Finite Group Databasebeta

← #11792407

Subgroups — #11792407

Order 1152.

919 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596293C211yesmaximal, characteristic, complemented
2C3×#5828C211yesmaximal, characteristic, complemented
3#10595023C211yesmaximal, characteristic, complemented
4C3×#5236C211yesmaximal, characteristic, complemented
5#10591113C211yesmaximal, characteristic, complemented
6#10591069C211yesmaximal, characteristic, complemented
7#10589157C211yesmaximal, characteristic, complemented
8#71715—31nomaximal
9#70406—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C2×#3828C2211yescharacteristic
12C22×C3×C4×D3C2211yescharacteristic
13#64160—21no—
14#64159—22no—
15#64158—21no—
16#64151—21no—
17#64141—21no—
18C2×#3748C2211yescharacteristic
19C3×#946—21no—
20C3×#938—21no—
21C3×#937—21no—
22C3×#935—21no—
23C3×C4×#67—22no—
24C3×#926C2211yescharacteristic
25C3×#926C2211yescharacteristic
26C2×C3×#208C2211yescharacteristic
27#63977—21no—
28#63966—21no—
29#63909—21no—
30C4×#626—22no—
31#63857—21no—
32C3×#837—22no—
33#63570—22no—
34(C2×D3)⋊(C3⋊C8)—22no—
35C3×#525—31no—
36#5828D311yescharacteristic, complemented
37#5822—31no—
38#5822—31no—
39#5822—61no—
40#5791—31no—
41#5524—31no—
42C3×#421—31no—
43#5236D311yescharacteristic, complemented
44#5207—31no—
45#5139—31no—
46#5126—31no—
47#5005—31no—
48#4531—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×#638—21no—
61#3828—21no—
62#3828—21no—
63#3828—21no—
64#3828—21no—
65C2×C4⋊(C3⋊D3)D411yescharacteristic, complemented
66C2×C4×C3⋊D3—21no—
67C2×#634D411yescharacteristic, complemented
68C2×C3×#67—22no—
69C22×C3×Dic3D411yescharacteristic
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×C4×D3—21no—
76C2×#626—22no—
77#3756—22no—
78#3755—22no—
79#3754—22no—
80#3753—22no—
81#3748—21no—
82#3748—21no—
83C2×C3⋊(C3⋊C8)D412yescomplemented
84C3×#217—22no—
85C3×#217—21no—
86C3×#217—21no—
87C3×(C2×D3)⋊C4—22no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3—21no—
90C3×Dic3⋊C4—22no—
91C3×C4×Dic3D412yescomplemented
92C3×C4×Dic3D412yescomplemented
93C3×#208—21no—
94C3×#208—21no—
95C2×C3×C3⋊C8—21no—
96Dic3⋊Dic3—22no—
97#3722—22no—
98(C2×D3)⋊Dic3—22no—
99#2010—91noSylow
100C2×C3×#41—21no—
101C2×C3×#41C2×D311yescharacteristic
102C2×C3×#41C2×D311yescharacteristic
103C23×C3×C4—31no—
104C2×#235—31no—
105C2×#235—31no—
106C2×#235—61no—
107C22×C4×D3C2×D311yescharacteristic
108C2×C3×M16—31no—
109C3×#123—61no—
110C3×C22⋊Q8—61no—
111C3×#121—61no—
112C3×#120—61no—
113C3×C4×D4—62no—
114C3×#117—31no—
115C3×#117—31no—
116#953—61no—
117#951—61no—
118#951—61no—
119#951—62no—
120#950—62no—
121#950—62no—
122#950—64no—
123#949—61no—
124#949—61no—
125#949—62no—
126#946—21no—
127#942—62no—
128#942—61no—
129#942—61no—
130#938—21no—
131#937—21no—
132#935—21no—
133#932—62no—
134#932—61no—
135#932—61no—
136#930—61no—
137#929—61no—
138C4×#67—22no—
139C4×#67—62no—
140#926C2×D311yescharacteristic
141#926C2×D311yescharacteristic
142#924—61no—
143C2×#208—31no—
144C2×#208—31no—
145C2×#208—61no—
146C2×#208C2×D311yescharacteristic
147#897—61no—
148#895—61no—
149#886—61no—
150#882—61no—
151C4×D12—62no—
152C3×#104—62no—
153#837—22no—
154#830—62no—
155#825—62no—
156(C2×D3)⋊C8—62no—
157#805—62no—
158C23×C32—21no—
159C23×C32C2×D411yescharacteristic
160C22×C3⋊D3—21no—
161C22×C3×D3—21no—
162C22×C3×D3—21no—
163C22×C3×D3—21no—
164C22×C3×D3—42no—
165C32×Q8—21no—
166C32×Q8—21no—
167C32×D4—21no—
168C32×D4—21no—
169C32×D4—41no—
170C32×D4—41no—
171C2×C32×C4—21no—
172C2×C32×C4—41no—
173C2×C32×C4—41no—
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2×D411yescharacteristic
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4C2×D411yescharacteristic
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4#4111yescharacteristic
180#638—41no—
181#638—41no—
182C2×C3⋊Dic3—21no—
183C4⋊(C3⋊D3)—21no—
184C4⋊(C3⋊D3)—21no—
185C4×C3⋊D3—41no—
186C4×C3⋊D3—41no—
187#634—21no—
188#634—21no—
189C3×#67—44no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—21no—
194C2×C3×Dic3—21no—
195C3×C4×D3—41no—
196C3×C4×D3—41no—
197C3×C4×D3—41no—
198C3×C4×D3—41no—
199#626—44no—
200C3⋊(C3⋊C8)—22no—
201C3×C3⋊C8—41no—
202#575—91no—
203#525—31no—
204#525—91no—
205#421—31no—
206#421—91no—
207#407—91no—
208H(3,ℤ/4)—91no—
209C24×C3—31no—
210C23×D3#6711yescharacteristic
211C3×#41—22no—
212C3×#41—22no—
213C3×#41—21no—
214C3×#41—21no—
215C3×#41—21no—
216C3×#41—21no—
217C3×#41—21no—
218C3×#41—21no—
219C3×#41—21no—
220C3×#41—21no—
221C3×#41—41no—
222C3×#41—41no—
223C2×C3×Q8—21no—
224C2×C3×Q8D1211yescharacteristic, complemented
225C2×C3×Q8#6711yescharacteristic, complemented
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—41no—
230C2×C3×D4—62no—
231C2×C3×D4D1211yescharacteristic, complemented
232C2×C3×D4#6711yescharacteristic, complemented
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—31no—
237C22×C3×C4—41no—
238C22×C3×C4—61no—
239C22×C3×C4—61no—
240C22×C3×C4—61no—
241C22×C3×C4—61no—
242C22×C3×C4—61no—
243C22×C3×C4—61no—
244C22×C3×C4C22×D311yescharacteristic
245C22×C3×C4C22×D311yescharacteristic
246C2×#67—22no—
247C2×#67—62no—
248C2×#67—61no—
249C2×#67—61no—
250C2×#67—121no—
251C22×Dic3#6711yescharacteristic
252#235—62no—
253#235—62no—
254#235—61no—
255#235—61no—
256#235—61no—
257#235—61no—
258#235—61no—
259#235—61no—
260#235—61no—
261#235—61no—
262#235—121no—
263#235—121no—
264C2×D12—31no—
265C2×D12—31no—
266C2×D12—61no—
267C2×D12—62no—
268C2×C4×D3—21no—
269C2×C4×D3—21no—
270C2×C4×D3—21no—
271C2×C4×D3—21no—
272C2×C4×D3—21no—
273C2×C4×D3—21no—
274C2×C4×D3—61no—
275C2×C4×D3—61no—
276C2×C4×D3—121no—
277C2×Dic6—31no—
278C2×Dic6—31no—
279C2×Dic6—61no—
280C3×M16—61no—
281C3×M16—61no—
282C2×C3×C8—61no—
283C3×C4⋊C4—62no—
284C3×C4⋊C4—61no—
285C3×C4⋊C4—61no—
286C3×C22⋊C4—62no—
287C3×C22⋊C4—62no—
288C3×C22⋊C4—61no—
289C3×C22⋊C4—61no—
290C3×C42—32no—
291C3×C42—32no—
292#217—22no—
293#217—21no—
294#217—21no—
295#217—62no—
296#216—64no—
297#216—62no—
298#216—62no—
299#215—64no—
300#215—62no—
301#215—62no—
302#214—64no—
303#214—62no—
304#214—62no—
305#213—64no—
306#213—62no—
307#213—62no—
308(C2×D3)⋊C4—22no—
309(C2×D3)⋊C4—62no—
310(C2×D3)⋊C4—62no—
311(C2×D3)⋊C4—62no—
312C4⋊Dic3—21no—
313C4⋊Dic3—21no—
314C4⋊Dic3—62no—
315Dic3⋊C4—22no—
316Dic3⋊C4—62no—
317C4×Dic3#6712yescomplemented
318C4×Dic3#6712yescomplemented
319#208—21no—
320#208—21no—
321#208—62no—
322#208—62no—
323#208—61no—
324#208—61no—
325#208—61no—
326#208—61no—
327C2×C3⋊C8—21no—
328C2×C3⋊C8—32no—
329C2×C3⋊C8—32no—
330C2×C3⋊C8—62no—
331C22×C32—41no—
332C22×C32—41no—
333C22×C32—42no—
334C22×C32#12011yescharacteristic
335C22×C32#12011yescharacteristic
336C22×C32#12111yescharacteristic
337C2×C3⋊D3—41no—
338C2×C3⋊D3—42no—
339C2×C3×D3—22no—
340C2×C3×D3—22no—
341C2×C3×D3—22no—
342C2×C3×D3—41no—
343C2×C3×D3—41no—
344C2×C3×D3—41no—
345C2×C3×D3—41no—
346C32×C4—41no—
347C32×C4#12011yescharacteristic
348C32×C4#12111yescharacteristic
349C32×C4#12111yescharacteristic
350C32×C4#12711yescharacteristic
351C3⋊Dic3—41no—
352C3×Dic3—42no—
353C3×Dic3—42no—
354C3×Dic3—41no—
355C2×#41—91no—
356C2×#41D3211yescharacteristic
357C23×C4—31no—
358#137—181no—
359#137—181no—
360AGL(1,ℤ/8)—181no—
361AGL(1,ℤ/8)—181no—
362#135—182no—
363C2×M16—31no—
364C2×M16—91no—
365#123—61no—
366#123—181no—
367C22⋊Q8—61no—
368C22⋊Q8—181no—
369#121—61no—
370#121—181no—
371#120—61no—
372#120—181no—
373C4×D4—62no—
374C4×D4—182no—
375#117—31no—
376#117—31no—
377#104—62no—
378#104—182no—
379C22⋊C8—182no—
380C23×C3—21no—
381C23×C3—21no—
382C23×C3—21no—
383C23×C3—41no—
384C23×C3—61no—
385C23×C3—61no—
386C23×C3—61no—
387C23×C3—122no—
388C23×C3D3×D411yescharacteristic
389C23×C3C2×#6711yescharacteristic
390C22×D3—21no—
391C22×D3—21no—
392C22×D3—21no—
393C22×D3—42no—
394C22×D3—61no—
395C22×D3—61no—
396C22×D3—121no—
397C3×Q8—22no—
398C3×Q8—21no—
399C3×Q8—21no—
400C3×Q8—21no—
401C3×Q8—21no—
402C3×Q8—41no—
403C3×D4—22no—
404C3×D4—21no—
405C3×D4—21no—
406C3×D4—21no—
407C3×D4—21no—
408C3×D4—41no—
409C3×D4—42no—
410C3×D4—42no—
411C3×D4—41no—
412C3×D4—41no—
413C3×D4—41no—
414C3×D4—41no—
415C3×D4—124no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—21no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
423C2×C3×C4—21no—
424C2×C3×C4—41no—
425C2×C3×C4—42no—
426C2×C3×C4—42no—
427C2×C3×C4—41no—
428C2×C3×C4—41no—
429C2×C3×C4—41no—
430C2×C3×C4—41no—
431C2×C3×C4—62no—
432C2×C3×C4—61no—
433C2×C3×C4—61no—
434C2×C3×C4—61no—
435C2×C3×C4—62no—
436C2×C3×C4—121no—
437C2×C3×C4—121no—
438C2×C3×C4—121no—
439C2×C3×C4—121no—
440C2×C3×C4C2×D1211yescharacteristic
441C2×C3×C4#23511yescharacteristic
442C2×C3×C4D3×D411yescharacteristic
443C2×C3×C4D3×D411yescharacteristic
444C2×C3×C4D3×D411yescharacteristic
445C2×C3×C4D3×D411yescharacteristic
446C2×C3×C4D3×D411yescharacteristic
447C2×C3×C4D3×D411yescharacteristic
448C2×C3×C4#23711yescharacteristic
449C2×C3×C4C2×#6711yescharacteristic
450C2×C3×C4C2×#6711yescharacteristic
451C2×C3×C4C2×#6711yescharacteristic
452#67—44no—
453#67—124no—
454#67—122no—
455#67—122no—
456#67—121no—
457#67—121no—
458#67—121no—
459#67—121no—
460C2×Dic3—22no—
461C2×Dic3—21no—
462C2×Dic3—21no—
463C2×Dic3—22no—
464C2×Dic3—21no—
465C2×Dic3—61no—
466C2×Dic3—61no—
467C2×Dic3—121no—
468D12—62no—
469D12—61no—
470D12—61no—
471D12—61no—
472D12—61no—
473D12—121no—
474D12—124no—
475C4×D3—41no—
476C4×D3—41no—
477C4×D3—41no—
478C4×D3—41no—
479C4×D3—122no—
480C4×D3—122no—
481C4×D3—121no—
482C4×D3—121no—
483C4×D3—121no—
484C4×D3—121no—
485Dic6—62no—
486Dic6—61no—
487Dic6—61no—
488Dic6—61no—
489Dic6—61no—
490Dic6—121no—
491C3×C8—121no—
492C3⋊C8—41no—
493C3⋊C8—64no—
494C3⋊C8—62no—
495C3⋊C8—62no—
496C2×C32—21no—
497C2×C32—21no—
498C2×C32—21no—
499C2×C32—81no—
500C2×C32#39211yescharacteristic
501C3⋊D3—81no—
502C3×D3—42no—
503C24—31no—
504#41—21no—
505#41—21no—
506#41—21no—
507#41—21no—
508#41—181no—
509#41—181no—
510#41—181no—
511#41—181no—
512C2×Q8—91no—
513C2×Q8#62611yescharacteristic, complemented
514C2×D4—21no—
515C2×D4—62no—
516C2×D4—91no—
517C2×D4—182no—
518C2×D4—181no—
519C2×D4#62611yescharacteristic, complemented
520C22×C4—21no—
521C22×C4—31no—
522C22×C4—61no—
523C22×C4—61no—
524C22×C4—61no—
525C22×C4—61no—
526C22×C4—61no—
527C22×C4—61no—
528C22×C4—181no—
529C22×C4C2×D3211yescharacteristic
530Q16—182no—
531SD16—182no—
532SD16—182no—
533D8—182no—
534M16—61no—
535M16—61no—
536M16—181no—
537M16—181no—
538C2×C8—61no—
539C2×C8—92no—
540C4⋊C4—62no—
541C4⋊C4—61no—
542C4⋊C4—61no—
543C4⋊C4—182no—
544C22⋊C4—62no—
545C22⋊C4—62no—
546C22⋊C4—61no—
547C22⋊C4—61no—
548C22⋊C4—182no—
549C22⋊C4—182no—
550C42—32no—
551C42—32no—
552C22×C3—21no—
553C22×C3—21no—
554C22×C3—21no—
555C22×C3—41no—
556C22×C3—41no—
557C22×C3—42no—
558C22×C3—42no—
559C22×C3—42no—
560C22×C3—41no—
561C22×C3—41no—
562C22×C3—62no—
563C22×C3—62no—
564C22×C3—62no—
565C22×C3—81no—
566C22×C3—82no—
567C22×C3—121no—
568C22×C3—121no—
569C22×C3—121no—
570C22×C3—121no—
571C22×C3#88211yescharacteristic
572C22×C3#88411yescharacteristic
573C22×C3#93711yescharacteristic
574C22×C3#93711yescharacteristic
575C22×C3#93911yescharacteristic
576C22×C3#95311yescharacteristic
577C2×D3—22no—
578C2×D3—22no—
579C2×D3—22no—
580C2×D3—41no—
581C2×D3—41no—
582C2×D3—41no—
583C2×D3—41no—
584C2×D3—122no—
585C2×D3—122no—
586C2×D3—122no—
587C2×D3—121no—
588C2×D3—121no—
589C2×D3—242no—
590C3×C4—21no—
591C3×C4—21no—
592C3×C4—21no—
593C3×C4—21no—
594C3×C4—42no—
595C3×C4—41no—
596C3×C4—41no—
597C3×C4—122no—
598C3×C4—122no—
599C3×C4—121no—
600C3×C4#88211yescharacteristic
601C3×C4#88411yescharacteristic
602C3×C4#93011yescharacteristic
603C3×C4#93711yescharacteristic
604C3×C4#93811yescharacteristic
605C3×C4#93911yescharacteristic
606C3×C4#94011yescharacteristic
607C3×C4#94011yescharacteristic
608Dic3—42no—
609Dic3—42no—
610Dic3—41no—
611Dic3—122no—
612Dic3—121no—
613Dic3—121no—
614C32#201011yescharacteristic, complemented, Sylow
615C23—21no—
616C23—61no—
617C23—61no—
618C23—61no—
619C23—122no—
620C23—181no—
621C23D3×#6711yescharacteristic
622Q8—21no—
623Q8—21no—
624Q8—181no—
625Q8—181no—
626D4—21no—
627D4—21no—
628D4—41no—
629D4—41no—
630D4—124no—
631D4—181no—
632D4—181no—
633D4—364no—
634D4—361no—
635D4—361no—
636C2×C4—21no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—61no—
640C2×C4—62no—
641C2×C4—61no—
642C2×C4—62no—
643C2×C4—61no—
644C2×C4—121no—
645C2×C4—121no—
646C2×C4—121no—
647C2×C4—121no—
648C2×C4—181no—
649C2×C4—361no—
650C2×C4—361no—
651C2×C4#380411yescharacteristic
652C2×C4C2×#62611yescharacteristic
653C2×C4D3×#6711yescharacteristic
654C2×C4D3×#6711yescharacteristic
655C2×C4#381111yescharacteristic
656C2×C4#381111yescharacteristic
657C8—121no—
658C8—182no—
659C2×C3—21no—
660C2×C3—21no—
661C2×C3—21no—
662C2×C3—21no—
663C2×C3—21no—
664C2×C3—21no—
665C2×C3—21no—
666C2×C3—41no—
667C2×C3—41no—
668C2×C3—41no—
669C2×C3—82no—
670C2×C3—81no—
671C2×C3—81no—
672C2×C3—122no—
673C2×C3#496011yescharacteristic
674C2×C3#522311yescharacteristic
675D3—42no—
676D3—242no—
677D3—241no—
678D3—241no—
679C22—41no—
680C22—42no—
681C22—41no—
682C22—62no—
683C22—62no—
684C22—62no—
685C22—121no—
686C22—121no—
687C22—121no—
688C22—121no—
689C22—362no—
690C22—361no—
691C22#6397111yescharacteristic
692C22#6397711yescharacteristic
693C22#6398311yescharacteristic
694C4—41no—
695C4—122no—
696C4—122no—
697C4—121no—
698C4—361no—
699C4#6395811yescharacteristic
700C4#6397811yescharacteristic
701C4#6397911yescharacteristic
702C4#6398111yescharacteristic
703C3—21no—
704C3#7040611yescharacteristic, complemented
705C3#7171511yescharacteristic, complemented
706C2—21no—
707C2—21no—
708C2—21no—
709C2—81no—
710C2—122no—
711C2—721no—
712C2#1059172411yescharacteristic
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. #10596293C2semidirect
2. C3×#5828C2semidirect
3. #10595023C2semidirect
4. C3×#5236C2semidirect
5. #10591113C2semidirect
6. #10591069C2semidirect
7. #10589157C2semidirect
36. #5828D3semidirect
43. #5236D3semidirect
55. C2×C32×Q8D4semidirect
57. C2×C32×D4D4semidirect
65. C2×C4⋊(C3⋊D3)D4semidirect
67. C2×#634D4semidirect
83. C2×C3⋊(C3⋊C8)D4semidirect
91. C3×C4×Dic3D4semidirect
92. C3×C4×Dic3D4semidirect
224. C2×C3×Q8D12semidirect
225. C2×C3×Q8#67semidirect
231. C2×C3×D4D12semidirect
232. C2×C3×D4#67semidirect
317. C4×Dic3#67semidirect
318. C4×Dic3#67semidirect
513. C2×Q8#626semidirect
519. C2×D4#626semidirect
614. C32#2010semidirect
704. C3#70406semidirect
705. C3#71715semidirect

Maximal subgroups

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

subgroupindex
#105962932
C3×#58282
#105950232
C3×#52362
#105911132
#105910692
#105891572
#717153
#704063