Finite Group Databasebeta

← #11787546

Subgroups — #11787546

Order 1152.

1005 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#213C211yesmaximal, characteristic
2C2×#63898C211yesmaximal, characteristic, complemented
3#10592920C211yesmaximal, characteristic, complemented
4C2×C3×#832C211yesmaximal, characteristic, complemented
5C2×#63563C211yesmaximal, characteristic, complemented
6#10589164C211yesmaximal, characteristic, complemented
7#10589156C211yesmaximal, characteristic, complemented
8#72037—31nomaximal
9#70208—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C22×D3×Dic3—21no—
13C2×#3757—21no—
14C2×#3757—21no—
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C2×C3×#213—22no—
18C2×C3×#213—22no—
19C2×C3×#213C414yescomplemented
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C22×C3×C3⋊C8C2211yescharacteristic
23C2×(C2×D3)⋊Dic3—21no—
24#63898—22no—
25#63898—22no—
26C3×#832—22no—
27#63563—22no—
28C22×C3×D8—31no—
29C2×D4×Dic3—31no—
30C22×#213D311yescharacteristic
31C2×#893—31no—
32C2×C3×#102—31no—
33#5221—31no—
34#5221—31no—
35#5221—61no—
36C2×#832—31no—
37C2×#832D311yescharacteristic, complemented
38C2×#821—31no—
39#4551—31no—
40#4550—31no—
41#4550—31no—
42#4529—31no—
43C24×C32—21no—
44C23×C3×D3—21no—
45C2×C32×D4—21no—
46C2×C32×D4—21no—
47C2×C32×D4—21no—
48C2×C32×D4—21no—
49C2×C32×D4—21no—
50C2×C32×D4C2×C412yescomplemented
51C22×C32×C4C2311yescharacteristic
52C22×C3⋊Dic3—21no—
53C22×C3⋊Dic3D411yescharacteristic
54C22×C3⋊Dic3D411yescharacteristic
55C22×C3×Dic3—21no—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12—21no—
59C2×C3×D12C2×C412yes—
60C2×C3×D12D412yes—
61C2×C3×D12D412yes—
62C2×D3×Dic3—24no—
63C2×D3×Dic3—42no—
64C2×D3×Dic3—42no—
65#3757—42no—
66#3757—42no—
67C4⋊(C3⋊Dic3)—21no—
68C4⋊(C3⋊Dic3)—21no—
69C4×C3⋊Dic3—21no—
70C4×C3⋊Dic3—21no—
71C3×#213—28no—
72C3×C4⋊Dic3—21no—
73C3×C4⋊Dic3D412yes—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8—21no—
78C2×C3×C3⋊C8—21no—
79C2×C3×C3⋊C8C2×C412yescomplemented
80(C2×D3)⋊Dic3—24no—
81#1879—91noSylow
82C22×C3×D4—21no—
83C22×C3×D4—31no—
84C22×C3×D4C2×D311yescharacteristic
85C22×C3×D4C2×D311yescharacteristic
86C23×Dic3—61no—
87C22×D12C2×D311yescharacteristic
88C22×C4×D3—61no—
89C2×C3×D8—34no—
90C2×C3×D8—62no—
91C2×C3×D8—62no—
92C22×C3×C8—31no—
93C22×C3×C8—31no—
94C2×C3×C4⋊C4—31no—
95C2×#217—61no—
96C2×#217—61no—
97C2×#217—61no—
98C2×#217—61no—
99C2×#217—61no—
100C2×#217—62no—
101C2×#217—62no—
102D4×Dic3—62no—
103D4×Dic3—62no—
104C2×#213—22no—
105C2×#213—22no—
106C2×#213Dic314yescomplemented
107C2×(C2×D3)⋊C4—61no—
108C2×C4⋊Dic3—31no—
109C2×C4⋊Dic3—31no—
110C2×C4⋊Dic3—61no—
111C2×C4⋊Dic3C2×D311yescharacteristic
112C2×C4×Dic3—31no—
113C2×C4×Dic3—31no—
114C2×C4×Dic3—61no—
115C22×C3⋊C8C2×D311yescharacteristic
116C22×C3⋊C8C2×D311yescharacteristic
117#893—62no—
118#893—62no—
119C3×#102—62no—
120#832—22no—
121#832—62no—
122#821—62no—
123C23×C32—22no—
124C23×C32—41no—
125C23×C32—41no—
126C23×C32—41no—
127C23×C32—41no—
128C23×C32—41no—
129C23×C32—41no—
130C23×C32C2×D411yescharacteristic
131C22×C3×D3—22no—
132C22×C3×D3—22no—
133C22×C3×D3—22no—
134C22×C3×D3—41no—
135C22×C3×D3—41no—
136C22×C3×D3—41no—
137C22×C3×D3—41no—
138C32×D4—22no—
139C32×D4—22no—
140C32×D4—41no—
141C32×D4—41no—
142C2×C32×C4C22×C411yescharacteristic
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4#4111yescharacteristic
147C2×C32×C4#4111yescharacteristic
148C2×C3⋊Dic3—21no—
149C2×C3⋊Dic3—21no—
150C2×C3⋊Dic3—21no—
151C2×C3⋊Dic3—21no—
152C2×C3⋊Dic3—21no—
153C2×C3⋊Dic3—41no—
154C2×C3⋊Dic3—41no—
155C2×C3⋊Dic3—41no—
156C2×C3⋊Dic3D812yescomplemented
157C2×C3×Dic3—22no—
158C2×C3×Dic3—41no—
159C2×C3×Dic3—41no—
160C3×D12—22no—
161C3×D12—22no—
162C3×D12—22no—
163C3×D12C22⋊C414yescomplemented
164D3×Dic3—48no—
165C3×C3⋊C8—22no—
166C3×C3⋊C8—41no—
167C22×D8—31no—
168C2×C4×D4—91no—
169C2×#102—31no—
170C2×#102—91no—
171#390—91no—
172#340—91no—
173#336—91no—
174C24×C3—22no—
175C24×C3—21no—
176C24×C3—21no—
177C24×C3—61no—
178C23×D3—21no—
179C2×C3×D4—22no—
180C2×C3×D4—21no—
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—22no—
191C2×C3×D4—32no—
192C2×C3×D4—32no—
193C2×C3×D4—32no—
194C2×C3×D4—41no—
195C2×C3×D4—41no—
196C2×C3×D4—41no—
197C2×C3×D4—41no—
198C2×C3×D4—61no—
199C2×C3×D4—61no—
200C2×C3×D4—61no—
201C2×C3×D4C4×D312yescomplemented
202C2×C3×D4C2×Dic312yescomplemented
203C22×C3×C4—21no—
204C22×C3×C4—61no—
205C22×C3×C4C22×D311yescharacteristic
206C22×C3×C4C22×D311yescharacteristic
207C22×Dic3—21no—
208C22×Dic3—31no—
209C22×Dic3—31no—
210C22×Dic3—31no—
211C22×Dic3—31no—
212C22×Dic3—61no—
213C22×Dic3—61no—
214C22×Dic3—64no—
215C22×Dic3—62no—
216C22×Dic3—61no—
217C22×Dic3—61no—
218C22×Dic3—122no—
219C22×Dic3—122no—
220C2×D12—21no—
221C2×D12—21no—
222C2×D12—21no—
223C2×D12C2×Dic312yes—
224C2×D12#6712yes—
225C2×D12#6712yes—
226C2×C4×D3—64no—
227C2×C4×D3—122no—
228C2×C4×D3—122no—
229C3×D8—68no—
230C2×C3×C8—32no—
231C2×C3×C8—61no—
232C2×C3×C8—61no—
233C2×C3×C8—61no—
234C2×C3×C8—61no—
235C2×C3×C8—61no—
236C3×C4⋊C4—32no—
237C3×C4⋊C4—61no—
238#217—64no—
239#217—122no—
240#217—122no—
241#217—124no—
242#217—124no—
243#217—122no—
244#217—122no—
245#213—28no—
246(C2×D3)⋊C4—64no—
247C4⋊Dic3—21no—
248C4⋊Dic3—61no—
249C4⋊Dic3—61no—
250C4⋊Dic3—61no—
251C4⋊Dic3—61no—
252C4⋊Dic3—121no—
253C4⋊Dic3—121no—
254C4⋊Dic3#6712yes—
255C4×Dic3—61no—
256C4×Dic3—61no—
257C4×Dic3—61no—
258C4×Dic3—61no—
259C4×Dic3—121no—
260C4×Dic3—121no—
261C2×C3⋊C8—21no—
262C2×C3⋊C8—21no—
263C2×C3⋊C8—21no—
264C2×C3⋊C8—21no—
265C2×C3⋊C8—21no—
266C2×C3⋊C8C2×Dic312yescomplemented
267C22×C32—42no—
268C22×C32—42no—
269C22×C32—42no—
270C22×C32—81no—
271C22×C32—81no—
272C22×C32—81no—
273C22×C32—81no—
274C22×C32C4×D411yescharacteristic
275C22×C32#12011yescharacteristic
276C22×C32#12111yescharacteristic
277C22×C32C2×D811yescharacteristic
278C22×C32#13511yescharacteristic
279C22×C32AGL(1,ℤ/8)11yescharacteristic
280C22×C32AGL(1,ℤ/8)11yescharacteristic
281C2×C3×D3—24no—
282C2×C3×D3—42no—
283C2×C3×D3—42no—
284C2×C3×D3—42no—
285C2×C3×D3—42no—
286C2×C3×D3—42no—
287C2×C3×D3—42no—
288C32×C4C2×C22⋊C411yescharacteristic
289C32×C4C4×D411yescharacteristic
290C32×C4#12111yescharacteristic
291C32×C4#12311yescharacteristic
292C3⋊Dic3—22no—
293C3⋊Dic3—41no—
294C3⋊Dic3—81no—
295C3×Dic3—42no—
296C22×D4—31no—
297C22×D4D3211yescharacteristic
298C23×C4—181no—
299C2×D8—34no—
300C2×D8—62no—
301C2×D8—62no—
302C22×C8—31no—
303C22×C8—31no—
304C4×D4—182no—
305C4×D4—182no—
306C2×C4⋊C4—31no—
307C2×C4⋊C4—91no—
308C2×C22⋊C4—181no—
309C2×C22⋊C4—181no—
310C2×C22⋊C4—181no—
311C2×C42—91no—
312#102—62no—
313#102—182no—
314C23×C3—24no—
315C23×C3—22no—
316C23×C3—22no—
317C23×C3—21no—
318C23×C3—42no—
319C23×C3—42no—
320C23×C3—42no—
321C23×C3—42no—
322C23×C3—42no—
323C23×C3—42no—
324C23×C3—41no—
325C23×C3—41no—
326C23×C3—41no—
327C23×C3—41no—
328C23×C3—41no—
329C23×C3—41no—
330C23×C3—41no—
331C23×C3—41no—
332C23×C3—41no—
333C23×C3—41no—
334C23×C3—41no—
335C23×C3—41no—
336C23×C3—62no—
337C23×C3—62no—
338C23×C3—62no—
339C23×C3—121no—
340C23×C3—121no—
341C23×C3—121no—
342C23×C3—121no—
343C23×C3D3×D411yescharacteristic
344C23×C3D3×D411yescharacteristic
345C22×D3—22no—
346C22×D3—22no—
347C22×D3—22no—
348C22×D3—41no—
349C22×D3—41no—
350C22×D3—41no—
351C22×D3—41no—
352C3×D4—22no—
353C3×D4—22no—
354C3×D4—22no—
355C3×D4—22no—
356C3×D4—34no—
357C3×D4—42no—
358C3×D4—42no—
359C3×D4—42no—
360C3×D4—42no—
361C3×D4—41no—
362C3×D4—41no—
363C3×D4—41no—
364C3×D4—41no—
365C3×D4—62no—
366C3×D4—62no—
367C3×D4—62no—
368C2×C3×C4—21no—
369C2×C3×C4—21no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—62no—
375C2×C3×C4—121no—
376C2×C3×C4—121no—
377C2×C3×C4C2×C4×D311yescharacteristic
378C2×C3×C4#23511yescharacteristic
379C2×C3×C4D3×D411yescharacteristic
380C2×C3×C4D3×D411yescharacteristic
381C2×C3×C4D3×D411yescharacteristic
382C2×C3×C4#23711yescharacteristic
383C2×C3×C4#23711yescharacteristic
384C2×C3×C4#23711yescharacteristic
385C2×C3×C4C22×Dic311yescharacteristic
386C2×C3×C4C2×#6711yescharacteristic
387C2×C3×C4C2×#6711yescharacteristic
388C2×C3×C4C2×#6711yescharacteristic
389C2×Dic3—22no—
390C2×Dic3—32no—
391C2×Dic3—32no—
392C2×Dic3—41no—
393C2×Dic3—41no—
394C2×Dic3—62no—
395C2×Dic3—61no—
396C2×Dic3—61no—
397C2×Dic3—61no—
398C2×Dic3—61no—
399C2×Dic3—62no—
400C2×Dic3—61no—
401C2×Dic3—61no—
402C2×Dic3—61no—
403C2×Dic3—61no—
404C2×Dic3—61no—
405C2×Dic3—61no—
406C2×Dic3—121no—
407C2×Dic3—121no—
408C2×Dic3—121no—
409C2×Dic3—121no—
410C2×Dic3—128no—
411C2×Dic3—122no—
412C2×Dic3—122no—
413C2×Dic3—122no—
414C2×Dic3—121no—
415C2×Dic3—121no—
416C2×Dic3—121no—
417C2×Dic3—121no—
418C2×Dic3—121no—
419C2×Dic3—121no—
420D12—22no—
421D12—22no—
422D12—22no—
423D12#21714yescomplemented
424C4×D3—128no—
425C3×C8—62no—
426C3×C8—121no—
427C3⋊C8—22no—
428C3⋊C8—41no—
429C2×C32—82no—
430C2×C32#38611yescharacteristic
431C2×C32C4×D811yescharacteristic
432C2×C32#44211yescharacteristic
433C2×C32#44711yescharacteristic
434C2×C32#44911yescharacteristic
435C2×C32#45911yescharacteristic
436C2×C32#46311yescharacteristic
437C3×D3—44no—
438C24—21no—
439C24—61no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—32no—
446C2×D4—32no—
447C2×D4—32no—
448C2×D4—61no—
449C2×D4—61no—
450C2×D4—61no—
451C2×D4D3×Dic312yescomplemented
452C22×C4—61no—
453C22×C4—91no—
454C22×C4—91no—
455C22×C4—184no—
456C22×C4—181no—
457C22×C4—362no—
458C22×C4—362no—
459C22×C4C2×D3211yescharacteristic
460D8—68no—
461C2×C8—32no—
462C2×C8—61no—
463C2×C8—61no—
464C2×C8—61no—
465C2×C8—61no—
466C2×C8—61no—
467C4⋊C4—32no—
468C4⋊C4—61no—
469C4⋊C4—181no—
470C4⋊C4—181no—
471C22⋊C4—184no—
472C22⋊C4—362no—
473C22⋊C4—362no—
474C42—181no—
475C42—181no—
476C22×C3—21no—
477C22×C3—21no—
478C22×C3—21no—
479C22×C3—21no—
480C22×C3—21no—
481C22×C3—21no—
482C22×C3—21no—
483C22×C3—44no—
484C22×C3—44no—
485C22×C3—44no—
486C22×C3—42no—
487C22×C3—42no—
488C22×C3—42no—
489C22×C3—42no—
490C22×C3—42no—
491C22×C3—42no—
492C22×C3—64no—
493C22×C3—82no—
494C22×C3—82no—
495C22×C3—82no—
496C22×C3—82no—
497C22×C3—81no—
498C22×C3—81no—
499C22×C3—81no—
500C22×C3—81no—
501C22×C3—81no—
502C22×C3—81no—
503C22×C3—81no—
504C22×C3—81no—
505C22×C3—122no—
506C22×C3—122no—
507C22×C3—122no—
508C22×C3—122no—
509C22×C3—122no—
510C22×C3—122no—
511C22×C3#67⋊C411yescharacteristic
512C22×C3#88411yescharacteristic
513C22×C3D3×D811yescharacteristic
514C22×C3D3×D811yescharacteristic
515C22×C3#91111yescharacteristic
516C22×C3#91111yescharacteristic
517C22×C3#91111yescharacteristic
518C22×C3#91211yescharacteristic
519C22×C3#91411yescharacteristic
520C22×C3#91611yescharacteristic
521C22×C3D4×Dic311yescharacteristic
522C22×C3#93711yescharacteristic
523C22×C3#93711yescharacteristic
524C22×C3#93911yescharacteristic
525C2×D3—24no—
526C2×D3—42no—
527C2×D3—42no—
528C2×D3—42no—
529C2×D3—42no—
530C2×D3—42no—
531C2×D3—42no—
532C3×C4—21no—
533C3×C4—21no—
534C3×C4—21no—
535C3×C4—21no—
536C3×C4—122no—
537C3×C4D3×C22⋊C411yescharacteristic
538C3×C4#88311yescharacteristic
539C3×C4C4×#6711yescharacteristic
540C3×C4D4×Dic311yescharacteristic
541C3×C4#93511yescharacteristic
542C3×C4#93811yescharacteristic
543C3×C4#93911yescharacteristic
544C3×C4C2×#21711yescharacteristic
545Dic3—42no—
546Dic3—62no—
547Dic3—62no—
548Dic3—122no—
549Dic3—122no—
550Dic3—121no—
551Dic3—121no—
552Dic3—242no—
553Dic3—241no—
554Dic3—241no—
555C32#187911yescharacteristic, complemented, Sylow
556C23—22no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—62no—
564C23—62no—
565C23—62no—
566C23—121no—
567C23—121no—
568C23—121no—
569C23—121no—
570C23#381111yescharacteristic
571D4—22no—
572D4—22no—
573D4—34no—
574D4—41no—
575D4—41no—
576D4—62no—
577D4—62no—
578D4—62no—
579C2×C4—62no—
580C2×C4—92no—
581C2×C4—121no—
582C2×C4—121no—
583C2×C4—181no—
584C2×C4—181no—
585C2×C4—181no—
586C2×C4—181no—
587C2×C4—181no—
588C2×C4—368no—
589C2×C4—361no—
590C2×C4—361no—
591C2×C4—361no—
592C2×C4C2×D3×Dic311yescharacteristic
593C2×C4#380411yescharacteristic
594C2×C4#380511yescharacteristic
595C2×C4D3×#6711yescharacteristic
596C2×C4D3×#6711yescharacteristic
597C2×C4D3×#6711yescharacteristic
598C8—62no—
599C8—121no—
600C2×C3—21no—
601C2×C3—21no—
602C2×C3—21no—
603C2×C3—21no—
604C2×C3—21no—
605C2×C3—21no—
606C2×C3—21no—
607C2×C3—84no—
608C2×C3—82no—
609C2×C3—82no—
610C2×C3—124no—
611C2×C3#475611yescharacteristic
612C2×C3#478511yescharacteristic
613C2×C3#478611yescharacteristic
614C2×C3#478711yescharacteristic
615C2×C3#495611yescharacteristic
616C2×C3Dic3×D811yescharacteristic
617C2×C3#515011yescharacteristic
618C2×C3#515211yescharacteristic
619C2×C3#515311yescharacteristic
620C2×C3#515611yescharacteristic
621C2×C3#515611yescharacteristic
622C2×C3#515811yescharacteristic
623C2×C3#517211yescharacteristic
624C2×C3#522011yescharacteristic
625D3—44no—
626C22—42no—
627C22—42no—
628C22—42no—
629C22—64no—
630C22—81no—
631C22—81no—
632C22—81no—
633C22—81no—
634C22—122no—
635C22—122no—
636C22—122no—
637C22—122no—
638C22—122no—
639C22—122no—
640C22#6392611yescharacteristic
641C22#6392711yescharacteristic
642C22#6393611yescharacteristic
643C22#6393711yescharacteristic
644C22#6397111yescharacteristic
645C22#67⋊Dic311yescharacteristic
646C22#6398311yescharacteristic
647C4—122no—
648C4—182no—
649C4—361no—
650C4—721no—
651C4D3×#21711yescharacteristic
652C4#6396911yescharacteristic
653C4#6397011yescharacteristic
654C4Dic3×#6711yescharacteristic
655C3—21no—
656C3#7020811yescharacteristic, complemented
657C3#7203711yescharacteristic, complemented
658C2—82no—
659C2—124no—
660C2#1059143311yescharacteristic
661C2#1059143411yescharacteristic
662C2#1059143511yescharacteristic
663C2#1059143611yescharacteristic
664C2#1059151611yescharacteristic
665C2#1059152011yescharacteristic
666C2#1059172111yescharacteristic
subgroupG/H
centerC23#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×D4C22
socleC23×C32C2×D4
prime radicalC22×C3×#213C2
cosocleC22×C32×C4C23
hypercenterC22×D4D32
hypocenterC32#1879
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#63898C2semidirect
3. #10592920C2semidirect
4. C2×C3×#832C2semidirect
5. C2×#63563C2semidirect
6. #10589164C2semidirect
7. #10589156C2semidirect
19. C2×C3×#213C4semidirect
37. C2×#832D3semidirect
50. C2×C32×D4C2×C4semidirect
79. C2×C3×C3⋊C8C2×C4semidirect
106. C2×#213Dic3semidirect
156. C2×C3⋊Dic3D8semidirect
163. C3×D12C22⋊C4semidirect
201. C2×C3×D4C4×D3semidirect
202. C2×C3×D4C2×Dic3semidirect
266. C2×C3⋊C8C2×Dic3semidirect
423. D12#217semidirect
451. C2×D4D3×Dic3semidirect
555. C32#1879semidirect
656. C3#70208semidirect
657. C3#72037semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2132
C2×#638982
#105929202
C2×C3×#8322
C2×#635632
#105891642
#105891562
#720373
#702083