Finite Group Databasebeta

← #11801313

Subgroups — #11801313

Order 1152.

3833 conjugacy classes of subgroups.

The subgroup lattice has 645 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×C3⋊D3C211yesmaximal, characteristic, complemented
2C22×#3811C211yesmaximal, characteristic
3C2×#63974C211yesmaximal, characteristic, complemented
4C2×#63921C212yesmaximal, complemented
5C3×#5213C212yesmaximal, complemented
6#10591713C212yesmaximal, complemented
7#10591387C214yesmaximal, complemented
8#10591370C212yesmaximal, complemented
9D3×#386—32nomaximal
10C24×C3⋊D3C2211yescharacteristic
11C23×D32C2211yescharacteristic
12C23×C32×C4C2211yescharacteristic, complemented
13C23×C3⋊Dic3C2211yescharacteristic, complemented
14C22×C4×C3⋊D3—28no—
15C22×C4×C3⋊D3—24no—
16C22×C4×C3⋊D3C2212yes—
17C22×C4×C3⋊D3C2212yescomplemented
18C22×C3×#67C2212yes—
19C2×#3811—24no—
20C2×#3811—24no—
21C2×#3811C418yescomplemented
22C22×#626C2212yes—
23C22×#624C2212yes—
24C22×#624C2211yescharacteristic
25C2×C3×#217C2212yescomplemented
26C2×C3×(C2×D3)⋊C4C2214yescomplemented
27#63974—24no—
28C2×#3722C2212yescomplemented
29C2×(C2×D3)⋊Dic3C2214yescomplemented
30#63921—28no—
31C3×C3⋊#95C2214yescomplemented
32#63579C2214yescomplemented
33C22×D3×D4—32no—
34C23×C4×D3—32no—
35C23×C4×D3—61no—
36C2×D3×C22⋊C4—32no—
37C2×D3×C22⋊C4—34no—
38C3×#386—32no—
39#5220—32no—
40#5213D312yescomplemented
41#4958—32no—
42#4956—34no—
43#4665—34no—
44D3×#95—34no—
45C24×C32C2311yescharacteristic
46C23×C3⋊D3—24no—
47C23×C3⋊D3—24no—
48C23×C3⋊D3C2×C414yes—
49C23×C3⋊D3D414yes—
50C23×C3⋊D3D414yes—
51C23×C3⋊D3C2311yescharacteristic
52C23×C3⋊D3C2311yescharacteristic
53C23×C3×D3C2312yes—
54C22×D32—22no—
55C22×D32—22no—
56C22×D32—24no—
57C22×D32—24no—
58C22×D32C2×C414yescomplemented
59C22×C32×C4—22no—
60C22×C32×C4—24no—
61C22×C32×C4C2312yes—
62C22×C3⋊Dic3—22no—
63C22×C3⋊Dic3—24no—
64C22×C3⋊Dic3C2312yes—
65C2×C4×C3⋊D3—232no—
66C2×C4×C3⋊D3—24no—
67C2×C4×C3⋊D3—24no—
68C2×C4×C3⋊D3—24no—
69C2×C4×C3⋊D3—24no—
70C2×C4×C3⋊D3—24no—
71C2×C4×C3⋊D3D418yescomplemented
72C2×C3×#67—24no—
73C2×C3×#67—24no—
74C2×C3×#67C2×C418yescomplemented
75C22×C3×Dic3C2314yes—
76C22×C3×Dic3C2312yes—
77#3811—232no—
78C2×#626—24no—
79C2×#626—24no—
80C2×#626C2×C418yescomplemented
81C2×#624—22no—
82C2×#624—22no—
83C2×#624—24no—
84C2×#624—24no—
85C2×#624—24no—
86C2×#624C2×C414yescomplemented
87C3×#217—24no—
88C3×(C2×D3)⋊C4—28no—
89#3722—24no—
90(C2×D3)⋊Dic3—28no—
91C2×#386—91noSylow
92C24×D3—32no—
93C24×D3—32no—
94C24×D3—61no—
95C22×C3×D4—32no—
96C23×C3×C4—21no—
97C23×C3×C4C2×D312yescomplemented
98C22×#67—32no—
99C22×#67C2×D312yes—
100C23×Dic3—32no—
101C23×Dic3—61no—
102C2×D3×D4—316no—
103C2×D3×D4—68no—
104C2×D3×D4—68no—
105C22×D12—32no—
106C22×C4×D3—34no—
107C22×C4×D3—32no—
108C22×C4×D3—34no—
109C22×C4×D3—34no—
110C22×C4×D3—62no—
111C22×C4×D3—62no—
112C22×C4×D3—616no—
113C22×C4×D3—68no—
114C22×C4×D3—616no—
115C22×C4×D3—68no—
116C2×C3×C22⋊C4—32no—
117C2×C3×C22⋊C4—34no—
118C2×#217—34no—
119C2×#217C2×D312yescomplemented
120C2×(C2×D3)⋊C4—34no—
121C2×(C2×D3)⋊C4—34no—
122C2×(C2×D3)⋊C4C2×D314yescomplemented
123D3×C22⋊C4—616no—
124D3×C22⋊C4—68no—
125C3×#95—34no—
126C3⋊#95—34no—
127C3⋊#95—34no—
128C3⋊#95C2×D314yescomplemented
129C23×C32—22no—
130C23×C32—22no—
131C23×C32C22×C412yes—
132C23×C32C2×D412yes—
133C23×C32C2×D412yes—
134C23×C32C2411yescharacteristic
135C22×C3⋊D3—22no—
136C22×C3⋊D3—22no—
137C22×C3⋊D3—216no—
138C22×C3⋊D3—28no—
139C22×C3⋊D3—216no—
140C22×C3⋊D3—28no—
141C22×C3⋊D3C22⋊C4116yescomplemented
142C22×C3⋊D3C22×C412yes—
143C22×C3⋊D3C22×C412yes—
144C22×C3⋊D3C2×D412yes—
145C22×C3⋊D3C2×D412yes—
146C22×C3⋊D3C2×D412yes—
147C22×C3⋊D3C2×D412yes—
148C22×C3⋊D3C2×D414yes—
149C22×C3⋊D3#4114yes—
150C22×C3×D3—24no—
151C22×C3×D3—22no—
152C22×C3×D3—22no—
153C22×C3×D3—24no—
154C22×C3×D3C22×C414yescomplemented
155C2×D32—28no—
156C2×D32—216no—
157C2×D32—44no—
158C2×D32—48no—
159C2×D32—44no—
160C2×C32×C4—28no—
161C2×C32×C4—22no—
162C2×C32×C4—22no—
163C2×C32×C4C2×D414yescomplemented
164C2×C3⋊Dic3—28no—
165C2×C3⋊Dic3—22no—
166C2×C3⋊Dic3—22no—
167C2×C3⋊Dic3C2×D414yescomplemented
168C4×C3⋊D3—216no—
169C4×C3⋊D3—216no—
170C3×#67—216no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—24no—
174C2×C3×Dic3—24no—
175C2×C3×Dic3—24no—
176C2×C3×Dic3C22×C414yescomplemented
177#626—216no—
178#624—28no—
179#624—48no—
180C23×D4—91no—
181C24×C4—91no—
182C22×C22⋊C4—91no—
183C22×C22⋊C4—92no—
184#386—32no—
185#386—94no—
186#386—92no—
187C2×#95—92no—
188C24×C3—21no—
189C24×C3—32no—
190C24×C3C22×D312yes—
191C23×D3—32no—
192C23×D3—38no—
193C23×D3—38no—
194C23×D3—38no—
195C23×D3—32no—
196C23×D3—38no—
197C23×D3—64no—
198C23×D3—64no—
199C23×D3—64no—
200C23×D3—61no—
201C23×D3—61no—
202C23×D3—68no—
203C23×D3—64no—
204C23×D3—64no—
205C23×D3—68no—
206C23×D3—68no—
207C23×D3—68no—
208C23×D3—68no—
209C23×D3—68no—
210C23×D3C22×D312yes—
211C2×C3×D4—38no—
212C2×C3×D4—64no—
213C2×C3×D4—64no—
214C22×C3×C4—24no—
215C22×C3×C4—28no—
216C22×C3×C4—24no—
217C22×C3×C4—28no—
218C22×C3×C4—22no—
219C22×C3×C4—32no—
220C22×C3×C4—34no—
221C22×C3×C4C22×D314yes—
222C2×#67—24no—
223C2×#67—24no—
224C2×#67—38no—
225C2×#67—64no—
226C2×#67—64no—
227C2×#67C4×D318yescomplemented
228C22×Dic3—34no—
229C22×Dic3—62no—
230C22×Dic3—68no—
231C22×Dic3—68no—
232C22×Dic3—64no—
233C22×Dic3—64no—
234C22×Dic3C22×D314yes—
235C22×Dic3C22×D312yes—
236D3×D4—664no—
237C2×D12—38no—
238C2×D12—64no—
239C2×D12—64no—
240C2×C4×D3—316no—
241C2×C4×D3—38no—
242C2×C4×D3—68no—
243C2×C4×D3—64no—
244C2×C4×D3—64no—
245C2×C4×D3—68no—
246C2×C4×D3—68no—
247C2×C4×D3—68no—
248C2×C4×D3—68no—
249C2×C4×D3—68no—
250C2×C4×D3—68no—
251C2×C4×D3—68no—
252C2×C4×D3—68no—
253C2×C4×D3—664no—
254C2×C4×D3—664no—
255C2×C4×D3—68no—
256C2×C4×D3—68no—
257C2×C4×D3—68no—
258C2×C4×D3—68no—
259C2×C4×D3—68no—
260C3×C22⋊C4—64no—
261C3×C22⋊C4—68no—
262#217—24no—
263#217—68no—
264(C2×D3)⋊C4—28no—
265(C2×D3)⋊C4—68no—
266(C2×D3)⋊C4—68no—
267C22×C32—24no—
268C22×C32—22no—
269C22×C32—24no—
270C22×C32—22no—
271C22×C32C2×C22⋊C414yescomplemented
272C22×C32C23×C411yescharacteristic
273C22×C32C22×D411yescharacteristic
274C22×C32C22×D411yescharacteristic
275C22×C32C22×D412yes—
276C22×C32C2×#4112yes—
277C2×C3⋊D3—24no—
278C2×C3⋊D3—22no—
279C2×C3⋊D3—24no—
280C2×C3⋊D3—22no—
281C2×C3⋊D3—232no—
282C2×C3⋊D3C2×C22⋊C414yes—
283C2×C3⋊D3C2×C22⋊C414yescomplemented
284C2×C3⋊D3C4×D418yes—
285C2×C3⋊D3#12014yes—
286C2×C3⋊D3#12118yes—
287C2×C3⋊D3#12314yes—
288C2×C3×D3—24no—
289C2×C3×D3—28no—
290C2×C3×D3—42no—
291C2×C3×D3—44no—
292C2×C3×D3—42no—
293D32—416no—
294C32×C4—24no—
295C3⋊Dic3—24no—
296C3×Dic3—24no—
297C3×Dic3—44no—
298C25—91no—
299C25—91no—
300C22×D4—32no—
301C22×D4—92no—
302C22×D4—98no—
303C22×D4—184no—
304C22×D4—184no—
305C23×C4—91no—
306C23×C4—92no—
307C23×C4—92no—
308C23×C4—91no—
309C23×C4—92no—
310C23×C4—188no—
311C23×C4—184no—
312C23×C4D3211yescharacteristic, complemented
313C2×C22⋊C4—32no—
314C2×C22⋊C4—34no—
315C2×C22⋊C4—92no—
316C2×C22⋊C4—94no—
317C2×C22⋊C4—188no—
318C2×C22⋊C4—184no—
319#95—34no—
320#95—94no—
321C23×C3—24no—
322C23×C3—24no—
323C23×C3—24no—
324C23×C3—24no—
325C23×C3—21no—
326C23×C3—22no—
327C23×C3—22no—
328C23×C3—22no—
329C23×C3—34no—
330C23×C3—64no—
331C23×C3—62no—
332C23×C3—62no—
333C23×C3—64no—
334C23×C3C2×C4×D314yes—
335C23×C3D3×D414yes—
336C23×C3D3×D414yes—
337C23×C3C23×D312yes—
338C22×D3—24no—
339C22×D3—22no—
340C22×D3—22no—
341C22×D3—24no—
342C22×D3—34no—
343C22×D3—38no—
344C22×D3—34no—
345C22×D3—34no—
346C22×D3—38no—
347C22×D3—332no—
348C22×D3—34no—
349C22×D3—34no—
350C22×D3—34no—
351C22×D3—616no—
352C22×D3—62no—
353C22×D3—62no—
354C22×D3—64no—
355C22×D3—62no—
356C22×D3—62no—
357C22×D3—62no—
358C22×D3—62no—
359C22×D3—64no—
360C22×D3—616no—
361C22×D3—632no—
362C22×D3—616no—
363C22×D3—616no—
364C22×D3—632no—
365C22×D3—632no—
366C22×D3—616no—
367C22×D3—64no—
368C22×D3—632no—
369C22×D3—632no—
370C22×D3—616no—
371C22×D3—64no—
372C22×D3—64no—
373C22×D3—64no—
374C22×D3—128no—
375C22×D3—128no—
376C22×D3—1216no—
377C22×D3C2×C4×D314yescomplemented
378C3×D4—616no—
379C2×C3×C4—216no—
380C2×C3×C4—216no—
381C2×C3×C4—24no—
382C2×C3×C4—24no—
383C2×C3×C4—24no—
384C2×C3×C4—24no—
385C2×C3×C4—24no—
386C2×C3×C4—34no—
387C2×C3×C4—62no—
388C2×C3×C4—62no—
389C2×C3×C4—64no—
390C2×C3×C4—64no—
391C2×C3×C4—64no—
392C2×C3×C4D3×D418yescomplemented
393#67—216no—
394#67—616no—
395C2×Dic3—22no—
396C2×Dic3—22no—
397C2×Dic3—24no—
398C2×Dic3—24no—
399C2×Dic3—24no—
400C2×Dic3—38no—
401C2×Dic3—64no—
402C2×Dic3—616no—
403C2×Dic3—616no—
404C2×Dic3—64no—
405C2×Dic3—64no—
406C2×Dic3—64no—
407C2×Dic3—64no—
408C2×Dic3C2×C4×D314yescomplemented
409D12—616no—
410C4×D3—616no—
411C4×D3—632no—
412C4×D3—632no—
413C4×D3—632no—
414C4×D3—632no—
415C4×D3—1216no—
416C2×C32—24no—
417C2×C32C22×C22⋊C411yescharacteristic
418C2×C32C2×C4×D412yes—
419C2×C32C2×#12011yescharacteristic
420C2×C32C2×#12112yes—
421C2×C32C2×#12311yescharacteristic
422C3⋊D3—24no—
423C3⋊D3#38618yescomplemented
424C3×D3—44no—
425C24—32no—
426C24—94no—
427C24—91no—
428C24—91no—
429C24—94no—
430C24—94no—
431C24—94no—
432C24—184no—
433C24—184no—
434C24—184no—
435C24—182no—
436C24—182no—
437C24—184no—
438C24C2×D3211yescharacteristic
439C2×D4—38no—
440C2×D4—64no—
441C2×D4—64no—
442C2×D4—98no—
443C2×D4—184no—
444C2×D4—184no—
445C2×D4—1832no—
446C22×C4—22no—
447C22×C4—24no—
448C22×C4—32no—
449C22×C4—34no—
450C22×C4—94no—
451C22×C4—92no—
452C22×C4—98no—
453C22×C4—184no—
454C22×C4—184no—
455C22×C4—184no—
456C22×C4—184no—
457C22×C4—1832no—
458C22×C4—182no—
459C22×C4—182no—
460C22×C4—184no—
461C22×C4—184no—
462C22×C4—184no—
463C22×C4—184no—
464C22×C4—182no—
465C22×C4—184no—
466C22×C4C2×D3212yes—
467C22⋊C4—64no—
468C22⋊C4—68no—
469C22⋊C4—184no—
470C22⋊C4—188no—
471C22×C3—24no—
472C22×C3—24no—
473C22×C3—28no—
474C22×C3—28no—
475C22×C3—24no—
476C22×C3—28no—
477C22×C3—24no—
478C22×C3—28no—
479C22×C3—21no—
480C22×C3—21no—
481C22×C3—22no—
482C22×C3—21no—
483C22×C3—22no—
484C22×C3—24no—
485C22×C3—64no—
486C22×C3—68no—
487C22×C3—122no—
488C22×C3—122no—
489C22×C3—124no—
490C22×C3D3×C22⋊C418yescomplemented
491C22×C3C22×C4×D312yes—
492C22×C3C2×D3×D412yes—
493C22×C3C2×D3×D412yes—
494C22×C3C2×D3×D414yes—
495C22×C3D3×#4114yes—
496C2×D3—24no—
497C2×D3—28no—
498C2×D3—38no—
499C2×D3—38no—
500C2×D3—316no—
501C2×D3—38no—
502C2×D3—316no—
503C2×D3—38no—
504C2×D3—42no—
505C2×D3—42no—
506C2×D3—44no—
507C2×D3—64no—
508C2×D3—64no—
509C2×D3—64no—
510C2×D3—68no—
511C2×D3—68no—
512C2×D3—64no—
513C2×D3—664no—
514C2×D3—64no—
515C2×D3—664no—
516C2×D3—64no—
517C2×D3—68no—
518C2×D3—68no—
519C2×D3—64no—
520C2×D3—68no—
521C2×D3—64no—
522C2×D3—68no—
523C2×D3—1232no—
524C3×C4—28no—
525C3×C4—28no—
526C3×C4—64no—
527C3×C4—124no—
528Dic3—24no—
529Dic3—44no—
530Dic3—68no—
531Dic3—68no—
532C32C2×#38611yescharacteristic, complemented, Sylow
533C23—22no—
534C23—22no—
535C23—34no—
536C23—62no—
537C23—64no—
538C23—64no—
539C23—62no—
540C23—92no—
541C23—92no—
542C23—94no—
543C23—94no—
544C23—92no—
545C23—92no—
546C23—92no—
547C23—92no—
548C23—916no—
549C23—188no—
550C23—188no—
551C23—1816no—
552C23—1816no—
553C23—188no—
554C23—1816no—
555C23—182no—
556C23—182no—
557C23—364no—
558C23—368no—
559C23—364no—
560C23C4×D3212yes—
561C23#380212yes—
562C23#381112yes—
563C23C22×D3211yescharacteristic
564D4—616no—
565D4—1816no—
566C2×C4—28no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—34no—
570C2×C4—62no—
571C2×C4—62no—
572C2×C4—64no—
573C2×C4—64no—
574C2×C4—64no—
575C2×C4—94no—
576C2×C4—1816no—
577C2×C4—1816no—
578C2×C4—188no—
579C2×C4—188no—
580C2×C4—182no—
581C2×C4—182no—
582C2×C4—368no—
583C2×C4#381114yescomplemented
584C2×C3—28no—
585C2×C3—28no—
586C2×C3—21no—
587C2×C3—22no—
588C2×C3—21no—
589C2×C3—21no—
590C2×C3—22no—
591C2×C3—124no—
592C2×C3C2×D3×C22⋊C412yes—
593C2×C3C4×D3×D414yes—
594C2×C3D3×#12012yes—
595C2×C3D3×#12114yes—
596C2×C3D3×#12312yes—
597D3—316no—
598D3—44no—
599D3—68no—
600D3—68no—
601D3—68no—
602C22—22no—
603C22—24no—
604C22—22no—
605C22—24no—
606C22—64no—
607C22—68no—
608C22—94no—
609C22—98no—
610C22—94no—
611C22—94no—
612C22—98no—
613C22—94no—
614C22—122no—
615C22—124no—
616C22—122no—
617C22—1832no—
618C22—182no—
619C22—184no—
620C22—182no—
621C22—184no—
622C22—3616no—
623C22#6392114yescomplemented
624C22C2×C4×D3211yescharacteristic
625C22C2×#380211yescharacteristic
626C22#6430612yes—
627C22C2×#381111yescharacteristic
628C22C2×#381112yes—
629C4—24no—
630C4—64no—
631C4—124no—
632C4—184no—
633C3—21no—
634C3D3×#38612yescomplemented
635C2—24no—
636C2—98no—
637C2—124no—
638C2—184no—
639C2C2×#6392111yescharacteristic
640C2C4×#381112yes—
641C2#1059507911yescharacteristic
642C2#1059508112yes—
643C2#1059552711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC22×#3811C2
hypercenterC23×C4D32
hypocenterC32C2×#386
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C23×C4×C3⋊D3C2semidirect
3. C2×#63974C2semidirect
4. C2×#63921C2semidirect
5. C3×#5213C2semidirect
6. #10591713C2semidirect
7. #10591387C2semidirect
8. #10591370C2semidirect
12. C23×C32×C4C22semidirect
13. C23×C3⋊Dic3C22semidirect
17. C22×C4×C3⋊D3C22semidirect
21. C2×#3811C4semidirect
25. C2×C3×#217C22semidirect
26. C2×C3×(C2×D3)⋊C4C22semidirect
28. C2×#3722C22semidirect
29. C2×(C2×D3)⋊Dic3C22semidirect
31. C3×C3⋊#95C22semidirect
32. #63579C22semidirect
40. #5213D3semidirect
58. C22×D32C2×C4semidirect
71. C2×C4×C3⋊D3D4semidirect
74. C2×C3×#67C2×C4semidirect
80. C2×#626C2×C4semidirect
86. C2×#624C2×C4semidirect
97. C23×C3×C4C2×D3semidirect
119. C2×#217C2×D3semidirect
122. C2×(C2×D3)⋊C4C2×D3semidirect
128. C3⋊#95C2×D3semidirect
141. C22×C3⋊D3C22⋊C4semidirect
154. C22×C3×D3C22×C4semidirect
163. C2×C32×C4C2×D4semidirect
167. C2×C3⋊Dic3C2×D4semidirect
176. C2×C3×Dic3C22×C4semidirect
227. C2×#67C4×D3semidirect
271. C22×C32C2×C22⋊C4semidirect
283. C2×C3⋊D3C2×C22⋊C4semidirect
312. C23×C4D32semidirect
377. C22×D3C2×C4×D3semidirect
392. C2×C3×C4D3×D4semidirect
408. C2×Dic3C2×C4×D3semidirect
423. C3⋊D3#386semidirect
490. C22×C3D3×C22⋊C4semidirect
532. C32C2×#386semidirect
583. C2×C4#3811semidirect
623. C22#63921semidirect
634. C3D3×#386semidirect

Maximal subgroups

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

subgroupindex
C23×C4×C3⋊D32
C22×#38112
C2×#639742
C2×#639212
C3×#52132
#105917132
#105913872
#105913702
D3×#3863