Finite Group Databasebeta

← #11868029

Subgroups — #11868029

Order 1152.

956 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×#131C211yesmaximal, characteristic, complemented
2#10595470C211yesmaximal, characteristic, complemented
3#10595469C211yesmaximal, characteristic, complemented
4C2×#63806C211yesmaximal, characteristic, complemented
5#10592840C211yesmaximal, characteristic, complemented
6C3×#5141C211yesmaximal, characteristic, complemented
7#10591682C211yesmaximal, characteristic, complemented
8#10591677C211yesmaximal, characteristic, complemented
9#10591007C211yesmaximal, characteristic, complemented
10#10591006C211yesmaximal, characteristic, complemented
11#10590999C211yesmaximal, characteristic, complemented
12#10590997C211yesmaximal, characteristic, complemented
13#10590931C211yesmaximal, characteristic, complemented
14#10590925C211yesmaximal, characteristic, complemented
15D3×#819C211yesmaximal, characteristic, complemented
16#83805—31nomaximal
17#80929—31nomaximal
18C3×D3×#41C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20C2×#3795C2211yescharacteristic
21C32×#131C2211yescharacteristic
22#64160C2211yescharacteristic
23#64158C2211yescharacteristic
24C2×#3744C2211yescharacteristic, complemented
25C3×#951C2211yescharacteristic
26C3×#949C2211yescharacteristic
27C3×#948C2211yescharacteristic
28C3×#907—21no—
29C3×#907C2211yescharacteristic
30C3×D3×M16—21no—
31C3×D3×M16C2211yescharacteristic
32C2×C3×#204C2211yescharacteristic, complemented
33C3×#901—21no—
34C3×#901C2211yescharacteristic
35C2×C3×D3×C8—21no—
36C2×C3×D3×C8C2211yescharacteristic
37#63949—21no—
38#63948—21no—
39#63947—21no—
40#63946—21no—
41#63935—21no—
42#63934—21no—
43#63933—21no—
44#63932—21no—
45C2×#3719C2211yescharacteristic, complemented
46#63831C2211yescharacteristic
47#63827C2211yescharacteristic
48#63825C2211yescharacteristic
49C2×#3714C2211yescharacteristic, complemented
50#63823C2211yescharacteristic
51D3×#208C2211yescharacteristic
52D3×#208C2211yescharacteristic
53#63806—21no—
54#63806—21no—
55#63806—21no—
56#63806—21no—
57#63651C2211yescharacteristic, complemented
58#63650C2211yescharacteristic, complemented
59#63646C2211yescharacteristic, complemented
60C3×#824C2211yescharacteristic, complemented
61C3×#823C2211yescharacteristic, complemented
62C3×#819C2211yescharacteristic, complemented
63#63577C2211yescharacteristic, complemented
64#63577C2211yescharacteristic, complemented
65#63561C2211yescharacteristic, complemented
66#63560C2211yescharacteristic, complemented
67#63559C2211yescharacteristic, complemented
68#63558C2211yescharacteristic, complemented
69C2×C3×#131—31no—
70#5822—31no—
71#5822—31no—
72#5777—31no—
73#5773—31no—
74C2×#916—31no—
75D3×#131D311yescharacteristic, complemented
76C2×#904—31no—
77C3×#471—31no—
78#5204—31no—
79#5199—31no—
80#5177—31no—
81#5143—31no—
82#5143—31no—
83#5142—31no—
84#5142—31no—
85#5141—31no—
86#5141—31no—
87#5141—31no—
88#5141—31no—
89#5141—61no—
90#5141D311yescharacteristic, complemented
91#5132—31no—
92#5132—31no—
93C2×#819—31no—
94#4898—31no—
95D3×#108—31no—
96#4755—31no—
97#4751—31no—
98#4749—31no—
99#4745—31no—
100C32×#41C2311yescharacteristic
101C2×C4⋊(C3⋊D3)C2311yescharacteristic
102C2×#634C2311yescharacteristic
103C3×#239D411yescharacteristic
104C3×D3×Q8D411yescharacteristic
105C3×#237—21no—
106C3×#237D411yescharacteristic
107C3×D3×D4—21no—
108C3×D3×D4D411yescharacteristic
109C3×#235—21no—
110C3×#235C2311yescharacteristic
111C2×C3×D12C2311yescharacteristic
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3C2311yescharacteristic
114C2×C3×Dic6C2311yescharacteristic
115C2×#626—21no—
116C2×#625—21no—
117C2×#624—21no—
118C2×D3×Dic3—21no—
119#3799—21no—
120#3799—21no—
121#3799—21no—
122#3799—21no—
123#3795—21no—
124#3795—21no—
125#3795—21no—
126#3795—21no—
127C32×M16—21no—
128C32×M16C2311yescharacteristic
129C2×C32×C8—21no—
130C2×C32×C8C2311yescharacteristic
131#3756—21no—
132#3755—21no—
133#3754—21no—
134#3753—21no—
135#3748C2311yescharacteristic
136#3748C2311yescharacteristic
137#3744—21no—
138#3744—21no—
139C3×#216—21no—
140C3×#215—21no—
141C3×#214—21no—
142C3×#213—21no—
143C3×#208—21no—
144C3×#208C2311yescharacteristic
145C3×#208C2311yescharacteristic
146C3×#208C2311yescharacteristic
147C2×C3×C3⋊C8—21no—
148C2×C3×C3⋊C8C2311yescharacteristic
149C3×#204—21no—
150C3×#204—21no—
151C3×ΓL(1,𝔽25)—21no—
152C3×ΓL(1,𝔽25)—21no—
153C3×ΓL(1,𝔽25)—21no—
154C3×D3×C8—21no—
155C3×D3×C8—21no—
156C3×D3×C8—21no—
157C3×D3×C8D411yescharacteristic
158C3×D3×C8D411yescharacteristic
159C3×D3×C8D411yescharacteristic
160C3×D3×C8D411yescharacteristic
161#3719—21no—
162#3719—21no—
163#3719—21no—
164#3718—21no—
165#3717—21no—
166#3716—21no—
167#3715—21no—
168#3715—21no—
169#3714—21no—
170#3714—21no—
171#3714—21no—
172#3713—21no—
173#3711—21no—
174#3711—21no—
175D3×C3⋊C8—21no—
176D3×C3⋊C8—21no—
177#3067—91noSylow
178C2×C3×#41—31no—
179D3×#41C2×D311yescharacteristic
180C2×#239—31no—
181C2×#237—31no—
182C2×#235—31no—
183C2×#235—31no—
184C3×#137—31no—
185C3×AGL(1,ℤ/8)—31no—
186C2×C3×SD16—31no—
187C3×#131—21no—
188C3×#131—31no—
189C3×#131—31no—
190C3×#131—31no—
191C3×#131—61no—
192C3×#131—61no—
193C3×#131C2×D311yescharacteristic
194C3×#131C2×D311yescharacteristic
195C2×C3×M16—31no—
196C2×C3×M16—61no—
197C22×C3×C8—31no—
198C22×C3×C8—61no—
199#951—31no—
200#951—31no—
201#951—31no—
202#951—31no—
203#951—61no—
204#951C2×D311yescharacteristic
205#950—61no—
206#950—61no—
207#950—61no—
208#950—61no—
209#949—31no—
210#949—31no—
211#949—31no—
212#949—31no—
213#949—61no—
214#949C2×D311yescharacteristic
215#948C2×D311yescharacteristic
216C2×#216—31no—
217#942—31no—
218#942—61no—
219#942—61no—
220#932—31no—
221#932—61no—
222#932—61no—
223C2×#213—31no—
224C2×#208—31no—
225C2×#208—31no—
226#919—61no—
227#918—61no—
228#916—61no—
229#916—61no—
230#916—61no—
231#916—61no—
232#916—61no—
233#916—61no—
234#915—61no—
235#914—61no—
236#912—61no—
237#911—61no—
238#909—31no—
239#908—31no—
240#907—21no—
241#907C2×D311yescharacteristic
242D3×M16—21no—
243D3×M16—31no—
244D3×M16—31no—
245D3×M16C2×D311yescharacteristic
246C2×Dic12—31no—
247#904—61no—
248#904—61no—
249#904—61no—
250#904—61no—
251C2×D24—31no—
252C2×#204—31no—
253C2×#204—31no—
254C2×#204—61no—
255C2×#204C2×D311yescharacteristic, complemented
256#901—21no—
257#901C2×D311yescharacteristic
258C2×D3×C8—21no—
259C2×D3×C8C2×D311yescharacteristic
260C3×#108—31no—
261C3×#101—31no—
262C3×#100—31no—
263#836—31no—
264#833—31no—
265#824—31no—
266#824—31no—
267#824—31no—
268#824—31no—
269#824—31no—
270#824—61no—
271#824C2×D311yescharacteristic, complemented
272#823—31no—
273#823—31no—
274#823—31no—
275#823—31no—
276#823—31no—
277#823—61no—
278#823C2×D311yescharacteristic, complemented
279#822—31no—
280#822—31no—
281#819—31no—
282#819—31no—
283#819—31no—
284#819—31no—
285#819—61no—
286#819C2×D311yescharacteristic, complemented
287C22×C3⋊D3—21no—
288C22×C3×D3—21no—
289C22×C3×D3—21no—
290C22×C3×D3#4111yescharacteristic
291C32×Q8C2×D411yescharacteristic
292C32×D4—21no—
293C32×D4C2×D411yescharacteristic
294C2×C32×C4—21no—
295C2×C32×C4C2411yescharacteristic
296C2×C3⋊Dic3—21no—
297C4⋊(C3⋊D3)—21no—
298C4⋊(C3⋊D3)—21no—
299#634—21no—
300#634—21no—
301C3×#67—21no—
302C3×#67—21no—
303C3×#67—21no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3#4111yescharacteristic
307C3×D12—21no—
308C3×D12—21no—
309C3×D12—21no—
310C3×D12C2×D411yescharacteristic
311C3×C4×D3—21no—
312C3×C4×D3—21no—
313C3×C4×D3—21no—
314C3×C4×D3C2×D411yescharacteristic
315C3×C4×D3C2×D411yescharacteristic
316C3×C4×D3C2×D411yescharacteristic
317C3×C4×D3C2×D411yescharacteristic
318C3×Dic6—21no—
319C3×Dic6—21no—
320C3×Dic6—21no—
321C3×Dic6C2×D411yescharacteristic
322#626—41no—
323#626—41no—
324#625—41no—
325#625—41no—
326#624—41no—
327#624—41no—
328D3×Dic3—41no—
329D3×Dic3—41no—
330C32×C8—21no—
331C32×C8C2×D411yescharacteristic
332C32×C8C2×D411yescharacteristic
333C3⋊(C3⋊C8)—21no—
334C3⋊(C3⋊C8)—21no—
335C3×C3⋊C8—21no—
336C3×C3⋊C8—21no—
337C3×C3⋊C8—21no—
338C3×C3⋊C8C2×D411yescharacteristic
339C3×C3⋊C8C2×D411yescharacteristic
340#575—91no—
341#575—91no—
342C2×#135—91no—
343C2×#131—31no—
344#473—91no—
345#473—91no—
346#472—91no—
347#472—91no—
348#471—31no—
349#471—91no—
350#471—91no—
351#471—91no—
352C2×#108—91no—
353#413—91no—
354#413—91no—
355C3×#41—21no—
356C3×#41—31no—
357C3×#41—31no—
358C3×#41—31no—
359C3×#41—61no—
360C3×#41—61no—
361C3×#41C22×D311yescharacteristic
362C3×#41C22×D311yescharacteristic
363C2×C3×Q8—31no—
364C2×C3×Q8—31no—
365C2×C3×D4—31no—
366C2×C3×D4—31no—
367C2×C3×D4—61no—
368C22×C3×C4—31no—
369C22×C3×C4—61no—
370C2×#67—61no—
371C2×#67—61no—
372C2×#67—61no—
373C22×Dic3—61no—
374#239—61no—
375#239—61no—
376#239—61no—
377#239—61no—
378#239D1211yescharacteristic
379D3×Q8D1211yescharacteristic
380#237—21no—
381#237—61no—
382#237—61no—
383#237—61no—
384#237—61no—
385#237D1211yescharacteristic
386D3×D4—21no—
387D3×D4D1211yescharacteristic
388#235—21no—
389#235—61no—
390#235—61no—
391#235—61no—
392#235—61no—
393#235—61no—
394#235—61no—
395#235—61no—
396#235—61no—
397#235C22×D311yescharacteristic
398C2×D12—31no—
399C2×D12—31no—
400C2×D12—61no—
401C2×D12—61no—
402C2×D12C22×D311yescharacteristic
403C2×C4×D3—21no—
404C2×C4×D3—61no—
405C2×C4×D3—61no—
406C2×C4×D3—61no—
407C2×C4×D3C22×D311yescharacteristic
408C2×Dic6—31no—
409C2×Dic6—31no—
410C2×Dic6—61no—
411C2×Dic6C22×D311yescharacteristic
412C3×Q16—61no—
413C3×SD16—61no—
414C3×SD16—61no—
415C3×SD16—61no—
416C3×SD16—61no—
417C3×D8—61no—
418C3×M16—21no—
419C3×M16—21no—
420C3×M16—21no—
421C3×M16—31no—
422C3×M16—31no—
423C3×M16—31no—
424C3×M16—41no—
425C3×M16—61no—
426C3×M16—61no—
427C3×M16—61no—
428C3×M16—61no—
429C3×M16C22×D311yescharacteristic
430C3×M16C22×D311yescharacteristic
431C2×C3×C8—21no—
432C2×C3×C8—21no—
433C2×C3×C8—21no—
434C2×C3×C8—31no—
435C2×C3×C8—31no—
436C2×C3×C8—31no—
437C2×C3×C8—31no—
438C2×C3×C8—31no—
439C2×C3×C8—41no—
440C2×C3×C8—61no—
441C2×C3×C8—61no—
442C2×C3×C8—61no—
443C2×C3×C8—61no—
444C2×C3×C8C22×D311yescharacteristic
445C2×C3×C8C22×D311yescharacteristic
446#216—21no—
447#216—61no—
448#216—61no—
449#216—61no—
450#216—61no—
451#216—61no—
452#216—61no—
453#216—61no—
454#216—121no—
455#215—21no—
456#215—61no—
457#215—61no—
458#215—61no—
459#215—61no—
460#215—61no—
461#215—121no—
462#214—21no—
463#214—61no—
464#214—61no—
465#214—61no—
466#214—61no—
467#214—61no—
468#214—121no—
469#213—21no—
470#213—61no—
471#213—61no—
472#213—61no—
473#213—61no—
474#213—61no—
475#213—61no—
476#213—61no—
477#213—121no—
478#208—21no—
479#208—31no—
480#208—31no—
481#208—31no—
482#208—31no—
483#208—61no—
484#208—61no—
485#208—61no—
486#208—61no—
487#208C22×D311yescharacteristic
488#208C22×D311yescharacteristic
489#208C22×D311yescharacteristic
490C2×C3⋊C8—21no—
491C2×C3⋊C8—61no—
492C2×C3⋊C8—61no—
493C2×C3⋊C8C22×D311yescharacteristic
494Dic12—61no—
495Dic12—61no—
496Dic12—61no—
497D24—61no—
498D24—61no—
499D24—61no—
500#204—21no—
501#204—21no—
502#204—61no—
503#204—61no—
504#204—61no—
505#204—61no—
506#204—61no—
507#204—61no—
508#204—121no—
509#204—121no—
510ΓL(1,𝔽25)—21no—
511ΓL(1,𝔽25)—21no—
512ΓL(1,𝔽25)—21no—
513ΓL(1,𝔽25)—61no—
514ΓL(1,𝔽25)—61no—
515D3×C8—21no—
516D3×C8—21no—
517D3×C8—21no—
518D3×C8—61no—
519D3×C8—61no—
520D3×C8#6711yescharacteristic
521D3×C8#6711yescharacteristic
522D3×C8#6711yescharacteristic
523D3×C8#6711yescharacteristic
524C22×C32—21no—
525C22×C32C2×#4111yescharacteristic
526C2×C3⋊D3—41no—
527C2×C3⋊D3—81no—
528C2×C3×D3—21no—
529C2×C3×D3—41no—
530C2×C3×D3—42no—
531C2×C3×D3—41no—
532C2×C3×D3—81no—
533C2×C3×D3#12111yescharacteristic
534C2×C3×D3#12111yescharacteristic
535C32×C4—21no—
536C32×C4C22×D411yescharacteristic
537C32×C4C22×D411yescharacteristic
538C3⋊Dic3—41no—
539C3×Dic3—21no—
540C3×Dic3—41no—
541C3×Dic3#12111yescharacteristic
542C3×Dic3#12111yescharacteristic
543C2×#41—31no—
544C2×#41—91no—
545C2×#41—91no—
546#137—31no—
547#137—91no—
548#137—91no—
549#137—91no—
550#137—181no—
551#137—181no—
552AGL(1,ℤ/8)—31no—
553AGL(1,ℤ/8)—91no—
554AGL(1,ℤ/8)—91no—
555AGL(1,ℤ/8)—91no—
556AGL(1,ℤ/8)—181no—
557AGL(1,ℤ/8)—181no—
558#135—181no—
559#135—181no—
560#135—181no—
561#135—181no—
562#135—181no—
563#135—181no—
564#135—181no—
565#135—181no—
566C2×Q16—91no—
567C2×SD16—31no—
568C2×SD16—91no—
569C2×D8—91no—
570#131—31no—
571#131—31no—
572#131—31no—
573#131—61no—
574#131—61no—
575#131D3211yescharacteristic
576C2×M16—31no—
577C2×M16—61no—
578C2×M16—91no—
579C2×M16—91no—
580C22×C8—31no—
581C22×C8—61no—
582#108—31no—
583#108—91no—
584#108—91no—
585#108—91no—
586#101—31no—
587#101—91no—
588#101—91no—
589#101—91no—
590#100—31no—
591#100—91no—
592#100—91no—
593#100—91no—
594C23×C3—31no—
595C23×C3—61no—
596C23×C3—61no—
597C22×D3—21no—
598C22×D3—21no—
599C22×D3—61no—
600C22×D3—61no—
601C22×D3—121no—
602C22×D3#23511yescharacteristic
603C3×Q8—21no—
604C3×Q8—31no—
605C3×Q8—61no—
606C3×Q8—61no—
607C3×Q8—61no—
608C3×Q8C2×D1211yescharacteristic
609C3×Q8D3×D411yescharacteristic
610C3×D4—21no—
611C3×D4—21no—
612C3×D4—21no—
613C3×D4—31no—
614C3×D4—41no—
615C3×D4—61no—
616C3×D4—61no—
617C3×D4—61no—
618C3×D4—61no—
619C3×D4—61no—
620C3×D4—61no—
621C3×D4C2×D1211yescharacteristic
622C3×D4D3×D411yescharacteristic
623C2×C3×C4—21no—
624C2×C3×C4—21no—
625C2×C3×C4—21no—
626C2×C3×C4—31no—
627C2×C3×C4—31no—
628C2×C3×C4—31no—
629C2×C3×C4—31no—
630C2×C3×C4—31no—
631C2×C3×C4—41no—
632C2×C3×C4—61no—
633C2×C3×C4—61no—
634C2×C3×C4—61no—
635C2×C3×C4—61no—
636C2×C3×C4—61no—
637C2×C3×C4C23×D311yescharacteristic
638C2×C3×C4C23×D311yescharacteristic
639#67—21no—
640#67—21no—
641#67—21no—
642#67—121no—
643#67—121no—
644#67—121no—
645#67—121no—
646#67—121no—
647#67—121no—
648C2×Dic3—21no—
649C2×Dic3—21no—
650C2×Dic3—61no—
651C2×Dic3—61no—
652C2×Dic3—121no—
653C2×Dic3—121no—
654C2×Dic3—121no—
655C2×Dic3#23511yescharacteristic
656D12—21no—
657D12—21no—
658D12—21no—
659D12—61no—
660D12—61no—
661D12—61no—
662D12—61no—
663D12—121no—
664D12—121no—
665D12—121no—
666D12—121no—
667D12C2×D1211yescharacteristic
668C4×D3—21no—
669C4×D3—21no—
670C4×D3—21no—
671C4×D3—121no—
672C4×D3—121no—
673C4×D3—121no—
674C4×D3—121no—
675C4×D3—121no—
676C4×D3—121no—
677C4×D3C2×D1211yescharacteristic
678C4×D3C2×D1211yescharacteristic
679C4×D3C2×#6711yescharacteristic
680C4×D3C2×#6711yescharacteristic
681Dic6—21no—
682Dic6—21no—
683Dic6—21no—
684Dic6—61no—
685Dic6—61no—
686Dic6—61no—
687Dic6—61no—
688Dic6—121no—
689Dic6—121no—
690Dic6C2×D1211yescharacteristic
691C3×C8—21no—
692C3×C8—21no—
693C3×C8—21no—
694C3×C8—21no—
695C3×C8—31no—
696C3×C8—31no—
697C3×C8—41no—
698C3×C8—61no—
699C3×C8—61no—
700C3×C8—61no—
701C3×C8D3×D411yescharacteristic
702C3×C8D3×D411yescharacteristic
703C3×C8C2×#6711yescharacteristic
704C3×C8C2×#6711yescharacteristic
705C3⋊C8—21no—
706C3⋊C8—21no—
707C3⋊C8—21no—
708C3⋊C8—61no—
709C3⋊C8—61no—
710C3⋊C8—61no—
711C3⋊C8—61no—
712C3⋊C8—121no—
713C3⋊C8—121no—
714C3⋊C8C2×#6711yescharacteristic
715C3⋊C8C2×#6711yescharacteristic
716C2×C32—21no—
717C2×C32—41no—
718C2×C32C2×#12111yescharacteristic
719C3⋊D3—81no—
720C3×D3—21no—
721C3×D3—21no—
722C3×D3—41no—
723C3×D3—81no—
724#41—31no—
725#41—31no—
726#41—31no—
727#41—61no—
728#41—61no—
729#41—181no—
730#41—181no—
731#41—181no—
732#41—181no—
733#41—181no—
734#41—181no—
735#41—181no—
736#41—181no—
737#41C2×D3211yescharacteristic
738C2×Q8—31no—
739C2×Q8—31no—
740C2×Q8—91no—
741C2×D4—31no—
742C2×D4—31no—
743C2×D4—61no—
744C2×D4—91no—
745C2×D4—181no—
746C2×D4—181no—
747C22×C4—31no—
748C22×C4—61no—
749C22×C4—181no—
750C22×C4—181no—
751Q16—61no—
752Q16—181no—
753Q16—181no—
754Q16—181no—
755Q16—181no—
756Q16—181no—
757SD16—61no—
758SD16—61no—
759SD16—61no—
760SD16—61no—
761SD16—181no—
762SD16—181no—
763SD16—181no—
764SD16—181no—
765SD16—181no—
766SD16—181no—
767SD16—181no—
768SD16—181no—
769D8—61no—
770D8—181no—
771D8—181no—
772D8—181no—
773D8—181no—
774D8—181no—
775M16—21no—
776M16—31no—
777M16—31no—
778M16—31no—
779M16—61no—
780M16—61no—
781M16—61no—
782M16—61no—
783M16—91no—
784M16—91no—
785M16—181no—
786M16—181no—
787M16C2×D3211yescharacteristic
788C2×C8—21no—
789C2×C8—31no—
790C2×C8—31no—
791C2×C8—31no—
792C2×C8—31no—
793C2×C8—31no—
794C2×C8—61no—
795C2×C8—61no—
796C2×C8—61no—
797C2×C8—61no—
798C2×C8—181no—
799C2×C8—181no—
800C2×C8C2×D3211yescharacteristic
801C22×C3—21no—
802C22×C3—21no—
803C22×C3—21no—
804C22×C3—31no—
805C22×C3—31no—
806C22×C3—41no—
807C22×C3—61no—
808C22×C3—121no—
809C22×C3—122no—
810C22×C3—121no—
811C22×C3—241no—
812C22×C3C2×#23511yescharacteristic
813C22×C3D3×#4111yescharacteristic
814C2×D3—21no—
815C2×D3—41no—
816C2×D3—42no—
817C2×D3—41no—
818C2×D3—81no—
819C2×D3—121no—
820C2×D3—121no—
821C2×D3—241no—
822C2×D3—241no—
823C2×D3—241no—
824C2×D3—481no—
825C2×D3#93011yescharacteristic
826C2×D3#93011yescharacteristic
827C3×C4—21no—
828C3×C4—21no—
829C3×C4—21no—
830C3×C4—21no—
831C3×C4—31no—
832C3×C4—31no—
833C3×C4—41no—
834C3×C4—61no—
835C3×C4—121no—
836C3×C4C22×D1211yescharacteristic
837C3×C4C2×D3×D411yescharacteristic
838C3×C4C2×D3×D411yescharacteristic
839C3×C4C22×#6711yescharacteristic
840Dic3—21no—
841Dic3—41no—
842Dic3—121no—
843Dic3—121no—
844Dic3—241no—
845Dic3#93011yescharacteristic
846Dic3#93011yescharacteristic
847C32#306711yescharacteristic, complemented, Sylow
848C23—31no—
849C23—61no—
850C23—61no—
851C23—181no—
852Q8—31no—
853Q8—61no—
854Q8—61no—
855Q8—61no—
856Q8—181no—
857Q8—181no—
858Q8D3×D1211yescharacteristic
859D4—21no—
860D4—31no—
861D4—61no—
862D4—61no—
863D4—61no—
864D4—61no—
865D4—61no—
866D4—61no—
867D4—181no—
868D4—181no—
869D4—361no—
870D4—361no—
871D4—361no—
872D4—361no—
873D4D3×D1211yescharacteristic
874C2×C4—21no—
875C2×C4—31no—
876C2×C4—31no—
877C2×C4—31no—
878C2×C4—31no—
879C2×C4—31no—
880C2×C4—61no—
881C2×C4—61no—
882C2×C4—61no—
883C2×C4—61no—
884C2×C4—61no—
885C2×C4—181no—
886C2×C4—361no—
887C2×C4—361no—
888C2×C4—361no—
889C2×C4—361no—
890C2×C4C22×D3211yescharacteristic
891C8—21no—
892C8—31no—
893C8—31no—
894C8—61no—
895C8—61no—
896C8—61no—
897C8—181no—
898C8—181no—
899C8D3×#6711yescharacteristic
900C8D3×#6711yescharacteristic
901C2×C3—21no—
902C2×C3—21no—
903C2×C3—21no—
904C2×C3—41no—
905C2×C3—41no—
906C2×C3—41no—
907C2×C3—61no—
908C2×C3—61no—
909C2×C3—81no—
910C2×C3—121no—
911C2×C3—241no—
912C2×C3D3×#12111yescharacteristic
913C2×C3C2×#93011yescharacteristic
914D3—21no—
915D3—21no—
916D3—41no—
917D3—81no—
918D3—241no—
919D3—241no—
920D3—481no—
921C22—21no—
922C22—31no—
923C22—31no—
924C22—61no—
925C22—121no—
926C22—122no—
927C22—121no—
928C22—241no—
929C22—361no—
930C22—721no—
931C22D3×#23511yescharacteristic
932C4—21no—
933C4—31no—
934C4—31no—
935C4—61no—
936C4—121no—
937C4—361no—
938C4C2×D3×D1211yescharacteristic
939C4C2×D3×#6711yescharacteristic
940C3—21no—
941C3#8092911yescharacteristic, complemented
942C3#8380511yescharacteristic, complemented
943C2—21no—
944C2—41no—
945C2—61no—
946C2—61no—
947C2—121no—
948C2—241no—
949C2—721no—
950C2D3×#93011yescharacteristic
subgroupG/H
centerC2D3×#930
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#131C22
socleC2×C32C2×#121
hypercenter#131D32
hypocenterC32#3067
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #131

Complements

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

NH ≅ G/Ntype
1. C3×D3×#131C2semidirect
2. #10595470C2semidirect
3. #10595469C2semidirect
4. C2×#63806C2semidirect
5. #10592840C2semidirect
6. C3×#5141C2semidirect
7. #10591682C2semidirect
8. #10591677C2semidirect
9. #10591007C2semidirect
10. #10591006C2semidirect
11. #10590999C2semidirect
12. #10590997C2semidirect
13. #10590931C2semidirect
14. #10590925C2semidirect
15. D3×#819C2semidirect
24. C2×#3744C22semidirect
32. C2×C3×#204C22semidirect
45. C2×#3719C22semidirect
49. C2×#3714C22semidirect
57. #63651C22semidirect
58. #63650C22semidirect
59. #63646C22semidirect
60. C3×#824C22semidirect
61. C3×#823C22semidirect
62. C3×#819C22semidirect
63. #63577C22semidirect
64. #63577C22semidirect
65. #63561C22semidirect
66. #63560C22semidirect
67. #63559C22semidirect
68. #63558C22semidirect
75. D3×#131D3semidirect
90. #5141D3semidirect
255. C2×#204C2×D3semidirect
271. #824C2×D3semidirect
278. #823C2×D3semidirect
286. #819C2×D3semidirect
847. C32#3067semidirect
941. C3#80929semidirect
942. C3#83805semidirect

Maximal subgroups

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

subgroupindex
C3×D3×#1312
#105954702
#105954692
C2×#638062
#105928402
C3×#51412
#105916822
#105916772
#105910072
#105910062
#105909992
#105909972
#105909312
#105909252
D3×#8192
#838053
#809293