Finite Group Databasebeta

← #11866265

Subgroups — #11866265

Order 1152.

1050 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×SD16C211yesmaximal, characteristic, complemented
2#10595340C211yesmaximal, characteristic, complemented
3#10595215C211yesmaximal, characteristic, complemented
4C2×#63934C211yesmaximal, characteristic
5#10592864C211yesmaximal, characteristic, complemented
6C3×#5162C211yesmaximal, characteristic, complemented
7#10591570C211yesmaximal, characteristic, complemented
8#10591564C211yesmaximal, characteristic, complemented
9#10591557C211yesmaximal, characteristic, complemented
10#10591497C211yesmaximal, characteristic, complemented
11#10591471C211yesmaximal, characteristic, complemented
12#10590754C211yesmaximal, characteristic, complemented
13#10590748C211yesmaximal, characteristic, complemented
14#10590694C211yesmaximal, characteristic, complemented
15#10590690C211yesmaximal, characteristic, complemented
16#83848—31nomaximal
17#80430—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C2×#3799C2211yescharacteristic
21C2×C32×SD16C2211yescharacteristic
22#64156C2211yescharacteristic, complemented
23D4×C3⋊Dic3C2211yescharacteristic
24C2×#3753C2211yescharacteristic
25C3×#944C2211yescharacteristic, complemented
26C2×C3×#215C2211yescharacteristic
27C3×D4×Dic3C2211yescharacteristic
28C2×C3×#214C2211yescharacteristic
29C2×C3×#214C2211yescharacteristic
30C3×D3×SD16—24no—
31C2×C3×#204C2211yescharacteristic
32C2×C3×D3×C8C2211yescharacteristic
33#67⋊Dic3—21no—
34Dic3×#67—21no—
35D3×#217—21no—
36C2×(C2×D3)⋊Dic3—21no—
37#63934—24no—
38#63898C2211yescharacteristic
39Dic3×D12C2211yescharacteristic
40#63888—21no—
41#63888—21no—
42#63873C2211yescharacteristic, complemented
43#63864C2211yescharacteristic, complemented
44#63855C2211yescharacteristic
45#63850—21no—
46#63850—21no—
47#63841C2211yescharacteristic
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#63566C2211yescharacteristic, complemented
61#63565C2211yescharacteristic, complemented
62#63564C2211yescharacteristic, complemented
63C22×C3×SD16—31no—
64#5816—31no—
65#5798—31no—
66C2×#932—31no—
67C2×#914—31no—
68C2×D3×SD16D311yescharacteristic, complemented
69#5724—31no—
70#5545—31no—
71C3×#461—31no—
72#5225—31no—
73#5165—31no—
74#5165—31no—
75#5165—31no—
76#5165—31no—
77#5165—31no—
78#5165—61no—
79#5162—31no—
80#5162—31no—
81#5162—31no—
82#5162—31no—
83#5162D311yescharacteristic, complemented
84#5113—31no—
85#5102—31no—
86#5083—31no—
87#5016—31no—
88#4844—31no—
89#4839—31no—
90#4819—31no—
91#4818—31no—
92#4804—31no—
93#4802—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×D3×Q8—22no—
102C3×D3×Q8—22no—
103C3×D3×D4—22no—
104C3×D3×D4D414yes—
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6—21no—
109C2×C3×Dic6C2311yescharacteristic
110C2×C3×Dic6C2311yescharacteristic
111C2×#626—21no—
112C2×#624—21no—
113C2×D3×Dic3—21no—
114C2×D3×Dic3—21no—
115#3799—22no—
116#3799—22no—
117C32×SD16—22no—
118C2×C32×C8C2311yescharacteristic
119#3757—21no—
120#3753—22no—
121#3752—21no—
122#3752—21no—
123C4⋊(C3⋊Dic3)C2311yescharacteristic
124C4×C3⋊Dic3C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C3×#217—21no—
127C3×#215—22no—
128C3×#214—22no—
129C3×#214—22no—
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×C4×Dic3C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C3×#204—22no—
137C3×D3×C8—22no—
138#3724—21no—
139#3724—21no—
140Dic3⋊Dic3D411yescharacteristic
141Dic3⋊Dic3D411yescharacteristic
142#3722—21no—
143#3722—21no—
144(C2×D3)⋊Dic3—21no—
145(C2×D3)⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3D411yescharacteristic
148(C2×D3)⋊Dic3D411yescharacteristic
149Dic32—21no—
150#3715—22no—
151#3714—22no—
152#3711—22no—
153#3042—91noSylow
154C22×C3×Q8—31no—
155C22×C3×D4—31no—
156C2×#239—31no—
157C2×D3×Q8C2×D311yescharacteristic
158C2×D3×D4C2×D311yescharacteristic
159C2×#235—31no—
160C2×C3×SD16—21no—
161C2×C3×SD16—31no—
162C2×C3×SD16—31no—
163C2×C3×SD16—31no—
164C2×C3×SD16—31no—
165C2×C3×SD16—64no—
166C2×C3×SD16C2×D311yescharacteristic
167C2×C3×SD16C2×D311yescharacteristic
168C22×C3×C8—31no—
169C3×C4⋊Q8—31no—
170C3×C4×D4—31no—
171C2×#217—61no—
172C2×#217—61no—
173#947—31no—
174#947—31no—
175#947—31no—
176#947—61no—
177#946—61no—
178#946—61no—
179#944—31no—
180#944—31no—
181#944C2×D311yescharacteristic, complemented
182C2×#215—31no—
183C2×#215C2×D311yescharacteristic
184D4×Dic3—31no—
185D4×Dic3—31no—
186D4×Dic3—31no—
187D4×Dic3—31no—
188D4×Dic3—61no—
189D4×Dic3—61no—
190D4×Dic3—61no—
191D4×Dic3C2×D311yescharacteristic
192C2×#214—31no—
193C2×#214C2×D311yescharacteristic
194C2×#214C2×D311yescharacteristic
195#932—64no—
196C2×#213—31no—
197C2×#213—31no—
198C2×#213—31no—
199C2×#213—61no—
200#929—61no—
201#929—61no—
202C4×#67—61no—
203C2×(C2×D3)⋊C4—61no—
204#926—31no—
205#926—31no—
206C2×#208—31no—
207#914—64no—
208D3×SD16—24no—
209C2×D24—31no—
210C2×#204C2×D311yescharacteristic
211C2×ΓL(1,𝔽25)—31no—
212C2×D3×C8C2×D311yescharacteristic
213#896—61no—
214#896—61no—
215#894—61no—
216#894—61no—
217#893—31no—
218#892—31no—
219#67⋊C4—61no—
220D3×C22⋊C4—61no—
221#875—31no—
222C4×D12—31no—
223#872—31no—
224C3×C4⋊C8—31no—
225C3×#103—31no—
226C3×#103—31no—
227#835—31no—
228#835—31no—
229#835—31no—
230#835—31no—
231#835—31no—
232#835—61no—
233#835C2×D311yescharacteristic, complemented
234#821—31no—
235#821—31no—
236#821—31no—
237#821—61no—
238#816—31no—
239#816—31no—
240#816C2×D311yescharacteristic, complemented
241Dic3⋊C8—31no—
242Dic3⋊C8—31no—
243Dic3⋊C8—31no—
244Dic3⋊C8—31no—
245Dic3⋊C8—31no—
246Dic3⋊C8—61no—
247Dic3⋊C8C2×D311yescharacteristic, complemented
248#810—31no—
249#809—31no—
250C4⋊(C3⋊C8)—31no—
251C23×C32—21no—
252C22×C3⋊D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3—24no—
255C22×C3×D3—81no—
256C22×C3×D3—81no—
257C22×C3×D3C2×D411yescharacteristic
258C32×Q8—21no—
259C32×Q8—21no—
260C32×D4—21no—
261C32×D4C2×D412yes—
262C2×C32×C4—21no—
263C2×C32×C4C2411yescharacteristic
264C2×C3⋊Dic3—21no—
265C2×C3⋊Dic3—81no—
266C2×C3⋊Dic3C2×D411yescharacteristic
267C2×C3⋊Dic3C2×D411yescharacteristic
268C4⋊(C3⋊D3)—21no—
269C4⋊(C3⋊D3)—21no—
270C3×#67—24no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—81no—
275C2×C3×Dic3C2×D411yescharacteristic
276C2×C3×Dic3C2×D411yescharacteristic
277C2×C3×Dic3C2×D411yescharacteristic
278C3×D12—21no—
279C3×D12C2×D412yes—
280C3×C4×D3—42no—
281C3×C4×D3C2×D412yes—
282C3×C4×D3#4112yes—
283C3×Dic6—21no—
284C3×Dic6—21no—
285C3×Dic6—21no—
286C3×Dic6—21no—
287C3×Dic6—42no—
288#626—42no—
289#624—42no—
290D3×Dic3—81no—
291D3×Dic3—81no—
292C32×C8—21no—
293C3⋊(C3⋊C8)—21no—
294C3×C3⋊C8—21no—
295C3×C3⋊C8—21no—
296C2×AGL(1,ℤ/8)—91no—
297C22×SD16—31no—
298#536—91no—
299#518—91no—
300#463—91no—
301#463—91no—
302#463—91no—
303#463—91no—
304#461—31no—
305#461—91no—
306#461—91no—
307#461—91no—
308#424—91no—
309#419—91no—
310#416—91no—
311C24×C3—61no—
312C23×D3—21no—
313C2×C3×Q8—21no—
314C2×C3×Q8—31no—
315C2×C3×Q8—31no—
316C2×C3×Q8—61no—
317C2×C3×Q8—62no—
318C2×C3×Q8—62no—
319C2×C3×Q8C22×D311yescharacteristic
320C2×C3×Q8C22×D311yescharacteristic
321C2×C3×D4—21no—
322C2×C3×D4—34no—
323C2×C3×D4—31no—
324C2×C3×D4—62no—
325C2×C3×D4—61no—
326C2×C3×D4C22×D311yescharacteristic
327C2×C3×D4C22×D311yescharacteristic
328C22×C3×C4—31no—
329C22×C3×C4—61no—
330C22×C3×C4—61no—
331C2×#67—21no—
332C2×#67—61no—
333C22×Dic3—21no—
334C22×Dic3—61no—
335C22×Dic3—61no—
336C22×Dic3—61no—
337C22×Dic3—61no—
338C22×Dic3—121no—
339#239—62no—
340#239—62no—
341D3×Q8—22no—
342D3×Q8—22no—
343D3×D4—22no—
344D3×D4#6714yes—
345#235—62no—
346#235—62no—
347C2×D12—31no—
348C2×D12—31no—
349C2×D12—61no—
350C2×D12—61no—
351C2×D12C22×D311yescharacteristic
352C2×C4×D3—21no—
353C2×C4×D3—61no—
354C2×C4×D3—61no—
355C2×C4×D3—61no—
356C2×C4×D3—61no—
357C2×C4×D3C22×D311yescharacteristic
358C2×Dic6—21no—
359C2×Dic6C22×D311yescharacteristic
360C2×Dic6C22×D311yescharacteristic
361C3×SD16—22no—
362C3×SD16—22no—
363C3×SD16—42no—
364C3×SD16—62no—
365C3×SD16—62no—
366C3×SD16—62no—
367C3×SD16—62no—
368C2×C3×C8—21no—
369C2×C3×C8—31no—
370C2×C3×C8—31no—
371C2×C3×C8—62no—
372C2×C3×C8C22×D311yescharacteristic
373C2×C3×C8C22×D311yescharacteristic
374C3×C4⋊C4—31no—
375C3×C4⋊C4—61no—
376C3×C4⋊C4—61no—
377C3×C22⋊C4—61no—
378C3×C42—31no—
379#217—21no—
380#217—31no—
381#217—31no—
382#217—61no—
383#217—61no—
384#217—61no—
385#217—61no—
386#217—61no—
387#217—121no—
388#215—22no—
389#215—62no—
390#214—22no—
391#214—22no—
392#214—62no—
393#213—62no—
394#213—62no—
395#213—62no—
396#213—122no—
397(C2×D3)⋊C4—31no—
398(C2×D3)⋊C4—31no—
399(C2×D3)⋊C4—61no—
400(C2×D3)⋊C4—61no—
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—61no—
407(C2×D3)⋊C4—61no—
408(C2×D3)⋊C4—61no—
409(C2×D3)⋊C4—61no—
410(C2×D3)⋊C4—121no—
411(C2×D3)⋊C4—121no—
412C4⋊Dic3—31no—
413C4⋊Dic3—31no—
414C4⋊Dic3—31no—
415C4⋊Dic3—31no—
416C4⋊Dic3—61no—
417C4⋊Dic3C22×D311yescharacteristic
418Dic3⋊C4—21no—
419Dic3⋊C4—21no—
420Dic3⋊C4—31no—
421Dic3⋊C4—31no—
422Dic3⋊C4—61no—
423Dic3⋊C4—61no—
424Dic3⋊C4—61no—
425Dic3⋊C4—61no—
426C4×Dic3—31no—
427C4×Dic3—31no—
428C4×Dic3—61no—
429C4×Dic3—61no—
430C4×Dic3—61no—
431C4×Dic3C22×D311yescharacteristic
432#208—62no—
433C2×C3⋊C8—31no—
434C2×C3⋊C8—31no—
435C2×C3⋊C8—61no—
436C2×C3⋊C8C22×D311yescharacteristic
437C2×C3⋊C8C22×D311yescharacteristic
438D24—62no—
439#204—22no—
440ΓL(1,𝔽25)—62no—
441D3×C8—22no—
442C22×C32—22no—
443C22×C32—41no—
444C22×C32—41no—
445C22×C32C22×D411yescharacteristic
446C2×C3⋊D3—41no—
447C2×C3⋊D3—41no—
448C2×C3⋊D3—41no—
449C2×C3×D3—21no—
450C2×C3×D3—21no—
451C2×C3×D3—22no—
452C2×C3×D3—41no—
453C2×C3×D3—41no—
454C2×C3×D3—84no—
455C2×C3×D3#12112yes—
456C32×C4—41no—
457C32×C4C22×D411yescharacteristic
458C32×C4C2×#4111yescharacteristic
459C3⋊Dic3—21no—
460C3⋊Dic3—21no—
461C3⋊Dic3—41no—
462C3×Dic3—21no—
463C3×Dic3—21no—
464C3×Dic3—41no—
465C3×Dic3—41no—
466C3×Dic3—41no—
467C3×Dic3#12112yes—
468C2×#41—91no—
469C22×Q8—31no—
470C22×D4—31no—
471AGL(1,ℤ/8)—184no—
472C2×SD16—31no—
473C2×SD16—31no—
474C2×SD16—31no—
475C2×SD16—31no—
476C2×SD16—64no—
477C2×SD16—91no—
478C2×SD16D3211yescharacteristic
479C2×D8—91no—
480C2×D8—91no—
481C2×M16—91no—
482C22×C8—31no—
483C4⋊Q8—31no—
484C4⋊Q8—91no—
485#124—91no—
486#124—91no—
487#123—181no—
488#123—181no—
489C22⋊Q8—181no—
490C22⋊Q8—181no—
491C4×D4—31no—
492C4×D4—91no—
493C4×D4—91no—
494C4×D4—91no—
495C4×D4—181no—
496C4×D4—181no—
497#117—91no—
498#117—91no—
499C2×C22⋊C4—181no—
500C2×C22⋊C4—181no—
501C4⋊C8—31no—
502C4⋊C8—91no—
503C4⋊C8—91no—
504C4⋊C8—91no—
505#103—31no—
506#103—31no—
507#103—91no—
508#103—91no—
509#103—91no—
510#103—91no—
511#102—91no—
512#102—91no—
513C23×C3—21no—
514C23×C3—21no—
515C23×C3—31no—
516C23×C3—41no—
517C23×C3—64no—
518C23×C3—61no—
519C23×C3—241no—
520C23×C3—241no—
521C22×D3—21no—
522C22×D3—24no—
523C22×D3—61no—
524C22×D3—61no—
525C22×D3—81no—
526C22×D3—81no—
527C22×D3—121no—
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—22no—
543C3×D4—32no—
544C3×D4—41no—
545C3×D4—64no—
546C3×D4—61no—
547C3×D4D3×D412yes—
548C3×D4C2×#6712yes—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—31no—
553C2×C3×C4—32no—
554C2×C3×C4—32no—
555C2×C3×C4—31no—
556C2×C3×C4—31no—
557C2×C3×C4—41no—
558C2×C3×C4—61no—
559C2×C3×C4—61no—
560C2×C3×C4—61no—
561C2×C3×C4—122no—
562C2×C3×C4—241no—
563C2×C3×C4C23×D311yescharacteristic
564C2×C3×C4C23×D311yescharacteristic
565#67—24no—
566#67—122no—
567C2×Dic3—21no—
568C2×Dic3—21no—
569C2×Dic3—21no—
570C2×Dic3—31no—
571C2×Dic3—31no—
572C2×Dic3—31no—
573C2×Dic3—31no—
574C2×Dic3—61no—
575C2×Dic3—61no—
576C2×Dic3—61no—
577C2×Dic3—61no—
578C2×Dic3—81no—
579C2×Dic3—121no—
580C2×Dic3—241no—
581C2×Dic3—241no—
582C2×Dic3—241no—
583C2×Dic3—241no—
584C2×Dic3—242no—
585C2×Dic3D3×D411yescharacteristic
586C2×Dic3D3×D411yescharacteristic
587C2×Dic3D3×D411yescharacteristic
588D12—21no—
589D12—61no—
590D12—61no—
591D12—61no—
592D12—61no—
593D12—121no—
594D12—121no—
595D12—122no—
596D12C2×#6712yes—
597C4×D3—42no—
598C4×D3—122no—
599C4×D3—122no—
600C4×D3—241no—
601C4×D3—241no—
602C4×D3#23712yes—
603C4×D3C2×#6712yes—
604Dic6—21no—
605Dic6—21no—
606Dic6—21no—
607Dic6—21no—
608Dic6—42no—
609C3×C8—21no—
610C3×C8—21no—
611C3×C8—41no—
612C3×C8—61no—
613C3×C8—61no—
614C3⋊C8—21no—
615C3⋊C8—21no—
616C3⋊C8—61no—
617C3⋊C8—61no—
618C3⋊C8—121no—
619C2×C32—42no—
620C2×C32C2×#12111yescharacteristic
621C2×C32#57711yescharacteristic
622C2×C32#57711yescharacteristic
623C3⋊D3—81no—
624C3×D3—22no—
625C3×D3—42no—
626C24—61no—
627#41—182no—
628#41—182no—
629C2×Q8—31no—
630C2×Q8—31no—
631C2×Q8—61no—
632C2×Q8—62no—
633C2×Q8—62no—
634C2×Q8C2×D3211yescharacteristic
635C2×D4—34no—
636C2×D4—31no—
637C2×D4—62no—
638C2×D4—61no—
639C2×D4—91no—
640C2×D4—181no—
641C2×D4C2×D3211yescharacteristic
642C22×C4—31no—
643C22×C4—61no—
644C22×C4—61no—
645C22×C4—181no—
646C22×C4—181no—
647C22×C4—181no—
648C22×C4—181no—
649SD16—22no—
650SD16—62no—
651SD16—62no—
652SD16—62no—
653SD16—62no—
654SD16—182no—
655D8—182no—
656D8—182no—
657M16—182no—
658C2×C8—31no—
659C2×C8—31no—
660C2×C8—62no—
661C2×C8—91no—
662C2×C8C2×D3211yescharacteristic
663C4⋊C4—31no—
664C4⋊C4—61no—
665C4⋊C4—61no—
666C4⋊C4—91no—
667C4⋊C4—91no—
668C4⋊C4—91no—
669C4⋊C4—181no—
670C4⋊C4—181no—
671C22⋊C4—61no—
672C22⋊C4—91no—
673C22⋊C4—91no—
674C22⋊C4—181no—
675C22⋊C4—181no—
676C22⋊C4—181no—
677C22⋊C4—181no—
678C22⋊C4—181no—
679C22⋊C4—181no—
680C22⋊C4—181no—
681C22⋊C4—181no—
682C42—31no—
683C42—91no—
684C42—181no—
685C22×C3—22no—
686C22×C3—22no—
687C22×C3—21no—
688C22×C3—32no—
689C22×C3—42no—
690C22×C3—41no—
691C22×C3—41no—
692C22×C3—41no—
693C22×C3—41no—
694C22×C3—61no—
695C22×C3—61no—
696C22×C3—62no—
697C22×C3—81no—
698C22×C3—81no—
699C22×C3—121no—
700C22×C3—121no—
701C22×C3—244no—
702C22×C3C2×D3×D411yescharacteristic
703C22×C3C2×D3×D411yescharacteristic
704C2×D3—21no—
705C2×D3—21no—
706C2×D3—22no—
707C2×D3—41no—
708C2×D3—41no—
709C2×D3—84no—
710C2×D3—121no—
711C2×D3—121no—
712C2×D3—121no—
713C2×D3—121no—
714C2×D3—121no—
715C2×D3—121no—
716C2×D3—241no—
717C2×D3—241no—
718C2×D3—241no—
719C2×D3#93912yes—
720C3×C4—21no—
721C3×C4—21no—
722C3×C4—32no—
723C3×C4—41no—
724C3×C4—41no—
725C3×C4—61no—
726C3×C4—61no—
727C3×C4—81no—
728C3×C4—121no—
729C3×C4—121no—
730C3×C4—121no—
731C3×C4C2×D3×D411yescharacteristic
732C3×C4C2×#23711yescharacteristic
733C3×C4D3×#4111yescharacteristic
734C3×C4C22×#6711yescharacteristic
735Dic3—21no—
736Dic3—21no—
737Dic3—41no—
738Dic3—41no—
739Dic3—41no—
740Dic3—61no—
741Dic3—61no—
742Dic3—61no—
743Dic3—61no—
744Dic3—121no—
745Dic3—121no—
746Dic3—121no—
747Dic3—121no—
748Dic3—241no—
749Dic3#93912yes—
750C32#304211yescharacteristic, complemented, Sylow
751C23—21no—
752C23—31no—
753C23—64no—
754C23—61no—
755C23—181no—
756C23—241no—
757C23—241no—
758Q8—21no—
759Q8—21no—
760Q8—61no—
761Q8—61no—
762Q8—61no—
763Q8—61no—
764Q8—122no—
765D4—21no—
766D4—32no—
767D4—64no—
768D4—61no—
769D4—181no—
770D4—181no—
771D4—362no—
772D4D3×#6712yes—
773C2×C4—21no—
774C2×C4—31no—
775C2×C4—32no—
776C2×C4—32no—
777C2×C4—31no—
778C2×C4—31no—
779C2×C4—61no—
780C2×C4—61no—
781C2×C4—61no—
782C2×C4—91no—
783C2×C4—91no—
784C2×C4—122no—
785C2×C4—181no—
786C2×C4—241no—
787C2×C4—362no—
788C2×C4—721no—
789C2×C4—721no—
790C2×C4—721no—
791C2×C4C22×D3211yescharacteristic
792C8—21no—
793C8—61no—
794C8—61no—
795C8—181no—
796C2×C3—21no—
797C2×C3—21no—
798C2×C3—21no—
799C2×C3—42no—
800C2×C3—42no—
801C2×C3—62no—
802C2×C3—82no—
803C2×C3—122no—
804C2×C3D3×#12111yescharacteristic
805C2×C3#576211yescharacteristic
806C2×C3#576211yescharacteristic
807C2×C3#576211yescharacteristic
808C2×C3#577811yescharacteristic
809C2×C3C2×#93911yescharacteristic
810D3—22no—
811D3—42no—
812D3—241no—
813D3—241no—
814D3—481no—
815C22—22no—
816C22—32no—
817C22—41no—
818C22—41no—
819C22—61no—
820C22—61no—
821C22—62no—
822C22—121no—
823C22—121no—
824C22—244no—
825C22—361no—
826C22—361no—
827C22—361no—
828C22D32×D411yescharacteristic
829C4—32no—
830C4—41no—
831C4—61no—
832C4—61no—
833C4—121no—
834C4—121no—
835C4—121no—
836C4—181no—
837C4—181no—
838C4—361no—
839C4D3×#23711yescharacteristic
840C4C2×D3×#6711yescharacteristic
841C3—21no—
842C3#8043011yescharacteristic, complemented
843C3#8384811yescharacteristic, complemented
844C2—42no—
845C2—62no—
846C2—122no—
847C2—721no—
848C2#1059474811yescharacteristic
849C2#1059475111yescharacteristic
850C2D3×#93911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
prime radicalC2×#63934C2
hypercenterC2×SD16D32
hypocenterC32#3042
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. #10595340C2semidirect
3. #10595215C2semidirect
5. #10592864C2semidirect
6. C3×#5162C2semidirect
7. #10591570C2semidirect
8. #10591564C2semidirect
9. #10591557C2semidirect
10. #10591497C2semidirect
11. #10591471C2semidirect
12. #10590754C2semidirect
13. #10590748C2semidirect
14. #10590694C2semidirect
15. #10590690C2semidirect
22. #64156C22semidirect
25. C3×#944C22semidirect
42. #63873C22semidirect
43. #63864C22semidirect
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. #63566C22semidirect
61. #63565C22semidirect
62. #63564C22semidirect
68. C2×D3×SD16D3semidirect
83. #5162D3semidirect
181. #944C2×D3semidirect
233. #835C2×D3semidirect
240. #816C2×D3semidirect
247. Dic3⋊C8C2×D3semidirect
750. C32#3042semidirect
842. C3#80430semidirect
843. C3#83848semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×SD162
#105953402
#105952152
C2×#639342
#105928642
C3×#51622
#105915702
#105915642
#105915572
#105914972
#105914712
#105907542
#105907482
#105906942
#105906902
#838483
#804303