Finite Group Databasebeta

← D3×#4868 #11869528

Subgroups — D3×#4868 #11869528

Order 1152.

880 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#897C211yesmaximal, characteristic
2D3×#892C211yesmaximal, characteristic
3#10592567C211yesmaximal, characteristic, complemented
4C3×#4868C211yesmaximal, characteristic, complemented
5C3×D3×#106C211yesmaximal, characteristic, complemented
6D3×(C2×D3)⋊C8C211yesmaximal, characteristic
7#10590713C211yesmaximal, characteristic, complemented
8#10590709C211yesmaximal, characteristic, complemented
9D3×#816C211yesmaximal, characteristic, complemented
10D3×#810C211yesmaximal, characteristic, complemented
11D3×#807C211yesmaximal, characteristic, complemented
12#10590527C211yesmaximal, characteristic, complemented
13#10590450C211yesmaximal, characteristic, complemented
14#10590447C211yesmaximal, characteristic, complemented
15#10590428C211yesmaximal, characteristic, complemented
16D3×#485—31nomaximal
17C2×#4868—31nomaximal
18C2×C4×D32C2211yescharacteristic
19C2×D3×Dic6C2211yescharacteristic
20#64106C2211yescharacteristic
21#64101C2211yescharacteristic
22C2×C3×D3×C8C2211yescharacteristic
23C3×#897C2211yescharacteristic
24C3×#892C2211yescharacteristic
25C3×D3×C4⋊C4C2211yescharacteristic
26C3×D3×C4⋊C4C2211yescharacteristic
27D3×(C2×D3)⋊C4—21no—
28D3×(C2×D3)⋊C4—21no—
29#63895—21no—
30#63893—21no—
31D3×C4⋊Dic3—21no—
32D3×C4⋊Dic3C2211yescharacteristic
33#63878—21no—
34C4×D3×Dic3—21no—
35#63871C2211yescharacteristic
36#63857C2211yescharacteristic
37#63849C2211yescharacteristic
38#63841C2211yescharacteristic
39#63836—21no—
40C2×D3×C3⋊C8C2211yescharacteristic
41C32×#106C2211yescharacteristic, complemented
42#63647C2211yescharacteristic
43#63643C2211yescharacteristic, complemented
44#63637C2211yescharacteristic, complemented
45#63634C2211yescharacteristic, complemented
46C3×(C2×D3)⋊C8C2211yescharacteristic
47C3×#817C2211yescharacteristic, complemented
48C3×#816C2211yescharacteristic, complemented
49C3×#810C2211yescharacteristic, complemented
50C3×#808C2211yescharacteristic, complemented
51C3×#808C2211yescharacteristic, complemented
52C3×#807C2211yescharacteristic, complemented
53#63576C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63567C2211yescharacteristic, complemented
57#63566C2211yescharacteristic, complemented
58#63565C2211yescharacteristic, complemented
59#63557C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61D3×C22⋊Q8—31no—
62D3×#117—31no—
63C2×#897—31no—
64C2×#892—31no—
65C3×#485—31no—
66C2×C3×#106—31no—
67C2×(C2×D3)⋊C8—31no—
68C2×#816—31no—
69#5045—31no—
70#4996—31no—
71C2×#810—31no—
72C2×#807—31no—
73#4888—31no—
74D3×#107—31no—
75#4868—31no—
76#4868—31no—
77#4868—31no—
78#4868—31no—
79#4868—31no—
80#4868—31no—
81#4868—31no—
82#4868—31no—
83#4868—61no—
84#4868D311yescharacteristic, direct product factor
85D3×#106D311yescharacteristic, complemented
86#4815—31no—
87#4814—31no—
88D3×#103—31no—
89D3×#103—31no—
90D3×C22⋊C8—31no—
91#4723—31no—
92C22×D32D411yescharacteristic
93C2×C4×C3⋊D3C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C2×C3×C4×D3—21no—
96C2×C3×C4×D3—21no—
97C2×C3×C4×D3C2311yescharacteristic
98C2×C3×C4×D3C2311yescharacteristic
99C2×C3×Dic6C2311yescharacteristic
100C2×#627—21no—
101C2×#624D411yescharacteristic
102C2×D3×Dic3—21no—
103C2×D3×Dic3—21no—
104C2×D3×Dic3D411yescharacteristic
105C2×D3×Dic3D411yescharacteristic
106C4×D32—22no—
107C4×D32—22no—
108D3×Dic6—22no—
109D3×Dic6—22no—
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113#3752—21no—
114#3752—21no—
115C4⋊(C3⋊Dic3)—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C4×C3⋊Dic3—21no—
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×C4×Dic3—21no—
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C3×D3×C8—22no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134#3722—21no—
135#3722—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138Dic32—21no—
139Dic32—21no—
140D3×C3⋊C8—22no—
141C2×#485—91noSylow
142C2×D3×Q8—31no—
143C22×C4×D3—31no—
144C22×C4×D3—31no—
145C22×Dic6—31no—
146C22×C3×C8—31no—
147C3×C22⋊Q8—31no—
148C3×#117—31no—
149C2×C3×C4⋊C4—31no—
150C2×C3×C4⋊C4—31no—
151#946—31no—
152C2×(C2×D3)⋊C4—61no—
153C2×(C2×D3)⋊C4—61no—
154#926—31no—
155C2×C4⋊Dic3—31no—
156C2×C4⋊Dic3—61no—
157#924—31no—
158C2×C4×Dic3—61no—
159C22×C3⋊C8—31no—
160C2×D3×C8—31no—
161C2×D3×C8C2×D311yescharacteristic
162#897—31no—
163#897—31no—
164#897—31no—
165#897—31no—
166#897—61no—
167#897—61no—
168#897—61no—
169#897C2×D311yescharacteristic
170#896—61no—
171#892—31no—
172#892—31no—
173#892—31no—
174#892—31no—
175#892—31no—
176#892—61no—
177#892—61no—
178#892—61no—
179#892C2×D311yescharacteristic
180D3×C4⋊C4—31no—
181D3×C4⋊C4—61no—
182D3×C4⋊C4C2×D311yescharacteristic
183D3×C4⋊C4C2×D311yescharacteristic
184D3×C22⋊C4—61no—
185D3×C22⋊C4—61no—
186#878—61no—
187#877—61no—
188#872—61no—
189C42×D3—61no—
190C3×#107—31no—
191C3×#106—21no—
192C3×#106—31no—
193C3×#106—31no—
194C3×#106—31no—
195C3×#106C2×D311yescharacteristic, complemented
196C3×#106C2×D311yescharacteristic, complemented
197C3×#103—31no—
198C3×#103—31no—
199C3×C22⋊C8—31no—
200#835—31no—
201#835—31no—
202#830—31no—
203(C2×D3)⋊C8—31no—
204(C2×D3)⋊C8—31no—
205(C2×D3)⋊C8—31no—
206(C2×D3)⋊C8—31no—
207(C2×D3)⋊C8—31no—
208(C2×D3)⋊C8—61no—
209(C2×D3)⋊C8C2×D311yescharacteristic
210#818—31no—
211#817C2×D311yescharacteristic, complemented
212#816—31no—
213#816—31no—
214#816—31no—
215#816—31no—
216#816—31no—
217#816—61no—
218#816C2×D311yescharacteristic, complemented
219#810—31no—
220#810—31no—
221#810—31no—
222#810—31no—
223#810—31no—
224#810—61no—
225#810C2×D311yescharacteristic, complemented
226#808C2×D311yescharacteristic, complemented
227#808C2×D311yescharacteristic, complemented
228#807—31no—
229#807—31no—
230#807—31no—
231#807—31no—
232#807—31no—
233#807—61no—
234#807C2×D311yescharacteristic, complemented
235C22×C3⋊D3C2×D411yescharacteristic
236C22×C3×D3C2×D411yescharacteristic
237C22×C3×D3C2×D411yescharacteristic
238C2×D32—22no—
239C2×D32—22no—
240C2×D32—22no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4C2411yescharacteristic
244C2×C3⋊Dic3—21no—
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3C2×D411yescharacteristic
247C4×C3⋊D3—21no—
248C4×C3⋊D3—21no—
249#634—21no—
250#634—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C3×C4×D3—21no—
258C3×C4×D3—21no—
259C3×C4×D3—42no—
260C3×C4×D3—42no—
261C3×C4×D3#4112yes—
262C3×C4×D3#4112yes—
263C3×Dic6—21no—
264C3×Dic6—21no—
265#627—42no—
266#624—22no—
267D3×Dic3—22no—
268D3×Dic3—22no—
269D3×Dic3—42no—
270D3×Dic3—42no—
271C32×C8—21no—
272C3⋊(C3⋊C8)—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275C2×C22⋊Q8—91no—
276C2×#117—91no—
277#485—31no—
278#485—91no—
279#485—91no—
280#485—91no—
281#485—91no—
282#485—91no—
283#485—91no—
284#485—91no—
285C2×#107—91no—
286C2×#106—31no—
287C2×#103—91no—
288C2×#103—91no—
289C2×C22⋊C8—91no—
290C23×D3—31no—
291C23×D3—31no—
292C2×C3×Q8—31no—
293C22×C3×C4—31no—
294C22×C3×C4—31no—
295C22×C3×C4—61no—
296C22×C3×C4—61no—
297C22×Dic3—31no—
298C22×Dic3—31no—
299C22×Dic3—61no—
300C22×Dic3—61no—
301D3×Q8—62no—
302D3×Q8—62no—
303C2×C4×D3—21no—
304C2×C4×D3—21no—
305C2×C4×D3—31no—
306C2×C4×D3—31no—
307C2×C4×D3—31no—
308C2×C4×D3—31no—
309C2×C4×D3—31no—
310C2×C4×D3—31no—
311C2×C4×D3—61no—
312C2×C4×D3—62no—
313C2×C4×D3—62no—
314C2×C4×D3—62no—
315C2×C4×D3—62no—
316C2×C4×D3—61no—
317C2×C4×D3—61no—
318C2×C4×D3C22×D311yescharacteristic
319C2×C4×D3C22×D311yescharacteristic
320C2×Dic6—31no—
321C2×Dic6—31no—
322C2×Dic6—61no—
323C2×Dic6—62no—
324C2×Dic6—62no—
325C2×Dic6—61no—
326C2×Dic6—61no—
327C2×Dic6C22×D311yescharacteristic
328C2×C3×C8—21no—
329C2×C3×C8—31no—
330C2×C3×C8—31no—
331C2×C3×C8—62no—
332C2×C3×C8C22×D311yescharacteristic
333C2×C3×C8C22×D311yescharacteristic
334C3×C4⋊C4—21no—
335C3×C4⋊C4—21no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4C22×D311yescharacteristic
343C3×C4⋊C4C22×D311yescharacteristic
344C3×C4⋊C4C22×D311yescharacteristic
345C3×C4⋊C4C22×D311yescharacteristic
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C42—61no—
349#217—61no—
350#217—61no—
351(C2×D3)⋊C4—21no—
352(C2×D3)⋊C4—21no—
353(C2×D3)⋊C4—61no—
354(C2×D3)⋊C4—61no—
355(C2×D3)⋊C4—61no—
356(C2×D3)⋊C4—61no—
357(C2×D3)⋊C4—61no—
358(C2×D3)⋊C4—61no—
359(C2×D3)⋊C4—61no—
360(C2×D3)⋊C4—61no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—121no—
364(C2×D3)⋊C4—121no—
365C4⋊Dic3—21no—
366C4⋊Dic3—31no—
367C4⋊Dic3—31no—
368C4⋊Dic3—61no—
369C4⋊Dic3—61no—
370C4⋊Dic3—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3—121no—
375C4⋊Dic3C22×D311yescharacteristic
376C4⋊Dic3C22×D311yescharacteristic
377C4⋊Dic3C22×D311yescharacteristic
378Dic3⋊C4—21no—
379Dic3⋊C4—21no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383C4×Dic3—21no—
384C4×Dic3—61no—
385C4×Dic3—61no—
386C4×Dic3—61no—
387C4×Dic3—61no—
388C4×Dic3—61no—
389C4×Dic3—61no—
390C4×Dic3—121no—
391C2×C3⋊C8—31no—
392C2×C3⋊C8—31no—
393C2×C3⋊C8—61no—
394C2×C3⋊C8—62no—
395C2×C3⋊C8C22×D311yescharacteristic
396C2×C3⋊C8C22×D311yescharacteristic
397D3×C8—22no—
398D3×C8—62no—
399C22×C32C22×D411yescharacteristic
400C2×C3⋊D3—21no—
401C2×C3⋊D3—21no—
402C2×C3⋊D3—21no—
403C2×C3×D3—21no—
404C2×C3×D3—21no—
405C2×C3×D3—21no—
406C2×C3×D3#12312yes—
407C2×C3×D3#13512yes—
408C2×C3×D3#13712yes—
409D32—44no—
410C32×C4—41no—
411C32×C4—41no—
412C32×C4C2×#4111yescharacteristic
413C32×C4C2×#4111yescharacteristic
414C3⋊Dic3—21no—
415C3⋊Dic3—41no—
416C3⋊Dic3—41no—
417C3×Dic3—21no—
418C3×Dic3—41no—
419C3×Dic3—41no—
420C3×Dic3—41no—
421C3×Dic3—41no—
422C3×Dic3#12312yes—
423C22×Q8—91no—
424C23×C4—91no—
425C22×C8—31no—
426C22×C8—91no—
427C22⋊Q8—31no—
428C22⋊Q8—91no—
429C22⋊Q8—91no—
430C22⋊Q8—91no—
431C22⋊Q8—181no—
432C22⋊Q8—181no—
433#117—31no—
434#117—91no—
435#117—91no—
436#117—91no—
437#117—181no—
438#117—181no—
439C2×C4⋊C4—31no—
440C2×C4⋊C4—31no—
441C2×C4⋊C4—91no—
442C2×C4⋊C4—181no—
443C2×C22⋊C4—181no—
444C2×C22⋊C4—181no—
445C2×C42—181no—
446#107—31no—
447#107—91no—
448#107—91no—
449#107—91no—
450#106—31no—
451#106—31no—
452#106—31no—
453#106D3211yescharacteristic, complemented
454#103—31no—
455#103—31no—
456#103—91no—
457#103—91no—
458#103—91no—
459#103—91no—
460#103—91no—
461#103—91no—
462C22⋊C8—31no—
463C22⋊C8—91no—
464C22⋊C8—91no—
465C22⋊C8—91no—
466C23×C3—31no—
467C23×C3—31no—
468C22×D3—31no—
469C22×D3—31no—
470C22×D3—61no—
471C22×D3—62no—
472C22×D3—62no—
473C22×D3—62no—
474C22×D3—62no—
475C22×D3—62no—
476C22×D3—62no—
477C22×D3D3×D411yescharacteristic
478C22×D3D3×D411yescharacteristic
479C3×Q8—61no—
480C3×Q8—61no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—31no—
487C2×C3×C4—32no—
488C2×C3×C4—32no—
489C2×C3×C4—31no—
490C2×C3×C4—41no—
491C2×C3×C4—41no—
492C2×C3×C4—61no—
493C2×C3×C4—61no—
494C2×C3×C4—61no—
495C2×C3×C4—61no—
496C2×C3×C4—61no—
497C2×C3×C4—61no—
498C2×C3×C4—122no—
499C2×C3×C4—122no—
500C2×C3×C4C23×D311yescharacteristic
501C2×C3×C4C23×D311yescharacteristic
502C2×Dic3—21no—
503C2×Dic3—21no—
504C2×Dic3—21no—
505C2×Dic3—21no—
506C2×Dic3—31no—
507C2×Dic3—31no—
508C2×Dic3—61no—
509C2×Dic3—62no—
510C2×Dic3—62no—
511C2×Dic3—61no—
512C2×Dic3—61no—
513C2×Dic3—61no—
514C2×Dic3—61no—
515C2×Dic3—121no—
516C2×Dic3—121no—
517C2×Dic3—122no—
518C2×Dic3—122no—
519C2×Dic3D3×D411yescharacteristic
520C2×Dic3D3×D411yescharacteristic
521C4×D3—21no—
522C4×D3—21no—
523C4×D3—42no—
524C4×D3—42no—
525C4×D3—62no—
526C4×D3—62no—
527C4×D3—62no—
528C4×D3—61no—
529C4×D3—61no—
530C4×D3—61no—
531C4×D3—61no—
532C4×D3—62no—
533C4×D3—121no—
534C4×D3—121no—
535C4×D3—122no—
536C4×D3—122no—
537C4×D3#23512yes—
538C4×D3#23912yes—
539Dic6—21no—
540Dic6—21no—
541Dic6—61no—
542Dic6—61no—
543Dic6—61no—
544Dic6—61no—
545Dic6—121no—
546Dic6—121no—
547Dic6—122no—
548Dic6—122no—
549C3×C8—21no—
550C3×C8—21no—
551C3×C8—41no—
552C3×C8—61no—
553C3×C8—61no—
554C3⋊C8—21no—
555C3⋊C8—21no—
556C3⋊C8—61no—
557C3⋊C8—61no—
558C3⋊C8—121no—
559C2×C32C2×#12311yescharacteristic
560C2×C32C2×#13511yescharacteristic
561C2×C32C2×#13711yescharacteristic
562C3⋊D3—41no—
563C3×D3—41no—
564C3×D3#48514yescomplemented
565C24—91no—
566C2×Q8—31no—
567C2×Q8—91no—
568C2×Q8—181no—
569C2×Q8—182no—
570C2×Q8—182no—
571C22×C4—31no—
572C22×C4—31no—
573C22×C4—61no—
574C22×C4—61no—
575C22×C4—91no—
576C22×C4—91no—
577C22×C4—91no—
578C22×C4—91no—
579C22×C4—182no—
580C22×C4—182no—
581C22×C4—181no—
582C22×C4—181no—
583C2×C8—31no—
584C2×C8—31no—
585C2×C8—62no—
586C2×C8—91no—
587C2×C8—182no—
588C2×C8C2×D3211yescharacteristic
589C4⋊C4—31no—
590C4⋊C4—31no—
591C4⋊C4—31no—
592C4⋊C4—61no—
593C4⋊C4—61no—
594C4⋊C4—61no—
595C4⋊C4—91no—
596C4⋊C4—181no—
597C4⋊C4—181no—
598C4⋊C4—181no—
599C4⋊C4—181no—
600C4⋊C4C2×D3211yescharacteristic
601C4⋊C4C2×D3211yescharacteristic
602C22⋊C4—61no—
603C22⋊C4—61no—
604C22⋊C4—181no—
605C22⋊C4—181no—
606C22⋊C4—181no—
607C22⋊C4—181no—
608C22⋊C4—181no—
609C22⋊C4—181no—
610C42—61no—
611C42—181no—
612C42—181no—
613C42—181no—
614C22×C3—21no—
615C22×C3—32no—
616C22×C3—32no—
617C22×C3—32no—
618C22×C3—61no—
619C22×C3—61no—
620C22×C3—61no—
621C22×C3C2×D3×D411yescharacteristic
622C22×C3C2×D3×D411yescharacteristic
623C2×D3—21no—
624C2×D3—21no—
625C2×D3—21no—
626C2×D3—61no—
627C2×D3—61no—
628C2×D3—61no—
629C2×D3—61no—
630C2×D3—61no—
631C2×D3—61no—
632C2×D3—121no—
633C2×D3—121no—
634C2×D3—121no—
635C2×D3—124no—
636C2×D3—124no—
637C2×D3#89412yes—
638C2×D3#91512yes—
639C2×D3#91612yes—
640C3×C4—21no—
641C3×C4—21no—
642C3×C4—32no—
643C3×C4—41no—
644C3×C4—41no—
645C3×C4—41no—
646C3×C4—41no—
647C3×C4—61no—
648C3×C4—81no—
649C3×C4—81no—
650C3×C4—121no—
651C3×C4—121no—
652C3×C4—121no—
653C3×C4—121no—
654C3×C4C2×#23511yescharacteristic
655C3×C4C2×#23911yescharacteristic
656C3×C4D3×#4111yescharacteristic
657C3×C4D3×#4111yescharacteristic
658Dic3—21no—
659Dic3—41no—
660Dic3—41no—
661Dic3—41no—
662Dic3—41no—
663Dic3—61no—
664Dic3—61no—
665Dic3—121no—
666Dic3—121no—
667Dic3—121no—
668Dic3—121no—
669Dic3—121no—
670Dic3—241no—
671Dic3—241no—
672Dic3#89412yes—
673C32C2×#48511yescharacteristic, complemented, Sylow
674C23—31no—
675C23—31no—
676C23—91no—
677C23—182no—
678C23—182no—
679C23—182no—
680Q8—61no—
681Q8—61no—
682Q8—181no—
683Q8—181no—
684Q8—362no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—31no—
688C2×C4—32no—
689C2×C4—32no—
690C2×C4—31no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—91no—
698C2×C4—122no—
699C2×C4—122no—
700C2×C4—182no—
701C2×C4—182no—
702C2×C4—182no—
703C2×C4—181no—
704C2×C4—181no—
705C2×C4—181no—
706C2×C4—181no—
707C2×C4—362no—
708C2×C4—362no—
709C2×C4C22×D3211yescharacteristic
710C8—21no—
711C8—61no—
712C8—61no—
713C8—181no—
714C2×C3—21no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—34no—
718C2×C3—121no—
719C2×C3C2×#89411yescharacteristic
720C2×C3D3×#12311yescharacteristic
721C2×C3C2×#91511yescharacteristic
722C2×C3C2×#91611yescharacteristic
723C2×C3D3×#13511yescharacteristic
724C2×C3D3×#13711yescharacteristic
725D3—41no—
726D3—121no—
727D3—121no—
728D3—241no—
729D3#486814yesdirect product factor
730C22—32no—
731C22—32no—
732C22—32no—
733C22—61no—
734C22—61no—
735C22—61no—
736C22—181no—
737C22—181no—
738C22—181no—
739C22—364no—
740C22D32×D411yescharacteristic
741C4—32no—
742C4—41no—
743C4—41no—
744C4—61no—
745C4—121no—
746C4—121no—
747C4—121no—
748C4—121no—
749C4—181no—
750C4—361no—
751C4—361no—
752C4D3×#23511yescharacteristic
753C4D3×#23911yescharacteristic
754C3—21no—
755C3C2×#486811yescharacteristic, complemented
756C3D3×#48511yescharacteristic, complemented
757C2—34no—
758C2—121no—
759C2—361no—
760C2D3×#89411yescharacteristic
761C2D3×#91511yescharacteristic
762C2D3×#91611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radicalC22×D32D4
hypercenter#106D32
hypocenterC32C2×#485
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
3. #10592567C2semidirect
4. C3×#4868C2semidirect
5. C3×D3×#106C2semidirect
7. #10590713C2semidirect
8. #10590709C2semidirect
9. D3×#816C2semidirect
10. D3×#810C2semidirect
11. D3×#807C2semidirect
12. #10590527C2semidirect
13. #10590450C2semidirect
14. #10590447C2semidirect
15. #10590428C2semidirect
41. C32×#106C22semidirect
43. #63643C22semidirect
44. #63637C22semidirect
45. #63634C22semidirect
47. C3×#817C22semidirect
48. C3×#816C22semidirect
49. C3×#810C22semidirect
50. C3×#808C22semidirect
51. C3×#808C22semidirect
52. C3×#807C22semidirect
53. #63576C22semidirect
54. #63575C22semidirect
55. #63567C22semidirect
56. #63567C22semidirect
57. #63566C22semidirect
58. #63565C22semidirect
84. #4868D3direct (N × H)
85. D3×#106D3semidirect
195. C3×#106C2×D3semidirect
196. C3×#106C2×D3semidirect
211. #817C2×D3semidirect
218. #816C2×D3semidirect
225. #810C2×D3semidirect
226. #808C2×D3semidirect
227. #808C2×D3semidirect
234. #807C2×D3semidirect
453. #106D32semidirect
564. C3×D3#485semidirect
673. C32C2×#485semidirect
729. D3#4868direct (N × H)
755. C3C2×#4868semidirect
756. C3D3×#485semidirect

Maximal subgroups

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

subgroupindex
D3×#8972
D3×#8922
#105925672
C3×#48682
C3×D3×#1062
D3×(C2×D3)⋊C82
#105907132
#105907092
D3×#8162
D3×#8102
D3×#8072
#105905272
#105904502
#105904472
#105904282
D3×#4853
C2×#48683