Finite Group Databasebeta

← #11784903

Subgroups — #11784903

Order 1152.

1189 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1010C211yesmaximal, characteristic
2C2×#63664C211yesmaximal, characteristic, complemented
3C3×#5232C211yesmaximal, characteristic, complemented
4#10591221C211yesmaximal, characteristic, complemented
5C2×#63568C211yesmaximal, characteristic, complemented
6#10591087C211yesmaximal, characteristic, complemented
7C2×#63560C211yesmaximal, characteristic, complemented
8#72143—31nomaximal
9#70308—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C3×#1010—22no—
12C3×#1010—22no—
13C3×#1010—22no—
14C3×#1010C414yescomplemented
15C2×C3×D3×Q8—21no—
16C2×C3×#237—21no—
17C2×C3×#237—22no—
18C2×C3×#235—21no—
19C2×C3×#235C2211yescharacteristic
20C22×C3×Dic6—21no—
21C22×C3×Dic6C2211yescharacteristic
22C2×C4×C3⋊Dic3C2211yescharacteristic
23C2×#3748C2211yescharacteristic
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×#208C2211yescharacteristic
26#63664—22no—
27C3×#835—21no—
28C3×#832—21no—
29#63579—22no—
30#63568—22no—
31#63565—21no—
32#63562—21no—
33#63560—22no—
34C2×C3×2−1+4—31no—
35C2×#1010D311yescharacteristic
36C3×#417—31no—
37C2×#837—31no—
38C2×#837—31no—
39C2×#837—31no—
40C2×#837—61no—
41#5232—31no—
42#5232D311yescharacteristic, complemented
43#5229—31no—
44C2×#836—31no—
45C2×#825—31no—
46C2×#824—31no—
47#4973—31no—
48#4966—31no—
49C32×#41—21no—
50C32×#41—21no—
51C32×#41C2×C412yes—
52C32×#41D412yes—
53C2×C32×Q8D411yescharacteristic
54C2×C32×D4—21no—
55C2×C32×D4D411yescharacteristic
56C22×C32×C4—21no—
57C22×C32×C4C2311yescharacteristic
58C22×C3⋊Dic3—21no—
59C2×C3×#67—22no—
60C2×C3×#67—21no—
61C22×C3×Dic3—22no—
62C22×C3×Dic3—21no—
63C22×C3×Dic3D412yes—
64C3×D3×Q8—24no—
65C3×D3×Q8—24no—
66C3×#237—28no—
67C3×#237—24no—
68C3×#237—24no—
69C3×#237—28no—
70C3×#235—24no—
71C3×#235—21no—
72C3×#235—21no—
73C3×#235—24no—
74C3×#235C2×C412yes—
75C3×#235D412yes—
76C2×C3×D12D411yescharacteristic
77C2×C3×C4×D3—22no—
78C2×C3×C4×D3—21no—
79C2×C3×Dic6—22no—
80C2×C3×Dic6—24no—
81C2×C3×Dic6—21no—
82C2×C3×Dic6—21no—
83C2×C3×Dic6—21no—
84C2×C3×Dic6—21no—
85C2×C3×Dic6—24no—
86C2×C3×Dic6C2×C412yes—
87C2×C3×Dic6D412yes—
88C2×C3×Dic6D411yescharacteristic
89C4×C3⋊Dic3—21no—
90C4×C3⋊Dic3—21no—
91#3748—21no—
92#3748—21no—
93C2×C3⋊(C3⋊C8)—21no—
94C3×C4⋊Dic3—21no—
95C3×C4⋊Dic3—21no—
96C3×#208—21no—
97C3×#208—21no—
98C2×C3×C3⋊C8—21no—
99#1793—91noSylow
100C3×2−1+4—34no—
101C3×2−1+4—62no—
102C3×2−1+4—62no—
103C3×2−1+4—62no—
104C2×C3×#41—21no—
105C2×C3×#41—31no—
106C2×C3×#41—61no—
107C2×C3×#41—62no—
108C2×C3×#41—61no—
109C2×C3×#41C2×D311yescharacteristic
110C2×C3×#41C2×D311yescharacteristic
111C22×C3×Q8—31no—
112C22×C3×Q8—61no—
113C22×C3×Q8—61no—
114#1010—22no—
115#1010—22no—
116#1010—22no—
117#1010Dic314yescomplemented
118C2×D3×Q8—21no—
119C2×#237—21no—
120C2×#237—22no—
121C2×#235—21no—
122C2×#235C2×D311yescharacteristic
123C22×Dic6—21no—
124C22×Dic6C2×D311yescharacteristic
125C2×C3×M16—31no—
126C2×C3×C4⋊C4—31no—
127C2×C4⋊Dic3C2×D311yescharacteristic
128C2×C4×Dic3—31no—
129C2×C4×Dic3—31no—
130C2×C4×Dic3—61no—
131C2×#208—31no—
132C2×#208—31no—
133C2×#208—61no—
134C2×#208C2×D311yescharacteristic
135C3×#103—61no—
136C3×#102—61no—
137#837—62no—
138#837—64no—
139#837—62no—
140#837—62no—
141#836—62no—
142#835—21no—
143#835—61no—
144#832—21no—
145#832—61no—
146C3⋊#95—62no—
147C3⋊#95—62no—
148#825—62no—
149#824—62no—
150#810—61no—
151#809—61no—
152C23×C32—21no—
153C23×C32C2×D411yescharacteristic
154C22×C3×D3—21no—
155C32×Q8—21no—
156C32×Q8C22⋊C412yes—
157C32×D4—22no—
158C32×D4—22no—
159C32×D4—21no—
160C32×D4C22⋊C412yes—
161C2×C32×C4—21no—
162C2×C32×C4—22no—
163C2×C32×C4—22no—
164C2×C32×C4C22×C411yescharacteristic
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2×D411yescharacteristic
170C2×C3⋊Dic3—22no—
171C2×C3⋊Dic3—41no—
172C2×C3⋊Dic3—41no—
173C3×#67—28no—
174C3×#67—22no—
175C3×#67—22no—
176C2×C3×Dic3—28no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—42no—
181C2×C3×Dic3—41no—
182C2×C3×Dic3C22⋊C414yes—
183C3×D12—21no—
184C3×D12C22⋊C412yes—
185C3×C4×D3—28no—
186C3×C4×D3—22no—
187C3×C4×D3—22no—
188C3×Dic6—28no—
189C3×Dic6—22no—
190C3×Dic6—22no—
191C3×Dic6—22no—
192C3×Dic6—21no—
193C3×Dic6—22no—
194C3×Dic6C22⋊C412yes—
195C3⋊(C3⋊C8)—41no—
196C3×C3⋊C8—41no—
197C2×2−1+4—31no—
198C2×#104—91no—
199C2×#104—91no—
200#417—31no—
201#417—91no—
202C2×#101—91no—
203#391—91no—
204C3×#41—21no—
205C3×#41—21no—
206C3×#41—21no—
207C3×#41—21no—
208C3×#41—22no—
209C3×#41—22no—
210C3×#41—32no—
211C3×#41—32no—
212C3×#41—41no—
213C3×#41—41no—
214C3×#41—64no—
215C3×#41—64no—
216C3×#41—68no—
217C3×#41—68no—
218C3×#41—64no—
219C3×#41—64no—
220C3×#41—61no—
221C3×#41—61no—
222C3×#41C4×D312yes—
223C3×#41D1212yes—
224C3×#41C2×Dic312yes—
225C3×#41#6712yes—
226C2×C3×Q8—21no—
227C2×C3×Q8—32no—
228C2×C3×Q8—32no—
229C2×C3×Q8—31no—
230C2×C3×Q8—64no—
231C2×C3×Q8—62no—
232C2×C3×Q8—64no—
233C2×C3×Q8—64no—
234C2×C3×Q8—64no—
235C2×C3×Q8—61no—
236C2×C3×Q8—61no—
237C2×C3×Q8—61no—
238C2×C3×Q8—61no—
239C2×C3×Q8#6711yescharacteristic
240C2×C3×Q8#6711yescharacteristic
241C2×C3×D4—21no—
242C2×C3×D4—21no—
243C2×C3×D4—21no—
244C2×C3×D4—31no—
245C2×C3×D4—41no—
246C2×C3×D4—62no—
247C2×C3×D4—61no—
248C2×C3×D4#6711yescharacteristic
249C2×C3×D4#6711yescharacteristic
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—32no—
254C22×C3×C4—41no—
255C22×C3×C4—62no—
256C22×C3×C4—62no—
257C22×C3×C4—61no—
258C22×C3×C4—61no—
259C22×C3×C4C22×D311yescharacteristic
260C22×C3×C4C22×D311yescharacteristic
261C2×#67—22no—
262C2×#67—21no—
263C22×Dic3—22no—
264C22×Dic3—21no—
265C22×Dic3—61no—
266C22×Dic3—61no—
267C22×Dic3—121no—
268C22×Dic3#6712yes—
269D3×Q8—24no—
270D3×Q8—24no—
271#237—28no—
272#237—24no—
273#237—24no—
274#237—28no—
275#235—24no—
276#235—21no—
277#235—21no—
278#235—24no—
279#235C2×Dic312yes—
280#235#6712yes—
281C2×D12#6711yescharacteristic
282C2×C4×D3—22no—
283C2×C4×D3—21no—
284C2×Dic6—22no—
285C2×Dic6—24no—
286C2×Dic6—21no—
287C2×Dic6—21no—
288C2×Dic6—21no—
289C2×Dic6—21no—
290C2×Dic6—24no—
291C2×Dic6C2×Dic312yes—
292C2×Dic6#6712yes—
293C2×Dic6#6711yescharacteristic
294C3×M16—61no—
295C3×M16—61no—
296C2×C3×C8—61no—
297C3×C4⋊C4—61no—
298C3×C4⋊C4—61no—
299C4⋊Dic3—21no—
300C4⋊Dic3—21no—
301C4×Dic3—62no—
302C4×Dic3—61no—
303C4×Dic3—61no—
304C4×Dic3—61no—
305C4×Dic3—61no—
306C4×Dic3—121no—
307#208—21no—
308#208—21no—
309#208—62no—
310#208—61no—
311#208—61no—
312#208—61no—
313#208—61no—
314#208—121no—
315C2×C3⋊C8—21no—
316C2×C3⋊C8—61no—
317C2×C3⋊C8—61no—
318C2×C3⋊C8—121no—
319C22×C32—21no—
320C22×C32—21no—
321C22×C32—22no—
322C22×C32—41no—
323C22×C32—41no—
324C22×C32C2×C22⋊C411yescharacteristic
325C22×C32#12011yescharacteristic
326C22×C32#12011yescharacteristic
327C2×C3×D3—22no—
328C2×C3×D3—41no—
329C2×C3×D3—41no—
330C32×C4—22no—
331C32×C4C2×C22⋊C411yescharacteristic
332C32×C4C2×C22⋊C411yescharacteristic
333C32×C4#12011yescharacteristic
334C32×C4#12011yescharacteristic
335C3⋊Dic3—42no—
336C3×Dic3—24no—
337C3×Dic3—22no—
338C3×Dic3—81no—
3392−1+4—34no—
3402−1+4—62no—
3412−1+4—62no—
3422−1+4—62no—
343C2×#41—31no—
344C2×#41—61no—
345C2×#41—62no—
346C2×#41—61no—
347C2×#41D3211yescharacteristic
348C22×Q8—31no—
349C22×Q8—61no—
350C22×Q8—61no—
351C2×M16—31no—
352C2×M16—91no—
353C2×C4⋊C4—31no—
354C2×C42—91no—
355#104—182no—
356#104—182no—
357#103—61no—
358#103—181no—
359#102—61no—
360#102—181no—
361#101—182no—
362#95—182no—
363C23×C3—21no—
364C23×C3—21no—
365C23×C3—21no—
366C23×C3—41no—
367C23×C3—61no—
368C23×C3D3×D411yescharacteristic
369C23×C3C2×#6711yescharacteristic
370C22×D3—21no—
371C3×Q8—21no—
372C3×Q8—21no—
373C3×Q8—22no—
374C3×Q8—32no—
375C3×Q8—41no—
376C3×Q8—68no—
377C3×Q8—62no—
378C3×Q8—62no—
379C3×Q8—61no—
380C3×Q8—62no—
381C3×Q8—62no—
382C3×Q8(C2×D3)⋊C412yes—
383C3×Q8#21712yes—
384C3×D4—22no—
385C3×D4—22no—
386C3×D4—22no—
387C3×D4—22no—
388C3×D4—21no—
389C3×D4—21no—
390C3×D4—22no—
391C3×D4—32no—
392C3×D4—41no—
393C3×D4—42no—
394C3×D4—42no—
395C3×D4—68no—
396C3×D4—62no—
397C3×D4—62no—
398C3×D4—61no—
399C3×D4(C2×D3)⋊C412yes—
400C3×D4#21712yes—
401C2×C3×C4—21no—
402C2×C3×C4—21no—
403C2×C3×C4—22no—
404C2×C3×C4—22no—
405C2×C3×C4—22no—
406C2×C3×C4—22no—
407C2×C3×C4—21no—
408C2×C3×C4—21no—
409C2×C3×C4—21no—
410C2×C3×C4—21no—
411C2×C3×C4—21no—
412C2×C3×C4—21no—
413C2×C3×C4—34no—
414C2×C3×C4—42no—
415C2×C3×C4—42no—
416C2×C3×C4—41no—
417C2×C3×C4—68no—
418C2×C3×C4—68no—
419C2×C3×C4—62no—
420C2×C3×C4—62no—
421C2×C3×C4—61no—
422C2×C3×C4—62no—
423C2×C3×C4—62no—
424C2×C3×C4—122no—
425C2×C3×C4—121no—
426C2×C3×C4C2×C4×D311yescharacteristic
427C2×C3×C4C2×D1211yescharacteristic
428C2×C3×C4D3×D411yescharacteristic
429C2×C3×C4D3×D411yescharacteristic
430C2×C3×C4D3×D411yescharacteristic
431C2×C3×C4C22×Dic311yescharacteristic
432C2×C3×C4C2×#6711yescharacteristic
433C2×C3×C4C2×#6711yescharacteristic
434C2×C3×C4C2×#6711yescharacteristic
435C2×C3×C4C2×#6711yescharacteristic
436C2×C3×C4C2×#6711yescharacteristic
437C2×C3×C4C2×#6711yescharacteristic
438#67—28no—
439#67—22no—
440#67—22no—
441C2×Dic3—28no—
442C2×Dic3—22no—
443C2×Dic3—21no—
444C2×Dic3—22no—
445C2×Dic3—42no—
446C2×Dic3—41no—
447C2×Dic3—62no—
448C2×Dic3—62no—
449C2×Dic3—122no—
450C2×Dic3—122no—
451C2×Dic3—121no—
452C2×Dic3—121no—
453C2×Dic3—122no—
454C2×Dic3—121no—
455C2×Dic3—121no—
456C2×Dic3#21714yes—
457D12—21no—
458D12#21712yes—
459C4×D3—28no—
460C4×D3—22no—
461C4×D3—22no—
462Dic6—28no—
463Dic6—22no—
464Dic6—22no—
465Dic6—22no—
466Dic6—21no—
467Dic6—22no—
468Dic6#21712yes—
469C3×C8—121no—
470C3⋊C8—41no—
471C3⋊C8—122no—
472C3⋊C8—121no—
473C3⋊C8—121no—
474C2×C32—21no—
475C2×C32—21no—
476C2×C32—42no—
477C2×C32#37911yescharacteristic
478C2×C32#45411yescharacteristic
479C2×C32#45611yescharacteristic
480C3×D3—42no—
481#41—21no—
482#41—21no—
483#41—32no—
484#41—32no—
485#41—64no—
486#41—64no—
487#41—68no—
488#41—68no—
489#41—64no—
490#41—64no—
491#41—61no—
492#41—61no—
493#41D3×Dic312yes—
494#41#62612yes—
495C2×Q8—32no—
496C2×Q8—32no—
497C2×Q8—31no—
498C2×Q8—64no—
499C2×Q8—62no—
500C2×Q8—64no—
501C2×Q8—64no—
502C2×Q8—64no—
503C2×Q8—61no—
504C2×Q8—61no—
505C2×Q8—61no—
506C2×Q8—61no—
507C2×Q8#62511yescharacteristic
508C2×D4—21no—
509C2×D4—31no—
510C2×D4—62no—
511C2×D4—61no—
512C2×D4#62511yescharacteristic
513C22×C4—21no—
514C22×C4—32no—
515C22×C4—62no—
516C22×C4—62no—
517C22×C4—61no—
518C22×C4—61no—
519C22×C4—181no—
520C22×C4C2×D3211yescharacteristic
521M16—61no—
522M16—61no—
523M16—181no—
524M16—181no—
525C2×C8—61no—
526C2×C8—181no—
527C4⋊C4—61no—
528C4⋊C4—61no—
529C42—181no—
530C42—181no—
531C22×C3—21no—
532C22×C3—21no—
533C22×C3—21no—
534C22×C3—21no—
535C22×C3—22no—
536C22×C3—22no—
537C22×C3—21no—
538C22×C3—21no—
539C22×C3—21no—
540C22×C3—41no—
541C22×C3—41no—
542C22×C3—42no—
543C22×C3—41no—
544C22×C3—41no—
545C22×C3—41no—
546C22×C3—41no—
547C22×C3—62no—
548C22×C3—81no—
549C22×C3—81no—
550C22×C3—121no—
551C22×C3—121no—
552C22×C3D3×C22⋊C411yescharacteristic
553C22×C3#88211yescharacteristic
554C22×C3#93711yescharacteristic
555C22×C3C2×#21711yescharacteristic
556C22×C3#95311yescharacteristic
557C22×C3#95311yescharacteristic
558C2×D3—22no—
559C2×D3—41no—
560C2×D3—41no—
561C3×C4—22no—
562C3×C4—22no—
563C3×C4—21no—
564C3×C4—21no—
565C3×C4—21no—
566C3×C4—21no—
567C3×C4—42no—
568C3×C4—64no—
569C3×C4—62no—
570C3×C4—241no—
571C3×C4D3×C22⋊C411yescharacteristic
572C3×C4#88211yescharacteristic
573C3×C4C2×(C2×D3)⋊C411yescharacteristic
574C3×C4#93711yescharacteristic
575C3×C4C2×#21711yescharacteristic
576C3×C4C2×#21711yescharacteristic
577C3×C4#95311yescharacteristic
578C3×C4#95311yescharacteristic
579Dic3—24no—
580Dic3—22no—
581Dic3—81no—
582Dic3—122no—
583Dic3—122no—
584Dic3—124no—
585C32#179311yescharacteristic, complemented, Sylow
586C23—21no—
587C23—61no—
588C23D3×#6711yescharacteristic
589Q8—21no—
590Q8—32no—
591Q8—68no—
592Q8—62no—
593Q8—62no—
594Q8—62no—
595Q8—62no—
596Q8—61no—
597Q8(C2×D3)⋊Dic312yes—
598D4—22no—
599D4—22no—
600D4—21no—
601D4—32no—
602D4—68no—
603D4—62no—
604D4—62no—
605D4—61no—
606D4(C2×D3)⋊Dic312yes—
607C2×C4—21no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—34no—
611C2×C4—68no—
612C2×C4—68no—
613C2×C4—62no—
614C2×C4—61no—
615C2×C4—62no—
616C2×C4—62no—
617C2×C4—62no—
618C2×C4—122no—
619C2×C4—121no—
620C2×C4—182no—
621C2×C4—361no—
622C2×C4—361no—
623C2×C4C2×D3×Dic311yescharacteristic
624C2×C4C2×#62511yescharacteristic
625C2×C4C2×#62611yescharacteristic
626C2×C4D3×#6711yescharacteristic
627C2×C4D3×#6711yescharacteristic
628C2×C4D3×#6711yescharacteristic
629C8—121no—
630C8—361no—
631C2×C3—21no—
632C2×C3—21no—
633C2×C3—21no—
634C2×C3—21no—
635C2×C3—21no—
636C2×C3—21no—
637C2×C3—21no—
638C2×C3—41no—
639C2×C3—41no—
640C2×C3—42no—
641C2×C3—42no—
642C2×C3—82no—
643C2×C3—122no—
644C2×C3#495511yescharacteristic
645C2×C3#520111yescharacteristic
646C2×C3#520511yescharacteristic
647C2×C3#524511yescharacteristic
648C2×C3#524611yescharacteristic
649C2×C3#524711yescharacteristic
650D3—42no—
651C22—21no—
652C22—21no—
653C22—22no—
654C22—41no—
655C22—41no—
656C22—62no—
657C22—121no—
658C22—121no—
659C22D3×#21711yescharacteristic
660C22#6397611yescharacteristic
661C22#6397711yescharacteristic
662C4—22no—
663C4—64no—
664C4—62no—
665C4—241no—
666C4—362no—
667C4C2×(C2×D3)⋊Dic311yescharacteristic
668C4D3×#21711yescharacteristic
669C4#6397611yescharacteristic
670C4#6397711yescharacteristic
671C3—21no—
672C3#7030811yescharacteristic, complemented
673C3#7214311yescharacteristic, complemented
674C2—21no—
675C2—21no—
676C2—42no—
677C2—122no—
678C2#1059168411yescharacteristic
679C2#1059168711yescharacteristic
680C2#1059170611yescharacteristic
subgroupG/H
centerC22#63976
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×#41C22
socleC22×C32#120
prime radicalC2×C3×#1010C2
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1793
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C2×#63664C2semidirect
3. C3×#5232C2semidirect
4. #10591221C2semidirect
5. C2×#63568C2semidirect
6. #10591087C2semidirect
7. C2×#63560C2semidirect
14. C3×#1010C4semidirect
42. #5232D3semidirect
117. #1010Dic3semidirect
585. C32#1793semidirect
672. C3#70308semidirect
673. C3#72143semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10102
C2×#636642
C3×#52322
#105912212
C2×#635682
#105910872
C2×#635602
#721433
#703083