Finite Group Databasebeta

← #11787584

Subgroups — #11787584

Order 1152.

829 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63844C211yesmaximal, characteristic, complemented
2C22×#3716C211yesmaximal, characteristic
3C2×#63643C211yesmaximal, characteristic, complemented
4C2×C3×#821C211yesmaximal, characteristic
5#10591318C211yesmaximal, characteristic
6C3×#4550C211yesmaximal, characteristic, complemented
7#10589164C211yesmaximal, characteristic, complemented
8#70213—31nomaximal
9#68686—31nomaximal
10C22×#634C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C2×#3724—21no—
18C2×(C2×D3)⋊Dic3—21no—
19C2×(C2×D3)⋊Dic3—21no—
20C2×Dic32—21no—
21#63844—22no—
22#63844—22no—
23C2×#3716—22no—
24C2×#3716—22no—
25C2×#3716C414yescomplemented
26#63643—22no—
27C3×#821—22no—
28C22×#214—31no—
29C22×#204—31no—
30C2×#887—31no—
31C2×C4×Dic6—31no—
32C2×C3×#102—31no—
33#5221—31no—
34C2×#821D311yescharacteristic
35C2×#816—31no—
36C2×#816—31no—
37C2×#816—61no—
38#4939—31no—
39C3×#336—31no—
40#4551—31no—
41#4550D311yescharacteristic, complemented
42#4529—31no—
43C23×C3×D3—21no—
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3—21no—
46C22×C3⋊Dic3—21no—
47C2×#634—21no—
48C2×#634—21no—
49C2×#634—21no—
50C2×#634C2×C412yes—
51C2×#634D412yes—
52C2×#634D412yes—
53C22×C3×Dic3—21no—
54C22×C3×Dic3D411yescharacteristic
55C22×C3×Dic3D411yescharacteristic
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12—21no—
59C2×C3×D12—21no—
60C2×C3×D12—21no—
61C2×C3×D12C2×C412yes—
62C2×C32×C8—21no—
63C2×C32×C8—21no—
64C2×C32×C8—21no—
65C4⋊(C3⋊Dic3)—21no—
66C4⋊(C3⋊Dic3)—21no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3D412yes—
69C3×C4×Dic3—21no—
70C3×C4×Dic3—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8C2×C412yes—
74#3724—24no—
75(C2×D3)⋊Dic3—42no—
76(C2×D3)⋊Dic3—42no—
77Dic32—24no—
78#3716—28no—
79#1880—91noSylow
80C22×C3×D4—31no—
81C22×D12C2×D311yescharacteristic
82C22×Dic6—31no—
83C22×Dic6—31no—
84C22×Dic6—61no—
85C22×C3×C8—21no—
86C22×C3×C8—31no—
87C22×C3×C8C2×D311yescharacteristic
88C22×C3×C8C2×D311yescharacteristic
89C2×C3×C4⋊C4—31no—
90C2×C3×C42—31no—
91C2×#217—61no—
92C2×#217—61no—
93C2×#214—34no—
94C2×#214—62no—
95C2×#214—62no—
96C2×(C2×D3)⋊C4—61no—
97C2×(C2×D3)⋊C4—61no—
98C2×C4⋊Dic3—31no—
99C2×C4⋊Dic3—31no—
100C2×C4⋊Dic3—61no—
101C2×C4⋊Dic3C2×D311yescharacteristic
102C2×Dic3⋊C4—61no—
103C2×Dic3⋊C4—61no—
104C2×C4×Dic3—61no—
105C2×C4×Dic3—61no—
106C2×C4×Dic3C2×D311yescharacteristic
107C22×C3⋊C8C2×D311yescharacteristic
108C2×#204—34no—
109C2×#204—62no—
110C2×#204—62no—
111#887—62no—
112#887—62no—
113C4×Dic6—62no—
114C4×Dic6—62no—
115C3×#102—62no—
116#821—22no—
117#816—62no—
118#816—62no—
119#816—64no—
120C23×C32C2×D411yescharacteristic
121C22×C3×D3—22no—
122C22×C3×D3—41no—
123C22×C3×D3—41no—
124C22×C3×D3—41no—
125C22×C3×D3—41no—
126C22×C3×D3—41no—
127C22×C3×D3—41no—
128C2×C32×C4C22×C411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4#4111yescharacteristic
133C2×C32×C4#4111yescharacteristic
134C2×C3⋊Dic3—22no—
135C2×C3⋊Dic3—22no—
136C2×C3⋊Dic3—22no—
137C2×C3⋊Dic3—41no—
138C2×C3⋊Dic3—41no—
139C2×C3⋊Dic3—41no—
140#634—22no—
141#634—22no—
142#634—22no—
143#634C22⋊C414yescomplemented
144C2×C3×Dic3—21no—
145C2×C3×Dic3—21no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—21no—
148C2×C3×Dic3—21no—
149C2×C3×Dic3—21no—
150C2×C3×Dic3—41no—
151C2×C3×Dic3—41no—
152C2×C3×Dic3SD1612yescomplemented
153C3×D12—22no—
154C3×D12—22no—
155C3×D12—41no—
156C3×D12—41no—
157C32×C8—41no—
158C3×C3⋊C8—22no—
159C22×SD16—91no—
160C2×C4×Q8—91no—
161C2×#103—91no—
162C2×#102—31no—
163#390—91no—
164#340—91no—
165#336—31no—
166C24×C3—61no—
167C23×D3—21no—
168C2×C3×D4—32no—
169C2×C3×D4—61no—
170C2×C3×D4—61no—
171C2×C3×D4—61no—
172C2×C3×D4—61no—
173C2×C3×D4—61no—
174C22×C3×C4—21no—
175C22×C3×C4—31no—
176C22×C3×C4—31no—
177C22×C3×C4—61no—
178C22×C3×C4C22×D311yescharacteristic
179C22×C3×C4C22×D311yescharacteristic
180C22×Dic3—21no—
181C22×Dic3—61no—
182C22×Dic3—61no—
183C22×Dic3—61no—
184C22×Dic3—61no—
185C22×Dic3—121no—
186C22×Dic3—121no—
187C22×Dic3D1211yescharacteristic
188C22×Dic3D1211yescharacteristic
189C2×D12—21no—
190C2×D12—21no—
191C2×D12—21no—
192C2×D12—21no—
193C2×D12—21no—
194C2×D12C4×D312yes—
195C2×Dic6—32no—
196C2×Dic6—32no—
197C2×Dic6—32no—
198C2×Dic6—32no—
199C2×Dic6—32no—
200C2×Dic6—32no—
201C2×Dic6—62no—
202C2×Dic6—62no—
203C2×Dic6—62no—
204C2×Dic6—61no—
205C2×Dic6—61no—
206C2×Dic6—61no—
207C2×Dic6—61no—
208C2×Dic6—61no—
209C2×Dic6—61no—
210C2×Dic6—121no—
211C2×Dic6—121no—
212C2×Dic6—121no—
213C2×C3×C8—22no—
214C2×C3×C8—21no—
215C2×C3×C8—21no—
216C2×C3×C8—21no—
217C2×C3×C8—21no—
218C2×C3×C8—21no—
219C2×C3×C8—21no—
220C2×C3×C8—32no—
221C2×C3×C8—41no—
222C2×C3×C8—41no—
223C2×C3×C8—61no—
224C2×C3×C8—61no—
225C3×C4⋊C4—32no—
226C3×C4⋊C4—61no—
227C3×C42—61no—
228C3×C42—61no—
229#217—122no—
230#217—122no—
231#214—68no—
232(C2×D3)⋊C4—122no—
233(C2×D3)⋊C4—122no—
234C4⋊Dic3—21no—
235C4⋊Dic3—62no—
236C4⋊Dic3—61no—
237C4⋊Dic3—61no—
238C4⋊Dic3—61no—
239C4⋊Dic3—61no—
240C4⋊Dic3—121no—
241C4⋊Dic3#6712yes—
242Dic3⋊C4—64no—
243Dic3⋊C4—64no—
244C4×Dic3—21no—
245C4×Dic3—21no—
246C4×Dic3—64no—
247C4×Dic3—64no—
248C2×C3⋊C8—21no—
249C2×C3⋊C8—21no—
250C2×C3⋊C8C4×D312yes—
251#204—68no—
252C22×C32C4×D411yescharacteristic
253C22×C32#12011yescharacteristic
254C22×C32#12111yescharacteristic
255C22×C32C2×SD1611yescharacteristic
256C22×C32#13511yescharacteristic
257C22×C32AGL(1,ℤ/8)11yescharacteristic
258C22×C32#13711yescharacteristic
259C2×C3×D3—42no—
260C2×C3×D3—42no—
261C2×C3×D3—42no—
262C2×C3×D3—81no—
263C2×C3×D3—81no—
264C2×C3×D3—81no—
265C2×C3×D3—81no—
266C32×C4C2×C22⋊C411yescharacteristic
267C32×C4C4×D411yescharacteristic
268C32×C4#12111yescharacteristic
269C32×C4#12311yescharacteristic
270C3⋊Dic3—24no—
271C3⋊Dic3—81no—
272C3×Dic3—22no—
273C3×Dic3—41no—
274C3×Dic3—42no—
275C22×Q8—91no—
276C22×D4—31no—
277C2×SD16—94no—
278C2×SD16—182no—
279C2×SD16—182no—
280C22×C8—31no—
281C22×C8D3211yescharacteristic
282C4×Q8—182no—
283C4×Q8—182no—
284C2×C4⋊C4—31no—
285C2×C4⋊C4—91no—
286C2×C4⋊C4—181no—
287C2×C22⋊C4—181no—
288C2×C22⋊C4—181no—
289C2×C42—31no—
290C2×C42—181no—
291#103—182no—
292#102—62no—
293C23×C3—21no—
294C23×C3—62no—
295C23×C3—121no—
296C23×C3—121no—
297C23×C3—121no—
298C23×C3—121no—
299C23×C3—121no—
300C23×C3—121no—
301C23×C3C2×D1211yescharacteristic
302C23×C3D3×D411yescharacteristic
303C22×D3—22no—
304C22×D3—41no—
305C22×D3—41no—
306C22×D3—41no—
307C22×D3—41no—
308C22×D3—41no—
309C22×D3—41no—
310C3×D4—62no—
311C3×D4—62no—
312C3×D4—121no—
313C3×D4—121no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—32no—
321C2×C3×C4—61no—
322C2×C3×C4—61no—
323C2×C3×C4—62no—
324C2×C3×C4—61no—
325C2×C3×C4—61no—
326C2×C3×C4—61no—
327C2×C3×C4—121no—
328C2×C3×C4—121no—
329C2×C3×C4C2×C4×D311yescharacteristic
330C2×C3×C4C2×C4×D311yescharacteristic
331C2×C3×C4#23511yescharacteristic
332C2×C3×C4#23511yescharacteristic
333C2×C3×C4D3×D411yescharacteristic
334C2×C3×C4D3×D411yescharacteristic
335C2×C3×C4D3×D411yescharacteristic
336C2×C3×C4D3×D411yescharacteristic
337C2×C3×C4D3×D411yescharacteristic
338C2×C3×C4#23711yescharacteristic
339C2×C3×C4#23911yescharacteristic
340C2×C3×C4C2×#6711yescharacteristic
341C2×Dic3—21no—
342C2×Dic3—21no—
343C2×Dic3—21no—
344C2×Dic3—21no—
345C2×Dic3—21no—
346C2×Dic3—22no—
347C2×Dic3—41no—
348C2×Dic3—41no—
349C2×Dic3—62no—
350C2×Dic3—62no—
351C2×Dic3—62no—
352C2×Dic3—62no—
353C2×Dic3—62no—
354C2×Dic3—62no—
355C2×Dic3—122no—
356C2×Dic3—122no—
357C2×Dic3—122no—
358C2×Dic3—122no—
359C2×Dic3—121no—
360C2×Dic3—121no—
361C2×Dic3—121no—
362C2×Dic3—121no—
363C2×Dic3—121no—
364C2×Dic3—121no—
365C2×Dic3—241no—
366C2×Dic3—241no—
367C2×Dic3#20412yescomplemented
368D12—22no—
369D12—22no—
370D12—41no—
371D12—41no—
372Dic6—34no—
373Dic6—34no—
374Dic6—64no—
375Dic6—62no—
376Dic6—62no—
377Dic6—62no—
378Dic6—62no—
379Dic6—62no—
380Dic6—62no—
381Dic6—122no—
382Dic6—122no—
383Dic6—122no—
384C3×C8—42no—
385C3×C8—41no—
386C3×C8—41no—
387C3×C8—62no—
388C3⋊C8—22no—
389C2×C32#38611yescharacteristic
390C2×C32C4×SD1611yescharacteristic
391C2×C32#44011yescharacteristic
392C2×C32#44811yescharacteristic
393C2×C32#44911yescharacteristic
394C2×C32#46011yescharacteristic
395C2×C32#46411yescharacteristic
396C3×D3—82no—
397C24—61no—
398C2×Q8—92no—
399C2×Q8—92no—
400C2×Q8—92no—
401C2×Q8—181no—
402C2×Q8—181no—
403C2×Q8—181no—
404C2×D4—32no—
405C2×D4—61no—
406C2×D4—61no—
407C2×D4—61no—
408C2×D4—61no—
409C2×D4—61no—
410C22×C4—31no—
411C22×C4—31no—
412C22×C4—61no—
413C22×C4—181no—
414C22×C4—181no—
415C22×C4C2×D3211yescharacteristic
416SD16—188no—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—32no—
421C2×C8—61no—
422C2×C8—61no—
423C4⋊C4—32no—
424C4⋊C4—61no—
425C4⋊C4—184no—
426C4⋊C4—181no—
427C4⋊C4—181no—
428C22⋊C4—362no—
429C22⋊C4—362no—
430C42—61no—
431C42—61no—
432C42—184no—
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—21no—
436C22×C3—21no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—122no—
441C22×C3—122no—
442C22×C3—122no—
443C22×C3—241no—
444C22×C3—241no—
445C22×C3—241no—
446C22×C3—241no—
447C22×C3C4×D1211yescharacteristic
448C22×C3#67⋊C411yescharacteristic
449C22×C3#88211yescharacteristic
450C22×C3#88411yescharacteristic
451C22×C3#89511yescharacteristic
452C22×C3C2×#20411yescharacteristic
453C22×C3#90411yescharacteristic
454C22×C3#90811yescharacteristic
455C22×C3#90911yescharacteristic
456C22×C3#91111yescharacteristic
457C22×C3#91211yescharacteristic
458C22×C3D3×SD1611yescharacteristic
459C22×C3#91511yescharacteristic
460C22×C3#93711yescharacteristic
461C2×D3—42no—
462C2×D3—42no—
463C2×D3—42no—
464C2×D3—81no—
465C2×D3—81no—
466C2×D3—81no—
467C2×D3—81no—
468C3×C4—21no—
469C3×C4—21no—
470C3×C4—21no—
471C3×C4—21no—
472C3×C4—62no—
473C3×C4—121no—
474C3×C4—122no—
475C3×C4D3×C22⋊C411yescharacteristic
476C3×C4D3×C22⋊C411yescharacteristic
477C3×C4#88311yescharacteristic
478C3×C4#88411yescharacteristic
479C3×C4#89311yescharacteristic
480C3×C4#89411yescharacteristic
481C3×C4C4×#6711yescharacteristic
482C3×C4#93811yescharacteristic
483Dic3—22no—
484Dic3—42no—
485Dic3—41no—
486Dic3—64no—
487Dic3—64no—
488Dic3—124no—
489Dic3—242no—
490Dic3—241no—
491Dic3—241no—
492C32#188011yescharacteristic, complemented, Sylow
493C23—62no—
494C23—121no—
495C23—121no—
496C23—121no—
497C23—121no—
498C23—121no—
499C23—121no—
500C23D3×D1211yescharacteristic
501Q8—94no—
502Q8—182no—
503Q8—182no—
504Q8—182no—
505D4—62no—
506D4—62no—
507D4—121no—
508D4—121no—
509C2×C4—32no—
510C2×C4—61no—
511C2×C4—61no—
512C2×C4—61no—
513C2×C4—61no—
514C2×C4—61no—
515C2×C4—62no—
516C2×C4—121no—
517C2×C4—121no—
518C2×C4—182no—
519C2×C4—182no—
520C2×C4—182no—
521C2×C4—361no—
522C2×C4—361no—
523C2×C4—361no—
524C2×C4#379911yescharacteristic
525C2×C4C4×D3211yescharacteristic
526C2×C4#380211yescharacteristic
527C2×C4#380411yescharacteristic
528C2×C4D3×#6711yescharacteristic
529C2×C4#381111yescharacteristic
530C8—41no—
531C8—62no—
532C2×C3—21no—
533C2×C3—21no—
534C2×C3—21no—
535C2×C3—21no—
536C2×C3—21no—
537C2×C3—21no—
538C2×C3—21no—
539C2×C3—242no—
540C2×C3#466511yescharacteristic
541C2×C3C4×#20411yescharacteristic
542C2×C3#471011yescharacteristic
543C2×C3#473411yescharacteristic
544C2×C3#473811yescharacteristic
545C2×C3#475711yescharacteristic
546C2×C3#475811yescharacteristic
547C2×C3#476211yescharacteristic
548C2×C3#476711yescharacteristic
549C2×C3#484511yescharacteristic
550C2×C3#484811yescharacteristic
551C2×C3#495611yescharacteristic
552C2×C3#515811yescharacteristic
553C2×C3#517011yescharacteristic
554D3—82no—
555C22—122no—
556C22—122no—
557C22—122no—
558C22—241no—
559C22—241no—
560C22—241no—
561C22—241no—
562C22D3×#20411yescharacteristic
563C22#6379511yescharacteristic
564C22#6380011yescharacteristic
565C22#6380711yescharacteristic
566C22#6388011yescharacteristic
567C22#6391011yescharacteristic
568C22#6392211yescharacteristic
569C4—62no—
570C4—121no—
571C4—122no—
572C4—184no—
573C4—721no—
574C4#6385411yescharacteristic
575C4#6390411yescharacteristic
576C4#6392111yescharacteristic
577C4#6395811yescharacteristic
578C3—21no—
579C3#6868611yescharacteristic, complemented
580C3#7021311yescharacteristic, complemented
581C2—242no—
582C2#1059074411yescharacteristic
583C2#1059074711yescharacteristic
584C2#1059082211yescharacteristic
585C2#1059086111yescharacteristic
586C2#1059087911yescharacteristic
587C2#1059096211yescharacteristic
588C2#1059127511yescharacteristic
subgroupG/H
centerC23D3×D12
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1880
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C2×#63844C2semidirect
3. C2×#63643C2semidirect
6. C3×#4550C2semidirect
7. #10589164C2semidirect
25. C2×#3716C4semidirect
41. #4550D3semidirect
143. #634C22⋊C4semidirect
152. C2×C3×Dic3SD16semidirect
367. C2×Dic3#204semidirect
492. C32#1880semidirect
579. C3#68686semidirect
580. C3#70213semidirect

Maximal subgroups

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

subgroupindex
C2×#638442
C22×#37162
C2×#636432
C2×C3×#8212
#105913182
C3×#45502
#105891642
#702133
#686863