Finite Group Databasebeta

← #11787553

Subgroups — #11787553

Order 1152.

933 conjugacy classes of subgroups.

The subgroup lattice has 637 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D24C211yesmaximal, characteristic
2C2×Dic3×D12C211yesmaximal, characteristic, complemented
3#10591318C211yesmaximal, characteristic, complemented
4C2×#63563C211yesmaximal, characteristic, complemented
5C2×#63563C211yesmaximal, characteristic, complemented
6#10589417C211yesmaximal, characteristic, complemented
7C3×#4550C211yesmaximal, characteristic, complemented
8#72037—31nomaximal
9#68673—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C22×D3×Dic3—21no—
13C22×C32×C8C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C2×C3×D24—22no—
19C2×C3×D24—22no—
20C2×C3×D24C414yescomplemented
21C2×(C2×D3)⋊Dic3—21no—
22C2×(C2×D3)⋊Dic3—21no—
23C2×(C2×D3)⋊Dic3—21no—
24Dic3×D12—22no—
25Dic3×D12—22no—
26#63563—22no—
27#63563—22no—
28C22×C3×D8—31no—
29C2×D4×Dic3—31no—
30C22×D24D311yescharacteristic
31C2×C4×D12—31no—
32#5221—31no—
33C2×#832—31no—
34C2×#832—31no—
35C2×#821—31no—
36C2×#821—31no—
37#4939—31no—
38C3×#336—31no—
39#4551—31no—
40#4551—31no—
41#4551—61no—
42#4550D311yescharacteristic, complemented
43C23×C3×D3—21no—
44C23×C3×D3—21no—
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—21no—
47C22×C3⋊Dic3—21no—
48C22×C3×Dic3D411yescharacteristic
49C22×C3×Dic3D411yescharacteristic
50C2×C3×D12—21no—
51C2×C3×D12—21no—
52C2×C3×D12—21no—
53C2×C3×D12—21no—
54C2×C3×D12—21no—
55C2×C3×D12—21no—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12C2×C412yes—
59C2×C3×D12C2×C412yescomplemented
60C2×C3×D12D412yes—
61C2×C3×D12D412yes—
62C2×D3×Dic3—24no—
63C2×D3×Dic3—42no—
64C2×D3×Dic3—42no—
65C2×C32×C8—21no—
66C2×C32×C8—21no—
67C2×C32×C8C2×C412yescomplemented
68C4⋊(C3⋊Dic3)—21no—
69C4⋊(C3⋊Dic3)—21no—
70C4⋊(C3⋊Dic3)—21no—
71C4⋊(C3⋊Dic3)D412yes—
72C3×C4×Dic3—21no—
73C3×C4×Dic3—21no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8—21no—
77C3×D24—28no—
78(C2×D3)⋊Dic3—24no—
79(C2×D3)⋊Dic3—42no—
80(C2×D3)⋊Dic3—42no—
81#1879—91noSylow
82C22×C3×D4—31no—
83C22×C3×D4—31no—
84C23×Dic3—61no—
85C22×D12C2×D311yescharacteristic
86C22×D12C2×D311yescharacteristic
87C22×C4×D3—61no—
88C2×C3×D8—34no—
89C2×C3×D8—62no—
90C2×C3×D8—62no—
91C22×C3×C8—21no—
92C22×C3×C8—31no—
93C22×C3×C8C2×D311yescharacteristic
94C22×C3×C8C2×D311yescharacteristic
95C2×C3×C42—31no—
96C2×#217—61no—
97C2×#217—61no—
98C2×#217—61no—
99D4×Dic3—62no—
100D4×Dic3—62no—
101C2×(C2×D3)⋊C4—61no—
102C2×(C2×D3)⋊C4—61no—
103C2×(C2×D3)⋊C4—61no—
104C2×C4⋊Dic3—31no—
105C2×C4⋊Dic3—31no—
106C2×C4⋊Dic3—31no—
107C2×C4⋊Dic3—31no—
108C2×C4⋊Dic3—61no—
109C2×C4⋊Dic3—61no—
110C2×C4×Dic3C2×D311yescharacteristic
111C22×C3⋊C8C2×D311yescharacteristic
112C2×D24—22no—
113C2×D24—22no—
114C2×D24Dic314yescomplemented
115C4×D12—62no—
116C4×D12—62no—
117#832—62no—
118#832—62no—
119#821—62no—
120#821—62no—
121C23×C32C2×D411yescharacteristic
122C22×C3×D3—22no—
123C22×C3×D3—22no—
124C22×C3×D3—22no—
125C22×C3×D3—22no—
126C22×C3×D3—41no—
127C22×C3×D3—41no—
128C22×C3×D3—41no—
129C22×C3×D3—41no—
130C22×C3×D3—41no—
131C22×C3×D3—41no—
132C22×C3×D3—41no—
133C22×C3×D3—41no—
134C22×C3×D3—41no—
135C22×C3×D3—41no—
136C2×C32×C4C22×C411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4#4111yescharacteristic
141C2×C32×C4#4111yescharacteristic
142C2×C3⋊Dic3—22no—
143C2×C3⋊Dic3—41no—
144C2×C3⋊Dic3—41no—
145C2×C3⋊Dic3—41no—
146C2×C3⋊Dic3—41no—
147C2×C3⋊Dic3—41no—
148C2×C3×Dic3—21no—
149C2×C3×Dic3—21no—
150C2×C3×Dic3—21no—
151C2×C3×Dic3—21no—
152C2×C3×Dic3—21no—
153C2×C3×Dic3D812yescomplemented
154C3×D12—22no—
155C3×D12—22no—
156C3×D12—22no—
157C3×D12—22no—
158C3×D12—22no—
159C3×D12—41no—
160C3×D12—41no—
161C3×D12C22⋊C414yescomplemented
162D3×Dic3—48no—
163C32×C8—22no—
164C3×C3⋊C8—41no—
165C22×D8—31no—
166C2×C4×D4—91no—
167C2×#102—91no—
168C2×#102—91no—
169#390—91no—
170#340—91no—
171#336—31no—
172C24×C3—61no—
173C24×C3—61no—
174C23×D3—21no—
175C23×D3—21no—
176C2×C3×D4—32no—
177C2×C3×D4—32no—
178C2×C3×D4—32no—
179C2×C3×D4—32no—
180C2×C3×D4—61no—
181C2×C3×D4—61no—
182C2×C3×D4—61no—
183C2×C3×D4—61no—
184C2×C3×D4—61no—
185C2×C3×D4—61no—
186C2×C3×D4—61no—
187C2×C3×D4—61no—
188C22×C3×C4—21no—
189C22×C3×C4—31no—
190C22×C3×C4—31no—
191C22×C3×C4C22×D311yescharacteristic
192C22×C3×C4C22×D311yescharacteristic
193C22×Dic3—64no—
194C22×Dic3—61no—
195C22×Dic3—61no—
196C22×Dic3—61no—
197C22×Dic3—61no—
198C22×Dic3—121no—
199C22×Dic3—121no—
200C22×Dic3—122no—
201C22×Dic3—122no—
202C22×Dic3D1211yescharacteristic
203C22×Dic3D1211yescharacteristic
204C2×D12—21no—
205C2×D12—21no—
206C2×D12—21no—
207C2×D12—21no—
208C2×D12—21no—
209C2×D12—21no—
210C2×D12—21no—
211C2×D12—21no—
212C2×D12C2×Dic312yes—
213C2×D12C2×Dic312yescomplemented
214C2×D12#6712yes—
215C2×D12#6712yes—
216C2×C4×D3—64no—
217C2×C4×D3—122no—
218C2×C4×D3—122no—
219C3×D8—68no—
220C2×C3×C8—21no—
221C2×C3×C8—21no—
222C2×C3×C8—21no—
223C2×C3×C8—21no—
224C2×C3×C8—22no—
225C2×C3×C8—41no—
226C2×C3×C8—41no—
227C2×C3×C8—61no—
228C2×C3×C8—61no—
229C2×C3×C8—61no—
230C2×C3×C8C4×D312yescomplemented
231C2×C3×C8C2×Dic312yescomplemented
232C3×C42—61no—
233C3×C42—61no—
234#217—64no—
235#217—122no—
236#217—122no—
237(C2×D3)⋊C4—64no—
238(C2×D3)⋊C4—122no—
239(C2×D3)⋊C4—122no—
240C4⋊Dic3—32no—
241C4⋊Dic3—32no—
242C4⋊Dic3—62no—
243C4⋊Dic3—61no—
244C4⋊Dic3—61no—
245C4⋊Dic3—62no—
246C4⋊Dic3—61no—
247C4⋊Dic3—61no—
248C4⋊Dic3—61no—
249C4⋊Dic3—61no—
250C4⋊Dic3—121no—
251C4⋊Dic3—121no—
252C4×Dic3—21no—
253C4×Dic3—21no—
254C2×C3⋊C8—21no—
255C2×C3⋊C8—21no—
256C2×C3⋊C8—21no—
257D24—28no—
258C22×C32C4×D411yescharacteristic
259C22×C32#12011yescharacteristic
260C22×C32#12111yescharacteristic
261C22×C32C2×D811yescharacteristic
262C22×C32#13511yescharacteristic
263C22×C32AGL(1,ℤ/8)11yescharacteristic
264C22×C32AGL(1,ℤ/8)11yescharacteristic
265C2×C3×D3—24no—
266C2×C3×D3—42no—
267C2×C3×D3—42no—
268C2×C3×D3—42no—
269C2×C3×D3—42no—
270C2×C3×D3—42no—
271C2×C3×D3—42no—
272C2×C3×D3—42no—
273C2×C3×D3—42no—
274C2×C3×D3—42no—
275C2×C3×D3—81no—
276C2×C3×D3—81no—
277C2×C3×D3—81no—
278C2×C3×D3—81no—
279C32×C4C2×C22⋊C411yescharacteristic
280C32×C4C4×D411yescharacteristic
281C32×C4#12111yescharacteristic
282C32×C4#12311yescharacteristic
283C3⋊Dic3—42no—
284C3⋊Dic3—81no—
285C3×Dic3—22no—
286C3×Dic3—41no—
287C22×D4—31no—
288C22×D4—31no—
289C23×C4—181no—
290C2×D8—34no—
291C2×D8—62no—
292C2×D8—62no—
293C22×C8—31no—
294C22×C8D3211yescharacteristic
295C4×D4—182no—
296C4×D4—182no—
297C2×C4⋊C4—91no—
298C2×C4⋊C4—91no—
299C2×C22⋊C4—181no—
300C2×C22⋊C4—181no—
301C2×C22⋊C4—181no—
302C2×C42—31no—
303#102—182no—
304#102—182no—
305C23×C3—21no—
306C23×C3—62no—
307C23×C3—62no—
308C23×C3—62no—
309C23×C3—62no—
310C23×C3—121no—
311C23×C3—121no—
312C23×C3—121no—
313C23×C3—121no—
314C23×C3—121no—
315C23×C3—121no—
316C23×C3—121no—
317C23×C3—121no—
318C23×C3—121no—
319C23×C3—121no—
320C23×C3C2×D1211yescharacteristic
321C23×C3D3×D411yescharacteristic
322C22×D3—22no—
323C22×D3—22no—
324C22×D3—22no—
325C22×D3—22no—
326C22×D3—41no—
327C22×D3—41no—
328C22×D3—41no—
329C22×D3—41no—
330C22×D3—41no—
331C22×D3—41no—
332C22×D3—41no—
333C22×D3—41no—
334C22×D3—41no—
335C22×D3—41no—
336C3×D4—34no—
337C3×D4—62no—
338C3×D4—62no—
339C3×D4—62no—
340C3×D4—62no—
341C3×D4—62no—
342C3×D4—121no—
343C3×D4—121no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—32no—
351C2×C3×C4—61no—
352C2×C3×C4—61no—
353C2×C3×C4—61no—
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×C4D3×D411yescharacteristic
362C2×C3×C4#23711yescharacteristic
363C2×C3×C4#23711yescharacteristic
364C2×C3×C4#23911yescharacteristic
365C2×C3×C4C22×Dic311yescharacteristic
366C2×C3×C4C2×#6711yescharacteristic
367C2×C3×C4C2×#6711yescharacteristic
368C2×Dic3—21no—
369C2×Dic3—21no—
370C2×Dic3—21no—
371C2×Dic3—21no—
372C2×Dic3—21no—
373C2×Dic3—62no—
374C2×Dic3—62no—
375C2×Dic3—122no—
376C2×Dic3—128no—
377C2×Dic3—121no—
378C2×Dic3—121no—
379C2×Dic3—121no—
380C2×Dic3—121no—
381C2×Dic3—122no—
382C2×Dic3—121no—
383C2×Dic3—121no—
384C2×Dic3—121no—
385C2×Dic3—121no—
386C2×Dic3—121no—
387C2×Dic3—121no—
388C2×Dic3—241no—
389C2×Dic3—241no—
390C2×Dic3—241no—
391C2×Dic3—241no—
392C2×Dic3D2412yescomplemented
393D12—22no—
394D12—22no—
395D12—22no—
396D12—22no—
397D12—22no—
398D12—41no—
399D12—41no—
400D12#21714yescomplemented
401C4×D3—128no—
402C3×C8—22no—
403C3×C8—22no—
404C3×C8—42no—
405C3×C8—121no—
406C3⋊C8—41no—
407C2×C32#38611yescharacteristic
408C2×C32C4×D811yescharacteristic
409C2×C32#44211yescharacteristic
410C2×C32#44711yescharacteristic
411C2×C32#44911yescharacteristic
412C2×C32#45911yescharacteristic
413C2×C32#46311yescharacteristic
414C3×D3—44no—
415C3×D3—82no—
416C24—61no—
417C24—61no—
418C2×D4—32no—
419C2×D4—32no—
420C2×D4—32no—
421C2×D4—32no—
422C2×D4—61no—
423C2×D4—61no—
424C2×D4—61no—
425C2×D4—61no—
426C2×D4—61no—
427C2×D4—61no—
428C2×D4—61no—
429C2×D4—61no—
430C22×C4—31no—
431C22×C4—31no—
432C22×C4—184no—
433C22×C4—181no—
434C22×C4—181no—
435C22×C4—362no—
436C22×C4—362no—
437C22×C4C2×D3211yescharacteristic
438D8—68no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—61no—
442C2×C8—61no—
443C2×C8—61no—
444C2×C8D3×Dic312yescomplemented
445C4⋊C4—92no—
446C4⋊C4—181no—
447C4⋊C4—181no—
448C4⋊C4—181no—
449C22⋊C4—184no—
450C22⋊C4—362no—
451C22⋊C4—362no—
452C42—61no—
453C42—61no—
454C22×C3—21no—
455C22×C3—21no—
456C22×C3—21no—
457C22×C3—21no—
458C22×C3—21no—
459C22×C3—21no—
460C22×C3—21no—
461C22×C3—64no—
462C22×C3—122no—
463C22×C3—122no—
464C22×C3—122no—
465C22×C3—122no—
466C22×C3—122no—
467C22×C3—122no—
468C22×C3—122no—
469C22×C3—122no—
470C22×C3—122no—
471C22×C3—241no—
472C22×C3—241no—
473C22×C3—241no—
474C22×C3—241no—
475C22×C3C4×D1211yescharacteristic
476C22×C3#88211yescharacteristic
477C22×C3#89511yescharacteristic
478C22×C3C2×D2411yescharacteristic
479C22×C3#90411yescharacteristic
480C22×C3#90811yescharacteristic
481C22×C3#90811yescharacteristic
482C22×C3D3×D811yescharacteristic
483C22×C3#91111yescharacteristic
484C22×C3#91111yescharacteristic
485C22×C3#91211yescharacteristic
486C22×C3D4×Dic311yescharacteristic
487C22×C3#93711yescharacteristic
488C22×C3#93911yescharacteristic
489C2×D3—24no—
490C2×D3—42no—
491C2×D3—42no—
492C2×D3—42no—
493C2×D3—42no—
494C2×D3—42no—
495C2×D3—42no—
496C2×D3—42no—
497C2×D3—42no—
498C2×D3—42no—
499C2×D3—81no—
500C2×D3—81no—
501C2×D3—81no—
502C2×D3—81no—
503C3×C4—21no—
504C3×C4—21no—
505C3×C4—21no—
506C3×C4—21no—
507C3×C4—62no—
508C3×C4—121no—
509C3×C4D3×C22⋊C411yescharacteristic
510C3×C4#88411yescharacteristic
511C3×C4#89311yescharacteristic
512C3×C4#89411yescharacteristic
513C3×C4D4×Dic311yescharacteristic
514C3×C4#93511yescharacteristic
515C3×C4#93911yescharacteristic
516C3×C4C2×#21711yescharacteristic
517Dic3—22no—
518Dic3—41no—
519Dic3—122no—
520Dic3—122no—
521Dic3—242no—
522Dic3—242no—
523Dic3—241no—
524Dic3—241no—
525C32#187911yescharacteristic, complemented, Sylow
526C23—62no—
527C23—62no—
528C23—62no—
529C23—62no—
530C23—121no—
531C23—121no—
532C23—121no—
533C23—121no—
534C23—121no—
535C23—121no—
536C23—121no—
537C23—121no—
538C23—121no—
539C23—121no—
540C23D3×D1211yescharacteristic
541D4—34no—
542D4—62no—
543D4—62no—
544D4—62no—
545D4—62no—
546D4—62no—
547D4—121no—
548D4—121no—
549C2×C4—32no—
550C2×C4—61no—
551C2×C4—61no—
552C2×C4—61no—
553C2×C4—61no—
554C2×C4—61no—
555C2×C4—182no—
556C2×C4—368no—
557C2×C4—361no—
558C2×C4—361no—
559C2×C4—361no—
560C2×C4—361no—
561C2×C4—361no—
562C2×C4#379511yescharacteristic
563C2×C4#379611yescharacteristic
564C2×C4#380211yescharacteristic
565C2×C4C2×D3×Dic311yescharacteristic
566C2×C4D3×#6711yescharacteristic
567C2×C4D3×#6711yescharacteristic
568C8—22no—
569C8—121no—
570C2×C3—21no—
571C2×C3—21no—
572C2×C3—21no—
573C2×C3—21no—
574C2×C3—21no—
575C2×C3—21no—
576C2×C3—21no—
577C2×C3—124no—
578C2×C3—242no—
579C2×C3#466511yescharacteristic
580C2×C3C4×D2411yescharacteristic
581C2×C3#471111yescharacteristic
582C2×C3#473211yescharacteristic
583C2×C3#473411yescharacteristic
584C2×C3#484311yescharacteristic
585C2×C3#484411yescharacteristic
586C2×C3Dic3×D811yescharacteristic
587C2×C3#515011yescharacteristic
588C2×C3#515211yescharacteristic
589C2×C3#515311yescharacteristic
590C2×C3#515611yescharacteristic
591C2×C3#515811yescharacteristic
592C2×C3#522011yescharacteristic
593D3—44no—
594D3—82no—
595C22—64no—
596C22—122no—
597C22—122no—
598C22—122no—
599C22—122no—
600C22—122no—
601C22—122no—
602C22—122no—
603C22—122no—
604C22—122no—
605C22—241no—
606C22—241no—
607C22—241no—
608C22—241no—
609C22D3×D2411yescharacteristic
610C22#6379511yescharacteristic
611C22#6379511yescharacteristic
612C22#6380711yescharacteristic
613C22#6388611yescharacteristic
614C22Dic3×D1211yescharacteristic
615C22#6392211yescharacteristic
616C4—62no—
617C4—121no—
618C4—362no—
619C4—721no—
620C4#6388411yescharacteristic
621C4#6388511yescharacteristic
622C4#6389811yescharacteristic
623C4D3×#21711yescharacteristic
624C3—21no—
625C3#6867311yescharacteristic, complemented
626C3#7203711yescharacteristic, complemented
627C2—124no—
628C2—242no—
629C2#1059075311yescharacteristic
630C2#1059075511yescharacteristic
631C2Dic3×D2411yescharacteristic
632C2#1059077111yescharacteristic
633C2#1059094411yescharacteristic
634C2#1059096211yescharacteristic
635C2#1059137611yescharacteristic
subgroupG/H
centerC23D3×D12
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C3×D24C2
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1879
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
2. C2×Dic3×D12C2semidirect
3. #10591318C2semidirect
4. C2×#63563C2semidirect
5. C2×#63563C2semidirect
6. #10589417C2semidirect
7. C3×#4550C2semidirect
20. C2×C3×D24C4semidirect
42. #4550D3semidirect
59. C2×C3×D12C2×C4semidirect
67. C2×C32×C8C2×C4semidirect
114. C2×D24Dic3semidirect
153. C2×C3×Dic3D8semidirect
161. C3×D12C22⋊C4semidirect
213. C2×D12C2×Dic3semidirect
230. C2×C3×C8C4×D3semidirect
231. C2×C3×C8C2×Dic3semidirect
392. C2×Dic3D24semidirect
400. D12#217semidirect
444. C2×C8D3×Dic3semidirect
525. C32#1879semidirect
625. C3#68673semidirect
626. C3#72037semidirect

Maximal subgroups

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

subgroupindex
C22×C3×D242
C2×Dic3×D122
#105913182
C2×#635632
#105894172
C3×#45502
#720373
#686733