Finite Group Databasebeta

← D3×#4749 #11867943

Subgroups — D3×#4749 #11867943

Order 1152.

1030 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#932C211yesmaximal, characteristic, complemented
2C2×D3×#213C211yesmaximal, characteristic, complemented
3D3×#908C211yesmaximal, characteristic, complemented
4D3×#907C211yesmaximal, characteristic, complemented
5#10592448C211yesmaximal, characteristic, complemented
6C3×#4749C211yesmaximal, characteristic, complemented
7C3×D3×#100C211yesmaximal, characteristic, complemented
8#10591508C211yesmaximal, characteristic, complemented
9#10591406C211yesmaximal, characteristic, complemented
10D3×#823C211yesmaximal, characteristic, complemented
11#10590997C211yesmaximal, characteristic, complemented
12#10590988C211yesmaximal, characteristic, complemented
13#10590987C211yesmaximal, characteristic, complemented
14#10590982C211yesmaximal, characteristic, complemented
15D3×#822C211yesmaximal, characteristic, complemented
16D3×#472—31nomaximal
17C2×#4749—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19D3×#235C2211yescharacteristic
20C2×D3×D12C2211yescharacteristic
21#64141C2211yescharacteristic, complemented
22C2×#3753C2211yescharacteristic, complemented
23#64117C2211yescharacteristic, complemented
24#64116C2211yescharacteristic, complemented
25C3×#932C2211yescharacteristic, complemented
26C2×C3×#213C2211yescharacteristic, complemented
27C3×#908C2211yescharacteristic, complemented
28C3×#907C2211yescharacteristic, complemented
29C3×D3×M16C2211yescharacteristic
30C3×D3×M16C2211yescharacteristic
31#63934—21no—
32#63932—21no—
33D3×#214—21no—
34D3×#213—21no—
35D3×#213—21no—
36D3×#213—21no—
37D3×#213—21no—
38D3×#213—21no—
39#63830C2211yescharacteristic, complemented
40#63830C2211yescharacteristic, complemented
41#63825C2211yescharacteristic, complemented
42C2×#3714C2211yescharacteristic, complemented
43#63823C2211yescharacteristic, complemented
44C2×#3713C2211yescharacteristic, complemented
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×#100C2211yescharacteristic, complemented
58#63650C2211yescharacteristic, complemented
59#63649C2211yescharacteristic, complemented
60C3×#833C2211yescharacteristic, complemented
61C3×#823C2211yescharacteristic, complemented
62C3×#823C2211yescharacteristic, complemented
63C3×#823C2211yescharacteristic, complemented
64C3×#822C2211yescharacteristic, complemented
65#63578C2211yescharacteristic, complemented
66#63577C2211yescharacteristic, complemented
67#63559C2211yescharacteristic, complemented
68#63558C2211yescharacteristic, complemented
69C2×#932—31no—
70C22×#213—31no—
71D3×AGL(1,ℤ/8)—31no—
72D3×AGL(1,ℤ/8)—31no—
73C2×D3×D8—31no—
74D3×#131—31no—
75C2×#908—31no—
76C2×#907—31no—
77C3×#472—31no—
78C2×C3×#100—31no—
79#5199—31no—
80#5199—31no—
81#5160—31no—
82#5142—31no—
83C2×#823—31no—
84C2×#822—31no—
85#4897—31no—
86D3×#108—31no—
87#4749—31no—
88#4749—31no—
89#4749—31no—
90#4749—31no—
91#4749—31no—
92#4749—31no—
93#4749—31no—
94#4749—31no—
95#4749—31no—
96#4749—61no—
97#4749D311yescharacteristic, direct product factor
98D3×#100—31no—
99D3×#100D311yescharacteristic, complemented
100C23×C3×D3—21no—
101C22×D32—21no—
102C2×C32×D4C2311yescharacteristic
103#3828C2311yescharacteristic
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C3×#67—21no—
106C3×D3×D4—21no—
107C3×D3×D4—21no—
108C3×D3×D4—21no—
109C3×D3×D4—21no—
110C3×#235C2311yescharacteristic
111C2×C3×D12C2311yescharacteristic
112C2×C3×D12C2311yescharacteristic
113C2×C3×C4×D3C2311yescharacteristic
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#3754—21no—
130#3753—21no—
131#3753—21no—
132#3753—21no—
133#3748C2311yescharacteristic
134C2×C3⋊(C3⋊C8)C2311yescharacteristic
135#3745—21no—
136#3744—21no—
137#3743—21no—
138C8×C3⋊D3—21no—
139C3×#214—21no—
140C3×#213—21no—
141C3×#213—21no—
142C3×#213—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#3717—21no—
156#3716—21no—
157#3716—21no—
158#3715—21no—
159#3714—21no—
160#3714—21no—
161#3714—21no—
162#3714—21no—
163#3714—21no—
164#3713—21no—
165#3713—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×#472—91noSylow
178C22×C3×D4—31no—
179D3×#41—31no—
180C2×D3×D4—31no—
181C2×D3×D4C2×D311yescharacteristic
182C2×#235—31no—
183C22×D12—31no—
184C3×AGL(1,ℤ/8)—31no—
185C3×AGL(1,ℤ/8)—31no—
186C2×C3×D8—31no—
187C3×#131—31no—
188C2×C3×M16—31no—
189C2×C3×M16—31no—
190#949—31no—
191#949—31no—
192#948—31no—
193C2×#214—61no—
194#932—31no—
195#932—31no—
196#932—31no—
197#932—31no—
198#932—31no—
199#932—61no—
200#932—61no—
201#932—61no—
202#932C2×D311yescharacteristic, complemented
203C2×#213—31no—
204C2×#213—31no—
205C2×#213—31no—
206C2×#213—31no—
207C2×#213—31no—
208C2×#213—61no—
209C2×#213—61no—
210C2×#213—61no—
211C2×#213—61no—
212C2×#213—61no—
213C2×#213—61no—
214C2×#213C2×D311yescharacteristic, complemented
215C2×#208—31no—
216C22×C3⋊C8—31no—
217#914—61no—
218#914—61no—
219D3×SD16—61no—
220D3×SD16—61no—
221#911—61no—
222#911—61no—
223D3×D8—61no—
224D3×D8—61no—
225D3×D8—61no—
226D3×D8—61no—
227D3×D8—61no—
228D3×D8—61no—
229#908—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, complemented
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—31no—
252C2×D24—61no—
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×#100—21no—
262C3×#100—31no—
263C3×#100—31no—
264C3×#100—31no—
265C3×#100—31no—
266C3×#100C2×D311yescharacteristic, complemented
267C3×#100C2×D311yescharacteristic, complemented
268#833—31no—
269#833C2×D311yescharacteristic, complemented
270#823—31no—
271#823—31no—
272#823—31no—
273#823—31no—
274#823—31no—
275#823—61no—
276#823C2×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—21no—
290C22×C3×D3—21no—
291C22×C3×D3—41no—
292C22×C3×D3—41no—
293C22×C3×D3—82no—
294C22×C3×D3#4111yescharacteristic
295C2×D32—21no—
296C2×D32—41no—
297C2×D32—41no—
298C2×D32—82no—
299C32×D4—21no—
300C32×D4—21no—
301C2×C32×C4C2411yescharacteristic
302#638—21no—
303C4⋊(C3⋊D3)—21no—
304C4⋊(C3⋊D3)—21no—
305C4⋊(C3⋊D3)C2×D411yescharacteristic
306C4×C3⋊D3—21no—
307#634C2×D411yescharacteristic
308C3×#67—21no—
309C3×#67—41no—
310C3×#67—41no—
311C2×C3×Dic3#4111yescharacteristic
312C3×D12—21no—
313C3×D12—21no—
314C3×D12—21no—
315C3×D12—21no—
316C3×D12C2×D411yescharacteristic
317C3×C4×D3—21no—
318C3×C4×D3C2×D411yescharacteristic
319C3×C4×D3C2×D411yescharacteristic
320C3×C4×D3C2×D411yescharacteristic
321C3×C4×D3C2×D411yescharacteristic
322C3×Dic6C2×D411yescharacteristic
323#627—21no—
324#626—21no—
325#626—21no—
326#626—41no—
327#626—41no—
328#625—21no—
329#624—21no—
330D3×Dic3—21no—
331D3×Dic3—21no—
332C32×C8—21no—
333C32×C8—21no—
334C3⋊(C3⋊C8)—21no—
335C3⋊(C3⋊C8)C2×D411yescharacteristic
336C3⋊(C3⋊C8)C2×D411yescharacteristic
337C3×C3⋊C8—21no—
338C3×C3⋊C8—21no—
339C3×C3⋊C8—21no—
340C3×C3⋊C8C2×D411yescharacteristic
341C3×C3⋊C8C2×D411yescharacteristic
342C2×AGL(1,ℤ/8)—91no—
343C2×AGL(1,ℤ/8)—91no—
344C22×D8—91no—
345C2×#131—91no—
346#472—31no—
347#472—91no—
348#472—91no—
349#472—91no—
350#472—91no—
351#472—91no—
352#472—91no—
353#472—91no—
354C2×#108—91no—
355C2×#100—31no—
356C2×#100—91no—
357C24×C3—61no—
358C23×D3—21no—
359C23×D3—61no—
360C23×D3—61no—
361C3×#41—31no—
362C2×C3×D4—21no—
363C2×C3×D4—31no—
364C2×C3×D4—31no—
365C2×C3×D4—61no—
366C2×C3×D4—61no—
367C2×C3×D4—61no—
368C2×C3×D4—61no—
369C2×C3×D4—61no—
370C2×C3×D4C22×D311yescharacteristic
371C2×C3×D4C22×D311yescharacteristic
372C22×C3×C4—31no—
373C2×#67—21no—
374C2×#67—61no—
375C2×#67—61no—
376#239—31no—
377D3×Q8—31no—
378#237—31no—
379#237—61no—
380D3×D4—21no—
381D3×D4—21no—
382D3×D4—21no—
383D3×D4—21no—
384D3×D4—31no—
385D3×D4—61no—
386D3×D4—61no—
387D3×D4—61no—
388D3×D4—61no—
389D3×D4—61no—
390#235—31no—
391#235—31no—
392#235—31no—
393#235—31no—
394#235—61no—
395#235—61no—
396#235—61no—
397#235—61no—
398#235C22×D311yescharacteristic
399C2×D12—31no—
400C2×D12—31no—
401C2×D12—31no—
402C2×D12—61no—
403C2×D12—61no—
404C2×D12—61no—
405C2×D12—61no—
406C2×D12—61no—
407C2×D12—61no—
408C2×D12C22×D311yescharacteristic
409C2×D12C22×D311yescharacteristic
410C2×C4×D3—61no—
411C2×C4×D3—61no—
412C2×C4×D3C22×D311yescharacteristic
413C2×Dic6—31no—
414C3×SD16—61no—
415C3×SD16—61no—
416C3×D8—61no—
417C3×D8—61no—
418C3×D8—61no—
419C3×D8—61no—
420C3×M16—21no—
421C3×M16—21no—
422C3×M16—31no—
423C3×M16—31no—
424C3×M16—31no—
425C3×M16—61no—
426C3×M16—61no—
427C3×M16—61no—
428C3×M16C22×D311yescharacteristic
429C3×M16C22×D311yescharacteristic
430C3×M16C22×D311yescharacteristic
431C3×M16C22×D311yescharacteristic
432C2×C3×C8—31no—
433C2×C3×C8—61no—
434C2×C3×C8—61no—
435C2×C3×C8—61no—
436#215—61no—
437#215—61no—
438#214—21no—
439#214—61no—
440#214—61no—
441#214—61no—
442#214—61no—
443#214—61no—
444#214—121no—
445#213—21no—
446#213—21no—
447#213—21no—
448#213—61no—
449#213—61no—
450#213—61no—
451#213—61no—
452#213—61no—
453#213—61no—
454#213—61no—
455#213—61no—
456#213—61no—
457#213—61no—
458#213—61no—
459#213—61no—
460#213—61no—
461#213—61no—
462#213—61no—
463#213—61no—
464#213—61no—
465#213—121no—
466#213—121no—
467#213—121no—
468#208—31no—
469#208—31no—
470#208—61no—
471#208—61no—
472#208—61no—
473#208C22×D311yescharacteristic
474#208C22×D311yescharacteristic
475#208C22×D311yescharacteristic
476C2×C3⋊C8—31no—
477C2×C3⋊C8—31no—
478C2×C3⋊C8—31no—
479C2×C3⋊C8—31no—
480C2×C3⋊C8—31no—
481C2×C3⋊C8—31no—
482C2×C3⋊C8—61no—
483C2×C3⋊C8—61no—
484C2×C3⋊C8—61no—
485C2×C3⋊C8C22×D311yescharacteristic
486D24—21no—
487D24—61no—
488D24—61no—
489D24—61no—
490D24—61no—
491D24—61no—
492D24—61no—
493D24—61no—
494D24—121no—
495#204—21no—
496#204—61no—
497#204—61no—
498#204—61no—
499#204—61no—
500#204—61no—
501#204—121no—
502ΓL(1,𝔽25)—21no—
503ΓL(1,𝔽25)—21no—
504ΓL(1,𝔽25)—21no—
505ΓL(1,𝔽25)—61no—
506ΓL(1,𝔽25)—61no—
507ΓL(1,𝔽25)—61no—
508ΓL(1,𝔽25)—61no—
509ΓL(1,𝔽25)—61no—
510ΓL(1,𝔽25)—61no—
511ΓL(1,𝔽25)—121no—
512D3×C8—21no—
513D3×C8—21no—
514D3×C8—21no—
515D3×C8—31no—
516D3×C8—31no—
517D3×C8—31no—
518D3×C8—31no—
519D3×C8—61no—
520D3×C8—61no—
521D3×C8—61no—
522D3×C8—61no—
523D3×C8—61no—
524D3×C8—61no—
525D3×C8—121no—
526C22×C32—41no—
527C22×C32—81no—
528C22×C32C2×#4111yescharacteristic
529C2×C3⋊D3—21no—
530C2×C3⋊D3—41no—
531C2×C3⋊D3—81no—
532C2×C3×D3—22no—
533C2×C3×D3—21no—
534C2×C3×D3—41no—
535C2×C3×D3—41no—
536C2×C3×D3—82no—
537C2×C3×D3—82no—
538C2×C3×D3—81no—
539C2×C3×D3—81no—
540C2×C3×D3#12111yescharacteristic
541C2×C3×D3#12111yescharacteristic
542D32—42no—
543D32—82no—
544D32—82no—
545C32×C4C22×D411yescharacteristic
546C32×C4C22×D411yescharacteristic
547C3⋊Dic3—21no—
548C3×Dic3—21no—
549C3×Dic3#12111yescharacteristic
550C3×Dic3#12111yescharacteristic
551C2×#41—91no—
552C22×D4—31no—
553C22×D4—91no—
554AGL(1,ℤ/8)—31no—
555AGL(1,ℤ/8)—31no—
556AGL(1,ℤ/8)—91no—
557AGL(1,ℤ/8)—91no—
558AGL(1,ℤ/8)—91no—
559AGL(1,ℤ/8)—91no—
560AGL(1,ℤ/8)—91no—
561AGL(1,ℤ/8)—91no—
562AGL(1,ℤ/8)—181no—
563AGL(1,ℤ/8)—181no—
564AGL(1,ℤ/8)—181no—
565AGL(1,ℤ/8)—181no—
566C2×SD16—181no—
567C2×SD16—181no—
568C2×D8—31no—
569C2×D8—91no—
570C2×D8—91no—
571C2×D8—91no—
572C2×D8—181no—
573C2×D8—181no—
574C2×D8—181no—
575C2×D8—181no—
576C2×D8—181no—
577C2×D8—181no—
578#131—31no—
579#131—91no—
580#131—91no—
581#131—91no—
582#131—181no—
583#131—181no—
584C2×M16—31no—
585C2×M16—31no—
586C2×M16—91no—
587C2×M16—181no—
588C22×C8—91no—
589C22×C8—181no—
590#108—31no—
591#108—91no—
592#108—91no—
593#108—91no—
594#100—31no—
595#100—31no—
596#100—31no—
597#100—31no—
598#100—91no—
599#100—91no—
600#100—91no—
601#100D3211yescharacteristic, complemented
602C23×C3—21no—
603C23×C3—21no—
604C23×C3—31no—
605C23×C3—41no—
606C23×C3—61no—
607C23×C3—61no—
608C23×C3—121no—
609C23×C3—121no—
610C23×C3—242no—
611C22×D3—21no—
612C22×D3—21no—
613C22×D3—41no—
614C22×D3—41no—
615C22×D3—61no—
616C22×D3—61no—
617C22×D3—61no—
618C22×D3—61no—
619C22×D3—82no—
620C22×D3—121no—
621C22×D3—121no—
622C22×D3—121no—
623C22×D3—121no—
624C22×D3—121no—
625C22×D3—242no—
626C22×D3—242no—
627C22×D3#23511yescharacteristic
628C3×Q8—31no—
629C3×D4—21no—
630C3×D4—21no—
631C3×D4—21no—
632C3×D4—21no—
633C3×D4—31no—
634C3×D4—41no—
635C3×D4—41no—
636C3×D4—61no—
637C3×D4—61no—
638C3×D4—61no—
639C3×D4—61no—
640C3×D4—61no—
641C3×D4—121no—
642C3×D4—121no—
643C2×C3×C4—21no—
644C2×C3×C4—31no—
645C2×C3×C4—31no—
646C2×C3×C4—31no—
647C2×C3×C4—31no—
648C2×C3×C4—31no—
649C2×C3×C4—61no—
650C2×C3×C4C23×D311yescharacteristic
651C2×C3×C4C23×D311yescharacteristic
652#67—21no—
653#67—41no—
654#67—41no—
655#67—61no—
656#67—61no—
657#67—61no—
658#67—61no—
659#67—61no—
660#67—61no—
661#67—121no—
662#67—121no—
663#67—121no—
664C2×Dic3—61no—
665C2×Dic3—61no—
666C2×Dic3#23511yescharacteristic
667D12—21no—
668D12—21no—
669D12—21no—
670D12—21no—
671D12—31no—
672D12—31no—
673D12—61no—
674D12—61no—
675D12—61no—
676D12—61no—
677D12—61no—
678D12—61no—
679D12—61no—
680D12—121no—
681D12—121no—
682D12—121no—
683D12—121no—
684D12D3×D411yescharacteristic
685C4×D3—21no—
686C4×D3—61no—
687C4×D3—61no—
688C4×D3—61no—
689C4×D3—61no—
690C4×D3—61no—
691C4×D3—61no—
692C4×D3—121no—
693C4×D3D3×D411yescharacteristic
694C4×D3D3×D411yescharacteristic
695C4×D3D3×D411yescharacteristic
696C4×D3D3×D411yescharacteristic
697Dic6—31no—
698Dic6—31no—
699Dic6—61no—
700Dic6—61no—
701Dic6—61no—
702Dic6D3×D411yescharacteristic
703C3×C8—21no—
704C3×C8—21no—
705C3×C8—21no—
706C3×C8—21no—
707C3×C8—31no—
708C3×C8—31no—
709C3×C8—41no—
710C3×C8—41no—
711C3×C8—61no—
712C3×C8—61no—
713C3×C8—61no—
714C3⋊C8—21no—
715C3⋊C8—21no—
716C3⋊C8—21no—
717C3⋊C8—31no—
718C3⋊C8—31no—
719C3⋊C8—31no—
720C3⋊C8—31no—
721C3⋊C8—61no—
722C3⋊C8—61no—
723C3⋊C8—61no—
724C3⋊C8—61no—
725C3⋊C8—121no—
726C3⋊C8D3×D411yescharacteristic
727C3⋊C8D3×D411yescharacteristic
728C2×C32—21no—
729C2×C32—81no—
730C2×C32C2×#12111yescharacteristic
731C3⋊D3—41no—
732C3⋊D3—81no—
733C3×D3—21no—
734C3×D3—41no—
735C3×D3—81no—
736C3×D3—81no—
737C3×D3#47212yescomplemented
738C24—61no—
739C24—181no—
740#41—31no—
741#41—91no—
742#41—91no—
743#41—91no—
744#41—181no—
745#41—181no—
746C2×Q8—91no—
747C2×D4—31no—
748C2×D4—31no—
749C2×D4—61no—
750C2×D4—61no—
751C2×D4—61no—
752C2×D4—61no—
753C2×D4—61no—
754C2×D4—91no—
755C2×D4—91no—
756C2×D4—181no—
757C2×D4—181no—
758C2×D4—181no—
759C2×D4—181no—
760C2×D4—181no—
761C2×D4—181no—
762C2×D4C2×D3211yescharacteristic
763C22×C4—31no—
764C22×C4—181no—
765SD16—61no—
766SD16—61no—
767SD16—181no—
768SD16—181no—
769SD16—181no—
770SD16—181no—
771SD16—181no—
772SD16—181no—
773D8—61no—
774D8—61no—
775D8—61no—
776D8—61no—
777D8—181no—
778D8—181no—
779D8—181no—
780D8—181no—
781D8—181no—
782D8—181no—
783D8—181no—
784D8—181no—
785D8—181no—
786D8—181no—
787D8—181no—
788D8—181no—
789M16—31no—
790M16—31no—
791M16—31no—
792M16—61no—
793M16—61no—
794M16—61no—
795M16—91no—
796M16—181no—
797M16—181no—
798M16—181no—
799M16—181no—
800M16C2×D3211yescharacteristic
801M16C2×D3211yescharacteristic
802C2×C8—31no—
803C2×C8—61no—
804C2×C8—61no—
805C2×C8—61no—
806C2×C8—91no—
807C2×C8—91no—
808C2×C8—91no—
809C2×C8—91no—
810C2×C8—91no—
811C2×C8—181no—
812C2×C8—181no—
813C2×C8—181no—
814C2×C8—181no—
815C22×C3—21no—
816C22×C3—31no—
817C22×C3—31no—
818C22×C3—41no—
819C22×C3—41no—
820C22×C3—62no—
821C22×C3—61no—
822C22×C3—81no—
823C22×C3—81no—
824C22×C3—81no—
825C22×C3—121no—
826C22×C3—121no—
827C22×C3—161no—
828C22×C3—241no—
829C22×C3—241no—
830C22×C3—242no—
831C22×C3—242no—
832C22×C3C2×#23511yescharacteristic
833C22×C3D3×#4111yescharacteristic
834C2×D3—22no—
835C2×D3—21no—
836C2×D3—41no—
837C2×D3—41no—
838C2×D3—61no—
839C2×D3—61no—
840C2×D3—82no—
841C2×D3—82no—
842C2×D3—81no—
843C2×D3—81no—
844C2×D3—121no—
845C2×D3—122no—
846C2×D3—122no—
847C2×D3—121no—
848C2×D3—121no—
849C2×D3—241no—
850C2×D3—242no—
851C2×D3—242no—
852C2×D3—242no—
853C2×D3—242no—
854C2×D3—241no—
855C2×D3—241no—
856C2×D3—481no—
857C2×D3#88411yescharacteristic
858C2×D3#88411yescharacteristic
859C3×C4—21no—
860C3×C4—21no—
861C3×C4—31no—
862C3×C4—31no—
863C3×C4—61no—
864C3×C4C2×D3×D411yescharacteristic
865C3×C4C2×D3×D411yescharacteristic
866C3×C4C2×D3×D411yescharacteristic
867C3×C4C2×D3×D411yescharacteristic
868Dic3—21no—
869Dic3—61no—
870Dic3—61no—
871Dic3—121no—
872Dic3#88411yescharacteristic
873Dic3#88411yescharacteristic
874C32C2×#47211yescharacteristic, complemented, Sylow
875C23—21no—
876C23—31no—
877C23—61no—
878C23—61no—
879C23—121no—
880C23—121no—
881C23—181no—
882C23—181no—
883C23—242no—
884C23—361no—
885C23—361no—
886C23—722no—
887Q8—31no—
888Q8—91no—
889Q8—181no—
890D4—21no—
891D4—21no—
892D4—31no—
893D4—61no—
894D4—61no—
895D4—61no—
896D4—61no—
897D4—61no—
898D4—91no—
899D4—121no—
900D4—121no—
901D4—181no—
902D4—181no—
903D4—181no—
904D4—181no—
905D4—181no—
906D4—181no—
907D4—361no—
908D4—361no—
909C2×C4—31no—
910C2×C4—31no—
911C2×C4—31no—
912C2×C4—31no—
913C2×C4—31no—
914C2×C4—61no—
915C2×C4—181no—
916C2×C4—181no—
917C2×C4—181no—
918C2×C4—181no—
919C2×C4C22×D3211yescharacteristic
920C8—21no—
921C8—21no—
922C8—31no—
923C8—31no—
924C8—61no—
925C8—61no—
926C8—61no—
927C8—91no—
928C8—91no—
929C8—181no—
930C2×C3—21no—
931C2×C3—21no—
932C2×C3—21no—
933C2×C3—32no—
934C2×C3—41no—
935C2×C3—61no—
936C2×C3—81no—
937C2×C3—81no—
938C2×C3—121no—
939C2×C3—161no—
940C2×C3—241no—
941C2×C3—241no—
942C2×C3C2×#88411yescharacteristic
943C2×C3D3×#12111yescharacteristic
944D3—21no—
945D3—41no—
946D3—81no—
947D3—81no—
948D3—121no—
949D3—121no—
950D3—241no—
951D3—241no—
952D3—241no—
953D3—481no—
954D3#474912yesdirect product factor
955C22—31no—
956C22—31no—
957C22—41no—
958C22—62no—
959C22—61no—
960C22—81no—
961C22—121no—
962C22—121no—
963C22—181no—
964C22—241no—
965C22—241no—
966C22—242no—
967C22—242no—
968C22—362no—
969C22—361no—
970C22—721no—
971C22—722no—
972C22—722no—
973C22D3×#23511yescharacteristic
974C4—31no—
975C4—31no—
976C4—61no—
977C4—181no—
978C4D32×D411yescharacteristic
979C4D32×D411yescharacteristic
980C3—21no—
981C3C2×#474911yescharacteristic, complemented
982C3D3×#47211yescharacteristic, complemented
983C2—21no—
984C2—32no—
985C2—61no—
986C2—81no—
987C2—121no—
988C2—241no—
989C2—241no—
990C2—361no—
991C2—721no—
992C2D3×#88411yescharacteristic
subgroupG/H
centerC2D3×#884
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#100C22
socleC2×C32C2×#121
hypercenter#100D32
hypocenterC32C2×#472
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. D3×#932C2semidirect
2. C2×D3×#213C2semidirect
3. D3×#908C2semidirect
4. D3×#907C2semidirect
5. #10592448C2semidirect
6. C3×#4749C2semidirect
7. C3×D3×#100C2semidirect
8. #10591508C2semidirect
9. #10591406C2semidirect
10. D3×#823C2semidirect
11. #10590997C2semidirect
12. #10590988C2semidirect
13. #10590987C2semidirect
14. #10590982C2semidirect
15. D3×#822C2semidirect
21. #64141C22semidirect
22. C2×#3753C22semidirect
23. #64117C22semidirect
24. #64116C22semidirect
25. C3×#932C22semidirect
26. C2×C3×#213C22semidirect
27. C3×#908C22semidirect
28. C3×#907C22semidirect
39. #63830C22semidirect
40. #63830C22semidirect
41. #63825C22semidirect
42. C2×#3714C22semidirect
43. #63823C22semidirect
44. C2×#3713C22semidirect
45. #63817C22semidirect
46. #63815C22semidirect
57. C32×#100C22semidirect
58. #63650C22semidirect
59. #63649C22semidirect
60. C3×#833C22semidirect
61. C3×#823C22semidirect
62. C3×#823C22semidirect
63. C3×#823C22semidirect
64. C3×#822C22semidirect
65. #63578C22semidirect
66. #63577C22semidirect
67. #63559C22semidirect
68. #63558C22semidirect
97. #4749D3direct (N × H)
99. D3×#100D3semidirect
202. #932C2×D3semidirect
214. C2×#213C2×D3semidirect
237. #908C2×D3semidirect
246. #907C2×D3semidirect
266. C3×#100C2×D3semidirect
267. C3×#100C2×D3semidirect
269. #833C2×D3semidirect
276. #823C2×D3semidirect
277. #823C2×D3semidirect
278. #823C2×D3semidirect
285. #822C2×D3semidirect
601. #100D32semidirect
737. C3×D3#472semidirect
874. C32C2×#472semidirect
954. D3#4749direct (N × H)
981. C3C2×#4749semidirect
982. C3D3×#472semidirect

Maximal subgroups

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

subgroupindex
D3×#9322
C2×D3×#2132
D3×#9082
D3×#9072
#105924482
C3×#47492
C3×D3×#1002
#105915082
#105914062
D3×#8232
#105909972
#105909882
#105909872
#105909822
D3×#8222
D3×#4723
C2×#47493