Finite Group Databasebeta

← D3×#5203 #11867871

Subgroups — D3×#5203 #11867871

Order 1152.

988 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×#137C211yesmaximal, characteristic, complemented
2D3×#949C211yesmaximal, characteristic
3D3×#948C211yesmaximal, characteristic, complemented
4C2×D3×#215C211yesmaximal, characteristic, complemented
5#10592902C211yesmaximal, characteristic, complemented
6C3×#5203C211yesmaximal, characteristic, complemented
7#10591681C211yesmaximal, characteristic, complemented
8#10591680C211yesmaximal, characteristic, complemented
9#10591643C211yesmaximal, characteristic, complemented
10#10591642C211yesmaximal, characteristic, complemented
11D3×#836C211yesmaximal, characteristic, complemented
12D3×#823C211yesmaximal, characteristic, complemented
13#10590985C211yesmaximal, characteristic, complemented
14#10590979C211yesmaximal, characteristic, complemented
15D3×#822C211yesmaximal, characteristic, complemented
16C2×#5203—31nomaximal
17D3×#471—31nomaximal
18C3×D3×#41C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C2×D3×D12C2211yescharacteristic
21C32×#137C2211yescharacteristic, complemented
22#64158C2211yescharacteristic
23#64157C2211yescharacteristic, complemented
24C2×#3755C2211yescharacteristic, complemented
25C3×#951C2211yescharacteristic, complemented
26C3×#949C2211yescharacteristic
27C3×#948C2211yescharacteristic, complemented
28C3×#942C2211yescharacteristic, complemented
29C2×C3×#215C2211yescharacteristic, complemented
30C3×#918—21no—
31C3×D3×Q16—21no—
32C3×#915—21no—
33C3×D3×SD16—21no—
34C3×#909C2211yescharacteristic, complemented
35C3×D3×M16C2211yescharacteristic
36#63939—21no—
37D3×#215—21no—
38D3×#215—21no—
39D3×#215—21no—
40D3×#215—21no—
41D3×#215—21no—
42#63925—21no—
43D3×#213—21no—
44C2×#3717C2211yescharacteristic, complemented
45C2×#3715C2211yescharacteristic, complemented
46#63825C2211yescharacteristic
47#63823C2211yescharacteristic
48#63815—21no—
49#63815C2211yescharacteristic, complemented
50#63814—21no—
51#63814C2211yescharacteristic, complemented
52D3×#208—21no—
53D3×#208C2211yescharacteristic
54D3×#208C2211yescharacteristic
55C2×D3×C3⋊C8—21no—
56C2×D3×C3⋊C8C2211yescharacteristic
57#63663C2211yescharacteristic, complemented
58#63650C2211yescharacteristic, complemented
59#63649C2211yescharacteristic, complemented
60C3×#836C2211yescharacteristic, complemented
61C3×#823C2211yescharacteristic, complemented
62C3×#822C2211yescharacteristic, complemented
63#63578C2211yescharacteristic, complemented
64#63577C2211yescharacteristic, complemented
65#63560C2211yescharacteristic, complemented
66#63560C2211yescharacteristic, complemented
67#63559C2211yescharacteristic, complemented
68#63558C2211yescharacteristic, complemented
69C2×C3×#137—31no—
70C2×#949—31no—
71C2×#948—31no—
72C22×#215—31no—
73D3×#137D311yescharacteristic, complemented
74D3×AGL(1,ℤ/8)—31no—
75C2×D3×SD16—31no—
76D3×#131—31no—
77C3×#471—31no—
78C2×#836—31no—
79#5203—31no—
80#5203—31no—
81#5203—31no—
82#5203—31no—
83#5203—31no—
84#5203—31no—
85#5203—31no—
86#5203—31no—
87#5203—61no—
88#5203D311yescharacteristic, direct product factor
89#5200—31no—
90#5177—31no—
91#5141—31no—
92C2×#823—31no—
93C2×#822—31no—
94#4898—31no—
95D3×#108—31no—
96#4754—31no—
97D3×#101—31no—
98#4748—31no—
99D3×#100—31no—
100C22×D32—21no—
101C32×#41C2311yescharacteristic
102C2×C32×Q8C2311yescharacteristic
103C2×C4⋊(C3⋊D3)C2311yescharacteristic
104C3×#239D411yescharacteristic
105C3×D3×Q8—21no—
106C3×D3×Q8—21no—
107C3×D3×Q8—21no—
108C3×D3×Q8—21no—
109C3×D3×Q8D411yescharacteristic
110C3×#237—21no—
111C3×#237D411yescharacteristic
112C3×D3×D4—21no—
113C3×D3×D4D411yescharacteristic
114C3×#235—21no—
115C3×#235C2311yescharacteristic
116C2×C3×D12C2311yescharacteristic
117C2×C3×C4×D3—21no—
118C2×C3×C4×D3—21no—
119C2×C3×C4×D3C2311yescharacteristic
120C2×C3×Dic6—21no—
121C2×C3×Dic6C2311yescharacteristic
122C2×#626—21no—
123D3×D12—21no—
124D3×D12—21no—
125D3×D12—21no—
126D3×D12—21no—
127C32×Q16—21no—
128C32×SD16—21no—
129C32×M16C2311yescharacteristic
130#3755—21no—
131#3755—21no—
132#3755—21no—
133#3753—21no—
134#3748—21no—
135#3748C2311yescharacteristic
136#3748C2311yescharacteristic
137C2×C3⋊(C3⋊C8)—21no—
138C2×C3⋊(C3⋊C8)C2311yescharacteristic
139C3×#216—21no—
140C3×#216—21no—
141C3×#215—21no—
142C3×#215—21no—
143C3×#215—21no—
144C3×#215—21no—
145C3×#214—21no—
146C3×#213—21no—
147C3×#208—21no—
148C3×#208C2311yescharacteristic
149C3×#208C2311yescharacteristic
150C3×#208C2311yescharacteristic
151C2×C3×C3⋊C8—21no—
152C2×C3×C3⋊C8C2311yescharacteristic
153C3×Dic12—21no—
154C3×#204—21no—
155C3×ΓL(1,𝔽25)—21no—
156C3×D3×C8—21no—
157#3717—21no—
158#3717—21no—
159#3717—21no—
160#3715—21no—
161#3715—21no—
162#3715—21no—
163#3714—21no—
164#3713—21no—
165#3711—21no—
166#3711—21no—
167#3711—21no—
168#3711—21no—
169D3×C3⋊C8—21no—
170D3×C3⋊C8—21no—
171D3×C3⋊C8—21no—
172D3×C3⋊C8—21no—
173D3×C3⋊C8D411yescharacteristic
174D3×C3⋊C8D411yescharacteristic
175D3×C3⋊C8D411yescharacteristic
176D3×C3⋊C8D411yescharacteristic
177C2×#471—91noSylow
178C2×C3×#41—31no—
179C22×C3×Q8—31no—
180D3×#41C2×D311yescharacteristic
181C2×D3×Q8C2×D311yescharacteristic
182C2×D3×D4—31no—
183C22×D12—31no—
184C3×#137—21no—
185C3×#137—31no—
186C3×#137—31no—
187C3×#137—31no—
188C3×#137—61no—
189C3×#137—61no—
190C3×#137C2×D311yescharacteristic, complemented
191C3×#137C2×D311yescharacteristic, complemented
192C3×AGL(1,ℤ/8)—31no—
193C2×C3×Q16—61no—
194C2×C3×SD16—31no—
195C2×C3×SD16—61no—
196C3×#131—31no—
197C2×C3×M16—31no—
198#951C2×D311yescharacteristic, complemented
199#949—31no—
200#949—31no—
201#949—31no—
202#949—31no—
203#949—61no—
204#949—61no—
205#949—61no—
206#949C2×D311yescharacteristic
207#948—31no—
208#948—31no—
209#948—31no—
210#948—31no—
211#948—61no—
212#948—61no—
213#948—61no—
214#948C2×D311yescharacteristic, complemented
215#942C2×D311yescharacteristic, complemented
216C2×#215—31no—
217C2×#215—31no—
218C2×#215—31no—
219C2×#215—31no—
220C2×#215—61no—
221C2×#215—61no—
222C2×#215—61no—
223C2×#215—61no—
224C2×#215—61no—
225C2×#215—61no—
226C2×#215C2×D311yescharacteristic, complemented
227C2×#214—31no—
228#932—31no—
229C2×#213—61no—
230C2×#208—31no—
231C2×#208—31no—
232C2×#208—61no—
233C22×C3⋊C8—31no—
234C22×C3⋊C8—61no—
235#918—21no—
236D3×Q16—21no—
237#915—21no—
238#914—61no—
239D3×SD16—21no—
240D3×SD16—61no—
241D3×SD16—61no—
242D3×SD16—61no—
243D3×SD16—61no—
244D3×SD16—61no—
245#911—61no—
246D3×D8—61no—
247#909C2×D311yescharacteristic, complemented
248#908—31no—
249#907—31no—
250#907—61no—
251D3×M16—31no—
252D3×M16—31no—
253D3×M16—61no—
254D3×M16C2×D311yescharacteristic
255C2×#204—31no—
256#901—31no—
257#901—61no—
258C2×D3×C8—31no—
259C2×D3×C8—61no—
260C3×#108—31no—
261C3×#101—31no—
262C3×#100—31no—
263#836—31no—
264#836—31no—
265#836—31no—
266#836—31no—
267#836—61no—
268#836C2×D311yescharacteristic, complemented
269#833—31no—
270#824—31no—
271#824—31no—
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#822—31no—
282#822—31no—
283#822—31no—
284#822—61no—
285#822C2×D311yescharacteristic, complemented
286#819—31no—
287C22×C3⋊D3—21no—
288C22×C3×D3—21no—
289C22×C3×D3—21no—
290C22×C3×D3#4111yescharacteristic
291C2×D32—41no—
292C2×D32—41no—
293C2×D32—82no—
294C32×Q8—21no—
295C32×Q8—21no—
296C32×Q8C2×D411yescharacteristic
297C32×D4—21no—
298C32×D4C2×D411yescharacteristic
299C2×C32×C4—21no—
300C2×C32×C4—21no—
301C2×C32×C4C2411yescharacteristic
302C4⋊(C3⋊D3)—21no—
303C4⋊(C3⋊D3)—21no—
304C3×#67—21no—
305C3×#67—21no—
306C3×#67—21no—
307C2×C3×Dic3—21no—
308C2×C3×Dic3—21no—
309C2×C3×Dic3#4111yescharacteristic
310C3×D12—21no—
311C3×D12—21no—
312C3×D12—21no—
313C3×D12C2×D411yescharacteristic
314C3×C4×D3—21no—
315C3×C4×D3—21no—
316C3×C4×D3—21no—
317C3×C4×D3—41no—
318C3×C4×D3—41no—
319C3×C4×D3C2×D411yescharacteristic
320C3×C4×D3C2×D411yescharacteristic
321C3×C4×D3C2×D411yescharacteristic
322C3×C4×D3C2×D411yescharacteristic
323C3×Dic6—21no—
324C3×Dic6—21no—
325C3×Dic6—21no—
326C3×Dic6—41no—
327C3×Dic6—41no—
328C3×Dic6C2×D411yescharacteristic
329#626—41no—
330#626—41no—
331C32×C8—21no—
332C3⋊(C3⋊C8)—21no—
333C3⋊(C3⋊C8)—21no—
334C3⋊(C3⋊C8)C2×D411yescharacteristic
335C3⋊(C3⋊C8)C2×D411yescharacteristic
336C3×C3⋊C8—21no—
337C3×C3⋊C8—21no—
338C3×C3⋊C8—21no—
339C3×C3⋊C8C2×D411yescharacteristic
340C3×C3⋊C8C2×D411yescharacteristic
341C2×#137—31no—
342C2×AGL(1,ℤ/8)—91no—
343C22×SD16—91no—
344C2×#131—91no—
345#471—31no—
346#471—91no—
347#471—91no—
348#471—91no—
349#471—91no—
350#471—91no—
351#471—91no—
352#471—91no—
353C2×#108—91no—
354C2×#101—91no—
355C2×#100—91no—
356C23×D3—61no—
357C23×D3—61no—
358C3×#41—21no—
359C3×#41—31no—
360C3×#41—31no—
361C3×#41—31no—
362C3×#41—61no—
363C3×#41—61no—
364C3×#41C22×D311yescharacteristic
365C3×#41C22×D311yescharacteristic
366C2×C3×Q8—21no—
367C2×C3×Q8—31no—
368C2×C3×Q8—31no—
369C2×C3×Q8—61no—
370C2×C3×Q8—61no—
371C2×C3×Q8—61no—
372C2×C3×Q8—61no—
373C2×C3×Q8—61no—
374C2×C3×Q8C22×D311yescharacteristic
375C2×C3×Q8C22×D311yescharacteristic
376C2×C3×D4—31no—
377C2×C3×D4—31no—
378C2×C3×D4—61no—
379C22×C3×C4—31no—
380C22×C3×C4—61no—
381C22×C3×C4—61no—
382C2×#67—61no—
383#239#6711yescharacteristic
384D3×Q8—21no—
385D3×Q8—21no—
386D3×Q8—21no—
387D3×Q8—21no—
388D3×Q8#6711yescharacteristic
389#237—21no—
390#237#6711yescharacteristic
391D3×D4—21no—
392D3×D4—61no—
393D3×D4—61no—
394D3×D4—61no—
395D3×D4—61no—
396D3×D4#6711yescharacteristic
397#235—21no—
398#235C22×D311yescharacteristic
399C2×D12—31no—
400C2×D12—31no—
401C2×D12—61no—
402C2×D12—61no—
403C2×D12—61no—
404C2×D12—61no—
405C2×D12—61no—
406C2×D12—61no—
407C2×D12C22×D311yescharacteristic
408C2×C4×D3—21no—
409C2×C4×D3—21no—
410C2×C4×D3C22×D311yescharacteristic
411C2×Dic6—21no—
412C2×Dic6C22×D311yescharacteristic
413C3×Q16—21no—
414C3×Q16—21no—
415C3×Q16—41no—
416C3×Q16—61no—
417C3×Q16—61no—
418C3×Q16—61no—
419C3×SD16—21no—
420C3×SD16—21no—
421C3×SD16—41no—
422C3×SD16—61no—
423C3×SD16—61no—
424C3×SD16—61no—
425C3×SD16—61no—
426C3×SD16—61no—
427C3×SD16—61no—
428C3×D8—61no—
429C3×M16—21no—
430C3×M16—31no—
431C3×M16—31no—
432C3×M16—31no—
433C3×M16—61no—
434C3×M16—61no—
435C3×M16C22×D311yescharacteristic
436C3×M16C22×D311yescharacteristic
437C2×C3×C8—31no—
438C2×C3×C8—61no—
439C2×C3×C8—61no—
440#216—21no—
441#216—21no—
442#215—21no—
443#215—21no—
444#215—21no—
445#215—21no—
446#215—61no—
447#215—61no—
448#215—61no—
449#215—61no—
450#215—61no—
451#215—61no—
452#215—61no—
453#215—61no—
454#215—61no—
455#215—61no—
456#215—61no—
457#215—61no—
458#215—121no—
459#215—121no—
460#215—121no—
461#214—21no—
462#214—61no—
463#214—61no—
464#214—61no—
465#213—21no—
466#213—61no—
467#213—61no—
468#213—61no—
469#213—61no—
470#213—61no—
471#213—121no—
472#208—21no—
473#208—31no—
474#208—31no—
475#208—31no—
476#208—31no—
477#208—61no—
478#208—61no—
479#208—61no—
480#208—61no—
481#208—61no—
482#208—61no—
483#208—61no—
484#208—61no—
485#208—121no—
486#208C22×D311yescharacteristic
487#208C22×D311yescharacteristic
488#208C22×D311yescharacteristic
489C2×C3⋊C8—21no—
490C2×C3⋊C8—31no—
491C2×C3⋊C8—31no—
492C2×C3⋊C8—31no—
493C2×C3⋊C8—31no—
494C2×C3⋊C8—31no—
495C2×C3⋊C8—31no—
496C2×C3⋊C8—61no—
497C2×C3⋊C8—61no—
498C2×C3⋊C8—61no—
499C2×C3⋊C8—61no—
500C2×C3⋊C8—61no—
501C2×C3⋊C8—61no—
502C2×C3⋊C8—61no—
503C2×C3⋊C8—121no—
504C2×C3⋊C8C22×D311yescharacteristic
505Dic12—21no—
506D24—61no—
507#204—21no—
508#204—61no—
509#204—61no—
510#204—61no—
511ΓL(1,𝔽25)—21no—
512ΓL(1,𝔽25)—61no—
513ΓL(1,𝔽25)—61no—
514ΓL(1,𝔽25)—61no—
515ΓL(1,𝔽25)—61no—
516D3×C8—21no—
517D3×C8—31no—
518D3×C8—31no—
519D3×C8—31no—
520D3×C8—31no—
521D3×C8—61no—
522D3×C8—61no—
523D3×C8—61no—
524D3×C8—61no—
525C22×C32—21no—
526C22×C32C2×#4111yescharacteristic
527C2×C3⋊D3—41no—
528C2×C3⋊D3—81no—
529C2×C3×D3—22no—
530C2×C3×D3—21no—
531C2×C3×D3—42no—
532C2×C3×D3—41no—
533C2×C3×D3—81no—
534C2×C3×D3#12111yescharacteristic
535C2×C3×D3#12111yescharacteristic
536D32—82no—
537D32—82no—
538C32×C4—21no—
539C32×C4—41no—
540C32×C4C22×D411yescharacteristic
541C32×C4C22×D411yescharacteristic
542C3×Dic3—21no—
543C3×Dic3—41no—
544C3×Dic3#12111yescharacteristic
545C3×Dic3#12111yescharacteristic
546C2×#41—31no—
547C22×Q8—31no—
548C22×D4—91no—
549#137—31no—
550#137—31no—
551#137—31no—
552#137—61no—
553#137—61no—
554#137D3211yescharacteristic, complemented
555AGL(1,ℤ/8)—31no—
556AGL(1,ℤ/8)—91no—
557AGL(1,ℤ/8)—91no—
558AGL(1,ℤ/8)—91no—
559AGL(1,ℤ/8)—181no—
560AGL(1,ℤ/8)—181no—
561C2×Q16—61no—
562C2×SD16—31no—
563C2×SD16—61no—
564C2×SD16—91no—
565C2×SD16—91no—
566C2×SD16—91no—
567C2×SD16—181no—
568C2×SD16—181no—
569C2×SD16—181no—
570C2×SD16—181no—
571C2×SD16—181no—
572C2×D8—181no—
573#131—31no—
574#131—91no—
575#131—91no—
576#131—91no—
577#131—181no—
578#131—181no—
579C2×M16—31no—
580C2×M16—91no—
581C2×M16—91no—
582C2×M16—181no—
583C22×C8—91no—
584C22×C8—181no—
585#108—31no—
586#108—91no—
587#108—91no—
588#108—91no—
589#101—31no—
590#101—91no—
591#101—91no—
592#101—91no—
593#100—31no—
594#100—91no—
595#100—91no—
596#100—91no—
597C23×C3—31no—
598C23×C3—61no—
599C23×C3—61no—
600C22×D3—21no—
601C22×D3—21no—
602C22×D3—61no—
603C22×D3—61no—
604C22×D3—121no—
605C22×D3—121no—
606C22×D3—121no—
607C22×D3—121no—
608C22×D3—121no—
609C22×D3—242no—
610C22×D3—242no—
611C22×D3#23711yescharacteristic
612C3×Q8—21no—
613C3×Q8—21no—
614C3×Q8—21no—
615C3×Q8—21no—
616C3×Q8—21no—
617C3×Q8—31no—
618C3×Q8—41no—
619C3×Q8—41no—
620C3×Q8—61no—
621C3×Q8—61no—
622C3×Q8—61no—
623C3×Q8—121no—
624C3×Q8—121no—
625C3×Q8D3×D411yescharacteristic
626C3×Q8C2×#6711yescharacteristic
627C3×D4—21no—
628C3×D4—21no—
629C3×D4—21no—
630C3×D4—31no—
631C3×D4—41no—
632C3×D4—61no—
633C3×D4—61no—
634C3×D4—61no—
635C3×D4—61no—
636C3×D4—61no—
637C3×D4—61no—
638C3×D4D3×D411yescharacteristic
639C3×D4C2×#6711yescharacteristic
640C2×C3×C4—21no—
641C2×C3×C4—21no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—31no—
646C2×C3×C4—31no—
647C2×C3×C4—31no—
648C2×C3×C4—31no—
649C2×C3×C4—31no—
650C2×C3×C4—41no—
651C2×C3×C4—41no—
652C2×C3×C4—61no—
653C2×C3×C4—61no—
654C2×C3×C4—61no—
655C2×C3×C4—61no—
656C2×C3×C4—61no—
657C2×C3×C4—121no—
658C2×C3×C4—121no—
659C2×C3×C4C23×D311yescharacteristic
660C2×C3×C4C23×D311yescharacteristic
661#67—21no—
662#67—21no—
663#67—21no—
664#67—121no—
665#67—121no—
666C2×Dic3—21no—
667C2×Dic3—21no—
668C2×Dic3#23711yescharacteristic
669D12—21no—
670D12—21no—
671D12—21no—
672D12—61no—
673D12—61no—
674D12—61no—
675D12—61no—
676D12—121no—
677D12—121no—
678D12—121no—
679D12—121no—
680D12C2×#6711yescharacteristic
681C4×D3—21no—
682C4×D3—21no—
683C4×D3—21no—
684C4×D3—41no—
685C4×D3—41no—
686C4×D3D3×D411yescharacteristic
687C4×D3D3×D411yescharacteristic
688C4×D3C2×#6711yescharacteristic
689C4×D3C2×#6711yescharacteristic
690Dic6—21no—
691Dic6—21no—
692Dic6—21no—
693Dic6—41no—
694Dic6—41no—
695Dic6C2×#6711yescharacteristic
696C3×C8—21no—
697C3×C8—21no—
698C3×C8—31no—
699C3×C8—31no—
700C3×C8—41no—
701C3×C8—61no—
702C3×C8—61no—
703C3×C8—61no—
704C3⋊C8—21no—
705C3⋊C8—21no—
706C3⋊C8—21no—
707C3⋊C8—31no—
708C3⋊C8—31no—
709C3⋊C8—31no—
710C3⋊C8—31no—
711C3⋊C8—61no—
712C3⋊C8—61no—
713C3⋊C8—61no—
714C3⋊C8—61no—
715C3⋊C8—61no—
716C3⋊C8—61no—
717C3⋊C8—121no—
718C3⋊C8—121no—
719C3⋊C8D3×D411yescharacteristic
720C3⋊C8D3×D411yescharacteristic
721C2×C32—21no—
722C2×C32—41no—
723C2×C32C2×#12111yescharacteristic
724C3⋊D3—81no—
725C3×D3—21no—
726C3×D3—41no—
727C3×D3—81no—
728C3×D3#47112yescomplemented
729C24—181no—
730#41—31no—
731#41—31no—
732#41—31no—
733#41—61no—
734#41—61no—
735#41C2×D3211yescharacteristic
736C2×Q8—31no—
737C2×Q8—31no—
738C2×Q8—61no—
739C2×Q8—61no—
740C2×Q8—61no—
741C2×Q8—61no—
742C2×Q8—61no—
743C2×Q8C2×D3211yescharacteristic
744C2×D4—31no—
745C2×D4—31no—
746C2×D4—61no—
747C2×D4—91no—
748C2×D4—181no—
749C2×D4—181no—
750C2×D4—181no—
751C2×D4—181no—
752C2×D4—181no—
753C22×C4—31no—
754C22×C4—61no—
755C22×C4—61no—
756Q16—21no—
757Q16—61no—
758Q16—61no—
759Q16—61no—
760SD16—21no—
761SD16—61no—
762SD16—61no—
763SD16—61no—
764SD16—61no—
765SD16—61no—
766SD16—61no—
767SD16—181no—
768SD16—181no—
769SD16—181no—
770SD16—181no—
771SD16—181no—
772SD16—181no—
773SD16—181no—
774SD16—181no—
775SD16—181no—
776D8—61no—
777D8—181no—
778D8—181no—
779D8—181no—
780M16—31no—
781M16—31no—
782M16—31no—
783M16—61no—
784M16—61no—
785M16—91no—
786M16—91no—
787M16—181no—
788M16—181no—
789M16—181no—
790M16—181no—
791M16—181no—
792M16C2×D3211yescharacteristic
793C2×C8—31no—
794C2×C8—61no—
795C2×C8—61no—
796C2×C8—91no—
797C2×C8—91no—
798C2×C8—91no—
799C2×C8—91no—
800C2×C8—91no—
801C2×C8—181no—
802C2×C8—181no—
803C2×C8—181no—
804C2×C8—181no—
805C2×C8—181no—
806C22×C3—21no—
807C22×C3—21no—
808C22×C3—21no—
809C22×C3—31no—
810C22×C3—31no—
811C22×C3—41no—
812C22×C3—62no—
813C22×C3—61no—
814C22×C3—122no—
815C22×C3—121no—
816C22×C3—241no—
817C22×C3C2×#23711yescharacteristic
818C22×C3D3×#4111yescharacteristic
819C2×D3—22no—
820C2×D3—21no—
821C2×D3—42no—
822C2×D3—41no—
823C2×D3—81no—
824C2×D3—121no—
825C2×D3—121no—
826C2×D3—241no—
827C2×D3—242no—
828C2×D3—242no—
829C2×D3—242no—
830C2×D3—242no—
831C2×D3—241no—
832C2×D3—241no—
833C2×D3—481no—
834C2×D3#93911yescharacteristic
835C2×D3#93911yescharacteristic
836C3×C4—21no—
837C3×C4—21no—
838C3×C4—21no—
839C3×C4—21no—
840C3×C4—31no—
841C3×C4—31no—
842C3×C4—41no—
843C3×C4—41no—
844C3×C4—41no—
845C3×C4—61no—
846C3×C4—81no—
847C3×C4—121no—
848C3×C4C2×D3×D411yescharacteristic
849C3×C4C2×D3×D411yescharacteristic
850C3×C4C2×D3×D411yescharacteristic
851C3×C4C22×#6711yescharacteristic
852Dic3—21no—
853Dic3—41no—
854Dic3#93911yescharacteristic
855Dic3#93911yescharacteristic
856C32C2×#47111yescharacteristic, complemented, Sylow
857C23—31no—
858C23—61no—
859C23—61no—
860C23—181no—
861C23—361no—
862C23—361no—
863C23—722no—
864Q8—21no—
865Q8—21no—
866Q8—31no—
867Q8—61no—
868Q8—61no—
869Q8—61no—
870Q8—121no—
871Q8—121no—
872Q8D3×#6711yescharacteristic
873D4—21no—
874D4—31no—
875D4—61no—
876D4—61no—
877D4—61no—
878D4—61no—
879D4—61no—
880D4—61no—
881D4—181no—
882D4—181no—
883D4—361no—
884D4—361no—
885D4D3×#6711yescharacteristic
886C2×C4—21no—
887C2×C4—21no—
888C2×C4—31no—
889C2×C4—31no—
890C2×C4—31no—
891C2×C4—31no—
892C2×C4—31no—
893C2×C4—61no—
894C2×C4—61no—
895C2×C4—61no—
896C2×C4—61no—
897C2×C4—61no—
898C2×C4—121no—
899C2×C4—121no—
900C2×C4C22×D3211yescharacteristic
901C8—21no—
902C8—31no—
903C8—31no—
904C8—61no—
905C8—61no—
906C8—61no—
907C8—91no—
908C8—91no—
909C8—181no—
910C8—181no—
911C2×C3—21no—
912C2×C3—21no—
913C2×C3—21no—
914C2×C3—32no—
915C2×C3—41no—
916C2×C3—41no—
917C2×C3—41no—
918C2×C3—61no—
919C2×C3—81no—
920C2×C3—121no—
921C2×C3—241no—
922C2×C3D3×#12111yescharacteristic
923C2×C3C2×#93911yescharacteristic
924D3—21no—
925D3—41no—
926D3—81no—
927D3—241no—
928D3—241no—
929D3—481no—
930D3#520312yesdirect product factor
931C22—21no—
932C22—31no—
933C22—31no—
934C22—62no—
935C22—61no—
936C22—122no—
937C22—121no—
938C22—241no—
939C22—361no—
940C22—721no—
941C22—722no—
942C22—722no—
943C22D3×#23711yescharacteristic
944C4—21no—
945C4—31no—
946C4—31no—
947C4—41no—
948C4—61no—
949C4—121no—
950C4D32×D411yescharacteristic
951C4C2×D3×#6711yescharacteristic
952C3—21no—
953C3D3×#47111yescharacteristic, complemented
954C3C2×#520311yescharacteristic, complemented
955C2—21no—
956C2—32no—
957C2—41no—
958C2—61no—
959C2—121no—
960C2—241no—
961C2—721no—
962C2D3×#93911yescharacteristic
subgroupG/H
centerC2D3×#939
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#137C22
socleC2×C32C2×#121
prime radicalD3×#949C2
hypercenter#137D32
hypocenterC32C2×#471
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
1. C3×D3×#137C2semidirect
3. D3×#948C2semidirect
4. C2×D3×#215C2semidirect
5. #10592902C2semidirect
6. C3×#5203C2semidirect
7. #10591681C2semidirect
8. #10591680C2semidirect
9. #10591643C2semidirect
10. #10591642C2semidirect
11. D3×#836C2semidirect
12. D3×#823C2semidirect
13. #10590985C2semidirect
14. #10590979C2semidirect
15. D3×#822C2semidirect
21. C32×#137C22semidirect
23. #64157C22semidirect
24. C2×#3755C22semidirect
25. C3×#951C22semidirect
27. C3×#948C22semidirect
28. C3×#942C22semidirect
29. C2×C3×#215C22semidirect
34. C3×#909C22semidirect
44. C2×#3717C22semidirect
45. C2×#3715C22semidirect
49. #63815C22semidirect
51. #63814C22semidirect
57. #63663C22semidirect
58. #63650C22semidirect
59. #63649C22semidirect
60. C3×#836C22semidirect
61. C3×#823C22semidirect
62. C3×#822C22semidirect
63. #63578C22semidirect
64. #63577C22semidirect
65. #63560C22semidirect
66. #63560C22semidirect
67. #63559C22semidirect
68. #63558C22semidirect
73. D3×#137D3semidirect
88. #5203D3direct (N × H)
190. C3×#137C2×D3semidirect
191. C3×#137C2×D3semidirect
198. #951C2×D3semidirect
214. #948C2×D3semidirect
215. #942C2×D3semidirect
226. C2×#215C2×D3semidirect
247. #909C2×D3semidirect
268. #836C2×D3semidirect
278. #823C2×D3semidirect
285. #822C2×D3semidirect
554. #137D32semidirect
728. C3×D3#471semidirect
856. C32C2×#471semidirect
930. D3#5203direct (N × H)
953. C3D3×#471semidirect
954. C3C2×#5203semidirect

Maximal subgroups

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

subgroupindex
C3×D3×#1372
D3×#9492
D3×#9482
C2×D3×#2152
#105929022
C3×#52032
#105916812
#105916802
#105916432
#105916422
D3×#8362
D3×#8232
#105909852
#105909792
D3×#8222
C2×#52033
D3×#4713