Finite Group Databasebeta

← #11803864

Subgroups — #11803864

Order 1152.

1569 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63914C211yesmaximal, characteristic
2C2×#63902C211yesmaximal, characteristic, complemented
3C2×C4×#625C211yesmaximal, characteristic, complemented
4#10592347C211yesmaximal, characteristic, complemented
5C3×#4665C212yesmaximal, complemented
6#10591385C211yesmaximal, characteristic, complemented
7#10591385C211yesmaximal, characteristic, complemented
8#10591381C212yesmaximal, complemented
9#10591376C212yesmaximal, complemented
10#10591363C212yesmaximal, complemented
11#10591360C211yesmaximal, characteristic, complemented
12#74667—32nomaximal
13C22×C3×D12C2212yes—
14C22×C3×C4×D3C2212yes—
15C22×#625C2211yescharacteristic
16C22×#625C2211yescharacteristic
17C22×#625C2212yes—
18C22×D3×Dic3C2212yes—
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×C4×C3⋊Dic3C2211yescharacteristic
21C2×C4×C3⋊Dic3C2211yescharacteristic
22C2×C3×(C2×D3)⋊C4C2212yes—
23C2×C3×(C2×D3)⋊C4C2212yes—
24C2×C3×(C2×D3)⋊C4C2212yes—
25C2×#3724C2211yescharacteristic
26C2×#3724C2211yescharacteristic
27C2×(C2×D3)⋊Dic3C2212yes—
28C2×(C2×D3)⋊Dic3C2212yes—
29C2×(C2×D3)⋊Dic3C2212yes—
30#63914C418yescomplemented
31#63902—24no—
32C4×#625—24no—
33C32×#95C2211yescharacteristic
34#63658C2211yescharacteristic
35#63658C2211yescharacteristic
36#63658C2211yescharacteristic
37C3×C3⋊#95C2212yes—
38#63579C2212yes—
39C2×#940—32no—
40C2×C4×#67—32no—
41C2×#67⋊C4—32no—
42C3×#386—32no—
43#5220—32no—
44#5213—32no—
45#4958—32no—
46#4957—32no—
47#4957—32no—
48#4956—32no—
49#4956—32no—
50#4665—32no—
51#4665D312yescomplemented
52#4650—32no—
53#4648—32no—
54#4648—61no—
55C23×C3×D3C2312yes—
56C23×C3×D3C2312yes—
57C22×C32×C4C2311yescharacteristic
58C22×C32×C4C2311yescharacteristic
59C22×C32×C4C2311yescharacteristic
60C22×C3⋊Dic3C2311yescharacteristic
61C22×C3⋊Dic3C2311yescharacteristic
62C22×C3⋊Dic3C2311yescharacteristic
63C22×C3⋊Dic3C2311yescharacteristic
64C22×C3×Dic3C2312yes—
65C22×C3×Dic3C2312yes—
66C2×C3×D12—42no—
67C2×C3×D12—42no—
68C2×C3×D12C2×C418yescomplemented
69C2×C3×C4×D3—24no—
70C2×C3×C4×D3—42no—
71C2×C3×C4×D3—42no—
72C2×#625—22no—
73C2×#625—22no—
74C2×#625—22no—
75C2×#625—22no—
76C2×#625—42no—
77C2×#625—42no—
78C2×#625C2×C414yescomplemented
79C2×#625C2×C414yescomplemented
80C2×#625C2×C418yescomplemented
81C2×D3×Dic3—24no—
82C2×D3×Dic3—42no—
83C2×D3×Dic3—42no—
84C4×C3⋊Dic3—22no—
85C4×C3⋊Dic3C2×C414yescomplemented
86C4×C3⋊Dic3D414yescomplemented
87C3×(C2×D3)⋊C4—24no—
88C3×(C2×D3)⋊C4—42no—
89C3×(C2×D3)⋊C4—42no—
90#3724—22no—
91#3724—22no—
92(C2×D3)⋊Dic3—24no—
93(C2×D3)⋊Dic3—42no—
94(C2×D3)⋊Dic3—42no—
95#2328—91noSylow
96C22×C3×D4—32no—
97C23×C3×C4—32no—
98C22×#67—32no—
99C22×#67—32no—
100C22×#67—32no—
101C22×#67—32no—
102C23×Dic3—32no—
103C22×D12C2×D312yes—
104C22×C4×D3—32no—
105C22×C4×D3C2×D312yes—
106C2×C3×C22⋊C4—32no—
107C2×C3×C22⋊C4—32no—
108C2×C3×C22⋊C4—32no—
109C2×#217—32no—
110C2×#217—32no—
111C2×#217—32no—
112#940—316no—
113C4×#67—68no—
114C2×(C2×D3)⋊C4—32no—
115C2×(C2×D3)⋊C4—32no—
116C2×(C2×D3)⋊C4—32no—
117C2×(C2×D3)⋊C4C2×D312yes—
118C2×(C2×D3)⋊C4C2×D312yes—
119C2×(C2×D3)⋊C4C2×D312yes—
120C2×Dic3⋊C4—32no—
121C2×Dic3⋊C4—32no—
122C2×C4×Dic3—32no—
123C2×C4×Dic3—32no—
124C2×C4×Dic3—32no—
125C2×C4×Dic3—61no—
126C2×C4×Dic3—61no—
127C2×C4×Dic3—61no—
128#67⋊C4—68no—
129C3×#95—21no—
130C3×#95—32no—
131C3×#95C2×D312yes—
132C3⋊#95—32no—
133C3⋊#95—32no—
134C3⋊#95—32no—
135C3⋊#95—32no—
136C3⋊#95—32no—
137C3⋊#95—61no—
138C3⋊#95—61no—
139C3⋊#95—61no—
140C3⋊#95C2×D312yes—
141C23×C32C2411yescharacteristic
142C22×C3×D3—22no—
143C22×C3×D3—22no—
144C22×C3×D3—22no—
145C22×C3×D3—22no—
146C22×C3×D3—22no—
147C22×C3×D3—22no—
148C22×C3×D3—22no—
149C22×C3×D3—22no—
150C22×C3×D3—22no—
151C22×C3×D3—22no—
152C22×C3×D3—22no—
153C22×C3×D3—22no—
154C22×C3×D3C22×C414yes—
155C22×C3×D3C22×C414yes—
156C2×C32×C4—21no—
157C2×C32×C4—21no—
158C2×C32×C4—21no—
159C2×C32×C4—21no—
160C2×C32×C4—21no—
161C2×C32×C4—21no—
162C2×C32×C4—21no—
163C2×C32×C4C22×C412yes—
164C2×C32×C4C2×D412yes—
165C2×C3⋊Dic3—21no—
166C2×C3⋊Dic3—21no—
167C2×C3⋊Dic3—21no—
168C2×C3⋊Dic3—21no—
169C2×C3⋊Dic3—21no—
170C2×C3⋊Dic3—21no—
171C2×C3⋊Dic3—21no—
172C2×C3⋊Dic3C22×C412yes—
173C2×C3⋊Dic3C22×C412yes—
174C2×C3⋊Dic3C2×D412yes—
175C2×C3⋊Dic3C2×D412yes—
176C2×C3⋊Dic3#4112yes—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—22no—
183C3×D12—48no—
184C3×C4×D3—48no—
185#625—28no—
186#625—28no—
187#625—48no—
188D3×Dic3—48no—
189C2×#127—91no—
190C2×C4×D4—91no—
191C2×C4×D4—91no—
192#390—91no—
193#390—91no—
194#386—32no—
195#386—92no—
196#386—92no—
197#386—92no—
198#382—91no—
199#376—91no—
200C24×C3—32no—
201C24×C3—32no—
202C23×D3C22×D312yes—
203C23×D3C22×D312yes—
204C2×C3×D4—38no—
205C2×C3×D4—122no—
206C2×C3×D4—122no—
207C22×C3×C4—21no—
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4—32no—
211C22×C3×C4—32no—
212C22×C3×C4—64no—
213C22×C3×C4—122no—
214C22×C3×C4—122no—
215C22×C3×C4C22×D312yes—
216C22×C3×C4C22×D312yes—
217C22×C3×C4C22×D312yes—
218C2×#67—38no—
219C2×#67—38no—
220C2×#67—38no—
221C2×#67—38no—
222C2×#67—64no—
223C2×#67—64no—
224C2×#67—64no—
225C2×#67—64no—
226C2×#67—122no—
227C2×#67—122no—
228C2×#67—122no—
229C2×#67—122no—
230C22×Dic3—32no—
231C22×Dic3—32no—
232C22×Dic3—32no—
233C22×Dic3—32no—
234C22×Dic3—61no—
235C22×Dic3—61no—
236C22×Dic3—61no—
237C22×Dic3—61no—
238C22×Dic3—64no—
239C22×Dic3—122no—
240C22×Dic3—122no—
241C22×Dic3C22×D312yes—
242C22×Dic3C22×D312yes—
243C2×D12—42no—
244C2×D12—42no—
245C2×D12C4×D318yescomplemented
246C2×C4×D3—24no—
247C2×C4×D3—42no—
248C2×C4×D3—42no—
249C2×C4×D3—64no—
250C2×C4×D3—122no—
251C2×C4×D3—122no—
252C3×C22⋊C4—64no—
253C3×C22⋊C4—122no—
254C3×C22⋊C4—122no—
255#217—64no—
256#217—122no—
257#217—122no—
258(C2×D3)⋊C4—24no—
259(C2×D3)⋊C4—42no—
260(C2×D3)⋊C4—42no—
261(C2×D3)⋊C4—64no—
262(C2×D3)⋊C4—122no—
263(C2×D3)⋊C4—122no—
264Dic3⋊C4—64no—
265Dic3⋊C4—64no—
266C4×Dic3—38no—
267C4×Dic3—38no—
268C4×Dic3—64no—
269C4×Dic3—64no—
270C4×Dic3—64no—
271C4×Dic3—64no—
272C22×C32C23×C411yescharacteristic
273C22×C32C22×D411yescharacteristic
274C22×C32C2×#4111yescharacteristic
275C22×C32H(5,𝔽2)11yescharacteristic
276C22×C32H(5,𝔽2)11yescharacteristic
277C22×C32H(5,𝔽2)11yescharacteristic
278C22×C32H(5,𝔽2)11yescharacteristic
279C2×C3×D3—24no—
280C2×C3×D3—24no—
281C2×C3×D3—24no—
282C2×C3×D3—24no—
283C2×C3×D3—24no—
284C2×C3×D3—24no—
285C2×C3×D3—42no—
286C2×C3×D3—42no—
287C2×C3×D3—42no—
288C2×C3×D3—42no—
289C2×C3×D3—42no—
290C2×C3×D3—42no—
291C2×C3×D3—42no—
292C2×C3×D3—42no—
293C32×C4—22no—
294C32×C4—22no—
295C32×C4—41no—
296C3⋊Dic3—22no—
297C3⋊Dic3—22no—
298C3⋊Dic3—41no—
299C3⋊Dic3C4×D414yes—
300C3×Dic3—42no—
301C3×Dic3—42no—
302C22×D4—32no—
303C22×D4—91no—
304C22×D4—91no—
305C22×D4—92no—
306C23×C4—32no—
307C23×C4—92no—
308#127—98no—
309C4×D4—184no—
310C4×D4—184no—
311C2×C4⋊C4—91no—
312C2×C4⋊C4—91no—
313C2×C22⋊C4—32no—
314C2×C22⋊C4—32no—
315C2×C22⋊C4—32no—
316C2×C22⋊C4—92no—
317C2×C22⋊C4—92no—
318C2×C22⋊C4—92no—
319C2×C42—91no—
320C2×C42—91no—
321C2×C42—91no—
322#95—32no—
323#95—92no—
324#95—91no—
325#95—91no—
326#95—91no—
327#95D3211yescharacteristic
328C23×C3—21no—
329C23×C3—34no—
330C23×C3—34no—
331C23×C3—62no—
332C23×C3—62no—
333C23×C3—62no—
334C23×C3—62no—
335C23×C3—62no—
336C23×C3—62no—
337C23×C3—62no—
338C23×C3—62no—
339C23×C3—62no—
340C23×C3—62no—
341C23×C3—62no—
342C23×C3—62no—
343C23×C3C23×D312yes—
344C22×D3—22no—
345C22×D3—22no—
346C22×D3—22no—
347C22×D3—22no—
348C22×D3—22no—
349C22×D3—22no—
350C22×D3—22no—
351C22×D3—22no—
352C22×D3—22no—
353C22×D3—22no—
354C22×D3—22no—
355C22×D3—22no—
356C22×D3C2×C4×D314yes—
357C22×D3C2×C4×D314yes—
358C3×D4—128no—
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—22no—
362C2×C3×C4—22no—
363C2×C3×C4—22no—
364C2×C3×C4—22no—
365C2×C3×C4—22no—
366C2×C3×C4—22no—
367C2×C3×C4—22no—
368C2×C3×C4—22no—
369C2×C3×C4—41no—
370C2×C3×C4—41no—
371C2×C3×C4—41no—
372C2×C3×C4—41no—
373C2×C3×C4—41no—
374C2×C3×C4—41no—
375C2×C3×C4—62no—
376C2×C3×C4—62no—
377C2×C3×C4—62no—
378C2×C3×C4—62no—
379C2×C3×C4—62no—
380C2×C3×C4—62no—
381C2×C3×C4—128no—
382C2×C3×C4C2×C4×D314yes—
383C2×C3×C4D3×D414yes—
384#67—616no—
385#67—616no—
386#67—128no—
387#67—128no—
388C2×Dic3—22no—
389C2×Dic3—22no—
390C2×Dic3—22no—
391C2×Dic3—22no—
392C2×Dic3—22no—
393C2×Dic3—22no—
394C2×Dic3—34no—
395C2×Dic3—34no—
396C2×Dic3—34no—
397C2×Dic3—34no—
398C2×Dic3—34no—
399C2×Dic3—62no—
400C2×Dic3—62no—
401C2×Dic3—62no—
402C2×Dic3—62no—
403C2×Dic3—62no—
404C2×Dic3—62no—
405C2×Dic3—62no—
406C2×Dic3—62no—
407C2×Dic3—62no—
408C2×Dic3—62no—
409C2×Dic3—62no—
410C2×Dic3—62no—
411C2×Dic3—62no—
412C2×Dic3—121no—
413C2×Dic3—121no—
414C2×Dic3—121no—
415C2×Dic3—121no—
416C2×Dic3—121no—
417C2×Dic3—121no—
418C2×Dic3—128no—
419D12—48no—
420C4×D3—48no—
421C4×D3—128no—
422C2×C32C2×C4×D411yescharacteristic
423C2×C32#51811yescharacteristic
424C2×C32#51811yescharacteristic
425C2×C32#53511yescharacteristic
426C2×C32#53511yescharacteristic
427C2×C32#54011yescharacteristic
428C2×C32#54011yescharacteristic
429C3×D3—44no—
430C3×D3—44no—
431C24—32no—
432C24—32no—
433C2×D4—38no—
434C2×D4—94no—
435C2×D4—94no—
436C2×D4—98no—
437C2×D4—122no—
438C2×D4—122no—
439C2×D4—182no—
440C2×D4—182no—
441C2×D4—182no—
442C2×D4—182no—
443C2×D4—362no—
444C2×D4—362no—
445C22×C4—32no—
446C22×C4—32no—
447C22×C4—64no—
448C22×C4—91no—
449C22×C4—91no—
450C22×C4—91no—
451C22×C4—91no—
452C22×C4—122no—
453C22×C4—122no—
454C22×C4—184no—
455C22×C4—362no—
456C22×C4—362no—
457C22×C4C2×D3211yescharacteristic
458C22×C4C2×D3211yescharacteristic
459C22×C4C2×D3211yescharacteristic
460C4⋊C4—182no—
461C4⋊C4—182no—
462C22⋊C4—64no—
463C22⋊C4—122no—
464C22⋊C4—122no—
465C22⋊C4—184no—
466C22⋊C4—362no—
467C22⋊C4—362no—
468C42—94no—
469C42—94no—
470C42—182no—
471C22×C3—21no—
472C22×C3—21no—
473C22×C3—21no—
474C22×C3—21no—
475C22×C3—21no—
476C22×C3—21no—
477C22×C3—21no—
478C22×C3—64no—
479C22×C3—64no—
480C22×C3—64no—
481C22×C3—64no—
482C22×C3—64no—
483C22×C3—64no—
484C22×C3—122no—
485C22×C3—122no—
486C22×C3—122no—
487C22×C3—122no—
488C22×C3—122no—
489C22×C3—122no—
490C22×C3—122no—
491C22×C3—122no—
492C22×C3C22×C4×D312yes—
493C22×C3C2×D3×D412yes—
494C22×C3#100412yes—
495C22×C3#100412yes—
496C22×C3#100412yes—
497C22×C3D3×#4112yes—
498C22×C3#100912yes—
499C2×D3—24no—
500C2×D3—24no—
501C2×D3—24no—
502C2×D3—24no—
503C2×D3—24no—
504C2×D3—24no—
505C2×D3—42no—
506C2×D3—42no—
507C2×D3—42no—
508C2×D3—42no—
509C2×D3—42no—
510C2×D3—42no—
511C2×D3—42no—
512C2×D3—42no—
513C3×C4—24no—
514C3×C4—24no—
515C3×C4—42no—
516C3×C4—42no—
517C3×C4—42no—
518C3×C4—42no—
519C3×C4—122no—
520C3×C4—122no—
521Dic3—38no—
522Dic3—42no—
523Dic3—42no—
524Dic3—64no—
525Dic3—64no—
526Dic3—64no—
527Dic3—122no—
528Dic3—122no—
529Dic3—122no—
530Dic3—122no—
531C32#232811yescharacteristic, complemented, Sylow
532C23—34no—
533C23—34no—
534C23—62no—
535C23—62no—
536C23—62no—
537C23—62no—
538C23—62no—
539C23—62no—
540C23—62no—
541C23—62no—
542C23—62no—
543C23—62no—
544C23—62no—
545C23—62no—
546C23C22×D3211yescharacteristic
547D4—128no—
548D4—188no—
549D4—188no—
550D4—368no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—62no—
559C2×C4—62no—
560C2×C4—62no—
561C2×C4—62no—
562C2×C4—62no—
563C2×C4—62no—
564C2×C4—92no—
565C2×C4—92no—
566C2×C4—92no—
567C2×C4—92no—
568C2×C4—92no—
569C2×C4—128no—
570C2×C4—181no—
571C2×C4—181no—
572C2×C4—181no—
573C2×C4—181no—
574C2×C4—181no—
575C2×C4—181no—
576C2×C4—181no—
577C2×C4—368no—
578C2×C4C4×D3212yes—
579C2×C4#380212yes—
580C2×C3—21no—
581C2×C3—21no—
582C2×C3—21no—
583C2×C3—21no—
584C2×C3—21no—
585C2×C3—21no—
586C2×C3—21no—
587C2×C3—124no—
588C2×C3—124no—
589C2×C3#548612yes—
590C2×C3C4×D3×D412yes—
591C2×C3#554512yes—
592C2×C3#559212yes—
593C2×C3#560712yes—
594C2×C3#561512yes—
595C2×C3#566312yes—
596D3—44no—
597D3—44no—
598C22—64no—
599C22—64no—
600C22—64no—
601C22—64no—
602C22—64no—
603C22—64no—
604C22—122no—
605C22—122no—
606C22—122no—
607C22—122no—
608C22—122no—
609C22—122no—
610C22—122no—
611C22—122no—
612C22C2×C4×D3211yescharacteristic
613C22C2×#380211yescharacteristic
614C22#6430611yescharacteristic
615C22#6431311yescharacteristic
616C22#6431311yescharacteristic
617C22#6431311yescharacteristic
618C22#6432011yescharacteristic
619C4—22no—
620C4—22no—
621C4—41no—
622C4—94no—
623C4—122no—
624C4—122no—
625C4—182no—
626C4—182no—
627C4—361no—
628C3—21no—
629C3#7466712yescomplemented
630C2—124no—
631C2—124no—
632C2C4×#380211yescharacteristic
633C2#1059418111yescharacteristic
634C2#1059419211yescharacteristic
635C2#1059422311yescharacteristic
636C2#1059456811yescharacteristic
637C2#1059460611yescharacteristic
638C2#1059463411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC2×#63914C2
hypercenter#95D32
hypocenterC32#2328
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C2×#63902C2semidirect
3. C2×C4×#625C2semidirect
4. #10592347C2semidirect
5. C3×#4665C2semidirect
6. #10591385C2semidirect
7. #10591385C2semidirect
8. #10591381C2semidirect
9. #10591376C2semidirect
10. #10591363C2semidirect
11. #10591360C2semidirect
30. #63914C4semidirect
51. #4665D3semidirect
68. C2×C3×D12C2×C4semidirect
78. C2×#625C2×C4semidirect
79. C2×#625C2×C4semidirect
80. C2×#625C2×C4semidirect
85. C4×C3⋊Dic3C2×C4semidirect
86. C4×C3⋊Dic3D4semidirect
245. C2×D12C4×D3semidirect
531. C32#2328semidirect
629. C3#74667semidirect

Maximal subgroups

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

subgroupindex
C2×#639142
C2×#639022
C2×C4×#6252
#105923472
C3×#46652
#105913852
#105913812
#105913762
#105913632
#105913602
#746673