Finite Group Databasebeta

← #11787072

Subgroups — #11787072

Order 1152.

865 conjugacy classes of subgroups.

The subgroup lattice has 705 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595506C211yesmaximal, characteristic
2#10592909C211yesmaximal, characteristic, complemented
3C3×#5213C211yesmaximal, characteristic
4C3×#5210C211yesmaximal, characteristic, complemented
5C2×#63580C211yesmaximal, characteristic
6#10589187C211yesmaximal, characteristic, complemented
7#10589186C211yesmaximal, characteristic, complemented
8#69597—31nomaximal
9#69595—31nomaximal
10C23×C32×C4C2211yescharacteristic
11C22×C3×#67C2211yescharacteristic
12C2×#3757C2211yescharacteristic
13C2×#3757C2211yescharacteristic
14C2×#3750—21no—
15C2×C3×#217C2211yescharacteristic
16C2×C3×#217C2211yescharacteristic
17C2×C3×#217C2211yescharacteristic
18C2×C3×(C2×D3)⋊C4—21no—
19C2×C3×Dic3⋊C4—21no—
20#67⋊Dic3—21no—
21#67⋊Dic3—21no—
22Dic3×#67—21no—
23Dic3×#67—21no—
24D3×#217—21no—
25#63955—21no—
26#63658—21no—
27C3×C3⋊#95—21no—
28C3×C3⋊#95—21no—
29#63580C414yescomplemented
30#5798—31no—
31#5486—31no—
32C3×#386—31no—
33C3×#385—31no—
34C2×#834—31no—
35#5213D311yescharacteristic
36#5210—31no—
37#5210—31no—
38#5210—61no—
39#5210D311yescharacteristic, complemented
40C2×#806—31no—
41#4527—31no—
42#4527—31no—
43#4527—31no—
44#4526—31no—
45C24×C32C2311yescharacteristic
46C23×C3×D3D411yescharacteristic
47C22×C32×C4—21no—
48C22×C32×C4—21no—
49C22×C32×C4—21no—
50C22×C32×C4—42no—
51C22×C3⋊Dic3—21no—
52C22×C3⋊Dic3D411yescharacteristic
53C22×C3⋊Dic3D411yescharacteristic
54C2×C3×#67—21no—
55C2×C3×#67—21no—
56C2×C3×#67—21no—
57C2×C3×#67—21no—
58C2×C3×#67C2×C412yes—
59C2×C3×#67Q812yes—
60C22×C3×Dic3—21no—
61C22×C3×Dic3—21no—
62C22×C3×Dic3D411yescharacteristic
63C22×C3×Dic3D411yescharacteristic
64C22×C3×Dic3D411yescharacteristic
65C2×D3×Dic3—21no—
66C2×D3×Dic3—21no—
67#3757—21no—
68#3757—21no—
69#3757—21no—
70#3757C2×C412yescomplemented
71#3750—42no—
72C3×#217—21no—
73C3×#217—21no—
74C3×#217—21no—
75C3×#217—21no—
76C3×#217—21no—
77C3×#217C2×C412yescomplemented
78C3×(C2×D3)⋊C4—42no—
79C3×Dic3⋊C4—42no—
80Dic3⋊Dic3—21no—
81Dic3⋊Dic3—21no—
82(C2×D3)⋊Dic3—21no—
83(C2×D3)⋊Dic3—21no—
84Dic32—21no—
85Dic32—21no—
86#1867—91noSylow
87C22×C3×D4—31no—
88C23×C3×C4—21no—
89C23×C3×C4C2×D311yescharacteristic
90C23×C3×C4C2×D311yescharacteristic
91C22×#67C2×D311yescharacteristic
92C2×C3×C4⋊C4—61no—
93C2×C3×C22⋊C4—31no—
94C2×C3×C22⋊C4—31no—
95C2×C3×C22⋊C4—31no—
96C2×C3×C22⋊C4—61no—
97C2×#217—31no—
98C2×#217—31no—
99C2×#217—31no—
100C2×#217—31no—
101C2×#217—61no—
102C2×#217—61no—
103C2×#217—61no—
104C2×#217C2×D311yescharacteristic
105C2×#217C2×D311yescharacteristic
106C2×#217C2×D311yescharacteristic
107D4×Dic3—61no—
108D4×Dic3—61no—
109D4×Dic3—61no—
110D4×Dic3—61no—
111C4×#67—61no—
112C4×#67—61no—
113C2×(C2×D3)⋊C4—21no—
114#926—61no—
115C2×Dic3⋊C4—21no—
116C2×Dic3⋊C4—61no—
117C2×Dic3⋊C4—61no—
118C2×Dic3⋊C4—62no—
119#67⋊C4—61no—
120#67⋊C4—61no—
121D3×C22⋊C4—61no—
122#877—61no—
123C3×#95—61no—
124C3×#95—61no—
125#834—34no—
126C3⋊#95—21no—
127C3⋊#95—21no—
128C3⋊#95—61no—
129C3⋊#95—61no—
130C3⋊#95—62no—
131#806—34no—
132C23×C32—41no—
133C23×C32—41no—
134C23×C32C22×C411yescharacteristic
135C23×C32C2×D411yescharacteristic
136C23×C32C2×D411yescharacteristic
137C23×C32C2×D411yescharacteristic
138C23×C32C2×Q811yescharacteristic
139C23×C32#4111yescharacteristic
140C23×C32#4111yescharacteristic
141C22×C3×D3—21no—
142C22×C3×D3—21no—
143C22×C3×D3—41no—
144C22×C3×D3—41no—
145C22×C3×D3C4⋊C412yescomplemented
146C2×C32×C4—22no—
147C2×C32×C4—22no—
148C2×C32×C4—22no—
149C2×C32×C4—41no—
150C2×C32×C4—41no—
151C2×C32×C4—41no—
152C2×C32×C4—41no—
153C2×C3⋊Dic3—22no—
154C2×C3⋊Dic3—21no—
155C2×C3⋊Dic3—21no—
156C2×C3⋊Dic3—41no—
157C2×C3⋊Dic3—41no—
158C2×C3⋊Dic3—41no—
159C2×C3⋊Dic3—41no—
160C3×#67—22no—
161C3×#67—22no—
162C3×#67—22no—
163C3×#67—22no—
164C2×C3×Dic3—21no—
165C2×C3×Dic3—21no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—21no—
168C2×C3×Dic3—21no—
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—
176C2×C3×Dic3C4⋊C412yescomplemented
177D3×Dic3—81no—
178D3×Dic3—81no—
179#518—91no—
180C2×#99—91no—
181#386—31no—
182#385—31no—
183#385—91no—
184#342—91no—
185#342—91no—
186C24×C3—21no—
187C24×C3—31no—
188C24×C3C22×D311yescharacteristic
189C24×C3C22×D311yescharacteristic
190C23×D3#6711yescharacteristic
191C2×C3×D4—32no—
192C2×C3×D4—32no—
193C2×C3×D4—61no—
194C2×C3×D4—61no—
195C2×C3×D4—61no—
196C2×C3×D4—61no—
197C22×C3×C4—22no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—31no—
205C22×C3×C4—31no—
206C22×C3×C4—31no—
207C22×C3×C4—41no—
208C22×C3×C4—41no—
209C22×C3×C4—42no—
210C22×C3×C4—42no—
211C22×C3×C4—44no—
212C22×C3×C4—61no—
213C22×C3×C4—61no—
214C2×#67—21no—
215C2×#67—21no—
216C2×#67—21no—
217C2×#67—21no—
218C2×#67Dic612yes—
219C2×#67C4×D312yes—
220C22×Dic3—21no—
221C22×Dic3—21no—
222C22×Dic3—31no—
223C22×Dic3—31no—
224C22×Dic3—31no—
225C22×Dic3—31no—
226C22×Dic3—61no—
227C22×Dic3—61no—
228C22×Dic3—61no—
229C22×Dic3—61no—
230C22×Dic3—62no—
231C22×Dic3—61no—
232C22×Dic3—61no—
233C22×Dic3#6711yescharacteristic
234C22×Dic3#6711yescharacteristic
235C22×Dic3#6711yescharacteristic
236C2×C4×D3—61no—
237C2×C4×D3—61no—
238C3×C4⋊C4—122no—
239C3×C22⋊C4—32no—
240C3×C22⋊C4—61no—
241C3×C22⋊C4—61no—
242C3×C22⋊C4—61no—
243C3×C22⋊C4—61no—
244C3×C22⋊C4—61no—
245C3×C22⋊C4—122no—
246#217—21no—
247#217—21no—
248#217—21no—
249#217—21no—
250#217—21no—
251#217—32no—
252#217—32no—
253#217—62no—
254#217—61no—
255#217—61no—
256#217—62no—
257#217—61no—
258#217—61no—
259#217—61no—
260#217—61no—
261#217—61no—
262#217—61no—
263#217—121no—
264#217—121no—
265#217C4×D312yescomplemented
266(C2×D3)⋊C4—42no—
267(C2×D3)⋊C4—61no—
268(C2×D3)⋊C4—61no—
269C4⋊Dic3—61no—
270C4⋊Dic3—61no—
271Dic3⋊C4—42no—
272Dic3⋊C4—61no—
273Dic3⋊C4—61no—
274Dic3⋊C4—122no—
275Dic3⋊C4—122no—
276Dic3⋊C4—124no—
277C4×Dic3—61no—
278C4×Dic3—61no—
279C4×Dic3—61no—
280C4×Dic3—61no—
281C22×C32—21no—
282C22×C32—21no—
283C22×C32—21no—
284C22×C32—21no—
285C22×C32—21no—
286C22×C32—21no—
287C22×C32—41no—
288C22×C32—41no—
289C22×C32—41no—
290C22×C32—41no—
291C22×C32C2×C4⋊C411yescharacteristic
292C22×C32C4×D411yescharacteristic
293C22×C32C4×D411yescharacteristic
294C22×C32#12011yescharacteristic
295C22×C32C22⋊Q811yescharacteristic
296C22×C32C22⋊Q811yescharacteristic
297C22×C32#12311yescharacteristic
298C2×C3×D3—22no—
299C2×C3×D3—41no—
300C2×C3×D3—41no—
301C2×C3×D3—42no—
302C2×C3×D3—81no—
303C32×C4—42no—
304C3⋊Dic3—42no—
305C3⋊Dic3—41no—
306C3⋊Dic3—41no—
307C3×Dic3—22no—
308C3×Dic3—42no—
309C3×Dic3—41no—
310C3×Dic3—41no—
311C3×Dic3—81no—
312C22×D4—31no—
313C23×C4D3211yescharacteristic
314C4×D4—181no—
315C4×D4—181no—
316C4×D4—181no—
317C4×D4—181no—
318#117—181no—
319C2×C4⋊C4—61no—
320C2×C4⋊C4—181no—
321C2×C22⋊C4—31no—
322C2×C22⋊C4—31no—
323C2×C22⋊C4—31no—
324C2×C22⋊C4—61no—
325C2×C22⋊C4—91no—
326C2×C22⋊C4—91no—
327C2×C22⋊C4—181no—
328#99—94no—
329#95—61no—
330#95—61no—
331#95—181no—
332C23×C3—21no—
333C23×C3—21no—
334C23×C3—21no—
335C23×C3—21no—
336C23×C3—21no—
337C23×C3—21no—
338C23×C3—21no—
339C23×C3—32no—
340C23×C3—41no—
341C23×C3—41no—
342C23×C3—41no—
343C23×C3—41no—
344C23×C3—42no—
345C23×C3—42no—
346C23×C3—61no—
347C23×C3—61no—
348C23×C3—121no—
349C23×C3—121no—
350C23×C3C2×Dic611yescharacteristic
351C23×C3C2×C4×D311yescharacteristic
352C23×C3C2×C4×D311yescharacteristic
353C23×C3#23511yescharacteristic
354C23×C3D3×D411yescharacteristic
355C23×C3D3×D411yescharacteristic
356C23×C3D3×D411yescharacteristic
357C23×C3D3×D411yescharacteristic
358C23×C3#23711yescharacteristic
359C23×C3#23711yescharacteristic
360C23×C3D3×Q811yescharacteristic
361C23×C3#23911yescharacteristic
362C23×C3C2×#6711yescharacteristic
363C23×C3C2×#6711yescharacteristic
364C22×D3—21no—
365C22×D3—21no—
366C22×D3—41no—
367C22×D3—41no—
368C22×D3Dic3⋊C412yescomplemented
369C3×D4—62no—
370C3×D4—62no—
371C3×D4—62no—
372C3×D4—62no—
373C2×C3×C4—22no—
374C2×C3×C4—24no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—22no—
380C2×C3×C4—32no—
381C2×C3×C4—42no—
382C2×C3×C4—42no—
383C2×C3×C4—42no—
384C2×C3×C4—41no—
385C2×C3×C4—41no—
386C2×C3×C4—41no—
387C2×C3×C4—41no—
388C2×C3×C4—41no—
389C2×C3×C4—41no—
390C2×C3×C4—42no—
391C2×C3×C4—42no—
392C2×C3×C4—42no—
393C2×C3×C4—41no—
394C2×C3×C4—41no—
395C2×C3×C4—61no—
396C2×C3×C4—61no—
397C2×C3×C4—62no—
398C2×C3×C4—61no—
399C2×C3×C4—61no—
400C2×C3×C4—121no—
401C2×C3×C4—121no—
402C2×C3×C4—121no—
403C2×C3×C4—121no—
404C2×C3×C4—121no—
405C2×C3×C4—121no—
406C2×C3×C4—121no—
407#67—22no—
408#67—22no—
409#67—22no—
410#67—22no—
411C2×Dic3—21no—
412C2×Dic3—21no—
413C2×Dic3—22no—
414C2×Dic3—21no—
415C2×Dic3—21no—
416C2×Dic3—41no—
417C2×Dic3—41no—
418C2×Dic3—41no—
419C2×Dic3—41no—
420C2×Dic3—41no—
421C2×Dic3—41no—
422C2×Dic3—41no—
423C2×Dic3—64no—
424C2×Dic3—62no—
425C2×Dic3—62no—
426C2×Dic3—61no—
427C2×Dic3—61no—
428C2×Dic3—61no—
429C2×Dic3—61no—
430C2×Dic3—121no—
431C2×Dic3—121no—
432C2×Dic3—122no—
433C2×Dic3—121no—
434C2×Dic3—121no—
435C2×Dic3—122no—
436C2×Dic3—121no—
437C2×Dic3—121no—
438C2×Dic3—121no—
439C2×Dic3—121no—
440C2×Dic3—121no—
441C2×Dic3—121no—
442C2×Dic3—122no—
443C2×Dic3—122no—
444C2×Dic3—241no—
445C2×Dic3—241no—
446C2×Dic3Dic3⋊C412yescomplemented
447C4×D3—241no—
448C4×D3—241no—
449C2×C32—21no—
450C2×C32—21no—
451C2×C32—21no—
452C2×C32—21no—
453C2×C32—21no—
454C2×C32—21no—
455C2×C32#38511yescharacteristic
456C2×C32B(4,𝔽2)11yescharacteristic
457C2×C32#45811yescharacteristic
458C3×D3—42no—
459C24—31no—
460C24C2×D3211yescharacteristic
461C2×D4—32no—
462C2×D4—32no—
463C2×D4—61no—
464C2×D4—61no—
465C2×D4—61no—
466C2×D4—61no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—31no—
471C22×C4—31no—
472C22×C4—31no—
473C22×C4—42no—
474C22×C4—61no—
475C22×C4—61no—
476C22×C4—91no—
477C22×C4—91no—
478C22×C4—181no—
479C22×C4—181no—
480C22×C4—181no—
481C4⋊C4—122no—
482C4⋊C4—181no—
483C4⋊C4—181no—
484C4⋊C4—362no—
485C22⋊C4—32no—
486C22⋊C4—61no—
487C22⋊C4—61no—
488C22⋊C4—61no—
489C22⋊C4—61no—
490C22⋊C4—61no—
491C22⋊C4—92no—
492C22⋊C4—122no—
493C22⋊C4—181no—
494C22⋊C4—181no—
495C22⋊C4—181no—
496C22⋊C4—181no—
497C22⋊C4—181no—
498C42—181no—
499C42—181no—
500C22×C3—22no—
501C22×C3—22no—
502C22×C3—21no—
503C22×C3—21no—
504C22×C3—21no—
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—41no—
522C22×C3—41no—
523C22×C3—41no—
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—42no—
534C22×C3—42no—
535C22×C3—42no—
536C22×C3—42no—
537C22×C3—62no—
538C22×C3—122no—
539C22×C3—121no—
540C22×C3—121no—
541C22×C3—241no—
542C22×C3#87811yescharacteristic
543C22×C3#87811yescharacteristic
544C22×C3#67⋊C411yescharacteristic
545C22×C3#67⋊C411yescharacteristic
546C22×C3D3×C4⋊C411yescharacteristic
547C22×C3#89311yescharacteristic
548C22×C3#89411yescharacteristic
549C22×C3#89611yescharacteristic
550C22×C3C2×Dic3⋊C411yescharacteristic
551C22×C3C4×#6711yescharacteristic
552C22×C3#93511yescharacteristic
553C22×C3#93711yescharacteristic
554C22×C3#93711yescharacteristic
555C22×C3#94611yescharacteristic
556C2×D3—22no—
557C2×D3—41no—
558C2×D3—41no—
559C2×D3—42no—
560C2×D3—81no—
561C3×C4—44no—
562C3×C4—42no—
563C3×C4—42no—
564C3×C4—62no—
565C3×C4—122no—
566C3×C4—121no—
567C3×C4—121no—
568C3×C4—241no—
569Dic3—22no—
570Dic3—42no—
571Dic3—41no—
572Dic3—41no—
573Dic3—81no—
574Dic3—124no—
575Dic3—122no—
576Dic3—122no—
577Dic3—121no—
578Dic3—121no—
579Dic3—121no—
580Dic3—121no—
581Dic3—241no—
582Dic3—241no—
583C32#186711yescharacteristic, complemented, Sylow
584C23—32no—
585C23—41no—
586C23—41no—
587C23—61no—
588C23—61no—
589C23—121no—
590C23—121no—
591C23D3×Dic611yescharacteristic
592C23#379511yescharacteristic
593C23#379611yescharacteristic
594C23C4×D3211yescharacteristic
595C23D3×#6711yescharacteristic
596C23D3×#6711yescharacteristic
597C23#381111yescharacteristic
598D4—62no—
599D4—62no—
600D4—62no—
601D4—62no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—32no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—61no—
611C2×C4—61no—
612C2×C4—62no—
613C2×C4—61no—
614C2×C4—61no—
615C2×C4—121no—
616C2×C4—121no—
617C2×C4—121no—
618C2×C4—121no—
619C2×C4—121no—
620C2×C4—121no—
621C2×C4—121no—
622C2×C4—182no—
623C2×C4—181no—
624C2×C4—181no—
625C2×C4—361no—
626C2×C4—361no—
627C2×C4—361no—
628C2×C4—361no—
629C2×C4—721no—
630C2×C4—721no—
631C2×C3—22no—
632C2×C3—22no—
633C2×C3—21no—
634C2×C3—21no—
635C2×C3—21no—
636C2×C3—21no—
637C2×C3—21no—
638C2×C3—21no—
639C2×C3—21no—
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—41no—
649C2×C3—41no—
650C2×C3—41no—
651C2×C3—41no—
652C2×C3—122no—
653C2×C3#494611yescharacteristic
654C2×C3#498911yescharacteristic
655C2×C3#503211yescharacteristic
656C2×C3#503211yescharacteristic
657C2×C3#505311yescharacteristic
658C2×C3#505311yescharacteristic
659D3—42no—
660C22—21no—
661C22—21no—
662C22—21no—
663C22—21no—
664C22—21no—
665C22—21no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22—62no—
671C22—122no—
672C22—121no—
673C22—121no—
674C22—241no—
675C22D3×Dic3⋊C411yescharacteristic
676C22#6387911yescharacteristic
677C22#6388111yescharacteristic
678C22#6388411yescharacteristic
679C22#6388711yescharacteristic
680C22#6389611yescharacteristic
681C22#6398311yescharacteristic
682C4—42no—
683C4—62no—
684C4—122no—
685C4—121no—
686C4—121no—
687C4—241no—
688C4—362no—
689C4—361no—
690C4—361no—
691C3—21no—
692C3#6959511yescharacteristic, complemented
693C3#6959711yescharacteristic, complemented
694C2—21no—
695C2—21no—
696C2—21no—
697C2—21no—
698C2—21no—
699C2—21no—
700C2—122no—
701C2#1059137211yescharacteristic
702C2#1059139811yescharacteristic
703C2#1059172511yescharacteristic
subgroupG/H
centerC22#63983
commutatorC23×C32C22×C4
FrattiniC24C2×D32
FittingC23×C32×C4C22
socleC22×C32#120
prime radicalC22×C3×#67C22
cosocleC24×C32C23
hypercenterC23×C4D32
hypocenterC32#1867
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. #10592909C2semidirect
4. C3×#5210C2semidirect
6. #10589187C2semidirect
7. #10589186C2semidirect
29. #63580C4semidirect
39. #5210D3semidirect
70. #3757C2×C4semidirect
77. C3×#217C2×C4semidirect
145. C22×C3×D3C4⋊C4semidirect
176. C2×C3×Dic3C4⋊C4semidirect
265. #217C4×D3semidirect
368. C22×D3Dic3⋊C4semidirect
446. C2×Dic3Dic3⋊C4semidirect
583. C32#1867semidirect
692. C3#69595semidirect
693. C3#69597semidirect

Maximal subgroups

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

subgroupindex
#105955062
#105929092
C3×#52132
C3×#52102
C2×#635802
#105891872
#105891862
#695973
#695953