Finite Group Databasebeta

← D3×#4807 #11866715

Subgroups — D3×#4807 #11866715

Order 1152.

1190 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#946C211yesmaximal, characteristic, complemented
2C2×D3×#215C211yesmaximal, characteristic, complemented
3C2×D32×C8C211yesmaximal, characteristic, complemented
4D3×#895C211yesmaximal, characteristic
5#10592506C211yesmaximal, characteristic, complemented
6C3×#4807C211yesmaximal, characteristic, complemented
7C3×D3×#103C211yesmaximal, characteristic, complemented
8#10591591C211yesmaximal, characteristic, complemented
9#10591585C211yesmaximal, characteristic, complemented
10D3×#821C211yesmaximal, characteristic, complemented
11#10590847C211yesmaximal, characteristic, complemented
12#10590841C211yesmaximal, characteristic, complemented
13D3×#808C211yesmaximal, characteristic, complemented
14#10590523C211yesmaximal, characteristic, complemented
15#10590514C211yesmaximal, characteristic, complemented
16D3×#465—31nomaximal
17C2×#4807—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×D3×D12—21no—
20C2×D3×D12C2211yescharacteristic
21C2×C4×D32C2211yescharacteristic
22#64155C2211yescharacteristic, complemented
23C2×#3755C2211yescharacteristic, complemented
24C2×C8×C3⋊D3C2211yescharacteristic, complemented
25#64104C2211yescharacteristic
26C3×#946C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic, complemented
28C2×C3×D3×C8C2211yescharacteristic
29C2×C3×D3×C8C2211yescharacteristic, complemented
30C3×#895C2211yescharacteristic
31C3×D3×C4⋊C4C2211yescharacteristic
32D3×#215—24no—
33D3×(C2×D3)⋊C4—21no—
34D3×(C2×D3)⋊C4—21no—
35#63916C2211yescharacteristic
36#63910—21no—
37#63909C2211yescharacteristic
38D3×C4⋊Dic3C2211yescharacteristic
39#63888—21no—
40#63887—21no—
41#63886—21no—
42D3×Dic3⋊C4—21no—
43#63871C2211yescharacteristic, complemented
44#63856C2211yescharacteristic, complemented
45C2×#3717C2211yescharacteristic, complemented
46C2×#3715C2211yescharacteristic, complemented
47C2×#3710C2211yescharacteristic, complemented
48C2×D3×C3⋊C8C2211yescharacteristic
49C2×D3×C3⋊C8C2211yescharacteristic, complemented
50D32×C8—24no—
51C32×#103C2211yescharacteristic, complemented
52#63648C2211yescharacteristic, complemented
53#63635C2211yescharacteristic, complemented
54C3×#835C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic, complemented
56C3×#816C2211yescharacteristic, complemented
57C3×#810C2211yescharacteristic, complemented
58C3×#808C2211yescharacteristic, complemented
59#63574C2211yescharacteristic, complemented
60#63573C2211yescharacteristic, complemented
61#63564C2211yescharacteristic, complemented
62#63563C2211yescharacteristic, complemented
63C2×#946—31no—
64C22×#215—31no—
65C2×D3×SD16—31no—
66C22×D3×C8—31no—
67C22×D3×C8—31no—
68D3×C22⋊Q8—31no—
69D3×#121—31no—
70C2×#895—31no—
71C3×#465—31no—
72C2×C3×#103—31no—
73#5171—31no—
74#5114—31no—
75C2×#821—31no—
76#5048—31no—
77#5041—31no—
78C2×#808—31no—
79#4864—31no—
80D3×#106—31no—
81#4807—31no—
82#4807—31no—
83#4807—31no—
84#4807—31no—
85#4807—31no—
86#4807—31no—
87#4807—31no—
88#4807—31no—
89#4807—61no—
90#4807D311yescharacteristic, direct product factor
91D3×#103D311yescharacteristic, complemented
92#4778—31no—
93D3×#102—31no—
94C22×D32—21no—
95C22×D32D411yescharacteristic
96C2×C32×Q8C2311yescharacteristic
97C2×C4⋊(C3⋊D3)—21no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4×C3⋊D3C2311yescharacteristic
100C3×D3×Q8—22no—
101C3×D3×Q8—22no—
102C2×C3×D12—21no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6—21no—
109C2×C3×Dic6C2311yescharacteristic
110C2×#626—21no—
111C2×#626—21no—
112C2×#626—21no—
113C2×#624D411yescharacteristic
114C2×D3×Dic3—21no—
115C2×D3×Dic3D411yescharacteristic
116C2×D3×Dic3D411yescharacteristic
117D3×D12—22no—
118D3×D12—22no—
119D3×D12—44no—
120C4×D32—22no—
121C4×D32—22no—
122C2×C32×C8C2311yescharacteristic
123C32×C4⋊C4C2311yescharacteristic
124#3755—22no—
125#3752—21no—
126#3752—21no—
127C4⋊(C3⋊Dic3)C2311yescharacteristic
128#3750—21no—
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130C8×C3⋊D3—22no—
131C3×#215—22no—
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×C4⋊Dic3C2311yescharacteristic
135C3×C4⋊Dic3C2311yescharacteristic
136C3×Dic3⋊C4—21no—
137C3×Dic3⋊C4—21no—
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C3×D3×C8—22no—
141C3×D3×C8—22no—
142#3724—21no—
143Dic3⋊Dic3—21no—
144Dic3⋊Dic3—21no—
145#3722—21no—
146#3722—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149#3717—22no—
150#3715—22no—
151#3710—22no—
152D3×C3⋊C8—22no—
153D3×C3⋊C8D414yescomplemented
154C2×#465—91noSylow
155C22×C3×Q8—31no—
156C2×D3×Q8C2×D311yescharacteristic
157C2×D3×D4—31no—
158C2×D3×D4—61no—
159C22×D12—31no—
160C22×D12—61no—
161C22×C4×D3—31no—
162C22×C4×D3—31no—
163C2×C3×SD16—31no—
164C22×C3×C8—31no—
165C22×C3×C8—31no—
166C3×C22⋊Q8—31no—
167C3×#121—31no—
168C2×C3×C4⋊C4—31no—
169#946—31no—
170#946—31no—
171#946—31no—
172#946—31no—
173#946—61no—
174#946—61no—
175#946—61no—
176#946C2×D311yescharacteristic, complemented
177C2×#215—31no—
178C2×#215—31no—
179C2×#215—31no—
180C2×#215—31no—
181C2×#215—61no—
182C2×#215—64no—
183C2×#215C2×D311yescharacteristic, complemented
184#939—61no—
185#938—31no—
186C2×#214—31no—
187#930—31no—
188C2×(C2×D3)⋊C4—61no—
189C2×(C2×D3)⋊C4—61no—
190C2×C4⋊Dic3—31no—
191#924—31no—
192C2×Dic3⋊C4—61no—
193C22×C3⋊C8—31no—
194C22×C3⋊C8—31no—
195D3×SD16—64no—
196C2×#204—31no—
197C2×D3×C8—31no—
198C2×D3×C8—31no—
199C2×D3×C8—31no—
200C2×D3×C8—31no—
201C2×D3×C8—31no—
202C2×D3×C8—31no—
203C2×D3×C8—61no—
204C2×D3×C8—64no—
205C2×D3×C8—64no—
206C2×D3×C8C2×D311yescharacteristic
207C2×D3×C8C2×D311yescharacteristic, complemented
208#897—31no—
209#896—61no—
210#895—31no—
211#895—31no—
212#895—31no—
213#895—31no—
214#895—61no—
215#895—61no—
216#895—61no—
217#895C2×D311yescharacteristic
218D3×C4⋊C4—31no—
219D3×C4⋊C4—61no—
220D3×C4⋊C4C2×D311yescharacteristic
221#884—61no—
222D3×C22⋊C4—61no—
223D3×C22⋊C4—61no—
224#878—61no—
225C3×#106—31no—
226C3×#103—21no—
227C3×#103—31no—
228C3×#103—31no—
229C3×#103—31no—
230C3×#103C2×D311yescharacteristic, complemented
231C3×#103C2×D311yescharacteristic, complemented
232C3×#102—31no—
233#835C2×D311yescharacteristic, complemented
234#832—31no—
235#821—31no—
236#821—31no—
237#821—31no—
238#821—31no—
239#821—61no—
240#821C2×D311yescharacteristic, complemented
241#817—31no—
242#816C2×D311yescharacteristic, complemented
243#810C2×D311yescharacteristic, complemented
244#809—31no—
245#808—31no—
246#808—31no—
247#808—31no—
248#808—31no—
249#808—31no—
250#808—61no—
251#808C2×D311yescharacteristic, complemented
252C22×C3⋊D3—21no—
253C22×C3⋊D3C2×D411yescharacteristic
254C22×C3×D3—21no—
255C22×C3×D3C2×D411yescharacteristic
256C22×C3×D3C2×D411yescharacteristic
257C2×D32—22no—
258C2×D32—22no—
259C2×D32—42no—
260C2×D32—42no—
261C2×D32—42no—
262C2×D32SD1614yescomplemented
263C32×Q8—21no—
264C32×Q8—21no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4C2411yescharacteristic
268C2×C3⋊Dic3—21no—
269C2×C3⋊Dic3C2×D411yescharacteristic
270C4⋊(C3⋊D3)—21no—
271C4⋊(C3⋊D3)—21no—
272C4⋊(C3⋊D3)—42no—
273C4×C3⋊D3—21no—
274C4×C3⋊D3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3C2×D411yescharacteristic
279C2×C3×Dic3C2×D411yescharacteristic
280C3×D12—21no—
281C3×D12—21no—
282C3×D12—42no—
283C3×C4×D3—21no—
284C3×C4×D3—21no—
285C3×C4×D3—42no—
286C3×C4×D3—42no—
287C3×C4×D3C2×D412yes—
288C3×C4×D3#4112yes—
289C3×Dic6—21no—
290C3×Dic6—21no—
291C3×Dic6—42no—
292#626—42no—
293#626—42no—
294#626—42no—
295#624—22no—
296D3×Dic3—22no—
297D3×Dic3—22no—
298D3×Dic3—42no—
299C32×C8—21no—
300C3⋊(C3⋊C8)C2×D412yescomplemented
301C3×C3⋊C8—21no—
302C3×C3⋊C8C2×D412yescomplemented
303C22×SD16—91no—
304C23×C8—91no—
305C2×C22⋊Q8—91no—
306C2×#121—91no—
307#465—31no—
308#465—91no—
309#465—91no—
310#465—91no—
311#465—91no—
312#465—91no—
313#465—91no—
314#465—91no—
315C2×#106—91no—
316C2×#103—31no—
317C2×#102—91no—
318C23×D3—31no—
319C23×D3—31no—
320C23×D3—61no—
321C23×D3—61no—
322C2×C3×Q8—21no—
323C2×C3×Q8—31no—
324C2×C3×Q8—61no—
325C2×C3×Q8—62no—
326C2×C3×Q8—62no—
327C2×C3×Q8C22×D311yescharacteristic
328C2×C3×Q8C22×D311yescharacteristic
329C2×C3×D4—31no—
330C2×C3×D4—61no—
331C22×C3×C4—31no—
332C22×C3×C4—31no—
333C22×C3×C4—61no—
334C22×C3×C4—61no—
335C2×#67—61no—
336C2×#67—61no—
337C2×#67—61no—
338C22×Dic3—31no—
339C22×Dic3—31no—
340C22×Dic3—61no—
341D3×Q8—22no—
342D3×Q8—22no—
343D3×D4—62no—
344D3×D4—62no—
345D3×D4—124no—
346C2×D12—21no—
347C2×D12—31no—
348C2×D12—31no—
349C2×D12—61no—
350C2×D12—62no—
351C2×D12—62no—
352C2×D12—61no—
353C2×D12—61no—
354C2×D12—61no—
355C2×D12—61no—
356C2×D12—61no—
357C2×D12—121no—
358C2×D12—124no—
359C2×D12C22×D311yescharacteristic
360C2×C4×D3—21no—
361C2×C4×D3—21no—
362C2×C4×D3—31no—
363C2×C4×D3—31no—
364C2×C4×D3—31no—
365C2×C4×D3—31no—
366C2×C4×D3—31no—
367C2×C4×D3—31no—
368C2×C4×D3—61no—
369C2×C4×D3—62no—
370C2×C4×D3—62no—
371C2×C4×D3—62no—
372C2×C4×D3—62no—
373C2×C4×D3—61no—
374C2×C4×D3C22×D311yescharacteristic
375C2×C4×D3C22×D311yescharacteristic
376C2×Dic6—21no—
377C2×Dic6C22×D311yescharacteristic
378C3×SD16—62no—
379C2×C3×C8—21no—
380C2×C3×C8—31no—
381C2×C3×C8—31no—
382C2×C3×C8—62no—
383C2×C3×C8—62no—
384C2×C3×C8C22×D311yescharacteristic
385C2×C3×C8C22×D311yescharacteristic
386C3×C4⋊C4—21no—
387C3×C4⋊C4—31no—
388C3×C4⋊C4—31no—
389C3×C4⋊C4—61no—
390C3×C4⋊C4—61no—
391C3×C4⋊C4C22×D311yescharacteristic
392C3×C4⋊C4C22×D311yescharacteristic
393C3×C22⋊C4—61no—
394C3×C22⋊C4—61no—
395#217—61no—
396#217—61no—
397#215—22no—
398#215—62no—
399#215—62no—
400#215—62no—
401#215—62no—
402#215—122no—
403#214—62no—
404(C2×D3)⋊C4—21no—
405(C2×D3)⋊C4—21no—
406(C2×D3)⋊C4—61no—
407(C2×D3)⋊C4—61no—
408(C2×D3)⋊C4—61no—
409(C2×D3)⋊C4—61no—
410(C2×D3)⋊C4—61no—
411(C2×D3)⋊C4—61no—
412(C2×D3)⋊C4—61no—
413(C2×D3)⋊C4—61no—
414(C2×D3)⋊C4—61no—
415(C2×D3)⋊C4—61no—
416(C2×D3)⋊C4—121no—
417(C2×D3)⋊C4—121no—
418C4⋊Dic3—31no—
419C4⋊Dic3—31no—
420C4⋊Dic3—61no—
421C4⋊Dic3—61no—
422C4⋊Dic3—61no—
423C4⋊Dic3C22×D311yescharacteristic
424C4⋊Dic3C22×D311yescharacteristic
425Dic3⋊C4—21no—
426Dic3⋊C4—21no—
427Dic3⋊C4—61no—
428Dic3⋊C4—61no—
429Dic3⋊C4—61no—
430Dic3⋊C4—61no—
431Dic3⋊C4—61no—
432Dic3⋊C4—61no—
433Dic3⋊C4—121no—
434C2×C3⋊C8—31no—
435C2×C3⋊C8—31no—
436C2×C3⋊C8—34no—
437C2×C3⋊C8—61no—
438C2×C3⋊C8—62no—
439C2×C3⋊C8C22×D311yescharacteristic
440C2×C3⋊C8C22×D311yescharacteristic
441#204—62no—
442D3×C8—22no—
443D3×C8—22no—
444D3×C8—34no—
445D3×C8—62no—
446D3×C8—62no—
447D3×C8—62no—
448D3×C8—62no—
449D3×C8—62no—
450D3×C8—122no—
451C22×C32C22×D411yescharacteristic
452C2×C3⋊D3—21no—
453C2×C3⋊D3—21no—
454C2×C3⋊D3—41no—
455C2×C3⋊D3—41no—
456C2×C3⋊D3—41no—
457C2×C3⋊D3C2×SD1612yescomplemented
458C2×C3×D3—21no—
459C2×C3×D3—21no—
460C2×C3×D3—41no—
461C2×C3×D3—41no—
462C2×C3×D3—41no—
463C2×C3×D3#12112yes—
464C2×C3×D3C2×SD1612yes—
465C2×C3×D3C2×SD1612yescomplemented
466C2×C3×D3#13512yes—
467D32—28no—
468D32—84no—
469C32×C4—41no—
470C32×C4—41no—
471C32×C4C22×D411yescharacteristic
472C32×C4C2×#4111yescharacteristic
473C3⋊Dic3—21no—
474C3⋊Dic3—41no—
475C3×Dic3—21no—
476C3×Dic3—41no—
477C3×Dic3—41no—
478C3×Dic3—41no—
479C3×Dic3#12112yes—
480C22×Q8—31no—
481C22×D4—91no—
482C22×D4—181no—
483C23×C4—91no—
484C2×SD16—31no—
485C2×SD16—91no—
486C2×SD16—91no—
487C2×SD16—91no—
488C2×SD16—184no—
489C22×C8—31no—
490C22×C8—31no—
491C22×C8—91no—
492C22×C8—91no—
493C22×C8—91no—
494C22×C8—91no—
495C22×C8—184no—
496C22⋊Q8—31no—
497C22⋊Q8—91no—
498C22⋊Q8—91no—
499C22⋊Q8—91no—
500C22⋊Q8—181no—
501C22⋊Q8—181no—
502#121—31no—
503#121—91no—
504#121—91no—
505#121—91no—
506#121—181no—
507#121—181no—
508C2×C4⋊C4—31no—
509C2×C4⋊C4—91no—
510C2×C4⋊C4—181no—
511C2×C22⋊C4—181no—
512C2×C22⋊C4—181no—
513#106—31no—
514#106—91no—
515#106—91no—
516#106—91no—
517#103—31no—
518#103—31no—
519#103—31no—
520#103D3211yescharacteristic, complemented
521#102—31no—
522#102—91no—
523#102—91no—
524#102—91no—
525C23×C3—31no—
526C23×C3—31no—
527C23×C3—61no—
528C22×D3—21no—
529C22×D3—31no—
530C22×D3—31no—
531C22×D3—34no—
532C22×D3—34no—
533C22×D3—61no—
534C22×D3—62no—
535C22×D3—62no—
536C22×D3—62no—
537C22×D3—62no—
538C22×D3—61no—
539C22×D3—61no—
540C22×D3—121no—
541C22×D3—122no—
542C22×D3—122no—
543C22×D3—122no—
544C22×D3—122no—
545C22×D3—122no—
546C22×D3—122no—
547C22×D3D3×D411yescharacteristic
548C22×D3D3×D411yescharacteristic
549C3×Q8—21no—
550C3×Q8—21no—
551C3×Q8—21no—
552C3×Q8—21no—
553C3×Q8—41no—
554C3×Q8—41no—
555C3×Q8—61no—
556C3×Q8—61no—
557C3×Q8—122no—
558C3×D4—61no—
559C3×D4—61no—
560C3×D4—122no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—31no—
567C2×C3×C4—32no—
568C2×C3×C4—32no—
569C2×C3×C4—31no—
570C2×C3×C4—41no—
571C2×C3×C4—41no—
572C2×C3×C4—61no—
573C2×C3×C4—61no—
574C2×C3×C4—61no—
575C2×C3×C4—61no—
576C2×C3×C4—61no—
577C2×C3×C4—122no—
578C2×C3×C4—122no—
579C2×C3×C4C23×D311yescharacteristic
580C2×C3×C4C23×D311yescharacteristic
581#67—122no—
582#67—122no—
583#67—122no—
584C2×Dic3—21no—
585C2×Dic3—21no—
586C2×Dic3—21no—
587C2×Dic3—31no—
588C2×Dic3—31no—
589C2×Dic3—61no—
590C2×Dic3—62no—
591C2×Dic3—62no—
592C2×Dic3—61no—
593C2×Dic3—61no—
594C2×Dic3—121no—
595C2×Dic3—122no—
596C2×Dic3D3×D411yescharacteristic
597C2×Dic3D3×D411yescharacteristic
598D12—21no—
599D12—21no—
600D12—42no—
601D12—61no—
602D12—61no—
603D12—61no—
604D12—61no—
605D12—121no—
606D12—121no—
607D12—122no—
608D12—122no—
609D12—122no—
610D12—122no—
611D12—122no—
612D12—242no—
613C4×D3—21no—
614C4×D3—21no—
615C4×D3—42no—
616C4×D3—42no—
617C4×D3—62no—
618C4×D3—62no—
619C4×D3—62no—
620C4×D3—61no—
621C4×D3—61no—
622C4×D3—61no—
623C4×D3—61no—
624C4×D3—62no—
625C4×D3—121no—
626C4×D3—121no—
627C4×D3—122no—
628C4×D3#23512yes—
629C4×D3D3×D412yes—
630Dic6—21no—
631Dic6—21no—
632Dic6—42no—
633C3×C8—21no—
634C3×C8—21no—
635C3×C8—32no—
636C3×C8—41no—
637C3×C8—61no—
638C3⋊C8—21no—
639C3⋊C8—32no—
640C3⋊C8—32no—
641C3⋊C8—62no—
642C3⋊C8D3×D412yescomplemented
643C2×C32C2×#12111yescharacteristic
644C2×C32C22×SD1611yescharacteristic
645C2×C32C2×#13511yescharacteristic
646C3⋊D3—22no—
647C3⋊D3—81no—
648C3×D3—22no—
649C3×D3—81no—
650C3×D3#46514yescomplemented
651C24—91no—
652C24—181no—
653C2×Q8—31no—
654C2×Q8—61no—
655C2×Q8—62no—
656C2×Q8—62no—
657C2×Q8C2×D3211yescharacteristic
658C2×D4—31no—
659C2×D4—61no—
660C2×D4—91no—
661C2×D4—181no—
662C2×D4—182no—
663C2×D4—182no—
664C2×D4—181no—
665C2×D4—181no—
666C2×D4—181no—
667C2×D4—364no—
668C22×C4—31no—
669C22×C4—31no—
670C22×C4—61no—
671C22×C4—61no—
672C22×C4—91no—
673C22×C4—91no—
674C22×C4—91no—
675C22×C4—91no—
676C22×C4—182no—
677C22×C4—182no—
678C22×C4—181no—
679SD16—62no—
680SD16—182no—
681SD16—182no—
682SD16—182no—
683C2×C8—31no—
684C2×C8—31no—
685C2×C8—62no—
686C2×C8—62no—
687C2×C8—94no—
688C2×C8—91no—
689C2×C8—182no—
690C2×C8—182no—
691C2×C8—182no—
692C2×C8C2×D3211yescharacteristic
693C4⋊C4—31no—
694C4⋊C4—31no—
695C4⋊C4—61no—
696C4⋊C4—61no—
697C4⋊C4—91no—
698C4⋊C4—181no—
699C4⋊C4—181no—
700C4⋊C4—181no—
701C4⋊C4—181no—
702C4⋊C4C2×D3211yescharacteristic
703C22⋊C4—61no—
704C22⋊C4—61no—
705C22⋊C4—181no—
706C22⋊C4—181no—
707C22⋊C4—181no—
708C22⋊C4—181no—
709C22⋊C4—181no—
710C22⋊C4—181no—
711C22×C3—21no—
712C22×C3—32no—
713C22×C3—32no—
714C22×C3—32no—
715C22×C3—32no—
716C22×C3—61no—
717C22×C3—61no—
718C22×C3—121no—
719C22×C3—121no—
720C22×C3—121no—
721C22×C3C2×D3×D411yescharacteristic
722C22×C3C2×D3×D411yescharacteristic
723C2×D3—21no—
724C2×D3—21no—
725C2×D3—32no—
726C2×D3—32no—
727C2×D3—41no—
728C2×D3—41no—
729C2×D3—41no—
730C2×D3—62no—
731C2×D3—68no—
732C2×D3—61no—
733C2×D3—61no—
734C2×D3—61no—
735C2×D3—61no—
736C2×D3—68no—
737C2×D3—121no—
738C2×D3—121no—
739C2×D3—121no—
740C2×D3—121no—
741C2×D3—121no—
742C2×D3—121no—
743C2×D3—121no—
744C2×D3—121no—
745C2×D3—241no—
746C2×D3—241no—
747C2×D3—241no—
748C2×D3—244no—
749C2×D3—244no—
750C2×D3#88412yes—
751C2×D3D3×SD1612yes—
752C2×D3D3×SD1612yescomplemented
753C2×D3#91912yes—
754C3×C4—21no—
755C3×C4—21no—
756C3×C4—32no—
757C3×C4—41no—
758C3×C4—41no—
759C3×C4—41no—
760C3×C4—41no—
761C3×C4—61no—
762C3×C4—81no—
763C3×C4—81no—
764C3×C4—121no—
765C3×C4—121no—
766C3×C4—121no—
767C3×C4C2×#23511yescharacteristic
768C3×C4C2×D3×D411yescharacteristic
769C3×C4C2×D3×D411yescharacteristic
770C3×C4D3×#4111yescharacteristic
771Dic3—21no—
772Dic3—41no—
773Dic3—41no—
774Dic3—41no—
775Dic3—61no—
776Dic3—61no—
777Dic3—121no—
778Dic3—121no—
779Dic3—121no—
780Dic3—241no—
781Dic3#88412yes—
782C32C2×#46511yescharacteristic, complemented, Sylow
783C23—31no—
784C23—31no—
785C23—61no—
786C23—94no—
787C23—91no—
788C23—182no—
789C23—182no—
790C23—181no—
791C23—362no—
792C23—362no—
793C23—362no—
794Q8—21no—
795Q8—21no—
796Q8—61no—
797Q8—61no—
798Q8—122no—
799D4—61no—
800D4—61no—
801D4—122no—
802D4—181no—
803D4—181no—
804D4—362no—
805D4—362no—
806D4—362no—
807D4—362no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—31no—
811C2×C4—32no—
812C2×C4—32no—
813C2×C4—31no—
814C2×C4—61no—
815C2×C4—61no—
816C2×C4—61no—
817C2×C4—61no—
818C2×C4—61no—
819C2×C4—91no—
820C2×C4—122no—
821C2×C4—122no—
822C2×C4—182no—
823C2×C4—182no—
824C2×C4—182no—
825C2×C4—181no—
826C2×C4—181no—
827C2×C4—181no—
828C2×C4—362no—
829C2×C4C22×D3211yescharacteristic
830C8—21no—
831C8—32no—
832C8—61no—
833C8—92no—
834C2×C3—21no—
835C2×C3—21no—
836C2×C3—21no—
837C2×C3—34no—
838C2×C3—62no—
839C2×C3—241no—
840C2×C3C2×#88411yescharacteristic
841C2×C3D3×#12111yescharacteristic
842C2×C3C2×D3×SD1611yescharacteristic
843C2×C3C2×D3×SD1611yescharacteristic
844C2×C3C2×#91911yescharacteristic
845C2×C3D3×#13511yescharacteristic
846D3—22no—
847D3—62no—
848D3—62no—
849D3—81no—
850D3—122no—
851D3—241no—
852D3—241no—
853D3—481no—
854D3#480714yesdirect product factor
855C22—32no—
856C22—32no—
857C22—32no—
858C22—32no—
859C22—61no—
860C22—61no—
861C22—92no—
862C22—121no—
863C22—121no—
864C22—121no—
865C22—188no—
866C22—181no—
867C22—181no—
868C22—361no—
869C22—361no—
870C22—361no—
871C22—724no—
872C22D32×D411yescharacteristic
873C4—32no—
874C4—41no—
875C4—41no—
876C4—61no—
877C4—121no—
878C4—121no—
879C4—121no—
880C4—181no—
881C4—361no—
882C4D3×#23511yescharacteristic
883C4D32×D411yescharacteristic
884C3—21no—
885C3C2×#480711yescharacteristic, complemented
886C3D3×#46511yescharacteristic, complemented
887C2—34no—
888C2—62no—
889C2—182no—
890C2—241no—
891C2—721no—
892C2D3×#88411yescharacteristic
893C2D32×SD1611yescharacteristic
894C2D3×#91911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalD3×#895C2
hypercenter#103D32
hypocenterC32C2×#465
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
1. D3×#946C2semidirect
2. C2×D3×#215C2semidirect
3. C2×D32×C8C2semidirect
5. #10592506C2semidirect
6. C3×#4807C2semidirect
7. C3×D3×#103C2semidirect
8. #10591591C2semidirect
9. #10591585C2semidirect
10. D3×#821C2semidirect
11. #10590847C2semidirect
12. #10590841C2semidirect
13. D3×#808C2semidirect
14. #10590523C2semidirect
15. #10590514C2semidirect
22. #64155C22semidirect
23. C2×#3755C22semidirect
24. C2×C8×C3⋊D3C22semidirect
26. C3×#946C22semidirect
27. C2×C3×#215C22semidirect
29. C2×C3×D3×C8C22semidirect
43. #63871C22semidirect
44. #63856C22semidirect
45. C2×#3717C22semidirect
46. C2×#3715C22semidirect
47. C2×#3710C22semidirect
49. C2×D3×C3⋊C8C22semidirect
51. C32×#103C22semidirect
52. #63648C22semidirect
53. #63635C22semidirect
54. C3×#835C22semidirect
55. C3×#821C22semidirect
56. C3×#816C22semidirect
57. C3×#810C22semidirect
58. C3×#808C22semidirect
59. #63574C22semidirect
60. #63573C22semidirect
61. #63564C22semidirect
62. #63563C22semidirect
90. #4807D3direct (N × H)
91. D3×#103D3semidirect
153. D3×C3⋊C8D4semidirect
176. #946C2×D3semidirect
183. C2×#215C2×D3semidirect
207. C2×D3×C8C2×D3semidirect
230. C3×#103C2×D3semidirect
231. C3×#103C2×D3semidirect
233. #835C2×D3semidirect
240. #821C2×D3semidirect
242. #816C2×D3semidirect
243. #810C2×D3semidirect
251. #808C2×D3semidirect
262. C2×D32SD16semidirect
300. C3⋊(C3⋊C8)C2×D4semidirect
302. C3×C3⋊C8C2×D4semidirect
457. C2×C3⋊D3C2×SD16semidirect
465. C2×C3×D3C2×SD16semidirect
520. #103D32semidirect
642. C3⋊C8D3×D4semidirect
650. C3×D3#465semidirect
752. C2×D3D3×SD16semidirect
782. C32C2×#465semidirect
854. D3#4807direct (N × H)
885. C3C2×#4807semidirect
886. C3D3×#465semidirect

Maximal subgroups

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

subgroupindex
D3×#9462
C2×D3×#2152
C2×D32×C82
D3×#8952
#105925062
C3×#48072
C3×D3×#1032
#105915912
#105915852
D3×#8212
#105908472
#105908412
D3×#8082
#105905232
#105905142
D3×#4653
C2×#48073