Finite Group Databasebeta

← D3×#5175 #11874151

Subgroups — D3×#5175 #11874151

Order 1152.

1383 conjugacy classes of subgroups.

The subgroup lattice has 849 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×SD16C211yesmaximal, characteristic, complemented
2D3×#944C211yesmaximal, characteristic, complemented
3C2×D3×#215C211yesmaximal, characteristic, complemented
4D3×#940C211yesmaximal, characteristic
5C2×D3×#214C211yesmaximal, characteristic, complemented
6C2×D3×#204C211yesmaximal, characteristic, complemented
7#10592874C211yesmaximal, characteristic, complemented
8C3×#5175C211yesmaximal, characteristic, complemented
9#10591620C211yesmaximal, characteristic, complemented
10#10591618C211yesmaximal, characteristic, complemented
11#10591492C211yesmaximal, characteristic, complemented
12#10591490C211yesmaximal, characteristic, complemented
13#10590884C211yesmaximal, characteristic, complemented
14#10590877C211yesmaximal, characteristic, complemented
15D3×C8×Dic3C211yesmaximal, characteristic, complemented
16C2×#5175—31nomaximal
17D3×#492—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C2×D3×#67—22no—
21C2×D3×D12C2211yescharacteristic
22C2×D3×Dic6C2211yescharacteristic
23C2×C32×SD16C2211yescharacteristic, complemented
24#64153C2211yescharacteristic, complemented
25C2×#3755C2211yescharacteristic, complemented
26#64149C2211yescharacteristic
27C2×#3754C2211yescharacteristic, complemented
28C2×#3744C2211yescharacteristic, complemented
29C3×#944C2211yescharacteristic, complemented
30C2×C3×#215C2211yescharacteristic, complemented
31C2×C3×#215C2211yescharacteristic, complemented
32C3×#940C2211yescharacteristic
33C2×C3×#214C2211yescharacteristic, complemented
34C2×C3×#214C2211yescharacteristic, complemented
35C3×D3×SD16—24no—
36C2×C3×#204C2211yescharacteristic, complemented
37C2×C3×#204C2211yescharacteristic, complemented
38C2×C3×D3×C8C2211yescharacteristic
39#63979—22no—
40D3×#215—24no—
41D3×#214—24no—
42#63914C2211yescharacteristic
43#63911C2211yescharacteristic
44D3×Dic3⋊C4—22no—
45C4×D3×Dic3C2211yescharacteristic
46#63873C2211yescharacteristic, complemented
47#63866C2211yescharacteristic, complemented
48#63839—22no—
49C2×#3717C2211yescharacteristic, complemented
50C2×#3717C2211yescharacteristic, complemented
51C2×#3716C2211yescharacteristic, complemented
52C2×#3716C2211yescharacteristic, complemented
53C2×#3715C2211yescharacteristic, complemented
54C2×#3715C2211yescharacteristic, complemented
55C2×D3×C3⋊C8C2211yescharacteristic
56D3×#204—24no—
57C8×C3⋊Dic3C2211yescharacteristic, complemented
58C3×C8×Dic3C2211yescharacteristic, complemented
59#63553C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C22×C3×SD16—31no—
62C2×#944—31no—
63C22×#215—31no—
64C2×#940—31no—
65C22×#214—31no—
66C2×D3×SD16—31no—
67C2×D3×SD16—31no—
68C2×D3×SD16—31no—
69C2×D3×SD16D311yescharacteristic, complemented
70C22×#204—31no—
71D3×C4⋊Q8—31no—
72D3×#127—31no—
73C3×#492—31no—
74#5175—31no—
75#5175—31no—
76#5175—31no—
77#5175—31no—
78#5175—31no—
79#5175—31no—
80#5175—31no—
81#5175—31no—
82#5175—31no—
83#5175—31no—
84#5175—31no—
85#5175—61no—
86#5175D311yescharacteristic, direct product factor
87C2×C8×Dic3—31no—
88#5085—31no—
89#5076—31no—
90#4693—31no—
91C4×D3×C8—31no—
92C23×C3×D3—21no—
93C22×D32—21no—
94C2×C32×Q8C2311yescharacteristic
95C2×C32×D4C2311yescharacteristic
96C2×#638—22no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×#634C2311yescharacteristic
99C2×C3×#67—22no—
100C2×C3×#67—21no—
101C3×D3×Q8—22no—
102C3×D3×Q8—22no—
103C3×D3×D4—22no—
104C3×D3×D4—22no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×D12C2311yescharacteristic
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×Dic6—21no—
110C2×C3×Dic6C2311yescharacteristic
111C2×C3×Dic6C2311yescharacteristic
112D3×#67—48no—
113C2×#627—21no—
114C2×#626—21no—
115C2×#626—22no—
116C2×#625—22no—
117C2×D3×Dic3—21no—
118C2×D3×Dic3D412yes—
119D3×D12—22no—
120D3×D12—22no—
121D3×Dic6—22no—
122D3×Dic6—22no—
123C32×SD16—22no—
124C2×C32×C8C2311yescharacteristic
125#3755—22no—
126#3754—22no—
127#3750—22no—
128C4×C3⋊Dic3C2311yescharacteristic
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130#3744—22no—
131C3×#215—22no—
132C3×#215—22no—
133C3×#214—22no—
134C3×#214—22no—
135C3×Dic3⋊C4—22no—
136C3×C4×Dic3C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C3×#204—22no—
140C3×#204—22no—
141C3×D3×C8D414yescomplemented
142#3724—22no—
143Dic3⋊Dic3—22no—
144Dic32D412yes—
145#3717—22no—
146#3717—22no—
147#3716—22no—
148#3716—22no—
149#3715—22no—
150#3715—22no—
151D3×C3⋊C8D414yescomplemented
152C2×#492—91noSylow
153C22×C3×Q8—31no—
154C22×C3×D4—31no—
155C22×#67—62no—
156C2×D3×Q8—31no—
157C2×D3×Q8C2×D311yescharacteristic
158C2×D3×D4—31no—
159C2×D3×D4—62no—
160C2×D3×D4C2×D311yescharacteristic
161C22×D12—31no—
162C22×Dic6—31no—
163C2×C3×SD16—21no—
164C2×C3×SD16—31no—
165C2×C3×SD16—31no—
166C2×C3×SD16—31no—
167C2×C3×SD16—31no—
168C2×C3×SD16—31no—
169C2×C3×SD16—31no—
170C2×C3×SD16—64no—
171C2×C3×SD16C2×D311yescharacteristic, complemented
172C2×C3×SD16C2×D311yescharacteristic, complemented
173C22×C3×C8—31no—
174C3×C4⋊Q8—31no—
175C3×#127—31no—
176#944—31no—
177#944—31no—
178#944—31no—
179#944—31no—
180#944—31no—
181#944—61no—
182#944—62no—
183#944C2×D311yescharacteristic, complemented
184C2×#215—31no—
185C2×#215—31no—
186C2×#215—31no—
187C2×#215—31no—
188C2×#215—31no—
189C2×#215—31no—
190C2×#215—61no—
191C2×#215—64no—
192C2×#215C2×D311yescharacteristic, complemented
193C2×#215C2×D311yescharacteristic, complemented
194#940—31no—
195#940—31no—
196#940—31no—
197#940—31no—
198#940—31no—
199#940—61no—
200#940—62no—
201#940—62no—
202#940C2×D311yescharacteristic
203C2×#214—31no—
204C2×#214—31no—
205C2×#214—31no—
206C2×#214—31no—
207C2×#214—31no—
208C2×#214—31no—
209C2×#214—61no—
210C2×#214—64no—
211C2×#214C2×D311yescharacteristic, complemented
212C2×#214C2×D311yescharacteristic, complemented
213C2×Dic3⋊C4—62no—
214C2×C4×Dic3—31no—
215C22×C3⋊C8—31no—
216D3×SD16—24no—
217D3×SD16—64no—
218D3×SD16—64no—
219D3×SD16—64no—
220C2×#204—31no—
221C2×#204—31no—
222C2×#204—31no—
223C2×#204—31no—
224C2×#204—31no—
225C2×#204—31no—
226C2×#204—61no—
227C2×#204—64no—
228C2×#204C2×D311yescharacteristic, complemented
229C2×#204C2×D311yescharacteristic, complemented
230C2×D3×C8—31no—
231C2×D3×C8C2×D311yescharacteristic
232D3×C4⋊C4—62no—
233#888—62no—
234#874—31no—
235C42×D3—31no—
236#869—31no—
237C3×C4×C8—31no—
238C8×Dic3—31no—
239C8×Dic3—31no—
240C8×Dic3—31no—
241C8×Dic3—31no—
242C8×Dic3—31no—
243C8×Dic3—61no—
244C8×Dic3C2×D311yescharacteristic, complemented
245C4×C3⋊C8—31no—
246C23×C32—21no—
247C22×C3⋊D3—21no—
248C22×C3×D3—21no—
249C22×C3×D3—21no—
250C22×C3×D3—42no—
251C22×C3×D3—44no—
252C22×C3×D3C2×D411yescharacteristic
253C2×D32—42no—
254C2×D32—44no—
255C32×Q8—21no—
256C32×Q8—21no—
257C32×D4—21no—
258C32×D4—21no—
259C2×C32×C4—21no—
260C2×C32×C4C2411yescharacteristic
261#638—44no—
262C2×C3⋊Dic3—21no—
263C2×C3⋊Dic3C2×D412yes—
264C4⋊(C3⋊D3)—21no—
265C4⋊(C3⋊D3)—21no—
266#634—21no—
267#634—21no—
268C3×#67—42no—
269C3×#67—44no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3C2×D411yescharacteristic
273C2×C3×Dic3C2×D412yes—
274C3×D12—21no—
275C3×D12—21no—
276C3×D12—21no—
277C3×D12—21no—
278C3×C4×D3—42no—
279C3×C4×D3C2×D412yes—
280C3×C4×D3C2×D412yes—
281C3×Dic6—21no—
282C3×Dic6—21no—
283C3×Dic6—21no—
284C3×Dic6—21no—
285C3×Dic6—42no—
286#627—42no—
287#626—42no—
288#626—44no—
289#625—44no—
290D3×Dic3—42no—
291D3×Dic3SD1618yescomplemented
292C32×C8C2×D412yescomplemented
293C3⋊(C3⋊C8)C2×D412yescomplemented
294C3×C3⋊C8C2×D412yescomplemented
295C3×C3⋊C8C2×D412yescomplemented
296C22×SD16—31no—
297C22×SD16—91no—
298C22×SD16—91no—
299C22×SD16—91no—
300C2×C4⋊Q8—91no—
301C2×#127—91no—
302#492—31no—
303#492—91no—
304#492—91no—
305#492—91no—
306#492—91no—
307#492—91no—
308#492—91no—
309#492—91no—
310C2×C4×C8—91no—
311C24×C3—61no—
312C23×D3—21no—
313C23×D3—61no—
314C23×D3—61no—
315C2×C3×Q8—21no—
316C2×C3×Q8—31no—
317C2×C3×Q8—31no—
318C2×C3×Q8—61no—
319C2×C3×Q8—62no—
320C2×C3×Q8—62no—
321C2×C3×Q8C22×D311yescharacteristic
322C2×C3×Q8C22×D311yescharacteristic
323C2×C3×D4—21no—
324C2×C3×D4—31no—
325C2×C3×D4—31no—
326C2×C3×D4—62no—
327C2×C3×D4—62no—
328C2×C3×D4—61no—
329C2×C3×D4—62no—
330C2×C3×D4C22×D311yescharacteristic
331C2×C3×D4C22×D311yescharacteristic
332C22×C3×C4—31no—
333C22×C3×C4—61no—
334C2×#67—21no—
335C2×#67—22no—
336C2×#67—62no—
337C2×#67—62no—
338C2×#67—62no—
339C2×#67—62no—
340C2×#67—62no—
341C2×#67—61no—
342C2×#67—122no—
343C2×#67—128no—
344C22×Dic3—32no—
345C22×Dic3—61no—
346D3×Q8—22no—
347D3×Q8—22no—
348D3×Q8—62no—
349D3×Q8—62no—
350D3×D4—22no—
351D3×D4—22no—
352D3×D4—62no—
353D3×D4—62no—
354D3×D4—128no—
355C2×D12—31no—
356C2×D12—31no—
357C2×D12—61no—
358C2×D12—62no—
359C2×D12—62no—
360C2×D12—62no—
361C2×D12—61no—
362C2×D12C22×D311yescharacteristic
363C2×D12C22×D311yescharacteristic
364C2×C4×D3—21no—
365C2×C4×D3—32no—
366C2×C4×D3—61no—
367C2×C4×D3C22×D311yescharacteristic
368C2×Dic6—21no—
369C2×Dic6—31no—
370C2×Dic6—31no—
371C2×Dic6—61no—
372C2×Dic6—62no—
373C2×Dic6—62no—
374C2×Dic6—61no—
375C2×Dic6—61no—
376C2×Dic6C22×D311yescharacteristic
377C2×Dic6C22×D311yescharacteristic
378C3×SD16—22no—
379C3×SD16—22no—
380C3×SD16—42no—
381C3×SD16—62no—
382C3×SD16—62no—
383C3×SD16—62no—
384C3×SD16—62no—
385C3×SD16—62no—
386C3×SD16—62no—
387C2×C3×C8—21no—
388C2×C3×C8—31no—
389C2×C3×C8—31no—
390C2×C3×C8—34no—
391C2×C3×C8C22×D311yescharacteristic
392C2×C3×C8C22×D311yescharacteristic
393C3×C4⋊C4—62no—
394C3×C42—31no—
395#215—22no—
396#215—22no—
397#215—62no—
398#215—62no—
399#215—62no—
400#215—62no—
401#215—62no—
402#215—62no—
403#215—122no—
404#214—22no—
405#214—22no—
406#214—62no—
407#214—62no—
408#214—62no—
409#214—62no—
410#214—62no—
411#214—62no—
412#214—122no—
413C4⋊Dic3—62no—
414Dic3⋊C4—22no—
415Dic3⋊C4—62no—
416Dic3⋊C4—62no—
417Dic3⋊C4—62no—
418Dic3⋊C4—62no—
419Dic3⋊C4—62no—
420Dic3⋊C4—122no—
421C4×Dic3—31no—
422C4×Dic3—31no—
423C4×Dic3—32no—
424C4×Dic3—32no—
425C4×Dic3—61no—
426C4×Dic3C22×D311yescharacteristic
427C2×C3⋊C8—31no—
428C2×C3⋊C8—31no—
429C2×C3⋊C8—34no—
430C2×C3⋊C8—61no—
431C2×C3⋊C8C22×D311yescharacteristic
432C2×C3⋊C8C22×D311yescharacteristic
433#204—22no—
434#204—22no—
435#204—62no—
436#204—62no—
437#204—62no—
438#204—62no—
439#204—62no—
440#204—62no—
441#204—122no—
442D3×C8—34no—
443D3×C8#6714yescomplemented
444C22×C32—41no—
445C22×C32—42no—
446C22×C32C22×D411yescharacteristic
447C2×C3⋊D3—41no—
448C2×C3⋊D3—42no—
449C2×C3×D3—41no—
450C2×C3×D3—41no—
451C2×C3×D3—42no—
452C2×C3×D3—42no—
453C2×C3×D3—84no—
454C2×C3×D3#12712yes—
455C2×C3×D3C2×SD1614yes—
456D32—84no—
457C32×C4—41no—
458C32×C4C22×D411yescharacteristic
459C32×C4C22×D411yescharacteristic
460C3⋊Dic3—41no—
461C3⋊Dic3C2×SD1614yescomplemented
462C3×Dic3—41no—
463C3×Dic3—41no—
464C3×Dic3#12712yes—
465C3×Dic3C2×SD1614yescomplemented
466C22×Q8—31no—
467C22×Q8—91no—
468C22×D4—31no—
469C22×D4—91no—
470C22×D4—182no—
471C2×SD16—31no—
472C2×SD16—31no—
473C2×SD16—31no—
474C2×SD16—31no—
475C2×SD16—31no—
476C2×SD16—31no—
477C2×SD16—64no—
478C2×SD16—91no—
479C2×SD16—91no—
480C2×SD16—91no—
481C2×SD16—91no—
482C2×SD16—91no—
483C2×SD16—91no—
484C2×SD16—91no—
485C2×SD16—91no—
486C2×SD16—91no—
487C2×SD16—184no—
488C2×SD16—184no—
489C2×SD16—184no—
490C2×SD16D3211yescharacteristic, complemented
491C22×C8—31no—
492C22×C8—91no—
493C4⋊Q8—31no—
494C4⋊Q8—91no—
495C4⋊Q8—91no—
496C4⋊Q8—91no—
497C4⋊Q8—182no—
498#127—31no—
499#127—91no—
500#127—91no—
501#127—91no—
502#127—182no—
503C2×C4⋊C4—182no—
504C2×C42—91no—
505C4×C8—31no—
506C4×C8—91no—
507C4×C8—91no—
508C4×C8—91no—
509C23×C3—21no—
510C23×C3—21no—
511C23×C3—31no—
512C23×C3—41no—
513C23×C3—61no—
514C23×C3—61no—
515C23×C3—124no—
516C23×C3—122no—
517C22×D3—21no—
518C22×D3—21no—
519C22×D3—44no—
520C22×D3—42no—
521C22×D3—61no—
522C22×D3—61no—
523C22×D3—121no—
524C22×D3—122no—
525C22×D3—124no—
526C22×D3—124no—
527C22×D3—122no—
528C22×D3D3×D411yescharacteristic
529C3×Q8—21no—
530C3×Q8—21no—
531C3×Q8—21no—
532C3×Q8—21no—
533C3×Q8—41no—
534C3×Q8—41no—
535C3×Q8—61no—
536C3×Q8—61no—
537C3×Q8—61no—
538C3×Q8—61no—
539C3×Q8—122no—
540C3×D4—21no—
541C3×D4—21no—
542C3×D4—21no—
543C3×D4—21no—
544C3×D4—41no—
545C3×D4—41no—
546C3×D4—61no—
547C3×D4—61no—
548C3×D4—61no—
549C3×D4—61no—
550C3×D4—124no—
551C3×D4—122no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—31no—
556C2×C3×C4—32no—
557C2×C3×C4—32no—
558C2×C3×C4—32no—
559C2×C3×C4—41no—
560C2×C3×C4—61no—
561C2×C3×C4—61no—
562C2×C3×C4—122no—
563C2×C3×C4C23×D311yescharacteristic
564C2×C3×C4C23×D311yescharacteristic
565#67—44no—
566#67—42no—
567#67—124no—
568#67—124no—
569#67—124no—
570#67—124no—
571#67—124no—
572#67—122no—
573#67—244no—
574C2×Dic3—21no—
575C2×Dic3—21no—
576C2×Dic3—32no—
577C2×Dic3—32no—
578C2×Dic3—38no—
579C2×Dic3—62no—
580C2×Dic3—61no—
581C2×Dic3—61no—
582C2×Dic3—121no—
583C2×Dic3—122no—
584C2×Dic3D3×D412yes—
585C2×Dic3D3×D411yescharacteristic
586D12—21no—
587D12—21no—
588D12—21no—
589D12—21no—
590D12—61no—
591D12—61no—
592D12—61no—
593D12—61no—
594D12—121no—
595D12—121no—
596D12—122no—
597D12—124no—
598C4×D3—38no—
599C4×D3—42no—
600C4×D3—122no—
601C4×D3D3×D412yes—
602C4×D3C2×#6712yes—
603Dic6—21no—
604Dic6—21no—
605Dic6—21no—
606Dic6—21no—
607Dic6—42no—
608Dic6—61no—
609Dic6—61no—
610Dic6—61no—
611Dic6—61no—
612Dic6—121no—
613Dic6—121no—
614Dic6—122no—
615Dic6—122no—
616C3×C8—22no—
617C3×C8—32no—
618C3×C8—32no—
619C3×C8D3×D412yescomplemented
620C3×C8C2×#6712yescomplemented
621C3⋊C8—32no—
622C3⋊C8—32no—
623C3⋊C8—62no—
624C3⋊C8D3×D412yescomplemented
625C3⋊C8C2×#6712yescomplemented
626C2×C32—81no—
627C2×C32C2×#12711yescharacteristic
628C2×C32C22×SD1612yes—
629C3⋊D3—81no—
630C3×D3—81no—
631C3×D3—81no—
632C3×D3#49214yescomplemented
633C24—61no—
634C24—181no—
635C2×Q8—31no—
636C2×Q8—31no—
637C2×Q8—61no—
638C2×Q8—62no—
639C2×Q8—62no—
640C2×Q8—91no—
641C2×Q8—181no—
642C2×Q8—182no—
643C2×Q8—182no—
644C2×Q8C2×D3211yescharacteristic
645C2×D4—31no—
646C2×D4—31no—
647C2×D4—62no—
648C2×D4—62no—
649C2×D4—62no—
650C2×D4—61no—
651C2×D4—91no—
652C2×D4—182no—
653C2×D4—182no—
654C2×D4—182no—
655C2×D4—181no—
656C2×D4—182no—
657C2×D4—182no—
658C2×D4—368no—
659C2×D4C2×D3211yescharacteristic
660C22×C4—31no—
661C22×C4—61no—
662C22×C4—92no—
663C22×C4—181no—
664SD16—22no—
665SD16—62no—
666SD16—62no—
667SD16—62no—
668SD16—62no—
669SD16—62no—
670SD16—62no—
671SD16—182no—
672SD16—182no—
673SD16—182no—
674SD16—182no—
675SD16—182no—
676SD16—182no—
677SD16—182no—
678SD16—182no—
679SD16—182no—
680C2×C8—31no—
681C2×C8—31no—
682C2×C8—34no—
683C2×C8—94no—
684C2×C8—91no—
685C2×C8C2×D3211yescharacteristic
686C4⋊C4—62no—
687C4⋊C4—182no—
688C4⋊C4—182no—
689C4⋊C4—182no—
690C42—31no—
691C42—92no—
692C42—91no—
693C22×C3—21no—
694C22×C3—32no—
695C22×C3—34no—
696C22×C3—41no—
697C22×C3—42no—
698C22×C3—42no—
699C22×C3—41no—
700C22×C3—82no—
701C22×C3—81no—
702C22×C3—121no—
703C22×C3—122no—
704C22×C3—122no—
705C22×C3—121no—
706C22×C3—244no—
707C22×C3C2×D3×D411yescharacteristic
708C22×C3C2×D3×D411yescharacteristic
709C2×D3—41no—
710C2×D3—42no—
711C2×D3—42no—
712C2×D3—41no—
713C2×D3—84no—
714C2×D3—121no—
715C2×D3—122no—
716C2×D3—122no—
717C2×D3—121no—
718C2×D3—241no—
719C2×D3—242no—
720C2×D3—244no—
721C2×D3—244no—
722C2×D3D3×SD1614yes—
723C2×D3#94012yes—
724C3×C4—21no—
725C3×C4—21no—
726C3×C4—32no—
727C3×C4—34no—
728C3×C4—41no—
729C3×C4—41no—
730C3×C4—81no—
731C3×C4—121no—
732C3×C4—121no—
733C3×C4C2×D3×D411yescharacteristic
734C3×C4C2×D3×D411yescharacteristic
735C3×C4C2×D3×D411yescharacteristic
736C3×C4C22×#6711yescharacteristic
737Dic3—34no—
738Dic3—34no—
739Dic3—41no—
740Dic3—41no—
741Dic3—64no—
742Dic3—121no—
743Dic3—121no—
744Dic3—241no—
745Dic3D3×SD1614yescomplemented
746Dic3#94012yes—
747C32C2×#49211yescharacteristic, complemented, Sylow
748C23—21no—
749C23—31no—
750C23—61no—
751C23—61no—
752C23—122no—
753C23—124no—
754C23—181no—
755C23—362no—
756C23—364no—
757Q8—21no—
758Q8—21no—
759Q8—61no—
760Q8—61no—
761Q8—61no—
762Q8—61no—
763Q8—122no—
764Q8—181no—
765Q8—181no—
766Q8—362no—
767D4—21no—
768D4—21no—
769D4—61no—
770D4—61no—
771D4—61no—
772D4—61no—
773D4—122no—
774D4—124no—
775D4—181no—
776D4—181no—
777D4—362no—
778D4—364no—
779D4—364no—
780D4—364no—
781C2×C4—21no—
782C2×C4—32no—
783C2×C4—31no—
784C2×C4—32no—
785C2×C4—32no—
786C2×C4—61no—
787C2×C4—61no—
788C2×C4—98no—
789C2×C4—92no—
790C2×C4—122no—
791C2×C4—181no—
792C2×C4—362no—
793C2×C4C22×D3211yescharacteristic
794C8—32no—
795C8—32no—
796C8—92no—
797C8D3×#6712yescomplemented
798C2×C3—22no—
799C2×C3—21no—
800C2×C3—34no—
801C2×C3—81no—
802C2×C3—81no—
803C2×C3—161no—
804C2×C3—241no—
805C2×C3—241no—
806C2×C3D3×#12711yescharacteristic
807C2×C3C2×D3×SD1612yes—
808C2×C3C2×D3×SD1612yes—
809C2×C3C2×#94011yescharacteristic
810D3—81no—
811D3—81no—
812D3—241no—
813D3—241no—
814D3—481no—
815D3#517514yesdirect product factor
816C22—34no—
817C22—32no—
818C22—42no—
819C22—41no—
820C22—122no—
821C22—122no—
822C22—121no—
823C22—121no—
824C22—244no—
825C22—362no—
826C22—361no—
827C22—724no—
828C22D32×D411yescharacteristic
829C4—34no—
830C4—32no—
831C4—41no—
832C4—94no—
833C4—121no—
834C4—121no—
835C4—361no—
836C4D32×D411yescharacteristic
837C4C2×D3×#6711yescharacteristic
838C3—21no—
839C3D3×#49211yescharacteristic, complemented
840C3C2×#517511yescharacteristic, complemented
841C2—34no—
842C2—81no—
843C2—241no—
844C2—241no—
845C2—721no—
846C2D32×SD1612yes—
847C2D3×#94011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
prime radicalD3×#940C2
hypercenterC2×SD16D32
hypocenterC32C2×#492
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×SD16C2semidirect
2. D3×#944C2semidirect
3. C2×D3×#215C2semidirect
5. C2×D3×#214C2semidirect
6. C2×D3×#204C2semidirect
7. #10592874C2semidirect
8. C3×#5175C2semidirect
9. #10591620C2semidirect
10. #10591618C2semidirect
11. #10591492C2semidirect
12. #10591490C2semidirect
13. #10590884C2semidirect
14. #10590877C2semidirect
15. D3×C8×Dic3C2semidirect
23. C2×C32×SD16C22semidirect
24. #64153C22semidirect
25. C2×#3755C22semidirect
27. C2×#3754C22semidirect
28. C2×#3744C22semidirect
29. C3×#944C22semidirect
30. C2×C3×#215C22semidirect
31. C2×C3×#215C22semidirect
33. C2×C3×#214C22semidirect
34. C2×C3×#214C22semidirect
36. C2×C3×#204C22semidirect
37. C2×C3×#204C22semidirect
46. #63873C22semidirect
47. #63866C22semidirect
49. C2×#3717C22semidirect
50. C2×#3717C22semidirect
51. C2×#3716C22semidirect
52. C2×#3716C22semidirect
53. C2×#3715C22semidirect
54. C2×#3715C22semidirect
57. C8×C3⋊Dic3C22semidirect
58. C3×C8×Dic3C22semidirect
59. #63553C22semidirect
60. Dic3×C3⋊C8C22semidirect
69. C2×D3×SD16D3semidirect
86. #5175D3direct (N × H)
141. C3×D3×C8D4semidirect
151. D3×C3⋊C8D4semidirect
171. C2×C3×SD16C2×D3semidirect
172. C2×C3×SD16C2×D3semidirect
183. #944C2×D3semidirect
192. C2×#215C2×D3semidirect
193. C2×#215C2×D3semidirect
211. C2×#214C2×D3semidirect
212. C2×#214C2×D3semidirect
228. C2×#204C2×D3semidirect
229. C2×#204C2×D3semidirect
244. C8×Dic3C2×D3semidirect
291. D3×Dic3SD16semidirect
292. C32×C8C2×D4semidirect
293. C3⋊(C3⋊C8)C2×D4semidirect
294. C3×C3⋊C8C2×D4semidirect
295. C3×C3⋊C8C2×D4semidirect
443. D3×C8#67semidirect
461. C3⋊Dic3C2×SD16semidirect
465. C3×Dic3C2×SD16semidirect
490. C2×SD16D32semidirect
619. C3×C8D3×D4semidirect
620. C3×C8C2×#67semidirect
624. C3⋊C8D3×D4semidirect
625. C3⋊C8C2×#67semidirect
632. C3×D3#492semidirect
745. Dic3D3×SD16semidirect
747. C32C2×#492semidirect
797. C8D3×#67semidirect
815. D3#5175direct (N × H)
839. C3D3×#492semidirect
840. C3C2×#5175semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×SD162
D3×#9442
C2×D3×#2152
D3×#9402
C2×D3×#2142
C2×D3×#2042
#105928742
C3×#51752
#105916202
#105916182
#105914922
#105914902
#105908842
#105908772
D3×C8×Dic32
C2×#51753
D3×#4923