Finite Group Databasebeta

← #11787940

Subgroups — #11787940

Order 1152.

1325 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595957C211yesmaximal, characteristic, complemented
2C2×#63977C211yesmaximal, characteristic
3C3×#4955C211yesmaximal, characteristic, complemented
4#10591706C211yesmaximal, characteristic, complemented
5C2×#63581C211yesmaximal, characteristic, complemented
6C3×#4526C211yesmaximal, characteristic, complemented
7#10589187C211yesmaximal, characteristic, complemented
8#69499—31nomaximal
9#68962—31nomaximal
10C24×C3×D3C2211yescharacteristic
11C22×#638C2211yescharacteristic
12C22×#626—21no—
13C2×C32×C22⋊C4C2211yescharacteristic
14C2×#3757C2211yescharacteristic
15C4×#638—22no—
16#64090—22no—
17C22⋊C4×C3⋊D3—21no—
18#64086—21no—
19C2×C3×#217C2211yescharacteristic
20C2×C3×#217C2211yescharacteristic
21C2×C3×#217C2211yescharacteristic
22C2×C3×(C2×D3)⋊C4—22no—
23#63977—22no—
24#63977C414yescomplemented
25C2×(C2×D3)⋊Dic3—21no—
26C2×(C2×D3)⋊Dic3—22no—
27#63581—22no—
28C2×#953—31no—
29C2×#882—31no—
30#5486—31no—
31#5486—31no—
32#5486—61no—
33C3×#379—31no—
34#5247—31no—
35#4955—31no—
36#4955D311yescharacteristic, complemented
37C2×#806—31no—
38C2×#806—31no—
39C3×#342—31no—
40#4527—31no—
41#4527—31no—
42#4526D311yescharacteristic, complemented
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×C4D412yescomplemented
54C2×#638—21no—
55C2×#638—21no—
56C2×#638—21no—
57C2×#638—21no—
58C2×#638C2×C412yes—
59C2×#638D412yes—
60C22×C3⋊Dic3D411yescharacteristic
61C22×C3⋊Dic3D412yescomplemented
62C2×C4×C3⋊D3—22no—
63C22×C3×Dic3—21no—
64C22×C3×Dic3—21no—
65C22×C3×Dic3—21no—
66C2×#626—24no—
67C2×#626—44no—
68C32×C22⋊C4—21no—
69C32×C22⋊C4—21no—
70#3757—21no—
71#3757—21no—
72#3752—22no—
73#3750—22no—
74C4×C3⋊Dic3—22no—
75C3×#217—21no—
76C3×#217—21no—
77C3×#217—21no—
78C3×#217—21no—
79C3×#217—21no—
80C3×#217C2×C412yescomplemented
81C3×(C2×D3)⋊C4—44no—
82(C2×D3)⋊Dic3—24no—
83(C2×D3)⋊Dic3—44no—
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—64no—
110C4×#67—62no—
111C4×#67—62no—
112C2×(C2×D3)⋊C4—22no—
113C2×(C2×D3)⋊C4—61no—
114C2×(C2×D3)⋊C4—62no—
115#882—34no—
116#882—62no—
117#67⋊C4—62no—
118#67⋊C4—62no—
119#67⋊C4—64no—
120D3×C22⋊C4—61no—
121D3×C22⋊C4—61no—
122D3×C22⋊C4—62no—
123#877—61no—
124#877—61no—
125#877—62no—
126#806—62no—
127#806—62no—
128C23×C32—42no—
129C23×C32C22×C411yescharacteristic
130C23×C32C2×D411yescharacteristic
131C23×C32C2×D411yescharacteristic
132C23×C32C2×D411yescharacteristic
133C23×C32C2×D411yescharacteristic
134C23×C32#4111yescharacteristic
135C23×C32#4111yescharacteristic
136C22×C3⋊D3—21no—
137C22×C3⋊D3—21no—
138C22×C3⋊D3—42no—
139C22×C3⋊D3C22⋊C412yescomplemented
140C22×C3×D3—24no—
141C22×C3×D3—24no—
142C22×C3×D3—24no—
143C22×C3×D3—22no—
144C22×C3×D3—22no—
145C22×C3×D3—22no—
146C22×C3×D3—44no—
147C22×C3×D3—44no—
148C22×C3×D3—44no—
149C22×C3×D3—44no—
150C22×C3×D3—42no—
151C22×C3×D3—42no—
152C22×C3×D3—42no—
153C22×C3×D3—41no—
154C22×C3×D3—41no—
155C22×C3×D3—41no—
156C22×C3×D3—41no—
157C2×C32×C4—22no—
158C2×C32×C4—42no—
159#638—22no—
160#638—22no—
161#638—22no—
162#638—22no—
163C2×C3⋊Dic3—21no—
164C2×C3⋊Dic3—21no—
165C2×C3⋊Dic3—22no—
166C2×C3⋊Dic3—42no—
167C2×C3⋊Dic3C22⋊C412yescomplemented
168C4×C3⋊D3—82no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—42no—
171C2×C3×Dic3—42no—
172C2×C3×Dic3—42no—
173C2×C3×Dic3—41no—
174C2×C3×Dic3—41no—
175#626—48no—
176C2×#120—91no—
177#518—91no—
178C2×#99—91no—
179#379—31no—
180#379—91no—
181#342—31no—
182#342—91no—
183C24×C3—21no—
184C24×C3—32no—
185C24×C3—61no—
186C24×C3—61no—
187C24×C3—61no—
188C24×C3—61no—
189C24×C3—61no—
190C24×C3—61no—
191C24×C3—124no—
192C24×C3C22×D311yescharacteristic
193C24×C3C22×D311yescharacteristic
194C23×D3—21no—
195C23×D3—21no—
196C23×D3—21no—
197C23×D3—21no—
198C23×D3—21no—
199C23×D3—21no—
200C23×D3—31no—
201C23×D3—31no—
202C23×D3—44no—
203C23×D3—61no—
204C23×D3C4×D312yescomplemented
205C22×C3×C4—22no—
206C22×C3×C4—61no—
207C22×C3×C4—61no—
208C22×C3×C4—61no—
209C22×C3×C4D1212yescomplemented
210C22×C3×C4#6712yescomplemented
211C2×#67—32no—
212C2×#67—32no—
213C2×#67—32no—
214C2×#67—32no—
215C2×#67—62no—
216C2×#67—62no—
217C2×#67—64no—
218C2×#67—62no—
219C2×#67—62no—
220C2×#67—62no—
221C2×#67—62no—
222C2×#67—61no—
223C2×#67—61no—
224C2×#67—61no—
225C2×#67—61no—
226C2×#67—61no—
227C2×#67—61no—
228C2×#67—61no—
229C2×#67—61no—
230C2×#67—124no—
231C22×Dic3—21no—
232C22×Dic3—21no—
233C22×Dic3—21no—
234C22×Dic3—31no—
235C22×Dic3—31no—
236C22×Dic3—32no—
237C22×Dic3—32no—
238C22×Dic3—61no—
239C22×Dic3—62no—
240C2×D12—64no—
241C2×D12—124no—
242C2×C4×D3—64no—
243C2×C4×D3—62no—
244C2×C4×D3—62no—
245C3×C22⋊C4—22no—
246C3×C22⋊C4—22no—
247C3×C22⋊C4—21no—
248C3×C22⋊C4—21no—
249C3×C22⋊C4—21no—
250C3×C22⋊C4—21no—
251C3×C22⋊C4—32no—
252C3×C22⋊C4—61no—
253C3×C22⋊C4—61no—
254C3×C22⋊C4—61no—
255C3×C22⋊C4—61no—
256C3×C22⋊C4—61no—
257C3×C22⋊C4—124no—
258#217—21no—
259#217—21no—
260#217—21no—
261#217—21no—
262#217—21no—
263#217—64no—
264#217—62no—
265#217—62no—
266#217—61no—
267#217—61no—
268#217—61no—
269#217—61no—
270#217—124no—
271#217C4×D312yescomplemented
272(C2×D3)⋊C4—44no—
273(C2×D3)⋊C4—64no—
274(C2×D3)⋊C4—64no—
275(C2×D3)⋊C4—62no—
276(C2×D3)⋊C4—62no—
277(C2×D3)⋊C4—124no—
278Dic3⋊C4—64no—
279Dic3⋊C4—62no—
280Dic3⋊C4—62no—
281C4×Dic3—64no—
282C4×Dic3—62no—
283C4×Dic3—62no—
284C22×C32—22no—
285C22×C32—22no—
286C22×C32—22no—
287C22×C32—41no—
288C22×C32—41no—
289C22×C32—41no—
290C22×C32—41no—
291C22×C32C2×C22⋊C411yescharacteristic
292C22×C32C4×D411yescharacteristic
293C22×C32C4×D411yescharacteristic
294C22×C32#12011yescharacteristic
295C22×C32#12111yescharacteristic
296C22×C32#12111yescharacteristic
297C22×C32#12311yescharacteristic
298C2×C3⋊D3—22no—
299C2×C3⋊D3—42no—
300C2×C3⋊D3—42no—
301C2×C3⋊D3—81no—
302C2×C3×D3—24no—
303C2×C3×D3—24no—
304C2×C3×D3—24no—
305C2×C3×D3—42no—
306C2×C3×D3—44no—
307C2×C3×D3—44no—
308C2×C3×D3—42no—
309C2×C3×D3—42no—
310C2×C3×D3—44no—
311C2×C3×D3—42no—
312C2×C3×D3—44no—
313C32×C4—42no—
314C3⋊Dic3—22no—
315C3⋊Dic3—42no—
316C3×Dic3—42no—
317C3×Dic3—81no—
318C3×Dic3—81no—
319C25—31no—
320C22×D4—91no—
321C22×D4—181no—
322#120—94no—
323#120—182no—
324C4×D4—182no—
325C4×D4—182no—
326#117—181no—
327C2×C22⋊C4—31no—
328C2×C22⋊C4—31no—
329C2×C22⋊C4—31no—
330C2×C22⋊C4—62no—
331C2×C22⋊C4—91no—
332C2×C22⋊C4—181no—
333C2×C22⋊C4—181no—
334C2×C22⋊C4—182no—
335C2×C22⋊C4D3211yescharacteristic
336#99—182no—
337C23×C3—21no—
338C23×C3—21no—
339C23×C3—21no—
340C23×C3—21no—
341C23×C3—21no—
342C23×C3—21no—
343C23×C3—21no—
344C23×C3—42no—
345C23×C3—42no—
346C23×C3—64no—
347C23×C3—64no—
348C23×C3—64no—
349C23×C3—62no—
350C23×C3—62no—
351C23×C3—62no—
352C23×C3—82no—
353C23×C3—122no—
354C23×C3—122no—
355C23×C3—122no—
356C23×C3—124no—
357C23×C3—124no—
358C23×C3—124no—
359C23×C3—124no—
360C23×C3—121no—
361C23×C3—121no—
362C23×C3—121no—
363C23×C3—121no—
364C23×C3C2×C4×D311yescharacteristic
365C23×C3C2×C4×D311yescharacteristic
366C23×C3C2×D1211yescharacteristic
367C23×C3#23511yescharacteristic
368C23×C3#23511yescharacteristic
369C23×C3D3×D411yescharacteristic
370C23×C3D3×D411yescharacteristic
371C23×C3D3×D411yescharacteristic
372C23×C3D3×D411yescharacteristic
373C23×C3D3×D411yescharacteristic
374C23×C3D3×D411yescharacteristic
375C23×C3#23711yescharacteristic
376C23×C3#23911yescharacteristic
377C23×C3C2×#6711yescharacteristic
378C22×D3—24no—
379C22×D3—24no—
380C22×D3—24no—
381C22×D3—22no—
382C22×D3—22no—
383C22×D3—22no—
384C22×D3—32no—
385C22×D3—32no—
386C22×D3—44no—
387C22×D3—44no—
388C22×D3—44no—
389C22×D3—44no—
390C22×D3—42no—
391C22×D3—42no—
392C22×D3—42no—
393C22×D3—41no—
394C22×D3—41no—
395C22×D3—41no—
396C22×D3—41no—
397C22×D3—62no—
398C22×D3—62no—
399C22×D3—61no—
400C22×D3—61no—
401C22×D3—62no—
402C22×D3—61no—
403C22×D3—61no—
404C22×D3—122no—
405C22×D3—122no—
406C22×D3—242no—
407C2×C3×C4—24no—
408C2×C3×C4—22no—
409C2×C3×C4—22no—
410C2×C3×C4—42no—
411C2×C3×C4—42no—
412C2×C3×C4—62no—
413C2×C3×C4—82no—
414C2×C3×C4—122no—
415C2×C3×C4—122no—
416C2×C3×C4—122no—
417C2×C3×C4—121no—
418C2×C3×C4—121no—
419#67—64no—
420#67—64no—
421#67—64no—
422#67—64no—
423#67—62no—
424#67—62no—
425#67—62no—
426#67—62no—
427#67—62no—
428#67—62no—
429#67—62no—
430#67—62no—
431#67—128no—
432C2×Dic3—22no—
433C2×Dic3—32no—
434C2×Dic3—32no—
435C2×Dic3—42no—
436C2×Dic3—42no—
437C2×Dic3—42no—
438C2×Dic3—41no—
439C2×Dic3—41no—
440C2×Dic3—62no—
441C2×Dic3—62no—
442C2×Dic3—62no—
443C2×Dic3—61no—
444C2×Dic3—61no—
445C2×Dic3—61no—
446C2×Dic3—61no—
447C2×Dic3—64no—
448C2×Dic3—62no—
449C2×Dic3—62no—
450C2×Dic3—122no—
451C2×Dic3—122no—
452C2×Dic3—242no—
453D12—128no—
454C4×D3—244no—
455C4×D3—242no—
456C4×D3—242no—
457C2×C32—21no—
458C2×C32—21no—
459C2×C32—21no—
460C2×C32—21no—
461C2×C32—21no—
462C2×C32—21no—
463C2×C32#38611yescharacteristic
464C2×C32B(4,𝔽2)12yes—
465C3⋊D3—42no—
466C3×D3—44no—
467C24—32no—
468C24—61no—
469C24—61no—
470C24—61no—
471C24—61no—
472C24—61no—
473C24—61no—
474C24—91no—
475C24—124no—
476C24C2×D3211yescharacteristic
477C2×D4—92no—
478C2×D4—92no—
479C2×D4—184no—
480C2×D4—181no—
481C2×D4—181no—
482C2×D4—181no—
483C2×D4—181no—
484C2×D4—364no—
485C22×C4—61no—
486C22×C4—61no—
487C22×C4—61no—
488C22×C4—91no—
489C22×C4—92no—
490C22×C4—182no—
491C22×C4#62612yescomplemented
492C4⋊C4—182no—
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—32no—
496C22⋊C4—61no—
497C22⋊C4—61no—
498C22⋊C4—61no—
499C22⋊C4—61no—
500C22⋊C4—61no—
501C22⋊C4—124no—
502C22⋊C4—182no—
503C22⋊C4—184no—
504C22⋊C4—181no—
505C22⋊C4—181no—
506C22⋊C4—364no—
507C42—182no—
508C22×C3—22no—
509C22×C3—22no—
510C22×C3—22no—
511C22×C3—22no—
512C22×C3—22no—
513C22×C3—22no—
514C22×C3—21no—
515C22×C3—21no—
516C22×C3—21no—
517C22×C3—21no—
518C22×C3—21no—
519C22×C3—21no—
520C22×C3—21no—
521C22×C3—42no—
522C22×C3—42no—
523C22×C3—42no—
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—64no—
533C22×C3—64no—
534C22×C3—64no—
535C22×C3—81no—
536C22×C3—81no—
537C22×C3—81no—
538C22×C3—81no—
539C22×C3—122no—
540C22×C3—124no—
541C22×C3—124no—
542C22×C3—124no—
543C22×C3—122no—
544C22×C3—122no—
545C22×C3—122no—
546C22×C3—124no—
547C22×C3C4×D1211yescharacteristic
548C22×C3D3×C22⋊C411yescharacteristic
549C22×C3D3×C22⋊C411yescharacteristic
550C22×C3#67⋊C411yescharacteristic
551C22×C3#88211yescharacteristic
552C22×C3#88311yescharacteristic
553C22×C3#88411yescharacteristic
554C22×C3#88411yescharacteristic
555C22×C3#89311yescharacteristic
556C22×C3#89411yescharacteristic
557C22×C3#89511yescharacteristic
558C22×C3C4×#6711yescharacteristic
559C22×C3#93711yescharacteristic
560C22×C3#93811yescharacteristic
561C2×D3—24no—
562C2×D3—24no—
563C2×D3—24no—
564C2×D3—44no—
565C2×D3—42no—
566C2×D3—44no—
567C2×D3—42no—
568C2×D3—42no—
569C2×D3—44no—
570C2×D3—42no—
571C2×D3—44no—
572C2×D3—64no—
573C2×D3—62no—
574C2×D3—62no—
575C2×D3—124no—
576C2×D3—122no—
577C2×D3—122no—
578C2×D3—122no—
579C2×D3—122no—
580C2×D3—242no—
581C2×D3—241no—
582C2×D3—241no—
583C2×D3—242no—
584C3×C4—44no—
585C3×C4—42no—
586C3×C4—42no—
587C3×C4—122no—
588C3×C4—241no—
589C3×C4—241no—
590Dic3—42no—
591Dic3—64no—
592Dic3—62no—
593Dic3—62no—
594Dic3—81no—
595Dic3—81no—
596Dic3—124no—
597Dic3—122no—
598Dic3—122no—
599C32#188911yescharacteristic, complemented, Sylow
600C23—42no—
601C23—64no—
602C23—64no—
603C23—64no—
604C23—62no—
605C23—62no—
606C23—62no—
607C23—92no—
608C23—122no—
609C23—122no—
610C23—122no—
611C23—124no—
612C23—124no—
613C23—124no—
614C23—124no—
615C23—121no—
616C23—121no—
617C23—121no—
618C23—121no—
619C23—181no—
620C23—181no—
621C23—362no—
622C23#379611yescharacteristic
623C23#379811yescharacteristic
624C23C4×D3211yescharacteristic
625C23#380211yescharacteristic
626C23C2×#62611yescharacteristic
627C23#381111yescharacteristic
628C23#381111yescharacteristic
629D4—182no—
630D4—182no—
631D4—182no—
632D4—182no—
633D4—368no—
634C2×C4—22no—
635C2×C4—42no—
636C2×C4—62no—
637C2×C4—92no—
638C2×C4—122no—
639C2×C4—122no—
640C2×C4—122no—
641C2×C4—121no—
642C2×C4—121no—
643C2×C4—181no—
644C2×C4—181no—
645C2×C4—182no—
646C2×C4—362no—
647C2×C4—722no—
648C2×C3—21no—
649C2×C3—21no—
650C2×C3—21no—
651C2×C3—21no—
652C2×C3—21no—
653C2×C3—21no—
654C2×C3—21no—
655C2×C3—21no—
656C2×C3—21no—
657C2×C3—21no—
658C2×C3—21no—
659C2×C3—21no—
660C2×C3—22no—
661C2×C3—21no—
662C2×C3—41no—
663C2×C3—41no—
664C2×C3—41no—
665C2×C3—41no—
666C2×C3—41no—
667C2×C3—41no—
668C2×C3—124no—
669C2×C3#466511yescharacteristic
670C2×C3#474112yes—
671C2×C3#495611yescharacteristic
672C2×C3#503212yes—
673D3—44no—
674D3—124no—
675D3—122no—
676D3—122no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—64no—
685C22—64no—
686C22—64no—
687C22—122no—
688C22—124no—
689C22—124no—
690C22—122no—
691C22—122no—
692C22—124no—
693C22—124no—
694C22—122no—
695C22—182no—
696C22—362no—
697C22—362no—
698C22—721no—
699C22#6385311yescharacteristic
700C22#6388111yescharacteristic
701C22C4×#62611yescharacteristic
702C22#6391211yescharacteristic
703C22#6391611yescharacteristic
704C22#6392111yescharacteristic
705C22#6398111yescharacteristic
706C4—42no—
707C4—122no—
708C4—182no—
709C4—241no—
710C4—241no—
711C4—362no—
712C3—21no—
713C3#6896211yescharacteristic, complemented
714C3#6949911yescharacteristic, complemented
715C2—21no—
716C2—21no—
717C2—21no—
718C2—21no—
719C2—21no—
720C2—21no—
721C2—124no—
722C2—362no—
723C2#1059138711yescharacteristic
724C2#1059153212yes—
subgroupG/H
centerC22#63981
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
1. #10595957C2semidirect
3. C3×#4955C2semidirect
4. #10591706C2semidirect
5. C2×#63581C2semidirect
6. C3×#4526C2semidirect
7. #10589187C2semidirect
24. #63977C4semidirect
36. #4955D3semidirect
42. #4526D3semidirect
52. C23×C3×D3C2×C4semidirect
53. C22×C32×C4D4semidirect
61. C22×C3⋊Dic3D4semidirect
80. C3×#217C2×C4semidirect
139. C22×C3⋊D3C22⋊C4semidirect
167. C2×C3⋊Dic3C22⋊C4semidirect
204. C23×D3C4×D3semidirect
209. C22×C3×C4D12semidirect
210. C22×C3×C4#67semidirect
271. #217C4×D3semidirect
491. C22×C4#626semidirect
599. C32#1889semidirect
713. C3#68962semidirect
714. C3#69499semidirect

Maximal subgroups

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

subgroupindex
#105959572
C2×#639772
C3×#49552
#105917062
C2×#635812
C3×#45262
#105891872
#694993
#689623