Finite Group Databasebeta

← D3×#4845 #11865688

Subgroups — D3×#4845 #11865688

Order 1152.

1056 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×Dic12C211yesmaximal, characteristic, complemented
2C2×D3×#204C211yesmaximal, characteristic
3D3×#875C211yesmaximal, characteristic
4C4×D3×Dic6C211yesmaximal, characteristic, complemented
5#10592544C211yesmaximal, characteristic, complemented
6C3×#4845C211yesmaximal, characteristic, complemented
7C3×D3×C4⋊C8C211yesmaximal, characteristic, complemented
8D3×#821C211yesmaximal, characteristic
9#10590861C211yesmaximal, characteristic, complemented
10#10590859C211yesmaximal, characteristic, complemented
11#10590813C211yesmaximal, characteristic, complemented
12#10590801C211yesmaximal, characteristic, complemented
13D3×#816C211yesmaximal, characteristic, complemented
14#10590378C211yesmaximal, characteristic, complemented
15#10590368C211yesmaximal, characteristic, complemented
16D3×#464—31nomaximal
17C2×#4845—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×D3×Dic6C2211yescharacteristic
20C2×D3×Dic6C2211yescharacteristic
21C2×#3746C2211yescharacteristic, complemented
22C2×#3744C2211yescharacteristic
23#64084C2211yescharacteristic
24C4×#634C2211yescharacteristic, complemented
25C2×C3×Dic12C2211yescharacteristic, complemented
26C2×C3×#204C2211yescharacteristic
27C2×C3×D3×C8C2211yescharacteristic
28C2×C3×D3×C8C2211yescharacteristic
29C3×#875C2211yescharacteristic
30C3×C42×D3C2211yescharacteristic
31C3×C4×Dic6C2211yescharacteristic, complemented
32D3×(C2×D3)⋊C4—21no—
33D3×(C2×D3)⋊C4—21no—
34C4×#627—21no—
35D3×C4⋊Dic3C2211yescharacteristic
36D3×Dic3⋊C4—21no—
37C4×D3×Dic3—21no—
38#63864C2211yescharacteristic
39#63860C2211yescharacteristic
40#63852—21no—
41#63852—21no—
42#63844C2211yescharacteristic, complemented
43Dic3×Dic6C2211yescharacteristic, complemented
44#63837—21no—
45C2×#3719C2211yescharacteristic, complemented
46C2×#3719C2211yescharacteristic, complemented
47C2×#3717C2211yescharacteristic
48C2×#3716C2211yescharacteristic
49D3×Dic12—24no—
50D3×#204—24no—
51C32×C4⋊C8C2211yescharacteristic, complemented
52#63648C2211yescharacteristic
53#63643C2211yescharacteristic, complemented
54C3×#821C2211yescharacteristic
55C3×#816C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57C3×Dic3⋊C8C2211yescharacteristic, complemented
58C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63566C2211yescharacteristic, complemented
61#63564C2211yescharacteristic
62#63563C2211yescharacteristic
63C2×D3×Q16—31no—
64C2×D3×SD16—31no—
65C22×Dic12—31no—
66C22×#204—31no—
67D3×#124—31no—
68C4×D3×Q8—31no—
69C2×#875—31no—
70C2×C4×Dic6—31no—
71C3×#464—31no—
72C2×C3×C4⋊C8—31no—
73#5185—31no—
74#5166—31no—
75C2×#821—31no—
76C2×#816—31no—
77#5054—31no—
78#5028—31no—
79#4845—31no—
80#4845—31no—
81#4845—31no—
82#4845—31no—
83#4845—31no—
84#4845—31no—
85#4845—31no—
86#4845—31no—
87#4845—61no—
88#4845D311yescharacteristic, direct product factor
89D3×C4⋊C8D311yescharacteristic, complemented
90D3×#103—31no—
91#4798—31no—
92D3×#102—31no—
93#4767—31no—
94C22×D32—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×#634C2311yescharacteristic
97C2×#634C2311yescharacteristic
98C2×C3×D12C2311yescharacteristic
99C2×C3×C4×D3D411yescharacteristic
100C2×C3×C4×D3D411yescharacteristic
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×Dic6C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×#627—21no—
105C2×#627—21no—
106C2×#626—21no—
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110D3×D12—22no—
111D3×D12—22no—
112D3×Dic6—22no—
113D3×Dic6—22no—
114D3×Dic6—22no—
115D3×Dic6D414yes—
116C2×C32×C8C2311yescharacteristic
117C2×C32×C8C2311yescharacteristic
118C32×C42C2311yescharacteristic
119#3752—21no—
120#3752—21no—
121C4⋊(C3⋊Dic3)C2311yescharacteristic
122#3750—21no—
123C4×C3⋊Dic3—21no—
124#3746—22no—
125#3744—22no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×C4×Dic3—21no—
131C3×C4×Dic3D411yescharacteristic
132C3×C4×Dic3D411yescharacteristic
133C3×C4×Dic3C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C3×Dic12—22no—
137C3×#204—22no—
138C3×D3×C8—22no—
139C3×D3×C8—22no—
140#3724—21no—
141Dic3⋊Dic3—21no—
142Dic3⋊Dic3—21no—
143#3722—21no—
144#3722—21no—
145(C2×D3)⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147Dic32—21no—
148Dic32—21no—
149#3719—22no—
150#3719—22no—
151#3717—22no—
152#3716—22no—
153C2×#464—91noSylow
154C2×D3×Q8—31no—
155C2×D3×Q8—31no—
156C2×D3×D4—31no—
157C22×D12—31no—
158C22×Dic6—31no—
159C22×Dic6—31no—
160C2×C3×Q16—31no—
161C2×C3×SD16—31no—
162C22×C3×C8—31no—
163C22×C3×C8—31no—
164C3×#124—31no—
165C3×C4×Q8—31no—
166C2×C3×C42—31no—
167#947—31no—
168Q8×Dic3—31no—
169C2×#216—31no—
170C2×#216—31no—
171C2×#215—31no—
172#936—31no—
173C2×#214—31no—
174C2×(C2×D3)⋊C4—61no—
175C2×(C2×D3)⋊C4—61no—
176C2×C4⋊Dic3—31no—
177C2×Dic3⋊C4—61no—
178C2×C4×Dic3—61no—
179D3×Q16—64no—
180D3×SD16—64no—
181C2×Dic12—31no—
182C2×Dic12—31no—
183C2×Dic12—31no—
184C2×Dic12—31no—
185C2×Dic12—61no—
186C2×Dic12—64no—
187C2×Dic12C2×D311yescharacteristic, complemented
188C2×#204—31no—
189C2×#204—31no—
190C2×#204—31no—
191C2×#204—31no—
192C2×#204—61no—
193C2×#204—64no—
194C2×#204C2×D311yescharacteristic
195C2×D3×C8C2×D311yescharacteristic
196C2×D3×C8C2×D311yescharacteristic
197D3×C4⋊C4—31no—
198D3×C4⋊C4—61no—
199#887—31no—
200#887—61no—
201#885—61no—
202#885—61no—
203D3×C22⋊C4—61no—
204D3×C22⋊C4—61no—
205#875—31no—
206#875—31no—
207#875—31no—
208#875—31no—
209#875—61no—
210#875—61no—
211#875—61no—
212#875C2×D311yescharacteristic
213C42×D3—61no—
214C42×D3C2×D311yescharacteristic
215C4×Dic6—31no—
216C4×Dic6—31no—
217C4×Dic6—31no—
218C4×Dic6—31no—
219C4×Dic6—61no—
220C4×Dic6—61no—
221C4×Dic6—61no—
222C4×Dic6—61no—
223C4×Dic6C2×D311yescharacteristic, complemented
224C3×C4⋊C8—21no—
225C3×C4⋊C8—31no—
226C3×C4⋊C8—31no—
227C3×C4⋊C8—31no—
228C3×C4⋊C8C2×D311yescharacteristic, complemented
229C3×C4⋊C8C2×D311yescharacteristic, complemented
230C3×#103—31no—
231C3×#102—31no—
232#835—31no—
233#832—31no—
234#821—31no—
235#821—31no—
236#821—31no—
237#821—31no—
238#821—61no—
239#821C2×D311yescharacteristic
240#816—31no—
241#816—31no—
242#816—31no—
243#816—31no—
244#816—61no—
245#816C2×D311yescharacteristic, complemented
246Dic3⋊C8C2×D311yescharacteristic, complemented
247Dic3⋊C8C2×D311yescharacteristic, complemented
248#810—31no—
249#809—31no—
250C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
251C22×C3⋊D3—21no—
252C22×C3×D3—21no—
253C22×C3×D3C2×D411yescharacteristic
254C2×D32—42no—
255C2×D32—42no—
256C2×D32—42no—
257C2×C32×C4C2×D411yescharacteristic
258C2×C32×C4C2×D411yescharacteristic
259C2×C32×C4C2411yescharacteristic
260C2×C3⋊Dic3—21no—
261C2×C3⋊Dic3—21no—
262C2×C3⋊Dic3—21no—
263C4⋊(C3⋊D3)—21no—
264C4⋊(C3⋊D3)—21no—
265#634—21no—
266#634—21no—
267#634—21no—
268#634C2×D412yes—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3C2×D411yescharacteristic
273C2×C3×Dic3C2×D411yescharacteristic
274C2×C3×Dic3C2×D411yescharacteristic
275C3×D12—21no—
276C3×D12—21no—
277C3×C4×D3—22no—
278C3×C4×D3—22no—
279C3×C4×D3C2×D412yes—
280C3×C4×D3#4112yes—
281C3×Dic6—21no—
282C3×Dic6—21no—
283C3×Dic6—21no—
284C3×Dic6C2×D412yes—
285#627—24no—
286#627—42no—
287#626—42no—
288D3×Dic3—24no—
289D3×Dic3—42no—
290D3×Dic3—42no—
291C32×C8—21no—
292C32×C8—21no—
293C3×C3⋊C8—21no—
294C3×C3⋊C8—21no—
295C22×Q16—91no—
296C22×SD16—91no—
297C2×#124—91no—
298C2×C4×Q8—91no—
299#464—31no—
300#464—91no—
301#464—91no—
302#464—91no—
303#464—91no—
304#464—91no—
305#464—91no—
306#464—91no—
307C2×C4⋊C8—31no—
308C2×#103—91no—
309C2×#102—91no—
310C23×D3—61no—
311C23×D3—61no—
312C2×C3×Q8—31no—
313C2×C3×Q8—31no—
314C2×C3×D4—31no—
315C22×C3×C4—31no—
316C22×C3×C4—31no—
317C22×C3×C4—31no—
318C2×#67—61no—
319C22×Dic3—61no—
320C22×Dic3—61no—
321C22×Dic3—61no—
322D3×Q8—34no—
323D3×Q8—62no—
324D3×Q8—62no—
325D3×Q8—62no—
326D3×D4—62no—
327D3×D4—62no—
328C2×D12—31no—
329C2×D12—31no—
330C2×D12—61no—
331C2×D12—62no—
332C2×D12—62no—
333C2×D12—61no—
334C2×D12C22×D311yescharacteristic
335C2×C4×D3—61no—
336C2×C4×D3—61no—
337C2×C4×D3—61no—
338C2×C4×D3D1211yescharacteristic
339C2×C4×D3D1211yescharacteristic
340C2×C4×D3C22×D311yescharacteristic
341C2×Dic6—31no—
342C2×Dic6—31no—
343C2×Dic6—34no—
344C2×Dic6—31no—
345C2×Dic6—31no—
346C2×Dic6—61no—
347C2×Dic6—61no—
348C2×Dic6—62no—
349C2×Dic6—62no—
350C2×Dic6—62no—
351C2×Dic6—61no—
352C2×Dic6—61no—
353C2×Dic6—61no—
354C2×Dic6—61no—
355C2×Dic6C22×D311yescharacteristic
356C2×Dic6C22×D311yescharacteristic
357C3×Q16—62no—
358C3×SD16—62no—
359C2×C3×C8—21no—
360C2×C3×C8—21no—
361C2×C3×C8—31no—
362C2×C3×C8—31no—
363C2×C3×C8—62no—
364C2×C3×C8—62no—
365C2×C3×C8C22×D311yescharacteristic
366C2×C3×C8C22×D311yescharacteristic
367C2×C3×C8C22×D311yescharacteristic
368C2×C3×C8C22×D311yescharacteristic
369C3×C4⋊C4—31no—
370C3×C4⋊C4—61no—
371C3×C22⋊C4—61no—
372C3×C22⋊C4—61no—
373C3×C42—21no—
374C3×C42—31no—
375C3×C42—31no—
376C3×C42—31no—
377C3×C42—61no—
378C3×C42C22×D311yescharacteristic
379C3×C42C22×D311yescharacteristic
380#217—61no—
381#217—61no—
382#216—62no—
383#216—62no—
384#215—62no—
385#214—62no—
386(C2×D3)⋊C4—21no—
387(C2×D3)⋊C4—21no—
388(C2×D3)⋊C4—61no—
389(C2×D3)⋊C4—61no—
390(C2×D3)⋊C4—61no—
391(C2×D3)⋊C4—61no—
392(C2×D3)⋊C4—61no—
393(C2×D3)⋊C4—61no—
394(C2×D3)⋊C4—61no—
395(C2×D3)⋊C4—61no—
396(C2×D3)⋊C4—61no—
397(C2×D3)⋊C4—61no—
398(C2×D3)⋊C4—121no—
399(C2×D3)⋊C4—121no—
400C4⋊Dic3—31no—
401C4⋊Dic3—31no—
402C4⋊Dic3—61no—
403C4⋊Dic3—61no—
404C4⋊Dic3—61no—
405C4⋊Dic3C22×D311yescharacteristic
406Dic3⋊C4—21no—
407Dic3⋊C4—61no—
408Dic3⋊C4—61no—
409Dic3⋊C4—61no—
410Dic3⋊C4—61no—
411Dic3⋊C4—61no—
412Dic3⋊C4—61no—
413Dic3⋊C4—121no—
414C4×Dic3—21no—
415C4×Dic3—61no—
416C4×Dic3—61no—
417C4×Dic3—61no—
418C4×Dic3—61no—
419C4×Dic3—61no—
420C4×Dic3—61no—
421C4×Dic3—121no—
422C4×Dic3D1211yescharacteristic
423C4×Dic3D1211yescharacteristic
424C4×Dic3C22×D311yescharacteristic
425C2×C3⋊C8C22×D311yescharacteristic
426C2×C3⋊C8C22×D311yescharacteristic
427Dic12—22no—
428Dic12—62no—
429Dic12—62no—
430Dic12—62no—
431Dic12—62no—
432Dic12—122no—
433#204—22no—
434#204—62no—
435#204—62no—
436#204—62no—
437#204—62no—
438#204—122no—
439D3×C8—22no—
440D3×C8—22no—
441C22×C32C22×D411yescharacteristic
442C2×C3⋊D3—41no—
443C2×C3⋊D3—41no—
444C2×C3⋊D3—41no—
445C2×C3×D3—41no—
446C2×C3×D3—41no—
447C2×C3×D3—41no—
448C2×C3×D3#12112yes—
449C2×C3×D3#13512yes—
450C2×C3×D3#13712yes—
451D32—84no—
452C32×C4—21no—
453C32×C4—21no—
454C32×C4C22×D411yescharacteristic
455C32×C4C2×#4111yescharacteristic
456C3⋊Dic3—22no—
457C3⋊Dic3—41no—
458C3⋊Dic3—41no—
459C3×Dic3—22no—
460C3×Dic3—21no—
461C3×Dic3—21no—
462C3×Dic3—41no—
463C3×Dic3—41no—
464C3×Dic3#12112yes—
465C22×Q8—91no—
466C22×Q8—91no—
467C22×D4—91no—
468C2×Q16—31no—
469C2×Q16—91no—
470C2×Q16—91no—
471C2×Q16—91no—
472C2×Q16—184no—
473C2×SD16—31no—
474C2×SD16—91no—
475C2×SD16—91no—
476C2×SD16—91no—
477C2×SD16—184no—
478C22×C8—31no—
479C22×C8—31no—
480#124—31no—
481#124—91no—
482#124—91no—
483#124—91no—
484#124—181no—
485#124—181no—
486C4×Q8—31no—
487C4×Q8—91no—
488C4×Q8—91no—
489C4×Q8—91no—
490C4×Q8—181no—
491C4×Q8—181no—
492C2×C4⋊C4—91no—
493C2×C4⋊C4—181no—
494C2×C22⋊C4—181no—
495C2×C22⋊C4—181no—
496C2×C42—31no—
497C2×C42—181no—
498C4⋊C8—31no—
499C4⋊C8—31no—
500C4⋊C8—31no—
501C4⋊C8D3211yescharacteristic, complemented
502#103—31no—
503#103—91no—
504#103—91no—
505#103—91no—
506#102—31no—
507#102—91no—
508#102—91no—
509#102—91no—
510C23×C3—31no—
511C23×C3—61no—
512C22×D3—21no—
513C22×D3—61no—
514C22×D3—61no—
515C22×D3—121no—
516C22×D3—122no—
517C22×D3—122no—
518C22×D3—122no—
519C22×D3—122no—
520C22×D3—122no—
521C22×D3—122no—
522C22×D3C2×D1211yescharacteristic
523C3×Q8—32no—
524C3×Q8—61no—
525C3×Q8—61no—
526C3×Q8—61no—
527C3×D4—61no—
528C3×D4—61no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—31no—
533C2×C3×C4—32no—
534C2×C3×C4—32no—
535C2×C3×C4—31no—
536C2×C3×C4—31no—
537C2×C3×C4—62no—
538C2×C3×C4—62no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—61no—
542C2×C3×C4C2×D1211yescharacteristic
543C2×C3×C4C2×D1211yescharacteristic
544C2×C3×C4D3×D411yescharacteristic
545C2×C3×C4D3×D411yescharacteristic
546C2×C3×C4C23×D311yescharacteristic
547C2×C3×C4C23×D311yescharacteristic
548#67—122no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—21no—
552C2×Dic3—64no—
553C2×Dic3—61no—
554C2×Dic3—61no—
555C2×Dic3—61no—
556C2×Dic3—61no—
557C2×Dic3—61no—
558C2×Dic3—61no—
559C2×Dic3—121no—
560C2×Dic3—121no—
561C2×Dic3—121no—
562C2×Dic3—122no—
563C2×Dic3—122no—
564C2×Dic3C2×D1211yescharacteristic
565C2×Dic3C2×D1211yescharacteristic
566C2×Dic3C2×D1211yescharacteristic
567D12—21no—
568D12—21no—
569D12—61no—
570D12—61no—
571D12—61no—
572D12—61no—
573D12—121no—
574D12—121no—
575D12—122no—
576C4×D3—22no—
577C4×D3—22no—
578C4×D3—64no—
579C4×D3—122no—
580C4×D3—122no—
581C4×D3D3×D412yes—
582C4×D3#23912yes—
583Dic6—21no—
584Dic6—21no—
585Dic6—21no—
586Dic6—32no—
587Dic6—32no—
588Dic6—62no—
589Dic6—64no—
590Dic6—61no—
591Dic6—61no—
592Dic6—64no—
593Dic6—61no—
594Dic6—61no—
595Dic6—61no—
596Dic6—61no—
597Dic6—121no—
598Dic6—121no—
599Dic6—121no—
600Dic6—122no—
601Dic6—122no—
602Dic6D3×D412yes—
603C3×C8—21no—
604C3×C8—21no—
605C3×C8—21no—
606C3×C8—21no—
607C3×C8—41no—
608C3×C8—41no—
609C3×C8—61no—
610C3×C8—61no—
611C3⋊C8—21no—
612C3⋊C8—21no—
613C2×C32C2×#12111yescharacteristic
614C2×C32C2×#13511yescharacteristic
615C2×C32C2×#13711yescharacteristic
616C3⋊D3—81no—
617C3×D3—81no—
618C3×D3#46414yescomplemented
619C24—181no—
620C2×Q8—31no—
621C2×Q8—31no—
622C2×Q8—94no—
623C2×Q8—91no—
624C2×Q8—91no—
625C2×Q8—181no—
626C2×Q8—181no—
627C2×Q8—182no—
628C2×Q8—182no—
629C2×Q8—182no—
630C2×D4—31no—
631C2×D4—91no—
632C2×D4—182no—
633C2×D4—182no—
634C2×D4—181no—
635C22×C4—31no—
636C22×C4—31no—
637C22×C4—31no—
638C22×C4—181no—
639C22×C4—181no—
640C22×C4—181no—
641Q16—62no—
642Q16—182no—
643Q16—182no—
644Q16—182no—
645SD16—62no—
646SD16—182no—
647SD16—182no—
648SD16—182no—
649C2×C8—31no—
650C2×C8—31no—
651C2×C8—62no—
652C2×C8—62no—
653C2×C8C2×D3211yescharacteristic
654C2×C8C2×D3211yescharacteristic
655C4⋊C4—31no—
656C4⋊C4—61no—
657C4⋊C4—91no—
658C4⋊C4—181no—
659C4⋊C4—181no—
660C4⋊C4—181no—
661C4⋊C4—181no—
662C22⋊C4—61no—
663C22⋊C4—61no—
664C22⋊C4—181no—
665C22⋊C4—181no—
666C22⋊C4—181no—
667C22⋊C4—181no—
668C22⋊C4—181no—
669C22⋊C4—181no—
670C42—31no—
671C42—31no—
672C42—31no—
673C42—61no—
674C42—181no—
675C42—181no—
676C42—181no—
677C42C2×D3211yescharacteristic
678C22×C3—21no—
679C22×C3—32no—
680C22×C3—32no—
681C22×C3—32no—
682C22×C3—121no—
683C22×C3—121no—
684C22×C3—121no—
685C22×C3C22×D1211yescharacteristic
686C22×C3C2×D3×D411yescharacteristic
687C2×D3—41no—
688C2×D3—41no—
689C2×D3—41no—
690C2×D3—121no—
691C2×D3—121no—
692C2×D3—121no—
693C2×D3—121no—
694C2×D3—121no—
695C2×D3—121no—
696C2×D3—241no—
697C2×D3—241no—
698C2×D3—241no—
699C2×D3—244no—
700C2×D3—244no—
701C2×D3#89512yes—
702C2×D3#90412yes—
703C2×D3#90912yes—
704C3×C4—21no—
705C3×C4—21no—
706C3×C4—21no—
707C3×C4—21no—
708C3×C4—21no—
709C3×C4—21no—
710C3×C4—32no—
711C3×C4—41no—
712C3×C4—41no—
713C3×C4—62no—
714C3×C4—61no—
715C3×C4—61no—
716C3×C4—121no—
717C3×C4—121no—
718C3×C4C2×D3×D411yescharacteristic
719C3×C4C2×D3×D411yescharacteristic
720C3×C4C2×#23911yescharacteristic
721C3×C4D3×#4111yescharacteristic
722Dic3—21no—
723Dic3—21no—
724Dic3—22no—
725Dic3—41no—
726Dic3—41no—
727Dic3—62no—
728Dic3—62no—
729Dic3—122no—
730Dic3—121no—
731Dic3—121no—
732Dic3—121no—
733Dic3—121no—
734Dic3—241no—
735Dic3—241no—
736Dic3#89512yes—
737C32C2×#46411yescharacteristic, complemented, Sylow
738C23—31no—
739C23—61no—
740C23—181no—
741C23—362no—
742C23—362no—
743C23—362no—
744Q8—32no—
745Q8—61no—
746Q8—61no—
747Q8—61no—
748Q8—92no—
749Q8—184no—
750Q8—181no—
751Q8—181no—
752Q8—181no—
753Q8—362no—
754D4—61no—
755D4—61no—
756D4—181no—
757D4—181no—
758D4—362no—
759C2×C4—31no—
760C2×C4—32no—
761C2×C4—32no—
762C2×C4—31no—
763C2×C4—31no—
764C2×C4—62no—
765C2×C4—62no—
766C2×C4—61no—
767C2×C4—61no—
768C2×C4—61no—
769C2×C4—184no—
770C2×C4—181no—
771C2×C4—181no—
772C2×C4—181no—
773C2×C4—362no—
774C2×C4—362no—
775C2×C4D3×D1211yescharacteristic
776C2×C4D3×D1211yescharacteristic
777C2×C4C22×D3211yescharacteristic
778C8—21no—
779C8—21no—
780C8—61no—
781C8—61no—
782C2×C3—21no—
783C2×C3—21no—
784C2×C3—21no—
785C2×C3—34no—
786C2×C3—241no—
787C2×C3C2×#89511yescharacteristic
788C2×C3D3×#12111yescharacteristic
789C2×C3C2×#90411yescharacteristic
790C2×C3C2×#90911yescharacteristic
791C2×C3D3×#13511yescharacteristic
792C2×C3D3×#13711yescharacteristic
793D3—81no—
794D3—241no—
795D3—241no—
796D3—481no—
797D3#484514yesdirect product factor
798C22—32no—
799C22—32no—
800C22—32no—
801C22—121no—
802C22—121no—
803C22—121no—
804C22—361no—
805C22—361no—
806C22—361no—
807C22—724no—
808C22C2×D3×D1211yescharacteristic
809C4—21no—
810C4—21no—
811C4—32no—
812C4—62no—
813C4—61no—
814C4—61no—
815C4—121no—
816C4—121no—
817C4—182no—
818C4—361no—
819C4—361no—
820C4D32×D411yescharacteristic
821C4D3×#23911yescharacteristic
822C3—21no—
823C3C2×#484511yescharacteristic, complemented
824C3D3×#46411yescharacteristic, complemented
825C2—34no—
826C2—241no—
827C2—721no—
828C2D3×#89511yescharacteristic
829C2D3×#90411yescharacteristic
830C2D3×#90911yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radicalC2×D3×D12C22
hypercenterC4⋊C8D32
hypocenterC32C2×#464
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×D3×Dic12C2semidirect
4. C4×D3×Dic6C2semidirect
5. #10592544C2semidirect
6. C3×#4845C2semidirect
7. C3×D3×C4⋊C8C2semidirect
9. #10590861C2semidirect
10. #10590859C2semidirect
11. #10590813C2semidirect
12. #10590801C2semidirect
13. D3×#816C2semidirect
14. #10590378C2semidirect
15. #10590368C2semidirect
21. C2×#3746C22semidirect
24. C4×#634C22semidirect
25. C2×C3×Dic12C22semidirect
31. C3×C4×Dic6C22semidirect
42. #63844C22semidirect
43. Dic3×Dic6C22semidirect
45. C2×#3719C22semidirect
46. C2×#3719C22semidirect
51. C32×C4⋊C8C22semidirect
53. #63643C22semidirect
55. C3×#816C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. C3×Dic3⋊C8C22semidirect
58. C3×C4⋊(C3⋊C8)C22semidirect
59. #63567C22semidirect
60. #63566C22semidirect
88. #4845D3direct (N × H)
89. D3×C4⋊C8D3semidirect
187. C2×Dic12C2×D3semidirect
223. C4×Dic6C2×D3semidirect
228. C3×C4⋊C8C2×D3semidirect
229. C3×C4⋊C8C2×D3semidirect
245. #816C2×D3semidirect
246. Dic3⋊C8C2×D3semidirect
247. Dic3⋊C8C2×D3semidirect
250. C4⋊(C3⋊C8)C2×D3semidirect
501. C4⋊C8D32semidirect
618. C3×D3#464semidirect
737. C32C2×#464semidirect
797. D3#4845direct (N × H)
823. C3C2×#4845semidirect
824. C3D3×#464semidirect

Maximal subgroups

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

subgroupindex
C2×D3×Dic122
C2×D3×#2042
D3×#8752
C4×D3×Dic62
#105925442
C3×#48452
C3×D3×C4⋊C82
D3×#8212
#105908612
#105908592
#105908132
#105908012
D3×#8162
#105903782
#105903682
D3×#4643
C2×#48453