Finite Group Databasebeta

← #11787741

Subgroups — #11787741

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
1C2×C3×#932C211yesmaximal, characteristic
2#10594992C211yesmaximal, characteristic, complemented
3#10592920C211yesmaximal, characteristic, complemented
4C3×#5215C211yesmaximal, characteristic, complemented
5C2×#63568C211yesmaximal, characteristic, complemented
6#10589168C211yesmaximal, characteristic, complemented
7#10589160C211yesmaximal, characteristic, complemented
8#72088—31nomaximal
9#70328—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×#3757—22no—
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C2×C3×#214—21no—
16C3×#932—22no—
17C3×#932C414yescomplemented
18C2×C3×#213—21no—
19C3×#926C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C2×C3×#208C2211yescharacteristic
22#67⋊Dic3—22no—
23Dic3×D12—21no—
24D3×C4⋊Dic3—21no—
25Dic3×Dic6—21no—
26#63841—21no—
27C3×#832—21no—
28C3×#832—21no—
29#63568—22no—
30C2×C3×AGL(1,ℤ/8)—31no—
31#5827—31no—
32C2×#932D311yescharacteristic
33#5523—31no—
34C3×#418—31no—
35C2×#837—31no—
36#5221—31no—
37#5221—31no—
38#5221—61no—
39#5215D311yescharacteristic, complemented
40C2×#825—31no—
41#4555—31no—
42#4554—31no—
43#4554—31no—
44#4532—31no—
45C24×C32—21no—
46C2×C32×D4—21no—
47C2×C32×D4—21no—
48C2×C32×D4—21no—
49C2×C32×D4—21no—
50C2×C32×D4—21no—
51C2×C32×D4C2×C412yescomplemented
52C22×C32×C4C2311yescharacteristic
53C22×C3⋊Dic3—21no—
54C22×C3⋊Dic3D412yes—
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—
64#3757—44no—
65C4⋊(C3⋊Dic3)—21no—
66C4⋊(C3⋊Dic3)—21no—
67C4×C3⋊Dic3—21no—
68C4×C3⋊Dic3—21no—
69C3×#217—21no—
70C3×#214—24no—
71C3×#213—24no—
72C3×C4⋊Dic3D411yescharacteristic
73C3×C4⋊Dic3D411yescharacteristic
74C3×C4×Dic3—21no—
75C3×#208—21no—
76C3×#208—21no—
77C3×#208—21no—
78C3×#208C2×C412yescomplemented
79C2×C3×C3⋊C8—21no—
80C2×C3×C3⋊C8—21no—
81Dic3⋊Dic3—22no—
82(C2×D3)⋊Dic3—22no—
83Dic32—22no—
84#1883—91noSylow
85C2×C3×#41—31no—
86C22×C3×D4—21no—
87C22×C3×D4C2×D311yescharacteristic
88C22×C3×D4C2×D311yescharacteristic
89C2×#235C2×D311yescharacteristic
90C3×AGL(1,ℤ/8)—34no—
91C3×AGL(1,ℤ/8)—62no—
92C2×C3×SD16—61no—
93C2×C3×D8—61no—
94C2×C3×M16—31no—
95C2×C3×M16—31no—
96C3×#117—31no—
97C2×#217—62no—
98C2×#217—62no—
99C2×#217—64no—
100Q8×Dic3—61no—
101D4×Dic3—61no—
102D4×Dic3—62no—
103C2×#214—21no—
104#932—22no—
105#932Dic314yescomplemented
106C2×#213—21no—
107#926—61no—
108#926C2×D311yescharacteristic
109C2×C4⋊Dic3—31no—
110C2×C4⋊Dic3—31no—
111C2×C4⋊Dic3—61no—
112C2×C4⋊Dic3—61no—
113C2×C4×Dic3—31no—
114C2×C4×Dic3—31no—
115C2×C4×Dic3—61no—
116C2×#208C2×D311yescharacteristic
117C2×#208C2×D311yescharacteristic
118#892—61no—
119D3×C4⋊C4—61no—
120#67⋊C4—62no—
121C4×D12—61no—
122C4×Dic6—61no—
123C3×#102—61no—
124C3×#102—61no—
125#837—62no—
126#832—21no—
127#832—21no—
128#825—62no—
129C23×C32—22no—
130C23×C32—42no—
131C23×C32—42no—
132C23×C32—41no—
133C23×C32—41no—
134C23×C32C2×D411yescharacteristic
135C22×C3×D3—21no—
136C32×D4—22no—
137C32×D4—22no—
138C32×D4—41no—
139C32×D4—41no—
140C2×C32×C4C22×C411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4#4111yescharacteristic
145C2×C32×C4#4111yescharacteristic
146C2×C3⋊Dic3—22no—
147C2×C3⋊Dic3—22no—
148C2×C3⋊Dic3—41no—
149C2×C3⋊Dic3—41no—
150C2×C3⋊Dic3—42no—
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)—31no—
166#520—91no—
167C2×#104—91no—
168#418—31no—
169#390—91no—
170#343—91no—
171#339—91no—
172C24×C3—22no—
173C24×C3—21no—
174C24×C3—21no—
175C3×#41—32no—
176C3×#41—32no—
177C3×#41—61no—
178C3×#41—61no—
179C2×C3×Q8—31no—
180C2×C3×D4—22no—
181C2×C3×D4—21no—
182C2×C3×D4—21no—
183C2×C3×D4—21no—
184C2×C3×D4—21no—
185C2×C3×D4—21no—
186C2×C3×D4—21no—
187C2×C3×D4—21no—
188C2×C3×D4—21no—
189C2×C3×D4—21no—
190C2×C3×D4—21no—
191C2×C3×D4—22no—
192C2×C3×D4—31no—
193C2×C3×D4—41no—
194C2×C3×D4—41no—
195C2×C3×D4—41no—
196C2×C3×D4—41no—
197C2×C3×D4—61no—
198C2×C3×D4C4×D312yescomplemented
199C2×C3×D4C2×Dic312yescomplemented
200C22×C3×C4—21no—
201C22×C3×C4—61no—
202C22×C3×C4C22×D311yescharacteristic
203C22×C3×C4C22×D311yescharacteristic
204C2×#67—21no—
205C22×Dic3—32no—
206C22×Dic3—32no—
207C22×Dic3—62no—
208C22×Dic3—62no—
209C22×Dic3—62no—
210C22×Dic3—61no—
211C22×Dic3—61no—
212#235—21no—
213#235—21no—
214#235C2×Dic312yes—
215#235#6712yes—
216C2×D12#6711yescharacteristic
217C2×C4×D3—21no—
218C2×C4×D3—62no—
219C2×Dic6#6711yescharacteristic
220C3×SD16—64no—
221C3×D8—64no—
222C3×M16—32no—
223C3×M16—61no—
224C3×M16—61no—
225C3×M16—61no—
226C2×C3×C8—61no—
227C2×C3×C8—61no—
228C3×C4⋊C4—31no—
229C3×C4⋊C4—31no—
230C3×C22⋊C4—61no—
231C3×C42—61no—
232#217—21no—
233#217—62no—
234#217—124no—
235#217—124no—
236#217—128no—
237#214—24no—
238#213—24no—
239(C2×D3)⋊C4—62no—
240C4⋊Dic3—62no—
241C4⋊Dic3—61no—
242C4⋊Dic3—61no—
243C4⋊Dic3—61no—
244C4⋊Dic3—61no—
245C4⋊Dic3—121no—
246C4⋊Dic3—121no—
247C4⋊Dic3#6711yescharacteristic
248C4⋊Dic3#6711yescharacteristic
249Dic3⋊C4—62no—
250C4×Dic3—21no—
251C4×Dic3—62no—
252C4×Dic3—62no—
253C4×Dic3—61no—
254C4×Dic3—61no—
255C4×Dic3—61no—
256C4×Dic3—61no—
257C4×Dic3—121no—
258C4×Dic3—121no—
259#208—21no—
260#208—21no—
261#208—21no—
262#208C2×Dic312yescomplemented
263C2×C3⋊C8—21no—
264C2×C3⋊C8—21no—
265C22×C32—21no—
266C22×C32—21no—
267C22×C32—44no—
268C22×C32—42no—
269C22×C32—82no—
270C22×C32—81no—
271C22×C32—81no—
272C22×C32C4×D411yescharacteristic
273C22×C32#12011yescharacteristic
274C22×C32#12111yescharacteristic
275C2×C3×D3—22no—
276C2×C3×D3—41no—
277C2×C3×D3—41no—
278C32×C4C2×C22⋊C411yescharacteristic
279C32×C4C4×D411yescharacteristic
280C32×C4#12111yescharacteristic
281C32×C4#12311yescharacteristic
282C3⋊Dic3—42no—
283C3⋊Dic3—42no—
284C3×Dic3—22no—
285C3×Dic3—41no—
286C3×Dic3—41no—
287C2×#41—31no—
288C22×D4D3211yescharacteristic
289AGL(1,ℤ/8)—34no—
290AGL(1,ℤ/8)—62no—
291C2×SD16—61no—
292C2×D8—61no—
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×C42—91no—
304#104—182no—
305#102—61no—
306#102—61no—
307C23×C3—24no—
308C23×C3—22no—
309C23×C3—22no—
310C23×C3—21no—
311C23×C3—44no—
312C23×C3—42no—
313C23×C3—42no—
314C23×C3—42no—
315C23×C3—42no—
316C23×C3—44no—
317C23×C3—42no—
318C23×C3—42no—
319C23×C3—41no—
320C23×C3—41no—
321C23×C3—41no—
322C23×C3—41no—
323C23×C3—61no—
324C23×C3D3×D411yescharacteristic
325C23×C3D3×D411yescharacteristic
326C22×D3—21no—
327C3×Q8—32no—
328C3×Q8—61no—
329C3×D4—22no—
330C3×D4—22no—
331C3×D4—22no—
332C3×D4—22no—
333C3×D4—32no—
334C3×D4—42no—
335C3×D4—42no—
336C3×D4—42no—
337C3×D4—42no—
338C3×D4—41no—
339C3×D4—41no—
340C3×D4—41no—
341C3×D4—41no—
342C3×D4—62no—
343C3×D4—62no—
344C3×D4—61no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—61no—
352C2×C3×C4—62no—
353C2×C3×C4—62no—
354C2×C3×C4—61no—
355C2×C3×C4—61no—
356C2×C3×C4C2×C4×D311yescharacteristic
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#23711yescharacteristic
364C2×C3×C4C22×Dic311yescharacteristic
365C2×C3×C4C2×#6711yescharacteristic
366C2×C3×C4C2×#6711yescharacteristic
367C2×C3×C4C2×#6711yescharacteristic
368#67—22no—
369#67—22no—
370C2×Dic3—21no—
371C2×Dic3—21no—
372C2×Dic3—21no—
373C2×Dic3—64no—
374C2×Dic3—62no—
375C2×Dic3—62no—
376C2×Dic3—62no—
377C2×Dic3—62no—
378C2×Dic3—122no—
379C2×Dic3—122no—
380C2×Dic3—122no—
381C2×Dic3—121no—
382C2×Dic3—121no—
383C2×Dic3—121no—
384C2×Dic3—121no—
385C2×Dic3—122no—
386C2×Dic3—122no—
387C2×Dic3—124no—
388C2×Dic3—242no—
389D12—21no—
390D12#21712yescomplemented
391C4×D3—22no—
392C4×D3—22no—
393C4×D3—242no—
394Dic6—21no—
395Dic6#21712yescomplemented
396C3×C8—62no—
397C3×C8—121no—
398C3⋊C8—22no—
399C3⋊C8—41no—
400C2×C32—21no—
401C2×C32—21no—
402C2×C32—82no—
403C2×C32#38611yescharacteristic
404C2×C32#45311yescharacteristic
405C2×C32#45411yescharacteristic
406C3×D3—42no—
407C24—21no—
408#41—32no—
409#41—32no—
410#41—61no—
411#41—61no—
412C2×Q8—31no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—31no—
419C2×D4—61no—
420C2×D4D3×Dic312yescomplemented
421C22×C4—61no—
422C22×C4—92no—
423C22×C4—182no—
424C22×C4—181no—
425C22×C4C2×D3211yescharacteristic
426SD16—64no—
427D8—64no—
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—61no—
443C42—182no—
444C42—181no—
445C42—181no—
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—44no—
456C22×C3—48no—
457C22×C3—44no—
458C22×C3—44no—
459C22×C3—42no—
460C22×C3—42no—
461C22×C3—62no—
462C22×C3—84no—
463C22×C3—82no—
464C22×C3—82no—
465C22×C3—82no—
466C22×C3—82no—
467C22×C3—81no—
468C22×C3—81no—
469C22×C3—81no—
470C22×C3—81no—
471C22×C3—121no—
472C22×C3—121no—
473C22×C3#67⋊C411yescharacteristic
474C22×C3#88411yescharacteristic
475C22×C3D4×Dic311yescharacteristic
476C22×C3#93711yescharacteristic
477C22×C3#93711yescharacteristic
478C22×C3#93911yescharacteristic
479C2×D3—22no—
480C2×D3—41no—
481C2×D3—41no—
482C3×C4—21no—
483C3×C4—21no—
484C3×C4—21no—
485C3×C4—21no—
486C3×C4—62no—
487C3×C4—121no—
488C3×C4—121no—
489C3×C4D3×C22⋊C411yescharacteristic
490C3×C4#88311yescharacteristic
491C3×C4C4×#6711yescharacteristic
492C3×C4D4×Dic311yescharacteristic
493C3×C4#93511yescharacteristic
494C3×C4#93811yescharacteristic
495C3×C4#93911yescharacteristic
496C3×C4C2×#21711yescharacteristic
497Dic3—22no—
498Dic3—41no—
499Dic3—41no—
500Dic3—124no—
501Dic3—122no—
502Dic3—122no—
503Dic3—122no—
504Dic3—122no—
505Dic3—242no—
506C32#188311yescharacteristic, complemented, Sylow
507C23—22no—
508C23—42no—
509C23—42no—
510C23—41no—
511C23—41no—
512C23—61no—
513C23#381111yescharacteristic
514Q8—32no—
515Q8—61no—
516D4—22no—
517D4—22no—
518D4—32no—
519D4—41no—
520D4—41no—
521D4—62no—
522D4—62no—
523D4—61no—
524C2×C4—61no—
525C2×C4—62no—
526C2×C4—62no—
527C2×C4—61no—
528C2×C4—61no—
529C2×C4—182no—
530C2×C4—182no—
531C2×C4—361no—
532C2×C4—361no—
533C2×C4—362no—
534C2×C4—722no—
535C2×C4C2×D3×Dic311yescharacteristic
536C2×C4#380411yescharacteristic
537C2×C4#380511yescharacteristic
538C2×C4D3×#6711yescharacteristic
539C2×C4D3×#6711yescharacteristic
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—84no—
553C2×C3—82no—
554C2×C3—82no—
555C2×C3—122no—
556C2×C3#495611yescharacteristic
557C2×C3#519811yescharacteristic
558C2×C3#519811yescharacteristic
559C2×C3#520111yescharacteristic
560C2×C3#520111yescharacteristic
561C2×C3#522011yescharacteristic
562D3—42no—
563C22—21no—
564C22—21no—
565C22—44no—
566C22—42no—
567C22—62no—
568C22—82no—
569C22—81no—
570C22—81no—
571C22—121no—
572C22—121no—
573C22#6397111yescharacteristic
574C22#67⋊Dic311yescharacteristic
575C22#6398311yescharacteristic
576C4—62no—
577C4—121no—
578C4—121no—
579C4—362no—
580C4—362no—
581C4D3×#21711yescharacteristic
582C4#6396911yescharacteristic
583C4#6397011yescharacteristic
584C4Dic3×#6711yescharacteristic
585C3—21no—
586C3#7032811yescharacteristic, complemented
587C3#7208811yescharacteristic, complemented
588C2—21no—
589C2—21no—
590C2—82no—
591C2—122no—
592C2#1059152211yescharacteristic
593C2#1059152411yescharacteristic
594C2#1059172111yescharacteristic
subgroupG/H
centerC22#63983
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×D4C22
socleC22×C32#120
prime radicalC2×C3×#932C2
cosocleC22×C32×C4C23
hypercenterC22×D4D32
hypocenterC32#1883
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. #10594992C2semidirect
3. #10592920C2semidirect
4. C3×#5215C2semidirect
5. C2×#63568C2semidirect
6. #10589168C2semidirect
7. #10589160C2semidirect
17. C3×#932C4semidirect
39. #5215D3semidirect
51. C2×C32×D4C2×C4semidirect
78. C3×#208C2×C4semidirect
105. #932Dic3semidirect
157. C3×D12C22⋊C4semidirect
161. C3×Dic6C22⋊C4semidirect
198. C2×C3×D4C4×D3semidirect
199. C2×C3×D4C2×Dic3semidirect
262. #208C2×Dic3semidirect
390. D12#217semidirect
395. Dic6#217semidirect
420. C2×D4D3×Dic3semidirect
506. C32#1883semidirect
586. C3#70328semidirect
587. C3#72088semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9322
#105949922
#105929202
C3×#52152
C2×#635682
#105891682
#105891602
#720883
#703283