Finite Group Databasebeta

← #11792417

Subgroups — #11792417

Order 1152.

835 conjugacy classes of subgroups.

The subgroup lattice has 671 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5524C211yesmaximal, characteristic, complemented
2#10595022C211yesmaximal, characteristic, complemented
3#10594786C211yesmaximal, characteristic, complemented
4C3×#5005C211yesmaximal, characteristic, complemented
5#10591110C211yesmaximal, characteristic, complemented
6#10591069C211yesmaximal, characteristic, complemented
7#10589397C211yesmaximal, characteristic, complemented
8#71715—31nomaximal
9#70406—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C22×C3×C4×D3C2211yescharacteristic
13C32×#117C2211yescharacteristic
14#64135C2211yescharacteristic
15C2×#3748C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#897—21no—
18C3×#895—21no—
19C3×#886—21no—
20C3×#882—21no—
21C3×C4×D12—22no—
22#63976—21no—
23#63961—21no—
24#63908—21no—
25C4×#625—22no—
26#63856—21no—
27#63827—21no—
28#63827—21no—
29#63823—21no—
30#63823—21no—
31#63822—22no—
32C3×#805—22no—
33#63568—22no—
34(C2×D3)⋊(C3⋊C8)—22no—
35C3×#525—31no—
36#5828—31no—
37#5822—31no—
38#5822—31no—
39#5791—31no—
40#5524D311yescharacteristic, complemented
41C3×#421—31no—
42#5236—31no—
43#5207—31no—
44#5139—31no—
45#5126—31no—
46#5005D311yescharacteristic, complemented
47#4531—31no—
48#4531—31no—
49#4531—61no—
50C23×C3×D3D411yescharacteristic
51C22×C32×C4C2311yescharacteristic
52C2×C3×#67—21no—
53C2×C3×#67—21no—
54C22×C3×Dic3D411yescharacteristic
55C3×#235—21no—
56C3×#235—21no—
57C3×#235—21no—
58C3×#235—21no—
59C3×#235—21no—
60C3×#235—21no—
61C3×#235—21no—
62C3×#235—21no—
63C2×C3×D12—22no—
64C2×C3×D12D411yescharacteristic, complemented
65C2×C3×D12D411yescharacteristic, complemented
66C2×C3×C4×D3—21no—
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×C3×Dic6D411yescharacteristic, complemented
76C2×#625—22no—
77C32×C4⋊C4—21no—
78C32×C22⋊C4—21no—
79C32×C42D412yescomplemented
80#3757—21no—
81C4⋊(C3⋊Dic3)—21no—
82C4×C3⋊Dic3D412yescomplemented
83#3748—21no—
84#3748—21no—
85C2×C3⋊(C3⋊C8)D412yescomplemented
86C3×(C2×D3)⋊C4—22no—
87C3×(C2×D3)⋊C4—22no—
88C3×C4⋊Dic3—22no—
89C3×#208—21no—
90C3×#208—21no—
91C2×C3×C3⋊C8—21no—
92#3724—22no—
93(C2×D3)⋊Dic3—22no—
94(C2×D3)⋊Dic3—22no—
95#3718—22no—
96#3715—22no—
97#3715—22no—
98#3713—22no—
99#2010—91noSylow
100C2×C3×#41—31no—
101C2×C3×#41—31no—
102C23×C3×C4—31no—
103C2×#235C2×D311yescharacteristic
104C2×#235C2×D311yescharacteristic
105C22×C4×D3C2×D311yescharacteristic
106C2×C3×M16—31no—
107C3×#123—61no—
108C3×C22⋊Q8—61no—
109C3×#121—61no—
110C3×#120—61no—
111C3×C4×D4—62no—
112C3×#117—21no—
113C3×#117C2×D311yescharacteristic
114C3×#117C2×D311yescharacteristic
115#953—61no—
116#951—61no—
117#951—61no—
118#950—62no—
119#950—62no—
120#949—61no—
121#949—61no—
122#946—61no—
123#942—61no—
124#942—61no—
125#938—61no—
126#937—61no—
127#935—61no—
128#932—61no—
129#932—61no—
130#930—61no—
131#929—61no—
132C4×#67—62no—
133C4×#67—62no—
134#926—31no—
135#926—31no—
136#926—61no—
137#924—61no—
138C2×#208—31no—
139C2×#208—31no—
140C2×#208—61no—
141C2×#208C2×D311yescharacteristic
142#897—21no—
143#895—21no—
144#886—21no—
145#882—21no—
146C4×D12—22no—
147C3×#104—62no—
148#837—62no—
149#830—62no—
150#825—62no—
151(C2×D3)⋊C8—62no—
152#805—22no—
153C23×C32C2×D411yescharacteristic
154C22×C3×D3—21no—
155C22×C3×D3—21no—
156C22×C3×D3—21no—
157C22×C3×D3—21no—
158C22×C3×D3—21no—
159C22×C3×D3—42no—
160C2×C32×C4—22no—
161C2×C32×C4C2×D411yescharacteristic
162C2×C32×C4C2×D411yescharacteristic
163C2×C32×C4C2×D411yescharacteristic
164C2×C32×C4C2×D411yescharacteristic
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4#4111yescharacteristic
167C2×C3⋊Dic3—22no—
168C3×#67—41no—
169C3×#67—41no—
170C3×#67—41no—
171C3×#67—41no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—21no—
177C3×D12—21no—
178C3×D12—21no—
179C3×D12—21no—
180C3×D12—21no—
181C3×D12—44no—
182C3×C4×D3—41no—
183C3×C4×D3—41no—
184C3×C4×D3—41no—
185C3×C4×D3—41no—
186C3×C4×D3—41no—
187C3×C4×D3—41no—
188C3×C4×D3—41no—
189C3×C4×D3—41no—
190C3×Dic6—21no—
191C3×Dic6—21no—
192C3×Dic6—21no—
193C3×Dic6—21no—
194#625—44no—
195C3⋊(C3⋊C8)—22no—
196C3×C3⋊C8—41no—
197#575—91no—
198#525—31no—
199#525—91no—
200#421—31no—
201#421—91no—
202#407—91no—
203H(3,ℤ/4)—91no—
204C24×C3—31no—
205C23×D3#6711yescharacteristic
206C3×#41—61no—
207C3×#41—61no—
208C3×#41—61no—
209C3×#41—61no—
210C3×#41—61no—
211C3×#41—61no—
212C3×#41—61no—
213C3×#41—61no—
214C2×C3×Q8—31no—
215C2×C3×Q8—31no—
216C2×C3×D4—31no—
217C2×C3×D4—31no—
218C2×C3×D4—62no—
219C2×C3×D4—61no—
220C2×C3×D4—61no—
221C22×C3×C4—21no—
222C22×C3×C4—31no—
223C22×C3×C4—61no—
224C22×C3×C4—61no—
225C22×C3×C4—61no—
226C22×C3×C4—61no—
227C22×C3×C4—61no—
228C22×C3×C4—61no—
229C22×C3×C4—61no—
230C22×C3×C4—61no—
231C22×C3×C4C22×D311yescharacteristic
232C22×C3×C4C22×D311yescharacteristic
233C2×#67—21no—
234C2×#67—21no—
235C2×#67—62no—
236C2×#67—62no—
237C22×Dic3#6711yescharacteristic
238#235—21no—
239#235—21no—
240#235—21no—
241#235—21no—
242#235—21no—
243#235—21no—
244#235—21no—
245#235—21no—
246C2×D12—22no—
247C2×D12D1211yescharacteristic, complemented
248C2×D12#6711yescharacteristic, complemented
249C2×C4×D3—21no—
250C2×C4×D3—21no—
251C2×C4×D3—21no—
252C2×C4×D3—21no—
253C2×C4×D3—21no—
254C2×C4×D3—21no—
255C2×C4×D3—21no—
256C2×C4×D3—21no—
257C2×Dic6D1211yescharacteristic, complemented
258C2×Dic6#6711yescharacteristic, complemented
259C3×M16—61no—
260C3×M16—61no—
261C2×C3×C8—61no—
262C3×C4⋊C4—21no—
263C3×C4⋊C4—21no—
264C3×C4⋊C4—41no—
265C3×C4⋊C4—62no—
266C3×C22⋊C4—21no—
267C3×C22⋊C4—21no—
268C3×C22⋊C4—41no—
269C3×C22⋊C4—62no—
270C3×C22⋊C4—62no—
271C3×C42—22no—
272C3×C42#6712yescomplemented
273C3×C42#6712yescomplemented
274#217—62no—
275#217—62no—
276#217—61no—
277#217—61no—
278#217—121no—
279#216—62no—
280#216—62no—
281#215—62no—
282#215—62no—
283#214—62no—
284#214—62no—
285#213—62no—
286#213—62no—
287(C2×D3)⋊C4—22no—
288(C2×D3)⋊C4—22no—
289(C2×D3)⋊C4—62no—
290(C2×D3)⋊C4—62no—
291C4⋊Dic3—22no—
292C4⋊Dic3—61no—
293C4⋊Dic3—61no—
294C4⋊Dic3—121no—
295Dic3⋊C4—62no—
296Dic3⋊C4—62no—
297C4×Dic3—32no—
298C4×Dic3—32no—
299C4×Dic3—62no—
300#208—21no—
301#208—21no—
302#208—61no—
303#208—61no—
304#208—61no—
305#208—61no—
306#208—121no—
307#208—121no—
308C2×C3⋊C8—21no—
309C2×C3⋊C8—32no—
310C2×C3⋊C8—32no—
311C2×C3⋊C8—62no—
312C22×C32—41no—
313C22×C32#12011yescharacteristic
314C22×C32#12011yescharacteristic
315C22×C32#12111yescharacteristic
316C2×C3×D3—22no—
317C2×C3×D3—22no—
318C2×C3×D3—22no—
319C2×C3×D3—41no—
320C2×C3×D3—41no—
321C2×C3×D3—41no—
322C2×C3×D3—41no—
323C2×C3×D3—42no—
324C2×C3×D3—42no—
325C2×C3×D3—41no—
326C2×C3×D3—41no—
327C32×C4—42no—
328C32×C4#12011yescharacteristic
329C32×C4#12111yescharacteristic
330C32×C4#12111yescharacteristic
331C32×C4#12711yescharacteristic
332C3⋊Dic3—42no—
333C3×Dic3—41no—
334C3×Dic3—41no—
335C3×Dic3—41no—
336C2×#41—31no—
337C2×#41—31no—
338C23×C4—31no—
339#137—181no—
340#137—181no—
341AGL(1,ℤ/8)—181no—
342AGL(1,ℤ/8)—181no—
343#135—182no—
344C2×M16—31no—
345C2×M16—91no—
346#123—61no—
347#123—181no—
348C22⋊Q8—61no—
349C22⋊Q8—181no—
350#121—61no—
351#121—181no—
352#120—61no—
353#120—181no—
354C4×D4—62no—
355C4×D4—182no—
356#117—91no—
357#117D3211yescharacteristic
358#104—62no—
359#104—182no—
360C22⋊C8—182no—
361C23×C3—21no—
362C23×C3—61no—
363C23×C3—61no—
364C23×C3—61no—
365C23×C3—61no—
366C23×C3—61no—
367C23×C3—122no—
368C23×C3D3×D411yescharacteristic
369C23×C3C2×#6711yescharacteristic
370C22×D3—21no—
371C22×D3—21no—
372C22×D3—21no—
373C22×D3—21no—
374C22×D3—21no—
375C22×D3—42no—
376C3×Q8—61no—
377C3×Q8—61no—
378C3×Q8—61no—
379C3×Q8—61no—
380C3×D4—61no—
381C3×D4—61no—
382C3×D4—61no—
383C3×D4—61no—
384C3×D4—124no—
385C3×D4—121no—
386C3×D4—121no—
387C3×D4—121no—
388C3×D4—121no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—21no—
397C2×C3×C4—42no—
398C2×C3×C4—61no—
399C2×C3×C4—61no—
400C2×C3×C4—61no—
401C2×C3×C4—61no—
402C2×C3×C4—61no—
403C2×C3×C4—121no—
404C2×C3×C4—121no—
405C2×C3×C4—121no—
406C2×C3×C4—121no—
407C2×C3×C4—121no—
408C2×C3×C4—121no—
409C2×C3×C4—121no—
410C2×C3×C4—121no—
411C2×C3×C4C2×D1211yescharacteristic
412C2×C3×C4#23511yescharacteristic
413C2×C3×C4D3×D411yescharacteristic
414C2×C3×C4D3×D411yescharacteristic
415C2×C3×C4D3×D411yescharacteristic
416C2×C3×C4D3×D411yescharacteristic
417C2×C3×C4D3×D411yescharacteristic
418C2×C3×C4D3×D411yescharacteristic
419C2×C3×C4#23711yescharacteristic
420C2×C3×C4C2×#6711yescharacteristic
421C2×C3×C4C2×#6711yescharacteristic
422C2×C3×C4C2×#6711yescharacteristic
423#67—41no—
424#67—41no—
425#67—41no—
426#67—41no—
427#67—124no—
428#67—124no—
429C2×Dic3—21no—
430C2×Dic3—21no—
431C2×Dic3—21no—
432C2×Dic3—21no—
433C2×Dic3—21no—
434C2×Dic3—62no—
435C2×Dic3—62no—
436C2×Dic3—122no—
437D12—21no—
438D12—21no—
439D12—21no—
440D12—21no—
441D12—44no—
442C4×D3—41no—
443C4×D3—41no—
444C4×D3—41no—
445C4×D3—41no—
446C4×D3—41no—
447C4×D3—41no—
448C4×D3—41no—
449C4×D3—41no—
450Dic6—21no—
451Dic6—21no—
452Dic6—21no—
453Dic6—21no—
454C3×C8—121no—
455C3⋊C8—41no—
456C3⋊C8—62no—
457C3⋊C8—62no—
458C3⋊C8—122no—
459C2×C32—21no—
460C2×C32—21no—
461C2×C32—21no—
462C2×C32#39211yescharacteristic
463C3×D3—42no—
464C3×D3—81no—
465C3×D3—81no—
466C24—31no—
467#41—61no—
468#41—61no—
469#41—61no—
470#41—61no—
471#41—61no—
472#41—61no—
473#41—61no—
474#41—61no—
475C2×Q8—31no—
476C2×Q8—31no—
477C2×D4—31no—
478C2×D4—31no—
479C2×D4—62no—
480C2×D4—61no—
481C2×D4—61no—
482C2×D4—182no—
483C22×C4—31no—
484C22×C4—61no—
485C22×C4—61no—
486C22×C4—61no—
487C22×C4—61no—
488C22×C4—61no—
489C22×C4—61no—
490C22×C4—61no—
491C22×C4—61no—
492C22×C4C2×D3211yescharacteristic
493Q16—182no—
494SD16—182no—
495SD16—182no—
496D8—182no—
497M16—61no—
498M16—61no—
499M16—181no—
500M16—181no—
501C2×C8—61no—
502C2×C8—92no—
503C4⋊C4—21no—
504C4⋊C4—62no—
505C4⋊C4—182no—
506C4⋊C4—181no—
507C22⋊C4—21no—
508C22⋊C4—62no—
509C22⋊C4—62no—
510C22⋊C4—182no—
511C22⋊C4—182no—
512C22⋊C4—181no—
513C42—92no—
514C42#62512yescomplemented
515C22×C3—21no—
516C22×C3—21no—
517C22×C3—21no—
518C22×C3—41no—
519C22×C3—41no—
520C22×C3—62no—
521C22×C3—62no—
522C22×C3—62no—
523C22×C3—81no—
524C22×C3—121no—
525C22×C3—121no—
526C22×C3—121no—
527C22×C3—122no—
528C22×C3—122no—
529C22×C3—121no—
530C22×C3—121no—
531C22×C3—121no—
532C22×C3#88211yescharacteristic
533C22×C3#88411yescharacteristic
534C22×C3#93711yescharacteristic
535C22×C3#93711yescharacteristic
536C22×C3#93911yescharacteristic
537C22×C3#95311yescharacteristic
538C2×D3—22no—
539C2×D3—22no—
540C2×D3—22no—
541C2×D3—41no—
542C2×D3—41no—
543C2×D3—41no—
544C2×D3—41no—
545C2×D3—42no—
546C2×D3—42no—
547C2×D3—41no—
548C2×D3—41no—
549C3×C4—21no—
550C3×C4—21no—
551C3×C4—21no—
552C3×C4—21no—
553C3×C4—42no—
554C3×C4—42no—
555C3×C4—82no—
556C3×C4—121no—
557C3×C4—121no—
558C3×C4—121no—
559C3×C4#88211yescharacteristic
560C3×C4#88411yescharacteristic
561C3×C4#93011yescharacteristic
562C3×C4#93711yescharacteristic
563C3×C4#93811yescharacteristic
564C3×C4#93911yescharacteristic
565C3×C4#94011yescharacteristic
566C3×C4#94011yescharacteristic
567Dic3—41no—
568Dic3—41no—
569Dic3—41no—
570Dic3—122no—
571Dic3—122no—
572Dic3—242no—
573C32#201011yescharacteristic, complemented, Sylow
574C23—61no—
575C23—61no—
576C23—61no—
577C23—61no—
578C23—61no—
579C23—122no—
580C23D3×#6711yescharacteristic
581Q8—61no—
582Q8—61no—
583Q8—61no—
584Q8—61no—
585D4—61no—
586D4—61no—
587D4—61no—
588D4—61no—
589D4—124no—
590D4—121no—
591D4—121no—
592D4—121no—
593D4—121no—
594D4—364no—
595C2×C4—22no—
596C2×C4—61no—
597C2×C4—61no—
598C2×C4—61no—
599C2×C4—61no—
600C2×C4—61no—
601C2×C4—121no—
602C2×C4—121no—
603C2×C4—121no—
604C2×C4—121no—
605C2×C4—121no—
606C2×C4—121no—
607C2×C4—121no—
608C2×C4—121no—
609C2×C4—182no—
610C2×C4#379511yescharacteristic
611C2×C4D3×D1211yescharacteristic
612C2×C4#380211yescharacteristic
613C2×C4#380211yescharacteristic
614C2×C4C2×#62511yescharacteristic
615C2×C4D3×#6711yescharacteristic
616C8—121no—
617C8—182no—
618C2×C3—21no—
619C2×C3—21no—
620C2×C3—21no—
621C2×C3—21no—
622C2×C3—21no—
623C2×C3—21no—
624C2×C3—21no—
625C2×C3—41no—
626C2×C3—41no—
627C2×C3—41no—
628C2×C3—122no—
629C2×C3—241no—
630C2×C3—241no—
631C2×C3#496011yescharacteristic
632C2×C3#522311yescharacteristic
633D3—42no—
634D3—81no—
635D3—81no—
636C22—41no—
637C22—62no—
638C22—62no—
639C22—62no—
640C22—121no—
641C22—121no—
642C22—121no—
643C22—122no—
644C22—122no—
645C22—121no—
646C22—121no—
647C22—121no—
648C22#6388511yescharacteristic
649C22#6392211yescharacteristic
650C22#6397611yescharacteristic
651C4—42no—
652C4—121no—
653C4—121no—
654C4—121no—
655C4—362no—
656C4#6388511yescharacteristic
657C4#6390811yescharacteristic
658C4#6391411yescharacteristic
659C4#6392211yescharacteristic
660C3—21no—
661C3#7040611yescharacteristic, complemented
662C3#7171511yescharacteristic, complemented
663C2—21no—
664C2—21no—
665C2—21no—
666C2—122no—
667C2—241no—
668C2—241no—
669C2#1059138911yescharacteristic
subgroupG/H
centerC4#63914
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC2×C32#392
hypercenter#117D32
hypocenterC32#2010
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C3×#5524C2semidirect
2. #10595022C2semidirect
3. #10594786C2semidirect
4. C3×#5005C2semidirect
5. #10591110C2semidirect
6. #10591069C2semidirect
7. #10589397C2semidirect
40. #5524D3semidirect
46. #5005D3semidirect
64. C2×C3×D12D4semidirect
65. C2×C3×D12D4semidirect
74. C2×C3×Dic6D4semidirect
75. C2×C3×Dic6D4semidirect
79. C32×C42D4semidirect
82. C4×C3⋊Dic3D4semidirect
85. C2×C3⋊(C3⋊C8)D4semidirect
247. C2×D12D12semidirect
248. C2×D12#67semidirect
257. C2×Dic6D12semidirect
258. C2×Dic6#67semidirect
272. C3×C42#67semidirect
273. C3×C42#67semidirect
514. C42#625semidirect
573. C32#2010semidirect
661. C3#70406semidirect
662. C3#71715semidirect

Maximal subgroups

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

subgroupindex
C3×#55242
#105950222
#105947862
C3×#50052
#105911102
#105910692
#105893972
#717153
#704063