Finite Group Databasebeta

← D3×#4818 #11865501

Subgroups — D3×#4818 #11865501

Order 1152.

1148 conjugacy classes of subgroups.

The subgroup lattice has 853 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#944C211yesmaximal, characteristic, complemented
2C2×D3×#215C211yesmaximal, characteristic
3C2×D3×#204C211yesmaximal, characteristic
4D3×#893C211yesmaximal, characteristic
5#10592517C211yesmaximal, characteristic, complemented
6C3×#4818C211yesmaximal, characteristic, complemented
7C3×D3×#103C211yesmaximal, characteristic, complemented
8#10591569C211yesmaximal, characteristic, complemented
9#10591565C211yesmaximal, characteristic, complemented
10#10590760C211yesmaximal, characteristic, complemented
11#10590748C211yesmaximal, characteristic, complemented
12D3×Dic3⋊C8C211yesmaximal, characteristic, complemented
13D3×#810C211yesmaximal, characteristic, complemented
14#10590565C211yesmaximal, characteristic, complemented
15#10590559C211yesmaximal, characteristic, complemented
16D3×#461—31nomaximal
17C2×#4818—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C2×C4×D32—21no—
21C2×D3×Dic6C2211yescharacteristic
22#64153C2211yescharacteristic, complemented
23C2×#3755C2211yescharacteristic
24C2×#3744C2211yescharacteristic
25#64102C2211yescharacteristic
26C3×#944C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic
28C2×C3×#204C2211yescharacteristic
29C2×C3×D3×C8C2211yescharacteristic
30C3×#893C2211yescharacteristic
31C3×D3×C4⋊C4C2211yescharacteristic
32D3×#215—24no—
33D3×(C2×D3)⋊C4—21no—
34#63904—21no—
35#63898C2211yescharacteristic
36#63894C2211yescharacteristic
37#63881—21no—
38D3×Dic3⋊C4—21no—
39D3×Dic3⋊C4—21no—
40C4×D3×Dic3C2211yescharacteristic
41#63873C2211yescharacteristic, complemented
42#63866C2211yescharacteristic, complemented
43#63839—21no—
44#63839—21no—
45C2×#3717C2211yescharacteristic
46C2×#3717C2211yescharacteristic
47C2×#3716C2211yescharacteristic
48C2×#3715C2211yescharacteristic
49C2×D3×C3⋊C8C2211yescharacteristic
50D3×#204—24no—
51C32×#103C2211yescharacteristic, complemented
52#63641C2211yescharacteristic, complemented
53#63637C2211yescharacteristic, complemented
54C3×#835C2211yescharacteristic, complemented
55C3×#816C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57C3×#810C2211yescharacteristic, complemented
58C3×#810C2211yescharacteristic, complemented
59#63572C2211yescharacteristic, complemented
60Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
61#63567C2211yescharacteristic, complemented
62#63565C2211yescharacteristic, complemented
63C2×#944—31no—
64C22×#215—31no—
65C2×D3×SD16—31no—
66C2×D3×SD16—31no—
67C22×#204—31no—
68D3×C4⋊Q8—31no—
69C4×D3×D4—31no—
70C2×#893—31no—
71C3×#461—31no—
72C2×C3×#103—31no—
73#5162—31no—
74#5162—31no—
75C2×Dic3⋊C8—31no—
76#5083—31no—
77#5019—31no—
78C2×#810—31no—
79#4841—31no—
80D3×C4⋊C8—31no—
81#4818—31no—
82#4818—31no—
83#4818—31no—
84#4818—31no—
85#4818—31no—
86#4818—31no—
87#4818—31no—
88#4818—31no—
89#4818—31no—
90#4818—61no—
91#4818D311yescharacteristic, direct product factor
92D3×#103—31no—
93D3×#103D311yescharacteristic, complemented
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4×C3⋊D3—21no—
98C2×#634C2311yescharacteristic
99C3×D3×Q8—22no—
100C3×D3×Q8—22no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6—21no—
107C2×C3×Dic6C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×#627—21no—
110C2×#626—21no—
111C2×#624—21no—
112C2×D3×Dic3—21no—
113C2×D3×Dic3—21no—
114C2×D3×Dic3D411yescharacteristic
115C2×D3×Dic3D411yescharacteristic
116D3×D12—22no—
117D3×D12D414yes—
118C4×D32—44no—
119D3×Dic6—22no—
120D3×Dic6—22no—
121C2×C32×C8C2311yescharacteristic
122C32×C4⋊C4C2311yescharacteristic
123#3755—22no—
124#3752—21no—
125#3750—21no—
126#3750—21no—
127C4×C3⋊Dic3C2311yescharacteristic
128C2×C3⋊(C3⋊C8)C2311yescharacteristic
129#3744—22no—
130C3×#215—22no—
131C3×(C2×D3)⋊C4—21no—
132C3×C4⋊Dic3C2311yescharacteristic
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4—21no—
136C3×C4×Dic3C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C3×#204—22no—
140C3×D3×C8—22no—
141#3724—21no—
142#3724—21no—
143Dic3⋊Dic3—21no—
144Dic3⋊Dic3—21no—
145#3722—21no—
146(C2×D3)⋊Dic3—21no—
147Dic32D411yescharacteristic
148Dic32D411yescharacteristic
149#3717—22no—
150#3717—22no—
151#3716—22no—
152#3715—22no—
153D3×C3⋊C8—22no—
154C2×#461—91noSylow
155C22×C3×Q8—31no—
156C2×D3×Q8—31no—
157C2×D3×Q8C2×D311yescharacteristic
158C2×D3×D4—31no—
159C22×D12—31no—
160C22×C4×D3—61no—
161C22×C4×D3—61no—
162C22×Dic6—31no—
163C2×C3×SD16—31no—
164C2×C3×SD16—31no—
165C22×C3×C8—31no—
166C3×C4⋊Q8—31no—
167C3×C4×D4—31no—
168C2×C3×C4⋊C4—31no—
169#944—31no—
170#944—31no—
171#944—31no—
172#944—31no—
173#944—31no—
174#944—61no—
175#944—61no—
176#944—61no—
177#944C2×D311yescharacteristic, complemented
178C2×#215—31no—
179C2×#215—31no—
180C2×#215—31no—
181C2×#215—31no—
182C2×#215—31no—
183C2×#215—61no—
184C2×#215—64no—
185C2×#215C2×D311yescharacteristic
186D4×Dic3—31no—
187C2×#214—31no—
188C2×#214—31no—
189C4×#67—61no—
190C2×(C2×D3)⋊C4—61no—
191C2×Dic3⋊C4—61no—
192C2×Dic3⋊C4—61no—
193C2×C4×Dic3—31no—
194C22×C3⋊C8—31no—
195D3×SD16—64no—
196D3×SD16—64no—
197C2×#204—31no—
198C2×#204—31no—
199C2×#204—31no—
200C2×#204—31no—
201C2×#204—31no—
202C2×#204—61no—
203C2×#204—64no—
204C2×#204C2×D311yescharacteristic
205C2×D3×C8—31no—
206C2×D3×C8C2×D311yescharacteristic
207#893—31no—
208#893—31no—
209#893—31no—
210#893—31no—
211#893—61no—
212#893—61no—
213#893—61no—
214#893C2×D311yescharacteristic
215D3×C4⋊C4—61no—
216D3×C4⋊C4—61no—
217D3×C4⋊C4C2×D311yescharacteristic
218#888—61no—
219#888—61no—
220#67⋊C4—61no—
221D3×C22⋊C4—61no—
222C4×D12—31no—
223C42×D3—31no—
224#869—31no—
225C3×C4⋊C8—31no—
226C3×#103—21no—
227C3×#103—31no—
228C3×#103—31no—
229C3×#103—31no—
230C3×#103—31no—
231C3×#103C2×D311yescharacteristic, complemented
232C3×#103C2×D311yescharacteristic, complemented
233#835—31no—
234#835C2×D311yescharacteristic, complemented
235#816—31no—
236#816C2×D311yescharacteristic, complemented
237Dic3⋊C8—31no—
238Dic3⋊C8—31no—
239Dic3⋊C8—31no—
240Dic3⋊C8—31no—
241Dic3⋊C8—31no—
242Dic3⋊C8—61no—
243Dic3⋊C8C2×D311yescharacteristic, complemented
244#810—31no—
245#810—31no—
246#810—31no—
247#810—31no—
248#810—61no—
249#810C2×D311yescharacteristic, complemented
250#810C2×D311yescharacteristic, complemented
251C4⋊(C3⋊C8)—31no—
252C22×C3⋊D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3C2×D411yescharacteristic
255C2×D32—24no—
256C2×D32—42no—
257C2×D32—42no—
258C32×Q8—21no—
259C32×Q8—21no—
260C2×C32×C4—21no—
261C2×C32×C4—21no—
262C2×C32×C4C2411yescharacteristic
263C2×C3⋊Dic3—21no—
264C2×C3⋊Dic3C2×D411yescharacteristic
265C2×C3⋊Dic3C2×D411yescharacteristic
266C4⋊(C3⋊D3)—21no—
267C4⋊(C3⋊D3)C2×D412yes—
268C4×C3⋊D3—42no—
269#634—21no—
270#634—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3C2×D411yescharacteristic
275C2×C3×Dic3C2×D411yescharacteristic
276C2×C3×Dic3C2×D411yescharacteristic
277C3×D12—21no—
278C3×D12C2×D412yes—
279C3×C4×D3—42no—
280C3×C4×D3—42no—
281C3×C4×D3—42no—
282C3×C4×D3C2×D412yes—
283C3×C4×D3#4112yes—
284C3×Dic6—21no—
285C3×Dic6—21no—
286C3×Dic6—21no—
287C3×Dic6—21no—
288C3×Dic6—42no—
289#627—42no—
290#626—24no—
291#624—42no—
292D3×Dic3—22no—
293D3×Dic3—42no—
294D3×Dic3—42no—
295D3×Dic3SD1614yescomplemented
296C32×C8—21no—
297C3⋊(C3⋊C8)—21no—
298C3×C3⋊C8—21no—
299C3×C3⋊C8—21no—
300C22×SD16—91no—
301C22×SD16—91no—
302C2×C4⋊Q8—91no—
303C2×C4×D4—91no—
304#461—31no—
305#461—91no—
306#461—91no—
307#461—91no—
308#461—91no—
309#461—91no—
310#461—91no—
311#461—91no—
312C2×C4⋊C8—91no—
313C2×#103—31no—
314C2×#103—91no—
315C23×D3—61no—
316C23×D3—61no—
317C2×C3×Q8—21no—
318C2×C3×Q8—31no—
319C2×C3×Q8—31no—
320C2×C3×Q8—61no—
321C2×C3×Q8—62no—
322C2×C3×Q8—62no—
323C2×C3×Q8C22×D311yescharacteristic
324C2×C3×Q8C22×D311yescharacteristic
325C2×C3×D4—31no—
326C22×C3×C4—31no—
327C22×C3×C4—61no—
328C22×C3×C4—61no—
329C22×C3×C4—61no—
330C2×#67—61no—
331C22×Dic3—31no—
332C22×Dic3—31no—
333C22×Dic3—61no—
334C22×Dic3—61no—
335D3×Q8—22no—
336D3×Q8—22no—
337D3×Q8—62no—
338D3×Q8—62no—
339D3×D4—34no—
340D3×D4—62no—
341C2×D12—31no—
342C2×D12—31no—
343C2×D12—34no—
344C2×D12—61no—
345C2×D12—62no—
346C2×D12—61no—
347C2×D12C22×D311yescharacteristic
348C2×C4×D3—21no—
349C2×C4×D3—21no—
350C2×C4×D3—21no—
351C2×C4×D3—31no—
352C2×C4×D3—31no—
353C2×C4×D3—61no—
354C2×C4×D3—61no—
355C2×C4×D3—61no—
356C2×C4×D3—61no—
357C2×C4×D3—61no—
358C2×C4×D3—61no—
359C2×C4×D3—121no—
360C2×C4×D3—124no—
361C2×C4×D3—124no—
362C2×C4×D3C22×D311yescharacteristic
363C2×Dic6—21no—
364C2×Dic6—31no—
365C2×Dic6—31no—
366C2×Dic6—61no—
367C2×Dic6—62no—
368C2×Dic6—62no—
369C2×Dic6—61no—
370C2×Dic6—61no—
371C2×Dic6C22×D311yescharacteristic
372C2×Dic6C22×D311yescharacteristic
373C3×SD16—62no—
374C3×SD16—62no—
375C2×C3×C8—21no—
376C2×C3×C8—31no—
377C2×C3×C8—31no—
378C2×C3×C8—62no—
379C2×C3×C8C22×D311yescharacteristic
380C2×C3×C8C22×D311yescharacteristic
381C3×C4⋊C4—21no—
382C3×C4⋊C4—31no—
383C3×C4⋊C4—61no—
384C3×C4⋊C4—61no—
385C3×C4⋊C4—61no—
386C3×C4⋊C4C22×D311yescharacteristic
387C3×C4⋊C4C22×D311yescharacteristic
388C3×C22⋊C4—61no—
389C3×C42—31no—
390#217—61no—
391#215—22no—
392#215—62no—
393#215—62no—
394#215—62no—
395#215—62no—
396#215—62no—
397#215—122no—
398#214—62no—
399#214—62no—
400(C2×D3)⋊C4—21no—
401(C2×D3)⋊C4—61no—
402(C2×D3)⋊C4—61no—
403(C2×D3)⋊C4—61no—
404(C2×D3)⋊C4—61no—
405(C2×D3)⋊C4—61no—
406(C2×D3)⋊C4—121no—
407C4⋊Dic3—61no—
408C4⋊Dic3—61no—
409C4⋊Dic3C22×D311yescharacteristic
410Dic3⋊C4—21no—
411Dic3⋊C4—21no—
412Dic3⋊C4—21no—
413Dic3⋊C4—61no—
414Dic3⋊C4—61no—
415Dic3⋊C4—61no—
416Dic3⋊C4—61no—
417Dic3⋊C4—61no—
418Dic3⋊C4—61no—
419Dic3⋊C4—61no—
420Dic3⋊C4—61no—
421Dic3⋊C4—61no—
422Dic3⋊C4—61no—
423Dic3⋊C4—121no—
424Dic3⋊C4—121no—
425C4×Dic3—31no—
426C4×Dic3—31no—
427C4×Dic3—31no—
428C4×Dic3—31no—
429C4×Dic3—31no—
430C4×Dic3—31no—
431C4×Dic3—61no—
432C4×Dic3C22×D311yescharacteristic
433C2×C3⋊C8—31no—
434C2×C3⋊C8—31no—
435C2×C3⋊C8—61no—
436C2×C3⋊C8—62no—
437C2×C3⋊C8C22×D311yescharacteristic
438C2×C3⋊C8C22×D311yescharacteristic
439#204—22no—
440#204—62no—
441#204—62no—
442#204—62no—
443#204—62no—
444#204—62no—
445#204—122no—
446D3×C8—22no—
447D3×C8—62no—
448C22×C32C22×D411yescharacteristic
449C2×C3⋊D3—22no—
450C2×C3⋊D3—41no—
451C2×C3⋊D3—41no—
452C2×C3×D3—22no—
453C2×C3×D3—41no—
454C2×C3×D3—41no—
455C2×C3×D3#12112yes—
456C2×C3×D3C2×SD1612yes—
457C2×C3×D3#13712yes—
458D32—48no—
459C32×C4—41no—
460C32×C4—41no—
461C32×C4C22×D411yescharacteristic
462C32×C4C2×#4111yescharacteristic
463C3⋊Dic3—21no—
464C3⋊Dic3—41no—
465C3⋊Dic3C2×SD1612yescomplemented
466C3×Dic3—21no—
467C3×Dic3—41no—
468C3×Dic3—41no—
469C3×Dic3—41no—
470C3×Dic3#12112yes—
471C3×Dic3C2×SD1612yescomplemented
472C22×Q8—31no—
473C22×Q8—91no—
474C22×D4—91no—
475C23×C4—181no—
476C2×SD16—31no—
477C2×SD16—31no—
478C2×SD16—91no—
479C2×SD16—91no—
480C2×SD16—91no—
481C2×SD16—91no—
482C2×SD16—91no—
483C2×SD16—91no—
484C2×SD16—184no—
485C2×SD16—184no—
486C22×C8—31no—
487C22×C8—91no—
488C4⋊Q8—31no—
489C4⋊Q8—91no—
490C4⋊Q8—91no—
491C4⋊Q8—91no—
492C4⋊Q8—181no—
493C4⋊Q8—181no—
494C4×D4—31no—
495C4×D4—91no—
496C4×D4—91no—
497C4×D4—91no—
498C4×D4—181no—
499C4×D4—181no—
500C2×C4⋊C4—31no—
501C2×C4⋊C4—181no—
502C2×C4⋊C4—181no—
503C2×C22⋊C4—181no—
504C2×C42—91no—
505C4⋊C8—31no—
506C4⋊C8—91no—
507C4⋊C8—91no—
508C4⋊C8—91no—
509#103—31no—
510#103—31no—
511#103—31no—
512#103—31no—
513#103—91no—
514#103—91no—
515#103—91no—
516#103D3211yescharacteristic, complemented
517C23×C3—31no—
518C23×C3—61no—
519C22×D3—21no—
520C22×D3—64no—
521C22×D3—61no—
522C22×D3—61no—
523C22×D3—64no—
524C22×D3—121no—
525C22×D3—122no—
526C22×D3—122no—
527C22×D3—122no—
528C22×D3—122no—
529C22×D3D3×D411yescharacteristic
530C3×Q8—21no—
531C3×Q8—21no—
532C3×Q8—21no—
533C3×Q8—21no—
534C3×Q8—41no—
535C3×Q8—41no—
536C3×Q8—61no—
537C3×Q8—61no—
538C3×Q8—61no—
539C3×Q8—61no—
540C3×Q8—122no—
541C3×D4—32no—
542C3×D4—61no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—31no—
549C2×C3×C4—31no—
550C2×C3×C4—32no—
551C2×C3×C4—32no—
552C2×C3×C4—31no—
553C2×C3×C4—41no—
554C2×C3×C4—41no—
555C2×C3×C4—61no—
556C2×C3×C4—61no—
557C2×C3×C4—61no—
558C2×C3×C4—122no—
559C2×C3×C4—122no—
560C2×C3×C4—122no—
561C2×C3×C4C23×D311yescharacteristic
562C2×C3×C4C23×D311yescharacteristic
563#67—64no—
564C2×Dic3—21no—
565C2×Dic3—21no—
566C2×Dic3—21no—
567C2×Dic3—31no—
568C2×Dic3—31no—
569C2×Dic3—34no—
570C2×Dic3—31no—
571C2×Dic3—31no—
572C2×Dic3—61no—
573C2×Dic3—61no—
574C2×Dic3—62no—
575C2×Dic3—61no—
576C2×Dic3—61no—
577C2×Dic3—121no—
578C2×Dic3—122no—
579C2×Dic3—122no—
580C2×Dic3D3×D411yescharacteristic
581C2×Dic3D3×D411yescharacteristic
582C2×Dic3D3×D411yescharacteristic
583D12—21no—
584D12—32no—
585D12—32no—
586D12—62no—
587D12—64no—
588D12—61no—
589D12—61no—
590D12—121no—
591D12D3×D412yes—
592C4×D3—34no—
593C4×D3—42no—
594C4×D3—42no—
595C4×D3—42no—
596C4×D3—62no—
597C4×D3—122no—
598C4×D3—122no—
599C4×D3—122no—
600C4×D3—122no—
601C4×D3—122no—
602C4×D3—122no—
603C4×D3—242no—
604C4×D3#23512yes—
605C4×D3D3×D412yes—
606Dic6—21no—
607Dic6—21no—
608Dic6—21no—
609Dic6—21no—
610Dic6—42no—
611Dic6—61no—
612Dic6—61no—
613Dic6—61no—
614Dic6—61no—
615Dic6—121no—
616Dic6—121no—
617Dic6—122no—
618Dic6—122no—
619C3×C8—21no—
620C3×C8—21no—
621C3×C8—41no—
622C3×C8—61no—
623C3×C8—61no—
624C3⋊C8—21no—
625C3⋊C8—21no—
626C3⋊C8—61no—
627C3⋊C8—61no—
628C3⋊C8—121no—
629C2×C32C2×#12111yescharacteristic
630C2×C32C22×SD1611yescharacteristic
631C2×C32C2×#13711yescharacteristic
632C3⋊D3—42no—
633C3×D3—42no—
634C3×D3#46114yescomplemented
635C24—181no—
636C2×Q8—31no—
637C2×Q8—31no—
638C2×Q8—61no—
639C2×Q8—62no—
640C2×Q8—62no—
641C2×Q8—91no—
642C2×Q8—181no—
643C2×Q8—182no—
644C2×Q8—182no—
645C2×Q8C2×D3211yescharacteristic
646C2×D4—31no—
647C2×D4—94no—
648C2×D4—91no—
649C2×D4—182no—
650C2×D4—181no—
651C22×C4—31no—
652C22×C4—61no—
653C22×C4—61no—
654C22×C4—61no—
655C22×C4—91no—
656C22×C4—91no—
657C22×C4—181no—
658C22×C4—181no—
659C22×C4—181no—
660C22×C4—181no—
661C22×C4—364no—
662SD16—62no—
663SD16—62no—
664SD16—182no—
665SD16—182no—
666SD16—182no—
667SD16—182no—
668SD16—182no—
669SD16—182no—
670C2×C8—31no—
671C2×C8—31no—
672C2×C8—62no—
673C2×C8—91no—
674C2×C8—182no—
675C2×C8C2×D3211yescharacteristic
676C4⋊C4—31no—
677C4⋊C4—61no—
678C4⋊C4—61no—
679C4⋊C4—61no—
680C4⋊C4—181no—
681C4⋊C4—181no—
682C4⋊C4—181no—
683C4⋊C4—181no—
684C4⋊C4—181no—
685C4⋊C4—181no—
686C4⋊C4C2×D3211yescharacteristic
687C22⋊C4—61no—
688C22⋊C4—181no—
689C22⋊C4—181no—
690C22⋊C4—181no—
691C42—31no—
692C42—91no—
693C42—91no—
694C42—91no—
695C22×C3—21no—
696C22×C3—32no—
697C22×C3—32no—
698C22×C3—32no—
699C22×C3—62no—
700C22×C3—121no—
701C22×C3—121no—
702C22×C3C2×D3×D411yescharacteristic
703C22×C3C2×D3×D411yescharacteristic
704C2×D3—22no—
705C2×D3—41no—
706C2×D3—41no—
707C2×D3—62no—
708C2×D3—62no—
709C2×D3—122no—
710C2×D3—128no—
711C2×D3—121no—
712C2×D3—121no—
713C2×D3—121no—
714C2×D3—121no—
715C2×D3—128no—
716C2×D3—241no—
717C2×D3—241no—
718C2×D3#88412yes—
719C2×D3D3×SD1612yes—
720C2×D3#91812yes—
721C3×C4—21no—
722C3×C4—21no—
723C3×C4—32no—
724C3×C4—32no—
725C3×C4—41no—
726C3×C4—41no—
727C3×C4—41no—
728C3×C4—41no—
729C3×C4—61no—
730C3×C4—81no—
731C3×C4—81no—
732C3×C4—121no—
733C3×C4—121no—
734C3×C4—121no—
735C3×C4C2×#23511yescharacteristic
736C3×C4C2×D3×D411yescharacteristic
737C3×C4C2×D3×D411yescharacteristic
738C3×C4D3×#4111yescharacteristic
739Dic3—21no—
740Dic3—32no—
741Dic3—32no—
742Dic3—41no—
743Dic3—41no—
744Dic3—41no—
745Dic3—62no—
746Dic3—61no—
747Dic3—61no—
748Dic3—121no—
749Dic3—121no—
750Dic3—121no—
751Dic3—241no—
752Dic3#88412yes—
753Dic3D3×SD1612yescomplemented
754C32C2×#46111yescharacteristic, complemented, Sylow
755C23—31no—
756C23—61no—
757C23—184no—
758C23—181no—
759C23—362no—
760C23—362no—
761Q8—21no—
762Q8—21no—
763Q8—61no—
764Q8—61no—
765Q8—61no—
766Q8—61no—
767Q8—122no—
768Q8—181no—
769Q8—181no—
770Q8—362no—
771D4—32no—
772D4—61no—
773D4—92no—
774D4—184no—
775D4—181no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—31no—
779C2×C4—31no—
780C2×C4—32no—
781C2×C4—32no—
782C2×C4—31no—
783C2×C4—61no—
784C2×C4—61no—
785C2×C4—61no—
786C2×C4—94no—
787C2×C4—91no—
788C2×C4—91no—
789C2×C4—122no—
790C2×C4—122no—
791C2×C4—122no—
792C2×C4—182no—
793C2×C4—181no—
794C2×C4—362no—
795C2×C4—362no—
796C2×C4—362no—
797C2×C4—362no—
798C2×C4C22×D3211yescharacteristic
799C8—21no—
800C8—61no—
801C8—61no—
802C8—181no—
803C2×C3—21no—
804C2×C3—21no—
805C2×C3—21no—
806C2×C3—34no—
807C2×C3—122no—
808C2×C3C2×#88411yescharacteristic
809C2×C3D3×#12111yescharacteristic
810C2×C3C2×D3×SD1611yescharacteristic
811C2×C3C2×D3×SD1611yescharacteristic
812C2×C3C2×#91811yescharacteristic
813C2×C3D3×#13711yescharacteristic
814D3—42no—
815D3—122no—
816D3—122no—
817D3—242no—
818D3#481814yesdirect product factor
819C22—32no—
820C22—32no—
821C22—32no—
822C22—62no—
823C22—121no—
824C22—121no—
825C22—182no—
826C22—368no—
827C22—361no—
828C22—361no—
829C22D32×D411yescharacteristic
830C4—32no—
831C4—32no—
832C4—41no—
833C4—41no—
834C4—61no—
835C4—92no—
836C4—121no—
837C4—121no—
838C4—121no—
839C4—181no—
840C4—361no—
841C4D3×#23511yescharacteristic
842C4D32×D411yescharacteristic
843C3—21no—
844C3C2×#481811yescharacteristic, complemented
845C3D3×#46111yescharacteristic, complemented
846C2—34no—
847C2—122no—
848C2—362no—
849C2D3×#88411yescharacteristic
850C2D32×SD1611yescharacteristic
851C2D3×#91811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC2×D3×D12C22
hypercenter#103D32
hypocenterC32C2×#461
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×#944C2semidirect
5. #10592517C2semidirect
6. C3×#4818C2semidirect
7. C3×D3×#103C2semidirect
8. #10591569C2semidirect
9. #10591565C2semidirect
10. #10590760C2semidirect
11. #10590748C2semidirect
12. D3×Dic3⋊C8C2semidirect
13. D3×#810C2semidirect
14. #10590565C2semidirect
15. #10590559C2semidirect
22. #64153C22semidirect
26. C3×#944C22semidirect
41. #63873C22semidirect
42. #63866C22semidirect
51. C32×#103C22semidirect
52. #63641C22semidirect
53. #63637C22semidirect
54. C3×#835C22semidirect
55. C3×#816C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. C3×#810C22semidirect
58. C3×#810C22semidirect
59. #63572C22semidirect
60. Dic3⋊(C3⋊C8)C22semidirect
61. #63567C22semidirect
62. #63565C22semidirect
91. #4818D3direct (N × H)
93. D3×#103D3semidirect
177. #944C2×D3semidirect
231. C3×#103C2×D3semidirect
232. C3×#103C2×D3semidirect
234. #835C2×D3semidirect
236. #816C2×D3semidirect
243. Dic3⋊C8C2×D3semidirect
249. #810C2×D3semidirect
250. #810C2×D3semidirect
295. D3×Dic3SD16semidirect
465. C3⋊Dic3C2×SD16semidirect
471. C3×Dic3C2×SD16semidirect
516. #103D32semidirect
634. C3×D3#461semidirect
753. Dic3D3×SD16semidirect
754. C32C2×#461semidirect
818. D3#4818direct (N × H)
844. C3C2×#4818semidirect
845. C3D3×#461semidirect

Maximal subgroups

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

subgroupindex
D3×#9442
C2×D3×#2152
C2×D3×#2042
D3×#8932
#105925172
C3×#48182
C3×D3×#1032
#105915692
#105915652
#105907602
#105907482
D3×Dic3⋊C82
D3×#8102
#105905652
#105905592
D3×#4613
C2×#48183