Finite Group Databasebeta

← #11787937

Subgroups — #11787937

Order 1152.

1261 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63977C211yesmaximal, characteristic
2#10595510C211yesmaximal, characteristic, complemented
3C2×#63633C211yesmaximal, characteristic, complemented
4C3×#4955C211yesmaximal, characteristic, complemented
5#10591706C211yesmaximal, characteristic, complemented
6C3×#4527C211yesmaximal, characteristic, complemented
7#10589186C211yesmaximal, characteristic, complemented
8#69499—31nomaximal
9#68962—31nomaximal
10C24×C3×D3C2211yescharacteristic
11C22×#638C2211yescharacteristic
12C22×#626—21no—
13C2×C32×C22⋊C4C2211yescharacteristic
14C2×#3757C2211yescharacteristic
15C2×C3×#217C2211yescharacteristic
16C2×C3×#217C2211yescharacteristic
17C2×C3×#217C2211yescharacteristic
18C2×C3×(C2×D3)⋊C4—22no—
19#63977—22no—
20#63977C414yescomplemented
21#63974—21no—
22C2×(C2×D3)⋊Dic3—21no—
23C2×(C2×D3)⋊Dic3—22no—
24#63957—21no—
25#63952—22no—
26#63952—22no—
27#63633—22no—
28C2×#953—31no—
29C2×#882—31no—
30#5486—31no—
31#5486—31no—
32C3×#379—31no—
33#5247—31no—
34#4955—31no—
35#4955D311yescharacteristic, complemented
36C2×#806—31no—
37C2×#806—31no—
38C2×#806—61no—
39C3×#342—31no—
40#4527—31no—
41#4527D311yescharacteristic, complemented
42#4526—31no—
43C24×C32C2311yescharacteristic
44C23×C3⋊D3D411yescharacteristic
45C23×C3×D3—21no—
46C23×C3×D3—21no—
47C23×C3×D3—21no—
48C23×C3×D3—21no—
49C23×C3×D3—21no—
50C23×C3×D3—21no—
51C23×C3×D3—44no—
52C23×C3×D3C2×C412yescomplemented
53C22×C32×C4—21no—
54C2×#638—21no—
55C2×#638—21no—
56C2×#638—21no—
57C2×#638—21no—
58C2×#638C2×C412yes—
59C2×#638D412yes—
60C22×C3⋊Dic3—21no—
61C22×C3⋊Dic3D411yescharacteristic
62C22×C3×Dic3—21no—
63C22×C3×Dic3D412yescomplemented
64C22×C3×Dic3D412yescomplemented
65C2×#626—24no—
66C2×#626—44no—
67C2×#624—22no—
68C32×C22⋊C4—21no—
69C32×C22⋊C4—21no—
70#3757—21no—
71#3757—21no—
72C3×#217—21no—
73C3×#217—21no—
74C3×#217—21no—
75C3×#217—21no—
76C3×#217—21no—
77C3×#217C2×C412yescomplemented
78C3×(C2×D3)⋊C4—44no—
79#3724—22no—
80#3722—22no—
81(C2×D3)⋊Dic3—24no—
82(C2×D3)⋊Dic3—44no—
83Dic32—22no—
84#1889—91noSylow
85C25×C3—31no—
86C24×D3C2×D311yescharacteristic
87C22×#67—31no—
88C22×#67—31no—
89C22×#67—61no—
90C22×#67—61no—
91C22×D12—61no—
92C2×C3×C22⋊C4—21no—
93C2×C3×C22⋊C4—31no—
94C2×C3×C22⋊C4—31no—
95C2×C3×C22⋊C4—31no—
96C2×C3×C22⋊C4—62no—
97C2×C3×C22⋊C4C2×D311yescharacteristic
98C2×C3×C22⋊C4C2×D311yescharacteristic
99#953—34no—
100#953—62no—
101C2×#217—31no—
102C2×#217—31no—
103C2×#217—61no—
104C2×#217—61no—
105C2×#217—62no—
106C2×#217C2×D311yescharacteristic
107C2×#217C2×D311yescharacteristic
108C2×#217C2×D311yescharacteristic
109C4×#67—62no—
110C4×#67—62no—
111C2×(C2×D3)⋊C4—22no—
112C2×(C2×D3)⋊C4—61no—
113C2×(C2×D3)⋊C4—62no—
114#882—34no—
115#882—62no—
116#67⋊C4—62no—
117#67⋊C4—62no—
118D3×C22⋊C4—61no—
119D3×C22⋊C4—61no—
120#877—61no—
121#877—61no—
122#806—62no—
123#806—62no—
124#806—64no—
125C23×C32—42no—
126C23×C32C22×C411yescharacteristic
127C23×C32C2×D411yescharacteristic
128C23×C32C2×D411yescharacteristic
129C23×C32C2×D411yescharacteristic
130C23×C32C2×D411yescharacteristic
131C23×C32#4111yescharacteristic
132C23×C32#4111yescharacteristic
133C22×C3⋊D3—21no—
134C22×C3⋊D3—21no—
135C22×C3⋊D3—42no—
136C22×C3⋊D3C22⋊C412yescomplemented
137C22×C3×D3—24no—
138C22×C3×D3—24no—
139C22×C3×D3—24no—
140C22×C3×D3—22no—
141C22×C3×D3—22no—
142C22×C3×D3—22no—
143C22×C3×D3—44no—
144C22×C3×D3—44no—
145C22×C3×D3—44no—
146C22×C3×D3—44no—
147C22×C3×D3—42no—
148C22×C3×D3—42no—
149C22×C3×D3—42no—
150C22×C3×D3—41no—
151C22×C3×D3—41no—
152C22×C3×D3—41no—
153C22×C3×D3—41no—
154C2×C32×C4—41no—
155C2×C32×C4—42no—
156#638—22no—
157#638—22no—
158#638—22no—
159#638—22no—
160C2×C3⋊Dic3—21no—
161C2×C3⋊Dic3—21no—
162C2×C3⋊Dic3—41no—
163C2×C3⋊Dic3—42no—
164C2×C3⋊Dic3C22⋊C412yescomplemented
165C2×C3×Dic3—22no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—42no—
169C2×C3×Dic3—42no—
170C2×C3×Dic3—42no—
171#626—48no—
172#624—82no—
173C2×#120—91no—
174#518—91no—
175C2×#99—91no—
176#379—31no—
177#379—91no—
178#342—31no—
179#342—91no—
180C24×C3—21no—
181C24×C3—32no—
182C24×C3—61no—
183C24×C3—61no—
184C24×C3—61no—
185C24×C3—61no—
186C24×C3—61no—
187C24×C3—61no—
188C24×C3—124no—
189C24×C3C22×D311yescharacteristic
190C24×C3C22×D311yescharacteristic
191C23×D3—21no—
192C23×D3—21no—
193C23×D3—21no—
194C23×D3—21no—
195C23×D3—21no—
196C23×D3—21no—
197C23×D3—31no—
198C23×D3—31no—
199C23×D3—44no—
200C23×D3—61no—
201C23×D3C4×D312yescomplemented
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—32no—
205C22×C3×C4—32no—
206C22×C3×C4—41no—
207C22×C3×C4—61no—
208C2×#67—32no—
209C2×#67—32no—
210C2×#67—32no—
211C2×#67—32no—
212C2×#67—62no—
213C2×#67—62no—
214C2×#67—64no—
215C2×#67—61no—
216C2×#67—61no—
217C2×#67—61no—
218C2×#67—61no—
219C2×#67—61no—
220C2×#67—61no—
221C2×#67—61no—
222C2×#67—61no—
223C2×#67—121no—
224C2×#67—121no—
225C2×#67—121no—
226C2×#67—121no—
227C2×#67—124no—
228C22×Dic3—21no—
229C22×Dic3—31no—
230C22×Dic3—31no—
231C22×Dic3—61no—
232C22×Dic3—61no—
233C22×Dic3—61no—
234C22×Dic3—121no—
235C22×Dic3D1212yescomplemented
236C22×Dic3#6712yescomplemented
237C2×D12—64no—
238C2×D12—124no—
239C2×C4×D3—62no—
240C2×C4×D3—62no—
241C3×C22⋊C4—22no—
242C3×C22⋊C4—21no—
243C3×C22⋊C4—21no—
244C3×C22⋊C4—21no—
245C3×C22⋊C4—21no—
246C3×C22⋊C4—32no—
247C3×C22⋊C4—41no—
248C3×C22⋊C4—61no—
249C3×C22⋊C4—61no—
250C3×C22⋊C4—61no—
251C3×C22⋊C4—61no—
252C3×C22⋊C4—61no—
253C3×C22⋊C4—124no—
254#217—21no—
255#217—21no—
256#217—21no—
257#217—21no—
258#217—21no—
259#217—64no—
260#217—62no—
261#217—61no—
262#217—61no—
263#217—61no—
264#217—61no—
265#217—121no—
266#217—124no—
267#217C4×D312yescomplemented
268(C2×D3)⋊C4—44no—
269(C2×D3)⋊C4—62no—
270(C2×D3)⋊C4—62no—
271(C2×D3)⋊C4—64no—
272(C2×D3)⋊C4—124no—
273Dic3⋊C4—62no—
274Dic3⋊C4—62no—
275C4×Dic3—62no—
276C4×Dic3—62no—
277C22×C32—22no—
278C22×C32—22no—
279C22×C32—22no—
280C22×C32—41no—
281C22×C32—41no—
282C22×C32—41no—
283C22×C32—41no—
284C22×C32C2×C22⋊C411yescharacteristic
285C22×C32C4×D411yescharacteristic
286C22×C32C4×D411yescharacteristic
287C22×C32#12011yescharacteristic
288C22×C32#12111yescharacteristic
289C22×C32#12111yescharacteristic
290C22×C32#12311yescharacteristic
291C2×C3⋊D3—22no—
292C2×C3⋊D3—42no—
293C2×C3⋊D3—42no—
294C2×C3⋊D3—81no—
295C2×C3×D3—24no—
296C2×C3×D3—24no—
297C2×C3×D3—24no—
298C2×C3×D3—42no—
299C2×C3×D3—44no—
300C2×C3×D3—44no—
301C2×C3×D3—42no—
302C2×C3×D3—42no—
303C2×C3×D3—44no—
304C2×C3×D3—42no—
305C2×C3×D3—44no—
306C32×C4—81no—
307C3⋊Dic3—22no—
308C3⋊Dic3—81no—
309C3×Dic3—42no—
310C3×Dic3—42no—
311C3×Dic3—42no—
312C25—31no—
313C22×D4—91no—
314C22×D4—181no—
315#120—94no—
316#120—182no—
317C4×D4—182no—
318C4×D4—182no—
319#117—181no—
320C2×C22⋊C4—31no—
321C2×C22⋊C4—31no—
322C2×C22⋊C4—31no—
323C2×C22⋊C4—62no—
324C2×C22⋊C4—91no—
325C2×C22⋊C4—181no—
326C2×C22⋊C4—181no—
327C2×C22⋊C4—182no—
328C2×C22⋊C4D3211yescharacteristic
329#99—182no—
330C23×C3—21no—
331C23×C3—21no—
332C23×C3—21no—
333C23×C3—21no—
334C23×C3—21no—
335C23×C3—21no—
336C23×C3—21no—
337C23×C3—42no—
338C23×C3—42no—
339C23×C3—64no—
340C23×C3—64no—
341C23×C3—64no—
342C23×C3—62no—
343C23×C3—62no—
344C23×C3—62no—
345C23×C3—82no—
346C23×C3—122no—
347C23×C3—122no—
348C23×C3—122no—
349C23×C3—124no—
350C23×C3—124no—
351C23×C3—124no—
352C23×C3—124no—
353C23×C3—121no—
354C23×C3—121no—
355C23×C3—121no—
356C23×C3—121no—
357C23×C3C2×C4×D311yescharacteristic
358C23×C3C2×C4×D311yescharacteristic
359C23×C3C2×D1211yescharacteristic
360C23×C3#23511yescharacteristic
361C23×C3#23511yescharacteristic
362C23×C3D3×D411yescharacteristic
363C23×C3D3×D411yescharacteristic
364C23×C3D3×D411yescharacteristic
365C23×C3D3×D411yescharacteristic
366C23×C3D3×D411yescharacteristic
367C23×C3D3×D411yescharacteristic
368C23×C3#23711yescharacteristic
369C23×C3#23911yescharacteristic
370C23×C3C2×#6711yescharacteristic
371C22×D3—24no—
372C22×D3—24no—
373C22×D3—24no—
374C22×D3—22no—
375C22×D3—22no—
376C22×D3—22no—
377C22×D3—32no—
378C22×D3—32no—
379C22×D3—44no—
380C22×D3—44no—
381C22×D3—44no—
382C22×D3—44no—
383C22×D3—42no—
384C22×D3—42no—
385C22×D3—42no—
386C22×D3—41no—
387C22×D3—41no—
388C22×D3—41no—
389C22×D3—41no—
390C22×D3—62no—
391C22×D3—61no—
392C22×D3—61no—
393C22×D3—61no—
394C22×D3—61no—
395C22×D3—121no—
396C22×D3—121no—
397C22×D3—122no—
398C22×D3—122no—
399C22×D3—242no—
400C2×C3×C4—42no—
401C2×C3×C4—42no—
402C2×C3×C4—42no—
403C2×C3×C4—41no—
404C2×C3×C4—41no—
405C2×C3×C4—62no—
406C2×C3×C4—62no—
407C2×C3×C4—62no—
408C2×C3×C4—82no—
409C2×C3×C4—122no—
410C2×C3×C4—122no—
411C2×C3×C4—122no—
412#67—62no—
413#67—62no—
414#67—62no—
415#67—62no—
416#67—62no—
417#67—62no—
418#67—62no—
419#67—62no—
420#67—122no—
421#67—122no—
422#67—122no—
423#67—122no—
424#67—128no—
425C2×Dic3—22no—
426C2×Dic3—22no—
427C2×Dic3—22no—
428C2×Dic3—32no—
429C2×Dic3—32no—
430C2×Dic3—42no—
431C2×Dic3—42no—
432C2×Dic3—42no—
433C2×Dic3—62no—
434C2×Dic3—61no—
435C2×Dic3—61no—
436C2×Dic3—61no—
437C2×Dic3—61no—
438C2×Dic3—121no—
439C2×Dic3—121no—
440C2×Dic3—122no—
441C2×Dic3—122no—
442C2×Dic3—122no—
443C2×Dic3—121no—
444C2×Dic3—121no—
445C2×Dic3—242no—
446D12—128no—
447C4×D3—242no—
448C4×D3—242no—
449C2×C32—21no—
450C2×C32—21no—
451C2×C32—21no—
452C2×C32—21no—
453C2×C32—21no—
454C2×C32—21no—
455C2×C32#38611yescharacteristic
456C2×C32B(4,𝔽2)12yes—
457C3⋊D3—42no—
458C3×D3—44no—
459C24—32no—
460C24—61no—
461C24—61no—
462C24—61no—
463C24—61no—
464C24—61no—
465C24—61no—
466C24—91no—
467C24—124no—
468C24C2×D3211yescharacteristic
469C2×D4—92no—
470C2×D4—92no—
471C2×D4—184no—
472C2×D4—181no—
473C2×D4—181no—
474C2×D4—181no—
475C2×D4—181no—
476C2×D4—364no—
477C22×C4—21no—
478C22×C4—32no—
479C22×C4—32no—
480C22×C4—61no—
481C22×C4—91no—
482C22×C4—182no—
483C22×C4—181no—
484C4⋊C4—182no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—32no—
488C22⋊C4—61no—
489C22⋊C4—61no—
490C22⋊C4—61no—
491C22⋊C4—61no—
492C22⋊C4—61no—
493C22⋊C4—124no—
494C22⋊C4—182no—
495C22⋊C4—184no—
496C22⋊C4—181no—
497C22⋊C4—181no—
498C22⋊C4—364no—
499C42—182no—
500C22×C3—22no—
501C22×C3—22no—
502C22×C3—22no—
503C22×C3—22no—
504C22×C3—22no—
505C22×C3—22no—
506C22×C3—21no—
507C22×C3—21no—
508C22×C3—21no—
509C22×C3—21no—
510C22×C3—21no—
511C22×C3—21no—
512C22×C3—21no—
513C22×C3—42no—
514C22×C3—42no—
515C22×C3—42no—
516C22×C3—41no—
517C22×C3—41no—
518C22×C3—41no—
519C22×C3—41no—
520C22×C3—41no—
521C22×C3—41no—
522C22×C3—41no—
523C22×C3—41no—
524C22×C3—64no—
525C22×C3—64no—
526C22×C3—64no—
527C22×C3—81no—
528C22×C3—81no—
529C22×C3—81no—
530C22×C3—81no—
531C22×C3—122no—
532C22×C3—124no—
533C22×C3—124no—
534C22×C3—124no—
535C22×C3—122no—
536C22×C3—122no—
537C22×C3—122no—
538C22×C3—124no—
539C22×C3C4×D1211yescharacteristic
540C22×C3D3×C22⋊C411yescharacteristic
541C22×C3D3×C22⋊C411yescharacteristic
542C22×C3#67⋊C411yescharacteristic
543C22×C3#88211yescharacteristic
544C22×C3#88311yescharacteristic
545C22×C3#88411yescharacteristic
546C22×C3#88411yescharacteristic
547C22×C3#89311yescharacteristic
548C22×C3#89411yescharacteristic
549C22×C3#89511yescharacteristic
550C22×C3C4×#6711yescharacteristic
551C22×C3#93711yescharacteristic
552C22×C3#93811yescharacteristic
553C2×D3—24no—
554C2×D3—24no—
555C2×D3—24no—
556C2×D3—44no—
557C2×D3—44no—
558C2×D3—42no—
559C2×D3—42no—
560C2×D3—42no—
561C2×D3—44no—
562C2×D3—42no—
563C2×D3—44no—
564C2×D3—62no—
565C2×D3—62no—
566C2×D3—122no—
567C2×D3—122no—
568C2×D3—122no—
569C2×D3—122no—
570C2×D3—122no—
571C2×D3—242no—
572C2×D3—242no—
573C2×D3—241no—
574C2×D3—241no—
575C2×D3—242no—
576C3×C4—81no—
577C3×C4—81no—
578C3×C4—82no—
579C3×C4—122no—
580C3×C4—122no—
581C3×C4—122no—
582Dic3—42no—
583Dic3—42no—
584Dic3—42no—
585Dic3—62no—
586Dic3—62no—
587Dic3—122no—
588Dic3—241no—
589Dic3—241no—
590Dic3—242no—
591C32#188911yescharacteristic, complemented, Sylow
592C23—42no—
593C23—64no—
594C23—64no—
595C23—64no—
596C23—62no—
597C23—62no—
598C23—62no—
599C23—92no—
600C23—122no—
601C23—122no—
602C23—122no—
603C23—124no—
604C23—124no—
605C23—124no—
606C23—124no—
607C23—121no—
608C23—121no—
609C23—121no—
610C23—121no—
611C23—181no—
612C23—181no—
613C23—362no—
614C23#379911yescharacteristic
615C23C4×D3211yescharacteristic
616C23D3×D1211yescharacteristic
617C23#380211yescharacteristic
618C23#380411yescharacteristic
619C23D3×#6711yescharacteristic
620C23#381111yescharacteristic
621D4—182no—
622D4—182no—
623D4—182no—
624D4—182no—
625D4—368no—
626C2×C4—42no—
627C2×C4—41no—
628C2×C4—62no—
629C2×C4—62no—
630C2×C4—62no—
631C2×C4—92no—
632C2×C4—122no—
633C2×C4—122no—
634C2×C4—122no—
635C2×C4—181no—
636C2×C4—181no—
637C2×C4—362no—
638C2×C4—361no—
639C2×C4—722no—
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—22no—
654C2×C3—41no—
655C2×C3—41no—
656C2×C3—41no—
657C2×C3—41no—
658C2×C3—41no—
659C2×C3—41no—
660C2×C3—124no—
661C2×C3#466511yescharacteristic
662C2×C3#474112yes—
663C2×C3#495611yescharacteristic
664C2×C3#503212yes—
665D3—44no—
666D3—122no—
667D3—122no—
668D3—242no—
669C22—22no—
670C22—22no—
671C22—22no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—64no—
677C22—64no—
678C22—64no—
679C22—124no—
680C22—122no—
681C22—124no—
682C22—122no—
683C22—122no—
684C22—124no—
685C22—122no—
686C22—124no—
687C22—182no—
688C22—362no—
689C22—362no—
690C22—721no—
691C22#6385411yescharacteristic
692C22#6388011yescharacteristic
693C22#6390411yescharacteristic
694C22#6391011yescharacteristic
695C22#6392111yescharacteristic
696C22#6392211yescharacteristic
697C22#6395811yescharacteristic
698C4—81no—
699C4—122no—
700C4—122no—
701C4—122no—
702C4—182no—
703C4—721no—
704C3—21no—
705C3#6896211yescharacteristic, complemented
706C3#6949911yescharacteristic, complemented
707C2—21no—
708C2—21no—
709C2—21no—
710C2—21no—
711C2—21no—
712C2—21no—
713C2—124no—
714C2—362no—
715C2#1059040712yes—
716C2#1059127511yescharacteristic
subgroupG/H
centerC22#63922
commutatorC23×C32C22×C4
FrattiniC24C2×D32
FittingC2×C32×C22⋊C4C22
socleC22×C32#120
prime radicalC2×#63977C2
cosocleC24×C32C23
hypercenterC2×C22⋊C4D32
hypocenterC32#1889
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
2. #10595510C2semidirect
3. C2×#63633C2semidirect
4. C3×#4955C2semidirect
5. #10591706C2semidirect
6. C3×#4527C2semidirect
7. #10589186C2semidirect
20. #63977C4semidirect
35. #4955D3semidirect
41. #4527D3semidirect
52. C23×C3×D3C2×C4semidirect
63. C22×C3×Dic3D4semidirect
64. C22×C3×Dic3D4semidirect
77. C3×#217C2×C4semidirect
136. C22×C3⋊D3C22⋊C4semidirect
164. C2×C3⋊Dic3C22⋊C4semidirect
201. C23×D3C4×D3semidirect
235. C22×Dic3D12semidirect
236. C22×Dic3#67semidirect
267. #217C4×D3semidirect
591. C32#1889semidirect
705. C3#68962semidirect
706. C3#69499semidirect

Maximal subgroups

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

subgroupindex
C2×#639772
#105955102
C2×#636332
C3×#49552
#105917062
C3×#45272
#105891862
#694993
#689623