Finite Group Databasebeta

← #11787936

Subgroups — #11787936

Order 1152.

1409 conjugacy classes of subgroups.

The subgroup lattice has 731 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63981C211yesmaximal, characteristic
2#10595506C211yesmaximal, characteristic, complemented
3#10592654C211yesmaximal, characteristic, complemented
4C2×C3×#806C211yesmaximal, characteristic, complemented
5#10591714C211yesmaximal, characteristic, complemented
6C3×#4527C211yesmaximal, characteristic, complemented
7#10589187C211yesmaximal, characteristic, complemented
8#70022—31nomaximal
9#68962—31nomaximal
10C24×C3⋊D3C2211yescharacteristic
11C22×C3×#67C2211yescharacteristic
12C22×#626—21no—
13C2×C32×C22⋊C4C2211yescharacteristic
14C2×#3757C2211yescharacteristic
15C2×#3752—22no—
16C2×C3×#217C2211yescharacteristic
17C2×C3×#217C2211yescharacteristic
18C2×C3×#217C2211yescharacteristic
19#63981—22no—
20#63981C414yescomplemented
21#67⋊Dic3—22no—
22Dic3×#67—22no—
23D3×#217—21no—
24C2×#3722—21no—
25C2×#3722—22no—
26#63955—21no—
27C3×#806—22no—
28C2×#937—31no—
29#5798—31no—
30C2×#882—31no—
31#5486—31no—
32C2×C3×#99—31no—
33#4955—31no—
34#4955—31no—
35#4955—31no—
36#4955—31no—
37#4955—61no—
38C2×#806D311yescharacteristic, complemented
39C3×#342—31no—
40#4527—31no—
41#4527—31no—
42#4527D311yescharacteristic, complemented
43C24×C32C2311yescharacteristic
44C23×C3⋊D3—21no—
45C23×C3⋊D3—21no—
46C23×C3⋊D3—21no—
47C23×C3⋊D3—21no—
48C23×C3⋊D3—21no—
49C23×C3⋊D3—21no—
50C23×C3⋊D3—44no—
51C23×C3⋊D3C2×C412yescomplemented
52C23×C3×D3D411yescharacteristic
53C22×C32×C4—21no—
54C22×C3⋊Dic3D412yescomplemented
55C2×C3×#67—21no—
56C2×C3×#67—21no—
57C2×C3×#67—21no—
58C2×C3×#67—21no—
59C2×C3×#67C2×C412yes—
60C2×C3×#67D412yes—
61C22×C3×Dic3—21no—
62C22×C3×Dic3—21no—
63C22×C3×Dic3D411yescharacteristic
64C22×C3×Dic3D412yescomplemented
65C2×#626—24no—
66C2×#626—44no—
67C2×D3×Dic3—22no—
68C32×C22⋊C4—21no—
69C32×C22⋊C4—21no—
70#3757—21no—
71#3757—21no—
72#3752—44no—
73C3×#217—21no—
74C3×#217—21no—
75C3×#217—21no—
76C3×#217—21no—
77C3×#217—21no—
78C3×#217C2×C412yescomplemented
79Dic3⋊Dic3—22no—
80#3722—24no—
81#3722—44no—
82(C2×D3)⋊Dic3—22no—
83Dic32—22no—
84#1889—91noSylow
85C24×D3—31no—
86C24×D3—31no—
87C24×D3—61no—
88C22×C3×D4—31no—
89C22×#67—61no—
90C22×#67C2×D311yescharacteristic
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⋊C4C2×D311yescharacteristic
97C2×C3×C22⋊C4C2×D311yescharacteristic
98C2×#217—31no—
99C2×#217—31no—
100C2×#217—61no—
101C2×#217—61no—
102C2×#217C2×D311yescharacteristic
103C2×#217C2×D311yescharacteristic
104C2×#217C2×D311yescharacteristic
105#937—34no—
106#937—62no—
107D4×Dic3—62no—
108D4×Dic3—62no—
109C4×#67—62no—
110C2×(C2×D3)⋊C4—61no—
111C2×(C2×D3)⋊C4—61no—
112C2×(C2×D3)⋊C4—62no—
113C2×(C2×D3)⋊C4—62no—
114C2×(C2×D3)⋊C4—62no—
115C2×(C2×D3)⋊C4—64no—
116C2×(C2×D3)⋊C4—62no—
117#926—61no—
118#882—34no—
119#882—62no—
120#67⋊C4—62no—
121D3×C22⋊C4—61no—
122#877—61no—
123C3×#99—62no—
124#806—22no—
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—24no—
134C22×C3⋊D3—22no—
135C22×C3⋊D3—24no—
136C22×C3⋊D3—24no—
137C22×C3⋊D3—22no—
138C22×C3⋊D3—22no—
139C22×C3⋊D3—44no—
140C22×C3⋊D3—44no—
141C22×C3⋊D3—44no—
142C22×C3⋊D3—44no—
143C22×C3⋊D3—42no—
144C22×C3⋊D3—42no—
145C22×C3⋊D3—42no—
146C22×C3⋊D3—41no—
147C22×C3⋊D3—41no—
148C22×C3⋊D3—41no—
149C22×C3⋊D3—41no—
150C22×C3×D3—21no—
151C22×C3×D3—21no—
152C22×C3×D3—42no—
153C22×C3×D3C22⋊C412yescomplemented
154C2×C32×C4—42no—
155C2×C32×C4—41no—
156C2×C3⋊Dic3—22no—
157C2×C3⋊Dic3—42no—
158C3×#67—22no—
159C3×#67—22no—
160C3×#67—22no—
161C3×#67—22no—
162C2×C3×Dic3—21no—
163C2×C3×Dic3—21no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—42no—
167C2×C3×Dic3—42no—
168C2×C3×Dic3—42no—
169C2×C3×Dic3—41no—
170C2×C3×Dic3C22⋊C412yescomplemented
171#626—48no—
172D3×Dic3—82no—
173C2×#120—91no—
174#518—91no—
175C2×#99—31no—
176#379—91no—
177#379—91no—
178#342—31no—
179#342—91no—
180C24×C3—21no—
181C24×C3—31no—
182C24×C3C22×D311yescharacteristic
183C24×C3C22×D311yescharacteristic
184C23×D3—32no—
185C23×D3—32no—
186C23×D3—62no—
187C23×D3—62no—
188C23×D3—61no—
189C23×D3—61no—
190C23×D3—61no—
191C23×D3—61no—
192C23×D3—61no—
193C23×D3—61no—
194C23×D3—62no—
195C23×D3—61no—
196C23×D3—61no—
197C23×D3—61no—
198C23×D3—61no—
199C23×D3—61no—
200C23×D3—61no—
201C23×D3—121no—
202C23×D3—121no—
203C23×D3—121no—
204C23×D3—121no—
205C23×D3—124no—
206C23×D3—124no—
207C23×D3—128no—
208C23×D3D1211yescharacteristic
209C2×C3×D4—32no—
210C2×C3×D4—32no—
211C2×C3×D4—61no—
212C2×C3×D4—61no—
213C2×C3×D4—61no—
214C2×C3×D4—61no—
215C22×C3×C4—22no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—31no—
219C22×C3×C4—32no—
220C22×C3×C4—61no—
221C22×C3×C4—61no—
222C2×#67—21no—
223C2×#67—21no—
224C2×#67—21no—
225C2×#67—21no—
226C2×#67—64no—
227C2×#67—124no—
228C2×#67C4×D312yes—
229C2×#67#6712yes—
230C22×Dic3—21no—
231C22×Dic3—21no—
232C22×Dic3—32no—
233C22×Dic3—32no—
234C22×Dic3—62no—
235C22×Dic3—62no—
236C22×Dic3D1211yescharacteristic
237C22×Dic3D1212yescomplemented
238C2×D12—64no—
239C2×D12—124no—
240C2×C4×D3—62no—
241C3×C22⋊C4—21no—
242C3×C22⋊C4—21no—
243C3×C22⋊C4—21no—
244C3×C22⋊C4—21no—
245C3×C22⋊C4—32no—
246C3×C22⋊C4—41no—
247C3×C22⋊C4—41no—
248C3×C22⋊C4—61no—
249C3×C22⋊C4—61no—
250C3×C22⋊C4—61no—
251C3×C22⋊C4—61no—
252C3×C22⋊C4—61no—
253#217—21no—
254#217—21no—
255#217—21no—
256#217—21no—
257#217—21no—
258#217—62no—
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—64no—
267(C2×D3)⋊C4—62no—
268(C2×D3)⋊C4—64no—
269(C2×D3)⋊C4—124no—
270(C2×D3)⋊C4—124no—
271(C2×D3)⋊C4—124no—
272(C2×D3)⋊C4—124no—
273(C2×D3)⋊C4—128no—
274C4⋊Dic3—62no—
275Dic3⋊C4—62no—
276C4×Dic3—62no—
277C4×Dic3—62no—
278C22×C32—22no—
279C22×C32—22no—
280C22×C32—22no—
281C22×C32—41no—
282C22×C32—41no—
283C22×C32—41no—
284C22×C32—41no—
285C22×C32C2×C22⋊C411yescharacteristic
286C22×C32C4×D411yescharacteristic
287C22×C32C4×D411yescharacteristic
288C22×C32#12011yescharacteristic
289C22×C32#12111yescharacteristic
290C22×C32#12111yescharacteristic
291C22×C32#12311yescharacteristic
292C2×C3⋊D3—24no—
293C2×C3⋊D3—24no—
294C2×C3⋊D3—24no—
295C2×C3⋊D3—44no—
296C2×C3⋊D3—42no—
297C2×C3⋊D3—42no—
298C2×C3⋊D3—44no—
299C2×C3⋊D3—44no—
300C2×C3⋊D3—42no—
301C2×C3⋊D3—42no—
302C2×C3⋊D3—44no—
303C2×C3×D3—22no—
304C2×C3×D3—42no—
305C2×C3×D3—42no—
306C2×C3×D3—81no—
307C32×C4—81no—
308C3⋊Dic3—42no—
309C3×Dic3—22no—
310C3×Dic3—42no—
311C3×Dic3—42no—
312C3×Dic3—81no—
313C25—91no—
314C22×D4—31no—
315C22×D4—181no—
316#120—94no—
317#120—182no—
318C4×D4—182no—
319C4×D4—182no—
320#117—181no—
321C2×C22⋊C4—31no—
322C2×C22⋊C4—31no—
323C2×C22⋊C4—31no—
324C2×C22⋊C4—91no—
325C2×C22⋊C4—181no—
326C2×C22⋊C4—181no—
327C2×C22⋊C4—182no—
328C2×C22⋊C4—182no—
329C2×C22⋊C4D3211yescharacteristic
330#99—62no—
331C23×C3—21no—
332C23×C3—21no—
333C23×C3—21no—
334C23×C3—21no—
335C23×C3—21no—
336C23×C3—21no—
337C23×C3—21no—
338C23×C3—32no—
339C23×C3—42no—
340C23×C3—42no—
341C23×C3—44no—
342C23×C3—61no—
343C23×C3—61no—
344C23×C3—122no—
345C23×C3C2×C4×D311yescharacteristic
346C23×C3C2×C4×D311yescharacteristic
347C23×C3C2×D1211yescharacteristic
348C23×C3C2×D1211yescharacteristic
349C23×C3#23511yescharacteristic
350C23×C3D3×D411yescharacteristic
351C23×C3D3×D411yescharacteristic
352C23×C3D3×D411yescharacteristic
353C23×C3D3×D411yescharacteristic
354C23×C3D3×D411yescharacteristic
355C23×C3#23711yescharacteristic
356C23×C3#23711yescharacteristic
357C23×C3#23911yescharacteristic
358C23×C3C2×#6711yescharacteristic
359C22×D3—21no—
360C22×D3—21no—
361C22×D3—42no—
362C22×D3—68no—
363C22×D3—64no—
364C22×D3—64no—
365C22×D3—64no—
366C22×D3—64no—
367C22×D3—64no—
368C22×D3—64no—
369C22×D3—64no—
370C22×D3—62no—
371C22×D3—62no—
372C22×D3—62no—
373C22×D3—62no—
374C22×D3—62no—
375C22×D3—62no—
376C22×D3—122no—
377C22×D3—122no—
378C22×D3—124no—
379C22×D3—124no—
380C22×D3—124no—
381C22×D3—124no—
382C22×D3—128no—
383C22×D3—124no—
384C22×D3—124no—
385C22×D3—124no—
386C22×D3—124no—
387C22×D3—124no—
388C22×D3—124no—
389C22×D3—128no—
390C22×D3—124no—
391C22×D3—122no—
392C22×D3—122no—
393C22×D3—122no—
394C22×D3—122no—
395C22×D3—122no—
396C22×D3—122no—
397C22×D3—122no—
398C22×D3—122no—
399C22×D3—122no—
400C22×D3—122no—
401C22×D3—124no—
402C22×D3—124no—
403C22×D3—128no—
404C22×D3—128no—
405C22×D3—121no—
406C22×D3—121no—
407C22×D3—121no—
408C22×D3—121no—
409C22×D3—121no—
410C22×D3—121no—
411C22×D3—121no—
412C22×D3—121no—
413C22×D3(C2×D3)⋊C412yescomplemented
414C3×D4—62no—
415C3×D4—62no—
416C3×D4—62no—
417C3×D4—62no—
418C2×C3×C4—32no—
419C2×C3×C4—44no—
420C2×C3×C4—42no—
421C2×C3×C4—42no—
422C2×C3×C4—42no—
423C2×C3×C4—41no—
424C2×C3×C4—41no—
425C2×C3×C4—61no—
426C2×C3×C4—61no—
427C2×C3×C4—62no—
428C2×C3×C4—62no—
429C2×C3×C4—122no—
430C2×C3×C4—122no—
431C2×C3×C4—122no—
432C2×C3×C4—121no—
433#67—22no—
434#67—22no—
435#67—22no—
436#67—22no—
437#67—128no—
438C2×Dic3—21no—
439C2×Dic3—21no—
440C2×Dic3—22no—
441C2×Dic3—22no—
442C2×Dic3—42no—
443C2×Dic3—42no—
444C2×Dic3—42no—
445C2×Dic3—41no—
446C2×Dic3—62no—
447C2×Dic3—62no—
448C2×Dic3—122no—
449C2×Dic3—122no—
450C2×Dic3—122no—
451C2×Dic3—124no—
452C2×Dic3—242no—
453C2×Dic3(C2×D3)⋊C412yescomplemented
454D12—128no—
455C4×D3—242no—
456C2×C32—21no—
457C2×C32—21no—
458C2×C32—21no—
459C2×C32—21no—
460C2×C32—21no—
461C2×C32—21no—
462C2×C32#38611yescharacteristic
463C2×C32B(4,𝔽2)12yes—
464C3⋊D3—44no—
465C3×D3—42no—
466C24—31no—
467C24—92no—
468C24—181no—
469C24—181no—
470C24—181no—
471C24—181no—
472C24—181no—
473C24—181no—
474C24—364no—
475C24C2×D3211yescharacteristic
476C2×D4—32no—
477C2×D4—32no—
478C2×D4—61no—
479C2×D4—61no—
480C2×D4—61no—
481C2×D4—61no—
482C2×D4—184no—
483C2×D4—364no—
484C22×C4—21no—
485C22×C4—31no—
486C22×C4—32no—
487C22×C4—61no—
488C22×C4—61no—
489C22×C4—92no—
490C22×C4—182no—
491C4⋊C4—182no—
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—32no—
495C22⋊C4—61no—
496C22⋊C4—61no—
497C22⋊C4—61no—
498C22⋊C4—61no—
499C22⋊C4—61no—
500C22⋊C4—184no—
501C22⋊C4—182no—
502C22⋊C4—181no—
503C22⋊C4—181no—
504C22⋊C4—364no—
505C22⋊C4—364no—
506C42—182no—
507C22×C3—24no—
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—41no—
524C22×C3—41no—
525C22×C3—41no—
526C22×C3—41no—
527C22×C3—41no—
528C22×C3—41no—
529C22×C3—41no—
530C22×C3—41no—
531C22×C3—42no—
532C22×C3—42no—
533C22×C3—42no—
534C22×C3—42no—
535C22×C3—62no—
536C22×C3—122no—
537C22×C3—122no—
538C22×C3—241no—
539C22×C3C4×D1211yescharacteristic
540C22×C3D3×C22⋊C411yescharacteristic
541C22×C3#67⋊C411yescharacteristic
542C22×C3#67⋊C411yescharacteristic
543C22×C3#88211yescharacteristic
544C22×C3#88211yescharacteristic
545C22×C3#88411yescharacteristic
546C22×C3#88611yescharacteristic
547C22×C3#89311yescharacteristic
548C22×C3#89411yescharacteristic
549C22×C3#89511yescharacteristic
550C22×C3C2×(C2×D3)⋊C411yescharacteristic
551C22×C3#93911yescharacteristic
552C22×C3#93911yescharacteristic
553C2×D3—22no—
554C2×D3—42no—
555C2×D3—42no—
556C2×D3—64no—
557C2×D3—64no—
558C2×D3—68no—
559C2×D3—64no—
560C2×D3—64no—
561C2×D3—64no—
562C2×D3—64no—
563C2×D3—81no—
564C2×D3—124no—
565C2×D3—124no—
566C2×D3—128no—
567C2×D3—124no—
568C2×D3—122no—
569C2×D3—124no—
570C2×D3—124no—
571C2×D3—122no—
572C2×D3—122no—
573C2×D3—124no—
574C2×D3—124no—
575C2×D3—124no—
576C2×D3—122no—
577C2×D3—122no—
578C2×D3—122no—
579C2×D3—124no—
580C2×D3—124no—
581C2×D3—128no—
582C2×D3—124no—
583C2×D3—124no—
584C2×D3—128no—
585C2×D3—128no—
586C2×D3—122no—
587C2×D3—122no—
588C2×D3—124no—
589C2×D3—124no—
590C3×C4—62no—
591C3×C4—82no—
592C3×C4—81no—
593C3×C4—81no—
594C3×C4—122no—
595C3×C4—122no—
596C3×C4—241no—
597Dic3—22no—
598Dic3—42no—
599Dic3—42no—
600Dic3—81no—
601Dic3—122no—
602Dic3—122no—
603Dic3—242no—
604C32#188911yescharacteristic, complemented, Sylow
605C23—32no—
606C23—42no—
607C23—61no—
608C23—61no—
609C23—122no—
610C23—184no—
611C23—184no—
612C23—184no—
613C23—182no—
614C23—182no—
615C23—182no—
616C23—362no—
617C23—362no—
618C23—362no—
619C23—364no—
620C23—364no—
621C23—364no—
622C23—364no—
623C23—361no—
624C23—361no—
625C23—361no—
626C23—361no—
627C23#379611yescharacteristic
628C23C4×D3211yescharacteristic
629C23D3×D1211yescharacteristic
630C23D3×D1211yescharacteristic
631C23#380411yescharacteristic
632C23D3×#6711yescharacteristic
633C23#381111yescharacteristic
634D4—62no—
635D4—62no—
636D4—62no—
637D4—62no—
638D4—368no—
639C2×C4—32no—
640C2×C4—42no—
641C2×C4—41no—
642C2×C4—61no—
643C2×C4—61no—
644C2×C4—62no—
645C2×C4—62no—
646C2×C4—122no—
647C2×C4—122no—
648C2×C4—122no—
649C2×C4—121no—
650C2×C4—182no—
651C2×C4—362no—
652C2×C4—722no—
653C2×C3—22no—
654C2×C3—22no—
655C2×C3—21no—
656C2×C3—21no—
657C2×C3—21no—
658C2×C3—21no—
659C2×C3—21no—
660C2×C3—21no—
661C2×C3—21no—
662C2×C3—21no—
663C2×C3—21no—
664C2×C3—21no—
665C2×C3—21no—
666C2×C3—21no—
667C2×C3—21no—
668C2×C3—22no—
669C2×C3—41no—
670C2×C3—41no—
671C2×C3—41no—
672C2×C3—41no—
673C2×C3—122no—
674C2×C3#466511yescharacteristic
675C2×C3#474112yes—
676C2×C3#474112yes—
677C2×C3#495811yescharacteristic
678D3—42no—
679D3—128no—
680D3—124no—
681D3—124no—
682C22—22no—
683C22—22no—
684C22—22no—
685C22—41no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—62no—
690C22—122no—
691C22—122no—
692C22—184no—
693C22—184no—
694C22—184no—
695C22—241no—
696C22—364no—
697C22—362no—
698C22—364no—
699C22—362no—
700C22—362no—
701C22—364no—
702C22—362no—
703C22—364no—
704C22#6388011yescharacteristic
705C22#6388111yescharacteristic
706C22#6388611yescharacteristic
707C22#6389011yescharacteristic
708C22D3×(C2×D3)⋊C411yescharacteristic
709C22#6392311yescharacteristic
710C22#6397111yescharacteristic
711C4—62no—
712C4—81no—
713C4—122no—
714C4—122no—
715C4—241no—
716C4—362no—
717C3—21no—
718C3#6896211yescharacteristic, complemented
719C3#7002211yescharacteristic, complemented
720C2—21no—
721C2—21no—
722C2—21no—
723C2—21no—
724C2—21no—
725C2—21no—
726C2—122no—
727C2—364no—
728C2#1059041012yes—
729C2#1059136411yescharacteristic
subgroupG/H
centerC22#63923
commutatorC23×C32C22×C4
FrattiniC24C2×D32
FittingC2×C32×C22⋊C4C22
socleC22×C32#120
prime radicalC2×#63981C2
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. #10595506C2semidirect
3. #10592654C2semidirect
4. C2×C3×#806C2semidirect
5. #10591714C2semidirect
6. C3×#4527C2semidirect
7. #10589187C2semidirect
20. #63981C4semidirect
38. C2×#806D3semidirect
42. #4527D3semidirect
51. C23×C3⋊D3C2×C4semidirect
54. C22×C3⋊Dic3D4semidirect
64. C22×C3×Dic3D4semidirect
78. C3×#217C2×C4semidirect
153. C22×C3×D3C22⋊C4semidirect
170. C2×C3×Dic3C22⋊C4semidirect
237. C22×Dic3D12semidirect
265. #217C4×D3semidirect
413. C22×D3(C2×D3)⋊C4semidirect
453. C2×Dic3(C2×D3)⋊C4semidirect
604. C32#1889semidirect
718. C3#68962semidirect
719. C3#70022semidirect

Maximal subgroups

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

subgroupindex
C2×#639812
#105955062
#105926542
C2×C3×#8062
#105917142
C3×#45272
#105891872
#700223
#689623