Finite Group Databasebeta

← #11792410

Subgroups — #11792410

Order 1152.

953 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596262C211yesmaximal, characteristic, complemented
2C3×#5791C211yesmaximal, characteristic, complemented
3#10594795C211yesmaximal, characteristic, complemented
4C3×#5207C211yesmaximal, characteristic, complemented
5#10591113C211yesmaximal, characteristic, complemented
6#10591110C211yesmaximal, characteristic, complemented
7#10589158C211yesmaximal, characteristic, complemented
8#71715—31nomaximal
9#69993—31nomaximal
10C23×C32×C4C2211yescharacteristic
11C2×#3828C2211yescharacteristic
12C2×C3×#235C2211yescharacteristic
13#64162—21no—
14#64139—21no—
15#64138—21no—
16C4×#638—22no—
17#64135C2211yescharacteristic
18#64133—21no—
19C3×#953—21no—
20C3×#930—21no—
21C3×#929—21no—
22C3×C4×#67—22no—
23C3×#926C2211yescharacteristic
24C3×#924—21no—
25C2×C3×#208C2211yescharacteristic
26C2×C3×#208C2211yescharacteristic
27#63833—21no—
28#63831—21no—
29#63830—21no—
30#63829—22no—
31#63825—21no—
32C3×#830—22no—
33#63570—22no—
34#63568—22no—
35C3×#525—31no—
36#5822—31no—
37#5791—31no—
38#5791—31no—
39#5791—61no—
40#5791D311yescharacteristic, complemented
41#5748—31no—
42C3×#407—31no—
43#5236—31no—
44#5207D311yescharacteristic, complemented
45#5139—31no—
46#5139—31no—
47#5005—31no—
48#4557—31no—
49#4531—31no—
50C24×C32D411yescharacteristic
51C22×C32×C4—21no—
52C22×C32×C4—21no—
53C22×C32×C4—21no—
54C22×C32×C4—21no—
55C22×C32×C4—21no—
56C22×C32×C4—21no—
57C22×C32×C4D411yescharacteristic
58C22×C32×C4C2311yescharacteristic
59C2×#638—22no—
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—
69C2×C3×#67—21no—
70C3×#235—21no—
71C3×#235—21no—
72C3×#235—21no—
73C3×#235—21no—
74C2×C3×D12D411yescharacteristic, complemented
75C2×C3×C4×D3—21no—
76C2×C3×Dic6D411yescharacteristic, complemented
77#3757—22no—
78#3757—21no—
79#3752—22no—
80C4⋊(C3⋊Dic3)—21no—
81#3750—22no—
82C4×C3⋊Dic3D412yescomplemented
83C3×#217—22no—
84C3×#217—21no—
85C3×(C2×D3)⋊C4—22no—
86C3×C4⋊Dic3—21no—
87C3×Dic3⋊C4—22no—
88C3×C4×Dic3D412yescomplemented
89C3×#208—21no—
90C3×#208—21no—
91C3×#208—21no—
92C3×#208—21no—
93C2×C3×C3⋊C8—21no—
94C2×C3×C3⋊C8D412yescomplemented
95#3719—22no—
96#3717—22no—
97#3716—22no—
98#3714—22no—
99#2010—91noSylow
100C2×C3×#41—31no—
101C23×C3×C4—21no—
102C23×C3×C4C2×D311yescharacteristic
103C23×C3×C4C2×D311yescharacteristic
104C2×#235—31no—
105C2×#235—31no—
106C2×#235—61no—
107C2×#235C2×D311yescharacteristic
108C2×C3×M16—31no—
109C2×C3×M16—31no—
110C3×#123—61no—
111C3×C22⋊Q8—61no—
112C3×#121—61no—
113C3×#120—61no—
114C3×C4×D4—62no—
115C3×#117—31no—
116#953—21no—
117#953—62no—
118#953—61no—
119#953—61no—
120#951—61no—
121#950—62no—
122#949—61no—
123#942—61no—
124#932—61no—
125#930—21no—
126#930—61no—
127#930—61no—
128#930—62no—
129#929—21no—
130#929—62no—
131#929—61no—
132#929—61no—
133C4×#67—22no—
134C4×#67—62no—
135C4×#67—62no—
136C4×#67—64no—
137#926—31no—
138#926—31no—
139#926—61no—
140#926C2×D311yescharacteristic
141#924—21no—
142#924—61no—
143#924—61no—
144#924—62no—
145C2×#208C2×D311yescharacteristic
146C2×#208C2×D311yescharacteristic
147#909—61no—
148#909—61no—
149#908—61no—
150#908—61no—
151#904—62no—
152C3×C22⋊C8—62no—
153#837—62no—
154#830—22no—
155#825—62no—
156#825—62no—
157#805—62no—
158C23×C32—21no—
159C23×C32—21no—
160C23×C32—21no—
161C23×C32—42no—
162C23×C32C2×D411yescharacteristic
163C22×C3⋊D3—21no—
164C22×C3×D3—21no—
165C2×C32×C4—21no—
166C2×C32×C4—21no—
167C2×C32×C4—21no—
168C2×C32×C4—41no—
169C2×C32×C4—41no—
170C2×C32×C4—41no—
171C2×C32×C4—41no—
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2×D411yescharacteristic
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4#4111yescharacteristic
178#638—44no—
179#638—41no—
180#638—41no—
181C2×C3⋊Dic3—22no—
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—
190C3×#67—41no—
191C3×#67—41no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—21no—
194C3×D12—21no—
195C3×D12—21no—
196C3×C4×D3—41no—
197C3×C4×D3—41no—
198C3×Dic6—21no—
199C3×Dic6—21no—
200C3×C3⋊C8—22no—
201C3×C3⋊C8—41no—
202#575—91no—
203#525—31no—
204#525—91no—
205#421—91no—
206#421—91no—
207#407—31no—
208H(3,ℤ/4)—91no—
209C24×C3—21no—
210C24×C3D1211yescharacteristic
211C24×C3#6711yescharacteristic
212C3×#41—61no—
213C3×#41—61no—
214C3×#41—61no—
215C3×#41—61no—
216C2×C3×Q8—31no—
217C2×C3×D4—31no—
218C2×C3×D4—62no—
219C2×C3×D4—61no—
220C22×C3×C4—22no—
221C22×C3×C4—22no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—41no—
237C22×C3×C4—41no—
238C22×C3×C4—41no—
239C22×C3×C4—41no—
240C22×C3×C4—61no—
241C22×C3×C4D1211yescharacteristic
242C22×C3×C4#6711yescharacteristic
243C22×C3×C4C22×D311yescharacteristic
244C22×C3×C4C22×D311yescharacteristic
245C2×#67—22no—
246C2×#67—21no—
247C2×#67—64no—
248C2×#67—62no—
249C2×#67—62no—
250C2×#67—62no—
251C2×#67—61no—
252C2×#67—61no—
253#235—21no—
254#235—21no—
255#235—21no—
256#235—21no—
257#235—61no—
258#235—61no—
259#235—61no—
260#235—61no—
261#235—61no—
262#235—61no—
263#235—61no—
264#235—61no—
265#235—121no—
266#235—121no—
267#235—121no—
268#235—121no—
269C2×D12—31no—
270C2×D12—31no—
271C2×D12—61no—
272C2×D12#6711yescharacteristic, complemented
273C2×C4×D3—21no—
274C2×C4×D3—62no—
275C2×C4×D3—61no—
276C2×C4×D3—61no—
277C2×Dic6—31no—
278C2×Dic6—31no—
279C2×Dic6—61no—
280C2×Dic6#6711yescharacteristic, complemented
281C3×M16—61no—
282C3×M16—61no—
283C3×M16—61no—
284C3×M16—61no—
285C2×C3×C8—32no—
286C2×C3×C8—61no—
287C3×C4⋊C4—62no—
288C3×C4⋊C4—61no—
289C3×C22⋊C4—62no—
290C3×C22⋊C4—62no—
291C3×C22⋊C4—61no—
292C3×C42—32no—
293#217—22no—
294#217—21no—
295#217—64no—
296#217—62no—
297#217—62no—
298#217—62no—
299#217—61no—
300#217—61no—
301#216—62no—
302#215—62no—
303#214—62no—
304#213—62no—
305(C2×D3)⋊C4—22no—
306(C2×D3)⋊C4—64no—
307(C2×D3)⋊C4—62no—
308(C2×D3)⋊C4—62no—
309C4⋊Dic3—21no—
310C4⋊Dic3—62no—
311C4⋊Dic3—61no—
312C4⋊Dic3—61no—
313Dic3⋊C4—22no—
314Dic3⋊C4—64no—
315Dic3⋊C4—62no—
316Dic3⋊C4—62no—
317C4×Dic3—32no—
318C4×Dic3—32no—
319C4×Dic3—62no—
320C4×Dic3#6712yescomplemented
321#208—21no—
322#208—21no—
323#208—21no—
324#208—21no—
325C2×C3⋊C8—21no—
326C2×C3⋊C8#6712yescomplemented
327Dic12—62no—
328D24—62no—
329#204—62no—
330#204—62no—
331C22×C32—22no—
332C22×C32—22no—
333C22×C32—22no—
334C22×C32—41no—
335C22×C32—41no—
336C22×C32—41no—
337C22×C32—41no—
338C22×C32—41no—
339C22×C32#12011yescharacteristic
340C22×C32#12011yescharacteristic
341C22×C32#12111yescharacteristic
342C2×C3⋊D3—42no—
343C2×C3⋊D3—41no—
344C2×C3×D3—42no—
345C2×C3×D3—41no—
346C32×C4—41no—
347C32×C4#12011yescharacteristic
348C32×C4#12111yescharacteristic
349C32×C4#12111yescharacteristic
350C32×C4#12711yescharacteristic
351C3⋊Dic3—42no—
352C3⋊Dic3—41no—
353C3×Dic3—42no—
354C3×Dic3—41no—
355C2×#41—31no—
356C2×#41—91no—
357C23×C4D3211yescharacteristic
358#137—181no—
359#137—181no—
360AGL(1,ℤ/8)—181no—
361AGL(1,ℤ/8)—181no—
362#135—182no—
363C2×M16—31no—
364C2×M16—31no—
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—91no—
377#104—182no—
378#104—182no—
379C22⋊C8—62no—
380C23×C3—22no—
381C23×C3—21no—
382C23×C3—21no—
383C23×C3—21no—
384C23×C3—21no—
385C23×C3—21no—
386C23×C3—21no—
387C23×C3—21no—
388C23×C3—41no—
389C23×C3—41no—
390C23×C3—42no—
391C23×C3—42no—
392C23×C3—44no—
393C23×C3—61no—
394C23×C3C2×D1211yescharacteristic
395C23×C3C2×#6711yescharacteristic
396C22×D3—21no—
397C22×D3—62no—
398C22×D3—61no—
399C22×D3—61no—
400C3×Q8—61no—
401C3×Q8—61no—
402C3×D4—61no—
403C3×D4—61no—
404C3×D4—124no—
405C3×D4—121no—
406C3×D4—121no—
407C2×C3×C4—22no—
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—21no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—41no—
421C2×C3×C4—41no—
422C2×C3×C4—42no—
423C2×C3×C4—42no—
424C2×C3×C4—42no—
425C2×C3×C4—42no—
426C2×C3×C4—41no—
427C2×C3×C4—41no—
428C2×C3×C4—41no—
429C2×C3×C4—41no—
430C2×C3×C4—41no—
431C2×C3×C4—41no—
432C2×C3×C4—41no—
433C2×C3×C4—41no—
434C2×C3×C4—62no—
435C2×C3×C4—61no—
436C2×C3×C4—121no—
437C2×C3×C4—121no—
438C2×C3×C4#23511yescharacteristic
439C2×C3×C4D3×D411yescharacteristic
440C2×C3×C4D3×D411yescharacteristic
441C2×C3×C4D3×D411yescharacteristic
442C2×C3×C4D3×D411yescharacteristic
443C2×C3×C4D3×D411yescharacteristic
444C2×C3×C4D3×D411yescharacteristic
445C2×C3×C4D3×D411yescharacteristic
446C2×C3×C4#23711yescharacteristic
447C2×C3×C4C2×#6711yescharacteristic
448C2×C3×C4C2×#6711yescharacteristic
449C2×C3×C4C2×#6711yescharacteristic
450#67—44no—
451#67—41no—
452#67—41no—
453#67—122no—
454#67—122no—
455#67—128no—
456#67—124no—
457#67—124no—
458#67—121no—
459#67—121no—
460#67—121no—
461#67—121no—
462C2×Dic3—22no—
463C2×Dic3—21no—
464C2×Dic3—64no—
465C2×Dic3—62no—
466C2×Dic3—62no—
467C2×Dic3—61no—
468C2×Dic3—62no—
469C2×Dic3—61no—
470D12—21no—
471D12—21no—
472D12—61no—
473D12—61no—
474D12—61no—
475D12—61no—
476D12—121no—
477D12—121no—
478C4×D3—41no—
479C4×D3—41no—
480C4×D3—122no—
481C4×D3—122no—
482C4×D3—121no—
483C4×D3—121no—
484C4×D3—121no—
485C4×D3—121no—
486Dic6—21no—
487Dic6—21no—
488Dic6—61no—
489Dic6—61no—
490Dic6—61no—
491Dic6—61no—
492Dic6—121no—
493Dic6—121no—
494C3×C8—62no—
495C3×C8—121no—
496C3⋊C8—22no—
497C3⋊C8—41no—
498C2×C32—21no—
499C2×C32—21no—
500C2×C32—21no—
501C2×C32—42no—
502C2×C32#39211yescharacteristic
503C3⋊D3—81no—
504C3×D3—81no—
505C24#62611yescharacteristic
506#41—61no—
507#41—61no—
508#41—61no—
509#41—61no—
510#41—181no—
511#41—181no—
512#41—181no—
513#41—181no—
514C2×Q8—31no—
515C2×Q8—91no—
516C2×D4—31no—
517C2×D4—62no—
518C2×D4—61no—
519C2×D4—91no—
520C2×D4—182no—
521C2×D4—181no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—61no—
529C22×C4—181no—
530C22×C4#62611yescharacteristic
531C22×C4C2×D3211yescharacteristic
532Q16—182no—
533SD16—182no—
534SD16—182no—
535D8—182no—
536M16—61no—
537M16—61no—
538M16—61no—
539M16—61no—
540C2×C8—32no—
541C2×C8—61no—
542C4⋊C4—62no—
543C4⋊C4—61no—
544C4⋊C4—182no—
545C4⋊C4—181no—
546C22⋊C4—62no—
547C22⋊C4—62no—
548C22⋊C4—61no—
549C22⋊C4—182no—
550C22⋊C4—182no—
551C22⋊C4—181no—
552C42—32no—
553C42—92no—
554C22×C3—22no—
555C22×C3—24no—
556C22×C3—22no—
557C22×C3—22no—
558C22×C3—22no—
559C22×C3—22no—
560C22×C3—22no—
561C22×C3—21no—
562C22×C3—21no—
563C22×C3—21no—
564C22×C3—42no—
565C22×C3—42no—
566C22×C3—41no—
567C22×C3—41no—
568C22×C3—42no—
569C22×C3—42no—
570C22×C3—42no—
571C22×C3—41no—
572C22×C3—41no—
573C22×C3—41no—
574C22×C3—41no—
575C22×C3—41no—
576C22×C3—41no—
577C22×C3—42no—
578C22×C3—42no—
579C22×C3—41no—
580C22×C3—41no—
581C22×C3—122no—
582C22×C3—121no—
583C22×C3#88211yescharacteristic
584C22×C3#88211yescharacteristic
585C22×C3#93011yescharacteristic
586C22×C3#93711yescharacteristic
587C22×C3#93911yescharacteristic
588C22×C3#95311yescharacteristic
589C2×D3—42no—
590C2×D3—41no—
591C2×D3—122no—
592C2×D3—124no—
593C2×D3—122no—
594C2×D3—122no—
595C2×D3—121no—
596C2×D3—121no—
597C3×C4—21no—
598C3×C4—21no—
599C3×C4—21no—
600C3×C4—21no—
601C3×C4—42no—
602C3×C4—41no—
603C3×C4—41no—
604C3×C4—122no—
605C3×C4—121no—
606C3×C4#88411yescharacteristic
607C3×C4#88411yescharacteristic
608C3×C4#93711yescharacteristic
609C3×C4#93711yescharacteristic
610C3×C4#93811yescharacteristic
611C3×C4#93911yescharacteristic
612C3×C4#94011yescharacteristic
613C3×C4#94011yescharacteristic
614Dic3—42no—
615Dic3—41no—
616Dic3—122no—
617Dic3—124no—
618Dic3—122no—
619Dic3—122no—
620Dic3—121no—
621Dic3—121no—
622C32#201011yescharacteristic, complemented, Sylow
623C23—21no—
624C23—21no—
625C23—21no—
626C23—42no—
627C23—61no—
628C23—181no—
629C23C2×#62611yescharacteristic
630Q8—61no—
631Q8—61no—
632Q8—181no—
633Q8—181no—
634D4—61no—
635D4—61no—
636D4—124no—
637D4—121no—
638D4—121no—
639D4—181no—
640D4—181no—
641D4—364no—
642D4—361no—
643D4—361no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—62no—
652C2×C4—61no—
653C2×C4—121no—
654C2×C4—121no—
655C2×C4—182no—
656C2×C4—181no—
657C2×C4—361no—
658C2×C4—361no—
659C2×C4#380411yescharacteristic
660C2×C4D3×#6711yescharacteristic
661C2×C4D3×#6711yescharacteristic
662C2×C4D3×#6711yescharacteristic
663C2×C4#381111yescharacteristic
664C2×C4#381111yescharacteristic
665C8—62no—
666C8—121no—
667C2×C3—22no—
668C2×C3—21no—
669C2×C3—21no—
670C2×C3—21no—
671C2×C3—21no—
672C2×C3—21no—
673C2×C3—21no—
674C2×C3—21no—
675C2×C3—41no—
676C2×C3—41no—
677C2×C3—44no—
678C2×C3—42no—
679C2×C3—42no—
680C2×C3—241no—
681C2×C3#496011yescharacteristic
682C2×C3#522311yescharacteristic
683D3—81no—
684D3—242no—
685D3—241no—
686D3—241no—
687C22—22no—
688C22—22no—
689C22—22no—
690C22—41no—
691C22—41no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—122no—
696C22—121no—
697C22—362no—
698C22—361no—
699C22#6397711yescharacteristic
700C22#6397811yescharacteristic
701C22#6398111yescharacteristic
702C4—41no—
703C4—122no—
704C4—121no—
705C4—362no—
706C4—361no—
707C4#6395811yescharacteristic
708C4#6397111yescharacteristic
709C4#6397911yescharacteristic
710C4#6398311yescharacteristic
711C3—21no—
712C3#6999311yescharacteristic, complemented
713C3#7171511yescharacteristic, complemented
714C2—21no—
715C2—21no—
716C2—21no—
717C2—42no—
718C2—241no—
719C2—721no—
720C2#1059172411yescharacteristic
subgroupG/H
centerC4#63979
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC23×C32×C4C22
socleC2×C32#392
hypercenterC23×C4D32
hypocenterC32#2010
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. #10596262C2semidirect
2. C3×#5791C2semidirect
3. #10594795C2semidirect
4. C3×#5207C2semidirect
5. #10591113C2semidirect
6. #10591110C2semidirect
7. #10589158C2semidirect
40. #5791D3semidirect
44. #5207D3semidirect
65. C2×C4⋊(C3⋊D3)D4semidirect
67. C2×#634D4semidirect
74. C2×C3×D12D4semidirect
76. C2×C3×Dic6D4semidirect
82. C4×C3⋊Dic3D4semidirect
88. C3×C4×Dic3D4semidirect
94. C2×C3×C3⋊C8D4semidirect
272. C2×D12#67semidirect
280. C2×Dic6#67semidirect
320. C4×Dic3#67semidirect
326. C2×C3⋊C8#67semidirect
622. C32#2010semidirect
712. C3#69993semidirect
713. C3#71715semidirect

Maximal subgroups

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

subgroupindex
#105962622
C3×#57912
#105947952
C3×#52072
#105911132
#105911102
#105891582
#717153
#699933