Finite Group Databasebeta

← #11806060

Subgroups — #11806060

Order 1152.

1217 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63898C211yesmaximal, characteristic
2C4×#3750C211yesmaximal, characteristic, complemented
3C3×#4939C211yesmaximal, characteristic
4C3×C4×C4⋊Dic3C211yesmaximal, characteristic, complemented
5Dic3×(C2×D3)⋊C4C212yesmaximal, complemented
6#10591362C212yesmaximal, complemented
7#10591323C211yesmaximal, characteristic
8#10591281C212yesmaximal, complemented
9#10591280C212yesmaximal, complemented
10#10591274C211yesmaximal, characteristic, complemented
11#10591230C211yesmaximal, characteristic, complemented
12#76303—31nomaximal
13#73646—31nomaximal
14C22×C3×D12C2211yescharacteristic
15C22×D3×Dic3C2212yes—
16C2×C32×C42C2211yescharacteristic
17C2×#3750C2211yescharacteristic
18C2×#3750C2211yescharacteristic
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×C4×C3⋊Dic3C2211yescharacteristic
21C2×C3×(C2×D3)⋊C4C2212yes—
22C2×C3×(C2×D3)⋊C4C2212yes—
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×C4×Dic3C2212yes—
27C2×(C2×D3)⋊Dic3C2212yes—
28C2×(C2×D3)⋊Dic3C2212yes—
29C2×(C2×D3)⋊Dic3C2212yes—
30C2×Dic32C2212yes—
31#63898C418yescomplemented
32#63658C2211yescharacteristic
33#63658C2211yescharacteristic
34C3×C3⋊#95C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38C2×D4×Dic3—31no—
39C2×#893—31no—
40C3×#390—31no—
41C3×C4×C4⋊C4—31no—
42#5221—31no—
43#4988—31no—
44#4977—31no—
45#4977—31no—
46Dic3×C4⋊C4—31no—
47Dic3×C4⋊C4—31no—
48#4945—32no—
49#4944—32no—
50#4943—32no—
51Dic3×C22⋊C4—32no—
52#4940—32no—
53#4939D311yescharacteristic
54C4×(C2×D3)⋊C4—32no—
55C4×C4⋊Dic3D311yescharacteristic, complemented
56C4×Dic3⋊C4—31no—
57C4×Dic3⋊C4—31no—
58C4×Dic3⋊C4—61no—
59#4669—32no—
60#4664—32no—
61C23×C3×D3C2312yes—
62C22×C32×C4C2311yescharacteristic
63C22×C32×C4C2311yescharacteristic
64C22×C32×C4C2311yescharacteristic
65C22×C3⋊Dic3C2311yescharacteristic
66C22×C3⋊Dic3C2311yescharacteristic
67C22×C3⋊Dic3C2311yescharacteristic
68C22×C3⋊Dic3C2311yescharacteristic
69C22×C3×Dic3C2312yes—
70C22×C3×Dic3C2312yes—
71C22×C3×Dic3C2312yes—
72C2×C3×D12—22no—
73C2×C3×D12—22no—
74C2×C3×D12C2×C414yes—
75C2×D3×Dic3—42no—
76C2×D3×Dic3—42no—
77C2×D3×Dic3C2×C418yes—
78C32×C42—22no—
79#3750—22no—
80#3750—22no—
81C4×C3⋊Dic3—22no—
82C4×C3⋊Dic3C2×C414yes—
83C3×(C2×D3)⋊C4—24no—
84C3×(C2×D3)⋊C4—42no—
85C3×C4⋊Dic3—22no—
86C3×C4⋊Dic3—22no—
87C3×C4⋊Dic3C2×C414yes—
88C3×C4×Dic3—42no—
89(C2×D3)⋊Dic3—24no—
90(C2×D3)⋊Dic3—42no—
91(C2×D3)⋊Dic3C2×C418yes—
92Dic32—42no—
93#2357—91noSylow
94C22×C3×D4—31no—
95C23×Dic3—32no—
96C22×D12C2×D311yescharacteristic
97C22×C4×D3—32no—
98C2×C3×C4⋊C4—31no—
99C2×C3×C4⋊C4—31no—
100C2×C3×C4⋊C4—31no—
101C2×C3×C22⋊C4—32no—
102C2×C3×C22⋊C4—32no—
103C2×C3×C42—21no—
104C2×C3×C42—32no—
105C2×C3×C42C2×D311yescharacteristic
106C2×C3×C42C2×D311yescharacteristic
107C2×#217—32no—
108C2×#217—32no—
109C2×#217—32no—
110D4×Dic3—38no—
111C2×(C2×D3)⋊C4—32no—
112C2×(C2×D3)⋊C4—32no—
113C2×(C2×D3)⋊C4—32no—
114C2×(C2×D3)⋊C4C2×D312yes—
115C2×(C2×D3)⋊C4C2×D312yes—
116C2×C4⋊Dic3C2×D311yescharacteristic
117C2×C4⋊Dic3C2×D311yescharacteristic
118C2×C4⋊Dic3C2×D311yescharacteristic
119C2×Dic3⋊C4—31no—
120C2×Dic3⋊C4—31no—
121C2×Dic3⋊C4—31no—
122C2×Dic3⋊C4—31no—
123C2×Dic3⋊C4—61no—
124C2×Dic3⋊C4—61no—
125C2×C4×Dic3—31no—
126C2×C4×Dic3—31no—
127C2×C4×Dic3—31no—
128C2×C4×Dic3—31no—
129C2×C4×Dic3—32no—
130C2×C4×Dic3—32no—
131C2×C4×Dic3—61no—
132C2×C4×Dic3—61no—
133C2×C4×Dic3C2×D312yes—
134#893—38no—
135C3×#95—32no—
136C3⋊#95—31no—
137C3⋊#95—31no—
138C3⋊#95—31no—
139C3⋊#95—31no—
140C3⋊#95—32no—
141C3⋊#95—32no—
142C3⋊#95—32no—
143C3⋊#95—32no—
144C3⋊#95—32no—
145C3⋊#95—32no—
146C3⋊#95—61no—
147C3⋊#95—61no—
148C3⋊#95C2×D312yes—
149C23×C32C2411yescharacteristic
150C22×C3×D3—22no—
151C22×C3×D3—22no—
152C22×C3×D3—22no—
153C22×C3×D3—22no—
154C22×C3×D3—22no—
155C22×C3×D3—22no—
156C22×C3×D3C22×C414yes—
157C2×C32×C4—21no—
158C2×C32×C4—21no—
159C2×C32×C4—21no—
160C2×C32×C4—21no—
161C2×C32×C4—21no—
162C2×C32×C4C22×C412yes—
163C2×C32×C4#4112yes—
164C2×C32×C4#4112yes—
165C2×C32×C4#4112yes—
166C2×C3⋊Dic3—21no—
167C2×C3⋊Dic3—21no—
168C2×C3⋊Dic3—21no—
169C2×C3⋊Dic3—21no—
170C2×C3⋊Dic3—21no—
171C2×C3⋊Dic3—21no—
172C2×C3⋊Dic3—21no—
173C2×C3⋊Dic3—21no—
174C2×C3⋊Dic3—21no—
175C2×C3⋊Dic3C22×C412yes—
176C2×C3⋊Dic3C22×C412yes—
177C2×C3⋊Dic3#4112yes—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3C22×C414yes—
187C3×D12—28no—
188D3×Dic3—48no—
189C2×C4×D4—91no—
190#390—31no—
191#390—91no—
192#388—92no—
193#388—92no—
194#382—91no—
195#381—92no—
196C4×C4⋊C4—31no—
197C4×C4⋊C4—91no—
198C4×C4⋊C4—91no—
199C4×C22⋊C4—92no—
200C24×C3—32no—
201C23×D3C22×D312yes—
202C2×C3×D4—34no—
203C2×C3×D4—62no—
204C2×C3×D4—62no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C22×C3×C4—32no—
209C22×C3×C4—32no—
210C22×C3×C4—32no—
211C22×C3×C4C22×D311yescharacteristic
212C22×C3×C4C22×D311yescharacteristic
213C22×C3×C4C22×D311yescharacteristic
214C22×C3×C4C22×D311yescharacteristic
215C22×C3×C4C22×D311yescharacteristic
216C22×C3×C4C22×D311yescharacteristic
217C22×Dic3—31no—
218C22×Dic3—31no—
219C22×Dic3—31no—
220C22×Dic3—31no—
221C22×Dic3—31no—
222C22×Dic3—31no—
223C22×Dic3—38no—
224C22×Dic3—31no—
225C22×Dic3—31no—
226C22×Dic3—61no—
227C22×Dic3—61no—
228C22×Dic3—61no—
229C22×Dic3—61no—
230C22×Dic3—122no—
231C22×Dic3—122no—
232C22×Dic3C22×D312yes—
233C22×Dic3C22×D312yes—
234C22×Dic3C22×D312yes—
235C2×D12—22no—
236C2×D12—22no—
237C2×D12C4×D314yes—
238C2×C4×D3—38no—
239C2×C4×D3—122no—
240C2×C4×D3—122no—
241C3×C4⋊C4—34no—
242C3×C4⋊C4—62no—
243C3×C4⋊C4—62no—
244C3×C22⋊C4—64no—
245C3×C22⋊C4—122no—
246C3×C42—22no—
247C3×C42—22no—
248C3×C42—42no—
249C3×C42—122no—
250#217—38no—
251#217—64no—
252#217—122no—
253(C2×D3)⋊C4—24no—
254(C2×D3)⋊C4—38no—
255(C2×D3)⋊C4—42no—
256(C2×D3)⋊C4—64no—
257(C2×D3)⋊C4—122no—
258C4⋊Dic3—22no—
259C4⋊Dic3—22no—
260C4⋊Dic3C4×D314yes—
261Dic3⋊C4—62no—
262Dic3⋊C4—62no—
263Dic3⋊C4—64no—
264Dic3⋊C4—64no—
265Dic3⋊C4—62no—
266Dic3⋊C4—62no—
267C4×Dic3—34no—
268C4×Dic3—34no—
269C4×Dic3—42no—
270C4×Dic3—64no—
271C4×Dic3—62no—
272C4×Dic3—62no—
273C4×Dic3—122no—
274C4×Dic3—122no—
275C4×Dic3—122no—
276C22×C32C23×C411yescharacteristic
277C22×C32C2×#4111yescharacteristic
278C22×C32C2×#4111yescharacteristic
279C22×C32C2×#4111yescharacteristic
280C22×C32C2×#4111yescharacteristic
281C22×C32H(5,𝔽2)11yescharacteristic
282C22×C32H(5,𝔽2)11yescharacteristic
283C2×C3×D3—24no—
284C2×C3×D3—24no—
285C2×C3×D3—24no—
286C2×C3×D3—42no—
287C2×C3×D3—42no—
288C2×C3×D3—42no—
289C2×C3×D3—42no—
290C32×C4—22no—
291C32×C4—41no—
292C32×C4#11714yes—
293C3⋊Dic3—22no—
294C3⋊Dic3—22no—
295C3⋊Dic3—22no—
296C3⋊Dic3—41no—
297C3×Dic3—24no—
298C3×Dic3—42no—
299C3×Dic3—42no—
300C22×D4—31no—
301C23×C4—92no—
302C4×D4—98no—
303C2×C4⋊C4—31no—
304C2×C4⋊C4—31no—
305C2×C4⋊C4—31no—
306C2×C4⋊C4—91no—
307C2×C4⋊C4—91no—
308C2×C22⋊C4—32no—
309C2×C22⋊C4—32no—
310C2×C22⋊C4—92no—
311C2×C22⋊C4—92no—
312C2×C22⋊C4—92no—
313C2×C42—32no—
314C2×C42—91no—
315C2×C42—91no—
316C2×C42—92no—
317C2×C42D3211yescharacteristic
318#95—32no—
319#95—92no—
320#95—92no—
321#95—92no—
322#95—91no—
323#95—91no—
324C23×C3—21no—
325C23×C3—34no—
326C23×C3—62no—
327C23×C3—62no—
328C23×C3—62no—
329C23×C3—62no—
330C23×C3—62no—
331C23×C3—62no—
332C23×C3C23×D311yescharacteristic
333C23×C3C23×D311yescharacteristic
334C22×D3—22no—
335C22×D3—22no—
336C22×D3—22no—
337C22×D3—22no—
338C22×D3—22no—
339C22×D3—22no—
340C22×D3C2×C4×D314yes—
341C3×D4—68no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—22no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—22no—
354C2×C3×C4—22no—
355C2×C3×C4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—34no—
358C2×C3×C4—41no—
359C2×C3×C4—41no—
360C2×C3×C4—41no—
361C2×C3×C4—41no—
362C2×C3×C4—62no—
363C2×C3×C4—62no—
364C2×C3×C4—62no—
365C2×C3×C4—62no—
366C2×C3×C4—62no—
367C2×C3×C4—62no—
368C2×C3×C4—62no—
369C2×C3×C4—62no—
370C2×C3×C4C2×C4×D312yes—
371C2×C3×C4C2×C4×D312yes—
372C2×C3×C4#23512yes—
373C2×C3×C4#23512yes—
374C2×C3×C4#23712yes—
375C2×C3×C4#23712yes—
376C2×C3×C4#23712yes—
377C2×C3×C4#23912yes—
378C2×Dic3—22no—
379C2×Dic3—22no—
380C2×Dic3—22no—
381C2×Dic3—22no—
382C2×Dic3—22no—
383C2×Dic3—22no—
384C2×Dic3—22no—
385C2×Dic3—22no—
386C2×Dic3—32no—
387C2×Dic3—32no—
388C2×Dic3—32no—
389C2×Dic3—32no—
390C2×Dic3—32no—
391C2×Dic3—32no—
392C2×Dic3—62no—
393C2×Dic3—62no—
394C2×Dic3—62no—
395C2×Dic3—62no—
396C2×Dic3—62no—
397C2×Dic3—61no—
398C2×Dic3—61no—
399C2×Dic3—61no—
400C2×Dic3—61no—
401C2×Dic3—61no—
402C2×Dic3—61no—
403C2×Dic3—61no—
404C2×Dic3—61no—
405C2×Dic3—61no—
406C2×Dic3—61no—
407C2×Dic3—61no—
408C2×Dic3—61no—
409C2×Dic3—62no—
410C2×Dic3—61no—
411C2×Dic3—61no—
412C2×Dic3—61no—
413C2×Dic3—61no—
414C2×Dic3—61no—
415C2×Dic3—61no—
416C2×Dic3—121no—
417C2×Dic3—121no—
418C2×Dic3—121no—
419C2×Dic3—121no—
420C2×Dic3—121no—
421C2×Dic3—121no—
422C2×Dic3—128no—
423C2×Dic3C2×C4×D314yes—
424D12—28no—
425C4×D3—128no—
426C2×C32C2×#11711yescharacteristic
427C2×C32C4×#4111yescharacteristic
428C2×C32#51811yescharacteristic
429C2×C32#55311yescharacteristic
430C2×C32#55311yescharacteristic
431C2×C32#55911yescharacteristic
432C2×C32#55911yescharacteristic
433C3×D3—44no—
434C24—32no—
435C2×D4—34no—
436C2×D4—62no—
437C2×D4—62no—
438C22×C4—32no—
439C22×C4—32no—
440C22×C4—32no—
441C22×C4—98no—
442C22×C4—91no—
443C22×C4—91no—
444C22×C4—91no—
445C22×C4—91no—
446C22×C4—362no—
447C22×C4—362no—
448C22×C4C2×D3211yescharacteristic
449C22×C4C2×D3211yescharacteristic
450C22×C4C2×D3211yescharacteristic
451C4⋊C4—34no—
452C4⋊C4—62no—
453C4⋊C4—62no—
454C4⋊C4—182no—
455C4⋊C4—182no—
456C22⋊C4—64no—
457C22⋊C4—98no—
458C22⋊C4—122no—
459C22⋊C4—184no—
460C22⋊C4—362no—
461C42—22no—
462C42—94no—
463C42—122no—
464C42—182no—
465C42—362no—
466C22×C3—21no—
467C22×C3—21no—
468C22×C3—21no—
469C22×C3—21no—
470C22×C3—21no—
471C22×C3—21no—
472C22×C3—21no—
473C22×C3—64no—
474C22×C3—64no—
475C22×C3—64no—
476C22×C3—122no—
477C22×C3—122no—
478C22×C3—122no—
479C22×C3—122no—
480C22×C3C22×C4×D311yescharacteristic
481C22×C3C22×C4×D311yescharacteristic
482C22×C3C2×#23511yescharacteristic
483C22×C3C2×#23511yescharacteristic
484C22×C3C2×#23711yescharacteristic
485C22×C3C2×#23711yescharacteristic
486C22×C3C2×#23711yescharacteristic
487C22×C3#100411yescharacteristic
488C22×C3#100411yescharacteristic
489C22×C3C2×#23911yescharacteristic
490C22×C3D3×#4111yescharacteristic
491C22×C3D3×#4111yescharacteristic
492C22×C3#100911yescharacteristic
493C22×C3#100911yescharacteristic
494C2×D3—24no—
495C2×D3—24no—
496C2×D3—24no—
497C2×D3—42no—
498C2×D3—42no—
499C2×D3—42no—
500C2×D3—42no—
501C3×C4—22no—
502C3×C4—22no—
503C3×C4—24no—
504C3×C4—42no—
505C3×C4—42no—
506C3×C4—41no—
507C3×C4—41no—
508C3×C4—64no—
509C3×C4—122no—
510C3×C4—122no—
511C3×C4#87214yes—
512C3×C4#87714yes—
513Dic3—24no—
514Dic3—42no—
515Dic3—42no—
516Dic3—64no—
517Dic3—62no—
518Dic3—62no—
519Dic3—62no—
520Dic3—62no—
521Dic3—62no—
522Dic3—62no—
523Dic3—122no—
524Dic3—122no—
525Dic3—122no—
526Dic3—121no—
527Dic3—121no—
528C32#235711yescharacteristic, complemented, Sylow
529C23—34no—
530C23—62no—
531C23—62no—
532C23—62no—
533C23—62no—
534C23—62no—
535C23—62no—
536C23C22×D3211yescharacteristic
537D4—68no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—34no—
544C2×C4—62no—
545C2×C4—62no—
546C2×C4—62no—
547C2×C4—62no—
548C2×C4—62no—
549C2×C4—62no—
550C2×C4—62no—
551C2×C4—62no—
552C2×C4—92no—
553C2×C4—92no—
554C2×C4—92no—
555C2×C4—181no—
556C2×C4—181no—
557C2×C4—181no—
558C2×C4—181no—
559C2×C4—181no—
560C2×C4—181no—
561C2×C4—181no—
562C2×C4—181no—
563C2×C4—181no—
564C2×C4—368no—
565C2×C4#379512yes—
566C2×C4#379612yes—
567C2×C4C4×D3212yes—
568C2×C4#380412yes—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—21no—
572C2×C3—21no—
573C2×C3—21no—
574C2×C3—21no—
575C2×C3—21no—
576C2×C3—124no—
577C2×C3C2×#87211yescharacteristic
578C2×C3C2×#87711yescharacteristic
579C2×C3#551411yescharacteristic
580C2×C3#553011yescharacteristic
581C2×C3C4×#23711yescharacteristic
582C2×C3#554511yescharacteristic
583C2×C3#554511yescharacteristic
584C2×C3#555911yescharacteristic
585C2×C3C4×#23911yescharacteristic
586C2×C3#558511yescharacteristic
587C2×C3#561411yescharacteristic
588C2×C3#561811yescharacteristic
589C2×C3#568111yescharacteristic
590C2×C3#571311yescharacteristic
591D3—44no—
592C22—64no—
593C22—64no—
594C22—64no—
595C22—122no—
596C22—122no—
597C22—122no—
598C22—122no—
599C22C2×#379511yescharacteristic
600C22C2×#379611yescharacteristic
601C22C2×C4×D3211yescharacteristic
602C22#6430611yescharacteristic
603C22#6430711yescharacteristic
604C22#6430711yescharacteristic
605C22C2×#380411yescharacteristic
606C4—22no—
607C4—41no—
608C4—64no—
609C4—122no—
610C4—122no—
611C4—182no—
612C4—182no—
613C4—182no—
614C4—361no—
615C4#6387714yes—
616C3—21no—
617C3#7364611yescharacteristic, complemented
618C3#7630311yescharacteristic, complemented
619C2—124no—
620C2C4×#379611yescharacteristic
621C2#1059395111yescharacteristic
622C2#1059398111yescharacteristic
623C2#1059399611yescharacteristic
624C2C2×#6387711yescharacteristic
625C2#1059496711yescharacteristic
626C2#1059498911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC22×C3×D12C22
hypercenterC2×C42D32
hypocenterC32#2357
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C4×#3750C2semidirect
4. C3×C4×C4⋊Dic3C2semidirect
5. Dic3×(C2×D3)⋊C4C2semidirect
6. #10591362C2semidirect
8. #10591281C2semidirect
9. #10591280C2semidirect
10. #10591274C2semidirect
11. #10591230C2semidirect
31. #63898C4semidirect
55. C4×C4⋊Dic3D3semidirect
528. C32#2357semidirect
617. C3#73646semidirect
618. C3#76303semidirect

Maximal subgroups

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

subgroupindex
C2×#638982
C4×#37502
C3×#49392
C3×C4×C4⋊Dic32
Dic3×(C2×D3)⋊C42
#105913622
#105913232
#105912812
#105912802
#105912742
#105912302
#763033
#736463