Finite Group Databasebeta

← #11784823

Subgroups — #11784823

Order 1152.

1445 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1004C211yesmaximal, characteristic
2C2×#63661C211yesmaximal, characteristic, complemented
3C3×#5220C211yesmaximal, characteristic, complemented
4#10591710C212yesmaximal, complemented
5C2×#63580C212yesmaximal, complemented
6#72142—31nomaximal
7#69598—31nomaximal
8C22×C32×D4C2211yescharacteristic
9C22×C3×#67—21no—
10C22×C3×#67C2212yes—
11C23×C3×Dic3C2211yescharacteristic, complemented
12C3×#1004—22no—
13C3×#1004—24no—
14C3×#1004C414yescomplemented
15C2×C3×#237—22no—
16C2×C3×D3×D4—22no—
17C2×C3×#235—21no—
18C2×#3757C2212yescomplemented
19C2×C3×#217—21no—
20C2×C3×#217C2211yescharacteristic, complemented
21C2×(C2×D3)⋊Dic3—22no—
22#63661—22no—
23C3×C3⋊#95—21no—
24#63580—24no—
25#63579—22no—
26C2×C3×H(5,𝔽2)—31no—
27C2×#1004D311yescharacteristic
28C3×#386—31no—
29#5220—32no—
30#5220D311yescharacteristic, complemented
31C2×#834—31no—
32C2×#834—31no—
33C2×#834—32no—
34C2×#834—61no—
35#5213—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—22no—
47C2×C3×#67—22no—
48C2×C3×#67—24no—
49C2×C3×#67—24no—
50C2×C3×#67—22no—
51C2×C3×#67—22no—
52C2×C3×#67—22no—
53C2×C3×#67—22no—
54C2×C3×#67C2×C414yes—
55C2×C3×#67D414yes—
56C22×C3×Dic3—21no—
57C22×C3×Dic3—21no—
58C22×C3×Dic3—22no—
59C22×C3×Dic3—21no—
60C22×C3×Dic3—42no—
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—22no—
73C3×#217—22no—
74C3×#217—42no—
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
88C23×C3×C4—31no—
89C22×#67—21no—
90C22×#67C2×D312yes—
91C23×Dic3C2×D311yescharacteristic, complemented
92#1004—22no—
93#1004—24no—
94#1004Dic314yescomplemented
95C2×#237—22no—
96C2×D3×D4—22no—
97C2×#235—21no—
98C2×C3×C22⋊C4—31no—
99C2×C3×C22⋊C4—61no—
100C2×#217—21no—
101C2×#217—32no—
102C2×#217—32no—
103C2×#217—62no—
104C2×#217—62no—
105C2×#217C2×D311yescharacteristic, complemented
106C2×(C2×D3)⋊C4—62no—
107C3×#95—61no—
108#834—64no—
109#834—64no—
110#834—62no—
111#834—62no—
112C3⋊#95—21no—
113C3⋊#95—62no—
114C3⋊#95—62no—
115#806—64no—
116C23×C32—21no—
117C23×C32—21no—
118C23×C32—41no—
119C23×C32—41no—
120C23×C32—41no—
121C23×C32—41no—
122C23×C32C22⋊C412yescomplemented
123C23×C32C22×C411yescharacteristic
124C23×C32C2×D411yescharacteristic
125C23×C32C2×D412yes—
126C23×C32C2×D412yes—
127C23×C32C2×D411yescharacteristic
128C22×C3×D3—22no—
129C22×C3×D3—24no—
130C22×C3×D3—22no—
131C22×C3×D3—42no—
132C22×C3×D3—42no—
133C22×C3×D3—81no—
134C22×C3×D3—81no—
135C22×C3×D3C22⋊C414yescomplemented
136C32×D4—24no—
137C32×D4—24no—
138C2×C32×C4—21no—
139C2×C32×C4—21no—
140C2×C32×C4C22⋊C412yescomplemented
141C2×C3⋊Dic3—42no—
142C2×C3⋊Dic3—42no—
143C2×C3⋊Dic3—42no—
144C3×#67—28no—
145C3×#67—24no—
146C3×#67—24no—
147C3×#67—24no—
148C3×#67—24no—
149C2×C3×Dic3—24no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—24no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—41no—
155C2×C3×Dic3—42no—
156C2×C3×Dic3—41no—
157C2×C3×Dic3—41no—
158C2×C3×Dic3—41no—
159C2×C3×Dic3—41no—
160C2×C3×Dic3C22⋊C414yescomplemented
161C3×D12—24no—
162C3×C4×D3—28no—
163C3×Dic6—24no—
164C2×H(5,𝔽2)—31no—
165C2×#99—92no—
166C2×#99—91no—
167#386—31no—
168#386—92no—
169C24×C3—21no—
170C24×C3—21no—
171C24×C3—32no—
172C24×C3—61no—
173C24×C3#6711yescharacteristic
174C24×C3#6711yescharacteristic
175C24×C3C22×D311yescharacteristic
176C24×C3C22×D311yescharacteristic
177C23×D3—21no—
178C23×D3#6712yes—
179C3×#41—64no—
180C3×#41—68no—
181C3×#41—68no—
182C3×#41—64no—
183C2×C3×Q8—61no—
184C2×C3×D4—22no—
185C2×C3×D4—22no—
186C2×C3×D4—22no—
187C2×C3×D4—22no—
188C2×C3×D4—22no—
189C2×C3×D4—22no—
190C2×C3×D4—34no—
191C2×C3×D4—34no—
192C2×C3×D4—42no—
193C2×C3×D4—42no—
194C2×C3×D4—61no—
195C2×C3×D4—68no—
196C2×C3×D4—68no—
197C2×C3×D4—62no—
198C2×C3×D4—64no—
199C2×C3×D4—64no—
200C2×C3×D4—62no—
201C2×C3×D4—62no—
202C2×C3×D4—62no—
203C2×C3×D4—62no—
204C2×C3×D4C4×D312yes—
205C2×C3×D4D1212yes—
206C2×C3×D4C2×Dic312yes—
207C2×C3×D4#6712yes—
208C22×C3×C4—21no—
209C22×C3×C4—32no—
210C22×C3×C4—62no—
211C22×C3×C4—61no—
212C22×C3×C4—62no—
213C22×C3×C4—61no—
214C22×C3×C4—61no—
215C22×C3×C4—122no—
216C22×C3×C4#6711yescharacteristic
217C22×C3×C4#6711yescharacteristic
218C2×#67—22no—
219C2×#67—24no—
220C2×#67—24no—
221C2×#67—22no—
222C2×#67—22no—
223C2×#67—22no—
224C2×#67—22no—
225C2×#67C2×Dic314yes—
226C2×#67#6714yes—
227C22×Dic3—21no—
228C22×Dic3—22no—
229C22×Dic3—21no—
230C22×Dic3—21no—
231C22×Dic3—42no—
232C22×Dic3—62no—
233C22×Dic3—62no—
234C22×Dic3—122no—
235C22×Dic3#6712yes—
236#237—28no—
237#237—28no—
238D3×D4—28no—
239D3×D4—28no—
240#235—24no—
241#235—24no—
242C2×D12—21no—
243C2×C4×D3—22no—
244C2×Dic6—21no—
245C3×C22⋊C4—62no—
246C3×C22⋊C4—122no—
247#217—22no—
248#217—42no—
249#217—64no—
250#217—62no—
251#217—62no—
252#217—62no—
253#217—62no—
254#217—122no—
255#217—124no—
256(C2×D3)⋊C4—124no—
257C22×C32—21no—
258C22×C32—22no—
259C22×C32—21no—
260C22×C32—22no—
261C22×C32—22no—
262C22×C32—41no—
263C22×C32—41no—
264C22×C32—42no—
265C22×C32—42no—
266C22×C32—41no—
267C22×C32—41no—
268C22×C32—81no—
269C22×C32C2×C22⋊C412yes—
270C22×C32C2×C22⋊C411yescharacteristic
271C22×C32#12012yes—
272C22×C32#12011yescharacteristic
273C22×C32#12011yescharacteristic
274C2×C3×D3—24no—
275C2×C3×D3—42no—
276C2×C3×D3—42no—
277C2×C3×D3—44no—
278C2×C3×D3—82no—
279C2×C3×D3—84no—
280C32×C4—22no—
281C3⋊Dic3—82no—
282C3×Dic3—24no—
283C3×Dic3—42no—
284C3×Dic3—81no—
285H(5,𝔽2)—34no—
286H(5,𝔽2)—64no—
287H(5,𝔽2)—62no—
288C2×#41—62no—
289C2×#41—61no—
290C22×D4—32no—
291C22×D4—62no—
292C22×D4—61no—
293C22×D4D3211yescharacteristic
294C23×C4—31no—
295C2×C22⋊C4—31no—
296C2×C22⋊C4—61no—
297C2×C22⋊C4—92no—
298C2×C22⋊C4—182no—
299#99—184no—
300#99—182no—
301#95—61no—
302#95—182no—
303C23×C3—21no—
304C23×C3—21no—
305C23×C3—21no—
306C23×C3—21no—
307C23×C3—22no—
308C23×C3—21no—
309C23×C3—21no—
310C23×C3—21no—
311C23×C3—22no—
312C23×C3—22no—
313C23×C3—34no—
314C23×C3—41no—
315C23×C3—41no—
316C23×C3—41no—
317C23×C3—41no—
318C23×C3—41no—
319C23×C3—41no—
320C23×C3—41no—
321C23×C3—41no—
322C23×C3—41no—
323C23×C3—41no—
324C23×C3—64no—
325C23×C3—62no—
326C23×C3—62no—
327C23×C3—81no—
328C23×C3—81no—
329C23×C3—81no—
330C23×C3—81no—
331C23×C3—122no—
332C23×C3—122no—
333C23×C3—241no—
334C23×C3—241no—
335C23×C3(C2×D3)⋊C412yescomplemented
336C23×C3#21712yescomplemented
337C23×C3C2×C4×D311yescharacteristic
338C23×C3C2×D1211yescharacteristic
339C23×C3D3×D412yes—
340C23×C3D3×D412yes—
341C23×C3C22×Dic311yescharacteristic
342C23×C3C2×#6711yescharacteristic
343C23×C3C2×#6711yescharacteristic
344C23×C3C2×#6711yescharacteristic
345C23×C3C2×#6712yes—
346C23×C3C2×#6712yes—
347C22×D3—22no—
348C22×D3—24no—
349C22×D3—22no—
350C22×D3—42no—
351C22×D3—42no—
352C22×D3—81no—
353C22×D3—81no—
354C22×D3#21714yescomplemented
355C3×Q8—64no—
356C3×D4—24no—
357C3×D4—24no—
358C3×D4—24no—
359C3×D4—24no—
360C3×D4—44no—
361C3×D4—44no—
362C3×D4—64no—
363C3×D4—68no—
364C3×D4—64no—
365C3×D4—64no—
366C3×D4—64no—
367C3×D4—64no—
368C2×C3×C4—21no—
369C2×C3×C4—21no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—22no—
373C2×C3×C4—34no—
374C2×C3×C4—41no—
375C2×C3×C4—41no—
376C2×C3×C4—68no—
377C2×C3×C4—64no—
378C2×C3×C4—62no—
379C2×C3×C4—62no—
380C2×C3×C4—64no—
381C2×C3×C4—62no—
382C2×C3×C4—122no—
383C2×C3×C4—121no—
384C2×C3×C4—121no—
385C2×C3×C4—121no—
386C2×C3×C4—121no—
387C2×C3×C4—121no—
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—22no—
399C2×Dic3—24no—
400C2×Dic3—41no—
401C2×Dic3—42no—
402C2×Dic3—41no—
403C2×Dic3—41no—
404C2×Dic3—41no—
405C2×Dic3—41no—
406C2×Dic3—122no—
407C2×Dic3—124no—
408C2×Dic3—122no—
409C2×Dic3—122no—
410C2×Dic3—122no—
411C2×Dic3—122no—
412C2×Dic3—122no—
413C2×Dic3—242no—
414C2×Dic3—242no—
415C2×Dic3#21714yescomplemented
416D12—24no—
417C4×D3—28no—
418Dic6—24no—
419C2×C32—21no—
420C2×C32—22no—
421C2×C32—22no—
422C2×C32—21no—
423C2×C32—42no—
424C2×C32#37911yescharacteristic
425C2×C32B(4,𝔽2)11yescharacteristic
426C2×C32#45811yescharacteristic
427C3×D3—44no—
428C24—32no—
429C24—61no—
430C24#62511yescharacteristic
431C24C2×D3211yescharacteristic
432#41—64no—
433#41—68no—
434#41—68no—
435#41—64no—
436C2×Q8—61no—
437C2×D4—22no—
438C2×D4—22no—
439C2×D4—34no—
440C2×D4—34no—
441C2×D4—61no—
442C2×D4—68no—
443C2×D4—68no—
444C2×D4—62no—
445C2×D4—64no—
446C2×D4—64no—
447C2×D4—62no—
448C2×D4—62no—
449C2×D4—62no—
450C2×D4—62no—
451C2×D4D3×Dic312yes—
452C2×D4#62612yes—
453C22×C4—32no—
454C22×C4—62no—
455C22×C4—61no—
456C22×C4—61no—
457C22×C4—62no—
458C22×C4—61no—
459C22×C4—122no—
460C22×C4—182no—
461C22×C4#62511yescharacteristic
462C22⋊C4—62no—
463C22⋊C4—122no—
464C22⋊C4—182no—
465C22⋊C4—182no—
466C22⋊C4—364no—
467C22×C3—22no—
468C22×C3—21no—
469C22×C3—22no—
470C22×C3—21no—
471C22×C3—21no—
472C22×C3—22no—
473C22×C3—21no—
474C22×C3—22no—
475C22×C3—22no—
476C22×C3—22no—
477C22×C3—21no—
478C22×C3—22no—
479C22×C3—21no—
480C22×C3—21no—
481C22×C3—22no—
482C22×C3—42no—
483C22×C3—42no—
484C22×C3—41no—
485C22×C3—41no—
486C22×C3—42no—
487C22×C3—41no—
488C22×C3—41no—
489C22×C3—42no—
490C22×C3—41no—
491C22×C3—41no—
492C22×C3—42no—
493C22×C3—42no—
494C22×C3—42no—
495C22×C3—41no—
496C22×C3—41no—
497C22×C3—41no—
498C22×C3—41no—
499C22×C3—64no—
500C22×C3—81no—
501C22×C3—81no—
502C22×C3—81no—
503C22×C3—81no—
504C22×C3—82no—
505C22×C3—82no—
506C22×C3—81no—
507C22×C3—81no—
508C22×C3—82no—
509C22×C3—124no—
510C22×C3—122no—
511C22×C3—122no—
512C22×C3—242no—
513C22×C3—244no—
514C22×C3D3×C22⋊C412yes—
515C22×C3#88212yes—
516C22×C3C2×(C2×D3)⋊C411yescharacteristic
517C22×C3#93711yescharacteristic
518C22×C3#93711yescharacteristic
519C22×C3C2×#21711yescharacteristic
520C22×C3C2×#21712yes—
521C22×C3#95311yescharacteristic
522C22×C3#95311yescharacteristic
523C22×C3#95312yes—
524C2×D3—24no—
525C2×D3—42no—
526C2×D3—42no—
527C2×D3—44no—
528C2×D3—82no—
529C2×D3—84no—
530C3×C4—22no—
531C3×C4—22no—
532C3×C4—42no—
533C3×C4—64no—
534C3×C4—122no—
535C3×C4—241no—
536Dic3—24no—
537Dic3—42no—
538Dic3—81no—
539Dic3—242no—
540Dic3—242no—
541Dic3—244no—
542C32#179011yescharacteristic, complemented, Sylow
543C23—21no—
544C23—21no—
545C23—34no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23—41no—
550C23—64no—
551C23—62no—
552C23—62no—
553C23—122no—
554C23—122no—
555C23—241no—
556C23—241no—
557C23(C2×D3)⋊Dic312yescomplemented
558C23C2×D3×Dic311yescharacteristic
559C23C2×#62511yescharacteristic
560C23C2×#62611yescharacteristic
561C23D3×#6712yes—
562C23D3×#6712yes—
563Q8—64no—
564D4—24no—
565D4—24no—
566D4—64no—
567D4—68no—
568D4—64no—
569D4—64no—
570D4—64no—
571D4—64no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—34no—
575C2×C4—68no—
576C2×C4—64no—
577C2×C4—62no—
578C2×C4—62no—
579C2×C4—62no—
580C2×C4—64no—
581C2×C4—121no—
582C2×C4—122no—
583C2×C4—121no—
584C2×C4—121no—
585C2×C4—121no—
586C2×C4—121no—
587C2×C4—362no—
588C2×C4—362no—
589C2×C4—362no—
590C2×C4(C2×D3)⋊Dic312yescomplemented
591C2×C3—22no—
592C2×C3—21no—
593C2×C3—22no—
594C2×C3—21no—
595C2×C3—21no—
596C2×C3—22no—
597C2×C3—21no—
598C2×C3—22no—
599C2×C3—21no—
600C2×C3—21no—
601C2×C3—21no—
602C2×C3—42no—
603C2×C3—41no—
604C2×C3—41no—
605C2×C3—42no—
606C2×C3—42no—
607C2×C3—42no—
608C2×C3—82no—
609C2×C3—124no—
610C2×C3#495511yescharacteristic
611C2×C3#503211yescharacteristic
612C2×C3#505311yescharacteristic
613C2×C3#524311yescharacteristic
614C2×C3#524411yescharacteristic
615C2×C3#524711yescharacteristic
616D3—44no—
617C22—21no—
618C22—22no—
619C22—21no—
620C22—22no—
621C22—22no—
622C22—41no—
623C22—41no—
624C22—42no—
625C22—42no—
626C22—41no—
627C22—41no—
628C22—64no—
629C22—81no—
630C22—124no—
631C22—122no—
632C22—122no—
633C22—242no—
634C22—244no—
635C22C2×(C2×D3)⋊Dic311yescharacteristic
636C22D3×#21712yes—
637C22#6397611yescharacteristic
638C22#6397611yescharacteristic
639C22#6397712yes—
640C4—22no—
641C4—64no—
642C4—122no—
643C4—241no—
644C4—722no—
645C3—21no—
646C3#6959811yescharacteristic, complemented
647C3#7214211yescharacteristic, complemented
648C2—21no—
649C2—22no—
650C2—21no—
651C2—22no—
652C2—42no—
653C2—124no—
654C2#1059153011yescharacteristic
655C2#1059153311yescharacteristic
656C2#1059170611yescharacteristic
subgroupG/H
centerC22#63976
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. C2×#63661C2semidirect
3. C3×#5220C2semidirect
4. #10591710C2semidirect
5. C2×#63580C2semidirect
11. C23×C3×Dic3C22semidirect
14. C3×#1004C4semidirect
18. C2×#3757C22semidirect
20. C2×C3×#217C22semidirect
30. #5220D3semidirect
91. C23×Dic3C2×D3semidirect
94. #1004Dic3semidirect
105. C2×#217C2×D3semidirect
122. C23×C32C22⋊C4semidirect
135. C22×C3×D3C22⋊C4semidirect
140. C2×C32×C4C22⋊C4semidirect
160. C2×C3×Dic3C22⋊C4semidirect
335. C23×C3(C2×D3)⋊C4semidirect
336. C23×C3#217semidirect
354. C22×D3#217semidirect
388. C2×C3×C4(C2×D3)⋊C4semidirect
389. C2×C3×C4#217semidirect
415. C2×Dic3#217semidirect
542. C32#1790semidirect
557. C23(C2×D3)⋊Dic3semidirect
590. C2×C4(C2×D3)⋊Dic3semidirect
646. C3#69598semidirect
647. 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
C2×#636612
C3×#52202
#105917102
C2×#635802
#721423
#695983