Finite Group Databasebeta

← #11792409

Subgroups — #11792409

Order 1152.

865 conjugacy classes of subgroups.

The subgroup lattice has 689 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5828C211yesmaximal, characteristic, complemented
2C3×#5822C211yesmaximal, characteristic, complemented
3#10595022C211yesmaximal, characteristic, complemented
4#10592935C211yesmaximal, characteristic, complemented
5#10591111C211yesmaximal, characteristic, complemented
6#10591069C211yesmaximal, characteristic, complemented
7#10589158C211yesmaximal, characteristic, complemented
8#72118—31nomaximal
9#71715—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C22×C3×C4×D3C2211yescharacteristic
13#64135C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C3×#951—21no—
16C3×#950—22no—
17C3×#949—21no—
18C3×#946—21no—
19C3×#942—21no—
20C3×#938—21no—
21C3×#937—21no—
22C3×#935—21no—
23C3×#932—21no—
24C3×C4×#67—22no—
25C3×#926C2211yescharacteristic
26C2×C3×#208C2211yescharacteristic
27#63976—21no—
28#63961—21no—
29#63908—21no—
30C4×#625—22no—
31#63856—21no—
32#63664—22no—
33#63569—22no—
34(C2×D3)⋊(C3⋊C8)—22no—
35C3×#575—31no—
36C3×#525—31no—
37#5828—31no—
38#5828D311yescharacteristic, complemented
39#5822D311yescharacteristic, complemented
40#5791—31no—
41#5236—31no—
42#5236—31no—
43#5236—31no—
44#5236—61no—
45#5207—31no—
46#5126—31no—
47#5005—31no—
48#4557—31no—
49#4531—31no—
50C23×C3×D3D411yescharacteristic
51C32×#41—21no—
52C32×#41—21no—
53C32×#41—21no—
54C32×#41—21no—
55C2×C32×Q8D411yescharacteristic, complemented
56C2×C32×D4—21no—
57C2×C32×D4D411yescharacteristic, complemented
58C22×C32×C4—21no—
59C22×C32×C4C2311yescharacteristic
60C2×C3×#67—22no—
61C2×C3×#67—21no—
62C22×C3×Dic3D411yescharacteristic
63C3×#235—21no—
64C3×#235—21no—
65C3×#235—21no—
66C3×#235—21no—
67C2×C3×D12D411yescharacteristic, complemented
68C2×C3×C4×D3—21no—
69C2×C3×C4×D3—21no—
70C2×C3×C4×D3—21no—
71C2×C3×C4×D3—21no—
72C2×C3×C4×D3—21no—
73C2×C3×C4×D3—21no—
74C2×C3×C4×D3—21no—
75C2×C3×Dic6D411yescharacteristic, complemented
76C2×#625—22no—
77#3757—21no—
78C4⋊(C3⋊Dic3)—21no—
79C4×C3⋊Dic3D412yescomplemented
80#3748—21no—
81#3748—21no—
82C2×C3⋊(C3⋊C8)—21no—
83C3×#217—22no—
84C3×#217—21no—
85C3×#216—22no—
86C3×#215—22no—
87C3×#214—22no—
88C3×#213—22no—
89C3×(C2×D3)⋊C4—22no—
90C3×C4⋊Dic3—21no—
91C3×Dic3⋊C4—22no—
92C3×C4×Dic3D412yescomplemented
93C3×#208—21no—
94C3×#208—21no—
95C2×C3×C3⋊C8D412yescomplemented
96#3724—22no—
97(C2×D3)⋊Dic3—22no—
98(C2×D3)⋊Dic3—22no—
99#2010—91noSylow
100C2×C3×#41—21no—
101C2×C3×#41—31no—
102C2×C3×#41C2×D311yescharacteristic
103C2×C3×#41C2×D311yescharacteristic
104C23×C3×C4—31no—
105C2×#235C2×D311yescharacteristic
106C22×C4×D3C2×D311yescharacteristic
107C3×#137—61no—
108C3×#137—61no—
109C3×AGL(1,ℤ/8)—61no—
110C3×AGL(1,ℤ/8)—61no—
111C3×#135—62no—
112C2×C3×M16—31no—
113C3×#123—61no—
114C3×C22⋊Q8—61no—
115C3×#121—61no—
116C3×#120—61no—
117C3×C4×D4—62no—
118C3×#117—31no—
119#953—61no—
120#951—21no—
121#950—22no—
122#949—21no—
123#946—21no—
124#946—61no—
125#942—21no—
126#938—21no—
127#938—61no—
128#937—21no—
129#937—61no—
130#935—21no—
131#935—61no—
132#932—21no—
133#930—61no—
134#929—61no—
135C4×#67—22no—
136C4×#67—62no—
137C4×#67—62no—
138#926—31no—
139#926—31no—
140#926—61no—
141#926C2×D311yescharacteristic
142#924—61no—
143C2×#208—31no—
144C2×#208—31no—
145C2×#208—61no—
146C2×#208C2×D311yescharacteristic
147#837—62no—
148#837—62no—
149#837—64no—
150#837—62no—
151#830—62no—
152(C2×D3)⋊C8—62no—
153#805—62no—
154C23×C32—21no—
155C23×C32C2×D411yescharacteristic
156C22×C3×D3—21no—
157C22×C3×D3—21no—
158C22×C3×D3—21no—
159C22×C3×D3—21no—
160C22×C3×D3—42no—
161C32×Q8—21no—
162C32×Q8—21no—
163C32×D4—21no—
164C32×D4—21no—
165C32×D4—41no—
166C32×D4—41no—
167C2×C32×C4—21no—
168C2×C32×C4—41no—
169C2×C32×C4—41no—
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4#4111yescharacteristic
176C2×C3⋊Dic3—22no—
177C3×#67—44no—
178C3×#67—41no—
179C3×#67—41no—
180C2×C3×Dic3—21no—
181C2×C3×Dic3—21no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—21no—
184C2×C3×Dic3—21no—
185C3×D12—21no—
186C3×D12—21no—
187C3×C4×D3—41no—
188C3×C4×D3—41no—
189C3×C4×D3—41no—
190C3×C4×D3—41no—
191C3×C4×D3—41no—
192C3×C4×D3—41no—
193C3×Dic6—21no—
194C3×Dic6—21no—
195#625—44no—
196C3⋊(C3⋊C8)—41no—
197C3×C3⋊C8—22no—
198#575—31no—
199#525—31no—
200#525—91no—
201#421—91no—
202#421—91no—
203#407—91no—
204H(3,ℤ/4)—91no—
205C24×C3—31no—
206C23×D3#6711yescharacteristic
207C3×#41—22no—
208C3×#41—22no—
209C3×#41—21no—
210C3×#41—21no—
211C3×#41—21no—
212C3×#41—21no—
213C3×#41—21no—
214C3×#41—21no—
215C3×#41—21no—
216C3×#41—21no—
217C3×#41—41no—
218C3×#41—41no—
219C3×#41—61no—
220C3×#41—61no—
221C3×#41—61no—
222C3×#41—61no—
223C2×C3×Q8—21no—
224C2×C3×Q8—31no—
225C2×C3×Q8#6711yescharacteristic, complemented
226C2×C3×Q8#6711yescharacteristic, complemented
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—31no—
231C2×C3×D4—41no—
232C2×C3×D4—62no—
233C2×C3×D4—61no—
234C2×C3×D4#6711yescharacteristic, complemented
235C2×C3×D4#6711yescharacteristic, complemented
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—31no—
240C22×C3×C4—41no—
241C22×C3×C4—61no—
242C22×C3×C4—61no—
243C22×C3×C4—61no—
244C22×C3×C4—61no—
245C22×C3×C4—61no—
246C22×C3×C4—61no—
247C22×C3×C4—61no—
248C22×C3×C4C22×D311yescharacteristic
249C22×C3×C4C22×D311yescharacteristic
250C2×#67—22no—
251C2×#67—21no—
252C2×#67—62no—
253C2×#67—62no—
254C22×Dic3#6711yescharacteristic
255#235—21no—
256#235—21no—
257#235—21no—
258#235—21no—
259C2×D12#6711yescharacteristic, complemented
260C2×C4×D3—21no—
261C2×C4×D3—21no—
262C2×C4×D3—21no—
263C2×C4×D3—21no—
264C2×C4×D3—21no—
265C2×C4×D3—21no—
266C2×C4×D3—21no—
267C2×Dic6#6711yescharacteristic, complemented
268C3×Q16—62no—
269C3×SD16—62no—
270C3×SD16—62no—
271C3×D8—62no—
272C3×M16—61no—
273C3×M16—61no—
274C2×C3×C8—32no—
275C3×C4⋊C4—62no—
276C3×C4⋊C4—61no—
277C3×C22⋊C4—62no—
278C3×C22⋊C4—62no—
279C3×C22⋊C4—61no—
280C3×C42—32no—
281#217—22no—
282#217—21no—
283#217—62no—
284#217—62no—
285#217—61no—
286#217—61no—
287#217—121no—
288#216—22no—
289#215—22no—
290#214—22no—
291#213—22no—
292(C2×D3)⋊C4—22no—
293(C2×D3)⋊C4—62no—
294(C2×D3)⋊C4—62no—
295C4⋊Dic3—21no—
296C4⋊Dic3—61no—
297C4⋊Dic3—61no—
298C4⋊Dic3—121no—
299Dic3⋊C4—22no—
300Dic3⋊C4—62no—
301Dic3⋊C4—62no—
302C4×Dic3—32no—
303C4×Dic3—32no—
304C4×Dic3—62no—
305C4×Dic3#6712yescomplemented
306#208—21no—
307#208—21no—
308#208—62no—
309#208—61no—
310#208—61no—
311#208—61no—
312#208—61no—
313#208—121no—
314C2×C3⋊C8—61no—
315C2×C3⋊C8—61no—
316C2×C3⋊C8—121no—
317C2×C3⋊C8#6712yescomplemented
318C22×C32—41no—
319C22×C32—41no—
320C22×C32—42no—
321C22×C32#12011yescharacteristic
322C22×C32#12011yescharacteristic
323C22×C32#12111yescharacteristic
324C2×C3×D3—22no—
325C2×C3×D3—22no—
326C2×C3×D3—22no—
327C2×C3×D3—41no—
328C2×C3×D3—41no—
329C2×C3×D3—41no—
330C2×C3×D3—41no—
331C2×C3×D3—42no—
332C2×C3×D3—41no—
333C32×C4—41no—
334C32×C4#12011yescharacteristic
335C32×C4#12111yescharacteristic
336C32×C4#12111yescharacteristic
337C32×C4#12711yescharacteristic
338C3⋊Dic3—42no—
339C3×Dic3—42no—
340C3×Dic3—41no—
341C3×Dic3—41no—
342C2×#41—31no—
343C2×#41D3211yescharacteristic
344C23×C4—31no—
345#137—61no—
346#137—61no—
347AGL(1,ℤ/8)—61no—
348AGL(1,ℤ/8)—61no—
349#135—62no—
350C2×M16—31no—
351C2×M16—91no—
352#123—61no—
353#123—181no—
354C22⋊Q8—61no—
355C22⋊Q8—181no—
356#121—61no—
357#121—181no—
358#120—61no—
359#120—181no—
360C4×D4—62no—
361C4×D4—182no—
362#117—31no—
363#117—91no—
364#104—182no—
365#104—182no—
366C22⋊C8—182no—
367C23×C3—21no—
368C23×C3—21no—
369C23×C3—21no—
370C23×C3—41no—
371C23×C3—61no—
372C23×C3—61no—
373C23×C3—61no—
374C23×C3—61no—
375C23×C3—122no—
376C23×C3D3×D411yescharacteristic
377C23×C3C2×#6711yescharacteristic
378C22×D3—21no—
379C22×D3—21no—
380C22×D3—21no—
381C22×D3—21no—
382C22×D3—42no—
383C3×Q8—22no—
384C3×Q8—21no—
385C3×Q8—21no—
386C3×Q8—21no—
387C3×Q8—21no—
388C3×Q8—41no—
389C3×Q8—61no—
390C3×Q8—61no—
391C3×D4—22no—
392C3×D4—21no—
393C3×D4—21no—
394C3×D4—21no—
395C3×D4—21no—
396C3×D4—41no—
397C3×D4—42no—
398C3×D4—42no—
399C3×D4—41no—
400C3×D4—41no—
401C3×D4—41no—
402C3×D4—41no—
403C3×D4—61no—
404C3×D4—61no—
405C3×D4—124no—
406C3×D4—121no—
407C3×D4—121no—
408C2×C3×C4—21no—
409C2×C3×C4—21no—
410C2×C3×C4—21no—
411C2×C3×C4—21no—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—41no—
417C2×C3×C4—42no—
418C2×C3×C4—42no—
419C2×C3×C4—41no—
420C2×C3×C4—41no—
421C2×C3×C4—41no—
422C2×C3×C4—41no—
423C2×C3×C4—61no—
424C2×C3×C4—61no—
425C2×C3×C4—62no—
426C2×C3×C4—61no—
427C2×C3×C4—61no—
428C2×C3×C4—121no—
429C2×C3×C4—121no—
430C2×C3×C4—121no—
431C2×C3×C4—121no—
432C2×C3×C4—121no—
433C2×C3×C4—121no—
434C2×C3×C4D3×D411yescharacteristic
435C2×C3×C4D3×D411yescharacteristic
436C2×C3×C4D3×D411yescharacteristic
437C2×C3×C4D3×D411yescharacteristic
438C2×C3×C4D3×D411yescharacteristic
439C2×C3×C4#23711yescharacteristic
440C2×C3×C4#23711yescharacteristic
441C2×C3×C4C2×#6711yescharacteristic
442C2×C3×C4C2×#6711yescharacteristic
443C2×C3×C4C2×#6711yescharacteristic
444C2×C3×C4C2×#6711yescharacteristic
445C2×C3×C4C2×#6711yescharacteristic
446#67—44no—
447#67—41no—
448#67—41no—
449#67—124no—
450#67—124no—
451C2×Dic3—21no—
452C2×Dic3—21no—
453C2×Dic3—21no—
454C2×Dic3—22no—
455C2×Dic3—21no—
456C2×Dic3—62no—
457C2×Dic3—62no—
458C2×Dic3—122no—
459D12—21no—
460D12—21no—
461C4×D3—41no—
462C4×D3—41no—
463C4×D3—41no—
464C4×D3—41no—
465C4×D3—41no—
466C4×D3—41no—
467Dic6—21no—
468Dic6—21no—
469C3×C8—62no—
470C3⋊C8—22no—
471C3⋊C8—122no—
472C3⋊C8—121no—
473C3⋊C8—121no—
474C2×C32—21no—
475C2×C32—21no—
476C2×C32—21no—
477C2×C32—81no—
478C2×C32#39211yescharacteristic
479C3×D3—42no—
480C3×D3—81no—
481C24—31no—
482#41—21no—
483#41—21no—
484#41—21no—
485#41—21no—
486#41—61no—
487#41—61no—
488#41—61no—
489#41—61no—
490C2×Q8—31no—
491C2×Q8#62511yescharacteristic, complemented
492C2×D4—21no—
493C2×D4—31no—
494C2×D4—62no—
495C2×D4—61no—
496C2×D4—182no—
497C2×D4#62511yescharacteristic, complemented
498C22×C4—21no—
499C22×C4—31no—
500C22×C4—61no—
501C22×C4—61no—
502C22×C4—61no—
503C22×C4—61no—
504C22×C4—61no—
505C22×C4—61no—
506C22×C4—61no—
507C22×C4C2×D3211yescharacteristic
508Q16—62no—
509SD16—62no—
510SD16—62no—
511D8—62no—
512M16—61no—
513M16—61no—
514M16—181no—
515M16—181no—
516C2×C8—32no—
517C2×C8—181no—
518C4⋊C4—62no—
519C4⋊C4—61no—
520C4⋊C4—182no—
521C4⋊C4—181no—
522C22⋊C4—62no—
523C22⋊C4—62no—
524C22⋊C4—61no—
525C22⋊C4—182no—
526C22⋊C4—182no—
527C22⋊C4—181no—
528C42—32no—
529C42—92no—
530C22×C3—21no—
531C22×C3—21no—
532C22×C3—21no—
533C22×C3—41no—
534C22×C3—41no—
535C22×C3—42no—
536C22×C3—42no—
537C22×C3—42no—
538C22×C3—41no—
539C22×C3—41no—
540C22×C3—62no—
541C22×C3—62no—
542C22×C3—62no—
543C22×C3—81no—
544C22×C3—82no—
545C22×C3—121no—
546C22×C3—121no—
547C22×C3—121no—
548C22×C3—122no—
549C22×C3—121no—
550C22×C3—121no—
551C22×C3#93711yescharacteristic
552C22×C3#93711yescharacteristic
553C22×C3#93711yescharacteristic
554C22×C3#93811yescharacteristic
555C22×C3#93911yescharacteristic
556C22×C3#95311yescharacteristic
557C2×D3—22no—
558C2×D3—22no—
559C2×D3—22no—
560C2×D3—41no—
561C2×D3—41no—
562C2×D3—41no—
563C2×D3—41no—
564C2×D3—42no—
565C2×D3—41no—
566C3×C4—21no—
567C3×C4—21no—
568C3×C4—21no—
569C3×C4—21no—
570C3×C4—42no—
571C3×C4—41no—
572C3×C4—41no—
573C3×C4—122no—
574C3×C4—121no—
575C3×C4—121no—
576C3×C4#93711yescharacteristic
577C3×C4#93811yescharacteristic
578C3×C4#93911yescharacteristic
579C3×C4#93911yescharacteristic
580C3×C4#93911yescharacteristic
581C3×C4#94011yescharacteristic
582C3×C4#94011yescharacteristic
583C3×C4#95311yescharacteristic
584Dic3—42no—
585Dic3—41no—
586Dic3—41no—
587Dic3—122no—
588Dic3—122no—
589Dic3—242no—
590C32#201011yescharacteristic, complemented, Sylow
591C23—21no—
592C23—61no—
593C23—61no—
594C23—61no—
595C23—61no—
596C23—122no—
597C23D3×#6711yescharacteristic
598Q8—21no—
599Q8—21no—
600Q8—61no—
601Q8—61no—
602D4—21no—
603D4—21no—
604D4—41no—
605D4—41no—
606D4—61no—
607D4—61no—
608D4—124no—
609D4—121no—
610D4—121no—
611D4—364no—
612C2×C4—21no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—61no—
616C2×C4—62no—
617C2×C4—61no—
618C2×C4—61no—
619C2×C4—61no—
620C2×C4—121no—
621C2×C4—121no—
622C2×C4—121no—
623C2×C4—121no—
624C2×C4—121no—
625C2×C4—121no—
626C2×C4—182no—
627C2×C4#380511yescharacteristic
628C2×C4C2×#62511yescharacteristic
629C2×C4D3×#6711yescharacteristic
630C2×C4D3×#6711yescharacteristic
631C2×C4D3×#6711yescharacteristic
632C2×C4#381111yescharacteristic
633C8—62no—
634C8—361no—
635C2×C3—21no—
636C2×C3—21no—
637C2×C3—21no—
638C2×C3—21no—
639C2×C3—21no—
640C2×C3—21no—
641C2×C3—21no—
642C2×C3—41no—
643C2×C3—41no—
644C2×C3—41no—
645C2×C3—82no—
646C2×C3—81no—
647C2×C3—81no—
648C2×C3—122no—
649C2×C3—241no—
650C2×C3#522311yescharacteristic
651C2×C3#522311yescharacteristic
652D3—42no—
653D3—81no—
654C22—41no—
655C22—42no—
656C22—41no—
657C22—62no—
658C22—62no—
659C22—62no—
660C22—121no—
661C22—121no—
662C22—121no—
663C22—122no—
664C22—121no—
665C22—121no—
666C22#6397011yescharacteristic
667C22#6397611yescharacteristic
668C22#6398311yescharacteristic
669C4—41no—
670C4—122no—
671C4—121no—
672C4—121no—
673C4—362no—
674C4#6397011yescharacteristic
675C4#6397611yescharacteristic
676C4#6397911yescharacteristic
677C4#6398011yescharacteristic
678C3—21no—
679C3#7171511yescharacteristic, complemented
680C3#7211811yescharacteristic, complemented
681C2—21no—
682C2—21no—
683C2—21no—
684C2—81no—
685C2—122no—
686C2—241no—
687C2#1059172311yescharacteristic
subgroupG/H
centerC4#63979
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×#41C22
socleC2×C32#392
hypercenterC2×#41D32
hypocenterC32#2010
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C3×#5828C2semidirect
2. C3×#5822C2semidirect
3. #10595022C2semidirect
4. #10592935C2semidirect
5. #10591111C2semidirect
6. #10591069C2semidirect
7. #10589158C2semidirect
38. #5828D3semidirect
39. #5822D3semidirect
55. C2×C32×Q8D4semidirect
57. C2×C32×D4D4semidirect
67. C2×C3×D12D4semidirect
75. C2×C3×Dic6D4semidirect
79. C4×C3⋊Dic3D4semidirect
92. C3×C4×Dic3D4semidirect
95. C2×C3×C3⋊C8D4semidirect
225. C2×C3×Q8#67semidirect
226. C2×C3×Q8#67semidirect
234. C2×C3×D4#67semidirect
235. C2×C3×D4#67semidirect
259. C2×D12#67semidirect
267. C2×Dic6#67semidirect
305. C4×Dic3#67semidirect
317. C2×C3⋊C8#67semidirect
491. C2×Q8#625semidirect
497. C2×D4#625semidirect
590. C32#2010semidirect
679. C3#71715semidirect
680. C3#72118semidirect

Maximal subgroups

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

subgroupindex
C3×#58282
C3×#58222
#105950222
#105929352
#105911112
#105910692
#105891582
#721183
#717153