Finite Group Databasebeta

← D3×#12981 #72270375

Subgroups — D3×#12981 #72270375

Order 1536.

2732 conjugacy classes of subgroups.

The subgroup lattice has 1434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#3407C211yesmaximal, characteristic, complemented
2D3×#2929C211yesmaximal, characteristic
3D3×#2115C211yesmaximal, characteristic, complemented
4D3×#2112C212yesmaximal, complemented
5#10712072C211yesmaximal, characteristic, complemented
6#10712071C211yesmaximal, characteristic, complemented
7#10712070C212yesmaximal, complemented
8#10712069C211yesmaximal, characteristic, complemented
9#10712068C212yesmaximal, complemented
10D3×#1378C212yesmaximal, complemented
11C3×#12981C211yesmaximal, characteristic, complemented
12C2×#12981—31nomaximal, Sylow
13C2×D3×#131C2211yescharacteristic
14C23×D3×C8C2211yescharacteristic
15D3×#525C411yescharacteristic
16C3×#3407C2211yescharacteristic, complemented
17C3×#2929C2211yescharacteristic
18#83794C2211yescharacteristic
19#83780C2211yescharacteristic, complemented
20#83734C2211yescharacteristic
21#82916C411yescharacteristic
22#82012—24no—
23D3×#504—24no—
24#82007—22no—
25#82007C2212yescomplemented
26C2×D3×M32—22no—
27C2×D3×M32C2212yes—
28C2×D3×M32C2212yes—
29#79478—22no—
30D3×#435—22no—
31#79421—22no—
32D3×C8×D4—22no—
33D3×#424C411yescharacteristic
34#79073C411yescharacteristic
35D3×#408C411yescharacteristic
36#78655C411yescharacteristic
37D3×#407C411yescharacteristic
38#78626C411yescharacteristic
39#78553C2211yescharacteristic
40D3×#405C2211yescharacteristic
41C3×#2115C2211yescharacteristic, complemented
42C3×#2112C2212yescomplemented
43#72007C2211yescharacteristic, complemented
44#71963C2212yescomplemented
45#71435C2212yescomplemented
46#71431C2212yescomplemented
47#71431C2212yescomplemented
48#69119—22no—
49D3×#349—22no—
50#69106—24no—
51D3×C22⋊C16—24no—
52C3×#1378C2212yescomplemented
53#67814C2212yescomplemented
54#67813C2212yescomplemented
55#67672C2212yescomplemented
56C2×#3407—31no—
57C2×#2929—31no—
58C2×#2115—31no—
59C2×#2112—32no—
60#12981—31no—
61#12981—32no—
62#12981—31no—
63#12981—31no—
64#12981—32no—
65#12981D311yescharacteristic, direct product factor
66C2×#1378—32no—
67C2×D3×#41C2×C411yescharacteristic
68C23×C4×D3C2×C411yescharacteristic
69C2×C3×#131C2311yescharacteristic
70C23×C3×C8C2311yescharacteristic
71C3×#525C2×C411yescharacteristic
72#5828C2×C411yescharacteristic
73C2×#948C2×C411yescharacteristic
74#5791C2×C411yescharacteristic
75C23×C3⋊C8C2×C411yescharacteristic
76D3×#131—22no—
77D3×#131—22no—
78D3×#131—22no—
79D3×#131—22no—
80C2×#907C2×C411yescharacteristic
81C2×#907D412yes—
82C2×D3×M16C2×C411yescharacteristic
83C2×D3×M16C2×C411yescharacteristic
84C2×D3×M16D412yes—
85C2×#901D412yes—
86C2×#901C2311yescharacteristic
87C22×D3×C8—21no—
88C22×D3×C8—21no—
89C22×D3×C8—21no—
90C22×D3×C8—21no—
91C22×D3×C8—22no—
92C22×D3×C8—22no—
93C22×D3×C8—22no—
94C22×D3×C8—22no—
95C22×D3×C8C2×C411yescharacteristic
96C22×D3×C8C2×C411yescharacteristic
97C22×D3×C8D412yes—
98C22×D3×C8C2311yescharacteristic
99C22×D3×C8C2311yescharacteristic
100#5656C812yes—
101D3×#123C812yes—
102#5627—21no—
103D3×C22⋊Q8—21no—
104#5606—21no—
105D3×#121—21no—
106D3×#120C812yes—
107#5586C812yes—
108#5547—22no—
109C4×D3×D4—22no—
110#5524C2×C411yescharacteristic
111D3×#117C2×C411yescharacteristic
112C3×#504—24no—
113C2×C3×M32—22no—
114C2×C3×M32C2312yes—
115C2×C3×M32C2312yes—
116C3×#435—22no—
117C3×C8×D4—22no—
118C3×#424C2×C411yescharacteristic
119C3×#408C2×C411yescharacteristic
120C3×#407C2×C411yescharacteristic
121C3×#405C2311yescharacteristic
122#5234C2×C411yescharacteristic
123#5207C2×C411yescharacteristic
124#5140—24no—
125#5129C2×C411yescharacteristic
126#5127—22no—
127#5126C2×C411yescharacteristic
128#5126C2×C411yescharacteristic
129#5122C2×C411yescharacteristic
130#5119C2×C411yescharacteristic
131#5111—22no—
132#5110C2×C411yescharacteristic
133C8×#67—22no—
134C8×#67—22no—
135#5102C2×C411yescharacteristic
136#5101C2311yescharacteristic
137C2×#812—22no—
138C2×#812C2312yes—
139C2×#812C2312yes—
140#5011—22no—
141D4×C3⋊C8—22no—
142#4999C2×C411yescharacteristic
143#4997C2×C411yescharacteristic
144#4907—28no—
145#4907—24no—
146D3×M32—24no—
147D3×M32—24no—
148D3×M32—22no—
149D3×M32—24no—
150D3×M32—22no—
151D3×M32—22no—
152D3×M32—22no—
153D3×M32—22no—
154D3×M32—22no—
155D3×M32—22no—
156D3×M32—22no—
157#4901—28no—
158#4901—24no—
159C2×#798—24no—
160C2×#798—22no—
161C2×#798D414yescomplemented
162C2×D3×C16—24no—
163C2×D3×C16—22no—
164C2×D3×C16D414yescomplemented
165#4839—22no—
166#4836—22no—
167#4834—22no—
168D3×C4⋊C8—22no—
169#4730—22no—
170#4728—22no—
171#4727—22no—
172#4726—22no—
173#67⋊C8—22no—
174#67⋊C8—22no—
175D3×C22⋊C8—22no—
176D3×C22⋊C8—22no—
177#4708—21no—
178#4706—22no—
179D3×#97—21no—
180#4689—21no—
181C8×D12—22no—
182C4×D3×C8—21no—
183C3×#349—22no—
184C3×C22⋊C16—24no—
185#4553—22no—
186#4549—24no—
187#4514—24no—
188(C2×D3)⋊C16—24no—
189(C2×D3)⋊C16—24no—
190C22×#131—31no—
191C24×C8—31no—
192C2×#525—31no—
193#3407—32no—
194#3407—31no—
195#3407—62no—
196#3407—64no—
197#3407C2×D311yescharacteristic, complemented
198C2×#504—64no—
199C22×M32—32no—
200C22×M32—32no—
201C22×M32—62no—
202#2929—31no—
203#2929—31no—
204#2929—31no—
205#2929—31no—
206#2929—31no—
207#2929—31no—
208#2929—31no—
209#2929—62no—
210#2929—62no—
211#2929C2×D311yescharacteristic
212C2×#435—62no—
213C2×C8×D4—62no—
214C2×#424—31no—
215C2×#408—31no—
216C2×#407—31no—
217C2×#405—31no—
218#2115—32no—
219#2115—31no—
220#2115—62no—
221#2115C2×D311yescharacteristic, complemented
222C2×#349—62no—
223#2112—32no—
224#2112—32no—
225#2112—32no—
226#2112—64no—
227#2112C2×D312yescomplemented
228C2×C22⋊C16—64no—
229#1378—32no—
230#1378—32no—
231#1378—32no—
232#1378C2×D312yescomplemented
233C24×D3C2×C811yescharacteristic
234C2×C3×#41C22×C411yescharacteristic
235C23×C3×C4C22×C411yescharacteristic
236C23×Dic3C2×C811yescharacteristic
237D3×#41—22no—
238D3×#41—22no—
239D3×#41—22no—
240D3×#41—22no—
241C2×#239M1611yescharacteristic
242C2×D3×Q8M1611yescharacteristic
243C2×#237C2×C812yes—
244C2×#237M1611yescharacteristic
245C2×D3×D4—22no—
246C2×D3×D4C2×C812yes—
247C2×D3×D4M1611yescharacteristic
248C2×#235C22⋊C412yes—
249C2×#235C22×C411yescharacteristic
250C22×C4×D3—21no—
251C22×C4×D3—21no—
252C22×C4×D3—22no—
253C22×C4×D3—22no—
254C22×C4×D3—21no—
255C22×C4×D3—21no—
256C22×C4×D3—22no—
257C22×C4×D3—22no—
258C22×C4×D3C22⋊C412yes—
259C22×C4×D3C2×C811yescharacteristic
260C22×C4×D3C2×C811yescharacteristic
261C22×C4×D3C22×C411yescharacteristic
262C22×C4×D3C22×C411yescharacteristic
263C3×#131—22no—
264C3×#131—22no—
265C2×C3×M16C22×C411yescharacteristic
266C2×C3×M16C22×C411yescharacteristic
267C2×C3×M16C2×D412yes—
268C22×C3×C8—21no—
269C22×C3×C8—21no—
270C22×C3×C8—22no—
271C22×C3×C8—22no—
272C22×C3×C8C22×C411yescharacteristic
273C22×C3×C8C2×D412yes—
274C22×C3×C8C2411yescharacteristic
275C3×#123C2×C812yes—
276C3×C22⋊Q8—21no—
277C3×#121—21no—
278C3×#120C2×C812yes—
279C3×C4×D4—22no—
280C3×#117C22×C411yescharacteristic
281#953C2×C812yes—
282#948—22no—
283#948—22no—
284#946—21no—
285#939—22no—
286#938—21no—
287#937—22no—
288#937C2×C812yes—
289#935C2×C812yes—
290D4×Dic3—22no—
291#930—21no—
292#929C2×C812yes—
293C4×#67—22no—
294C4×#67—22no—
295#926C22×C411yescharacteristic
296#924—21no—
297C2×#208C22⋊C412yes—
298C2×#208C22×C411yescharacteristic
299C2×#208C22×C411yescharacteristic
300C22×C3⋊C8—21no—
301C22×C3⋊C8—21no—
302C22×C3⋊C8—22no—
303C22×C3⋊C8—22no—
304C22×C3⋊C8C22⋊C412yes—
305C22×C3⋊C8C22×C411yescharacteristic
306C22×C3⋊C8C22×C411yescharacteristic
307#907—22no—
308#907—22no—
309#907—24no—
310#907—24no—
311D3×M16—22no—
312D3×M16—22no—
313D3×M16—24no—
314D3×M16—24no—
315D3×M16—22no—
316D3×M16—22no—
317#901—22no—
318#901—22no—
319#901—24no—
320#901—24no—
321C2×ΓL(1,𝔽25)—21no—
322C2×ΓL(1,𝔽25)C22⋊C412yes—
323C2×ΓL(1,𝔽25)C22⋊C412yes—
324C2×ΓL(1,𝔽25)C2×D412yes—
325C2×D3×C8—22no—
326C2×D3×C8—22no—
327C2×D3×C8—22no—
328C2×D3×C8—22no—
329C2×D3×C8—21no—
330C2×D3×C8—21no—
331C2×D3×C8—21no—
332C2×D3×C8—22no—
333C2×D3×C8—22no—
334C2×D3×C8—21no—
335C2×D3×C8—21no—
336C2×D3×C8—22no—
337C2×D3×C8—22no—
338C2×D3×C8—21no—
339C2×D3×C8—21no—
340C2×D3×C8—22no—
341C2×D3×C8—22no—
342C2×D3×C8—41no—
343C2×D3×C8—42no—
344C2×D3×C8—41no—
345C2×D3×C8—42no—
346C2×D3×C8—42no—
347C2×D3×C8—42no—
348C2×D3×C8—42no—
349C2×D3×C8—41no—
350C2×D3×C8—41no—
351C2×D3×C8—42no—
352C2×D3×C8C22⋊C412yes—
353C2×D3×C8C22⋊C412yes—
354C2×D3×C8C2×D412yes—
355C2×D3×C8C2×D412yes—
356C2×D3×C8C2×D412yes—
357C2×D3×C8C2×D411yescharacteristic
358C2×D3×C8C2×D411yescharacteristic
359C2×D3×C8C2×D411yescharacteristic
360C2×D3×C8C2×D411yescharacteristic
361C2×D3×C8#4112yes—
362C2×D3×C8#4112yes—
363#897—21no—
364#896—22no—
365#895—21no—
366#894—22no—
367#893—22no—
368#892—21no—
369D3×C4⋊C4—22no—
370D3×C4⋊C4—21no—
371#886C2×C812yes—
372#884—22no—
373#883—22no—
374#882—22no—
375#882C2×C812yes—
376#67⋊C4—22no—
377#67⋊C4—22no—
378D3×C22⋊C4—22no—
379D3×C22⋊C4—22no—
380D3×C22⋊C4C2×C812yes—
381#878—22no—
382#877C2×C812yes—
383C4×D12—22no—
384#872—21no—
385C42×D3—21no—
386C3×M32—24no—
387C3×M32—22no—
388C3×M32—22no—
389C3×M32—22no—
390C3×M32—22no—
391C2×C3×C16—24no—
392C2×C3×C16—22no—
393C2×C3×C16C2×D414yescomplemented
394C3×C4⋊C8—22no—
395C3×C22⋊C8—22no—
396C3×C22⋊C8—22no—
397C3×#97—21no—
398C3×C4×C8—21no—
399#830—22no—
400#830—22no—
401(C2×D3)⋊C8—22no—
402(C2×D3)⋊C8—22no—
403(C2×D3)⋊C8—22no—
404(C2×D3)⋊C8—22no—
405#815—21no—
406#815—21no—
407Dic3⋊C8—22no—
408Dic3⋊C8—22no—
409C8×Dic3—21no—
410C8×Dic3—21no—
411#812—24no—
412#812—22no—
413#812—22no—
414#812—22no—
415#812—22no—
416C2×C3⋊C16—24no—
417C2×C3⋊C16—22no—
418C2×C3⋊C16C2×D414yescomplemented
419C4⋊(C3⋊C8)—22no—
420#803—21no—
421C4×C3⋊C8—21no—
422#798—28no—
423#798—24no—
424#798—24no—
425#798—42no—
426#798—42no—
427D3×C16—28no—
428D3×C16—24no—
429D3×C16—24no—
430D3×C16—42no—
431D3×C16—42no—
432C22×#41—31no—
433C24×C4—31no—
434C2×#131—31no—
435C2×#131—31no—
436C2×#131—32no—
437C2×#131—32no—
438C2×#131—31no—
439C2×#131—62no—
440C2×#131—62no—
441C2×#131—62no—
442C2×#131—62no—
443C2×#131C22×D311yescharacteristic
444C22×M16—31no—
445C22×M16—32no—
446C22×M16—31no—
447C23×C8—31no—
448C23×C8—32no—
449C23×C8—31no—
450C23×C8—31no—
451C23×C8—31no—
452C23×C8—31no—
453C23×C8—62no—
454C23×C8—62no—
455C23×C8—61no—
456C23×C8—61no—
457C23×C8—61no—
458C23×C8—61no—
459C23×C8—62no—
460C23×C8—62no—
461C23×C8C22×D311yescharacteristic
462#525—31no—
463#525—31no—
464#525—32no—
465#525—32no—
466#525—31no—
467#525—62no—
468#525—61no—
469#525—61no—
470#525C4×D311yescharacteristic
471C2×#123—32no—
472C2×C22⋊Q8—61no—
473C2×#121—61no—
474C2×#120—32no—
475C2×C4×D4—62no—
476C2×#117—31no—
477#504—24no—
478#504—68no—
479#504—64no—
480#504—64no—
481#504—68no—
482#504—64no—
483C2×M32—22no—
484C2×M32—32no—
485C2×M32—34no—
486C2×M32—32no—
487C2×M32—64no—
488C2×M32—62no—
489C2×M32—62no—
490C2×M32—62no—
491C2×M32—62no—
492C2×M32—62no—
493C2×M32—64no—
494C2×M32—64no—
495C2×M32—64no—
496C2×M32—62no—
497C2×M32—62no—
498C2×M32—62no—
499C2×M32—62no—
500C2×M32—62no—
501C2×M32C22×D312yes—
502C2×M32C22×D312yes—
503C22×C16—34no—
504C22×C16—64no—
505C22×C16—62no—
506#435—22no—
507#435—62no—
508#435—62no—
509#435—62no—
510#435—62no—
511#435—62no—
512#435—62no—
513#435—62no—
514C8×D4—22no—
515C8×D4—62no—
516C8×D4—62no—
517C8×D4—62no—
518C8×D4—62no—
519C8×D4—62no—
520C8×D4—62no—
521C8×D4—62no—
522#424—31no—
523#424—31no—
524#424—31no—
525#424—62no—
526#424C4×D311yescharacteristic
527C2×C4⋊C8—62no—
528#408—31no—
529#408—31no—
530#408—31no—
531#408—62no—
532#408C4×D311yescharacteristic
533#407—31no—
534#407—31no—
535#407—31no—
536#407—62no—
537#407C4×D311yescharacteristic
538C2×C22⋊C8—62no—
539C2×C22⋊C8—62no—
540#405—31no—
541#405—31no—
542#405—31no—
543#405—61no—
544#405—61no—
545#405C22×D311yescharacteristic
546C2×#97—61no—
547C2×C4×C8—61no—
548#349—22no—
549#349—64no—
550#349—62no—
551C22⋊C16—24no—
552C22⋊C16—64no—
553C22⋊C16—64no—
554C22⋊C16—64no—
555C24×C3C22×C811yescharacteristic
556C23×D3—21no—
557C23×D3—22no—
558C23×D3—21no—
559C23×D3—22no—
560C23×D3—44no—
561C23×D3C22⋊C812yes—
562C23×D3C22×C811yescharacteristic
563C23×D3C22×C811yescharacteristic
564C3×#41—22no—
565C3×#41—22no—
566C2×C3×Q8C2×M1611yescharacteristic
567C2×C3×D4—22no—
568C2×C3×D4C22×C812yes—
569C2×C3×D4C2×M1611yescharacteristic
570C22×C3×C4—21no—
571C22×C3×C4—22no—
572C22×C3×C4—21no—
573C22×C3×C4—22no—
574C22×C3×C4C2×C22⋊C412yes—
575C22×C3×C4C22×C811yescharacteristic
576C22×C3×C4C23×C411yescharacteristic
577C2×#67—22no—
578C2×#67—22no—
579C2×#67C22⋊C812yes—
580C2×#67C22⋊C812yes—
581C2×#67C22×C812yes—
582C22×Dic3—21no—
583C22×Dic3—21no—
584C22×Dic3—22no—
585C22×Dic3—22no—
586C22×Dic3C22⋊C812yes—
587C22×Dic3C22×C811yescharacteristic
588C22×Dic3C22×C811yescharacteristic
589#239—22no—
590#239—22no—
591D3×Q8—22no—
592D3×Q8—22no—
593#237—24no—
594#237—24no—
595#237—22no—
596#237—22no—
597D3×D4—24no—
598D3×D4—24no—
599D3×D4—22no—
600D3×D4—22no—
601D3×D4—48no—
602#235—22no—
603#235—22no—
604#235—24no—
605#235—24no—
606C2×D12—22no—
607C2×D12C22⋊C812yes—
608C2×D12C2×M1611yescharacteristic
609C2×C4×D3—22no—
610C2×C4×D3—22no—
611C2×C4×D3—22no—
612C2×C4×D3—22no—
613C2×C4×D3—22no—
614C2×C4×D3—21no—
615C2×C4×D3—21no—
616C2×C4×D3—22no—
617C2×C4×D3—22no—
618C2×C4×D3—21no—
619C2×C4×D3—22no—
620C2×C4×D3—21no—
621C2×C4×D3—22no—
622C2×C4×D3—21no—
623C2×C4×D3—21no—
624C2×C4×D3—22no—
625C2×C4×D3—22no—
626C2×C4×D3—41no—
627C2×C4×D3—41no—
628C2×C4×D3—42no—
629C2×C4×D3—41no—
630C2×C4×D3—41no—
631C2×C4×D3—42no—
632C2×C4×D3—42no—
633C2×C4×D3—42no—
634C2×C4×D3—42no—
635C2×C4×D3—42no—
636C2×C4×D3C22⋊C812yes—
637C2×C4×D3C22⋊C812yes—
638C2×C4×D3C2×C22⋊C412yes—
639C2×C4×D3C2×C22⋊C411yescharacteristic
640C2×C4×D3C2×C22⋊C411yescharacteristic
641C2×C4×D3C4×D412yes—
642C2×C4×D3C4×D412yes—
643C2×C4×D3C2×M1611yescharacteristic
644C2×C4×D3C2×M1611yescharacteristic
645C2×C4×D3#13112yes—
646C2×C4×D3#13112yes—
647C2×Dic6C22⋊C812yes—
648C2×Dic6C2×M1611yescharacteristic
649C3×M16—22no—
650C3×M16—24no—
651C3×M16—22no—
652C2×C3×C8—22no—
653C2×C3×C8—22no—
654C2×C3×C8—21no—
655C2×C3×C8—21no—
656C2×C3×C8—22no—
657C2×C3×C8—41no—
658C2×C3×C8—42no—
659C2×C3×C8—41no—
660C2×C3×C8C2×C22⋊C412yes—
661C2×C3×C8C22×D412yes—
662C2×C3×C8C22×D411yescharacteristic
663C2×C3×C8C22×D411yescharacteristic
664C2×C3×C8C2×#4112yes—
665C3×C4⋊C4—21no—
666C3×C4⋊C4—22no—
667C3×C22⋊C4—22no—
668C3×C22⋊C4—22no—
669C3×C22⋊C4C22×C812yes—
670C3×C42—21no—
671#217—22no—
672#217—22no—
673#217C22×C812yes—
674(C2×D3)⋊C4—22no—
675(C2×D3)⋊C4—22no—
676(C2×D3)⋊C4—22no—
677(C2×D3)⋊C4—22no—
678(C2×D3)⋊C4—22no—
679C4⋊Dic3—21no—
680C4⋊Dic3—22no—
681Dic3⋊C4—22no—
682Dic3⋊C4—22no—
683Dic3⋊C4—22no—
684C4×Dic3—21no—
685C4×Dic3—22no—
686#208—22no—
687#208—24no—
688#208—22no—
689C2×C3⋊C8—22no—
690C2×C3⋊C8—22no—
691C2×C3⋊C8—21no—
692C2×C3⋊C8—21no—
693C2×C3⋊C8—22no—
694C2×C3⋊C8—41no—
695C2×C3⋊C8—41no—
696C2×C3⋊C8—42no—
697C2×C3⋊C8C2×C22⋊C412yes—
698C2×C3⋊C8C2×C22⋊C411yescharacteristic
699C2×C3⋊C8C2×C22⋊C411yescharacteristic
700C2×C3⋊C8C4×D412yes—
701C2×C3⋊C8C4×D412yes—
702ΓL(1,𝔽25)—24no—
703ΓL(1,𝔽25)—24no—
704ΓL(1,𝔽25)—24no—
705ΓL(1,𝔽25)—42no—
706D3×C8—22no—
707D3×C8—22no—
708D3×C8—22no—
709D3×C8—22no—
710D3×C8—22no—
711D3×C8—22no—
712D3×C8—41no—
713D3×C8—41no—
714D3×C8—42no—
715D3×C8—41no—
716D3×C8—41no—
717D3×C8—41no—
718D3×C8—42no—
719D3×C8—41no—
720D3×C8—41no—
721D3×C8—41no—
722D3×C8—42no—
723D3×C8#12011yescharacteristic
724D3×C8#12012yes—
725D3×C8#12011yescharacteristic
726D3×C8#12112yes—
727D3×C8#12112yes—
728D3×C8#12112yes—
729D3×C8#12112yes—
730D3×C8#12311yescharacteristic
731D3×C8#12311yescharacteristic
732D3×C8#12312yes—
733C3×C16—24no—
734C3×C16—42no—
735C3⋊C16—24no—
736C3⋊C16—42no—
737C25—31no—
738C2×#41—31no—
739C2×#41—32no—
740C2×#41—31no—
741C2×#41—32no—
742C2×#41—31no—
743C2×#41—62no—
744C2×#41—62no—
745C2×#41—62no—
746C2×#41—62no—
747C2×#41C2×C4×D311yescharacteristic
748C22×Q8—31no—
749C22×D4—32no—
750C22×D4—31no—
751C22×D4—62no—
752C23×C4—31no—
753C23×C4—32no—
754C23×C4—31no—
755C23×C4—31no—
756C23×C4—31no—
757C23×C4—31no—
758C23×C4—61no—
759C23×C4—61no—
760C23×C4—61no—
761C23×C4—61no—
762C23×C4—62no—
763C23×C4—62no—
764C23×C4—62no—
765C23×C4—62no—
766C23×C4C2×C4×D311yescharacteristic
767#131—22no—
768#131—22no—
769#131—64no—
770#131—64no—
771#131—62no—
772#131—62no—
773#131—64no—
774#131—64no—
775#131—62no—
776#131—62no—
777#131—62no—
778#131—62no—
779C2×M16—32no—
780C2×M16—31no—
781C2×M16—32no—
782C2×M16—32no—
783C2×M16—32no—
784C2×M16—31no—
785C2×M16—61no—
786C2×M16—64no—
787C2×M16—64no—
788C2×M16—62no—
789C2×M16—62no—
790C2×M16—62no—
791C2×M16—62no—
792C2×M16C2×C4×D311yescharacteristic
793C2×M16C2×C4×D311yescharacteristic
794C2×M16D3×D412yes—
795C22×C8—22no—
796C22×C8—21no—
797C22×C8—21no—
798C22×C8—22no—
799C22×C8—31no—
800C22×C8—31no—
801C22×C8—31no—
802C22×C8—31no—
803C22×C8—31no—
804C22×C8—32no—
805C22×C8—32no—
806C22×C8—32no—
807C22×C8—32no—
808C22×C8—32no—
809C22×C8—32no—
810C22×C8—32no—
811C22×C8—32no—
812C22×C8—31no—
813C22×C8—62no—
814C22×C8—62no—
815C22×C8—62no—
816C22×C8—62no—
817C22×C8—62no—
818C22×C8—62no—
819C22×C8—61no—
820C22×C8—61no—
821C22×C8—62no—
822C22×C8—62no—
823C22×C8—61no—
824C22×C8—61no—
825C22×C8—61no—
826C22×C8—62no—
827C22×C8—62no—
828C22×C8—61no—
829C22×C8—61no—
830C22×C8—62no—
831C22×C8—61no—
832C22×C8—61no—
833C22×C8—62no—
834C22×C8—121no—
835C22×C8—121no—
836C22×C8—122no—
837C22×C8—121no—
838C22×C8—122no—
839C22×C8—121no—
840C22×C8—122no—
841C22×C8—122no—
842C22×C8—122no—
843C22×C8—122no—
844C22×C8C2×C4×D311yescharacteristic
845C22×C8D3×D412yes—
846C22×C8C23×D311yescharacteristic
847#123—32no—
848#123—32no—
849#123—32no—
850#123—62no—
851#123—62no—
852#123D3×C812yes—
853C22⋊Q8—21no—
854C22⋊Q8—62no—
855C22⋊Q8—62no—
856C22⋊Q8—61no—
857C22⋊Q8—61no—
858C22⋊Q8—61no—
859#121—21no—
860#121—62no—
861#121—61no—
862#121—61no—
863#121—62no—
864#121—61no—
865#120—32no—
866#120—32no—
867#120—32no—
868#120—62no—
869#120—62no—
870#120D3×C812yes—
871C4×D4—22no—
872C4×D4—62no—
873C4×D4—62no—
874C4×D4—62no—
875C4×D4—62no—
876C4×D4—62no—
877C4×D4—62no—
878C4×D4—62no—
879#117—31no—
880#117—32no—
881#117—61no—
882#117—61no—
883#117C2×C4×D311yescharacteristic
884C2×C4⋊C4—61no—
885C2×C4⋊C4—62no—
886C2×C22⋊C4—32no—
887C2×C22⋊C4—62no—
888C2×C22⋊C4—62no—
889C2×C42—61no—
890M32—24no—
891M32—22no—
892M32—22no—
893M32—22no—
894M32—22no—
895M32—64no—
896M32—64no—
897M32—68no—
898M32—64no—
899M32—62no—
900M32—62no—
901M32—62no—
902M32—62no—
903M32—122no—
904M32—122no—
905C2×C16—24no—
906C2×C16—22no—
907C2×C16—34no—
908C2×C16—64no—
909C2×C16—64no—
910C2×C16—68no—
911C2×C16—64no—
912C2×C16—62no—
913C2×C16—122no—
914C2×C16—122no—
915C2×C16D3×D414yescomplemented
916C4⋊C8—22no—
917C4⋊C8—62no—
918C4⋊C8—62no—
919C4⋊C8—62no—
920C22⋊C8—22no—
921C22⋊C8—22no—
922C22⋊C8—62no—
923C22⋊C8—62no—
924C22⋊C8—62no—
925C22⋊C8—62no—
926C22⋊C8—62no—
927C22⋊C8—62no—
928#97—21no—
929#97—61no—
930#97—61no—
931#97—61no—
932C4×C8—21no—
933C4×C8—61no—
934C4×C8—61no—
935C4×C8—61no—
936C23×C3—21no—
937C23×C3—22no—
938C23×C3—42no—
939C23×C3C2×C22⋊C812yes—
940C23×C3C23×C811yescharacteristic
941C22×D3—24no—
942C22×D3—28no—
943C22×D3—21no—
944C22×D3—22no—
945C22×D3—22no—
946C22×D3—22no—
947C22×D3—42no—
948C22×D3—42no—
949C22×D3—42no—
950C22×D3—44no—
951C22×D3—42no—
952C22×D3—44no—
953C22×D3—44no—
954C22×D3—42no—
955C22×D3—44no—
956C22×D3—41no—
957C22×D3—42no—
958C22×D3—41no—
959C22×D3C2×C22⋊C811yescharacteristic
960C22×D3C2×C22⋊C812yes—
961C22×D3C2×C22⋊C811yescharacteristic
962C22×D3C8×D412yes—
963C22×D3C8×D412yes—
964C3×Q8—22no—
965C3×D4—24no—
966C3×D4—22no—
967C3×D4—44no—
968C2×C3×C4—22no—
969C2×C3×C4—22no—
970C2×C3×C4—22no—
971C2×C3×C4—21no—
972C2×C3×C4—22no—
973C2×C3×C4—41no—
974C2×C3×C4—42no—
975C2×C3×C4—41no—
976C2×C3×C4C2×C22⋊C812yes—
977C2×C3×C4C22×C22⋊C411yescharacteristic
978C2×C3×C4C2×C4×D412yes—
979C2×C3×C4C22×M1611yescharacteristic
980C2×C3×C4C2×#13112yes—
981#67—24no—
982#67—24no—
983#67—24no—
984#67—44no—
985#67—44no—
986C2×Dic3—22no—
987C2×Dic3—22no—
988C2×Dic3—22no—
989C2×Dic3—21no—
990C2×Dic3—22no—
991C2×Dic3—42no—
992C2×Dic3—41no—
993C2×Dic3—41no—
994C2×Dic3C2×C22⋊C812yes—
995C2×Dic3C2×C22⋊C811yescharacteristic
996C2×Dic3C2×C22⋊C811yescharacteristic
997C2×Dic3C8×D412yes—
998C2×Dic3C8×D412yes—
999D12—24no—
1000D12—22no—
1001D12—44no—
1002C4×D3—22no—
1003C4×D3—22no—
1004C4×D3—22no—
1005C4×D3—22no—
1006C4×D3—22no—
1007C4×D3—22no—
1008C4×D3—44no—
1009C4×D3—41no—
1010C4×D3—42no—
1011C4×D3—41no—
1012C4×D3—41no—
1013C4×D3—42no—
1014C4×D3—41no—
1015C4×D3—42no—
1016C4×D3—41no—
1017C4×D3—41no—
1018C4×D3#38611yescharacteristic
1019C4×D3#38611yescharacteristic
1020C4×D3#38612yes—
1021C4×D3#40811yescharacteristic
1022C4×D3#40811yescharacteristic
1023C4×D3#40812yes—
1024C4×D3#43512yes—
1025C4×D3#43512yes—
1026C4×D3#43512yes—
1027C4×D3#43512yes—
1028Dic6—22no—
1029Dic6—24no—
1030C3×C8—22no—
1031C3×C8—41no—
1032C3×C8—41no—
1033C3×C8C2×#12011yescharacteristic
1034C3×C8C2×#12112yes—
1035C3×C8C2×#12311yescharacteristic
1036C3⋊C8—22no—
1037C3⋊C8—41no—
1038C3⋊C8—41no—
1039C3⋊C8#38611yescharacteristic
1040C3⋊C8#38611yescharacteristic
1041C3⋊C8#38612yes—
1042C24—31no—
1043C24—32no—
1044C24—31no—
1045C24—61no—
1046C24—62no—
1047C24—61no—
1048C24—62no—
1049C24—124no—
1050C24C2×D3×C811yescharacteristic
1051#41—22no—
1052#41—22no—
1053#41—64no—
1054#41—64no—
1055#41—64no—
1056#41—64no—
1057#41—62no—
1058#41—62no—
1059#41—62no—
1060#41—62no—
1061#41—62no—
1062#41—62no—
1063C2×Q8—31no—
1064C2×Q8—32no—
1065C2×Q8—62no—
1066C2×Q8—62no—
1067C2×Q8D3×M1611yescharacteristic
1068C2×D4—22no—
1069C2×D4—32no—
1070C2×D4—32no—
1071C2×D4—32no—
1072C2×D4—31no—
1073C2×D4—32no—
1074C2×D4—62no—
1075C2×D4—62no—
1076C2×D4—62no—
1077C2×D4—64no—
1078C2×D4—64no—
1079C2×D4—62no—
1080C2×D4—62no—
1081C2×D4—128no—
1082C2×D4C2×D3×C812yes—
1083C2×D4D3×M1611yescharacteristic
1084C22×C4—21no—
1085C22×C4—21no—
1086C22×C4—22no—
1087C22×C4—22no—
1088C22×C4—31no—
1089C22×C4—31no—
1090C22×C4—31no—
1091C22×C4—31no—
1092C22×C4—31no—
1093C22×C4—32no—
1094C22×C4—32no—
1095C22×C4—32no—
1096C22×C4—32no—
1097C22×C4—32no—
1098C22×C4—32no—
1099C22×C4—32no—
1100C22×C4—32no—
1101C22×C4—31no—
1102C22×C4—62no—
1103C22×C4—62no—
1104C22×C4—62no—
1105C22×C4—62no—
1106C22×C4—61no—
1107C22×C4—61no—
1108C22×C4—62no—
1109C22×C4—62no—
1110C22×C4—62no—
1111C22×C4—61no—
1112C22×C4—61no—
1113C22×C4—62no—
1114C22×C4—62no—
1115C22×C4—61no—
1116C22×C4—61no—
1117C22×C4—62no—
1118C22×C4—62no—
1119C22×C4—61no—
1120C22×C4—61no—
1121C22×C4—62no—
1122C22×C4—62no—
1123C22×C4—121no—
1124C22×C4—121no—
1125C22×C4—122no—
1126C22×C4—121no—
1127C22×C4—121no—
1128C22×C4—122no—
1129C22×C4—122no—
1130C22×C4—122no—
1131C22×C4—122no—
1132C22×C4—122no—
1133C22×C4D3×C22⋊C412yes—
1134C22×C4C2×D3×C811yescharacteristic
1135C22×C4C22×C4×D311yescharacteristic
1136M16—22no—
1137M16—24no—
1138M16—22no—
1139M16—64no—
1140M16—64no—
1141M16—64no—
1142M16—62no—
1143M16—64no—
1144M16—62no—
1145M16—122no—
1146C2×C8—22no—
1147C2×C8—22no—
1148C2×C8—21no—
1149C2×C8—21no—
1150C2×C8—22no—
1151C2×C8—31no—
1152C2×C8—31no—
1153C2×C8—32no—
1154C2×C8—32no—
1155C2×C8—31no—
1156C2×C8—31no—
1157C2×C8—32no—
1158C2×C8—31no—
1159C2×C8—32no—
1160C2×C8—31no—
1161C2×C8—32no—
1162C2×C8—32no—
1163C2×C8—32no—
1164C2×C8—32no—
1165C2×C8—32no—
1166C2×C8—41no—
1167C2×C8—41no—
1168C2×C8—42no—
1169C2×C8—62no—
1170C2×C8—62no—
1171C2×C8—62no—
1172C2×C8—62no—
1173C2×C8—62no—
1174C2×C8—62no—
1175C2×C8—62no—
1176C2×C8—62no—
1177C2×C8—61no—
1178C2×C8—61no—
1179C2×C8—62no—
1180C2×C8—121no—
1181C2×C8—121no—
1182C2×C8—122no—
1183C2×C8—121no—
1184C2×C8—121no—
1185C2×C8—122no—
1186C2×C8—121no—
1187C2×C8—121no—
1188C2×C8—122no—
1189C2×C8—121no—
1190C2×C8—121no—
1191C2×C8—121no—
1192C2×C8—121no—
1193C2×C8—122no—
1194C2×C8D3×C22⋊C412yes—
1195C2×C8C2×D3×D411yescharacteristic
1196C2×C8C2×D3×D412yes—
1197C2×C8C2×D3×D411yescharacteristic
1198C2×C8D3×#4112yes—
1199C4⋊C4—21no—
1200C4⋊C4—22no—
1201C4⋊C4—62no—
1202C4⋊C4—62no—
1203C4⋊C4—62no—
1204C4⋊C4—61no—
1205C4⋊C4—62no—
1206C22⋊C4—22no—
1207C22⋊C4—22no—
1208C22⋊C4—32no—
1209C22⋊C4—62no—
1210C22⋊C4—62no—
1211C22⋊C4—62no—
1212C22⋊C4—62no—
1213C22⋊C4—62no—
1214C22⋊C4—62no—
1215C22⋊C4—62no—
1216C22⋊C4C2×D3×C812yes—
1217C42—21no—
1218C42—62no—
1219C42—61no—
1220C16—24no—
1221C16—42no—
1222C16—64no—
1223C16—122no—
1224C22×C3—22no—
1225C22×C3—24no—
1226C22×C3—22no—
1227C22×C3—41no—
1228C22×C3—42no—
1229C22×C3—41no—
1230C22×C3—42no—
1231C22×C3—41no—
1232C22×C3C22×C22⋊C811yescharacteristic
1233C22×C3C2×C8×D412yes—
1234C2×D3—22no—
1235C2×D3—24no—
1236C2×D3—22no—
1237C2×D3—24no—
1238C2×D3—22no—
1239C2×D3—41no—
1240C2×D3—42no—
1241C2×D3—44no—
1242C2×D3—48no—
1243C2×D3—41no—
1244C2×D3—42no—
1245C2×D3—41no—
1246C2×D3—44no—
1247C2×D3—44no—
1248C2×D3—42no—
1249C2×D3—82no—
1250C2×D3#186911yescharacteristic
1251C2×D3#186912yes—
1252C2×D3#186911yescharacteristic
1253C3×C4—22no—
1254C3×C4—42no—
1255C3×C4—41no—
1256C3×C4C2×#38611yescharacteristic
1257C3×C4C2×#40811yescharacteristic
1258C3×C4C2×#43512yes—
1259Dic3—22no—
1260Dic3—42no—
1261Dic3—41no—
1262Dic3#186912yes—
1263Dic3#186911yescharacteristic
1264Dic3#186911yescharacteristic
1265C23—21no—
1266C23—22no—
1267C23—31no—
1268C23—32no—
1269C23—31no—
1270C23—32no—
1271C23—32no—
1272C23—42no—
1273C23—62no—
1274C23—62no—
1275C23—64no—
1276C23—68no—
1277C23—61no—
1278C23—62no—
1279C23—122no—
1280C23—124no—
1281C23—121no—
1282C23—121no—
1283C23—122no—
1284C23—122no—
1285C23—122no—
1286C23—122no—
1287C23—124no—
1288C23—122no—
1289C23—124no—
1290C23—124no—
1291C23D3×C22⋊C812yes—
1292C23C22×D3×C811yescharacteristic
1293Q8—22no—
1294Q8—64no—
1295Q8—62no—
1296D4—24no—
1297D4—22no—
1298D4—44no—
1299D4—64no—
1300D4—64no—
1301D4—64no—
1302D4—64no—
1303D4—62no—
1304D4—124no—
1305D4—124no—
1306D4—124no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—21no—
1311C2×C4—22no—
1312C2×C4—31no—
1313C2×C4—31no—
1314C2×C4—32no—
1315C2×C4—32no—
1316C2×C4—31no—
1317C2×C4—31no—
1318C2×C4—32no—
1319C2×C4—32no—
1320C2×C4—32no—
1321C2×C4—32no—
1322C2×C4—32no—
1323C2×C4—31no—
1324C2×C4—31no—
1325C2×C4—32no—
1326C2×C4—32no—
1327C2×C4—41no—
1328C2×C4—42no—
1329C2×C4—41no—
1330C2×C4—62no—
1331C2×C4—62no—
1332C2×C4—62no—
1333C2×C4—62no—
1334C2×C4—62no—
1335C2×C4—62no—
1336C2×C4—62no—
1337C2×C4—62no—
1338C2×C4—62no—
1339C2×C4—61no—
1340C2×C4—62no—
1341C2×C4—121no—
1342C2×C4—121no—
1343C2×C4—122no—
1344C2×C4—121no—
1345C2×C4—121no—
1346C2×C4—122no—
1347C2×C4—121no—
1348C2×C4—121no—
1349C2×C4—122no—
1350C2×C4—124no—
1351C2×C4—121no—
1352C2×C4—122no—
1353C2×C4—121no—
1354C2×C4D3×C22⋊C812yes—
1355C2×C4C2×D3×C22⋊C411yescharacteristic
1356C2×C4C4×D3×D412yes—
1357C2×C4C2×D3×M1611yescharacteristic
1358C2×C4D3×#13112yes—
1359C8—22no—
1360C8—31no—
1361C8—31no—
1362C8—32no—
1363C8—41no—
1364C8—41no—
1365C8—62no—
1366C8—121no—
1367C8—121no—
1368C8D3×#12011yescharacteristic
1369C8D3×#12112yes—
1370C8D3×#12311yescharacteristic
1371C2×C3—21no—
1372C2×C3—22no—
1373C2×C3—42no—
1374C2×C3—42no—
1375C2×C3C2×#186911yescharacteristic
1376D3—21no—
1377D3—22no—
1378D3—42no—
1379D3—42no—
1380D3#1298112yesdirect product factor
1381C22—22no—
1382C22—24no—
1383C22—22no—
1384C22—31no—
1385C22—31no—
1386C22—32no—
1387C22—41no—
1388C22—42no—
1389C22—41no—
1390C22—42no—
1391C22—41no—
1392C22—62no—
1393C22—64no—
1394C22—62no—
1395C22—64no—
1396C22—62no—
1397C22—121no—
1398C22—122no—
1399C22—122no—
1400C22—121no—
1401C22—122no—
1402C22—124no—
1403C22—124no—
1404C22—124no—
1405C22—128no—
1406C22—121no—
1407C22—242no—
1408C22C2×D3×C22⋊C811yescharacteristic
1409C22D3×C8×D412yes—
1410C4—22no—
1411C4—31no—
1412C4—31no—
1413C4—32no—
1414C4—42no—
1415C4—41no—
1416C4—62no—
1417C4—122no—
1418C4—121no—
1419C4D3×#38611yescharacteristic
1420C4D3×#40811yescharacteristic
1421C4D3×#43512yes—
1422C3C2×#1298111yescharacteristic, complemented, Sylow
1423C2—21no—
1424C2—22no—
1425C2—32no—
1426C2—42no—
1427C2—42no—
1428C2—61no—
1429C2—62no—
1430C2—122no—
1431C2—122no—
1432C2D3×#186911yescharacteristic
subgroupG/H
centerC8D3×#120
commutatorC23×C3C23×C8
FrattiniC22×C8C23×D3
FittingC3×#12981C2
socleC2×C3C2×#1869
prime radicalD3×#525C4
cosocleC22×C3×C8C24
hypercenter#12981D3
hypocenterC3C2×#12981
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C8 ◁ C22×C8 ◁ #12981

Complements

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

NH ≅ G/Ntype
1. D3×#3407C2semidirect
3. D3×#2115C2semidirect
4. D3×#2112C2semidirect
5. #10712072C2semidirect
6. #10712071C2semidirect
7. #10712070C2semidirect
8. #10712069C2semidirect
9. #10712068C2semidirect
10. D3×#1378C2semidirect
11. C3×#12981C2semidirect
16. C3×#3407C22semidirect
19. #83780C22semidirect
25. #82007C22semidirect
41. C3×#2115C22semidirect
42. C3×#2112C22semidirect
43. #72007C22semidirect
44. #71963C22semidirect
45. #71435C22semidirect
46. #71431C22semidirect
47. #71431C22semidirect
52. C3×#1378C22semidirect
53. #67814C22semidirect
54. #67813C22semidirect
55. #67672C22semidirect
65. #12981D3direct (N × H)
161. C2×#798D4semidirect
164. C2×D3×C16D4semidirect
197. #3407C2×D3semidirect
221. #2115C2×D3semidirect
227. #2112C2×D3semidirect
232. #1378C2×D3semidirect
393. C2×C3×C16C2×D4semidirect
418. C2×C3⋊C16C2×D4semidirect
915. C2×C16D3×D4semidirect
1380. D3#12981direct (N × H)
1422. C3C2×#12981semidirect

Maximal subgroups

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

subgroupindex
D3×#34072
D3×#29292
D3×#21152
D3×#21122
#107120722
#107120712
#107120702
#107120692
#107120682
D3×#13782
C3×#129812
C2×#129813