Finite Group Databasebeta

← #11787081

Subgroups — #11787081

Order 1152.

853 conjugacy classes of subgroups.

The subgroup lattice has 715 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595510C211yesmaximal, characteristic
2C2×#63633C211yesmaximal, characteristic
3C3×#4950C211yesmaximal, characteristic, complemented
4#10591711C211yesmaximal, characteristic
5#10591693C211yesmaximal, characteristic, complemented
6C3×#4527C211yesmaximal, characteristic, complemented
7#10589186C211yesmaximal, characteristic, complemented
8#69595—31nomaximal
9#68961—31nomaximal
10C22×#638C2211yescharacteristic
11C23×C3×Dic3C2211yescharacteristic
12C2×C32×C22⋊C4C2211yescharacteristic
13C2×#3757C2211yescharacteristic
14C2×C3×#217C2211yescharacteristic
15C2×C3×#217C2211yescharacteristic
16C2×C3×#217C2211yescharacteristic
17C2×C3×C4⋊Dic3—21no—
18#63974—21no—
19C2×#3724—21no—
20C2×#3722—21no—
21#63957—21no—
22#63952—21no—
23#63952—21no—
24#63952—21no—
25#63952—21no—
26#63633C414yescomplemented
27C3×C3⋊#95—21no—
28#63579—21no—
29#63579—21no—
30#5486—31no—
31#5486—31no—
32C3×#385—31no—
33#5213—31no—
34#5210—31no—
35#4958—31no—
36C2×#806—31no—
37C2×#806—31no—
38C2×#806—61no—
39#4950D311yescharacteristic, complemented
40#4946—31no—
41C3×#342—31no—
42#4527—31no—
43#4527D311yescharacteristic, complemented
44#4526—31no—
45C24×C32C2311yescharacteristic
46C23×C3⋊D3D411yescharacteristic
47C22×C32×C4—21no—
48C2×#638—21no—
49C2×#638—21no—
50C2×#638—21no—
51C2×#638—21no—
52C2×#638C2×C412yes—
53C2×#638Q812yes—
54C22×C3⋊Dic3—21no—
55C22×C3⋊Dic3D411yescharacteristic
56C22×C3×Dic3—21no—
57C22×C3×Dic3—21no—
58C22×C3×Dic3—21no—
59C22×C3×Dic3—21no—
60C22×C3×Dic3—42no—
61C22×C3×Dic3D411yescharacteristic
62C22×C3×Dic3D411yescharacteristic
63C22×C3×Dic3D411yescharacteristic
64C22×C3×Dic3D411yescharacteristic
65C2×#624—21no—
66C2×#624—21no—
67C32×C22⋊C4—21no—
68C32×C22⋊C4C2×C412yescomplemented
69#3757—21no—
70#3757C2×C412yescomplemented
71C3×#217—21no—
72C3×#217—21no—
73C3×#217—21no—
74C3×#217—21no—
75C3×#217—21no—
76C3×#217—21no—
77C3×C4⋊Dic3—42no—
78#3724—21no—
79#3724—21no—
80#3724—42no—
81#3722—21no—
82#3722—21no—
83#3722—42no—
84Dic32—21no—
85Dic32—21no—
86#1867—91noSylow
87C23×C3×C4—31no—
88C22×#67—31no—
89C22×#67—31no—
90C22×#67—61no—
91C23×Dic3C2×D311yescharacteristic
92C2×C3×C4⋊C4—61no—
93C2×C3×C22⋊C4—21no—
94C2×C3×C22⋊C4—31no—
95C2×C3×C22⋊C4—31no—
96C2×C3×C22⋊C4—31no—
97C2×C3×C22⋊C4C2×D311yescharacteristic
98C2×C3×C22⋊C4C2×D311yescharacteristic
99C2×#217—31no—
100C2×#217—31no—
101C2×#217—61no—
102C2×#217C2×D311yescharacteristic
103C2×#217C2×D311yescharacteristic
104C2×#217C2×D311yescharacteristic
105C4×#67—61no—
106C4×#67—61no—
107C4×#67—61no—
108C4×#67—61no—
109C2×(C2×D3)⋊C4—61no—
110C2×(C2×D3)⋊C4—61no—
111C2×C4⋊Dic3—21no—
112C2×Dic3⋊C4—61no—
113C2×Dic3⋊C4—61no—
114#67⋊C4—61no—
115#67⋊C4—61no—
116#67⋊C4—61no—
117#67⋊C4—61no—
118D3×C22⋊C4—61no—
119D3×C22⋊C4—61no—
120#877—61no—
121#877—61no—
122C3×#95—61no—
123C3⋊#95—21no—
124C3⋊#95—61no—
125C3⋊#95—61no—
126C3⋊#95—61no—
127C3⋊#95—61no—
128#806—34no—
129#806—34no—
130#806—64no—
131C23×C32—41no—
132C23×C32—41no—
133C23×C32C22×C411yescharacteristic
134C23×C32C2×D411yescharacteristic
135C23×C32C2×D411yescharacteristic
136C23×C32C2×D411yescharacteristic
137C23×C32C2×Q811yescharacteristic
138C23×C32#4111yescharacteristic
139C23×C32#4111yescharacteristic
140C22×C3⋊D3—21no—
141C22×C3⋊D3—21no—
142C22×C3⋊D3—41no—
143C22×C3⋊D3—41no—
144C22×C3⋊D3C4⋊C412yescomplemented
145C2×C32×C4—22no—
146C2×C32×C4—41no—
147C2×C32×C4—41no—
148#638—22no—
149#638—22no—
150#638—22no—
151#638—22no—
152C2×C3⋊Dic3—21no—
153C2×C3⋊Dic3—21no—
154C2×C3⋊Dic3—22no—
155C2×C3⋊Dic3—41no—
156C2×C3⋊Dic3—41no—
157C2×C3⋊Dic3C4⋊C412yescomplemented
158C2×C3×Dic3—22no—
159C2×C3×Dic3—22no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—21no—
162C2×C3×Dic3—21no—
163C2×C3×Dic3—21no—
164C2×C3×Dic3—21no—
165C2×C3×Dic3—41no—
166C2×C3×Dic3—41no—
167C2×C3×Dic3—41no—
168C2×C3×Dic3—41no—
169C2×C3×Dic3—41no—
170C2×C3×Dic3—41no—
171C2×C3×Dic3—41no—
172C2×C3×Dic3—41no—
173C2×C3×Dic3—41no—
174C2×C3×Dic3—41no—
175C2×C3×Dic3—41no—
176#624—81no—
177#624—81no—
178#518—91no—
179C2×#99—91no—
180#386—91no—
181#385—31no—
182#385—91no—
183#342—31no—
184#342—91no—
185C24×C3—21no—
186C24×C3C22×D311yescharacteristic
187C24×C3C22×D311yescharacteristic
188C23×D3—31no—
189C23×D3—31no—
190C23×D3—61no—
191C22×C3×C4—21no—
192C22×C3×C4—21no—
193C22×C3×C4—31no—
194C22×C3×C4—31no—
195C22×C3×C4—31no—
196C22×C3×C4—31no—
197C22×C3×C4—41no—
198C22×C3×C4—61no—
199C22×C3×C4—61no—
200C22×C3×C4—61no—
201C22×C3×C4—61no—
202C22×C3×C4—122no—
203C2×#67—32no—
204C2×#67—32no—
205C2×#67—32no—
206C2×#67—32no—
207C2×#67—62no—
208C2×#67—62no—
209C2×#67—61no—
210C2×#67—61no—
211C2×#67—61no—
212C2×#67—61no—
213C2×#67—61no—
214C2×#67—61no—
215C2×#67—61no—
216C2×#67—61no—
217C2×#67—121no—
218C2×#67—121no—
219C2×#67—121no—
220C2×#67—121no—
221C22×Dic3—21no—
222C22×Dic3—21no—
223C22×Dic3—21no—
224C22×Dic3—21no—
225C22×Dic3—31no—
226C22×Dic3—31no—
227C22×Dic3—42no—
228C22×Dic3—61no—
229C22×Dic3—61no—
230C22×Dic3—61no—
231C22×Dic3—121no—
232C22×Dic3D1211yescharacteristic
233C22×Dic3D1211yescharacteristic
234C22×Dic3#6711yescharacteristic
235C22×Dic3#6711yescharacteristic
236C2×C4×D3—61no—
237C2×C4×D3—61no—
238C2×C4×D3—61no—
239C2×C4×D3—61no—
240C3×C4⋊C4—122no—
241C3×C22⋊C4—21no—
242C3×C22⋊C4—21no—
243C3×C22⋊C4—22no—
244C3×C22⋊C4—41no—
245C3×C22⋊C4—61no—
246C3×C22⋊C4—61no—
247C3×C22⋊C4—61no—
248C3×C22⋊C4—61no—
249C3×C22⋊C4—61no—
250C3×C22⋊C4—61no—
251C3×C22⋊C4C4×D312yescomplemented
252C3×C22⋊C4C4×D312yescomplemented
253#217—21no—
254#217—21no—
255#217—21no—
256#217—21no—
257#217—21no—
258#217—21no—
259#217—32no—
260#217—32no—
261#217—62no—
262#217—61no—
263#217—61no—
264#217—121no—
265(C2×D3)⋊C4—61no—
266(C2×D3)⋊C4—61no—
267(C2×D3)⋊C4—61no—
268(C2×D3)⋊C4—61no—
269(C2×D3)⋊C4—122no—
270(C2×D3)⋊C4—122no—
271C4⋊Dic3—42no—
272Dic3⋊C4—61no—
273Dic3⋊C4—61no—
274Dic3⋊C4—61no—
275Dic3⋊C4—61no—
276Dic3⋊C4—122no—
277Dic3⋊C4—122no—
278C4×Dic3—61no—
279C4×Dic3—61no—
280C4×Dic3—61no—
281C4×Dic3—61no—
282C22×C32—21no—
283C22×C32—21no—
284C22×C32—21no—
285C22×C32—21no—
286C22×C32—21no—
287C22×C32—21no—
288C22×C32—41no—
289C22×C32—41no—
290C22×C32—41no—
291C22×C32—41no—
292C22×C32C2×C4⋊C411yescharacteristic
293C22×C32C4×D411yescharacteristic
294C22×C32C4×D411yescharacteristic
295C22×C32#12011yescharacteristic
296C22×C32C22⋊Q811yescharacteristic
297C22×C32C22⋊Q811yescharacteristic
298C22×C32#12311yescharacteristic
299C2×C3⋊D3—22no—
300C2×C3⋊D3—41no—
301C2×C3⋊D3—41no—
302C2×C3⋊D3—42no—
303C2×C3⋊D3—81no—
304C32×C4—42no—
305C3⋊Dic3—22no—
306C3⋊Dic3—42no—
307C3×Dic3—41no—
308C3×Dic3—41no—
309C3×Dic3—42no—
310C3×Dic3—41no—
311C3×Dic3—41no—
312C3×Dic3—81no—
313C22×D4—91no—
314C23×C4—31no—
315C4×D4—181no—
316C4×D4—181no—
317C4×D4—181no—
318C4×D4—181no—
319#117—181no—
320C2×C4⋊C4—61no—
321C2×C4⋊C4—181no—
322C2×C22⋊C4—31no—
323C2×C22⋊C4—31no—
324C2×C22⋊C4—31no—
325C2×C22⋊C4—91no—
326C2×C22⋊C4—181no—
327C2×C22⋊C4—181no—
328C2×C22⋊C4D3211yescharacteristic
329#99—94no—
330#95—61no—
331#95—181no—
332#95—181no—
333C23×C3—21no—
334C23×C3—21no—
335C23×C3—21no—
336C23×C3—21no—
337C23×C3—21no—
338C23×C3—21no—
339C23×C3—21no—
340C23×C3—41no—
341C23×C3—41no—
342C23×C3—41no—
343C23×C3—41no—
344C23×C3—81no—
345C23×C3—81no—
346C23×C3C2×C4×D311yescharacteristic
347C23×C3C2×C4×D311yescharacteristic
348C23×C3C2×D1211yescharacteristic
349C23×C3#23511yescharacteristic
350C23×C3#23511yescharacteristic
351C23×C3D3×D411yescharacteristic
352C23×C3D3×D411yescharacteristic
353C23×C3D3×D411yescharacteristic
354C23×C3D3×D411yescharacteristic
355C23×C3#23711yescharacteristic
356C23×C3D3×Q811yescharacteristic
357C23×C3D3×Q811yescharacteristic
358C23×C3#23911yescharacteristic
359C23×C3C2×#6711yescharacteristic
360C22×D3—32no—
361C22×D3—32no—
362C22×D3—62no—
363C22×D3—61no—
364C22×D3—61no—
365C22×D3—61no—
366C22×D3—61no—
367C22×D3—121no—
368C22×D3—121no—
369C22×D3—121no—
370C22×D3—121no—
371C22×D3—121no—
372C22×D3—121no—
373C22×D3—241no—
374C22×D3—241no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—42no—
378C2×C3×C4—41no—
379C2×C3×C4—41no—
380C2×C3×C4—41no—
381C2×C3×C4—41no—
382C2×C3×C4—62no—
383C2×C3×C4—62no—
384C2×C3×C4—62no—
385C2×C3×C4—61no—
386C2×C3×C4—61no—
387C2×C3×C4—61no—
388C2×C3×C4—61no—
389C2×C3×C4—81no—
390C2×C3×C4—81no—
391C2×C3×C4—121no—
392C2×C3×C4—121no—
393C2×C3×C4—121no—
394C2×C3×C4—121no—
395C2×C3×C4—121no—
396C2×C3×C4—121no—
397C2×C3×C4—121no—
398C2×C3×C4—121no—
399C2×C3×C4—121no—
400C2×C3×C4—121no—
401C2×C3×C4—121no—
402#67—62no—
403#67—62no—
404#67—62no—
405#67—62no—
406#67—62no—
407#67—62no—
408#67—62no—
409#67—62no—
410#67—122no—
411#67—122no—
412#67—122no—
413#67—122no—
414C2×Dic3—22no—
415C2×Dic3—22no—
416C2×Dic3—22no—
417C2×Dic3—21no—
418C2×Dic3—21no—
419C2×Dic3—21no—
420C2×Dic3—21no—
421C2×Dic3—32no—
422C2×Dic3—32no—
423C2×Dic3—41no—
424C2×Dic3—41no—
425C2×Dic3—41no—
426C2×Dic3—41no—
427C2×Dic3—41no—
428C2×Dic3—41no—
429C2×Dic3—41no—
430C2×Dic3—41no—
431C2×Dic3—41no—
432C2×Dic3—41no—
433C2×Dic3—41no—
434C2×Dic3—62no—
435C2×Dic3—61no—
436C2×Dic3—61no—
437C2×Dic3—61no—
438C2×Dic3—61no—
439C2×Dic3—62no—
440C2×Dic3—62no—
441C2×Dic3—121no—
442C2×Dic3—121no—
443C2×Dic3—122no—
444C2×Dic3—121no—
445C2×Dic3—121no—
446C2×Dic3—121no—
447C2×Dic3—121no—
448C2×Dic3—241no—
449C2×Dic3—241no—
450C4×D3—241no—
451C4×D3—241no—
452C4×D3—241no—
453C4×D3—241no—
454C2×C32—21no—
455C2×C32—21no—
456C2×C32—21no—
457C2×C32—21no—
458C2×C32—21no—
459C2×C32—21no—
460C2×C32#38511yescharacteristic
461C2×C32B(4,𝔽2)11yescharacteristic
462C2×C32#45811yescharacteristic
463C3⋊D3—42no—
464C24—91no—
465C24C2×D3211yescharacteristic
466C2×D4—92no—
467C2×D4—92no—
468C2×D4—181no—
469C2×D4—181no—
470C2×D4—181no—
471C2×D4—181no—
472C22×C4—21no—
473C22×C4—31no—
474C22×C4—31no—
475C22×C4—31no—
476C22×C4—31no—
477C22×C4—61no—
478C22×C4—61no—
479C22×C4—61no—
480C22×C4—61no—
481C22×C4—91no—
482C22×C4—122no—
483C22×C4—181no—
484C22×C4—181no—
485C22×C4—181no—
486C4⋊C4—122no—
487C4⋊C4—181no—
488C4⋊C4—181no—
489C4⋊C4—362no—
490C22⋊C4—21no—
491C22⋊C4—61no—
492C22⋊C4—61no—
493C22⋊C4—61no—
494C22⋊C4—61no—
495C22⋊C4—61no—
496C22⋊C4—61no—
497C22⋊C4—92no—
498C22⋊C4—181no—
499C22⋊C4—181no—
500C22⋊C4—181no—
501C22⋊C4—362no—
502C22⋊C4#62412yescomplemented
503C42—181no—
504C42—181no—
505C22×C3—21no—
506C22×C3—21no—
507C22×C3—21no—
508C22×C3—21no—
509C22×C3—21no—
510C22×C3—21no—
511C22×C3—21no—
512C22×C3—21no—
513C22×C3—21no—
514C22×C3—21no—
515C22×C3—21no—
516C22×C3—21no—
517C22×C3—21no—
518C22×C3—21no—
519C22×C3—21no—
520C22×C3—21no—
521C22×C3—21no—
522C22×C3—21no—
523C22×C3—21no—
524C22×C3—41no—
525C22×C3—41no—
526C22×C3—41no—
527C22×C3—41no—
528C22×C3—41no—
529C22×C3—41no—
530C22×C3—41no—
531C22×C3—41no—
532C22×C3—41no—
533C22×C3—41no—
534C22×C3—41no—
535C22×C3—41no—
536C22×C3—41no—
537C22×C3—41no—
538C22×C3—81no—
539C22×C3—81no—
540C22×C3—81no—
541C22×C3—81no—
542C22×C3C4×D1211yescharacteristic
543C22×C3#67⋊C411yescharacteristic
544C22×C3#88211yescharacteristic
545C22×C3#88311yescharacteristic
546C22×C3D3×C4⋊C411yescharacteristic
547C22×C3D3×C4⋊C411yescharacteristic
548C22×C3#89311yescharacteristic
549C22×C3#89411yescharacteristic
550C22×C3#89611yescharacteristic
551C22×C3#89611yescharacteristic
552C22×C3#89711yescharacteristic
553C22×C3C4×#6711yescharacteristic
554C22×C3#93711yescharacteristic
555C22×C3#94611yescharacteristic
556C2×D3—62no—
557C2×D3—62no—
558C2×D3—122no—
559C2×D3—121no—
560C2×D3—121no—
561C2×D3—121no—
562C2×D3—121no—
563C2×D3—122no—
564C2×D3—122no—
565C2×D3—241no—
566C2×D3—241no—
567C2×D3—242no—
568C2×D3—241no—
569C2×D3—241no—
570C2×D3—242no—
571C3×C4—42no—
572C3×C4—42no—
573C3×C4—82no—
574C3×C4—121no—
575C3×C4—122no—
576C3×C4—121no—
577C3×C4—121no—
578C3×C4—121no—
579C3×C4—241no—
580Dic3—41no—
581Dic3—41no—
582Dic3—41no—
583Dic3—42no—
584Dic3—41no—
585Dic3—62no—
586Dic3—62no—
587Dic3—81no—
588Dic3—122no—
589Dic3—122no—
590Dic3—122no—
591Dic3—242no—
592C32#186711yescharacteristic, complemented, Sylow
593C23—41no—
594C23—41no—
595C23—92no—
596C23—181no—
597C23—181no—
598C23—361no—
599C23—361no—
600C23#379711yescharacteristic
601C23#379911yescharacteristic
602C23D3×D1211yescharacteristic
603C23#380211yescharacteristic
604C23#380411yescharacteristic
605C23C2×#62411yescharacteristic
606C23D3×#6711yescharacteristic
607D4—182no—
608D4—182no—
609D4—182no—
610D4—182no—
611C2×C4—22no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—62no—
615C2×C4—62no—
616C2×C4—62no—
617C2×C4—61no—
618C2×C4—61no—
619C2×C4—61no—
620C2×C4—61no—
621C2×C4—92no—
622C2×C4—121no—
623C2×C4—121no—
624C2×C4—121no—
625C2×C4—121no—
626C2×C4—121no—
627C2×C4—121no—
628C2×C4—121no—
629C2×C4—121no—
630C2×C4—121no—
631C2×C4—121no—
632C2×C4—121no—
633C2×C4—181no—
634C2×C4—181no—
635C2×C4—182no—
636C2×C4—361no—
637C2×C4—361no—
638C2×C4—721no—
639C2×C4—721no—
640C2×C3—21no—
641C2×C3—21no—
642C2×C3—21no—
643C2×C3—21no—
644C2×C3—21no—
645C2×C3—21no—
646C2×C3—21no—
647C2×C3—21no—
648C2×C3—21no—
649C2×C3—21no—
650C2×C3—21no—
651C2×C3—21no—
652C2×C3—21no—
653C2×C3—21no—
654C2×C3—21no—
655C2×C3—41no—
656C2×C3—41no—
657C2×C3—41no—
658C2×C3—41no—
659C2×C3—41no—
660C2×C3—41no—
661C2×C3#466811yescharacteristic
662C2×C3#474111yescharacteristic
663C2×C3#474211yescharacteristic
664C2×C3#498911yescharacteristic
665C2×C3#503211yescharacteristic
666C2×C3#505311yescharacteristic
667D3—122no—
668D3—122no—
669D3—242no—
670C22—21no—
671C22—21no—
672C22—21no—
673C22—21no—
674C22—21no—
675C22—21no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22—41no—
680C22—182no—
681C22—362no—
682C22—361no—
683C22—361no—
684C22—721no—
685C22#6385411yescharacteristic
686C22#6388811yescharacteristic
687C22#6389411yescharacteristic
688C22#6389511yescharacteristic
689C22#6390011yescharacteristic
690C22#6392211yescharacteristic
691C22#6395211yescharacteristic
692C4—42no—
693C4—122no—
694C4—121no—
695C4—121no—
696C4—121no—
697C4—121no—
698C4—182no—
699C4—241no—
700C4—362no—
701C3—21no—
702C3#6896111yescharacteristic, complemented
703C3#6959511yescharacteristic, complemented
704C2—21no—
705C2—21no—
706C2—21no—
707C2—21no—
708C2—21no—
709C2—21no—
710C2—362no—
711C2#1059040711yescharacteristic
712C2#1059040811yescharacteristic
713C2#1059137811yescharacteristic
subgroupG/H
centerC22#63922
commutatorC23×C32C22×C4
FrattiniC24C2×D32
FittingC2×C32×C22⋊C4C22
socleC22×C32#120
prime radicalC22×#638C22
cosocleC24×C32C23
hypercenterC2×C22⋊C4D32
hypocenterC32#1867
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C3×#4950C2semidirect
5. #10591693C2semidirect
6. C3×#4527C2semidirect
7. #10589186C2semidirect
26. #63633C4semidirect
39. #4950D3semidirect
43. #4527D3semidirect
68. C32×C22⋊C4C2×C4semidirect
70. #3757C2×C4semidirect
144. C22×C3⋊D3C4⋊C4semidirect
157. C2×C3⋊Dic3C4⋊C4semidirect
251. C3×C22⋊C4C4×D3semidirect
252. C3×C22⋊C4C4×D3semidirect
502. C22⋊C4#624semidirect
592. C32#1867semidirect
702. C3#68961semidirect
703. C3#69595semidirect

Maximal subgroups

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

subgroupindex
#105955102
C2×#636332
C3×#49502
#105917112
#105916932
C3×#45272
#105891862
#695953
#689613