Finite Group Databasebeta

← D3×#4792 #11873398

Subgroups — D3×#4792 #11873398

Order 1152.

897 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#944C211yesmaximal, characteristic
2D3×#888C211yesmaximal, characteristic
3#10592491C211yesmaximal, characteristic, complemented
4C3×D3×#103C211yesmaximal, characteristic
5C3×#4792C211yesmaximal, characteristic, complemented
6#10591623C211yesmaximal, characteristic, complemented
7D3×#835C211yesmaximal, characteristic
8#10591538C211yesmaximal, characteristic, complemented
9#10590901C211yesmaximal, characteristic, complemented
10#10590890C211yesmaximal, characteristic, complemented
11D3×#816C211yesmaximal, characteristic
12D3×C8×Dic3C211yesmaximal, characteristic
13D3×#810C211yesmaximal, characteristic
14#10590567C211yesmaximal, characteristic, complemented
15#10590560C211yesmaximal, characteristic, complemented
16D3×#487—31nomaximal
17C2×#4792—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×D3×Dic6—21no—
20C2×D3×Dic6C2211yescharacteristic
21#64153C2211yescharacteristic
22#64097C2211yescharacteristic
23C3×#944C2211yescharacteristic
24C2×C3×D3×C8C2211yescharacteristic
25C3×D3×C4⋊C4C2211yescharacteristic
26C3×#888C2211yescharacteristic
27#63919C2211yescharacteristic
28#63918C2211yescharacteristic
29D3×C4⋊Dic3C2211yescharacteristic
30D3×Dic3⋊C4—21no—
31D3×Dic3⋊C4—21no—
32D3×Dic3⋊C4—21no—
33C4×D3×Dic3C2211yescharacteristic
34#63873C2211yescharacteristic
35#63866C2211yescharacteristic
36#63840—21no—
37#63839—21no—
38#63839—21no—
39#63839—21no—
40C2×D3×C3⋊C8C2211yescharacteristic
41C32×#103C2211yescharacteristic
42#63662C2211yescharacteristic
43#63643C2211yescharacteristic
44C8×C3⋊Dic3C2211yescharacteristic
45#63637C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#816C2211yescharacteristic
49C3×#816C2211yescharacteristic
50C3×C8×Dic3C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#810C2211yescharacteristic
53#63567C2211yescharacteristic
54#63567C2211yescharacteristic
55#63566C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59#63553C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C2×#944—31no—
62D3×C4⋊Q8—31no—
63D3×C4⋊Q8—31no—
64C2×#888—31no—
65C3×#487—31no—
66C2×C3×#103—31no—
67C2×#835—31no—
68C2×#816—31no—
69C2×C8×Dic3—31no—
70#5093—31no—
71#5079—31no—
72C2×#810—31no—
73D3×#103—31no—
74D3×#103—31no—
75D3×#103—31no—
76D3×#103D311yescharacteristic
77#4792—31no—
78#4792—31no—
79#4792—31no—
80#4792—31no—
81#4792—31no—
82#4792—31no—
83#4792—31no—
84#4792—31no—
85#4792—31no—
86#4792—31no—
87#4792—31no—
88#4792—61no—
89#4792D311yescharacteristic, direct product factor
90C4×D3×C8—31no—
91#4681—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×#634—21no—
94C2×#634C2311yescharacteristic
95C3×D3×Q8—22no—
96C3×D3×Q8—22no—
97C2×C3×C4×D3—21no—
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3C2311yescharacteristic
100C2×C3×Dic6—21no—
101C2×C3×Dic6—21no—
102C2×C3×Dic6C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×#627—21no—
105C2×#627—21no—
106C2×#627—21no—
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3D411yescharacteristic
110C2×D3×Dic3D411yescharacteristic
111D3×Dic6—22no—
112D3×Dic6—22no—
113D3×Dic6—44no—
114C2×C32×C8C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117#3750—21no—
118#3750—21no—
119#3750—21no—
120C4×C3⋊Dic3C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×D3×C8—22no—
132#3724—21no—
133#3724—21no—
134#3724—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139Dic32D411yescharacteristic
140Dic32D411yescharacteristic
141D3×C3⋊C8—22no—
142C2×#487—91noSylow
143C22×C3×Q8—31no—
144C2×D3×Q8—31no—
145C2×D3×Q8—61no—
146C2×D3×Q8C2×D311yescharacteristic
147C22×Dic6—31no—
148C22×Dic6—61no—
149C22×C3×C8—31no—
150C3×C4⋊Q8—31no—
151C3×C4⋊Q8—31no—
152C2×C3×C4⋊C4—31no—
153#944—31no—
154#944—31no—
155#944—31no—
156#944—31no—
157#944—31no—
158#944—61no—
159#944—61no—
160#944—61no—
161#944—61no—
162#944C2×D311yescharacteristic
163C2×C4⋊Dic3—31no—
164C2×Dic3⋊C4—61no—
165C2×Dic3⋊C4—61no—
166C2×Dic3⋊C4—61no—
167C2×C4×Dic3—31no—
168C22×C3⋊C8—31no—
169C2×D3×C8—31no—
170C2×D3×C8C2×D311yescharacteristic
171D3×C4⋊C4—31no—
172D3×C4⋊C4—61no—
173D3×C4⋊C4—61no—
174D3×C4⋊C4—61no—
175D3×C4⋊C4C2×D311yescharacteristic
176#888—31no—
177#888—31no—
178#888—31no—
179#888—31no—
180#888—31no—
181#888—61no—
182#888—61no—
183#888—61no—
184#888—61no—
185#888—61no—
186#888—61no—
187#888C2×D311yescharacteristic
188C42×D3—31no—
189#869—31no—
190#869—31no—
191C3×#103—21no—
192C3×#103—31no—
193C3×#103—31no—
194C3×#103—31no—
195C3×#103—31no—
196C3×#103—31no—
197C3×#103—31no—
198C3×#103C2×D311yescharacteristic
199C3×#103C2×D311yescharacteristic
200C3×C4×C8—31no—
201#835—31no—
202#835—31no—
203#835—31no—
204#835—31no—
205#835—31no—
206#835—31no—
207#835—61no—
208#835C2×D311yescharacteristic
209#835C2×D311yescharacteristic
210#816—31no—
211#816—31no—
212#816—31no—
213#816—31no—
214#816—31no—
215#816—31no—
216#816—61no—
217#816C2×D311yescharacteristic
218#816C2×D311yescharacteristic
219C8×Dic3—31no—
220C8×Dic3—31no—
221C8×Dic3—31no—
222C8×Dic3—31no—
223C8×Dic3—31no—
224C8×Dic3—61no—
225C8×Dic3C2×D311yescharacteristic
226#810—31no—
227#810—31no—
228#810—31no—
229#810—31no—
230#810—31no—
231#810—31no—
232#810—61no—
233#810C2×D311yescharacteristic
234#810C2×D311yescharacteristic
235C4×C3⋊C8—31no—
236C22×C3×D3C2×D411yescharacteristic
237C32×Q8—21no—
238C32×Q8—21no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4C2411yescharacteristic
242C2×C3⋊Dic3—21no—
243C2×C3⋊Dic3—21no—
244C2×C3⋊Dic3C2×D411yescharacteristic
245C2×C3⋊Dic3C2×D411yescharacteristic
246#634—21no—
247#634—21no—
248#634—42no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C2×C3×Dic3C2×D411yescharacteristic
256C3×C4×D3—42no—
257C3×C4×D3—42no—
258C3×C4×D3#4112yes—
259C3×C4×D3#4112yes—
260C3×Dic6—21no—
261C3×Dic6—21no—
262C3×Dic6—21no—
263C3×Dic6—21no—
264C3×Dic6—42no—
265C3×Dic6—42no—
266#627—42no—
267#627—42no—
268#627—42no—
269D3×Dic3—42no—
270D3×Dic3—42no—
271D3×Dic3SD1614yes—
272D3×Dic3Q1614yes—
273C32×C8—21no—
274C3⋊(C3⋊C8)—21no—
275C3×C3⋊C8—21no—
276C3×C3⋊C8—21no—
277C2×C4⋊Q8—91no—
278C2×C4⋊Q8—91no—
279#487—31no—
280#487—91no—
281#487—91no—
282#487—91no—
283#487—91no—
284#487—91no—
285#487—91no—
286#487—91no—
287C2×#103—31no—
288C2×#103—91no—
289C2×#103—91no—
290C2×#103—91no—
291C2×C4×C8—91no—
292C2×C3×Q8—21no—
293C2×C3×Q8—31no—
294C2×C3×Q8—31no—
295C2×C3×Q8—61no—
296C2×C3×Q8—61no—
297C2×C3×Q8—62no—
298C2×C3×Q8—62no—
299C2×C3×Q8C22×D311yescharacteristic
300C2×C3×Q8C22×D311yescharacteristic
301C22×C3×C4—31no—
302C22×C3×C4—61no—
303C22×C3×C4—61no—
304C22×Dic3—31no—
305C22×Dic3—31no—
306C22×Dic3—61no—
307C22×Dic3—61no—
308D3×Q8—22no—
309D3×Q8—22no—
310D3×Q8—62no—
311D3×Q8—62no—
312D3×Q8—124no—
313C2×C4×D3—21no—
314C2×C4×D3—21no—
315C2×C4×D3—31no—
316C2×C4×D3—31no—
317C2×C4×D3—61no—
318C2×C4×D3—61no—
319C2×C4×D3C22×D311yescharacteristic
320C2×Dic6—21no—
321C2×Dic6—21no—
322C2×Dic6—31no—
323C2×Dic6—31no—
324C2×Dic6—61no—
325C2×Dic6—62no—
326C2×Dic6—62no—
327C2×Dic6—61no—
328C2×Dic6—61no—
329C2×Dic6—61no—
330C2×Dic6—61no—
331C2×Dic6—61no—
332C2×Dic6—61no—
333C2×Dic6—61no—
334C2×Dic6—61no—
335C2×Dic6—121no—
336C2×Dic6—124no—
337C2×Dic6C22×D311yescharacteristic
338C2×Dic6C22×D311yescharacteristic
339C2×C3×C8—21no—
340C2×C3×C8—31no—
341C2×C3×C8—31no—
342C2×C3×C8—62no—
343C2×C3×C8C22×D311yescharacteristic
344C2×C3×C8C22×D311yescharacteristic
345C3×C4⋊C4—21no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4—61no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4C22×D311yescharacteristic
353C3×C4⋊C4C22×D311yescharacteristic
354C3×C42—31no—
355C4⋊Dic3—31no—
356C4⋊Dic3—31no—
357C4⋊Dic3—61no—
358C4⋊Dic3—61no—
359C4⋊Dic3—61no—
360C4⋊Dic3—61no—
361C4⋊Dic3—61no—
362C4⋊Dic3C22×D311yescharacteristic
363C4⋊Dic3C22×D311yescharacteristic
364Dic3⋊C4—21no—
365Dic3⋊C4—21no—
366Dic3⋊C4—21no—
367Dic3⋊C4—21no—
368Dic3⋊C4—61no—
369Dic3⋊C4—61no—
370Dic3⋊C4—61no—
371Dic3⋊C4—61no—
372Dic3⋊C4—61no—
373Dic3⋊C4—61no—
374Dic3⋊C4—61no—
375Dic3⋊C4—61no—
376Dic3⋊C4—61no—
377Dic3⋊C4—61no—
378Dic3⋊C4—61no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—121no—
385Dic3⋊C4—121no—
386Dic3⋊C4—121no—
387C4×Dic3—31no—
388C4×Dic3—31no—
389C4×Dic3—31no—
390C4×Dic3—31no—
391C4×Dic3—31no—
392C4×Dic3—31no—
393C4×Dic3—61no—
394C4×Dic3C22×D311yescharacteristic
395C2×C3⋊C8—31no—
396C2×C3⋊C8—31no—
397C2×C3⋊C8—61no—
398C2×C3⋊C8—62no—
399C2×C3⋊C8C22×D311yescharacteristic
400C2×C3⋊C8C22×D311yescharacteristic
401D3×C8—22no—
402D3×C8—62no—
403C22×C32C22×D411yescharacteristic
404C2×C3×D3#12412yes—
405C2×C3×D3C2×SD1612yes—
406C2×C3×D3C2×Q1612yes—
407C32×C4—41no—
408C32×C4—41no—
409C32×C4C2×#4111yescharacteristic
410C32×C4C2×#4111yescharacteristic
411C3⋊Dic3—41no—
412C3⋊Dic3—41no—
413C3⋊Dic3C2×SD1612yes—
414C3⋊Dic3C2×Q1612yes—
415C3×Dic3—41no—
416C3×Dic3—41no—
417C3×Dic3—41no—
418C3×Dic3—41no—
419C3×Dic3#12412yes—
420C3×Dic3C2×SD1612yes—
421C3×Dic3C2×Q1612yes—
422C22×Q8—31no—
423C22×Q8—91no—
424C22×Q8—181no—
425C22×C8—31no—
426C22×C8—91no—
427C4⋊Q8—31no—
428C4⋊Q8—31no—
429C4⋊Q8—91no—
430C4⋊Q8—91no—
431C4⋊Q8—91no—
432C4⋊Q8—91no—
433C4⋊Q8—91no—
434C4⋊Q8—91no—
435C4⋊Q8—181no—
436C4⋊Q8—181no—
437C4⋊Q8—181no—
438C4⋊Q8—181no—
439C2×C4⋊C4—31no—
440C2×C4⋊C4—91no—
441C2×C4⋊C4—181no—
442C2×C4⋊C4—181no—
443C2×C4⋊C4—181no—
444C2×C42—91no—
445#103—31no—
446#103—31no—
447#103—31no—
448#103—31no—
449#103—31no—
450#103—31no—
451#103—91no—
452#103—91no—
453#103—91no—
454#103—91no—
455#103—91no—
456#103—91no—
457#103—91no—
458#103—91no—
459#103—91no—
460#103D3211yescharacteristic
461C4×C8—31no—
462C4×C8—91no—
463C4×C8—91no—
464C4×C8—91no—
465C23×C3—31no—
466C22×D3D3×D411yescharacteristic
467C3×Q8—21no—
468C3×Q8—21no—
469C3×Q8—21no—
470C3×Q8—21no—
471C3×Q8—41no—
472C3×Q8—41no—
473C3×Q8—61no—
474C3×Q8—61no—
475C3×Q8—61no—
476C3×Q8—61no—
477C3×Q8—122no—
478C3×Q8—122no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—31no—
485C2×C3×C4—31no—
486C2×C3×C4—31no—
487C2×C3×C4—32no—
488C2×C3×C4—32no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4—61no—
492C2×C3×C4—61no—
493C2×C3×C4—61no—
494C2×C3×C4—61no—
495C2×C3×C4—122no—
496C2×C3×C4—122no—
497C2×C3×C4C23×D311yescharacteristic
498C2×C3×C4C23×D311yescharacteristic
499C2×Dic3—21no—
500C2×Dic3—21no—
501C2×Dic3—21no—
502C2×Dic3—21no—
503C2×Dic3—31no—
504C2×Dic3—31no—
505C2×Dic3—31no—
506C2×Dic3—31no—
507C2×Dic3—34no—
508C2×Dic3—34no—
509C2×Dic3—61no—
510C2×Dic3—61no—
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
521C2×Dic3D3×D411yescharacteristic
522C4×D3—34no—
523C4×D3—34no—
524C4×D3—42no—
525C4×D3—42no—
526C4×D3—122no—
527C4×D3—122no—
528C4×D3#23512yes—
529C4×D3#23712yes—
530Dic6—21no—
531Dic6—21no—
532Dic6—21no—
533Dic6—21no—
534Dic6—42no—
535Dic6—42no—
536Dic6—61no—
537Dic6—61no—
538Dic6—61no—
539Dic6—61no—
540Dic6—121no—
541Dic6—121no—
542Dic6—122no—
543Dic6—122no—
544Dic6—122no—
545Dic6—122no—
546Dic6—122no—
547Dic6—122no—
548Dic6—122no—
549Dic6—122no—
550Dic6—242no—
551C3×C8—21no—
552C3×C8—21no—
553C3×C8—41no—
554C3×C8—61no—
555C3×C8—61no—
556C3⋊C8—21no—
557C3⋊C8—21no—
558C3⋊C8—61no—
559C3⋊C8—61no—
560C3⋊C8—121no—
561C2×C32C2×#12411yescharacteristic
562C2×C32C22×SD1611yescharacteristic
563C2×C32C22×Q1611yescharacteristic
564C3×D3#48714yescomplemented
565C2×Q8—31no—
566C2×Q8—31no—
567C2×Q8—61no—
568C2×Q8—61no—
569C2×Q8—62no—
570C2×Q8—62no—
571C2×Q8—91no—
572C2×Q8—181no—
573C2×Q8—181no—
574C2×Q8—181no—
575C2×Q8—182no—
576C2×Q8—182no—
577C2×Q8—181no—
578C2×Q8—364no—
579C2×Q8C2×D3211yescharacteristic
580C22×C4—31no—
581C22×C4—61no—
582C22×C4—61no—
583C22×C4—91no—
584C22×C4—91no—
585C22×C4—181no—
586C22×C4—181no—
587C2×C8—31no—
588C2×C8—31no—
589C2×C8—62no—
590C2×C8—91no—
591C2×C8—182no—
592C2×C8C2×D3211yescharacteristic
593C4⋊C4—31no—
594C4⋊C4—31no—
595C4⋊C4—61no—
596C4⋊C4—61no—
597C4⋊C4—61no—
598C4⋊C4—61no—
599C4⋊C4—91no—
600C4⋊C4—181no—
601C4⋊C4—181no—
602C4⋊C4—181no—
603C4⋊C4—181no—
604C4⋊C4—181no—
605C4⋊C4—181no—
606C4⋊C4—181no—
607C4⋊C4—181no—
608C4⋊C4—181no—
609C4⋊C4—181no—
610C4⋊C4C2×D3211yescharacteristic
611C42—31no—
612C42—91no—
613C42—91no—
614C42—91no—
615C22×C3—21no—
616C22×C3—32no—
617C22×C3—32no—
618C22×C3—32no—
619C22×C3C2×D3×D411yescharacteristic
620C22×C3C2×D3×D411yescharacteristic
621C2×D3#88512yes—
622C2×D3D3×SD1612yes—
623C2×D3D3×Q1612yes—
624C3×C4—21no—
625C3×C4—21no—
626C3×C4—32no—
627C3×C4—32no—
628C3×C4—32no—
629C3×C4—41no—
630C3×C4—41no—
631C3×C4—41no—
632C3×C4—41no—
633C3×C4—81no—
634C3×C4—81no—
635C3×C4—121no—
636C3×C4—121no—
637C3×C4—121no—
638C3×C4—121no—
639C3×C4C2×#23511yescharacteristic
640C3×C4C2×#23711yescharacteristic
641C3×C4D3×#4111yescharacteristic
642C3×C4D3×#4111yescharacteristic
643Dic3—32no—
644Dic3—32no—
645Dic3—32no—
646Dic3—32no—
647Dic3—41no—
648Dic3—41no—
649Dic3—41no—
650Dic3—41no—
651Dic3—62no—
652Dic3—62no—
653Dic3—121no—
654Dic3—121no—
655Dic3—121no—
656Dic3—121no—
657Dic3—241no—
658Dic3—241no—
659Dic3#88512yes—
660Dic3D3×SD1612yes—
661Dic3D3×Q1612yes—
662C32C2×#48711yescharacteristic, complemented, Sylow
663C23—31no—
664Q8—21no—
665Q8—21no—
666Q8—61no—
667Q8—61no—
668Q8—61no—
669Q8—61no—
670Q8—122no—
671Q8—122no—
672Q8—181no—
673Q8—181no—
674Q8—362no—
675Q8—362no—
676Q8—362no—
677Q8—362no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—31no—
681C2×C4—31no—
682C2×C4—31no—
683C2×C4—32no—
684C2×C4—32no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—94no—
690C2×C4—94no—
691C2×C4—91no—
692C2×C4—91no—
693C2×C4—122no—
694C2×C4—122no—
695C2×C4—181no—
696C2×C4—181no—
697C2×C4—362no—
698C2×C4—362no—
699C2×C4C22×D3211yescharacteristic
700C8—21no—
701C8—61no—
702C8—61no—
703C8—181no—
704C2×C3—21no—
705C2×C3—21no—
706C2×C3—21no—
707C2×C3—34no—
708C2×C3C2×#88511yescharacteristic
709C2×C3D3×#12411yescharacteristic
710C2×C3C2×D3×SD1611yescharacteristic
711C2×C3C2×D3×SD1611yescharacteristic
712C2×C3C2×D3×Q1611yescharacteristic
713C2×C3C2×D3×Q1611yescharacteristic
714D3#479214yesdirect product factor
715C22—32no—
716C22—32no—
717C22—32no—
718C22D32×D411yescharacteristic
719C4—32no—
720C4—32no—
721C4—32no—
722C4—41no—
723C4—41no—
724C4—92no—
725C4—92no—
726C4—121no—
727C4—121no—
728C4—121no—
729C4—121no—
730C4—361no—
731C4—361no—
732C4D3×#23511yescharacteristic
733C4D3×#23711yescharacteristic
734C3—21no—
735C3C2×#479211yescharacteristic, complemented
736C3D3×#48711yescharacteristic, complemented
737C2—34no—
738C2D3×#88511yescharacteristic
739C2D32×SD1611yescharacteristic
740C2D32×Q1611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenter#103D32
hypocenterC32C2×#487
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
3. #10592491C2semidirect
5. C3×#4792C2semidirect
6. #10591623C2semidirect
8. #10591538C2semidirect
9. #10590901C2semidirect
10. #10590890C2semidirect
14. #10590567C2semidirect
15. #10590560C2semidirect
89. #4792D3direct (N × H)
564. C3×D3#487semidirect
662. C32C2×#487semidirect
714. D3#4792direct (N × H)
735. C3C2×#4792semidirect
736. C3D3×#487semidirect

Maximal subgroups

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

subgroupindex
D3×#9442
D3×#8882
#105924912
C3×D3×#1032
C3×#47922
#105916232
D3×#8352
#105915382
#105909012
#105908902
D3×#8162
D3×C8×Dic32
D3×#8102
#105905672
#105905602
D3×#4873
C2×#47923