Finite Group Databasebeta

← D3×#4772 #11857785

Subgroups — D3×#4772 #11857785

Order 1152.

1663 conjugacy classes of subgroups.

The subgroup lattice has 946 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#237C211yesmaximal, characteristic
2C2×D32×C8C211yesmaximal, characteristic, complemented
3D3×#892C211yesmaximal, characteristic, complemented
4#10592471C211yesmaximal, characteristic, complemented
5C3×#4772C211yesmaximal, characteristic, complemented
6C3×D3×#102C211yesmaximal, characteristic, complemented
7#10591424C211yesmaximal, characteristic, complemented
8#10591420C211yesmaximal, characteristic, complemented
9D3×#832C211yesmaximal, characteristic, complemented
10#10590956C211yesmaximal, characteristic, complemented
11#10590954C211yesmaximal, characteristic, complemented
12D3×#816C211yesmaximal, characteristic, complemented
13#10590611C211yesmaximal, characteristic, complemented
14#10590608C211yesmaximal, characteristic, complemented
15D3×#810C211yesmaximal, characteristic, complemented
16D3×#416—31nomaximal
17C2×#4772—31nomaximal
18C2×#3830C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C3×D3×D4C2211yescharacteristic
21C2×D3×#67—21no—
22C2×#3805—21no—
23C2×#3804—21no—
24C22×D3×Dic3—21no—
25D3×#237—24no—
26D3×#237C418yescomplemented
27C2×C4×D32C2211yescharacteristic
28C2×#3796C2211yescharacteristic
29C2×#3795C2211yescharacteristic
30C2×D3×Dic6C2211yescharacteristic
31C2×C8×C3⋊D3C2211yescharacteristic, complemented
32#64101C2211yescharacteristic, complemented
33C2×C3×D3×C8C2211yescharacteristic
34C2×C3×D3×C8C2211yescharacteristic, complemented
35C3×#892C2211yescharacteristic, complemented
36C3×D3×C4⋊C4C2211yescharacteristic
37D3×(C2×D3)⋊C4—21no—
38D3×C4⋊Dic3C2211yescharacteristic
39#63878—21no—
40C4×D3×Dic3—21no—
41#63849C2211yescharacteristic, complemented
42#63841C2211yescharacteristic, complemented
43#63836—21no—
44C2×#3710C2211yescharacteristic, complemented
45C2×D3×C3⋊C8C2211yescharacteristic
46C2×D3×C3⋊C8C2211yescharacteristic, complemented
47D32×C8—24no—
48C32×#102C2211yescharacteristic, complemented
49#63659C2211yescharacteristic, complemented
50#63643C2211yescharacteristic, complemented
51#63637C2211yescharacteristic, complemented
52C3×#832C2211yescharacteristic, complemented
53C3×#832C2211yescharacteristic, complemented
54C3×#821C2211yescharacteristic, complemented
55C3×#816C2211yescharacteristic, complemented
56C3×#810C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic, complemented
58#63567C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63566C2211yescharacteristic, complemented
61#63565C2211yescharacteristic, complemented
62#63563C2211yescharacteristic, complemented
63#63562C2211yescharacteristic, complemented
64C2×D3×#41—31no—
65C22×#237—31no—
66C22×D3×C8—31no—
67C22×D3×C8—31no—
68D3×#117—31no—
69C2×#892—31no—
70C3×#416—31no—
71C2×C3×#102—31no—
72#5233—31no—
73C2×#832—31no—
74#5113—31no—
75C2×#816—31no—
76#5002—31no—
77C2×#810—31no—
78#4804—31no—
79#4804—31no—
80D3×#103—31no—
81D3×#103—31no—
82#4772—31no—
83#4772—31no—
84#4772—31no—
85#4772—31no—
86#4772—31no—
87#4772—31no—
88#4772—31no—
89#4772—31no—
90#4772—31no—
91#4772—61no—
92#4772D311yescharacteristic, direct product factor
93D3×#102—31no—
94D3×#102D311yescharacteristic, complemented
95C23×C3×D3—21no—
96C22×D32D411yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C2×#638—21no—
99C22×C3⋊Dic3—21no—
100#3830—22no—
101#3830C2×C414yescomplemented
102C2×C4×C3⋊D3C2311yescharacteristic
103C2×#634C2311yescharacteristic
104C2×C3×#67—21no—
105C2×C3×#67—21no—
106C22×C3×Dic3—21no—
107C3×#237—22no—
108C3×#237C2×C414yescomplemented
109C3×D3×D4—22no—
110C3×D3×D4C2×C414yes—
111C2×C3×D12C2311yescharacteristic
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3C2311yescharacteristic
114C2×C3×C4×D3C2311yescharacteristic
115C2×C3×Dic6C2311yescharacteristic
116D3×#67—28no—
117C2×#627—21no—
118C2×#626—21no—
119C2×#625—21no—
120C2×#624D411yescharacteristic
121#3805—28no—
122#3804—28no—
123C2×D3×Dic3—21no—
124C2×D3×Dic3—21no—
125C2×D3×Dic3—21no—
126C2×D3×Dic3—28no—
127C2×D3×Dic3—21no—
128C2×D3×Dic3D411yescharacteristic
129C2×D3×Dic3D411yescharacteristic
130C4×D32C2×C414yes—
131C4×D32D414yes—
132#3796—22no—
133#3796C2×C414yescomplemented
134#3795—22no—
135#3795C2×C414yescomplemented
136D3×Dic6—22no—
137D3×Dic6C2×C414yes—
138C2×C32×C8C2311yescharacteristic
139C32×C4⋊C4C2311yescharacteristic
140#3752—21no—
141C4⋊(C3⋊Dic3)C2311yescharacteristic
142C4×C3⋊Dic3—21no—
143C2×C3⋊(C3⋊C8)C2311yescharacteristic
144C8×C3⋊D3—22no—
145C3×(C2×D3)⋊C4—21no—
146C3×C4⋊Dic3C2311yescharacteristic
147C3×C4⋊Dic3C2311yescharacteristic
148C3×Dic3⋊C4—21no—
149C3×C4×Dic3—21no—
150C2×C3×C3⋊C8C2311yescharacteristic
151C2×C3×C3⋊C8C2311yescharacteristic
152C3×D3×C8—22no—
153C3×D3×C8—22no—
154Dic3⋊Dic3—21no—
155#3722—21no—
156(C2×D3)⋊Dic3—21no—
157Dic32—21no—
158Dic32—21no—
159#3710—22no—
160D3×C3⋊C8—22no—
161D3×C3⋊C8—22no—
162C2×#416—91noSylow
163C2×C3×#41—31no—
164C22×C3×D4—31no—
165C22×#67—61no—
166C23×Dic3—61no—
167D3×#41—38no—
168D3×#41—64no—
169C2×#239—31no—
170C2×D3×Q8—31no—
171C2×#237—31no—
172C2×#237—31no—
173C2×#237—38no—
174C2×#237—31no—
175C2×#237—31no—
176C2×#237—61no—
177C2×#237—64no—
178C2×#237—61no—
179C2×#237—61no—
180C2×#237—61no—
181C2×#237C2×D311yescharacteristic
182C2×D3×D4—61no—
183C2×D3×D4C2×D311yescharacteristic
184C2×#235—31no—
185C2×#235—61no—
186C22×C4×D3—31no—
187C22×C4×D3—31no—
188C22×C4×D3—61no—
189C22×Dic6—31no—
190C22×C3×C8—31no—
191C22×C3×C8—31no—
192C3×#117—31no—
193C2×C3×C4⋊C4—31no—
194C2×(C2×D3)⋊C4—61no—
195#926—31no—
196C2×C4⋊Dic3—31no—
197C2×C4×Dic3—61no—
198C22×C3⋊C8—31no—
199C22×C3⋊C8—31no—
200C2×D3×C8—31no—
201C2×D3×C8—31no—
202C2×D3×C8—31no—
203C2×D3×C8—31no—
204C2×D3×C8—31no—
205C2×D3×C8—31no—
206C2×D3×C8—61no—
207C2×D3×C8—64no—
208C2×D3×C8—64no—
209C2×D3×C8C2×D311yescharacteristic
210C2×D3×C8C2×D311yescharacteristic, complemented
211#892—31no—
212#892—31no—
213#892—31no—
214#892—31no—
215#892—31no—
216#892—61no—
217#892—61no—
218#892—61no—
219#892C2×D311yescharacteristic, complemented
220D3×C4⋊C4—31no—
221D3×C4⋊C4C2×D311yescharacteristic
222D3×C22⋊C4—61no—
223#877—61no—
224#872—61no—
225C42×D3—61no—
226C3×#103—31no—
227C3×#103—31no—
228C3×#102—21no—
229C3×#102—31no—
230C3×#102—31no—
231C3×#102—31no—
232C3×#102—31no—
233C3×#102C2×D311yescharacteristic, complemented
234C3×#102C2×D311yescharacteristic, complemented
235#835—31no—
236#835—31no—
237#832—31no—
238#832—31no—
239#832—31no—
240#832—31no—
241#832—61no—
242#832C2×D311yescharacteristic, complemented
243#832C2×D311yescharacteristic, complemented
244#821—31no—
245#821C2×D311yescharacteristic, complemented
246#816—31no—
247#816—31no—
248#816—31no—
249#816—31no—
250#816—31no—
251#816—61no—
252#816C2×D311yescharacteristic, complemented
253#810—31no—
254#810—31no—
255#810—31no—
256#810—31no—
257#810—31no—
258#810—61no—
259#810C2×D311yescharacteristic, complemented
260#809—31no—
261#809C2×D311yescharacteristic, complemented
262C23×C32—21no—
263C22×C3⋊D3C2×D411yescharacteristic
264C22×C3×D3—21no—
265C22×C3×D3—24no—
266C22×C3×D3—42no—
267C22×C3×D3—42no—
268C22×C3×D3C2×D411yescharacteristic
269C22×C3×D3C2×D411yescharacteristic
270C2×D32—22no—
271C2×D32—22no—
272C2×D32C22⋊C414yes—
273C32×D4—21no—
274C32×D4C22×C412yes—
275C2×C32×C4—21no—
276C2×C32×C4C2411yescharacteristic
277#638—24no—
278C2×C3⋊Dic3—21no—
279C2×C3⋊Dic3—24no—
280C2×C3⋊Dic3—21no—
281C2×C3⋊Dic3C2×D411yescharacteristic
282C4×C3⋊D3C22×C412yes—
283C4×C3⋊D3C2×D412yes—
284#634—21no—
285#634C22×C412yes—
286C3×#67—24no—
287C3×#67—24no—
288C2×C3×Dic3—21no—
289C2×C3×Dic3—24no—
290C2×C3×Dic3—21no—
291C2×C3×Dic3—21no—
292C2×C3×Dic3C2×D411yescharacteristic
293C2×C3×Dic3C2×D411yescharacteristic
294C3×D12—21no—
295C3×D12C22×C412yes—
296C3×C4×D3—42no—
297C3×C4×D3C22×C412yes—
298C3×C4×D3C22×C412yes—
299C3×C4×D3C2×D412yes—
300C3×C4×D3C2×D412yes—
301C3×Dic6—21no—
302C3×Dic6C22×C412yes—
303#627—24no—
304#626—24no—
305#625—24no—
306#624C22⋊C414yes—
307D3×Dic3—24no—
308D3×Dic3—24no—
309D3×Dic3—24no—
310D3×Dic3—42no—
311D3×Dic3C22⋊C414yes—
312D3×Dic3C22⋊C414yes—
313C32×C8—21no—
314C3⋊(C3⋊C8)—21no—
315C3×C3⋊C8—21no—
316C3×C3⋊C8—21no—
317C22×#41—91no—
318C23×C8—91no—
319C2×#117—91no—
320#416—31no—
321#416—91no—
322#416—91no—
323#416—91no—
324#416—91no—
325#416—91no—
326#416—91no—
327#416—91no—
328C2×#103—91no—
329C2×#103—91no—
330C2×#102—31no—
331C2×#102—91no—
332C24×C3—61no—
333C23×D3—21no—
334C23×D3—31no—
335C23×D3—31no—
336C3×#41—34no—
337C3×#41—62no—
338C2×C3×Q8—31no—
339C2×C3×D4—21no—
340C2×C3×D4—34no—
341C2×C3×D4—31no—
342C2×C3×D4—62no—
343C2×C3×D4—61no—
344C2×C3×D4—61no—
345C2×C3×D4C22×D311yescharacteristic
346C2×C3×D4C22×D311yescharacteristic
347C22×C3×C4—31no—
348C22×C3×C4—31no—
349C22×C3×C4—61no—
350C22×C3×C4—61no—
351C2×#67—21no—
352C2×#67—21no—
353C2×#67—61no—
354C2×#67—68no—
355C2×#67—61no—
356C2×#67—61no—
357C2×#67—61no—
358C2×#67—61no—
359C2×#67—121no—
360C22×Dic3—21no—
361C22×Dic3—31no—
362C22×Dic3—31no—
363C22×Dic3—61no—
364C22×Dic3—68no—
365C22×Dic3—61no—
366C22×Dic3—61no—
367C22×Dic3—61no—
368C22×Dic3—61no—
369C22×Dic3—61no—
370C22×Dic3—121no—
371#239—34no—
372#239—62no—
373D3×Q8—34no—
374D3×Q8—62no—
375#237—22no—
376#237—34no—
377#237—34no—
378#237—34no—
379#237—34no—
380#237—64no—
381#237—62no—
382#237—68no—
383#237—68no—
384#237—62no—
385#237—62no—
386#237—68no—
387#237—62no—
388#237—122no—
389#237C4×D314yescomplemented
390D3×D4—22no—
391D3×D4—68no—
392D3×D4C4×D314yes—
393#235—34no—
394#235—68no—
395#235—62no—
396C2×D12—61no—
397C2×D12C22×D311yescharacteristic
398C2×C4×D3—21no—
399C2×C4×D3—31no—
400C2×C4×D3—31no—
401C2×C4×D3—31no—
402C2×C4×D3—31no—
403C2×C4×D3—31no—
404C2×C4×D3—31no—
405C2×C4×D3—34no—
406C2×C4×D3—34no—
407C2×C4×D3—34no—
408C2×C4×D3—34no—
409C2×C4×D3—61no—
410C2×C4×D3—68no—
411C2×C4×D3—61no—
412C2×C4×D3—61no—
413C2×C4×D3—61no—
414C2×C4×D3—61no—
415C2×C4×D3C22×D311yescharacteristic
416C2×C4×D3C22×D311yescharacteristic
417C2×Dic6—31no—
418C2×Dic6—31no—
419C2×Dic6—34no—
420C2×Dic6—61no—
421C2×Dic6—62no—
422C2×Dic6—61no—
423C2×Dic6—61no—
424C2×Dic6C22×D311yescharacteristic
425C2×C3×C8—21no—
426C2×C3×C8—31no—
427C2×C3×C8—31no—
428C2×C3×C8—62no—
429C2×C3×C8—62no—
430C2×C3×C8C22×D311yescharacteristic
431C2×C3×C8C22×D311yescharacteristic
432C3×C4⋊C4—21no—
433C3×C4⋊C4—31no—
434C3×C4⋊C4—31no—
435C3×C4⋊C4—61no—
436C3×C4⋊C4C22×D311yescharacteristic
437C3×C4⋊C4C22×D311yescharacteristic
438C3×C22⋊C4—61no—
439C3×C42—61no—
440#217—61no—
441(C2×D3)⋊C4—21no—
442(C2×D3)⋊C4—61no—
443(C2×D3)⋊C4—61no—
444(C2×D3)⋊C4—61no—
445(C2×D3)⋊C4—61no—
446(C2×D3)⋊C4—61no—
447(C2×D3)⋊C4—121no—
448C4⋊Dic3—31no—
449C4⋊Dic3—31no—
450C4⋊Dic3—61no—
451C4⋊Dic3—61no—
452C4⋊Dic3C22×D311yescharacteristic
453C4⋊Dic3C22×D311yescharacteristic
454Dic3⋊C4—21no—
455Dic3⋊C4—61no—
456C4×Dic3—21no—
457C4×Dic3—61no—
458C4×Dic3—61no—
459C4×Dic3—61no—
460C4×Dic3—61no—
461C4×Dic3—61no—
462C4×Dic3—61no—
463C4×Dic3—121no—
464C2×C3⋊C8—31no—
465C2×C3⋊C8—31no—
466C2×C3⋊C8—61no—
467C2×C3⋊C8—62no—
468C2×C3⋊C8—62no—
469C2×C3⋊C8C22×D311yescharacteristic
470C2×C3⋊C8C22×D311yescharacteristic
471D3×C8—22no—
472D3×C8—22no—
473D3×C8—62no—
474D3×C8—62no—
475D3×C8—62no—
476D3×C8—62no—
477D3×C8—62no—
478D3×C8—62no—
479D3×C8—122no—
480C22×C32—22no—
481C22×C32—41no—
482C22×C32—41no—
483C22×C32C22×D411yescharacteristic
484C2×C3⋊D3—21no—
485C2×C3⋊D3—21no—
486C2×C3⋊D3C2×C22⋊C412yes—
487C2×C3×D3—21no—
488C2×C3×D3—21no—
489C2×C3×D3—22no—
490C2×C3×D3—41no—
491C2×C3×D3—41no—
492C2×C3×D3—48no—
493C2×C3×D3C2×C22⋊C412yes—
494C2×C3×D3C2×C22⋊C412yes—
495C2×C3×D3#13512yes—
496C2×C3×D3#13512yes—
497D32—28no—
498C32×C4—41no—
499C32×C4C23×C411yescharacteristic
500C32×C4C22×D411yescharacteristic
501C3⋊Dic3—22no—
502C3⋊Dic3—41no—
503C3⋊Dic3C2×C22⋊C412yes—
504C3×Dic3—22no—
505C3×Dic3—41no—
506C3×Dic3—41no—
507C3×Dic3C2×C22⋊C412yes—
508C3×Dic3C2×C22⋊C412yes—
509C2×#41—31no—
510C2×#41—91no—
511C2×#41—91no—
512C2×#41—98no—
513C2×#41—91no—
514C2×#41—181no—
515C2×#41—181no—
516C2×#41—184no—
517C22×Q8—91no—
518C22×D4—31no—
519C22×D4—181no—
520C23×C4—91no—
521C23×C4—181no—
522C22×C8—31no—
523C22×C8—31no—
524C22×C8—91no—
525C22×C8—91no—
526C22×C8—91no—
527C22×C8—91no—
528C22×C8—184no—
529#117—31no—
530#117—91no—
531#117—91no—
532#117—91no—
533#117—181no—
534#117—181no—
535C2×C4⋊C4—31no—
536C2×C4⋊C4—91no—
537C2×C22⋊C4—181no—
538C2×C42—181no—
539#103—31no—
540#103—31no—
541#103—91no—
542#103—91no—
543#103—91no—
544#103—91no—
545#103—91no—
546#103—91no—
547#102—31no—
548#102—31no—
549#102—31no—
550#102—31no—
551#102—91no—
552#102—91no—
553#102—91no—
554#102D3211yescharacteristic, complemented
555C23×C3—21no—
556C23×C3—21no—
557C23×C3—31no—
558C23×C3—31no—
559C23×C3—41no—
560C23×C3—64no—
561C23×C3—61no—
562C23×C3—122no—
563C23×C3—122no—
564C22×D3—21no—
565C22×D3—24no—
566C22×D3—31no—
567C22×D3—31no—
568C22×D3—34no—
569C22×D3—34no—
570C22×D3—42no—
571C22×D3—42no—
572C22×D3—61no—
573C22×D3—62no—
574C22×D3—62no—
575C22×D3—62no—
576C22×D3—62no—
577C22×D3D3×D411yescharacteristic
578C22×D3D3×D411yescharacteristic
579C3×Q8—32no—
580C3×Q8—61no—
581C3×D4—21no—
582C3×D4—21no—
583C3×D4—22no—
584C3×D4—32no—
585C3×D4—41no—
586C3×D4—64no—
587C3×D4—64no—
588C3×D4—61no—
589C3×D4C2×C4×D312yes—
590C3×D4C2×C4×D312yes—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—31no—
595C2×C3×C4—31no—
596C2×C3×C4—32no—
597C2×C3×C4—32no—
598C2×C3×C4—32no—
599C2×C3×C4—32no—
600C2×C3×C4—41no—
601C2×C3×C4—64no—
602C2×C3×C4—61no—
603C2×C3×C4—61no—
604C2×C3×C4—61no—
605C2×C3×C4—122no—
606C2×C3×C4C23×D311yescharacteristic
607C2×C3×C4C23×D311yescharacteristic
608#67—24no—
609#67—24no—
610#67—64no—
611#67—64no—
612#67—64no—
613#67—64no—
614#67—64no—
615#67—124no—
616C2×Dic3—21no—
617C2×Dic3—24no—
618C2×Dic3—21no—
619C2×Dic3—21no—
620C2×Dic3—31no—
621C2×Dic3—31no—
622C2×Dic3—34no—
623C2×Dic3—34no—
624C2×Dic3—61no—
625C2×Dic3—64no—
626C2×Dic3—64no—
627C2×Dic3—64no—
628C2×Dic3—64no—
629C2×Dic3—61no—
630C2×Dic3—61no—
631C2×Dic3—64no—
632C2×Dic3—61no—
633C2×Dic3—61no—
634C2×Dic3—124no—
635C2×Dic3—121no—
636C2×Dic3—121no—
637C2×Dic3—122no—
638C2×Dic3D3×D411yescharacteristic
639C2×Dic3D3×D411yescharacteristic
640D12—21no—
641D12—64no—
642D12C2×C4×D312yes—
643C4×D3—34no—
644C4×D3—34no—
645C4×D3—32no—
646C4×D3—32no—
647C4×D3—32no—
648C4×D3—32no—
649C4×D3—34no—
650C4×D3—34no—
651C4×D3—42no—
652C4×D3—62no—
653C4×D3—62no—
654C4×D3—64no—
655C4×D3—64no—
656C4×D3—64no—
657C4×D3—122no—
658C4×D3C2×C4×D312yes—
659C4×D3C2×C4×D312yes—
660C4×D3D3×D412yes—
661C4×D3D3×D412yes—
662Dic6—21no—
663Dic6—32no—
664Dic6—32no—
665Dic6—62no—
666Dic6—64no—
667Dic6—61no—
668Dic6—61no—
669Dic6—64no—
670Dic6—121no—
671Dic6C2×C4×D312yes—
672C3×C8—21no—
673C3×C8—21no—
674C3×C8—41no—
675C3×C8—61no—
676C3×C8—61no—
677C3⋊C8—21no—
678C3⋊C8—21no—
679C3⋊C8—61no—
680C3⋊C8—61no—
681C3⋊C8—121no—
682C2×C32—42no—
683C2×C32C22×C22⋊C411yescharacteristic
684C2×C32C2×#13511yescharacteristic
685C2×C32C2×#13511yescharacteristic
686C3⋊D3—22no—
687C3×D3—22no—
688C3×D3—42no—
689C3×D3#41614yescomplemented
690C24—61no—
691C24—91no—
692#41—34no—
693#41—62no—
694#41—94no—
695#41—94no—
696#41—94no—
697#41—182no—
698#41—188no—
699#41—182no—
700#41—188no—
701#41—182no—
702C2×Q8—31no—
703C2×Q8—94no—
704C2×Q8—91no—
705C2×Q8—181no—
706C2×Q8—182no—
707C2×D4—34no—
708C2×D4—31no—
709C2×D4—62no—
710C2×D4—61no—
711C2×D4—61no—
712C2×D4—181no—
713C2×D4—188no—
714C2×D4—181no—
715C2×D4—181no—
716C2×D4C2×D3211yescharacteristic
717C22×C4—31no—
718C22×C4—31no—
719C22×C4—61no—
720C22×C4—61no—
721C22×C4—91no—
722C22×C4—94no—
723C22×C4—94no—
724C22×C4—91no—
725C22×C4—91no—
726C22×C4—91no—
727C22×C4—181no—
728C22×C4—188no—
729C22×C4—181no—
730C22×C4—181no—
731C22×C4—181no—
732C22×C4—181no—
733C2×C8—31no—
734C2×C8—31no—
735C2×C8—62no—
736C2×C8—62no—
737C2×C8—91no—
738C2×C8—182no—
739C2×C8—182no—
740C2×C8—182no—
741C2×C8—182no—
742C2×C8C2×D3211yescharacteristic
743C4⋊C4—31no—
744C4⋊C4—31no—
745C4⋊C4—61no—
746C4⋊C4—91no—
747C4⋊C4—181no—
748C4⋊C4C2×D3211yescharacteristic
749C22⋊C4—61no—
750C22⋊C4—181no—
751C22⋊C4—181no—
752C22⋊C4—181no—
753C42—61no—
754C42—181no—
755C42—181no—
756C42—181no—
757C22×C3—22no—
758C22×C3—22no—
759C22×C3—21no—
760C22×C3—32no—
761C22×C3—32no—
762C22×C3—32no—
763C22×C3—32no—
764C22×C3—42no—
765C22×C3—41no—
766C22×C3—41no—
767C22×C3—41no—
768C22×C3—41no—
769C22×C3—61no—
770C22×C3—61no—
771C22×C3—62no—
772C22×C3—81no—
773C22×C3—81no—
774C22×C3—128no—
775C22×C3—121no—
776C22×C3—121no—
777C22×C3C2×D3×D411yescharacteristic
778C22×C3C2×D3×D411yescharacteristic
779C2×D3—21no—
780C2×D3—21no—
781C2×D3—22no—
782C2×D3—32no—
783C2×D3—32no—
784C2×D3—41no—
785C2×D3—41no—
786C2×D3—48no—
787C2×D3—62no—
788C2×D3—68no—
789C2×D3—61no—
790C2×D3—61no—
791C2×D3—61no—
792C2×D3—61no—
793C2×D3—68no—
794C2×D3—121no—
795C2×D3—121no—
796C2×D3D3×C22⋊C412yes—
797C2×D3D3×C22⋊C412yes—
798C2×D3#91212yes—
799C2×D3#91612yes—
800C3×C4—21no—
801C3×C4—21no—
802C3×C4—32no—
803C3×C4—32no—
804C3×C4—41no—
805C3×C4—41no—
806C3×C4—62no—
807C3×C4—81no—
808C3×C4—121no—
809C3×C4—121no—
810C3×C4C22×C4×D311yescharacteristic
811C3×C4C22×C4×D311yescharacteristic
812C3×C4C2×D3×D411yescharacteristic
813C3×C4C2×D3×D411yescharacteristic
814Dic3—22no—
815Dic3—32no—
816Dic3—32no—
817Dic3—41no—
818Dic3—41no—
819Dic3—62no—
820Dic3—62no—
821Dic3—62no—
822Dic3—122no—
823Dic3—121no—
824Dic3—121no—
825Dic3—241no—
826Dic3D3×C22⋊C412yes—
827Dic3D3×C22⋊C412yes—
828C32C2×#41611yescharacteristic, complemented, Sylow
829C23—21no—
830C23—31no—
831C23—31no—
832C23—64no—
833C23—61no—
834C23—94no—
835C23—91no—
836C23—122no—
837C23—122no—
838C23—182no—
839C23—182no—
840Q8—32no—
841Q8—61no—
842Q8—92no—
843Q8—184no—
844Q8—181no—
845D4—21no—
846D4—32no—
847D4—64no—
848D4—64no—
849D4—61no—
850D4—184no—
851D4—184no—
852D4—184no—
853D4C4×D3212yes—
854C2×C4—21no—
855C2×C4—31no—
856C2×C4—31no—
857C2×C4—32no—
858C2×C4—32no—
859C2×C4—32no—
860C2×C4—32no—
861C2×C4—64no—
862C2×C4—61no—
863C2×C4—61no—
864C2×C4—61no—
865C2×C4—94no—
866C2×C4—94no—
867C2×C4—94no—
868C2×C4—91no—
869C2×C4—92no—
870C2×C4—92no—
871C2×C4—122no—
872C2×C4—184no—
873C2×C4—184no—
874C2×C4—184no—
875C2×C4—184no—
876C2×C4—181no—
877C2×C4—181no—
878C2×C4—362no—
879C2×C4C22×D3211yescharacteristic
880C8—21no—
881C8—61no—
882C8—61no—
883C8—181no—
884C2×C3—21no—
885C2×C3—21no—
886C2×C3—21no—
887C2×C3—34no—
888C2×C3—42no—
889C2×C3—42no—
890C2×C3—62no—
891C2×C3—82no—
892C2×C3—122no—
893C2×C3C2×D3×C22⋊C411yescharacteristic
894C2×C3C2×D3×C22⋊C411yescharacteristic
895C2×C3C2×#91211yescharacteristic
896C2×C3C2×#91611yescharacteristic
897C2×C3D3×#13511yescharacteristic
898C2×C3D3×#13511yescharacteristic
899D3—22no—
900D3—42no—
901D3—62no—
902D3—62no—
903D3—122no—
904D3#477214yesdirect product factor
905C22—22no—
906C22—32no—
907C22—32no—
908C22—32no—
909C22—32no—
910C22—41no—
911C22—41no—
912C22—61no—
913C22—61no—
914C22—62no—
915C22—92no—
916C22—128no—
917C22—121no—
918C22—121no—
919C22—188no—
920C22—181no—
921C22—181no—
922C22D32×D411yescharacteristic
923C4—32no—
924C4—32no—
925C4—41no—
926C4—62no—
927C4—92no—
928C4—121no—
929C4—121no—
930C4—182no—
931C4—361no—
932C4C2×C4×D3211yescharacteristic
933C4D32×D411yescharacteristic
934C3—21no—
935C3C2×#477211yescharacteristic, complemented
936C3D3×#41611yescharacteristic, complemented
937C2—34no—
938C2—42no—
939C2—62no—
940C2—122no—
941C2—182no—
942C2D32×C22⋊C411yescharacteristic
943C2D3×#91211yescharacteristic
944C2D3×#91611yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalC2×D3×#237C2
cosocleC2×C32×C4C24
hypercenter#102D32
hypocenterC32C2×#416
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. C2×D32×C8C2semidirect
3. D3×#892C2semidirect
4. #10592471C2semidirect
5. C3×#4772C2semidirect
6. C3×D3×#102C2semidirect
7. #10591424C2semidirect
8. #10591420C2semidirect
9. D3×#832C2semidirect
10. #10590956C2semidirect
11. #10590954C2semidirect
12. D3×#816C2semidirect
13. #10590611C2semidirect
14. #10590608C2semidirect
15. D3×#810C2semidirect
26. D3×#237C4semidirect
31. C2×C8×C3⋊D3C22semidirect
32. #64101C22semidirect
34. C2×C3×D3×C8C22semidirect
35. C3×#892C22semidirect
41. #63849C22semidirect
42. #63841C22semidirect
44. C2×#3710C22semidirect
46. C2×D3×C3⋊C8C22semidirect
48. C32×#102C22semidirect
49. #63659C22semidirect
50. #63643C22semidirect
51. #63637C22semidirect
52. C3×#832C22semidirect
53. C3×#832C22semidirect
54. C3×#821C22semidirect
55. C3×#816C22semidirect
56. C3×#810C22semidirect
57. C3×#809C22semidirect
58. #63567C22semidirect
59. #63567C22semidirect
60. #63566C22semidirect
61. #63565C22semidirect
62. #63563C22semidirect
63. #63562C22semidirect
92. #4772D3direct (N × H)
94. D3×#102D3semidirect
101. #3830C2×C4semidirect
108. C3×#237C2×C4semidirect
133. #3796C2×C4semidirect
135. #3795C2×C4semidirect
210. C2×D3×C8C2×D3semidirect
219. #892C2×D3semidirect
233. C3×#102C2×D3semidirect
234. C3×#102C2×D3semidirect
242. #832C2×D3semidirect
243. #832C2×D3semidirect
245. #821C2×D3semidirect
252. #816C2×D3semidirect
259. #810C2×D3semidirect
261. #809C2×D3semidirect
389. #237C4×D3semidirect
554. #102D32semidirect
689. C3×D3#416semidirect
828. C32C2×#416semidirect
904. D3#4772direct (N × H)
935. C3C2×#4772semidirect
936. C3D3×#416semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2372
C2×D32×C82
D3×#8922
#105924712
C3×#47722
C3×D3×#1022
#105914242
#105914202
D3×#8322
#105909562
#105909542
D3×#8162
#105906112
#105906082
D3×#8102
D3×#4163
C2×#47723