4—62no—
324C3×D4—62no—
325C3×D4—121no—
326C3×D4—121no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—42no—
336C2×C3×C4—42no—
337C2×C3×C4—41no—
338C2×C3×C4—41no—
339C2×C3×C4—42no—
340C2×C3×C4—41no—
341C2×C3×C4—41no—
342C2×C3×C4—62no—
343C2×C3×C4—61no—
344C2×C3×C4—61no—
345C2×C3×C4—122no—
346C2×C3×C4C2×C4×D311yescharacteristic
347C2×C3×C4C2×C4×D311yescharacteristic
348C2×C3×C4C2×D1211yescharacteristic
349C2×C3×C4#23511yescharacteristic
350C2×C3×C4#23511yescharacteristic
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4D3×D411yescharacteristic
353C2×C3×C4D3×D411yescharacteristic
354C2×C3×C4D3×D411yescharacteristic
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4#23711yescharacteristic
357C2×C3×C4#23911yescharacteristic
358#67—62no—
359#67—62no—
360#67—62no—
361#67—62no—
362#67—122no—
363#67—122no—
364C2×Dic3—21no—
365C2×Dic3—21no—
366C2×Dic3—22no—
367C2×Dic3—42no—
368C2×Dic3—61no—
369C2×Dic3—61no—
370C2×Dic3—121no—
371D12—22no—
372D12—22no—
373D12—32no—
374D12—32no—
375D12—41no—
376D12—41no—
377D12—62no—
378D12—61no—
379D12—61no—
380D12—121no—
381C4×D3—62no—
382C4×D3—62no—
383C4×D3—62no—
384C4×D3—62no—
385C4×D3—122no—
386C4×D3—122no—
387C4×D3—242no—
388C4×D3—242no—
389Dic6—32no—
390Dic6—32no—
391Dic6—62no—
392Dic6—61no—
393Dic6—61no—
394Dic6—121no—
395C3×C8—62no—
396C3⋊C8—22no—
397C3⋊C8—122no—
398C3⋊C8—121no—
399C3⋊C8—121no—
400C2×C32—21no—
401C2×C32—21no—
402C2×C32#38611yescharacteristic
403C2×C32#45311yescharacteristic
404C2×C32#45411yescharacteristic
405C3⋊D3—42no—
406C3×D3—82no—
407C24—61no—
408#41—92no—
409#41—92no—
410#41—181no—
411#41—181no—
412C2×Q8—91no—
413C2×D4—32no—
414C2×D4—61no—
415C2×D4—61no—
416C2×D4—61no—
417C2×D4—61no—
418C2×D4—61no—
419C2×D4—91no—
420C2×D4—181no—
421C22×C4—21no—
422C22×C4—32no—
423C22×C4—182no—
424C22×C4—181no—
425C22×C4C2×D3211yescharacteristic
426SD16—184no—
427D8—184no—
428M16—32no—
429M16—61no—
430M16—181no—
431M16—181no—
432C2×C8—61no—
433C2×C8—181no—
434C4⋊C4—31no—
435C4⋊C4—31no—
436C4⋊C4—61no—
437C4⋊C4—61no—
438C4⋊C4—182no—
439C22⋊C4—61no—
440C22⋊C4—124no—
441C22⋊C4—182no—
442C42—21no—
443C42—21no—
444C42—61no—
445C42—182no—
446C22×C3—21no—
447C22×C3—21no—
448C22×C3—21no—
449C22×C3—21no—
450C22×C3—21no—
451C22×C3—21no—
452C22×C3—21no—
453C22×C3—41no—
454C22×C3—41no—
455C22×C3—124no—
456C22×C3—122no—
457C22×C3—242no—
458C22×C3—241no—
459C22×C3—241no—
460C22×C3#88211yescharacteristic
461C22×C3#88411yescharacteristic
462C22×C3#89311yescharacteristic
463C22×C3C4×#6711yescharacteristic
464C22×C3#93711yescharacteristic
465C22×C3#93811yescharacteristic
466C2×D3—44no—
467C2×D3—42no—
468C2×D3—62no—
469C2×D3—62no—
470C2×D3—82no—
471C2×D3—81no—
472C2×D3—81no—
473C2×D3—122no—
474C2×D3—121no—
475C2×D3—121no—
476C2×D3—121no—
477C2×D3—121no—
478C2×D3—241no—
479C2×D3—241no—
480C3×C4—21no—
481C3×C4—21no—
482C3×C4—21no—
483C3×C4—21no—
484C3×C4—42no—
485C3×C4—42no—
486C3×C4—44no—
487C3×C4—121no—
488C3×C4—121no—
489C3×C4—122no—
490C3×C4C4×D1211yescharacteristic
491C3×C4D3×C22⋊C411yescharacteristic
492C3×C4D3×C22⋊C411yescharacteristic
493C3×C4#67⋊C411yescharacteristic
494C3×C4#88311yescharacteristic
495C3×C4#88411yescharacteristic
496C3×C4#89411yescharacteristic
497C3×C4#89511yescharacteristic
498Dic3—42no—
499Dic3—41no—
500Dic3—41no—
501Dic3—62no—
502Dic3—62no—
503Dic3—122no—
504C32#188311yescharacteristic, complemented, Sylow
505C23—62no—
506C23—122no—
507C23—122no—
508C23—121no—
509C23—121no—
510C23—181no—
511C23D3×#6711yescharacteristic
512Q8—92no—
513Q8—181no—
514D4—62no—
515D4—62no—
516D4—92no—
517D4—121no—
518D4—121no—
519D4—182no—
520D4—182no—
521D4—181no—
522C2×C4—22no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—61no—
526C2×C4—61no—
527C2×C4—62no—
528C2×C4—122no—
529C2×C4—181no—
530C2×C4—182no—
531C2×C4—182no—
532C2×C4—722no—
533C2×C4#379911yescharacteristic
534C2×C4C4×D3211yescharacteristic
535C2×C4D3×D1211yescharacteristic
536C2×C4#380211yescharacteristic
537C2×C4#380411yescharacteristic
538C2×C4#381111yescharacteristic
539C8—62no—
540C8—361no—
541C2×C3—21no—
542C2×C3—21no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—41no—
549C2×C3—41no—
550C2×C3—242no—
551C2×C3#466511yescharacteristic
552C2×C3#482211yescharacteristic
553C2×C3#482711yescharacteristic
554C2×C3#495611yescharacteristic
555C2×C3#506211yescharacteristic
556C2×C3#507711yescharacteristic
557D3—82no—
558D3—122no—
559D3—122no—
560D3—242no—
561C22—21no—
562C22—21no—
563C22—124no—
564C22—122no—
565C22—182no—
566C22—242no—
567C22—241no—
568C22—241no—
569C22—361no—
570C22—361no—
571C22#6390411yescharacteristic
572C22#6392211yescharacteristic
573C22#6395811yescharacteristic
574C4—42no—
575C4—122no—
576C4—121no—
577C4—121no—
578C4—182no—
579C4#6385411yescharacteristic
580C4#6388011yescharacteristic
581C4#6391011yescharacteristic
582C4#6392111yescharacteristic
583C3—21no—
584C3#6877611yescharacteristic, complemented
585C3#6966311yescharacteristic, complemented
586C2—21no—
587C2—21no—
588C2—242no—
589C2—362no—
590C2#1059039511yescharacteristic
591C2#1059040011yescharacteristic
592C2#1059127511yescharacteristic
subgroupG/H
centerC22#63922
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32#120
prime radicalC2×#63830C2
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1883
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. #10594990C2semidirect
3. C2×#63632C2semidirect
4. C3×#4939C2semidirect
5. #10591085C2semidirect
6. C3×#4523C2semidirect
7. #10589167C2semidirect
24. #63830C4semidirect
37. #4939D3semidirect
44. #4523D3semidirect
62. C2×C3×D12C2×C4semidirect
77. C3×#208C2×C4semidirect
149. C4⋊(C3⋊D3)C22⋊C4semidirect
153. #634C22⋊C4semidirect
211. C2×D12C4×D3semidirect
258. #208C4×D3semidirect
504. C32#1883semidirect
584. C3#68776semidirect
585. C3#69663semidirect

Maximal subgroups

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

subgroupindex
#105949902
C2×#638302
C2×#636322
C3×#49392
#105910852
C3×#45232
#105891672
#696633
#687763