Finite Group Databasebeta

← D3×#4754 #11867896

Subgroups — D3×#4754 #11867896

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
1D3×#942C211yesmaximal, characteristic, complemented
2C2×D3×#215C211yesmaximal, characteristic, complemented
3D3×#908C211yesmaximal, characteristic
4D3×#907C211yesmaximal, characteristic, complemented
5#10592453C211yesmaximal, characteristic, complemented
6C3×#4754C211yesmaximal, characteristic, complemented
7C3×D3×#101C211yesmaximal, characteristic, complemented
8#10591643C211yesmaximal, characteristic, complemented
9#10591542C211yesmaximal, characteristic, complemented
10D3×#823C211yesmaximal, characteristic, complemented
11#10590998C211yesmaximal, characteristic, complemented
12#10590991C211yesmaximal, characteristic, complemented
13#10590990C211yesmaximal, characteristic, complemented
14#10590980C211yesmaximal, characteristic, complemented
15D3×#822C211yesmaximal, characteristic, complemented
16D3×#471—31nomaximal
17C2×#4754—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19D3×#235C2211yescharacteristic
20C2×D3×D12C2211yescharacteristic
21#64151C2211yescharacteristic, complemented
22C2×#3755C2211yescharacteristic, complemented
23#64117C2211yescharacteristic
24#64116C2211yescharacteristic, complemented
25C3×#942C2211yescharacteristic, complemented
26C2×C3×#215C2211yescharacteristic, complemented
27C3×#908C2211yescharacteristic
28C3×#907C2211yescharacteristic, complemented
29C3×D3×M16C2211yescharacteristic
30C3×D3×M16C2211yescharacteristic
31#63948—21no—
32#63946—21no—
33D3×#216—21no—
34D3×#215—21no—
35D3×#215—21no—
36D3×#215—21no—
37D3×#215—21no—
38D3×#215—21no—
39#63833C2211yescharacteristic, complemented
40C2×#3717C2211yescharacteristic, complemented
41#63830C2211yescharacteristic
42#63827C2211yescharacteristic, complemented
43C2×#3715C2211yescharacteristic, complemented
44#63825C2211yescharacteristic
45#63817C2211yescharacteristic, complemented
46#63815C2211yescharacteristic, complemented
47D3×#208C2211yescharacteristic
48C2×D3×C3⋊C8C2211yescharacteristic
49#63805—21no—
50#63804—21no—
51#63795—21no—
52#63794—21no—
53D3×D24—21no—
54D3×#204—21no—
55D3×ΓL(1,𝔽25)—21no—
56D32×C8—21no—
57C32×#101C2211yescharacteristic, complemented
58#63650C2211yescharacteristic, complemented
59#63649C2211yescharacteristic, complemented
60C3×#836C2211yescharacteristic, complemented
61C3×#824C2211yescharacteristic, complemented
62C3×#824C2211yescharacteristic, complemented
63C3×#823C2211yescharacteristic, complemented
64C3×#822C2211yescharacteristic, complemented
65#63578C2211yescharacteristic, complemented
66#63577C2211yescharacteristic, complemented
67#63559C2211yescharacteristic, complemented
68#63558C2211yescharacteristic, complemented
69C2×#942—31no—
70C22×#215—31no—
71D3×#137—31no—
72D3×AGL(1,ℤ/8)—31no—
73C2×D3×SD16—31no—
74D3×#131—31no—
75C2×#908—31no—
76C2×#907—31no—
77C3×#471—31no—
78C2×C3×#101—31no—
79#5203—31no—
80#5200—31no—
81#5177—31no—
82#5141—31no—
83C2×#823—31no—
84C2×#822—31no—
85#4898—31no—
86D3×#108—31no—
87#4754—31no—
88#4754—31no—
89#4754—31no—
90#4754—31no—
91#4754—31no—
92#4754—31no—
93#4754—31no—
94#4754—31no—
95#4754—61no—
96#4754D311yescharacteristic, direct product factor
97D3×#101D311yescharacteristic, complemented
98#4748—31no—
99D3×#100—31no—
100C22×D32—21no—
101C2×C32×Q8C2311yescharacteristic
102#3828C2311yescharacteristic
103C2×C4⋊(C3⋊D3)C2311yescharacteristic
104C3×D3×Q8—21no—
105C3×D3×Q8—21no—
106C3×D3×Q8—21no—
107C3×D3×Q8—21no—
108C3×#235C2311yescharacteristic
109C2×C3×D12C2311yescharacteristic
110C2×C3×C4×D3—21no—
111C2×C3×C4×D3C2311yescharacteristic
112C2×C3×Dic6—21no—
113C2×C3×Dic6C2311yescharacteristic
114D3×#67—21no—
115C2×#626—21no—
116#3804—21no—
117D3×D12—21no—
118D3×D12—21no—
119D3×D12—21no—
120D3×D12—21no—
121D3×D12D411yescharacteristic
122C4×D32—21no—
123#3799D411yescharacteristic
124#3798—21no—
125#3795D411yescharacteristic
126D3×Dic6D411yescharacteristic
127C32×M16C2311yescharacteristic
128C32×M16C2311yescharacteristic
129#3756—21no—
130#3755—21no—
131#3755—21no—
132#3755—21no—
133#3748C2311yescharacteristic
134C2×C3⋊(C3⋊C8)C2311yescharacteristic
135#3745—21no—
136#3744—21no—
137#3743—21no—
138C8×C3⋊D3—21no—
139C3×#216—21no—
140C3×#215—21no—
141C3×#215—21no—
142C3×#215—21no—
143C3×#208C2311yescharacteristic
144C3×#208C2311yescharacteristic
145C3×#208C2311yescharacteristic
146C2×C3×C3⋊C8C2311yescharacteristic
147C3×D24—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#3718—21no—
157#3717—21no—
158#3717—21no—
159#3717—21no—
160#3717—21no—
161#3716—21no—
162#3715—21no—
163#3715—21no—
164#3715—21no—
165#3714—21no—
166#3714—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×Q8—31no—
179D3×#41—31no—
180C2×D3×Q8C2×D311yescharacteristic
181C2×D3×D4—31no—
182C2×#235—31no—
183C22×D12—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—
193C2×#216—61no—
194#942—31no—
195#942—31no—
196#942—31no—
197#942—31no—
198#942—61no—
199#942—61no—
200#942—61no—
201#942C2×D311yescharacteristic, complemented
202C2×#215—31no—
203C2×#215—31no—
204C2×#215—31no—
205C2×#215—31no—
206C2×#215—61no—
207C2×#215—61no—
208C2×#215—61no—
209C2×#215—61no—
210C2×#215—61no—
211C2×#215—61no—
212C2×#215C2×D311yescharacteristic, complemented
213C2×#214—31no—
214#932—31no—
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#908—31no—
231#908—31no—
232#908—31no—
233#908—31no—
234#908—61no—
235#908—61no—
236#908—61no—
237#908C2×D311yescharacteristic
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×D24—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—21no—
262C3×#101—31no—
263C3×#101—31no—
264C3×#101—31no—
265C3×#101C2×D311yescharacteristic, complemented
266C3×#101C2×D311yescharacteristic, complemented
267C3×#100—31no—
268#836C2×D311yescharacteristic, complemented
269#833—31no—
270#824C2×D311yescharacteristic, complemented
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#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#4111yescharacteristic
290C2×D32—21no—
291C2×D32—41no—
292C2×D32—41no—
293C2×D32—82no—
294C32×Q8—21no—
295C32×Q8—21no—
296C2×C32×C4—21no—
297C2×C32×C4C2411yescharacteristic
298#638—21no—
299C4⋊(C3⋊D3)—21no—
300C4⋊(C3⋊D3)—21no—
301C4⋊(C3⋊D3)C2×D411yescharacteristic
302C4×C3⋊D3—21no—
303#634C2×D411yescharacteristic
304C3×#67—21no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3#4111yescharacteristic
307C3×D12—21no—
308C3×D12—21no—
309C3×D12C2×D411yescharacteristic
310C3×C4×D3—21no—
311C3×C4×D3—41no—
312C3×C4×D3—41no—
313C3×C4×D3C2×D411yescharacteristic
314C3×C4×D3C2×D411yescharacteristic
315C3×C4×D3C2×D411yescharacteristic
316C3×C4×D3C2×D411yescharacteristic
317C3×Dic6—21no—
318C3×Dic6—21no—
319C3×Dic6—41no—
320C3×Dic6—41no—
321C3×Dic6C2×D411yescharacteristic
322#627—21no—
323#626—21no—
324#626—21no—
325#626—41no—
326#626—41no—
327#625—21no—
328#624—21no—
329D3×Dic3—21no—
330D3×Dic3—21no—
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—31no—
355C2×#100—91no—
356C23×D3—61no—
357C23×D3—61no—
358C3×#41—31no—
359C2×C3×Q8—21no—
360C2×C3×Q8—31no—
361C2×C3×Q8—61no—
362C2×C3×Q8—61no—
363C2×C3×Q8—61no—
364C2×C3×Q8—61no—
365C2×C3×Q8—61no—
366C2×C3×Q8C22×D311yescharacteristic
367C2×C3×Q8C22×D311yescharacteristic
368C2×C3×D4—31no—
369C22×C3×C4—31no—
370C22×C3×C4—61no—
371C2×#67—61no—
372C2×#67—61no—
373#239—31no—
374D3×Q8—21no—
375D3×Q8—21no—
376D3×Q8—21no—
377D3×Q8—21no—
378D3×Q8—31no—
379#237—31no—
380#237—61no—
381D3×D4—31no—
382D3×D4—61no—
383D3×D4—61no—
384D3×D4—61no—
385D3×D4—61no—
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×D12—31no—
398C2×D12—31no—
399C2×D12—61no—
400C2×D12—61no—
401C2×D12—61no—
402C2×D12—61no—
403C2×D12—61no—
404C2×D12—61no—
405C2×D12C22×D311yescharacteristic
406C2×C4×D3—21no—
407C2×C4×D3—61no—
408C2×C4×D3—61no—
409C2×C4×D3C22×D311yescharacteristic
410C2×Dic6—21no—
411C2×Dic6—31no—
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—21no—
436#216—61no—
437#216—61no—
438#216—61no—
439#216—61no—
440#216—61no—
441#216—121no—
442#215—21no—
443#215—21no—
444#215—21no—
445#215—61no—
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—61no—
462#214—61no—
463#214—61no—
464#214—61no—
465#213—61no—
466#213—61no—
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—61no—
486D24—21no—
487D24—61no—
488D24—61no—
489D24—61no—
490D24—61no—
491D24—121no—
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×C32C2×#4111yescharacteristic
526C2×C3⋊D3—21no—
527C2×C3⋊D3—41no—
528C2×C3⋊D3—81no—
529C2×C3×D3—22no—
530C2×C3×D3—21no—
531C2×C3×D3—41no—
532C2×C3×D3—81no—
533C2×C3×D3#12111yescharacteristic
534C2×C3×D3#12111yescharacteristic
535D32—42no—
536D32—82no—
537D32—82no—
538C32×C4—41no—
539C32×C4C22×D411yescharacteristic
540C32×C4C22×D411yescharacteristic
541C3⋊Dic3—21no—
542C3×Dic3—21no—
543C3×Dic3—41no—
544C3×Dic3#12111yescharacteristic
545C3×Dic3#12111yescharacteristic
546C2×#41—91no—
547C22×Q8—31no—
548C22×D4—91no—
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—31no—
591#101—31no—
592#101D3211yescharacteristic, complemented
593#100—31no—
594#100—91no—
595#100—91no—
596#100—91no—
597C23×C3—31no—
598C23×C3—61no—
599C22×D3—21no—
600C22×D3—61no—
601C22×D3—61no—
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#23511yescharacteristic
612C3×Q8—21no—
613C3×Q8—21no—
614C3×Q8—21no—
615C3×Q8—21no—
616C3×Q8—31no—
617C3×Q8—41no—
618C3×Q8—41no—
619C3×Q8—61no—
620C3×Q8—61no—
621C3×Q8—121no—
622C3×Q8—121no—
623C3×D4—31no—
624C3×D4—61no—
625C3×D4—61no—
626C3×D4—61no—
627C2×C3×C4—21no—
628C2×C3×C4—21no—
629C2×C3×C4—21no—
630C2×C3×C4—31no—
631C2×C3×C4—31no—
632C2×C3×C4—31no—
633C2×C3×C4—31no—
634C2×C3×C4—31no—
635C2×C3×C4—41no—
636C2×C3×C4—61no—
637C2×C3×C4—61no—
638C2×C3×C4—121no—
639C2×C3×C4—121no—
640C2×C3×C4C23×D311yescharacteristic
641C2×C3×C4C23×D311yescharacteristic
642#67—21no—
643#67—61no—
644#67—61no—
645#67—61no—
646#67—61no—
647#67—61no—
648#67—61no—
649#67—121no—
650#67—121no—
651#67—121no—
652C2×Dic3—21no—
653C2×Dic3—61no—
654C2×Dic3—61no—
655C2×Dic3#23511yescharacteristic
656D12—21no—
657D12—21no—
658D12—31no—
659D12—31no—
660D12—61no—
661D12—61no—
662D12—61no—
663D12—61no—
664D12—61no—
665D12—61no—
666D12—61no—
667D12—121no—
668D12—121no—
669D12—121no—
670D12—121no—
671D12D3×D411yescharacteristic
672C4×D3—21no—
673C4×D3—41no—
674C4×D3—41no—
675C4×D3—61no—
676C4×D3—61no—
677C4×D3—61no—
678C4×D3—61no—
679C4×D3—61no—
680C4×D3—61no—
681C4×D3—121no—
682C4×D3D3×D411yescharacteristic
683C4×D3D3×D411yescharacteristic
684C4×D3D3×D411yescharacteristic
685C4×D3D3×D411yescharacteristic
686Dic6—21no—
687Dic6—21no—
688Dic6—31no—
689Dic6—31no—
690Dic6—41no—
691Dic6—41no—
692Dic6—61no—
693Dic6—61no—
694Dic6—61no—
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×C32C2×#12111yescharacteristic
723C3⋊D3—41no—
724C3⋊D3—81no—
725C3×D3—21no—
726C3×D3—41no—
727C3×D3—81no—
728C3×D3#47112yescomplemented
729C24—181no—
730#41—31no—
731#41—91no—
732#41—91no—
733#41—91no—
734#41—181no—
735#41—181no—
736C2×Q8—31no—
737C2×Q8—61no—
738C2×Q8—61no—
739C2×Q8—61no—
740C2×Q8—61no—
741C2×Q8—61no—
742C2×Q8—91no—
743C2×Q8C2×D3211yescharacteristic
744C2×D4—31no—
745C2×D4—91no—
746C2×D4—91no—
747C2×D4—181no—
748C2×D4—181no—
749C2×D4—181no—
750C2×D4—181no—
751C2×D4—181no—
752C2×D4—181no—
753C22×C4—31no—
754C22×C4—61no—
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—62no—
810C22×C3—61no—
811C22×C3—121no—
812C22×C3—241no—
813C22×C3C2×#23511yescharacteristic
814C22×C3D3×#4111yescharacteristic
815C2×D3—22no—
816C2×D3—21no—
817C2×D3—41no—
818C2×D3—61no—
819C2×D3—61no—
820C2×D3—81no—
821C2×D3—121no—
822C2×D3—122no—
823C2×D3—122no—
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#88411yescharacteristic
835C2×D3#88411yescharacteristic
836C3×C4—21no—
837C3×C4—21no—
838C3×C4—31no—
839C3×C4—31no—
840C3×C4—41no—
841C3×C4—41no—
842C3×C4—61no—
843C3×C4—81no—
844C3×C4—121no—
845C3×C4C2×D3×D411yescharacteristic
846C3×C4C2×D3×D411yescharacteristic
847C3×C4C2×D3×D411yescharacteristic
848C3×C4C2×D3×D411yescharacteristic
849Dic3—21no—
850Dic3—41no—
851Dic3—61no—
852Dic3—61no—
853Dic3—121no—
854Dic3#88411yescharacteristic
855Dic3#88411yescharacteristic
856C32C2×#47111yescharacteristic, complemented, Sylow
857C23—31no—
858C23—61no—
859C23—181no—
860C23—181no—
861C23—361no—
862C23—361no—
863C23—722no—
864Q8—21no—
865Q8—21no—
866Q8—31no—
867Q8—61no—
868Q8—61no—
869Q8—91no—
870Q8—121no—
871Q8—121no—
872Q8—181no—
873D4—31no—
874D4—61no—
875D4—61no—
876D4—61no—
877D4—91no—
878D4—181no—
879D4—181no—
880D4—181no—
881D4—181no—
882D4—181no—
883D4—181no—
884D4—361no—
885D4—361no—
886C2×C4—21no—
887C2×C4—31no—
888C2×C4—31no—
889C2×C4—31no—
890C2×C4—31no—
891C2×C4—31no—
892C2×C4—61no—
893C2×C4—61no—
894C2×C4—121no—
895C2×C4—121no—
896C2×C4—181no—
897C2×C4—181no—
898C2×C4—181no—
899C2×C4—181no—
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—121no—
918C2×C3—241no—
919C2×C3C2×#88411yescharacteristic
920C2×C3D3×#12111yescharacteristic
921D3—21no—
922D3—41no—
923D3—81no—
924D3—121no—
925D3—121no—
926D3—241no—
927D3—241no—
928D3—241no—
929D3—481no—
930D3#475412yesdirect product factor
931C22—31no—
932C22—31no—
933C22—62no—
934C22—61no—
935C22—121no—
936C22—181no—
937C22—241no—
938C22—362no—
939C22—361no—
940C22—721no—
941C22—722no—
942C22—722no—
943C22D3×#23511yescharacteristic
944C4—31no—
945C4—31no—
946C4—41no—
947C4—61no—
948C4—121no—
949C4—181no—
950C4D32×D411yescharacteristic
951C4D32×D411yescharacteristic
952C3—21no—
953C3C2×#475411yescharacteristic, complemented
954C3D3×#47111yescharacteristic, complemented
955C2—21no—
956C2—32no—
957C2—61no—
958C2—121no—
959C2—241no—
960C2—361no—
961C2—721no—
962C2D3×#88411yescharacteristic
subgroupG/H
centerC2D3×#884
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#101C22
socleC2×C32C2×#121
prime radicalD3×#908C2
hypercenter#101D32
hypocenterC32C2×#471
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #101

Complements

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

NH ≅ G/Ntype
1. D3×#942C2semidirect
2. C2×D3×#215C2semidirect
4. D3×#907C2semidirect
5. #10592453C2semidirect
6. C3×#4754C2semidirect
7. C3×D3×#101C2semidirect
8. #10591643C2semidirect
9. #10591542C2semidirect
10. D3×#823C2semidirect
11. #10590998C2semidirect
12. #10590991C2semidirect
13. #10590990C2semidirect
14. #10590980C2semidirect
15. D3×#822C2semidirect
21. #64151C22semidirect
22. C2×#3755C22semidirect
24. #64116C22semidirect
25. C3×#942C22semidirect
26. C2×C3×#215C22semidirect
28. C3×#907C22semidirect
39. #63833C22semidirect
40. C2×#3717C22semidirect
42. #63827C22semidirect
43. C2×#3715C22semidirect
45. #63817C22semidirect
46. #63815C22semidirect
57. C32×#101C22semidirect
58. #63650C22semidirect
59. #63649C22semidirect
60. C3×#836C22semidirect
61. C3×#824C22semidirect
62. C3×#824C22semidirect
63. C3×#823C22semidirect
64. C3×#822C22semidirect
65. #63578C22semidirect
66. #63577C22semidirect
67. #63559C22semidirect
68. #63558C22semidirect
96. #4754D3direct (N × H)
97. D3×#101D3semidirect
201. #942C2×D3semidirect
212. C2×#215C2×D3semidirect
246. #907C2×D3semidirect
265. C3×#101C2×D3semidirect
266. C3×#101C2×D3semidirect
268. #836C2×D3semidirect
270. #824C2×D3semidirect
271. #824C2×D3semidirect
278. #823C2×D3semidirect
285. #822C2×D3semidirect
592. #101D32semidirect
728. C3×D3#471semidirect
856. C32C2×#471semidirect
930. D3#4754direct (N × H)
953. C3C2×#4754semidirect
954. C3D3×#471semidirect

Maximal subgroups

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

subgroupindex
D3×#9422
C2×D3×#2152
D3×#9082
D3×#9072
#105924532
C3×#47542
C3×D3×#1012
#105916432
#105915422
D3×#8232
#105909982
#105909912
#105909902
#105909802
D3×#8222
D3×#4713
C2×#47543