Finite Group Databasebeta

← #11865867

Subgroups — #11865867

Order 1152.

1158 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#914C211yesmaximal, characteristic, complemented
2#10595360C211yesmaximal, characteristic, complemented
3D3×D4×Dic3C211yesmaximal, characteristic, complemented
4C2×#63934C211yesmaximal, characteristic, complemented
5#10592864C211yesmaximal, characteristic, complemented
6C3×#5162C211yesmaximal, characteristic, complemented
7#10591570C211yesmaximal, characteristic, complemented
8#10591564C211yesmaximal, characteristic, complemented
9#10591550C211yesmaximal, characteristic, complemented
10#10591481C211yesmaximal, characteristic, complemented
11#10591476C211yesmaximal, characteristic, complemented
12#10590753C211yesmaximal, characteristic, complemented
13#10590751C211yesmaximal, characteristic, complemented
14#10590671C211yesmaximal, characteristic, complemented
15#10590663C211yesmaximal, characteristic, complemented
16#83931—31nomaximal
17#80428—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C22×D3×Dic3—21no—
21C2×#3799C2211yescharacteristic
22C2×C32×SD16C2211yescharacteristic
23#64156C2211yescharacteristic, complemented
24D4×C3⋊Dic3C2211yescharacteristic
25C2×#3753C2211yescharacteristic
26C3×#944C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic
28C3×D4×Dic3C2211yescharacteristic
29C2×C3×#214C2211yescharacteristic
30C2×C3×#213C2211yescharacteristic
31C3×#914—24no—
32C2×C3×D24C2211yescharacteristic
33C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
34#67⋊Dic3—21no—
35Dic3×#67—21no—
36D3×#217—21no—
37#63934—24no—
38#63911C2211yescharacteristic, complemented
39#63904—21no—
40#63904—21no—
41#63898C2211yescharacteristic
42Dic3×D12C2211yescharacteristic
43D3×C4⋊Dic3C2211yescharacteristic
44#63886—21no—
45#63886—21no—
46C4×D3×Dic3C2211yescharacteristic
47#63863C2211yescharacteristic, complemented
48C2×#3715C2211yescharacteristic
49C2×#3714C2211yescharacteristic
50C2×#3711C2211yescharacteristic
51#63662C2211yescharacteristic, complemented
52#63648C2211yescharacteristic, complemented
53#63641C2211yescharacteristic, complemented
54C3×#835C2211yescharacteristic, complemented
55C3×#816C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57#63572C2211yescharacteristic, complemented
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63564C2211yescharacteristic, complemented
61#63563C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63C2×C3×AGL(1,ℤ/8)—31no—
64#5832—31no—
65C2×D4×Dic3—31no—
66C2×#932—31no—
67C2×#914—31no—
68C2×#914D311yescharacteristic, complemented
69#5725—31no—
70C4×D3×D4—31no—
71C3×#461—31no—
72#5232—31no—
73#5165—31no—
74#5165—31no—
75#5165—31no—
76#5165—31no—
77#5165—61no—
78#5162—31no—
79#5162D311yescharacteristic, complemented
80#5153—31no—
81#5153—31no—
82#5150—31no—
83#5150—31no—
84#5133—31no—
85#5118—31no—
86#5083—31no—
87#5015—31no—
88#4843—31no—
89#4837—31no—
90#4819—31no—
91#4819—31no—
92#4803—31no—
93#4803—31no—
94C23×C3×D3—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×D4C2311yescharacteristic
97C22×C3⋊Dic3—21no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C3×#67—21no—
100C22×C3×Dic3—21no—
101C3×#239—22no—
102C3×#239—22no—
103C3×D3×D4—22no—
104C3×D3×D4D414yescomplemented
105C2×C3×D12—21no—
106C2×C3×D12C2311yescharacteristic
107C2×C3×D12C2311yescharacteristic
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×Dic6C2311yescharacteristic
111C2×#626—21no—
112C2×#626—21no—
113C2×#626—21no—
114C2×#624—21no—
115C2×D3×Dic3—21no—
116C2×D3×Dic3—21no—
117C2×D3×Dic3—21no—
118C2×D3×Dic3—44no—
119C2×D3×Dic3D411yescharacteristic
120C2×D3×Dic3D411yescharacteristic
121#3799—22no—
122#3799—22no—
123C32×SD16—22no—
124C2×C32×C8C2311yescharacteristic
125#3757—21no—
126#3753—22no—
127#3752—21no—
128#3752—21no—
129C4⋊(C3⋊Dic3)C2311yescharacteristic
130C4×C3⋊Dic3C2311yescharacteristic
131C2×C3⋊(C3⋊C8)C2311yescharacteristic
132C3×#217—21no—
133C3×#215—22no—
134C3×#214—22no—
135C3×#213—22no—
136C3×C4⋊Dic3C2311yescharacteristic
137C3×Dic3⋊C4—21no—
138C3×Dic3⋊C4—21no—
139C3×C4×Dic3C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C3×D24—22no—
143C3×ΓL(1,𝔽25)—22no—
144Dic3⋊Dic3—21no—
145(C2×D3)⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149Dic32D411yescharacteristic
150Dic32D411yescharacteristic
151#3715—22no—
152#3714—22no—
153#3711—22no—
154#3036—91noSylow
155C2×C3×#41—31no—
156C22×C3×D4—31no—
157C23×Dic3—61no—
158C2×#239—31no—
159C2×#239C2×D311yescharacteristic
160C2×D3×D4C2×D311yescharacteristic
161C2×#235—31no—
162C22×C4×D3—61no—
163C3×AGL(1,ℤ/8)—64no—
164C2×C3×SD16—21no—
165C2×C3×SD16—31no—
166C2×C3×SD16—31no—
167C2×C3×SD16C2×D311yescharacteristic
168C2×C3×SD16C2×D311yescharacteristic
169C2×C3×D8—31no—
170C2×C3×D8—31no—
171C2×C3×M16—31no—
172C3×C4⋊Q8—31no—
173C3×C4×D4—31no—
174C2×#217—61no—
175#947—31no—
176#947—31no—
177#947—31no—
178#947—61no—
179#944C2×D311yescharacteristic, complemented
180C2×#215—31no—
181C2×#215C2×D311yescharacteristic
182#940—31no—
183#939—61no—
184#939—61no—
185#936—31no—
186D4×Dic3—31no—
187D4×Dic3—31no—
188D4×Dic3—31no—
189D4×Dic3—31no—
190D4×Dic3—61no—
191D4×Dic3—61no—
192D4×Dic3—61no—
193D4×Dic3C2×D311yescharacteristic
194C2×#214—31no—
195C2×#214C2×D311yescharacteristic
196#932—64no—
197C2×#213—31no—
198C2×#213—31no—
199C2×#213—31no—
200C2×#213—61no—
201C2×#213C2×D311yescharacteristic
202C4×#67—61no—
203C4×#67—61no—
204C4×#67—61no—
205C2×C4⋊Dic3—31no—
206C2×C4×Dic3—31no—
207C2×#208—31no—
208#914—24no—
209#914—64no—
210C2×D24—31no—
211C2×D24C2×D311yescharacteristic
212C2×ΓL(1,𝔽25)—31no—
213C2×ΓL(1,𝔽25)C2×D311yescharacteristic
214#895—61no—
215#895—61no—
216#893—31no—
217#893—61no—
218#893—61no—
219D3×C4⋊C4—31no—
220#67⋊C4—61no—
221D3×C22⋊C4—61no—
222#874—31no—
223C4×D12—31no—
224C42×D3—31no—
225C3×C4⋊C8—31no—
226C3×#103—31no—
227C3×#103—31no—
228#835—31no—
229#835—31no—
230#835—31no—
231#835—61no—
232#835C2×D311yescharacteristic, complemented
233#832—31no—
234#832—31no—
235#821—31no—
236#821—31no—
237#821—31no—
238#821—31no—
239#821—61no—
240#816—31no—
241#816C2×D311yescharacteristic, complemented
242Dic3⋊C8—31no—
243Dic3⋊C8—31no—
244Dic3⋊C8—31no—
245Dic3⋊C8—31no—
246Dic3⋊C8—31no—
247Dic3⋊C8—61no—
248Dic3⋊C8C2×D311yescharacteristic, complemented
249#809—31no—
250#809—31no—
251C4⋊(C3⋊C8)—31no—
252C23×C32—21no—
253C22×C3⋊D3—21no—
254C22×C3×D3—21no—
255C22×C3×D3—24no—
256C22×C3×D3—21no—
257C22×C3×D3—42no—
258C22×C3×D3—42no—
259C22×C3×D3C2×D411yescharacteristic
260C32×Q8—21no—
261C32×Q8—21no—
262C32×D4—21no—
263C32×D4C2×D412yes—
264C2×C32×C4—21no—
265C2×C32×C4C2411yescharacteristic
266C2×C3⋊Dic3—21no—
267C2×C3⋊Dic3—42no—
268C2×C3⋊Dic3C2×D411yescharacteristic
269C2×C3⋊Dic3C2×D411yescharacteristic
270C4⋊(C3⋊D3)—21no—
271C4⋊(C3⋊D3)—21no—
272C3×#67—24no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—42no—
276C2×C3×Dic3C2×D411yescharacteristic
277C2×C3×Dic3C2×D411yescharacteristic
278C2×C3×Dic3C2×D411yescharacteristic
279C3×D12—21no—
280C3×D12—21no—
281C3×D12—21no—
282C3×D12—42no—
283C3×D12C2×D412yes—
284C3×C4×D3—42no—
285C3×C4×D3C2×D412yes—
286C3×C4×D3#4112yes—
287C3×Dic6—21no—
288C3×Dic6—21no—
289#626—42no—
290#626—42no—
291#626—42no—
292#624—42no—
293D3×Dic3—22no—
294D3×Dic3—41no—
295D3×Dic3—42no—
296D3×Dic3—42no—
297D3×Dic3—42no—
298C32×C8—21no—
299C3⋊(C3⋊C8)—21no—
300C3×C3⋊C8—21no—
301C3×C3⋊C8—21no—
302C2×AGL(1,ℤ/8)—31no—
303C2×AGL(1,ℤ/8)—91no—
304#532—91no—
305C2×C4×D4—91no—
306#463—91no—
307#463—91no—
308#463—91no—
309#463—91no—
310#461—31no—
311#461—91no—
312#459—91no—
313#459—91no—
314#423—91no—
315#417—91no—
316#417—91no—
317C24×C3—61no—
318C23×D3—21no—
319C3×#41—62no—
320C3×#41—62no—
321C2×C3×Q8—21no—
322C2×C3×Q8—31no—
323C2×C3×Q8C22×D311yescharacteristic
324C2×C3×Q8C22×D311yescharacteristic
325C2×C3×D4—21no—
326C2×C3×D4—34no—
327C2×C3×D4—31no—
328C2×C3×D4—31no—
329C2×C3×D4—61no—
330C2×C3×D4—62no—
331C2×C3×D4—61no—
332C2×C3×D4C22×D311yescharacteristic
333C2×C3×D4C22×D311yescharacteristic
334C22×C3×C4—31no—
335C22×C3×C4—61no—
336C22×C3×C4—61no—
337C2×#67—21no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341C22×Dic3—21no—
342C22×Dic3—31no—
343C22×Dic3—31no—
344C22×Dic3—61no—
345C22×Dic3—61no—
346C22×Dic3—61no—
347C22×Dic3—61no—
348C22×Dic3—61no—
349C22×Dic3—121no—
350C22×Dic3—124no—
351#239—22no—
352#239—22no—
353#239—62no—
354#239—62no—
355D3×D4—22no—
356D3×D4#6714yescomplemented
357#235—62no—
358#235—62no—
359C2×D12—21no—
360C2×D12—31no—
361C2×D12—31no—
362C2×D12—61no—
363C2×D12—61no—
364C2×D12—61no—
365C2×D12—61no—
366C2×D12C22×D311yescharacteristic
367C2×D12C22×D311yescharacteristic
368C2×C4×D3—21no—
369C2×C4×D3—31no—
370C2×C4×D3—31no—
371C2×C4×D3—61no—
372C2×C4×D3—61no—
373C2×C4×D3—61no—
374C2×C4×D3—61no—
375C2×C4×D3—61no—
376C2×C4×D3—124no—
377C2×C4×D3C22×D311yescharacteristic
378C2×Dic6C22×D311yescharacteristic
379C3×SD16—22no—
380C3×SD16—22no—
381C3×SD16—42no—
382C3×SD16—62no—
383C3×SD16—62no—
384C3×D8—62no—
385C3×D8—62no—
386C3×M16—62no—
387C2×C3×C8—21no—
388C2×C3×C8—31no—
389C2×C3×C8—31no—
390C2×C3×C8C22×D311yescharacteristic
391C2×C3×C8C22×D311yescharacteristic
392C3×C4⋊C4—31no—
393C3×C4⋊C4—61no—
394C3×C4⋊C4—61no—
395C3×C22⋊C4—61no—
396C3×C42—31no—
397#217—21no—
398#217—61no—
399#217—61no—
400#217—61no—
401#217—61no—
402#217—61no—
403#217—61no—
404#217—121no—
405#215—22no—
406#215—62no—
407#214—22no—
408#214—62no—
409#213—22no—
410#213—62no—
411#213—62no—
412#213—62no—
413#213—122no—
414(C2×D3)⋊C4—61no—
415(C2×D3)⋊C4—61no—
416(C2×D3)⋊C4—61no—
417(C2×D3)⋊C4—61no—
418(C2×D3)⋊C4—61no—
419(C2×D3)⋊C4—61no—
420(C2×D3)⋊C4—61no—
421(C2×D3)⋊C4—61no—
422(C2×D3)⋊C4—121no—
423(C2×D3)⋊C4—121no—
424C4⋊Dic3—31no—
425C4⋊Dic3—31no—
426C4⋊Dic3—61no—
427C4⋊Dic3—61no—
428C4⋊Dic3C22×D311yescharacteristic
429Dic3⋊C4—21no—
430Dic3⋊C4—21no—
431Dic3⋊C4—61no—
432C4×Dic3—31no—
433C4×Dic3—31no—
434C4×Dic3—31no—
435C4×Dic3—31no—
436C4×Dic3—31no—
437C4×Dic3—31no—
438C4×Dic3—61no—
439C4×Dic3C22×D311yescharacteristic
440#208—62no—
441C2×C3⋊C8—31no—
442C2×C3⋊C8—31no—
443C2×C3⋊C8—61no—
444C2×C3⋊C8C22×D311yescharacteristic
445C2×C3⋊C8C22×D311yescharacteristic
446D24—22no—
447D24—62no—
448ΓL(1,𝔽25)—22no—
449ΓL(1,𝔽25)—62no—
450C22×C32—22no—
451C22×C32—41no—
452C22×C32—41no—
453C22×C32C22×D411yescharacteristic
454C2×C3⋊D3—41no—
455C2×C3⋊D3—41no—
456C2×C3⋊D3—41no—
457C2×C3×D3—21no—
458C2×C3×D3—21no—
459C2×C3×D3—22no—
460C2×C3×D3—48no—
461C2×C3×D3—41no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3#12112yes—
467C32×C4—41no—
468C32×C4C22×D411yescharacteristic
469C32×C4C2×#4111yescharacteristic
470C3⋊Dic3—21no—
471C3⋊Dic3—21no—
472C3⋊Dic3—41no—
473C3×Dic3—21no—
474C3×Dic3—41no—
475C3×Dic3—41no—
476C3×Dic3#12112yes—
477C3×Dic3AGL(1,ℤ/8)12yescomplemented
478C2×#41—31no—
479C2×#41—91no—
480C22×D4—31no—
481C23×C4—181no—
482AGL(1,ℤ/8)—64no—
483AGL(1,ℤ/8)—184no—
484C2×SD16—31no—
485C2×SD16—31no—
486C2×SD16—91no—
487C2×SD16D3211yescharacteristic
488C2×D8—31no—
489C2×D8—31no—
490C2×D8—91no—
491C2×D8—91no—
492C2×M16—31no—
493C2×M16—91no—
494C4⋊Q8—31no—
495#127—91no—
496#124—91no—
497#124—91no—
498#121—181no—
499#121—181no—
500C4×D4—31no—
501C4×D4—91no—
502C4×D4—91no—
503C4×D4—91no—
504C4×D4—181no—
505C4×D4—181no—
506C4×D4—181no—
507C4×D4—181no—
508C2×C4⋊C4—91no—
509C2×C22⋊C4—181no—
510C2×C42—91no—
511C4⋊C8—31no—
512C4⋊C8—91no—
513C4⋊C8—91no—
514C4⋊C8—91no—
515#103—31no—
516#103—31no—
517#103—91no—
518#103—91no—
519#102—91no—
520#102—91no—
521#102—91no—
522#102—91no—
523C23×C3—21no—
524C23×C3—21no—
525C23×C3—31no—
526C23×C3—41no—
527C23×C3—64no—
528C23×C3—61no—
529C23×C3—61no—
530C23×C3—122no—
531C23×C3—122no—
532C22×D3—21no—
533C22×D3—24no—
534C22×D3—21no—
535C22×D3—42no—
536C22×D3—42no—
537C22×D3—61no—
538C22×D3—61no—
539C22×D3—121no—
540C22×D3D3×D411yescharacteristic
541C3×Q8—21no—
542C3×Q8—21no—
543C3×Q8—21no—
544C3×Q8—21no—
545C3×Q8—41no—
546C3×Q8—41no—
547C3×Q8—61no—
548C3×Q8—61no—
549C3×D4—21no—
550C3×D4—21no—
551C3×D4—22no—
552C3×D4—32no—
553C3×D4—41no—
554C3×D4—64no—
555C3×D4—61no—
556C3×D4—61no—
557C3×D4—61no—
558C3×D4—122no—
559C3×D4D3×D412yes—
560C3×D4C2×#6712yes—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—31no—
565C2×C3×C4—31no—
566C2×C3×C4—32no—
567C2×C3×C4—32no—
568C2×C3×C4—31no—
569C2×C3×C4—41no—
570C2×C3×C4—61no—
571C2×C3×C4—61no—
572C2×C3×C4—122no—
573C2×C3×C4—122no—
574C2×C3×C4C23×D311yescharacteristic
575C2×C3×C4C23×D311yescharacteristic
576#67—24no—
577#67—122no—
578#67—122no—
579#67—122no—
580C2×Dic3—21no—
581C2×Dic3—21no—
582C2×Dic3—31no—
583C2×Dic3—31no—
584C2×Dic3—31no—
585C2×Dic3—31no—
586C2×Dic3—42no—
587C2×Dic3—61no—
588C2×Dic3—61no—
589C2×Dic3—62no—
590C2×Dic3—61no—
591C2×Dic3—61no—
592C2×Dic3—121no—
593C2×Dic3—121no—
594C2×Dic3—122no—
595C2×Dic3—122no—
596C2×Dic3—122no—
597C2×Dic3—122no—
598C2×Dic3—122no—
599C2×Dic3—242no—
600C2×Dic3D3×D411yescharacteristic
601C2×Dic3D3×D411yescharacteristic
602C2×Dic3D3×D411yescharacteristic
603D12—21no—
604D12—21no—
605D12—21no—
606D12—42no—
607D12—61no—
608D12—61no—
609D12—61no—
610D12—61no—
611D12—121no—
612D12—121no—
613D12—122no—
614D12—122no—
615D12—122no—
616D12C2×#6712yes—
617C4×D3—42no—
618C4×D3—62no—
619C4×D3—122no—
620C4×D3—121no—
621C4×D3—122no—
622C4×D3—122no—
623C4×D3—122no—
624C4×D3—122no—
625C4×D3#23712yes—
626C4×D3C2×#6712yes—
627Dic6—21no—
628Dic6—21no—
629C3×C8—21no—
630C3×C8—21no—
631C3×C8—41no—
632C3×C8—61no—
633C3×C8—61no—
634C3⋊C8—21no—
635C3⋊C8—21no—
636C3⋊C8—61no—
637C3⋊C8—61no—
638C3⋊C8—121no—
639C2×C32—42no—
640C2×C32C2×#12111yescharacteristic
641C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
642C2×C32#57511yescharacteristic
643C3⋊D3—81no—
644C3×D3—22no—
645C3×D3—42no—
646C3×D3—81no—
647C24—61no—
648#41—62no—
649#41—62no—
650#41—182no—
651#41—182no—
652C2×Q8—31no—
653C2×Q8C2×D3211yescharacteristic
654C2×D4—34no—
655C2×D4—31no—
656C2×D4—31no—
657C2×D4—61no—
658C2×D4—62no—
659C2×D4—61no—
660C2×D4—91no—
661C2×D4—181no—
662C2×D4—181no—
663C2×D4—181no—
664C2×D4C2×D3211yescharacteristic
665C22×C4—31no—
666C22×C4—61no—
667C22×C4—61no—
668C22×C4—91no—
669C22×C4—91no—
670C22×C4—181no—
671C22×C4—181no—
672C22×C4—181no—
673C22×C4—181no—
674C22×C4—181no—
675C22×C4—364no—
676SD16—22no—
677SD16—62no—
678SD16—62no—
679SD16—182no—
680D8—62no—
681D8—62no—
682D8—182no—
683D8—182no—
684M16—62no—
685M16—182no—
686C2×C8—31no—
687C2×C8—31no—
688C2×C8—91no—
689C2×C8C2×D3211yescharacteristic
690C4⋊C4—31no—
691C4⋊C4—61no—
692C4⋊C4—61no—
693C4⋊C4—91no—
694C4⋊C4—181no—
695C22⋊C4—61no—
696C22⋊C4—181no—
697C22⋊C4—181no—
698C22⋊C4—181no—
699C22⋊C4—181no—
700C22⋊C4—181no—
701C22⋊C4—181no—
702C22⋊C4—181no—
703C42—31no—
704C42—91no—
705C42—91no—
706C42—91no—
707C22×C3—22no—
708C22×C3—22no—
709C22×C3—21no—
710C22×C3—32no—
711C22×C3—42no—
712C22×C3—41no—
713C22×C3—41no—
714C22×C3—41no—
715C22×C3—41no—
716C22×C3—61no—
717C22×C3—61no—
718C22×C3—62no—
719C22×C3—81no—
720C22×C3—81no—
721C22×C3—128no—
722C22×C3—121no—
723C22×C3—121no—
724C22×C3—121no—
725C22×C3—121no—
726C22×C3—121no—
727C22×C3C2×D3×D411yescharacteristic
728C22×C3C2×D3×D411yescharacteristic
729C2×D3—21no—
730C2×D3—21no—
731C2×D3—22no—
732C2×D3—48no—
733C2×D3—41no—
734C2×D3—41no—
735C2×D3—41no—
736C2×D3—41no—
737C2×D3—41no—
738C2×D3—121no—
739C2×D3—121no—
740C2×D3—121no—
741C2×D3—121no—
742C2×D3—121no—
743C2×D3—121no—
744C2×D3—241no—
745C2×D3—241no—
746C2×D3—241no—
747C2×D3#93912yes—
748C3×C4—21no—
749C3×C4—21no—
750C3×C4—32no—
751C3×C4—32no—
752C3×C4—41no—
753C3×C4—41no—
754C3×C4—61no—
755C3×C4—81no—
756C3×C4—121no—
757C3×C4—121no—
758C3×C4C2×D3×D411yescharacteristic
759C3×C4C2×#23711yescharacteristic
760C3×C4D3×#4111yescharacteristic
761C3×C4C22×#6711yescharacteristic
762Dic3—21no—
763Dic3—41no—
764Dic3—41no—
765Dic3—61no—
766Dic3—61no—
767Dic3—61no—
768Dic3—61no—
769Dic3—121no—
770Dic3—121no—
771Dic3—121no—
772Dic3—121no—
773Dic3—241no—
774Dic3#91412yescomplemented
775Dic3#93912yes—
776C32#303611yescharacteristic, complemented, Sylow
777C23—21no—
778C23—31no—
779C23—64no—
780C23—61no—
781C23—61no—
782C23—122no—
783C23—122no—
784C23—181no—
785Q8—21no—
786Q8—21no—
787Q8—61no—
788Q8—61no—
789D4—21no—
790D4—32no—
791D4—64no—
792D4—61no—
793D4—61no—
794D4—61no—
795D4—122no—
796D4—181no—
797D4—181no—
798D4—362no—
799D4—362no—
800D4—362no—
801D4D3×#6712yes—
802C2×C4—21no—
803C2×C4—31no—
804C2×C4—31no—
805C2×C4—32no—
806C2×C4—32no—
807C2×C4—31no—
808C2×C4—61no—
809C2×C4—61no—
810C2×C4—91no—
811C2×C4—91no—
812C2×C4—122no—
813C2×C4—122no—
814C2×C4—182no—
815C2×C4—181no—
816C2×C4—362no—
817C2×C4—362no—
818C2×C4—361no—
819C2×C4—362no—
820C2×C4—362no—
821C2×C4—362no—
822C2×C4C22×D3211yescharacteristic
823C8—21no—
824C8—61no—
825C8—61no—
826C8—181no—
827C2×C3—21no—
828C2×C3—21no—
829C2×C3—21no—
830C2×C3—42no—
831C2×C3—42no—
832C2×C3—62no—
833C2×C3—82no—
834C2×C3—122no—
835C2×C3—241no—
836C2×C3D3×#12111yescharacteristic
837C2×C3C2×#91411yescharacteristic
838C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
839C2×C3#577311yescharacteristic
840C2×C3#577711yescharacteristic
841C2×C3C2×#93911yescharacteristic
842D3—22no—
843D3—42no—
844D3—81no—
845D3—241no—
846D3—241no—
847D3—481no—
848C22—22no—
849C22—32no—
850C22—41no—
851C22—41no—
852C22—61no—
853C22—61no—
854C22—62no—
855C22—128no—
856C22—121no—
857C22—121no—
858C22—121no—
859C22—121no—
860C22—121no—
861C22—361no—
862C22—361no—
863C22—361no—
864C22D32×D411yescharacteristic
865C4—32no—
866C4—32no—
867C4—41no—
868C4—61no—
869C4—121no—
870C4—121no—
871C4—181no—
872C4—181no—
873C4—361no—
874C4D3×#23711yescharacteristic
875C4C2×D3×#6711yescharacteristic
876C3—21no—
877C3#8042811yescharacteristic, complemented
878C3#8393111yescharacteristic, complemented
879C2—42no—
880C2—62no—
881C2—122no—
882C2—241no—
883C2—721no—
884C2D3×#91411yescharacteristic
885C2#1059474411yescharacteristic
886C2D3×#93911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
hypercenterC2×SD16D32
hypocenterC32#3036
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×#914C2semidirect
2. #10595360C2semidirect
3. D3×D4×Dic3C2semidirect
4. C2×#63934C2semidirect
5. #10592864C2semidirect
6. C3×#5162C2semidirect
7. #10591570C2semidirect
8. #10591564C2semidirect
9. #10591550C2semidirect
10. #10591481C2semidirect
11. #10591476C2semidirect
12. #10590753C2semidirect
13. #10590751C2semidirect
14. #10590671C2semidirect
15. #10590663C2semidirect
23. #64156C22semidirect
26. C3×#944C22semidirect
38. #63911C22semidirect
47. #63863C22semidirect
51. #63662C22semidirect
52. #63648C22semidirect
53. #63641C22semidirect
54. C3×#835C22semidirect
55. C3×#816C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. #63572C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
59. #63566C22semidirect
60. #63564C22semidirect
61. #63563C22semidirect
62. #63562C22semidirect
68. C2×#914D3semidirect
79. #5162D3semidirect
104. C3×D3×D4D4semidirect
179. #944C2×D3semidirect
232. #835C2×D3semidirect
241. #816C2×D3semidirect
248. Dic3⋊C8C2×D3semidirect
356. D3×D4#67semidirect
477. C3×Dic3AGL(1,ℤ/8)semidirect
774. Dic3#914semidirect
776. C32#3036semidirect
877. C3#80428semidirect
878. C3#83931semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9142
#105953602
D3×D4×Dic32
C2×#639342
#105928642
C3×#51622
#105915702
#105915642
#105915502
#105914812
#105914762
#105907532
#105907512
#105906712
#105906632
#839313
#804283