Finite Group Databasebeta

← #11787744

Subgroups — #11787744

Order 1152.

869 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594992C211yesmaximal, characteristic, complemented
2C2×#63825C211yesmaximal, characteristic
3#10592638C211yesmaximal, characteristic, complemented
4C2×C3×#805C211yesmaximal, characteristic, complemented
5#10591096C211yesmaximal, characteristic, complemented
6C3×#4523C211yesmaximal, characteristic, complemented
7#10589168C211yesmaximal, characteristic, complemented
8#70366—31nomaximal
9#68776—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13C2×#3752—22no—
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C3×#926C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C2×C3×#208C2211yescharacteristic
18#67⋊Dic3—22no—
19Dic3×D12—21no—
20D3×C4⋊Dic3—21no—
21Dic3×Dic6—21no—
22#63841—21no—
23C2×#3717—21no—
24#63825—22no—
25#63825C414yescomplemented
26C2×#3714—21no—
27C3×#805—22no—
28#63564—21no—
29#63564—21no—
30#5827—31no—
31C2×#949—31no—
32C2×#908—31no—
33#5523—31no—
34C2×C3×#104—31no—
35#5131—31no—
36#5001—31no—
37#4939—31no—
38#4939—31no—
39#4939—61no—
40C2×#805D311yescharacteristic, complemented
41C3×#339—31no—
42#4554—31no—
43#4554—31no—
44#4523D311yescharacteristic, complemented
45C23×C3⋊D3—21no—
46C22×C32×C4—21no—
47C22×C32×C4C2311yescharacteristic
48C22×C3⋊Dic3D412yes—
49C2×C4⋊(C3⋊D3)—21no—
50C2×C4⋊(C3⋊D3)—21no—
51C2×C4⋊(C3⋊D3)—21no—
52C2×C4⋊(C3⋊D3)—21no—
53C2×C4⋊(C3⋊D3)—21no—
54C2×C4⋊(C3⋊D3)C2×C412yescomplemented
55C2×C3×#67—21no—
56C3×#235—21no—
57C3×#235—21no—
58C3×#235C2×C412yes—
59C3×#235D412yes—
60C2×C3×D12D411yescharacteristic
61C2×C3×C4×D3—21no—
62C2×C3×Dic6D411yescharacteristic
63C2×D3×Dic3—22no—
64C32×C42—21no—
65C32×C42—21no—
66#3752—44no—
67C4⋊(C3⋊Dic3)—21no—
68C4⋊(C3⋊Dic3)—21no—
69C3×#217—21no—
70C3×C4⋊Dic3D411yescharacteristic
71C3×C4⋊Dic3D411yescharacteristic
72C3×C4×Dic3—21no—
73C3×#208—21no—
74C3×#208—21no—
75C3×#208—21no—
76C3×#208C2×C412yescomplemented
77C2×C3×C3⋊C8—21no—
78C2×C3×C3⋊C8—21no—
79Dic3⋊Dic3—22no—
80(C2×D3)⋊Dic3—22no—
81Dic32—22no—
82#3717—24no—
83#3714—24no—
84#1883—91noSylow
85C2×C3×#41—31no—
86C2×#235C2×D311yescharacteristic
87C22×D12—31no—
88C22×D12—31no—
89C22×D12—61no—
90C2×C3×M16—31no—
91C2×C3×M16—31no—
92C3×#117—31no—
93C2×C3×C42—21no—
94C2×C3×C42C2×D311yescharacteristic
95C2×C3×C42C2×D311yescharacteristic
96#949—34no—
97#949—62no—
98Q8×Dic3—61no—
99C2×#215—61no—
100D4×Dic3—61no—
101D4×Dic3—62no—
102C2×#213—61no—
103C2×(C2×D3)⋊C4—62no—
104C2×(C2×D3)⋊C4—62no—
105C2×(C2×D3)⋊C4—64no—
106#926—61no—
107#926C2×D311yescharacteristic
108C2×C4⋊Dic3—31no—
109C2×C4⋊Dic3—31no—
110C2×C4⋊Dic3—61no—
111C2×C4⋊Dic3—61no—
112C2×#208C2×D311yescharacteristic
113C2×#208C2×D311yescharacteristic
114#908—34no—
115#908—62no—
116C2×D24—61no—
117C2×#204—61no—
118#892—61no—
119D3×C4⋊C4—61no—
120#67⋊C4—62no—
121C4×D12—61no—
122C4×Dic6—61no—
123C3×#104—62no—
124#821—61no—
125#821—61no—
126#809—61no—
127#809—61no—
128#805—22no—
129C23×C32C2×D411yescharacteristic
130C22×C3⋊D3—22no—
131C22×C3⋊D3—42no—
132C22×C3⋊D3—42no—
133C22×C3⋊D3—41no—
134C22×C3⋊D3—41no—
135C22×C3×D3—21no—
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
145C2×C3⋊Dic3—22no—
146C2×C3⋊Dic3—42no—
147C4⋊(C3⋊D3)—22no—
148C4⋊(C3⋊D3)—22no—
149C4⋊(C3⋊D3)—41no—
150C4⋊(C3⋊D3)—41no—
151C3×#67—22no—
152C3×#67—22no—
153C2×C3×Dic3—21no—
154C2×C3×Dic3—21no—
155C2×C3×Dic3—21no—
156C3×D12—21no—
157C3×D12C22⋊C412yescomplemented
158C3×C4×D3—22no—
159C3×C4×D3—22no—
160C3×Dic6—21no—
161C3×Dic6C22⋊C412yescomplemented
162D3×Dic3—82no—
163C3×C3⋊C8—22no—
164C3×C3⋊C8—41no—
165C2×AGL(1,ℤ/8)—91no—
166#520—91no—
167C2×#104—31no—
168#418—91no—
169#390—91no—
170#343—91no—
171#339—31no—
172C23×D3—62no—
173C23×D3—61no—
174C23×D3—61no—
175C3×#41—32no—
176C3×#41—32no—
177C3×#41—61no—
178C3×#41—61no—
179C2×C3×Q8—31no—
180C2×C3×D4—31no—
181C2×C3×D4—61no—
182C22×C3×C4—22no—
183C22×C3×C4—21no—
184C22×C3×C4—21no—
185C22×C3×C4—21no—
186C22×C3×C4—61no—
187C22×C3×C4C22×D311yescharacteristic
188C22×C3×C4C22×D311yescharacteristic
189C2×#67—21no—
190C22×Dic3—32no—
191C22×Dic3—32no—
192C22×Dic3—62no—
193C22×Dic3—62no—
194#235—21no—
195#235—21no—
196#235C4×D312yes—
197#235#6712yes—
198C2×D12—32no—
199C2×D12—32no—
200C2×D12—62no—
201C2×D12—61no—
202C2×D12—61no—
203C2×D12—61no—
204C2×D12—61no—
205C2×D12—61no—
206C2×D12—61no—
207C2×D12—61no—
208C2×D12—61no—
209C2×D12—62no—
210C2×D12—61no—
211C2×D12—61no—
212C2×D12—121no—
213C2×D12—121no—
214C2×D12—121no—
215C2×D12—121no—
216C2×D12D1211yescharacteristic
217C2×C4×D3—21no—
218C2×C4×D3—62no—
219C2×Dic6D1211yescharacteristic
220C3×M16—32no—
221C3×M16—61no—
222C3×M16—61no—
223C3×M16—61no—
224C2×C3×C8—61no—
225C2×C3×C8—61no—
226C3×C4⋊C4—31no—
227C3×C4⋊C4—31no—
228C3×C22⋊C4—61no—
229C3×C42—21no—
230C3×C42—21no—
231C3×C42—21no—
232C3×C42—21no—
233C3×C42—41no—
234C3×C42—41no—
235C3×C42—61no—
236#217—21no—
237#217—62no—
238#215—64no—
239#213—64no—
240(C2×D3)⋊C4—62no—
241(C2×D3)⋊C4—124no—
242(C2×D3)⋊C4—124no—
243(C2×D3)⋊C4—128no—
244C4⋊Dic3—62no—
245C4⋊Dic3—61no—
246C4⋊Dic3—61no—
247C4⋊Dic3—61no—
248C4⋊Dic3—61no—
249C4⋊Dic3—121no—
250C4⋊Dic3—121no—
251C4⋊Dic3D1211yescharacteristic
252C4⋊Dic3D1211yescharacteristic
253Dic3⋊C4—62no—
254C4×Dic3—21no—
255C4×Dic3—62no—
256C4×Dic3—62no—
257#208—21no—
258#208—21no—
259#208—21no—
260#208C4×D312yescomplemented
261C2×C3⋊C8—21no—
262C2×C3⋊C8—21no—
263D24—64no—
264#204—64no—
265C22×C32—21no—
266C22×C32—21no—
267C22×C32C4×D411yescharacteristic
268C22×C32#12011yescharacteristic
269C22×C32#12111yescharacteristic
270C2×C3⋊D3—44no—
271C2×C3⋊D3—42no—
272C2×C3⋊D3—82no—
273C2×C3⋊D3—81no—
274C2×C3⋊D3—81no—
275C2×C3×D3—22no—
276C2×C3×D3—41no—
277C2×C3×D3—41no—
278C32×C4—42no—
279C32×C4C2×C22⋊C411yescharacteristic
280C32×C4C4×D411yescharacteristic
281C32×C4#12111yescharacteristic
282C32×C4#12311yescharacteristic
283C3⋊Dic3—42no—
284C3×Dic3—22no—
285C3×Dic3—41no—
286C3×Dic3—41no—
287C2×#41—31no—
288C22×D4—91no—
289AGL(1,ℤ/8)—94no—
290AGL(1,ℤ/8)—182no—
291C2×SD16—181no—
292C2×D8—181no—
293C2×M16—31no—
294C2×M16—31no—
295C4×Q8—181no—
296C4×D4—181no—
297C4×D4—182no—
298#117—31no—
299#117—181no—
300C2×C4⋊C4—91no—
301C2×C4⋊C4—181no—
302C2×C22⋊C4—182no—
303C2×C42D3211yescharacteristic
304#104—62no—
305#102—181no—
306#102—181no—
307C23×C3—21no—
308C23×C3—61no—
309C23×C3D3×D411yescharacteristic
310C23×C3D3×D411yescharacteristic
311C22×D3—21no—
312C22×D3—64no—
313C22×D3—62no—
314C22×D3—62no—
315C22×D3—124no—
316C22×D3—122no—
317C22×D3—122no—
318C22×D3—122no—
319C22×D3—122no—
320C22×D3—124no—
321C22×D3—122no—
322C22×D3—122no—
323C22×D3—121no—
324C22×D3—121no—
325C22×D3—121no—
326C22×D3—121no—
327C3×Q8—32no—
328C3×Q8—61no—
329C3×D4—32no—
330C3×D4—62no—
331C3×D4—62no—
332C3×D4—61no—
333C2×C3×C4—24no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—42no—
343C2×C3×C4—42no—
344C2×C3×C4—41no—
345C2×C3×C4—41no—
346C2×C3×C4—41no—
347C2×C3×C4—41no—
348C2×C3×C4—61no—
349C2×C3×C4—62no—
350C2×C3×C4—62no—
351C2×C3×C4—61no—
352C2×C3×C4—61no—
353C2×C3×C4C2×C4×D311yescharacteristic
354C2×C3×C4C2×C4×D311yescharacteristic
355C2×C3×C4C2×D1211yescharacteristic
356C2×C3×C4C2×D1211yescharacteristic
357C2×C3×C4#23511yescharacteristic
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4D3×D411yescharacteristic
360C2×C3×C4D3×D411yescharacteristic
361C2×C3×C4#23711yescharacteristic
362C2×C3×C4#23711yescharacteristic
363C2×C3×C4#23911yescharacteristic
364C2×C3×C4C2×#6711yescharacteristic
365#67—22no—
366#67—22no—
367C2×Dic3—21no—
368C2×Dic3—21no—
369C2×Dic3—21no—
370C2×Dic3—62no—
371C2×Dic3—62no—
372C2×Dic3—122no—
373C2×Dic3—122no—
374C2×Dic3—122no—
375C2×Dic3—124no—
376C2×Dic3—242no—
377D12—21no—
378D12—62no—
379D12—62no—
380D12—62no—
381D12—62no—
382D12—122no—
383D12—122no—
384D12—122no—
385D12—122no—
386D12—121no—
387D12—121no—
388D12—121no—
389D12—121no—
390D12(C2×D3)⋊C412yescomplemented
391C4×D3—22no—
392C4×D3—22no—
393C4×D3—242no—
394Dic6—21no—
395Dic6(C2×D3)⋊C412yescomplemented
396C3×C8—62no—
397C3×C8—121no—
398C3⋊C8—22no—
399C3⋊C8—41no—
400C2×C32—21no—
401C2×C32—21no—
402C2×C32#38611yescharacteristic
403C2×C32#45311yescharacteristic
404C2×C32#45411yescharacteristic
405C3⋊D3—82no—
406C3×D3—42no—
407C24—181no—
408#41—32no—
409#41—32no—
410#41—61no—
411#41—61no—
412C2×Q8—31no—
413C2×D4—31no—
414C2×D4—61no—
415C2×D4—92no—
416C2×D4—181no—
417C2×D4—181no—
418C2×D4—181no—
419C2×D4—181no—
420C2×D4—181no—
421C22×C4—21no—
422C22×C4—61no—
423C22×C4—92no—
424C22×C4—182no—
425C22×C4C2×D3211yescharacteristic
426SD16—184no—
427D8—184no—
428M16—32no—
429M16—61no—
430M16—61no—
431M16—61no—
432C2×C8—61no—
433C2×C8—61no—
434C4⋊C4—31no—
435C4⋊C4—31no—
436C4⋊C4—182no—
437C4⋊C4—181no—
438C4⋊C4—181no—
439C22⋊C4—61no—
440C22⋊C4—182no—
441C22⋊C4—364no—
442C42—21no—
443C42—21no—
444C42—61no—
445C42—182no—
446C22×C3—22no—
447C22×C3—22no—
448C22×C3—21no—
449C22×C3—21no—
450C22×C3—21no—
451C22×C3—21no—
452C22×C3—21no—
453C22×C3—21no—
454C22×C3—21no—
455C22×C3—62no—
456C22×C3—121no—
457C22×C3—121no—
458C22×C3#67⋊C411yescharacteristic
459C22×C3#88211yescharacteristic
460C22×C3#88211yescharacteristic
461C22×C3#88411yescharacteristic
462C22×C3#89311yescharacteristic
463C22×C3#93911yescharacteristic
464C2×D3—22no—
465C2×D3—41no—
466C2×D3—41no—
467C2×D3—124no—
468C2×D3—128no—
469C2×D3—124no—
470C2×D3—124no—
471C2×D3—122no—
472C2×D3—122no—
473C2×D3—244no—
474C2×D3—242no—
475C2×D3—242no—
476C2×D3—242no—
477C2×D3—242no—
478C2×D3—241no—
479C2×D3—241no—
480C2×D3—241no—
481C2×D3—241no—
482C3×C4—21no—
483C3×C4—21no—
484C3×C4—21no—
485C3×C4—21no—
486C3×C4—44no—
487C3×C4—42no—
488C3×C4—42no—
489C3×C4—62no—
490C3×C4—121no—
491C3×C4—121no—
492C3×C4C4×D1211yescharacteristic
493C3×C4D3×C22⋊C411yescharacteristic
494C3×C4#67⋊C411yescharacteristic
495C3×C4#88611yescharacteristic
496C3×C4#89411yescharacteristic
497C3×C4#89511yescharacteristic
498C3×C4C2×(C2×D3)⋊C411yescharacteristic
499C3×C4#93911yescharacteristic
500Dic3—22no—
501Dic3—41no—
502Dic3—41no—
503Dic3—122no—
504Dic3—122no—
505Dic3—242no—
506C32#188311yescharacteristic, complemented, Sylow
507C23—61no—
508C23—182no—
509C23—362no—
510C23—362no—
511C23—361no—
512C23—361no—
513C23#381111yescharacteristic
514Q8—32no—
515Q8—61no—
516D4—32no—
517D4—62no—
518D4—62no—
519D4—61no—
520D4—182no—
521D4—182no—
522D4—361no—
523D4—361no—
524C2×C4—22no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—61no—
528C2×C4—62no—
529C2×C4—62no—
530C2×C4—61no—
531C2×C4—61no—
532C2×C4—182no—
533C2×C4—362no—
534C2×C4—722no—
535C2×C4#379611yescharacteristic
536C2×C4C4×D3211yescharacteristic
537C2×C4D3×D1211yescharacteristic
538C2×C4D3×D1211yescharacteristic
539C2×C4#380411yescharacteristic
540C2×C4D3×#6711yescharacteristic
541C8—62no—
542C8—121no—
543C2×C3—22no—
544C2×C3—22no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—21no—
550C2×C3—21no—
551C2×C3—21no—
552C2×C3—122no—
553C2×C3#466511yescharacteristic
554C2×C3#482211yescharacteristic
555C2×C3#482211yescharacteristic
556C2×C3#482711yescharacteristic
557C2×C3#482711yescharacteristic
558C2×C3#495811yescharacteristic
559D3—42no—
560D3—244no—
561D3—242no—
562D3—242no—
563C22—21no—
564C22—21no—
565C22—62no—
566C22—121no—
567C22—121no—
568C22—364no—
569C22—362no—
570C22—722no—
571C22—721no—
572C22—721no—
573C22#6388111yescharacteristic
574C22#6392311yescharacteristic
575C22#6397111yescharacteristic
576C4—42no—
577C4—62no—
578C4—121no—
579C4—121no—
580C4—362no—
581C4#6388011yescharacteristic
582C4#6388611yescharacteristic
583C4#6389011yescharacteristic
584C4D3×(C2×D3)⋊C411yescharacteristic
585C3—21no—
586C3#6877611yescharacteristic, complemented
587C3#7036611yescharacteristic, complemented
588C2—21no—
589C2—21no—
590C2—122no—
591C2—722no—
592C2#1059039711yescharacteristic
593C2#1059040211yescharacteristic
594C2#1059136411yescharacteristic
subgroupG/H
centerC22#63923
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32#120
prime radicalC2×#63825C2
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. #10594992C2semidirect
3. #10592638C2semidirect
4. C2×C3×#805C2semidirect
5. #10591096C2semidirect
6. C3×#4523C2semidirect
7. #10589168C2semidirect
25. #63825C4semidirect
40. C2×#805D3semidirect
44. #4523D3semidirect
54. C2×C4⋊(C3⋊D3)C2×C4semidirect
76. C3×#208C2×C4semidirect
157. C3×D12C22⋊C4semidirect
161. C3×Dic6C22⋊C4semidirect
260. #208C4×D3semidirect
390. D12(C2×D3)⋊C4semidirect
395. Dic6(C2×D3)⋊C4semidirect
506. C32#1883semidirect
586. C3#68776semidirect
587. C3#70366semidirect

Maximal subgroups

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

subgroupindex
#105949922
C2×#638252
#105926382
C2×C3×#8052
#105910962
C3×#45232
#105891682
#703663
#687763