Finite Group Databasebeta

← D3×#2031 #10822607

Subgroups — D3×#2031 #10822607

Order 768.

1234 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#533C211yesmaximal, characteristic, complemented
2D3×#421C211yesmaximal, characteristic
3C2×D3×#104C211yesmaximal, characteristic
4D3×#410C211yesmaximal, characteristic
5C3×#2031C211yesmaximal, characteristic, complemented
6#71842C211yesmaximal, characteristic, complemented
7#70394C211yesmaximal, characteristic, complemented
8#70368C211yesmaximal, characteristic, complemented
9#70038C211yesmaximal, characteristic, complemented
10#69042C211yesmaximal, characteristic, complemented
11D3×#344C211yesmaximal, characteristic, complemented
12#68779C211yesmaximal, characteristic, complemented
13D3×#339C211yesmaximal, characteristic, complemented
14#68714C211yesmaximal, characteristic, complemented
15D3×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
16C2×#2031—31nomaximal, Sylow
17C2×D3×#41C2211yescharacteristic
18C3×#533C2211yescharacteristic, complemented
19C2×D3×M16C2211yescharacteristic
20C2×D3×M16C2211yescharacteristic
21#5728—21no—
22D3×C4⋊Q8—21no—
23#5688—21no—
24D3×#125—21no—
25D3×C22⋊Q8—22no—
26#5622—22no—
27#5578—22no—
28C4×D3×Q8—22no—
29D3×#117C2211yescharacteristic
30D3×#117C2211yescharacteristic
31D3×#117C2211yescharacteristic
32#5517C2211yescharacteristic, complemented
33#5517C2211yescharacteristic, complemented
34C2×C42×D3C2211yescharacteristic
35#5470C2211yescharacteristic, complemented
36C3×#421C2211yescharacteristic
37C2×C3×#104C2211yescharacteristic
38C3×#410C2211yescharacteristic
39#5240C2211yescharacteristic
40#5236C2211yescharacteristic
41C2×#837C2211yescharacteristic
42#5139C2211yescharacteristic
43C2×#825C2211yescharacteristic
44#5006C2211yescharacteristic
45#5006C2211yescharacteristic
46#5005C2211yescharacteristic
47C2×#805C2211yescharacteristic
48#4821—22no—
49D3×#104—21no—
50D3×#104—21no—
51D3×#104—21no—
52D3×#104—21no—
53D3×#104—22no—
54D3×#99—22no—
55#4740—22no—
56C3×#344C2211yescharacteristic, complemented
57C3×#339C2211yescharacteristic, complemented
58C3×H(3,ℤ/4)C2211yescharacteristic, complemented
59#4559C2211yescharacteristic, complemented
60#4557C2211yescharacteristic, complemented
61#4556C2211yescharacteristic, complemented
62#4555C2211yescharacteristic, complemented
63#4533C2211yescharacteristic, complemented
64#4532C2211yescharacteristic, complemented
65#4531C2211yescharacteristic, complemented
66#4531C2211yescharacteristic, complemented
67#4523C2211yescharacteristic, complemented
68C2×#533—31no—
69C2×#421—31no—
70C22×#104—31no—
71C2×#410—31no—
72#2031—31no—
73#2031—31no—
74#2031—31no—
75#2031—31no—
76#2031—31no—
77#2031—31no—
78#2031—31no—
79#2031D311yescharacteristic, direct product factor
80C2×#344—31no—
81C2×#339—31no—
82C2×H(3,ℤ/4)—31no—
83C2×C3×#41C2311yescharacteristic
84D3×#41—21no—
85D3×#41—21no—
86D3×#41—21no—
87D3×#41—21no—
88D3×#41—21no—
89D3×#41—21no—
90D3×#41—21no—
91D3×#41—21no—
92C2×#239Q811yescharacteristic, complemented
93C2×D3×Q8—22no—
94C2×D3×Q8Q811yescharacteristic, complemented
95C2×#237—21no—
96C2×#237Q811yescharacteristic, complemented
97C2×D3×D4—21no—
98C2×D3×D4Q811yescharacteristic, complemented
99C2×#235—21no—
100C2×#235C2311yescharacteristic
101C22×C4×D3—21no—
102C22×C4×D3—21no—
103C22×C4×D3C2311yescharacteristic
104C2×C3×M16C2311yescharacteristic
105C2×C3×M16C2311yescharacteristic
106C3×C4⋊Q8—21no—
107C3×#125—21no—
108C3×C22⋊Q8—22no—
109C3×C4×Q8—22no—
110C3×#117C2311yescharacteristic
111C3×#117C2311yescharacteristic
112C3×#117C2311yescharacteristic
113C2×C3×C42C2311yescharacteristic
114#946—22no—
115Q8×Dic3—22no—
116#944—22no—
117#926C2311yescharacteristic
118#926C2311yescharacteristic
119#926C2311yescharacteristic
120#924—22no—
121C2×C4×Dic3—21no—
122C2×C4×Dic3C2311yescharacteristic
123C2×#208C2311yescharacteristic
124C2×#208C2311yescharacteristic
125D3×M16—21no—
126D3×M16—21no—
127D3×M16—21no—
128D3×M16—21no—
129D3×M16—21no—
130D3×M16—21no—
131D3×M16—21no—
132D3×M16—21no—
133C2×ΓL(1,𝔽25)—21no—
134C2×ΓL(1,𝔽25)—21no—
135C2×D3×C8—21no—
136C2×D3×C8—21no—
137#897—22no—
138#896—22no—
139#896—22no—
140#892—21no—
141#892—21no—
142#892—21no—
143D3×C4⋊C4—22no—
144D3×C4⋊C4—22no—
145D3×C4⋊C4—22no—
146D3×C4⋊C4—21no—
147D3×C4⋊C4—21no—
148D3×C4⋊C4—21no—
149#890—21no—
150#890—21no—
151#889—22no—
152#889—22no—
153#888—22no—
154#888—21no—
155#888—21no—
156#887—22no—
157#887—22no—
158#887—22no—
159D3×C22⋊C4—21no—
160D3×C22⋊C4—21no—
161D3×C22⋊C4D412yes—
162#878—22no—
163#878—22no—
164#877—21no—
165#877—21no—
166#877D412yes—
167#872—21no—
168#872—21no—
169#872D412yes—
170C42×D3—21no—
171C42×D3—21no—
172C42×D3—21no—
173C42×D3—21no—
174C42×D3D411yescharacteristic
175C42×D3D411yescharacteristic
176C42×D3D411yescharacteristic
177C42×D3D411yescharacteristic
178C42×D3D412yes—
179#870—21no—
180#869—21no—
181C4×Dic6—22no—
182C4×Dic6—22no—
183C4×Dic6—22no—
184C3×#104—21no—
185C3×#104—21no—
186C3×#104—22no—
187C3×#99—22no—
188#837—21no—
189#837—21no—
190#837—22no—
191#834—22no—
192#825—21no—
193#825—21no—
194#825—22no—
195#806—22no—
196#806—22no—
197#805—21no—
198#805—21no—
199#805—22no—
200C22×#41—31no—
201C22×M16—31no—
202C22×M16—31no—
203#533—31no—
204#533—31no—
205#533—31no—
206#533—61no—
207#533—61no—
208#533—62no—
209#533—62no—
210#533C2×D311yescharacteristic, complemented
211C2×C4⋊Q8—61no—
212C2×#125—61no—
213C2×C22⋊Q8—62no—
214C2×C4×Q8—62no—
215C2×#117—31no—
216C2×#117—31no—
217C2×#117—31no—
218C22×C42—31no—
219#421—31no—
220#421—31no—
221#421—31no—
222#421—62no—
223#421C2×D311yescharacteristic
224C2×#104—31no—
225C2×#104—31no—
226C2×#104—31no—
227C2×#104—61no—
228C2×#104—61no—
229C2×#104—61no—
230C2×#104—61no—
231C2×#104—62no—
232C2×#104C2×D311yescharacteristic
233#410—31no—
234#410—31no—
235#410—31no—
236#410—62no—
237#410C2×D311yescharacteristic
238C2×#99—62no—
239#344—31no—
240#344—31no—
241#344—31no—
242#344C2×D311yescharacteristic, complemented
243#339—31no—
244#339—31no—
245#339—31no—
246#339C2×D311yescharacteristic, complemented
247H(3,ℤ/4)—31no—
248H(3,ℤ/4)—31no—
249H(3,ℤ/4)—31no—
250H(3,ℤ/4)C2×D311yescharacteristic, complemented
251C23×D3—21no—
252C23×D3C2×D411yescharacteristic
253C3×#41—21no—
254C3×#41—21no—
255C3×#41—21no—
256C3×#41—21no—
257C2×C3×Q8—22no—
258C2×C3×Q8C2×Q811yescharacteristic, complemented
259C2×C3×D4—21no—
260C2×C3×D4C2×Q811yescharacteristic, complemented
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4C2411yescharacteristic
264C2×#67—21no—
265C2×#67—21no—
266C2×#67—21no—
267C22×Dic3—21no—
268C22×Dic3—21no—
269C22×Dic3C2×D411yescharacteristic
270#239—21no—
271#239—21no—
272#239—21no—
273#239—21no—
274D3×Q8—21no—
275D3×Q8—21no—
276D3×Q8—21no—
277D3×Q8—21no—
278D3×Q8—48no—
279#237—21no—
280#237—21no—
281#237—21no—
282#237—21no—
283#237—41no—
284#237—41no—
285#237—41no—
286#237—41no—
287D3×D4—21no—
288D3×D4—21no—
289D3×D4—21no—
290D3×D4—21no—
291D3×D4—41no—
292D3×D4—41no—
293D3×D4—41no—
294D3×D4—41no—
295#235—21no—
296#235—21no—
297#235—21no—
298#235—21no—
299#235—41no—
300#235—41no—
301#235—41no—
302#235—41no—
303C2×D12—21no—
304C2×D12C2×Q811yescharacteristic, complemented
305C2×C4×D3—21no—
306C2×C4×D3—21no—
307C2×C4×D3—21no—
308C2×C4×D3—21no—
309C2×C4×D3—22no—
310C2×C4×D3—22no—
311C2×C4×D3—21no—
312C2×C4×D3—21no—
313C2×C4×D3—21no—
314C2×C4×D3—44no—
315C2×C4×D3—41no—
316C2×C4×D3—41no—
317C2×C4×D3—41no—
318C2×C4×D3—41no—
319C2×C4×D3—41no—
320C2×C4×D3C2×D411yescharacteristic
321C2×C4×D3C2×D411yescharacteristic
322C2×C4×D3C2×D411yescharacteristic
323C2×C4×D3C2×D411yescharacteristic
324C2×C4×D3C2×Q811yescharacteristic
325C2×C4×D3C2×Q811yescharacteristic
326C2×C4×D3#4111yescharacteristic
327C2×C4×D3#4111yescharacteristic
328C2×C4×D3#4111yescharacteristic
329C2×C4×D3#4111yescharacteristic
330C2×C4×D3#4111yescharacteristic
331C2×C4×D3#4111yescharacteristic
332C2×Dic6—22no—
333C2×Dic6—22no—
334C2×Dic6—22no—
335C2×Dic6—21no—
336C2×Dic6C2×Q811yescharacteristic, complemented
337C3×M16—21no—
338C3×M16—21no—
339C3×M16—21no—
340C3×M16—21no—
341C2×C3×C8—21no—
342C2×C3×C8—21no—
343C3×C4⋊C4—22no—
344C3×C4⋊C4—22no—
345C3×C4⋊C4—22no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—21no—
348C3×C4⋊C4—21no—
349C3×C22⋊C4—21no—
350C3×C22⋊C4—21no—
351C3×C22⋊C4C2×D412yes—
352C3×C42—21no—
353C3×C42—21no—
354C3×C42—21no—
355C3×C42C2×D412yes—
356C3×C42C2×D411yescharacteristic
357C3×C42C2×D411yescharacteristic
358#217—21no—
359#217—21no—
360#217C2×D412yes—
361(C2×D3)⋊C4—22no—
362(C2×D3)⋊C4—22no—
363(C2×D3)⋊C4—41no—
364C4⋊Dic3—22no—
365C4⋊Dic3—22no—
366C4⋊Dic3—22no—
367C4⋊Dic3—21no—
368C4⋊Dic3—21no—
369C4⋊Dic3—21no—
370Dic3⋊C4—22no—
371Dic3⋊C4—22no—
372Dic3⋊C4—22no—
373Dic3⋊C4—22no—
374Dic3⋊C4—22no—
375Dic3⋊C4—22no—
376Dic3⋊C4—22no—
377Dic3⋊C4—22no—
378Dic3⋊C4—41no—
379C4×Dic3—21no—
380C4×Dic3—21no—
381C4×Dic3—21no—
382C4×Dic3—21no—
383C4×Dic3—21no—
384C4×Dic3—21no—
385C4×Dic3—22no—
386C4×Dic3—22no—
387C4×Dic3—21no—
388C4×Dic3—41no—
389C4×Dic3C2×D412yes—
390C4×Dic3C2×D411yescharacteristic
391C4×Dic3C2×D411yescharacteristic
392#208—21no—
393#208—21no—
394#208—21no—
395#208—21no—
396C2×C3⋊C8—21no—
397C2×C3⋊C8—21no—
398ΓL(1,𝔽25)—41no—
399ΓL(1,𝔽25)—41no—
400ΓL(1,𝔽25)—41no—
401ΓL(1,𝔽25)—41no—
402D3×C8—41no—
403D3×C8—41no—
404D3×C8—41no—
405D3×C8—41no—
406C2×#41—31no—
407C2×#41—31no—
408C2×#41—31no—
409C2×#41—61no—
410C2×#41—61no—
411C2×#41—61no—
412C2×#41—61no—
413C2×#41—61no—
414C2×#41—61no—
415C2×#41—61no—
416C2×#41—61no—
417C2×#41—61no—
418C2×#41—61no—
419C2×#41C22×D311yescharacteristic
420C22×Q8—31no—
421C22×Q8—62no—
422C22×D4—31no—
423C22×D4—61no—
424C23×C4—31no—
425C23×C4—61no—
426C23×C4—61no—
427C2×M16—31no—
428C2×M16—31no—
429C2×M16—61no—
430C2×M16—61no—
431C2×M16—61no—
432C2×M16—61no—
433C2×M16—61no—
434C2×M16—61no—
435C2×M16—61no—
436C2×M16—61no—
437C2×M16—61no—
438C2×M16—61no—
439C2×M16C22×D311yescharacteristic
440C2×M16C22×D311yescharacteristic
441C22×C8—61no—
442C22×C8—61no—
443C4⋊Q8—21no—
444C4⋊Q8—61no—
445C4⋊Q8—61no—
446C4⋊Q8—62no—
447C4⋊Q8—62no—
448C4⋊Q8—61no—
449#125—21no—
450#125—61no—
451#125—61no—
452#125—62no—
453#125—62no—
454#125—61no—
455C22⋊Q8—22no—
456C22⋊Q8—62no—
457C22⋊Q8—62no—
458C22⋊Q8—62no—
459C22⋊Q8—62no—
460C22⋊Q8—62no—
461C22⋊Q8—62no—
462C22⋊Q8—62no—
463C4×Q8—22no—
464C4×Q8—62no—
465C4×Q8—62no—
466C4×Q8—62no—
467C4×Q8—62no—
468C4×Q8—62no—
469C4×Q8—62no—
470C4×Q8—62no—
471#117—31no—
472#117—32no—
473#117—31no—
474#117—32no—
475#117—31no—
476#117—61no—
477#117—61no—
478#117—61no—
479#117—61no—
480#117—61no—
481#117—61no—
482#117—61no—
483#117C22×D311yescharacteristic
484#117C22×D311yescharacteristic
485#117C22×D311yescharacteristic
486C2×C4⋊C4—61no—
487C2×C4⋊C4—61no—
488C2×C4⋊C4—62no—
489C2×C4⋊C4—62no—
490C2×C4⋊C4—62no—
491C2×C4⋊C4—61no—
492C2×C22⋊C4—32no—
493C2×C22⋊C4—61no—
494C2×C22⋊C4—61no—
495C2×C42—31no—
496C2×C42—32no—
497C2×C42—31no—
498C2×C42—31no—
499C2×C42—31no—
500C2×C42—31no—
501C2×C42—61no—
502C2×C42—61no—
503C2×C42—61no—
504C2×C42—61no—
505C2×C42—61no—
506C2×C42C22×D311yescharacteristic
507#104—21no—
508#104—21no—
509#104—22no—
510#104—61no—
511#104—61no—
512#104—62no—
513#104—61no—
514#104—61no—
515#104—62no—
516#104—61no—
517#104—61no—
518#104—62no—
519#99—22no—
520#99—62no—
521#99—62no—
522#99—62no—
523C23×C3—21no—
524C23×C3C22×D411yescharacteristic
525C22×D3—21no—
526C22×D3—42no—
527C22×D3—41no—
528C22×D3—41no—
529C22×D3—82no—
530C22×D3#12011yescharacteristic
531C22×D3#12011yescharacteristic
532C22×D3C22⋊Q811yescharacteristic
533C22×D3C22⋊Q811yescharacteristic
534C22×D3#12411yescharacteristic
535C22×D3#12411yescharacteristic
536C3×Q8—21no—
537C3×Q8—21no—
538C3×Q8—44no—
539C3×D4—21no—
540C3×D4—21no—
541C3×D4—41no—
542C3×D4—41no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—22no—
546C2×C3×C4—22no—
547C2×C3×C4—21no—
548C2×C3×C4—42no—
549C2×C3×C4—41no—
550C2×C3×C4—41no—
551C2×C3×C4—41no—
552C2×C3×C4C22×D411yescharacteristic
553C2×C3×C4C22×D411yescharacteristic
554C2×C3×C4C22×Q811yescharacteristic
555C2×C3×C4C2×#4111yescharacteristic
556C2×C3×C4C2×#4111yescharacteristic
557C2×C3×C4C2×#4111yescharacteristic
558#67—41no—
559#67—41no—
560#67—41no—
561#67—41no—
562#67—41no—
563#67—41no—
564C2×Dic3—21no—
565C2×Dic3—21no—
566C2×Dic3—22no—
567C2×Dic3—22no—
568C2×Dic3—21no—
569C2×Dic3—42no—
570C2×Dic3—41no—
571C2×Dic3—41no—
572C2×Dic3—41no—
573C2×Dic3#12011yescharacteristic
574C2×Dic3#12011yescharacteristic
575C2×Dic3C22⋊Q811yescharacteristic
576C2×Dic3C22⋊Q811yescharacteristic
577C2×Dic3#12411yescharacteristic
578C2×Dic3#12411yescharacteristic
579D12—21no—
580D12—21no—
581D12—41no—
582D12—41no—
583C4×D3—24no—
584C4×D3—42no—
585C4×D3—42no—
586C4×D3—42no—
587C4×D3—44no—
588C4×D3—44no—
589C4×D3—41no—
590C4×D3—41no—
591C4×D3—41no—
592C4×D3—41no—
593C4×D3—41no—
594C4×D3—41no—
595C4×D3—82no—
596C4×D3C22⋊Q811yescharacteristic
597C4×D3C22⋊Q811yescharacteristic
598C4×D3C22⋊Q811yescharacteristic
599C4×D3C22⋊Q811yescharacteristic
600C4×D3C22⋊Q811yescharacteristic
601C4×D3C22⋊Q811yescharacteristic
602C4×D3C22⋊Q811yescharacteristic
603C4×D3C22⋊Q811yescharacteristic
604C4×D3#12411yescharacteristic
605C4×D3#12411yescharacteristic
606C4×D3#12411yescharacteristic
607C4×D3#12411yescharacteristic
608C4×D3#12411yescharacteristic
609C4×D3#12411yescharacteristic
610C4×D3#12411yescharacteristic
611C4×D3#12411yescharacteristic
612Dic6—21no—
613Dic6—21no—
614Dic6—44no—
615Dic6—44no—
616Dic6—44no—
617Dic6—41no—
618Dic6—41no—
619C3×C8—41no—
620C3×C8—41no—
621C3⋊C8—41no—
622C3⋊C8—41no—
623C24—31no—
624C24—61no—
625#41—21no—
626#41—21no—
627#41—21no—
628#41—21no—
629#41—61no—
630#41—61no—
631#41—61no—
632#41—61no—
633#41—61no—
634#41—61no—
635#41—61no—
636#41—61no—
637#41—61no—
638#41—61no—
639#41—61no—
640#41—61no—
641#41—121no—
642#41—121no—
643#41—121no—
644#41—121no—
645#41—121no—
646#41—121no—
647#41—121no—
648#41—121no—
649C2×Q8—22no—
650C2×Q8—31no—
651C2×Q8—61no—
652C2×Q8—62no—
653C2×Q8—62no—
654C2×Q8—62no—
655C2×Q8—61no—
656C2×Q8—61no—
657C2×Q8—61no—
658C2×Q8—61no—
659C2×Q8—128no—
660C2×Q8D3×Q811yescharacteristic, complemented
661C2×D4—21no—
662C2×D4—31no—
663C2×D4—61no—
664C2×D4—61no—
665C2×D4—61no—
666C2×D4—61no—
667C2×D4—61no—
668C2×D4—61no—
669C2×D4—61no—
670C2×D4—61no—
671C2×D4—121no—
672C2×D4—121no—
673C2×D4—121no—
674C2×D4—121no—
675C2×D4D3×Q811yescharacteristic, complemented
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—31no—
679C22×C4—31no—
680C22×C4—31no—
681C22×C4—31no—
682C22×C4—31no—
683C22×C4—31no—
684C22×C4—31no—
685C22×C4—31no—
686C22×C4—31no—
687C22×C4—31no—
688C22×C4—31no—
689C22×C4—31no—
690C22×C4—31no—
691C22×C4—61no—
692C22×C4—61no—
693C22×C4—61no—
694C22×C4—61no—
695C22×C4—61no—
696C22×C4—62no—
697C22×C4—62no—
698C22×C4—61no—
699C22×C4—61no—
700C22×C4—61no—
701C22×C4—61no—
702C22×C4—121no—
703C22×C4—121no—
704C22×C4—121no—
705C22×C4—121no—
706C22×C4—124no—
707C22×C4—121no—
708C22×C4C23×D311yescharacteristic
709M16—21no—
710M16—21no—
711M16—21no—
712M16—21no—
713M16—61no—
714M16—61no—
715M16—61no—
716M16—61no—
717M16—121no—
718M16—121no—
719M16—121no—
720M16—121no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—61no—
724C2×C8—61no—
725C2×C8—121no—
726C2×C8—121no—
727C2×C8—121no—
728C2×C8—121no—
729C4⋊C4—22no—
730C4⋊C4—22no—
731C4⋊C4—22no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—62no—
736C4⋊C4—62no—
737C4⋊C4—62no—
738C4⋊C4—62no—
739C4⋊C4—62no—
740C4⋊C4—62no—
741C4⋊C4—62no—
742C4⋊C4—62no—
743C4⋊C4—62no—
744C4⋊C4—62no—
745C4⋊C4—62no—
746C4⋊C4—61no—
747C4⋊C4—61no—
748C4⋊C4—61no—
749C4⋊C4—121no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—32no—
753C22⋊C4—62no—
754C22⋊C4—62no—
755C22⋊C4—61no—
756C22⋊C4—61no—
757C22⋊C4—121no—
758C22⋊C4D3×D412yes—
759C42—21no—
760C42—21no—
761C42—21no—
762C42—31no—
763C42—31no—
764C42—32no—
765C42—61no—
766C42—61no—
767C42—61no—
768C42—61no—
769C42—62no—
770C42—62no—
771C42—61no—
772C42—61no—
773C42—61no—
774C42—121no—
775C42D3×D411yescharacteristic
776C42D3×D411yescharacteristic
777C42D3×D412yes—
778C22×C3—41no—
779C22×C3—41no—
780C22×C3—81no—
781C22×C3C2×#12011yescharacteristic
782C22×C3C2×C22⋊Q811yescharacteristic
783C22×C3C2×#12411yescharacteristic
784C2×D3—22no—
785C2×D3—22no—
786C2×D3—22no—
787C2×D3—41no—
788C2×D3—41no—
789C2×D3—41no—
790C2×D3—41no—
791C2×D3—82no—
792C2×D3—82no—
793C2×D3—81no—
794C2×D3#39311yescharacteristic
795C2×D3#39311yescharacteristic
796C2×D3#39311yescharacteristic
797C2×D3#39311yescharacteristic
798C3×C4—22no—
799C3×C4—42no—
800C3×C4—42no—
801C3×C4—41no—
802C3×C4—41no—
803C3×C4—81no—
804C3×C4C2×C22⋊Q811yescharacteristic
805C3×C4C2×C22⋊Q811yescharacteristic
806C3×C4C2×#12411yescharacteristic
807C3×C4C2×#12411yescharacteristic
808Dic3—22no—
809Dic3—42no—
810Dic3—42no—
811Dic3—41no—
812Dic3—41no—
813Dic3—81no—
814Dic3#39311yescharacteristic
815Dic3#39311yescharacteristic
816Dic3#39311yescharacteristic
817Dic3#39311yescharacteristic
818C23—21no—
819C23—31no—
820C23—31no—
821C23—31no—
822C23—31no—
823C23—31no—
824C23—31no—
825C23—61no—
826C23—121no—
827C23—121no—
828C23—122no—
829C23—242no—
830C23C2×D3×D411yescharacteristic
831Q8—21no—
832Q8—21no—
833Q8—44no—
834Q8—61no—
835Q8—61no—
836Q8—124no—
837Q8—121no—
838Q8—121no—
839Q8—124no—
840Q8—124no—
841D4—21no—
842D4—21no—
843D4—41no—
844D4—41no—
845D4—61no—
846D4—61no—
847D4—121no—
848D4—121no—
849D4—121no—
850D4—121no—
851D4—121no—
852D4—121no—
853D4—121no—
854D4—121no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—21no—
860C2×C4—31no—
861C2×C4—31no—
862C2×C4—31no—
863C2×C4—31no—
864C2×C4—31no—
865C2×C4—31no—
866C2×C4—31no—
867C2×C4—31no—
868C2×C4—31no—
869C2×C4—31no—
870C2×C4—31no—
871C2×C4—31no—
872C2×C4—31no—
873C2×C4—31no—
874C2×C4—31no—
875C2×C4—31no—
876C2×C4—31no—
877C2×C4—31no—
878C2×C4—31no—
879C2×C4—31no—
880C2×C4—31no—
881C2×C4—31no—
882C2×C4—42no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—64no—
887C2×C4—61no—
888C2×C4—61no—
889C2×C4—62no—
890C2×C4—62no—
891C2×C4—61no—
892C2×C4—122no—
893C2×C4—121no—
894C2×C4—121no—
895C2×C4—121no—
896C2×C4—121no—
897C2×C4—122no—
898C2×C4—121no—
899C2×C4—121no—
900C2×C4—122no—
901C2×C4—124no—
902C2×C4—124no—
903C2×C4—122no—
904C2×C4—121no—
905C2×C4—121no—
906C2×C4—121no—
907C2×C4—242no—
908C2×C4C2×D3×D411yescharacteristic
909C2×C4C2×D3×D411yescharacteristic
910C2×C4C2×D3×Q811yescharacteristic
911C2×C4D3×#4111yescharacteristic
912C2×C4D3×#4111yescharacteristic
913C2×C4D3×#4111yescharacteristic
914C8—41no—
915C8—41no—
916C8—121no—
917C8—121no—
918C2×C3—21no—
919C2×C3—21no—
920C2×C3—21no—
921C2×C3—81no—
922C2×C3C2×#39311yescharacteristic
923D3—21no—
924D3—21no—
925D3—21no—
926D3—81no—
927D3#203112yesdirect product factor
928C22—31no—
929C22—31no—
930C22—31no—
931C22—31no—
932C22—41no—
933C22—41no—
934C22—62no—
935C22—62no—
936C22—62no—
937C22—81no—
938C22—121no—
939C22—121no—
940C22—121no—
941C22—121no—
942C22—241no—
943C22—242no—
944C22—242no—
945C22D3×#12011yescharacteristic
946C22D3×C22⋊Q811yescharacteristic
947C22D3×#12411yescharacteristic
948C4—22no—
949C4—31no—
950C4—31no—
951C4—31no—
952C4—31no—
953C4—41no—
954C4—42no—
955C4—42no—
956C4—41no—
957C4—62no—
958C4—81no—
959C4—121no—
960C4—122no—
961C4—122no—
962C4—121no—
963C4—241no—
964C4D3×C22⋊Q811yescharacteristic
965C4D3×C22⋊Q811yescharacteristic
966C4D3×#12411yescharacteristic
967C4D3×#12411yescharacteristic
968C3C2×#203111yescharacteristic, complemented, Sylow
969C2—21no—
970C2—21no—
971C2—21no—
972C2—32no—
973C2—61no—
974C2—61no—
975C2—61no—
976C2—81no—
977C2—241no—
978C2D3×#39311yescharacteristic
subgroupG/H
centerC4D3×#124
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2031C2
socleC2×C3C2×#393
prime radicalC2×D3×#41C22
hypercenter#2031D3
hypocenterC3C2×#2031
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C4 ◁ C22×C4 ◁ #2031

Complements

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

NH ≅ G/Ntype
1. D3×#533C2semidirect
5. C3×#2031C2semidirect
6. #71842C2semidirect
7. #70394C2semidirect
8. #70368C2semidirect
9. #70038C2semidirect
10. #69042C2semidirect
11. D3×#344C2semidirect
12. #68779C2semidirect
13. D3×#339C2semidirect
14. #68714C2semidirect
15. D3×H(3,ℤ/4)C2semidirect
18. C3×#533C22semidirect
32. #5517C22semidirect
33. #5517C22semidirect
35. #5470C22semidirect
56. C3×#344C22semidirect
57. C3×#339C22semidirect
58. C3×H(3,ℤ/4)C22semidirect
59. #4559C22semidirect
60. #4557C22semidirect
61. #4556C22semidirect
62. #4555C22semidirect
63. #4533C22semidirect
64. #4532C22semidirect
65. #4531C22semidirect
66. #4531C22semidirect
67. #4523C22semidirect
79. #2031D3direct (N × H)
92. C2×#239Q8semidirect
94. C2×D3×Q8Q8semidirect
96. C2×#237Q8semidirect
98. C2×D3×D4Q8semidirect
210. #533C2×D3semidirect
242. #344C2×D3semidirect
246. #339C2×D3semidirect
250. H(3,ℤ/4)C2×D3semidirect
258. C2×C3×Q8C2×Q8semidirect
260. C2×C3×D4C2×Q8semidirect
304. C2×D12C2×Q8semidirect
336. C2×Dic6C2×Q8semidirect
660. C2×Q8D3×Q8semidirect
675. C2×D4D3×Q8semidirect
927. D3#2031direct (N × H)
968. C3C2×#2031semidirect

Maximal subgroups

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

subgroupindex
D3×#5332
D3×#4212
C2×D3×#1042
D3×#4102
C3×#20312
#718422
#703942
#703682
#700382
#690422
D3×#3442
#687792
D3×#3392
#687142
D3×H(3,ℤ/4)2
C2×#20313