Finite Group Databasebeta

← #11792418

Subgroups — #11792418

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
1#10595023C211yesmaximal, characteristic, complemented
2#10595022C211yesmaximal, characteristic, complemented
3#10594795C211yesmaximal, characteristic, complemented
4#10592838C211yesmaximal, characteristic, complemented
5C3×#5139C211yesmaximal, characteristic, complemented
6C3×#5126C211yesmaximal, characteristic, complemented
7#10589158C211yesmaximal, characteristic, complemented
8#70406—31nomaximal
9#69993—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C22×C3×C4×D3C2211yescharacteristic
13C2×C32×M16C2211yescharacteristic
14#64135C2211yescharacteristic
15C3×#926C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63977—21no—
18#63976—21no—
19#63966—21no—
20#63961—21no—
21#63909—21no—
22#63908—21no—
23C4×#626—22no—
24C4×#625—22no—
25#63857—21no—
26#63856—21no—
27#63833—21no—
28#63831—21no—
29#63830—21no—
30#63829—22no—
31#63825—21no—
32#63652—22no—
33C3×#825—22no—
34C3×(C2×D3)⋊C8—22no—
35#5828—31no—
36#5822—31no—
37#5791—31no—
38#5791—31no—
39#5748—31no—
40#5524—31no—
41C3×#421—31no—
42C3×#407—31no—
43#5139—31no—
44#5139—31no—
45#5139—61no—
46#5139D311yescharacteristic, complemented
47#5126D311yescharacteristic, complemented
48#4557—31no—
49#4531—31no—
50C23×C3×D3D411yescharacteristic
51C22×C32×C4C2311yescharacteristic
52C2×#638—21no—
53#3828—21no—
54#3828—21no—
55#3828—21no—
56#3828—21no—
57C2×C4⋊(C3⋊D3)D411yescharacteristic, complemented
58C2×C4×C3⋊D3—21no—
59C2×#634D411yescharacteristic, complemented
60C2×C3×#67—21no—
61C22×C3×Dic3D411yescharacteristic
62C3×#235—21no—
63C3×#235—21no—
64C3×#235—21no—
65C3×#235—21no—
66C2×C3×D12D411yescharacteristic, complemented
67C2×C3×C4×D3—21no—
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×Dic6D411yescharacteristic, complemented
75C2×#626—22no—
76C2×#625—22no—
77C32×M16—21no—
78C32×M16—21no—
79C2×C32×C8—21no—
80#3757—21no—
81C4⋊(C3⋊Dic3)—21no—
82C4×C3⋊Dic3D412yescomplemented
83C3×#217—21no—
84C3×C4⋊Dic3—21no—
85C3×C4×Dic3D412yescomplemented
86C3×#208—21no—
87C3×#208—21no—
88C2×C3×C3⋊C8D412yescomplemented
89#3724—22no—
90Dic3⋊Dic3—22no—
91#3722—22no—
92(C2×D3)⋊Dic3—22no—
93(C2×D3)⋊Dic3—22no—
94(C2×D3)⋊Dic3—22no—
95#3719—22no—
96#3717—22no—
97#3716—22no—
98#3714—22no—
99#2010—91noSylow
100C2×C3×#41—31no—
101C23×C3×C4—31no—
102C2×#235—31no—
103C2×#235—31no—
104C2×#235—61no—
105C2×#235C2×D311yescharacteristic
106C22×C4×D3C2×D311yescharacteristic
107C2×C3×M16—21no—
108C2×C3×M16—31no—
109C2×C3×M16C2×D311yescharacteristic
110C2×C3×M16C2×D311yescharacteristic
111C3×#117—31no—
112#953—61no—
113#953—61no—
114#951—61no—
115#950—62no—
116#949—61no—
117#946—61no—
118#942—61no—
119#938—61no—
120#937—61no—
121#935—61no—
122#932—61no—
123#930—61no—
124#930—61no—
125#929—61no—
126#929—61no—
127C4×#67—62no—
128C4×#67—62no—
129C4×#67—62no—
130#926—31no—
131#926—31no—
132#926—61no—
133#926C2×D311yescharacteristic
134#924—61no—
135#924—61no—
136C2×#208C2×D311yescharacteristic
137#909—61no—
138#909—61no—
139#908—61no—
140#908—61no—
141#904—62no—
142#897—61no—
143#895—61no—
144#886—61no—
145#882—61no—
146C4×D12—62no—
147C3×#104—62no—
148C3×C22⋊C8—62no—
149#825—22no—
150#825—62no—
151#825—62no—
152#825—64no—
153(C2×D3)⋊C8—22no—
154C23×C32C2×D411yescharacteristic
155C22×C3⋊D3—21no—
156C22×C3×D3—21no—
157C22×C3×D3—21no—
158C22×C3×D3—21no—
159C22×C3×D3—21no—
160C22×C3×D3—42no—
161C2×C32×C4C2×D411yescharacteristic
162C2×C32×C4C2×D411yescharacteristic
163C2×C32×C4C2×D411yescharacteristic
164C2×C32×C4C2×D411yescharacteristic
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4#4111yescharacteristic
167#638—41no—
168#638—41no—
169C2×C3⋊Dic3—21no—
170C2×C3⋊Dic3—22no—
171C4⋊(C3⋊D3)—21no—
172C4⋊(C3⋊D3)—21no—
173C4×C3⋊D3—41no—
174C4×C3⋊D3—41no—
175#634—21no—
176#634—21no—
177C3×#67—41no—
178C3×#67—41no—
179C2×C3×Dic3—21no—
180C2×C3×Dic3—21no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—21no—
183C2×C3×Dic3—21no—
184C3×D12—21no—
185C3×D12—21no—
186C3×C4×D3—41no—
187C3×C4×D3—41no—
188C3×C4×D3—41no—
189C3×C4×D3—41no—
190C3×C4×D3—41no—
191C3×C4×D3—41no—
192C3×Dic6—21no—
193C3×Dic6—21no—
194#626—44no—
195#625—44no—
196C32×C8—41no—
197C3×C3⋊C8—22no—
198#575—91no—
199#525—91no—
200#525—91no—
201#421—31no—
202#421—91no—
203#407—31no—
204H(3,ℤ/4)—91no—
205C24×C3—31no—
206C23×D3D1211yescharacteristic
207C3×#41—61no—
208C3×#41—61no—
209C3×#41—61no—
210C3×#41—61no—
211C2×C3×Q8—31no—
212C2×C3×D4—31no—
213C2×C3×D4—61no—
214C22×C3×C4—21no—
215C22×C3×C4—31no—
216C22×C3×C4—61no—
217C22×C3×C4—61no—
218C22×C3×C4—61no—
219C22×C3×C4—61no—
220C22×C3×C4—61no—
221C22×C3×C4—61no—
222C22×C3×C4—61no—
223C22×C3×C4C22×D311yescharacteristic
224C22×C3×C4C22×D311yescharacteristic
225C2×#67—21no—
226C2×#67—62no—
227C2×#67—62no—
228C2×#67—62no—
229C2×#67—61no—
230C2×#67—61no—
231C2×#67—121no—
232C22×Dic3D1211yescharacteristic
233#235—21no—
234#235—21no—
235#235—21no—
236#235—21no—
237#235—62no—
238#235—62no—
239#235—61no—
240#235—61no—
241#235—61no—
242#235—61no—
243#235—61no—
244#235—61no—
245#235—61no—
246#235—61no—
247#235—121no—
248#235—121no—
249C2×D12—31no—
250C2×D12—31no—
251C2×D12—61no—
252C2×D12—62no—
253C2×D12D1211yescharacteristic, complemented
254C2×C4×D3—21no—
255C2×C4×D3—21no—
256C2×C4×D3—21no—
257C2×C4×D3—21no—
258C2×C4×D3—21no—
259C2×C4×D3—21no—
260C2×C4×D3—21no—
261C2×C4×D3—61no—
262C2×C4×D3—61no—
263C2×C4×D3—121no—
264C2×Dic6—31no—
265C2×Dic6—31no—
266C2×Dic6—61no—
267C2×Dic6D1211yescharacteristic, complemented
268C3×M16—22no—
269C3×M16—21no—
270C3×M16—21no—
271C3×M16—21no—
272C3×M16—21no—
273C3×M16—41no—
274C3×M16—61no—
275C3×M16—61no—
276C2×C3×C8—21no—
277C2×C3×C8—21no—
278C2×C3×C8—32no—
279C2×C3×C8—41no—
280C3×C4⋊C4—61no—
281C3×C22⋊C4—61no—
282C3×C42—32no—
283#217—21no—
284#217—62no—
285#217—62no—
286#217—62no—
287#217—61no—
288#217—61no—
289#217—121no—
290#216—62no—
291#215—62no—
292#214—62no—
293#213—62no—
294(C2×D3)⋊C4—62no—
295(C2×D3)⋊C4—62no—
296(C2×D3)⋊C4—62no—
297(C2×D3)⋊C4—62no—
298(C2×D3)⋊C4—62no—
299C4⋊Dic3—21no—
300C4⋊Dic3—62no—
301C4⋊Dic3—61no—
302C4⋊Dic3—61no—
303C4⋊Dic3—121no—
304Dic3⋊C4—62no—
305Dic3⋊C4—62no—
306Dic3⋊C4—62no—
307C4×Dic3—32no—
308C4×Dic3—32no—
309C4×Dic3—62no—
310C4×Dic3#6712yescomplemented
311#208—21no—
312#208—21no—
313C2×C3⋊C8#6712yescomplemented
314Dic12—62no—
315D24—62no—
316#204—62no—
317#204—62no—
318C22×C32—41no—
319C22×C32#12011yescharacteristic
320C22×C32#12011yescharacteristic
321C22×C32#12111yescharacteristic
322C2×C3⋊D3—41no—
323C2×C3⋊D3—42no—
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#12011yescharacteristic
334C32×C4#12111yescharacteristic
335C32×C4#12111yescharacteristic
336C32×C4#12711yescharacteristic
337C3⋊Dic3—41no—
338C3⋊Dic3—42no—
339C3×Dic3—42no—
340C3×Dic3—41no—
341C3×Dic3—41no—
342C2×#41—31no—
343C2×#41—91no—
344C23×C4—31no—
345#137—181no—
346#137—181no—
347AGL(1,ℤ/8)—181no—
348AGL(1,ℤ/8)—181no—
349#135—182no—
350C2×M16—31no—
351C2×M16D3211yescharacteristic
352#123—181no—
353#123—181no—
354C22⋊Q8—181no—
355C22⋊Q8—181no—
356#121—181no—
357#121—181no—
358#120—181no—
359#120—181no—
360C4×D4—182no—
361C4×D4—182no—
362#117—31no—
363#117—91no—
364#104—62no—
365#104—182no—
366C22⋊C8—62no—
367C23×C3—21no—
368C23×C3—61no—
369C23×C3—61no—
370C23×C3—61no—
371C23×C3—61no—
372C23×C3—122no—
373C23×C3C2×D1211yescharacteristic
374C23×C3D3×D411yescharacteristic
375C22×D3—21no—
376C22×D3—21no—
377C22×D3—21no—
378C22×D3—21no—
379C22×D3—42no—
380C22×D3—61no—
381C22×D3—61no—
382C22×D3—121no—
383C3×Q8—61no—
384C3×Q8—61no—
385C3×D4—61no—
386C3×D4—61no—
387C3×D4—121no—
388C3×D4—121no—
389C2×C3×C4—21no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4—21no—
395C2×C3×C4—61no—
396C2×C3×C4—61no—
397C2×C3×C4—62no—
398C2×C3×C4—61no—
399C2×C3×C4—61no—
400C2×C3×C4—121no—
401C2×C3×C4—121no—
402C2×C3×C4—121no—
403C2×C3×C4—121no—
404C2×C3×C4—121no—
405C2×C3×C4—121no—
406C2×C3×C4C2×D1211yescharacteristic
407C2×C3×C4#23511yescharacteristic
408C2×C3×C4#23511yescharacteristic
409C2×C3×C4D3×D411yescharacteristic
410C2×C3×C4D3×D411yescharacteristic
411C2×C3×C4D3×D411yescharacteristic
412C2×C3×C4D3×D411yescharacteristic
413C2×C3×C4D3×D411yescharacteristic
414C2×C3×C4D3×D411yescharacteristic
415C2×C3×C4D3×D411yescharacteristic
416C2×C3×C4C2×#6711yescharacteristic
417C2×C3×C4C2×#6711yescharacteristic
418#67—41no—
419#67—41no—
420#67—124no—
421#67—124no—
422#67—124no—
423#67—122no—
424#67—122no—
425#67—121no—
426#67—121no—
427#67—121no—
428#67—121no—
429C2×Dic3—21no—
430C2×Dic3—21no—
431C2×Dic3—21no—
432C2×Dic3—21no—
433C2×Dic3—22no—
434C2×Dic3—62no—
435C2×Dic3—62no—
436C2×Dic3—61no—
437C2×Dic3—61no—
438C2×Dic3—121no—
439C2×Dic3—122no—
440D12—21no—
441D12—21no—
442D12—62no—
443D12—61no—
444D12—61no—
445D12—61no—
446D12—61no—
447D12—121no—
448D12—124no—
449C4×D3—41no—
450C4×D3—41no—
451C4×D3—41no—
452C4×D3—41no—
453C4×D3—41no—
454C4×D3—41no—
455C4×D3—122no—
456C4×D3—122no—
457C4×D3—121no—
458C4×D3—121no—
459C4×D3—121no—
460C4×D3—121no—
461Dic6—21no—
462Dic6—21no—
463Dic6—62no—
464Dic6—61no—
465Dic6—61no—
466Dic6—61no—
467Dic6—61no—
468Dic6—121no—
469C3×C8—42no—
470C3×C8—41no—
471C3×C8—41no—
472C3×C8—62no—
473C3⋊C8—22no—
474C2×C32—21no—
475C2×C32—21no—
476C2×C32—21no—
477C2×C32#39211yescharacteristic
478C3⋊D3—81no—
479C3×D3—42no—
480C3×D3—81no—
481C24—31no—
482#41—61no—
483#41—61no—
484#41—61no—
485#41—61no—
486#41—181no—
487#41—181no—
488#41—181no—
489#41—181no—
490C2×Q8—31no—
491C2×Q8—91no—
492C2×D4—31no—
493C2×D4—61no—
494C2×D4—91no—
495C2×D4—182no—
496C2×D4—182no—
497C2×D4—181no—
498C22×C4—31no—
499C22×C4—61no—
500C22×C4—61no—
501C22×C4—61no—
502C22×C4—61no—
503C22×C4—61no—
504C22×C4—61no—
505C22×C4—61no—
506C22×C4—181no—
507C22×C4C2×D3211yescharacteristic
508Q16—182no—
509SD16—182no—
510SD16—182no—
511D8—182no—
512M16—21no—
513M16—21no—
514M16—61no—
515M16—61no—
516C2×C8—21no—
517C2×C8—32no—
518C4⋊C4—61no—
519C4⋊C4—182no—
520C4⋊C4—182no—
521C4⋊C4—181no—
522C22⋊C4—61no—
523C22⋊C4—182no—
524C22⋊C4—182no—
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—62no—
536C22×C3—62no—
537C22×C3—62no—
538C22×C3—81no—
539C22×C3—121no—
540C22×C3—121no—
541C22×C3—121no—
542C22×C3—122no—
543C22×C3—121no—
544C22×C3—121no—
545C22×C3#88211yescharacteristic
546C22×C3#88211yescharacteristic
547C22×C3#88211yescharacteristic
548C22×C3#88411yescharacteristic
549C22×C3#93011yescharacteristic
550C22×C3#93711yescharacteristic
551C2×D3—22no—
552C2×D3—22no—
553C2×D3—22no—
554C2×D3—41no—
555C2×D3—41no—
556C2×D3—41no—
557C2×D3—41no—
558C2×D3—42no—
559C2×D3—41no—
560C2×D3—122no—
561C2×D3—122no—
562C2×D3—122no—
563C2×D3—121no—
564C2×D3—121no—
565C2×D3—242no—
566C3×C4—21no—
567C3×C4—21no—
568C3×C4—21no—
569C3×C4—21no—
570C3×C4—122no—
571C3×C4—121no—
572C3×C4—121no—
573C3×C4#88211yescharacteristic
574C3×C4#88411yescharacteristic
575C3×C4#88411yescharacteristic
576C3×C4#88411yescharacteristic
577C3×C4#93011yescharacteristic
578C3×C4#93711yescharacteristic
579C3×C4#94011yescharacteristic
580C3×C4#94011yescharacteristic
581Dic3—42no—
582Dic3—41no—
583Dic3—41no—
584Dic3—122no—
585Dic3—122no—
586Dic3—122no—
587Dic3—121no—
588Dic3—121no—
589Dic3—242no—
590C32#201011yescharacteristic, complemented, Sylow
591C23—61no—
592C23—61no—
593C23—61no—
594C23—61no—
595C23—122no—
596C23—181no—
597C23D3×D1211yescharacteristic
598Q8—61no—
599Q8—61no—
600Q8—181no—
601Q8—181no—
602D4—61no—
603D4—61no—
604D4—121no—
605D4—121no—
606D4—181no—
607D4—181no—
608D4—364no—
609D4—364no—
610D4—361no—
611D4—361no—
612C2×C4—61no—
613C2×C4—62no—
614C2×C4—61no—
615C2×C4—61no—
616C2×C4—61no—
617C2×C4—121no—
618C2×C4—121no—
619C2×C4—121no—
620C2×C4—121no—
621C2×C4—121no—
622C2×C4—121no—
623C2×C4—181no—
624C2×C4—182no—
625C2×C4—361no—
626C2×C4—361no—
627C2×C4#379811yescharacteristic
628C2×C4D3×D1211yescharacteristic
629C2×C4#380211yescharacteristic
630C2×C4D3×#6711yescharacteristic
631C2×C4D3×#6711yescharacteristic
632C2×C4#381111yescharacteristic
633C8—41no—
634C8—62no—
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—122no—
646C2×C3—241no—
647C2×C3#496011yescharacteristic
648C2×C3#496011yescharacteristic
649D3—42no—
650D3—81no—
651D3—242no—
652D3—241no—
653D3—241no—
654C22—41no—
655C22—62no—
656C22—62no—
657C22—62no—
658C22—121no—
659C22—121no—
660C22—121no—
661C22—122no—
662C22—121no—
663C22—121no—
664C22—362no—
665C22—361no—
666C22#6390611yescharacteristic
667C22#6392211yescharacteristic
668C22#6392311yescharacteristic
669C4—122no—
670C4—121no—
671C4—121no—
672C4—362no—
673C4—361no—
674C4#6390611yescharacteristic
675C4#6391211yescharacteristic
676C4#6392211yescharacteristic
677C4#6397911yescharacteristic
678C3—21no—
679C3#6999311yescharacteristic, complemented
680C3#7040611yescharacteristic, complemented
681C2—21no—
682C2—21no—
683C2—21no—
684C2—122no—
685C2—241no—
686C2—721no—
687C2#1059139311yescharacteristic
subgroupG/H
centerC4#63979
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#392
hypercenterC2×M16D32
hypocenterC32#2010
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. #10595023C2semidirect
2. #10595022C2semidirect
3. #10594795C2semidirect
4. #10592838C2semidirect
5. C3×#5139C2semidirect
6. C3×#5126C2semidirect
7. #10589158C2semidirect
46. #5139D3semidirect
47. #5126D3semidirect
57. C2×C4⋊(C3⋊D3)D4semidirect
59. C2×#634D4semidirect
66. C2×C3×D12D4semidirect
74. C2×C3×Dic6D4semidirect
82. C4×C3⋊Dic3D4semidirect
85. C3×C4×Dic3D4semidirect
88. C2×C3×C3⋊C8D4semidirect
253. C2×D12D12semidirect
267. C2×Dic6D12semidirect
310. C4×Dic3#67semidirect
313. C2×C3⋊C8#67semidirect
590. C32#2010semidirect
679. C3#69993semidirect
680. C3#70406semidirect

Maximal subgroups

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

subgroupindex
#105950232
#105950222
#105947952
#105928382
C3×#51392
C3×#51262
#105891582
#704063
#699933