Finite Group Databasebeta

← #11787544

Subgroups — #11787544

Order 1152.

977 conjugacy classes of subgroups.

The subgroup lattice has 657 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#213C211yesmaximal, characteristic
2C2×Dic3×D12C211yesmaximal, characteristic, complemented
3C2×#63659C211yesmaximal, characteristic, complemented
4C3×#5221C211yesmaximal, characteristic, complemented
5C2×#63562C211yesmaximal, characteristic, complemented
6#10589164C211yesmaximal, characteristic, complemented
7#10589155C211yesmaximal, characteristic, complemented
8#72037—31nomaximal
9#69657—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C22×D3×Dic3—21no—
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C2×C3×#217—21no—
16C2×C3×#217—21no—
17C2×C3×#213—22no—
18C2×C3×#213—22no—
19C2×C3×#213C414yescomplemented
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×C4×Dic3C2211yescharacteristic
22C22×C3×C3⋊C8C2211yescharacteristic
23C2×(C2×D3)⋊Dic3—21no—
24Dic3×D12—22no—
25Dic3×D12—22no—
26#63659—22no—
27#63562—22no—
28C22×C3×D8—31no—
29C2×D4×Dic3—31no—
30C22×#213D311yescharacteristic
31C2×C4×D12—31no—
32C3×#390—31no—
33#5221D311yescharacteristic, complemented
34C2×#832—31no—
35C2×#832—31no—
36C2×#832—31no—
37C2×#832—61no—
38C2×#809—31no—
39#4551—31no—
40#4550—31no—
41#4529—31no—
42#4524—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×Dic3—21no—
54C22×C3×Dic3D411yescharacteristic
55C22×C3×Dic3D411yescharacteristic
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—
65C4⋊(C3⋊Dic3)—21no—
66C4⋊(C3⋊Dic3)D412yes—
67C2×C3⋊(C3⋊C8)—21no—
68C2×C3⋊(C3⋊C8)—21no—
69C2×C3⋊(C3⋊C8)—21no—
70C3×#217—42no—
71C3×#217—42no—
72C3×#213—28no—
73C3×C4⋊Dic3—21no—
74C3×C4⋊Dic3—21no—
75C3×C4×Dic3—21no—
76C3×C4×Dic3—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—
93C2×C3×C4⋊C4—31no—
94C2×C3×C22⋊C4—61no—
95C2×C3×C22⋊C4—61no—
96C2×C3×C42—31no—
97C2×#217—21no—
98C2×#217—21no—
99C2×#217—61no—
100D4×Dic3—62no—
101D4×Dic3—62no—
102C2×#213—22no—
103C2×#213—22no—
104C2×#213Dic314yescomplemented
105C2×(C2×D3)⋊C4—61no—
106C2×C4⋊Dic3—31no—
107C2×C4⋊Dic3—31no—
108C2×C4⋊Dic3—61no—
109C2×C4⋊Dic3C2×D311yescharacteristic
110C2×C4×Dic3C2×D311yescharacteristic
111C22×C3⋊C8—31no—
112C22×C3⋊C8—31no—
113C22×C3⋊C8—61no—
114C22×C3⋊C8C2×D311yescharacteristic
115C4×D12—62no—
116C4×D12—62no—
117#832—62no—
118#832—62no—
119#832—62no—
120#832—64no—
121#809—62no—
122C23×C32—22no—
123C23×C32—41no—
124C23×C32—41no—
125C23×C32—41no—
126C23×C32—41no—
127C23×C32—41no—
128C23×C32—41no—
129C23×C32C2×D411yescharacteristic
130C22×C3×D3—22no—
131C22×C3×D3—22no—
132C22×C3×D3—22no—
133C22×C3×D3—41no—
134C22×C3×D3—41no—
135C22×C3×D3—41no—
136C22×C3×D3—41no—
137C32×D4—22no—
138C32×D4—22no—
139C32×D4—41no—
140C32×D4—41no—
141C2×C32×C4C22×C411yescharacteristic
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4#4111yescharacteristic
146C2×C32×C4#4111yescharacteristic
147C2×C3⋊Dic3—22no—
148C2×C3⋊Dic3—41no—
149C2×C3⋊Dic3—41no—
150C2×C3×Dic3—21no—
151C2×C3×Dic3—21no—
152C2×C3×Dic3—21no—
153C2×C3×Dic3—21no—
154C2×C3×Dic3—21no—
155C2×C3×Dic3—41no—
156C2×C3×Dic3—41no—
157C2×C3×Dic3—41no—
158C2×C3×Dic3D812yescomplemented
159C3×D12—22no—
160C3×D12—22no—
161C3×D12—22no—
162C3×D12C22⋊C414yescomplemented
163D3×Dic3—48no—
164C3⋊(C3⋊C8)—41no—
165C3×C3⋊C8—22no—
166C22×D8—31no—
167C2×C4×D4—91no—
168C2×#102—91no—
169C2×#102—91no—
170#390—31no—
171#340—91no—
172#336—91no—
173C24×C3—21no—
174C24×C3—21no—
175C24×C3—41no—
176C24×C3—61no—
177C23×D3—21no—
178C2×C3×D4—22no—
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—61no—
198C2×C3×D4—61no—
199C2×C3×D4—61no—
200C2×C3×D4C4×D312yescomplemented
201C2×C3×D4C2×Dic312yescomplemented
202C22×C3×C4—21no—
203C22×C3×C4—31no—
204C22×C3×C4—31no—
205C22×C3×C4—61no—
206C22×C3×C4C22×D311yescharacteristic
207C22×C3×C4C22×D311yescharacteristic
208C22×Dic3—21no—
209C22×Dic3—64no—
210C22×Dic3—61no—
211C22×Dic3—61no—
212C22×Dic3—121no—
213C22×Dic3—122no—
214C22×Dic3—122no—
215C22×Dic3#6711yescharacteristic
216C22×Dic3#6711yescharacteristic
217C2×D12—21no—
218C2×D12—21no—
219C2×D12—21no—
220C2×D12C2×Dic312yes—
221C2×D12#6712yes—
222C2×D12#6712yes—
223C2×C4×D3—64no—
224C2×C4×D3—122no—
225C2×C4×D3—122no—
226C3×D8—68no—
227C2×C3×C8—32no—
228C2×C3×C8—61no—
229C2×C3×C8—61no—
230C3×C4⋊C4—61no—
231C3×C4⋊C4—61no—
232C3×C22⋊C4—122no—
233C3×C22⋊C4—122no—
234C3×C42—61no—
235C3×C42—61no—
236#217—42no—
237#217—42no—
238#217—64no—
239#213—28no—
240(C2×D3)⋊C4—64no—
241C4⋊Dic3—21no—
242C4⋊Dic3—21no—
243C4⋊Dic3—32no—
244C4⋊Dic3—32no—
245C4⋊Dic3—62no—
246C4⋊Dic3—61no—
247C4⋊Dic3—61no—
248C4⋊Dic3—121no—
249C4×Dic3—21no—
250C4×Dic3—21no—
251C2×C3⋊C8—21no—
252C2×C3⋊C8—21no—
253C2×C3⋊C8—62no—
254C2×C3⋊C8—61no—
255C2×C3⋊C8—61no—
256C2×C3⋊C8—61no—
257C2×C3⋊C8—61no—
258C2×C3⋊C8—61no—
259C2×C3⋊C8—61no—
260C2×C3⋊C8—121no—
261C2×C3⋊C8—121no—
262C2×C3⋊C8C2×Dic312yescomplemented
263C22×C32—42no—
264C22×C32—42no—
265C22×C32—42no—
266C22×C32—81no—
267C22×C32—81no—
268C22×C32—81no—
269C22×C32—81no—
270C22×C32C4×D411yescharacteristic
271C22×C32#12011yescharacteristic
272C22×C32#12111yescharacteristic
273C22×C32C2×D811yescharacteristic
274C22×C32#13511yescharacteristic
275C22×C32AGL(1,ℤ/8)11yescharacteristic
276C22×C32AGL(1,ℤ/8)11yescharacteristic
277C2×C3×D3—24no—
278C2×C3×D3—42no—
279C2×C3×D3—42no—
280C2×C3×D3—42no—
281C2×C3×D3—42no—
282C2×C3×D3—42no—
283C2×C3×D3—42no—
284C32×C4C2×C22⋊C411yescharacteristic
285C32×C4C4×D411yescharacteristic
286C32×C4#12111yescharacteristic
287C32×C4#12311yescharacteristic
288C3⋊Dic3—42no—
289C3×Dic3—22no—
290C3×Dic3—41no—
291C3×Dic3—81no—
292C22×D4—31no—
293C22×D4D3211yescharacteristic
294C23×C4—181no—
295C2×D8—34no—
296C2×D8—62no—
297C2×D8—62no—
298C22×C8—31no—
299C22×C8—91no—
300C4×D4—182no—
301C4×D4—182no—
302C2×C4⋊C4—31no—
303C2×C4⋊C4—91no—
304C2×C22⋊C4—61no—
305C2×C22⋊C4—61no—
306C2×C22⋊C4—181no—
307C2×C42—31no—
308#102—182no—
309#102—182no—
310C23×C3—22no—
311C23×C3—22no—
312C23×C3—21no—
313C23×C3—42no—
314C23×C3—42no—
315C23×C3—42no—
316C23×C3—41no—
317C23×C3—41no—
318C23×C3—41no—
319C23×C3—41no—
320C23×C3—41no—
321C23×C3—41no—
322C23×C3—41no—
323C23×C3—41no—
324C23×C3—41no—
325C23×C3—41no—
326C23×C3—41no—
327C23×C3—41no—
328C23×C3—62no—
329C23×C3—62no—
330C23×C3—62no—
331C23×C3—81no—
332C23×C3—81no—
333C23×C3—81no—
334C23×C3—81no—
335C23×C3—121no—
336C23×C3—121no—
337C23×C3—121no—
338C23×C3—121no—
339C23×C3D3×D411yescharacteristic
340C23×C3C2×#6711yescharacteristic
341C22×D3—22no—
342C22×D3—22no—
343C22×D3—22no—
344C22×D3—41no—
345C22×D3—41no—
346C22×D3—41no—
347C22×D3—41no—
348C3×D4—24no—
349C3×D4—22no—
350C3×D4—22no—
351C3×D4—22no—
352C3×D4—22no—
353C3×D4—34no—
354C3×D4—42no—
355C3×D4—42no—
356C3×D4—42no—
357C3×D4—41no—
358C3×D4—41no—
359C3×D4—41no—
360C3×D4—41no—
361C3×D4—62no—
362C3×D4—62no—
363C3×D4—62no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—21no—
368C2×C3×C4—21no—
369C2×C3×C4—21no—
370C2×C3×C4—32no—
371C2×C3×C4—61no—
372C2×C3×C4—61no—
373C2×C3×C4—61no—
374C2×C3×C4—61no—
375C2×C3×C4—61no—
376C2×C3×C4—121no—
377C2×C3×C4—121no—
378C2×C3×C4—121no—
379C2×C3×C4C2×C4×D311yescharacteristic
380C2×C3×C4#23511yescharacteristic
381C2×C3×C4D3×D411yescharacteristic
382C2×C3×C4D3×D411yescharacteristic
383C2×C3×C4D3×D411yescharacteristic
384C2×C3×C4D3×D411yescharacteristic
385C2×C3×C4#23711yescharacteristic
386C2×C3×C4#23711yescharacteristic
387C2×C3×C4#23711yescharacteristic
388C2×C3×C4C22×Dic311yescharacteristic
389C2×C3×C4C2×#6711yescharacteristic
390C2×C3×C4C2×#6711yescharacteristic
391C2×Dic3—21no—
392C2×Dic3—21no—
393C2×Dic3—21no—
394C2×Dic3—21no—
395C2×Dic3—21no—
396C2×Dic3—41no—
397C2×Dic3—41no—
398C2×Dic3—41no—
399C2×Dic3—62no—
400C2×Dic3—62no—
401C2×Dic3—122no—
402C2×Dic3—128no—
403C2×Dic3—121no—
404C2×Dic3—121no—
405C2×Dic3—121no—
406C2×Dic3—121no—
407C2×Dic3—241no—
408C2×Dic3—241no—
409C2×Dic3#21312yescomplemented
410D12—22no—
411D12—22no—
412D12—22no—
413D12#21714yescomplemented
414C4×D3—128no—
415C3×C8—62no—
416C3⋊C8—22no—
417C3⋊C8—122no—
418C3⋊C8—121no—
419C3⋊C8—121no—
420C2×C32—82no—
421C2×C32#38611yescharacteristic
422C2×C32C4×D811yescharacteristic
423C2×C32#44211yescharacteristic
424C2×C32#44711yescharacteristic
425C2×C32#44911yescharacteristic
426C2×C32#45911yescharacteristic
427C2×C32#46311yescharacteristic
428C3×D3—44no—
429C24—21no—
430C24—61no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—32no—
437C2×D4—32no—
438C2×D4—32no—
439C2×D4—61no—
440C2×D4—61no—
441C2×D4—61no—
442C2×D4D3×Dic312yescomplemented
443C22×C4—31no—
444C22×C4—31no—
445C22×C4—61no—
446C22×C4—184no—
447C22×C4—181no—
448C22×C4—362no—
449C22×C4—362no—
450C22×C4C2×D3211yescharacteristic
451D8—68no—
452C2×C8—32no—
453C2×C8—61no—
454C2×C8—61no—
455C2×C8—181no—
456C2×C8—181no—
457C2×C8—181no—
458C4⋊C4—61no—
459C4⋊C4—61no—
460C4⋊C4—92no—
461C4⋊C4—181no—
462C22⋊C4—122no—
463C22⋊C4—122no—
464C22⋊C4—184no—
465C42—61no—
466C42—61no—
467C22×C3—21no—
468C22×C3—21no—
469C22×C3—21no—
470C22×C3—21no—
471C22×C3—21no—
472C22×C3—21no—
473C22×C3—21no—
474C22×C3—44no—
475C22×C3—42no—
476C22×C3—42no—
477C22×C3—42no—
478C22×C3—42no—
479C22×C3—42no—
480C22×C3—42no—
481C22×C3—64no—
482C22×C3—82no—
483C22×C3—82no—
484C22×C3—82no—
485C22×C3—82no—
486C22×C3—82no—
487C22×C3—82no—
488C22×C3—81no—
489C22×C3—81no—
490C22×C3—81no—
491C22×C3—81no—
492C22×C3—81no—
493C22×C3—81no—
494C22×C3—81no—
495C22×C3—81no—
496C22×C3—122no—
497C22×C3—122no—
498C22×C3—122no—
499C22×C3—122no—
500C22×C3—122no—
501C22×C3—122no—
502C22×C3D3×D811yescharacteristic
503C22×C3#91111yescharacteristic
504C22×C3#91111yescharacteristic
505C22×C3#91211yescharacteristic
506C22×C3C4×#6711yescharacteristic
507C22×C3C2×#21311yescharacteristic
508C22×C3#93211yescharacteristic
509C22×C3D4×Dic311yescharacteristic
510C22×C3#93711yescharacteristic
511C22×C3#93711yescharacteristic
512C22×C3#93811yescharacteristic
513C22×C3#93911yescharacteristic
514C22×C3#94911yescharacteristic
515C22×C3#95011yescharacteristic
516C2×D3—24no—
517C2×D3—42no—
518C2×D3—42no—
519C2×D3—42no—
520C2×D3—42no—
521C2×D3—42no—
522C2×D3—42no—
523C3×C4—21no—
524C3×C4—21no—
525C3×C4—21no—
526C3×C4—21no—
527C3×C4—62no—
528C3×C4—121no—
529C3×C4—241no—
530C3×C4D3×C22⋊C411yescharacteristic
531C3×C4#67⋊C411yescharacteristic
532C3×C4#88311yescharacteristic
533C3×C4#88411yescharacteristic
534C3×C4D4×Dic311yescharacteristic
535C3×C4#93511yescharacteristic
536C3×C4#93911yescharacteristic
537C3×C4C2×#21711yescharacteristic
538Dic3—22no—
539Dic3—41no—
540Dic3—81no—
541Dic3—122no—
542Dic3—122no—
543Dic3—242no—
544C32#187911yescharacteristic, complemented, Sylow
545C23—22no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23—62no—
553C23—62no—
554C23—62no—
555C23—121no—
556C23—121no—
557C23—121no—
558C23—121no—
559C23D3×#6711yescharacteristic
560D4—22no—
561D4—22no—
562D4—34no—
563D4—41no—
564D4—41no—
565D4—62no—
566D4—62no—
567D4—62no—
568C2×C4—32no—
569C2×C4—61no—
570C2×C4—61no—
571C2×C4—61no—
572C2×C4—61no—
573C2×C4—61no—
574C2×C4—121no—
575C2×C4—121no—
576C2×C4—121no—
577C2×C4—182no—
578C2×C4—368no—
579C2×C4—361no—
580C2×C4—361no—
581C2×C4C2×D3×Dic311yescharacteristic
582C2×C4#380411yescharacteristic
583C2×C4#380511yescharacteristic
584C2×C4D3×#6711yescharacteristic
585C2×C4D3×#6711yescharacteristic
586C2×C4#381111yescharacteristic
587C8—62no—
588C8—361no—
589C2×C3—21no—
590C2×C3—21no—
591C2×C3—21no—
592C2×C3—21no—
593C2×C3—21no—
594C2×C3—21no—
595C2×C3—21no—
596C2×C3—84no—
597C2×C3—82no—
598C2×C3—82no—
599C2×C3—124no—
600C2×C3#495611yescharacteristic
601C2×C3C4×#21311yescharacteristic
602C2×C3#501411yescharacteristic
603C2×C3#503611yescharacteristic
604C2×C3#503711yescharacteristic
605C2×C3#505711yescharacteristic
606C2×C3#507211yescharacteristic
607C2×C3Dic3×D811yescharacteristic
608C2×C3#515011yescharacteristic
609C2×C3#515211yescharacteristic
610C2×C3#515311yescharacteristic
611C2×C3#515611yescharacteristic
612C2×C3#515811yescharacteristic
613C2×C3#522011yescharacteristic
614D3—44no—
615C22—42no—
616C22—42no—
617C22—42no—
618C22—64no—
619C22—81no—
620C22—81no—
621C22—81no—
622C22—81no—
623C22—122no—
624C22—122no—
625C22—122no—
626C22—122no—
627C22—122no—
628C22—122no—
629C22D3×#21311yescharacteristic
630C22#6392511yescharacteristic
631C22#6393211yescharacteristic
632C22#6393311yescharacteristic
633C22#6397011yescharacteristic
634C22Dic3×#6711yescharacteristic
635C22#6398311yescharacteristic
636C4—62no—
637C4—121no—
638C4—241no—
639C4—362no—
640C4D3×#21711yescharacteristic
641C4#6396911yescharacteristic
642C4#6397111yescharacteristic
643C4#67⋊Dic311yescharacteristic
644C3—21no—
645C3#6965711yescharacteristic, complemented
646C3#7203711yescharacteristic, complemented
647C2—82no—
648C2—124no—
649C2Dic3×#21311yescharacteristic
650C2#1059142811yescharacteristic
651C2#1059143011yescharacteristic
652C2#1059143111yescharacteristic
653C2#1059151511yescharacteristic
654C2#1059151911yescharacteristic
655C2#1059172111yescharacteristic
subgroupG/H
centerC23D3×#67
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×Dic3×D12C2semidirect
3. C2×#63659C2semidirect
4. C3×#5221C2semidirect
5. C2×#63562C2semidirect
6. #10589164C2semidirect
7. #10589155C2semidirect
19. C2×C3×#213C4semidirect
33. #5221D3semidirect
50. C2×C32×D4C2×C4semidirect
79. C2×C3×C3⋊C8C2×C4semidirect
104. C2×#213Dic3semidirect
158. C2×C3×Dic3D8semidirect
162. C3×D12C22⋊C4semidirect
200. C2×C3×D4C4×D3semidirect
201. C2×C3×D4C2×Dic3semidirect
262. C2×C3⋊C8C2×Dic3semidirect
409. C2×Dic3#213semidirect
413. D12#217semidirect
442. C2×D4D3×Dic3semidirect
544. C32#1879semidirect
645. C3#69657semidirect
646. 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×Dic3×D122
C2×#636592
C3×#52212
C2×#635622
#105891642
#105891552
#720373
#696573