Finite Group Databasebeta

← #11784825

Subgroups — #11784825

Order 1152.

1483 conjugacy classes of subgroups.

The subgroup lattice has 669 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1004C211yesmaximal, characteristic
2#10592919C211yesmaximal, characteristic, complemented
3C2×C3×#834C211yesmaximal, characteristic, complemented
4#10591713C212yesmaximal, complemented
5C2×#63580C212yesmaximal, complemented
6#72142—31nomaximal
7#70033—31nomaximal
8C22×C32×D4C2211yescharacteristic
9C23×C3⋊Dic3C2211yescharacteristic, complemented
10C22×C3×#67—21no—
11C22×C3×#67C2212yes—
12C3×#1004—22no—
13C3×#1004—24no—
14C3×#1004C414yescomplemented
15C2×C3×#237—22no—
16C2×C3×D3×D4—22no—
17C2×C3×#235—21no—
18C2×#3757—21no—
19C2×#3757C2211yescharacteristic, complemented
20C2×C3×#217C2212yescomplemented
21C2×(C2×D3)⋊Dic3—22no—
22#63658—21no—
23C3×#834—22no—
24#63580—24no—
25#63579—22no—
26C2×C3×H(5,𝔽2)—31no—
27C2×#1004D311yescharacteristic
28C2×C3×#99—31no—
29#5220—31no—
30#5220—31no—
31#5220—32no—
32#5220—61no—
33C2×#834—32no—
34C2×#834D311yescharacteristic, complemented
35#4958—32no—
36C2×#806—32no—
37C24×C32D411yescharacteristic
38C24×C32C2311yescharacteristic
39C23×C3×D3—21no—
40C23×C3×D3D412yes—
41C2×C32×D4—22no—
42C2×C32×D4—22no—
43C2×C32×D4C2×C412yes—
44C2×C32×D4D412yes—
45C22×C32×C4D411yescharacteristic
46C22×C3⋊Dic3—21no—
47C22×C3⋊Dic3—22no—
48C22×C3⋊Dic3—21no—
49C22×C3⋊Dic3—42no—
50C2×C3×#67—22no—
51C2×C3×#67—24no—
52C2×C3×#67—24no—
53C2×C3×#67—22no—
54C2×C3×#67—22no—
55C2×C3×#67—22no—
56C2×C3×#67—22no—
57C2×C3×#67C2×C414yes—
58C2×C3×#67D414yes—
59C22×C3×Dic3—21no—
60C22×C3×Dic3—22no—
61C22×C3×Dic3D412yes—
62C3×#237—28no—
63C3×#237—28no—
64C3×D3×D4—28no—
65C3×D3×D4—28no—
66C3×#235—24no—
67C3×#235—24no—
68C2×C3×D12—21no—
69C2×C3×C4×D3—22no—
70C2×C3×Dic6—21no—
71#3757—22no—
72#3757—42no—
73C3×#217—22no—
74C3×#217—22no—
75(C2×D3)⋊Dic3—44no—
76#1790—91noSylow
77C3×H(5,𝔽2)—34no—
78C3×H(5,𝔽2)—64no—
79C3×H(5,𝔽2)—62no—
80C2×C3×#41—62no—
81C2×C3×#41—61no—
82C22×C3×D4—21no—
83C22×C3×D4—32no—
84C22×C3×D4—62no—
85C22×C3×D4—61no—
86C22×C3×D4C2×D311yescharacteristic
87C22×C3×D4C2×D311yescharacteristic
88C22×#67—21no—
89C22×#67C2×D312yes—
90C23×Dic3—31no—
91C23×Dic3—31no—
92C23×Dic3—61no—
93#1004—22no—
94#1004—24no—
95#1004Dic314yescomplemented
96C2×#237—22no—
97C2×D3×D4—22no—
98C2×#235—21no—
99C2×C3×C22⋊C4—32no—
100C2×#217—31no—
101C2×#217—31no—
102C2×#217—61no—
103C2×#217—62no—
104C2×#217—62no—
105C2×#217—61no—
106C2×#217—61no—
107C2×#217C2×D312yescomplemented
108C2×(C2×D3)⋊C4—62no—
109C3×#99—62no—
110#834—22no—
111#834—64no—
112C3⋊#95—62no—
113C3⋊#95—62no—
114C3⋊#95—61no—
115C3⋊#95—61no—
116C3⋊#95—62no—
117#806—64no—
118C23×C32—21no—
119C23×C32—21no—
120C23×C32—41no—
121C23×C32—41no—
122C23×C32—41no—
123C23×C32—41no—
124C23×C32C22⋊C412yescomplemented
125C23×C32C22×C411yescharacteristic
126C23×C32C2×D411yescharacteristic
127C23×C32C2×D412yes—
128C23×C32C2×D412yes—
129C23×C32C2×D411yescharacteristic
130C22×C3×D3—22no—
131C22×C3×D3—24no—
132C22×C3×D3—22no—
133C22×C3×D3—42no—
134C22×C3×D3—42no—
135C22×C3×D3—81no—
136C22×C3×D3—81no—
137C22×C3×D3C22⋊C414yescomplemented
138C32×D4—24no—
139C32×D4—24no—
140C2×C32×C4—21no—
141C2×C32×C4—21no—
142C2×C32×C4C22⋊C412yescomplemented
143C2×C3⋊Dic3—22no—
144C2×C3⋊Dic3—24no—
145C2×C3⋊Dic3—41no—
146C2×C3⋊Dic3—42no—
147C2×C3⋊Dic3—41no—
148C2×C3⋊Dic3—41no—
149C2×C3⋊Dic3—41no—
150C2×C3⋊Dic3—41no—
151C3×#67—28no—
152C3×#67—24no—
153C3×#67—24no—
154C3×#67—24no—
155C3×#67—24no—
156C2×C3×Dic3—24no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—22no—
159C2×C3×Dic3—42no—
160C2×C3×Dic3—42no—
161C2×C3×Dic3—42no—
162C2×C3×Dic3C22⋊C414yescomplemented
163C3×D12—24no—
164C3×C4×D3—28no—
165C3×Dic6—24no—
166C2×H(5,𝔽2)—31no—
167C2×#99—31no—
168C2×#99—92no—
169#386—92no—
170#386—91no—
171C24×C3—21no—
172C24×C3—21no—
173C24×C3—32no—
174C24×C3—61no—
175C24×C3D1211yescharacteristic
176C24×C3#6711yescharacteristic
177C24×C3C22×D311yescharacteristic
178C24×C3C22×D311yescharacteristic
179C23×D3—21no—
180C23×D3#6712yes—
181C3×#41—64no—
182C3×#41—68no—
183C3×#41—68no—
184C3×#41—64no—
185C2×C3×Q8—61no—
186C2×C3×D4—22no—
187C2×C3×D4—22no—
188C2×C3×D4—22no—
189C2×C3×D4—22no—
190C2×C3×D4—22no—
191C2×C3×D4—22no—
192C2×C3×D4—34no—
193C2×C3×D4—34no—
194C2×C3×D4—42no—
195C2×C3×D4—42no—
196C2×C3×D4—61no—
197C2×C3×D4—68no—
198C2×C3×D4—68no—
199C2×C3×D4—62no—
200C2×C3×D4—64no—
201C2×C3×D4—64no—
202C2×C3×D4—62no—
203C2×C3×D4—62no—
204C2×C3×D4—62no—
205C2×C3×D4—62no—
206C2×C3×D4C4×D312yes—
207C2×C3×D4C2×Dic312yes—
208C2×C3×D4#6712yes—
209C2×C3×D4#6712yes—
210C22×C3×C4—21no—
211C22×C3×C4—32no—
212C22×C3×C4—62no—
213C22×C3×C4—61no—
214C22×C3×C4—62no—
215C22×C3×C4D1211yescharacteristic
216C22×C3×C4#6711yescharacteristic
217C2×#67—22no—
218C2×#67—24no—
219C2×#67—24no—
220C2×#67—22no—
221C2×#67—22no—
222C2×#67—22no—
223C2×#67—22no—
224C2×#67C2×Dic314yes—
225C2×#67#6714yes—
226C22×Dic3—21no—
227C22×Dic3—22no—
228C22×Dic3—62no—
229C22×Dic3—61no—
230C22×Dic3—62no—
231C22×Dic3—62no—
232C22×Dic3—61no—
233C22×Dic3—62no—
234C22×Dic3—61no—
235C22×Dic3—61no—
236C22×Dic3—122no—
237C22×Dic3—122no—
238C22×Dic3—122no—
239C22×Dic3—124no—
240C22×Dic3#6712yes—
241#237—28no—
242#237—28no—
243D3×D4—28no—
244D3×D4—28no—
245#235—24no—
246#235—24no—
247C2×D12—21no—
248C2×C4×D3—22no—
249C2×Dic6—21no—
250C3×C22⋊C4—62no—
251C3×C22⋊C4—62no—
252#217—22no—
253#217—22no—
254#217—62no—
255#217—62no—
256#217—122no—
257#217—124no—
258#217—122no—
259#217—122no—
260#217—124no—
261(C2×D3)⋊C4—124no—
262C22×C32—21no—
263C22×C32—21no—
264C22×C32—22no—
265C22×C32—22no—
266C22×C32—22no—
267C22×C32—41no—
268C22×C32—42no—
269C22×C32—41no—
270C22×C32—42no—
271C22×C32—41no—
272C22×C32—41no—
273C22×C32—81no—
274C22×C32C2×C22⋊C412yes—
275C22×C32C2×C22⋊C411yescharacteristic
276C22×C32#12011yescharacteristic
277C22×C32#12011yescharacteristic
278C22×C32#12012yes—
279C2×C3×D3—24no—
280C2×C3×D3—42no—
281C2×C3×D3—42no—
282C2×C3×D3—44no—
283C2×C3×D3—82no—
284C2×C3×D3—84no—
285C32×C4—22no—
286C3⋊Dic3—42no—
287C3⋊Dic3—81no—
288C3×Dic3—24no—
289C3×Dic3—82no—
290H(5,𝔽2)—34no—
291H(5,𝔽2)—64no—
292H(5,𝔽2)—62no—
293C2×#41—62no—
294C2×#41—61no—
295C22×D4—32no—
296C22×D4—62no—
297C22×D4—61no—
298C22×D4D3211yescharacteristic
299C23×C4—91no—
300C2×C22⋊C4—32no—
301C2×C22⋊C4—91no—
302C2×C22⋊C4—182no—
303C2×C22⋊C4—181no—
304#99—62no—
305#99—184no—
306#95—182no—
307#95—181no—
308C23×C3—21no—
309C23×C3—21no—
310C23×C3—21no—
311C23×C3—21no—
312C23×C3—22no—
313C23×C3—21no—
314C23×C3—21no—
315C23×C3—21no—
316C23×C3—22no—
317C23×C3—22no—
318C23×C3—34no—
319C23×C3—41no—
320C23×C3—41no—
321C23×C3—41no—
322C23×C3—41no—
323C23×C3—41no—
324C23×C3—41no—
325C23×C3—42no—
326C23×C3—42no—
327C23×C3—41no—
328C23×C3—41no—
329C23×C3—41no—
330C23×C3—41no—
331C23×C3—42no—
332C23×C3—42no—
333C23×C3—64no—
334C23×C3—62no—
335C23×C3—62no—
336C23×C3—122no—
337C23×C3—122no—
338C23×C3—241no—
339C23×C3—241no—
340C23×C3(C2×D3)⋊C412yescomplemented
341C23×C3#21712yescomplemented
342C23×C3C2×C4×D311yescharacteristic
343C23×C3C2×D1211yescharacteristic
344C23×C3D3×D412yes—
345C23×C3D3×D412yes—
346C23×C3C22×Dic311yescharacteristic
347C23×C3C2×#6711yescharacteristic
348C23×C3C2×#6711yescharacteristic
349C23×C3C2×#6711yescharacteristic
350C23×C3C2×#6712yes—
351C23×C3C2×#6712yes—
352C22×D3—22no—
353C22×D3—24no—
354C22×D3—22no—
355C22×D3—42no—
356C22×D3—42no—
357C22×D3—81no—
358C22×D3—81no—
359C22×D3#21714yescomplemented
360C3×Q8—64no—
361C3×D4—24no—
362C3×D4—24no—
363C3×D4—24no—
364C3×D4—24no—
365C3×D4—44no—
366C3×D4—44no—
367C3×D4—64no—
368C3×D4—68no—
369C3×D4—64no—
370C3×D4—64no—
371C3×D4—64no—
372C3×D4—64no—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—21no—
377C2×C3×C4—22no—
378C2×C3×C4—34no—
379C2×C3×C4—41no—
380C2×C3×C4—41no—
381C2×C3×C4—68no—
382C2×C3×C4—64no—
383C2×C3×C4—62no—
384C2×C3×C4—62no—
385C2×C3×C4—122no—
386C2×C3×C4—122no—
387C2×C3×C4—122no—
388C2×C3×C4(C2×D3)⋊C412yescomplemented
389C2×C3×C4#21712yescomplemented
390#67—28no—
391#67—24no—
392#67—24no—
393#67—24no—
394#67—24no—
395C2×Dic3—24no—
396C2×Dic3—22no—
397C2×Dic3—22no—
398C2×Dic3—42no—
399C2×Dic3—42no—
400C2×Dic3—42no—
401C2×Dic3—64no—
402C2×Dic3—64no—
403C2×Dic3—62no—
404C2×Dic3—62no—
405C2×Dic3—64no—
406C2×Dic3—124no—
407C2×Dic3—122no—
408C2×Dic3—121no—
409C2×Dic3—122no—
410C2×Dic3—122no—
411C2×Dic3—121no—
412C2×Dic3—122no—
413C2×Dic3—124no—
414C2×Dic3—121no—
415C2×Dic3—121no—
416C2×Dic3—122no—
417C2×Dic3—121no—
418C2×Dic3—121no—
419C2×Dic3—122no—
420C2×Dic3—122no—
421C2×Dic3—121no—
422C2×Dic3—121no—
423C2×Dic3—121no—
424C2×Dic3—121no—
425C2×Dic3#21714yescomplemented
426D12—24no—
427C4×D3—28no—
428Dic6—24no—
429C2×C32—21no—
430C2×C32—21no—
431C2×C32—22no—
432C2×C32—22no—
433C2×C32—42no—
434C2×C32#37911yescharacteristic
435C2×C32B(4,𝔽2)11yescharacteristic
436C2×C32#45811yescharacteristic
437C3×D3—44no—
438C24—32no—
439C24—61no—
440C24#62611yescharacteristic
441C24C2×D3211yescharacteristic
442#41—64no—
443#41—68no—
444#41—68no—
445#41—64no—
446C2×Q8—61no—
447C2×D4—22no—
448C2×D4—22no—
449C2×D4—34no—
450C2×D4—34no—
451C2×D4—61no—
452C2×D4—68no—
453C2×D4—68no—
454C2×D4—62no—
455C2×D4—64no—
456C2×D4—64no—
457C2×D4—62no—
458C2×D4—62no—
459C2×D4—62no—
460C2×D4—62no—
461C2×D4D3×Dic312yes—
462C2×D4#62512yes—
463C22×C4—32no—
464C22×C4—62no—
465C22×C4—61no—
466C22×C4—62no—
467C22×C4—181no—
468C22×C4—182no—
469C22×C4—181no—
470C22×C4—362no—
471C22×C4#62611yescharacteristic
472C22⋊C4—62no—
473C22⋊C4—62no—
474C22⋊C4—182no—
475C22⋊C4—364no—
476C22⋊C4—362no—
477C22×C3—22no—
478C22×C3—22no—
479C22×C3—21no—
480C22×C3—22no—
481C22×C3—21no—
482C22×C3—22no—
483C22×C3—22no—
484C22×C3—21no—
485C22×C3—22no—
486C22×C3—21no—
487C22×C3—22no—
488C22×C3—22no—
489C22×C3—21no—
490C22×C3—22no—
491C22×C3—22no—
492C22×C3—21no—
493C22×C3—21no—
494C22×C3—42no—
495C22×C3—42no—
496C22×C3—42no—
497C22×C3—41no—
498C22×C3—42no—
499C22×C3—41no—
500C22×C3—41no—
501C22×C3—41no—
502C22×C3—42no—
503C22×C3—42no—
504C22×C3—42no—
505C22×C3—42no—
506C22×C3—42no—
507C22×C3—44no—
508C22×C3—44no—
509C22×C3—41no—
510C22×C3—41no—
511C22×C3—41no—
512C22×C3—41no—
513C22×C3—64no—
514C22×C3—81no—
515C22×C3—81no—
516C22×C3—81no—
517C22×C3—81no—
518C22×C3—82no—
519C22×C3—124no—
520C22×C3—122no—
521C22×C3—122no—
522C22×C3—242no—
523C22×C3—244no—
524C22×C3D3×C22⋊C412yes—
525C22×C3#88211yescharacteristic
526C22×C3#88211yescharacteristic
527C22×C3C2×(C2×D3)⋊C411yescharacteristic
528C22×C3#93712yes—
529C22×C3C2×#21711yescharacteristic
530C22×C3C2×#21712yes—
531C22×C3#95312yes—
532C22×C3#95311yescharacteristic
533C22×C3#95311yescharacteristic
534C2×D3—24no—
535C2×D3—42no—
536C2×D3—42no—
537C2×D3—44no—
538C2×D3—82no—
539C2×D3—84no—
540C3×C4—22no—
541C3×C4—22no—
542C3×C4—42no—
543C3×C4—64no—
544C3×C4—242no—
545Dic3—24no—
546Dic3—82no—
547Dic3—124no—
548Dic3—122no—
549Dic3—122no—
550Dic3—242no—
551Dic3—241no—
552Dic3—241no—
553C32#179011yescharacteristic, complemented, Sylow
554C23—21no—
555C23—21no—
556C23—34no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—64no—
562C23—62no—
563C23—62no—
564C23—122no—
565C23—122no—
566C23—241no—
567C23—241no—
568C23(C2×D3)⋊Dic312yescomplemented
569C23C2×D3×Dic311yescharacteristic
570C23C2×#62511yescharacteristic
571C23C2×#62611yescharacteristic
572C23D3×#6712yes—
573C23D3×#6712yes—
574Q8—64no—
575D4—24no—
576D4—24no—
577D4—64no—
578D4—68no—
579D4—64no—
580D4—64no—
581D4—64no—
582D4—64no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—34no—
586C2×C4—68no—
587C2×C4—64no—
588C2×C4—62no—
589C2×C4—62no—
590C2×C4—122no—
591C2×C4—122no—
592C2×C4—122no—
593C2×C4—182no—
594C2×C4—184no—
595C2×C4—362no—
596C2×C4—361no—
597C2×C4—361no—
598C2×C4—361no—
599C2×C4—361no—
600C2×C4—361no—
601C2×C4(C2×D3)⋊Dic312yescomplemented
602C2×C3—22no—
603C2×C3—22no—
604C2×C3—22no—
605C2×C3—21no—
606C2×C3—21no—
607C2×C3—22no—
608C2×C3—21no—
609C2×C3—22no—
610C2×C3—22no—
611C2×C3—21no—
612C2×C3—21no—
613C2×C3—21no—
614C2×C3—21no—
615C2×C3—42no—
616C2×C3—42no—
617C2×C3—42no—
618C2×C3—42no—
619C2×C3—82no—
620C2×C3—124no—
621C2×C3#474111yescharacteristic
622C2×C3#474211yescharacteristic
623C2×C3#495511yescharacteristic
624C2×C3#524311yescharacteristic
625C2×C3#524411yescharacteristic
626C2×C3#524711yescharacteristic
627D3—44no—
628C22—22no—
629C22—21no—
630C22—22no—
631C22—21no—
632C22—22no—
633C22—41no—
634C22—41no—
635C22—42no—
636C22—42no—
637C22—41no—
638C22—41no—
639C22—64no—
640C22—81no—
641C22—124no—
642C22—122no—
643C22—122no—
644C22—242no—
645C22—244no—
646C22C2×(C2×D3)⋊Dic311yescharacteristic
647C22D3×#21712yes—
648C22#6397612yes—
649C22#6397711yescharacteristic
650C22#6397711yescharacteristic
651C4—22no—
652C4—64no—
653C4—242no—
654C4—362no—
655C4—721no—
656C3—21no—
657C3#7003311yescharacteristic, complemented
658C3#7214211yescharacteristic, complemented
659C2—22no—
660C2—21no—
661C2—21no—
662C2—22no—
663C2—42no—
664C2—124no—
665C2#1059153111yescharacteristic
666C2#1059153411yescharacteristic
667C2#1059170611yescharacteristic
subgroupG/H
centerC22#63977
commutatorC23×C32C22×C4
FrattiniC24C2×D32
FittingC22×C32×D4C22
socleC22×C32#120
prime radicalC2×C3×#1004C2
cosocleC24×C32C23
hypercenterC22×D4D32
hypocenterC32#1790
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. #10592919C2semidirect
3. C2×C3×#834C2semidirect
4. #10591713C2semidirect
5. C2×#63580C2semidirect
9. C23×C3⋊Dic3C22semidirect
14. C3×#1004C4semidirect
19. C2×#3757C22semidirect
20. C2×C3×#217C22semidirect
34. C2×#834D3semidirect
95. #1004Dic3semidirect
107. C2×#217C2×D3semidirect
124. C23×C32C22⋊C4semidirect
137. C22×C3×D3C22⋊C4semidirect
142. C2×C32×C4C22⋊C4semidirect
162. C2×C3×Dic3C22⋊C4semidirect
340. C23×C3(C2×D3)⋊C4semidirect
341. C23×C3#217semidirect
359. C22×D3#217semidirect
388. C2×C3×C4(C2×D3)⋊C4semidirect
389. C2×C3×C4#217semidirect
425. C2×Dic3#217semidirect
553. C32#1790semidirect
568. C23(C2×D3)⋊Dic3semidirect
601. C2×C4(C2×D3)⋊Dic3semidirect
657. C3#70033semidirect
658. C3#72142semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10042
#105929192
C2×C3×#8342
#105917132
C2×#635802
#721423
#700333