Finite Group Databasebeta

← D3×#4748 #11867894

Subgroups — D3×#4748 #11867894

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
1C2×D3×#214C211yesmaximal, characteristic, complemented
2D3×#932C211yesmaximal, characteristic
3D3×#909C211yesmaximal, characteristic, complemented
4D3×#907C211yesmaximal, characteristic, complemented
5#10592447C211yesmaximal, characteristic, complemented
6C3×#4748C211yesmaximal, characteristic, complemented
7C3×D3×#100C211yesmaximal, characteristic, complemented
8#10591507C211yesmaximal, characteristic, complemented
9#10591407C211yesmaximal, characteristic, complemented
10D3×#824C211yesmaximal, characteristic, complemented
11#10590996C211yesmaximal, characteristic, complemented
12#10590991C211yesmaximal, characteristic, complemented
13#10590989C211yesmaximal, characteristic, complemented
14#10590979C211yesmaximal, characteristic, complemented
15D3×#822C211yesmaximal, characteristic, complemented
16D3×#471—31nomaximal
17C2×#4748—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19D3×#235C2211yescharacteristic
20C2×D3×Dic6C2211yescharacteristic
21C2×#3754C2211yescharacteristic, complemented
22#64141C2211yescharacteristic
23#64118C2211yescharacteristic, complemented
24#64116C2211yescharacteristic, complemented
25C2×C3×#214C2211yescharacteristic, complemented
26C3×#932C2211yescharacteristic
27C3×#909C2211yescharacteristic, complemented
28C3×#907C2211yescharacteristic, complemented
29C3×D3×M16C2211yescharacteristic
30C3×D3×M16C2211yescharacteristic
31#63934—21no—
32#63932—21no—
33D3×#214—21no—
34D3×#214—21no—
35D3×#214—21no—
36D3×#214—21no—
37D3×#214—21no—
38D3×#213—21no—
39#63833C2211yescharacteristic, complemented
40#63831C2211yescharacteristic, complemented
41#63830C2211yescharacteristic
42C2×#3716C2211yescharacteristic, complemented
43C2×#3715C2211yescharacteristic, complemented
44#63823C2211yescharacteristic
45#63817C2211yescharacteristic, complemented
46#63815C2211yescharacteristic, complemented
47D3×#208C2211yescharacteristic
48C2×D3×C3⋊C8C2211yescharacteristic
49#63805—21no—
50#63804—21no—
51#63801—21no—
52#63800—21no—
53D3×Dic12—21no—
54D3×#204—21no—
55D3×ΓL(1,𝔽25)—21no—
56D32×C8—21no—
57C32×#100C2211yescharacteristic, complemented
58#63651C2211yescharacteristic, complemented
59#63649C2211yescharacteristic, complemented
60C3×#833C2211yescharacteristic, complemented
61C3×#824C2211yescharacteristic, complemented
62C3×#823C2211yescharacteristic, complemented
63C3×#823C2211yescharacteristic, complemented
64C3×#822C2211yescharacteristic, complemented
65#63578C2211yescharacteristic, complemented
66#63577C2211yescharacteristic, complemented
67#63561C2211yescharacteristic, complemented
68#63560C2211yescharacteristic, complemented
69C22×#214—31no—
70C2×#932—31no—
71D3×#137—31no—
72D3×AGL(1,ℤ/8)—31no—
73C2×D3×SD16—31no—
74D3×#131—31no—
75C2×#909—31no—
76C2×#907—31no—
77C3×#471—31no—
78C2×C3×#100—31no—
79#5203—31no—
80#5200—31no—
81#5177—31no—
82#5141—31no—
83C2×#824—31no—
84C2×#822—31no—
85#4898—31no—
86D3×#108—31no—
87#4754—31no—
88D3×#101—31no—
89#4748—31no—
90#4748—31no—
91#4748—31no—
92#4748—31no—
93#4748—31no—
94#4748—31no—
95#4748—31no—
96#4748—31no—
97#4748—61no—
98#4748D311yescharacteristic, direct product factor
99D3×#100D311yescharacteristic, complemented
100C23×C3×D3—21no—
101C2×C32×D4C2311yescharacteristic
102#3828C2311yescharacteristic
103C2×#634C2311yescharacteristic
104C2×C3×#67—21no—
105C3×D3×D4—21no—
106C3×D3×D4—21no—
107C3×D3×D4—21no—
108C3×D3×D4—21no—
109C3×#235C2311yescharacteristic
110C2×C3×D12C2311yescharacteristic
111C2×C3×C4×D3C2311yescharacteristic
112C2×C3×Dic6C2311yescharacteristic
113D3×#67—21no—
114C2×#627—21no—
115#3804—21no—
116C2×D3×Dic3—21no—
117D3×D12D411yescharacteristic
118C4×D32—21no—
119#3799D411yescharacteristic
120#3798—21no—
121#3795D411yescharacteristic
122D3×Dic6—21no—
123D3×Dic6—21no—
124D3×Dic6—21no—
125D3×Dic6—21no—
126D3×Dic6D411yescharacteristic
127C32×M16C2311yescharacteristic
128C32×M16C2311yescharacteristic
129#3754—21no—
130#3754—21no—
131#3754—21no—
132#3753—21no—
133#3748C2311yescharacteristic
134C2×C3⋊(C3⋊C8)C2311yescharacteristic
135#3746—21no—
136#3744—21no—
137#3743—21no—
138C8×C3⋊D3—21no—
139C3×#214—21no—
140C3×#214—21no—
141C3×#214—21no—
142C3×#213—21no—
143C3×#208C2311yescharacteristic
144C3×#208C2311yescharacteristic
145C3×#208C2311yescharacteristic
146C2×C3×C3⋊C8C2311yescharacteristic
147C3×Dic12—21no—
148C3×#204—21no—
149C3×ΓL(1,𝔽25)—21no—
150C3×ΓL(1,𝔽25)—21no—
151C3×ΓL(1,𝔽25)—21no—
152C3×D3×C8—21no—
153C3×D3×C8—21no—
154C3×D3×C8—21no—
155#3719—21no—
156#3719—21no—
157#3717—21no—
158#3716—21no—
159#3716—21no—
160#3716—21no—
161#3716—21no—
162#3715—21no—
163#3715—21no—
164#3715—21no—
165#3714—21no—
166#3713—21no—
167#3712—21no—
168#3711—21no—
169#3711—21no—
170#3710—21no—
171D3×C3⋊C8—21no—
172D3×C3⋊C8—21no—
173D3×C3⋊C8D411yescharacteristic
174D3×C3⋊C8D411yescharacteristic
175D3×C3⋊C8D411yescharacteristic
176D3×C3⋊C8D411yescharacteristic
177C2×#471—91noSylow
178C22×C3×D4—31no—
179D3×#41—31no—
180C2×D3×Q8—31no—
181C2×D3×D4C2×D311yescharacteristic
182C2×#235—31no—
183C22×Dic6—31no—
184C3×#137—31no—
185C3×AGL(1,ℤ/8)—31no—
186C2×C3×SD16—31no—
187C3×#131—31no—
188C2×C3×M16—31no—
189C2×C3×M16—31no—
190#951—31no—
191#949—31no—
192#948—31no—
193#942—31no—
194C2×#215—31no—
195C2×#214—31no—
196C2×#214—31no—
197C2×#214—31no—
198C2×#214—31no—
199C2×#214—61no—
200C2×#214—61no—
201C2×#214—61no—
202C2×#214—61no—
203C2×#214—61no—
204C2×#214—61no—
205C2×#214C2×D311yescharacteristic, complemented
206#932—31no—
207#932—31no—
208#932—31no—
209#932—31no—
210#932—61no—
211#932—61no—
212#932—61no—
213#932C2×D311yescharacteristic
214C2×#213—61no—
215C2×#208—31no—
216C22×C3⋊C8—31no—
217#918—61no—
218D3×Q16—61no—
219#915—61no—
220#914—61no—
221D3×SD16—61no—
222D3×SD16—61no—
223D3×SD16—61no—
224D3×SD16—61no—
225D3×SD16—61no—
226D3×SD16—61no—
227#911—61no—
228D3×D8—61no—
229#909—31no—
230#909—31no—
231#909—31no—
232#909—31no—
233#909—61no—
234#909—61no—
235#909—61no—
236#909C2×D311yescharacteristic, complemented
237#908—31no—
238#907—31no—
239#907—31no—
240#907—31no—
241#907—31no—
242#907—61no—
243#907—61no—
244#907—61no—
245#907—61no—
246#907C2×D311yescharacteristic, complemented
247D3×M16—31no—
248D3×M16—61no—
249D3×M16C2×D311yescharacteristic
250D3×M16C2×D311yescharacteristic
251C2×Dic12—61no—
252C2×#204—31no—
253C2×#204—61no—
254#901—31no—
255#901—61no—
256C2×ΓL(1,𝔽25)—61no—
257C2×D3×C8—31no—
258C2×D3×C8—61no—
259C2×D3×C8—61no—
260C3×#108—31no—
261C3×#101—31no—
262C3×#100—21no—
263C3×#100—31no—
264C3×#100—31no—
265C3×#100—31no—
266C3×#100C2×D311yescharacteristic, complemented
267C3×#100C2×D311yescharacteristic, complemented
268#836—31no—
269#833C2×D311yescharacteristic, complemented
270#824—31no—
271#824—31no—
272#824—31no—
273#824—31no—
274#824—31no—
275#824—61no—
276#824C2×D311yescharacteristic, complemented
277#823C2×D311yescharacteristic, complemented
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—
287C23×C32—21no—
288C22×C3×D3—21no—
289C22×C3×D3—41no—
290C22×C3×D3—41no—
291C22×C3×D3—82no—
292C22×C3×D3#4111yescharacteristic
293C2×D32—21no—
294C32×D4—21no—
295C32×D4—21no—
296C2×C32×C4C2411yescharacteristic
297#638—21no—
298C2×C3⋊Dic3—21no—
299C4⋊(C3⋊D3)C2×D411yescharacteristic
300C4×C3⋊D3—21no—
301#634—21no—
302#634—21no—
303#634C2×D411yescharacteristic
304C3×#67—21no—
305C3×#67—41no—
306C3×#67—41no—
307C2×C3×Dic3—21no—
308C2×C3×Dic3#4111yescharacteristic
309C3×D12—21no—
310C3×D12—21no—
311C3×D12C2×D411yescharacteristic
312C3×C4×D3—21no—
313C3×C4×D3C2×D411yescharacteristic
314C3×C4×D3C2×D411yescharacteristic
315C3×C4×D3C2×D411yescharacteristic
316C3×C4×D3C2×D411yescharacteristic
317C3×Dic6—21no—
318C3×Dic6—21no—
319C3×Dic6C2×D411yescharacteristic
320#627—21no—
321#627—41no—
322#627—41no—
323#626—21no—
324#626—21no—
325#625—21no—
326#624—21no—
327D3×Dic3—21no—
328D3×Dic3—21no—
329D3×Dic3—41no—
330D3×Dic3—41no—
331C32×C8—21no—
332C32×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—91no—
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—31no—
356C24×C3—61no—
357C23×D3—21no—
358C3×#41—31no—
359C2×C3×Q8—31no—
360C2×C3×D4—21no—
361C2×C3×D4—31no—
362C2×C3×D4—61no—
363C2×C3×D4—61no—
364C2×C3×D4—61no—
365C2×C3×D4—61no—
366C2×C3×D4—61no—
367C2×C3×D4C22×D311yescharacteristic
368C2×C3×D4C22×D311yescharacteristic
369C22×C3×C4—31no—
370C2×#67—21no—
371C2×#67—61no—
372C22×Dic3—61no—
373#239—31no—
374D3×Q8—31no—
375D3×Q8—61no—
376D3×Q8—61no—
377D3×Q8—61no—
378D3×Q8—61no—
379#237—31no—
380#237—61no—
381D3×D4—21no—
382D3×D4—21no—
383D3×D4—21no—
384D3×D4—21no—
385D3×D4—31no—
386D3×D4—61no—
387#235—31no—
388#235—31no—
389#235—31no—
390#235—31no—
391#235—61no—
392#235—61no—
393#235—61no—
394#235—61no—
395#235C22×D311yescharacteristic
396C2×D12—31no—
397C2×D12C22×D311yescharacteristic
398C2×C4×D3—61no—
399C2×C4×D3—61no—
400C2×C4×D3—61no—
401C2×C4×D3C22×D311yescharacteristic
402C2×Dic6—31no—
403C2×Dic6—31no—
404C2×Dic6—31no—
405C2×Dic6—61no—
406C2×Dic6—61no—
407C2×Dic6—61no—
408C2×Dic6—61no—
409C2×Dic6—61no—
410C2×Dic6—61no—
411C2×Dic6—61no—
412C2×Dic6C22×D311yescharacteristic
413C3×Q16—61no—
414C3×SD16—61no—
415C3×SD16—61no—
416C3×SD16—61no—
417C3×SD16—61no—
418C3×D8—61no—
419C3×M16—21no—
420C3×M16—21no—
421C3×M16—31no—
422C3×M16—31no—
423C3×M16—31no—
424C3×M16—61no—
425C3×M16—61no—
426C3×M16—61no—
427C3×M16C22×D311yescharacteristic
428C3×M16C22×D311yescharacteristic
429C3×M16C22×D311yescharacteristic
430C3×M16C22×D311yescharacteristic
431C2×C3×C8—31no—
432C2×C3×C8—61no—
433C2×C3×C8—61no—
434C2×C3×C8—61no—
435#216—61no—
436#216—61no—
437#215—61no—
438#215—61no—
439#215—61no—
440#215—61no—
441#214—21no—
442#214—21no—
443#214—21no—
444#214—61no—
445#214—61no—
446#214—61no—
447#214—61no—
448#214—61no—
449#214—61no—
450#214—61no—
451#214—61no—
452#214—61no—
453#214—61no—
454#214—61no—
455#214—61no—
456#214—61no—
457#214—121no—
458#214—121no—
459#214—121no—
460#213—21no—
461#213—61no—
462#213—61no—
463#213—61no—
464#213—61no—
465#213—61no—
466#213—121no—
467#208—31no—
468#208—31no—
469#208—61no—
470#208—61no—
471#208—61no—
472#208C22×D311yescharacteristic
473#208C22×D311yescharacteristic
474#208C22×D311yescharacteristic
475C2×C3⋊C8—31no—
476C2×C3⋊C8—31no—
477C2×C3⋊C8—31no—
478C2×C3⋊C8—31no—
479C2×C3⋊C8—31no—
480C2×C3⋊C8—31no—
481C2×C3⋊C8—61no—
482C2×C3⋊C8—61no—
483C2×C3⋊C8—61no—
484C2×C3⋊C8C22×D311yescharacteristic
485Dic12—21no—
486Dic12—61no—
487Dic12—61no—
488Dic12—61no—
489Dic12—61no—
490Dic12—121no—
491D24—61no—
492#204—21no—
493#204—61no—
494#204—61no—
495#204—61no—
496#204—61no—
497#204—61no—
498#204—61no—
499#204—61no—
500#204—121no—
501ΓL(1,𝔽25)—21no—
502ΓL(1,𝔽25)—21no—
503ΓL(1,𝔽25)—21no—
504ΓL(1,𝔽25)—61no—
505ΓL(1,𝔽25)—61no—
506ΓL(1,𝔽25)—61no—
507ΓL(1,𝔽25)—61no—
508ΓL(1,𝔽25)—61no—
509ΓL(1,𝔽25)—61no—
510ΓL(1,𝔽25)—121no—
511D3×C8—21no—
512D3×C8—21no—
513D3×C8—21no—
514D3×C8—31no—
515D3×C8—31no—
516D3×C8—31no—
517D3×C8—31no—
518D3×C8—61no—
519D3×C8—61no—
520D3×C8—61no—
521D3×C8—61no—
522D3×C8—61no—
523D3×C8—61no—
524D3×C8—121no—
525C22×C32—41no—
526C22×C32—81no—
527C22×C32C2×#4111yescharacteristic
528C2×C3⋊D3—21no—
529C2×C3×D3—22no—
530C2×C3×D3—21no—
531C2×C3×D3—41no—
532C2×C3×D3—82no—
533C2×C3×D3—82no—
534C2×C3×D3—81no—
535C2×C3×D3#12111yescharacteristic
536C2×C3×D3#12111yescharacteristic
537D32—42no—
538C32×C4C22×D411yescharacteristic
539C32×C4C22×D411yescharacteristic
540C3⋊Dic3—21no—
541C3⋊Dic3—41no—
542C3×Dic3—21no—
543C3×Dic3—41no—
544C3×Dic3#12111yescharacteristic
545C3×Dic3#12111yescharacteristic
546C2×#41—91no—
547C22×Q8—91no—
548C22×D4—31no—
549#137—31no—
550#137—91no—
551#137—91no—
552#137—91no—
553#137—181no—
554#137—181no—
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—181no—
562C2×SD16—31no—
563C2×SD16—91no—
564C2×SD16—91no—
565C2×SD16—91no—
566C2×SD16—181no—
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—31no—
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—31no—
595#100—31no—
596#100D3211yescharacteristic, complemented
597C23×C3—21no—
598C23×C3—21no—
599C23×C3—31no—
600C23×C3—41no—
601C23×C3—61no—
602C23×C3—121no—
603C23×C3—121no—
604C23×C3—242no—
605C22×D3—21no—
606C22×D3—41no—
607C22×D3—41no—
608C22×D3—61no—
609C22×D3—61no—
610C22×D3—82no—
611C22×D3#23511yescharacteristic
612C3×Q8—31no—
613C3×Q8—61no—
614C3×Q8—61no—
615C3×D4—21no—
616C3×D4—21no—
617C3×D4—21no—
618C3×D4—21no—
619C3×D4—31no—
620C3×D4—41no—
621C3×D4—41no—
622C3×D4—61no—
623C3×D4—61no—
624C3×D4—61no—
625C3×D4—121no—
626C3×D4—121no—
627C2×C3×C4—21no—
628C2×C3×C4—31no—
629C2×C3×C4—31no—
630C2×C3×C4—31no—
631C2×C3×C4—31no—
632C2×C3×C4—31no—
633C2×C3×C4—61no—
634C2×C3×C4—61no—
635C2×C3×C4C23×D311yescharacteristic
636C2×C3×C4C23×D311yescharacteristic
637#67—21no—
638#67—41no—
639#67—41no—
640#67—61no—
641#67—61no—
642#67—61no—
643#67—61no—
644#67—61no—
645#67—61no—
646#67—121no—
647C2×Dic3—21no—
648C2×Dic3—61no—
649C2×Dic3—61no—
650C2×Dic3—61no—
651C2×Dic3—61no—
652C2×Dic3—121no—
653C2×Dic3—121no—
654C2×Dic3—121no—
655C2×Dic3#23511yescharacteristic
656D12—21no—
657D12—21no—
658D12—31no—
659D12—31no—
660D12—61no—
661D12—61no—
662D12—61no—
663D12D3×D411yescharacteristic
664C4×D3—21no—
665C4×D3—61no—
666C4×D3—61no—
667C4×D3—61no—
668C4×D3—61no—
669C4×D3—61no—
670C4×D3—61no—
671C4×D3—121no—
672C4×D3—121no—
673C4×D3—121no—
674C4×D3D3×D411yescharacteristic
675C4×D3D3×D411yescharacteristic
676C4×D3D3×D411yescharacteristic
677C4×D3D3×D411yescharacteristic
678Dic6—21no—
679Dic6—21no—
680Dic6—31no—
681Dic6—31no—
682Dic6—61no—
683Dic6—61no—
684Dic6—61no—
685Dic6—61no—
686Dic6—61no—
687Dic6—61no—
688Dic6—61no—
689Dic6—121no—
690Dic6—121no—
691Dic6—121no—
692Dic6—121no—
693Dic6—121no—
694Dic6—121no—
695Dic6D3×D411yescharacteristic
696C3×C8—21no—
697C3×C8—21no—
698C3×C8—21no—
699C3×C8—21no—
700C3×C8—31no—
701C3×C8—31no—
702C3×C8—41no—
703C3×C8—41no—
704C3×C8—61no—
705C3×C8—61no—
706C3×C8—61no—
707C3⋊C8—21no—
708C3⋊C8—21no—
709C3⋊C8—21no—
710C3⋊C8—31no—
711C3⋊C8—31no—
712C3⋊C8—31no—
713C3⋊C8—31no—
714C3⋊C8—61no—
715C3⋊C8—61no—
716C3⋊C8—61no—
717C3⋊C8—61no—
718C3⋊C8—121no—
719C3⋊C8D3×D411yescharacteristic
720C3⋊C8D3×D411yescharacteristic
721C2×C32—21no—
722C2×C32—81no—
723C2×C32C2×#12111yescharacteristic
724C3⋊D3—41no—
725C3×D3—21no—
726C3×D3—41no—
727C3×D3—81no—
728C3×D3#47112yescomplemented
729C24—61no—
730#41—31no—
731#41—91no—
732#41—91no—
733#41—91no—
734#41—181no—
735#41—181no—
736C2×Q8—31no—
737C2×Q8—91no—
738C2×Q8—91no—
739C2×Q8—181no—
740C2×Q8—181no—
741C2×Q8—181no—
742C2×Q8—181no—
743C2×Q8—181no—
744C2×D4—31no—
745C2×D4—61no—
746C2×D4—61no—
747C2×D4—61no—
748C2×D4—61no—
749C2×D4—61no—
750C2×D4—91no—
751C2×D4—181no—
752C2×D4C2×D3211yescharacteristic
753C22×C4—31no—
754C22×C4—181no—
755C22×C4—181no—
756Q16—61no—
757Q16—181no—
758Q16—181no—
759Q16—181no—
760SD16—61no—
761SD16—61no—
762SD16—61no—
763SD16—61no—
764SD16—181no—
765SD16—181no—
766SD16—181no—
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—61no—
786M16—91no—
787M16—181no—
788M16—181no—
789M16—181no—
790M16—181no—
791M16C2×D3211yescharacteristic
792M16C2×D3211yescharacteristic
793C2×C8—31no—
794C2×C8—61no—
795C2×C8—61no—
796C2×C8—61no—
797C2×C8—91no—
798C2×C8—91no—
799C2×C8—91no—
800C2×C8—91no—
801C2×C8—91no—
802C2×C8—181no—
803C2×C8—181no—
804C2×C8—181no—
805C2×C8—181no—
806C22×C3—21no—
807C22×C3—31no—
808C22×C3—31no—
809C22×C3—41no—
810C22×C3—41no—
811C22×C3—62no—
812C22×C3—61no—
813C22×C3—81no—
814C22×C3—81no—
815C22×C3—81no—
816C22×C3—121no—
817C22×C3—161no—
818C22×C3—241no—
819C22×C3—242no—
820C22×C3—242no—
821C22×C3C2×#23511yescharacteristic
822C22×C3D3×#4111yescharacteristic
823C2×D3—22no—
824C2×D3—21no—
825C2×D3—41no—
826C2×D3—61no—
827C2×D3—61no—
828C2×D3—82no—
829C2×D3—82no—
830C2×D3—81no—
831C2×D3—121no—
832C2×D3—122no—
833C2×D3—122no—
834C2×D3#88411yescharacteristic
835C2×D3#88411yescharacteristic
836C3×C4—21no—
837C3×C4—21no—
838C3×C4—31no—
839C3×C4—31no—
840C3×C4—61no—
841C3×C4—121no—
842C3×C4C2×D3×D411yescharacteristic
843C3×C4C2×D3×D411yescharacteristic
844C3×C4C2×D3×D411yescharacteristic
845C3×C4C2×D3×D411yescharacteristic
846Dic3—21no—
847Dic3—41no—
848Dic3—61no—
849Dic3—61no—
850Dic3—121no—
851Dic3—121no—
852Dic3—121no—
853Dic3—241no—
854Dic3#88411yescharacteristic
855Dic3#88411yescharacteristic
856C32C2×#47111yescharacteristic, complemented, Sylow
857C23—21no—
858C23—31no—
859C23—61no—
860C23—121no—
861C23—121no—
862C23—181no—
863C23—242no—
864Q8—31no—
865Q8—61no—
866Q8—61no—
867Q8—91no—
868Q8—181no—
869Q8—181no—
870Q8—181no—
871Q8—361no—
872Q8—361no—
873D4—21no—
874D4—21no—
875D4—31no—
876D4—61no—
877D4—61no—
878D4—61no—
879D4—91no—
880D4—121no—
881D4—121no—
882D4—181no—
883D4—181no—
884D4—181no—
885D4—181no—
886C2×C4—31no—
887C2×C4—31no—
888C2×C4—31no—
889C2×C4—31no—
890C2×C4—31no—
891C2×C4—61no—
892C2×C4—61no—
893C2×C4—181no—
894C2×C4—181no—
895C2×C4—181no—
896C2×C4—181no—
897C2×C4—181no—
898C2×C4—361no—
899C2×C4—361no—
900C2×C4C22×D3211yescharacteristic
901C8—21no—
902C8—21no—
903C8—31no—
904C8—31no—
905C8—61no—
906C8—61no—
907C8—61no—
908C8—91no—
909C8—91no—
910C8—181no—
911C2×C3—21no—
912C2×C3—21no—
913C2×C3—21no—
914C2×C3—32no—
915C2×C3—41no—
916C2×C3—61no—
917C2×C3—81no—
918C2×C3—81no—
919C2×C3—121no—
920C2×C3—161no—
921C2×C3—241no—
922C2×C3C2×#88411yescharacteristic
923C2×C3D3×#12111yescharacteristic
924D3—21no—
925D3—41no—
926D3—81no—
927D3—121no—
928D3—121no—
929D3—241no—
930D3#474812yesdirect product factor
931C22—31no—
932C22—31no—
933C22—41no—
934C22—62no—
935C22—61no—
936C22—81no—
937C22—121no—
938C22—181no—
939C22—241no—
940C22—242no—
941C22—242no—
942C22—362no—
943C22D3×#23511yescharacteristic
944C4—31no—
945C4—31no—
946C4—61no—
947C4—121no—
948C4—181no—
949C4—361no—
950C4D32×D411yescharacteristic
951C4D32×D411yescharacteristic
952C3—21no—
953C3C2×#474811yescharacteristic, complemented
954C3D3×#47111yescharacteristic, complemented
955C2—21no—
956C2—32no—
957C2—61no—
958C2—81no—
959C2—121no—
960C2—241no—
961C2—361no—
962C2D3×#88411yescharacteristic
subgroupG/H
centerC2D3×#884
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#100C22
socleC2×C32C2×#121
prime radicalD3×#932C2
hypercenter#100D32
hypocenterC32C2×#471
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #100

Complements

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

NH ≅ G/Ntype
1. C2×D3×#214C2semidirect
3. D3×#909C2semidirect
4. D3×#907C2semidirect
5. #10592447C2semidirect
6. C3×#4748C2semidirect
7. C3×D3×#100C2semidirect
8. #10591507C2semidirect
9. #10591407C2semidirect
10. D3×#824C2semidirect
11. #10590996C2semidirect
12. #10590991C2semidirect
13. #10590989C2semidirect
14. #10590979C2semidirect
15. D3×#822C2semidirect
21. C2×#3754C22semidirect
23. #64118C22semidirect
24. #64116C22semidirect
25. C2×C3×#214C22semidirect
27. C3×#909C22semidirect
28. C3×#907C22semidirect
39. #63833C22semidirect
40. #63831C22semidirect
42. C2×#3716C22semidirect
43. C2×#3715C22semidirect
45. #63817C22semidirect
46. #63815C22semidirect
57. C32×#100C22semidirect
58. #63651C22semidirect
59. #63649C22semidirect
60. C3×#833C22semidirect
61. C3×#824C22semidirect
62. C3×#823C22semidirect
63. C3×#823C22semidirect
64. C3×#822C22semidirect
65. #63578C22semidirect
66. #63577C22semidirect
67. #63561C22semidirect
68. #63560C22semidirect
98. #4748D3direct (N × H)
99. D3×#100D3semidirect
205. C2×#214C2×D3semidirect
236. #909C2×D3semidirect
246. #907C2×D3semidirect
266. C3×#100C2×D3semidirect
267. C3×#100C2×D3semidirect
269. #833C2×D3semidirect
276. #824C2×D3semidirect
277. #823C2×D3semidirect
278. #823C2×D3semidirect
285. #822C2×D3semidirect
596. #100D32semidirect
728. C3×D3#471semidirect
856. C32C2×#471semidirect
930. D3#4748direct (N × H)
953. C3C2×#4748semidirect
954. C3D3×#471semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2142
D3×#9322
D3×#9092
D3×#9072
#105924472
C3×#47482
C3×D3×#1002
#105915072
#105914072
D3×#8242
#105909962
#105909912
#105909892
#105909792
D3×#8222
D3×#4713
C2×#47483