Finite Group Databasebeta

← #11866269

Subgroups — #11866269

Order 1152.

1048 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×#914C211yesmaximal, characteristic
2#10595356C211yesmaximal, characteristic, complemented
3#10595215C211yesmaximal, characteristic, complemented
4C2×D3×#214C211yesmaximal, characteristic, complemented
5#10592861C211yesmaximal, characteristic, complemented
6C3×#5162C211yesmaximal, characteristic, complemented
7#10591569C211yesmaximal, characteristic, complemented
8#10591564C211yesmaximal, characteristic, complemented
9#10591556C211yesmaximal, characteristic, complemented
10#10591476C211yesmaximal, characteristic, complemented
11#10591468C211yesmaximal, characteristic, complemented
12#10590948C211yesmaximal, characteristic, complemented
13#10590755C211yesmaximal, characteristic, complemented
14#10590751C211yesmaximal, characteristic, complemented
15#10590695C211yesmaximal, characteristic, complemented
16#83935—31nomaximal
17#80430—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C2×D3×Dic6C2211yescharacteristic
21C2×C32×SD16C2211yescharacteristic
22#64153C2211yescharacteristic, complemented
23D4×C3⋊Dic3C2211yescharacteristic
24C2×#3754C2211yescharacteristic
25C3×#944C2211yescharacteristic, complemented
26C2×C3×#215C2211yescharacteristic
27C3×D4×Dic3C2211yescharacteristic
28C2×C3×#214C2211yescharacteristic
29C2×C3×#213C2211yescharacteristic
30C3×#914—24no—
31C2×C3×D24C2211yescharacteristic
32C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
33#67⋊Dic3—21no—
34Dic3×#67—21no—
35D3×#217—21no—
36C2×(C2×D3)⋊Dic3—21no—
37D3×#214—24no—
38#63898C2211yescharacteristic
39Dic3×D12C2211yescharacteristic
40#63884—21no—
41#63884—21no—
42#63863C2211yescharacteristic, complemented
43#63860C2211yescharacteristic, complemented
44#63855C2211yescharacteristic
45#63851—21no—
46#63851—21no—
47#63841C2211yescharacteristic
48C2×#3716C2211yescharacteristic
49C2×#3715C2211yescharacteristic
50C2×D3×C3⋊C8C2211yescharacteristic
51#63662C2211yescharacteristic, complemented
52#63643C2211yescharacteristic, complemented
53#63641C2211yescharacteristic, complemented
54C3×#835C2211yescharacteristic, complemented
55C3×#816C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57#63572C2211yescharacteristic, complemented
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63566C2211yescharacteristic, complemented
61#63563C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63C2×C3×AGL(1,ℤ/8)—31no—
64#5825—31no—
65#5798—31no—
66C22×#214—31no—
67C2×#914D311yescharacteristic
68C2×D3×SD16—31no—
69#5724—31no—
70#5545—31no—
71C3×#461—31no—
72#5233—31no—
73#5165—31no—
74#5162—31no—
75#5162—31no—
76#5162—31no—
77#5162—31no—
78#5162—61no—
79#5162D311yescharacteristic, complemented
80#5153—31no—
81#5153—31no—
82#5153—31no—
83#5153—31no—
84#5120—31no—
85#5119—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×#634C2311yescharacteristic
99C2×C3×#67—21no—
100C22×C3×Dic3—21no—
101C3×#239—22no—
102C3×#239—22no—
103C3×D3×D4—22no—
104C3×D3×D4D414yes—
105C2×C3×D12—21no—
106C2×C3×D12C2311yescharacteristic
107C2×C3×D12C2311yescharacteristic
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×Dic6C2311yescharacteristic
111C2×#627—21no—
112C2×D3×Dic3—21no—
113C2×D3×Dic3—21no—
114C2×D3×Dic3—21no—
115D3×Dic6—22no—
116D3×Dic6—22no—
117C32×SD16—22no—
118C2×C32×C8C2311yescharacteristic
119#3757—21no—
120#3754—22no—
121C4⋊(C3⋊Dic3)C2311yescharacteristic
122#3750—21no—
123#3750—21no—
124C4×C3⋊Dic3C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C3×#217—21no—
127C3×#215—22no—
128C3×#214—22no—
129C3×#213—22no—
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×C4×Dic3C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C3×D24—22no—
137C3×ΓL(1,𝔽25)—22no—
138Dic3⋊Dic3D411yescharacteristic
139Dic3⋊Dic3D411yescharacteristic
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143(C2×D3)⋊Dic3—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#3716—22no—
151#3715—22no—
152D3×C3⋊C8—22no—
153#3042—91noSylow
154C2×C3×#41—31no—
155C22×C3×D4—31no—
156C2×#239C2×D311yescharacteristic
157C2×D3×Q8—31no—
158C2×D3×D4C2×D311yescharacteristic
159C22×Dic6—31no—
160C3×AGL(1,ℤ/8)—64no—
161C2×C3×SD16—21no—
162C2×C3×SD16—31no—
163C2×C3×SD16—31no—
164C2×C3×SD16C2×D311yescharacteristic
165C2×C3×SD16C2×D311yescharacteristic
166C2×C3×D8—31no—
167C2×C3×D8—31no—
168C2×C3×M16—31no—
169C3×C4⋊Q8—31no—
170C3×C4×D4—31no—
171C2×#217—61no—
172C2×#217—61no—
173#947—31no—
174#944—31no—
175#944—31no—
176#944—61no—
177#944C2×D311yescharacteristic, complemented
178C2×#215—31no—
179C2×#215C2×D311yescharacteristic
180#936—31no—
181#936—31no—
182#935—61no—
183#935—61no—
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×#214—31no—
194C2×#214—31no—
195C2×#214—31no—
196C2×#214—61no—
197C2×#214—64no—
198C2×#214C2×D311yescharacteristic
199C2×#213C2×D311yescharacteristic
200C4×#67—61no—
201C2×(C2×D3)⋊C4—61no—
202#926—31no—
203#926—31no—
204#924—61no—
205#924—61no—
206C22×C3⋊C8—31no—
207#914—24no—
208D3×SD16—64no—
209C2×D24C2×D311yescharacteristic
210C2×#204—31no—
211C2×ΓL(1,𝔽25)C2×D311yescharacteristic
212C2×D3×C8—31no—
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—61no—
231#835C2×D311yescharacteristic, complemented
232#832—31no—
233#832—31no—
234#821—31no—
235#816—31no—
236#816—31no—
237#816—31no—
238#816—31no—
239#816—61no—
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—24no—
254C22×C3×D3—21no—
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—21no—
266C2×C3⋊Dic3—81no—
267C2×C3⋊Dic3C2×D411yescharacteristic
268C2×C3⋊Dic3C2×D411yescharacteristic
269#634—21no—
270#634—21no—
271C3×#67—24no—
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×D12—21no—
280C3×D12—21no—
281C3×D12—42no—
282C3×D12C2×D412yes—
283C3×C4×D3—42no—
284C3×C4×D3C2×D412yes—
285C3×C4×D3#4112yes—
286C3×Dic6—21no—
287C3×Dic6—21no—
288#627—42no—
289D3×Dic3—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)—31no—
297C22×SD16—91no—
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—
313C3×#41—62no—
314C3×#41—62no—
315C2×C3×Q8—21no—
316C2×C3×Q8—31no—
317C2×C3×Q8C22×D311yescharacteristic
318C2×C3×Q8C22×D311yescharacteristic
319C2×C3×D4—21no—
320C2×C3×D4—34no—
321C2×C3×D4—31no—
322C2×C3×D4—31no—
323C2×C3×D4—61no—
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—
332C22×Dic3—21no—
333C22×Dic3—61no—
334C22×Dic3—61no—
335C22×Dic3—61no—
336C22×Dic3—61no—
337C22×Dic3—61no—
338C22×Dic3—121no—
339#239—22no—
340#239—22no—
341D3×Q8—62no—
342D3×Q8—62no—
343D3×D4—22no—
344D3×D4#6714yes—
345C2×D12—21no—
346C2×D12C22×D311yescharacteristic
347C2×D12C22×D311yescharacteristic
348C2×C4×D3—21no—
349C2×C4×D3—61no—
350C2×C4×D3—61no—
351C2×C4×D3—61no—
352C2×C4×D3C22×D311yescharacteristic
353C2×Dic6—31no—
354C2×Dic6—31no—
355C2×Dic6—61no—
356C2×Dic6—62no—
357C2×Dic6—62no—
358C2×Dic6—61no—
359C2×Dic6—61no—
360C2×Dic6C22×D311yescharacteristic
361C3×SD16—22no—
362C3×SD16—22no—
363C3×SD16—42no—
364C3×SD16—62no—
365C3×SD16—62no—
366C3×D8—62no—
367C3×D8—62no—
368C3×M16—62no—
369C2×C3×C8—21no—
370C2×C3×C8—31no—
371C2×C3×C8—31no—
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—61no—
388#217—61no—
389#217—61no—
390#217—61no—
391#217—121no—
392#215—22no—
393#215—62no—
394#214—22no—
395#214—62no—
396#214—62no—
397#214—62no—
398#214—62no—
399#214—122no—
400#213—22no—
401(C2×D3)⋊C4—31no—
402(C2×D3)⋊C4—31no—
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—
410C4⋊Dic3—31no—
411C4⋊Dic3—31no—
412C4⋊Dic3—31no—
413C4⋊Dic3—31no—
414C4⋊Dic3—61no—
415C4⋊Dic3C22×D311yescharacteristic
416Dic3⋊C4—21no—
417Dic3⋊C4—21no—
418Dic3⋊C4—31no—
419Dic3⋊C4—31no—
420Dic3⋊C4—61no—
421Dic3⋊C4—61no—
422Dic3⋊C4—61no—
423Dic3⋊C4—61no—
424Dic3⋊C4—121no—
425Dic3⋊C4—121no—
426C4×Dic3—31no—
427C4×Dic3—31no—
428C4×Dic3—61no—
429C4×Dic3—61no—
430C4×Dic3—61no—
431C4×Dic3C22×D311yescharacteristic
432C2×C3⋊C8—31no—
433C2×C3⋊C8—31no—
434C2×C3⋊C8—61no—
435C2×C3⋊C8—62no—
436C2×C3⋊C8C22×D311yescharacteristic
437C2×C3⋊C8C22×D311yescharacteristic
438D24—22no—
439#204—62no—
440ΓL(1,𝔽25)—22no—
441D3×C8—62no—
442C22×C32—22no—
443C22×C32—41no—
444C22×C32—41no—
445C22×C32C22×D411yescharacteristic
446C2×C3×D3—21no—
447C2×C3×D3—21no—
448C2×C3×D3—22no—
449C2×C3×D3—41no—
450C2×C3×D3—41no—
451C2×C3×D3—41no—
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—41no—
463C3×Dic3—21no—
464C3×Dic3—21no—
465C3×Dic3—41no—
466C3×Dic3—41no—
467C3×Dic3#12112yes—
468C2×#41—31no—
469C22×Q8—91no—
470C22×D4—31no—
471AGL(1,ℤ/8)—64no—
472C2×SD16—31no—
473C2×SD16—31no—
474C2×SD16—91no—
475C2×SD16—91no—
476C2×SD16—91no—
477C2×SD16—184no—
478C2×SD16D3211yescharacteristic
479C2×D8—31no—
480C2×D8—31no—
481C2×M16—31no—
482C22×C8—91no—
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—61no—
520C23×C3—241no—
521C23×C3—241no—
522C22×D3—21no—
523C22×D3—24no—
524C22×D3—21no—
525C22×D3—81no—
526C22×D3—81no—
527C22×D3D3×D411yescharacteristic
528C3×Q8—21no—
529C3×Q8—21no—
530C3×Q8—21no—
531C3×Q8—21no—
532C3×Q8—41no—
533C3×Q8—41no—
534C3×Q8—61no—
535C3×Q8—61no—
536C3×D4—21no—
537C3×D4—21no—
538C3×D4—22no—
539C3×D4—32no—
540C3×D4—41no—
541C3×D4—64no—
542C3×D4—61no—
543C3×D4—61no—
544C3×D4—61no—
545C3×D4—122no—
546C3×D4D3×D412yes—
547C3×D4C2×#6712yes—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—31no—
552C2×C3×C4—32no—
553C2×C3×C4—32no—
554C2×C3×C4—31no—
555C2×C3×C4—31no—
556C2×C3×C4—41no—
557C2×C3×C4—61no—
558C2×C3×C4—61no—
559C2×C3×C4—122no—
560C2×C3×C4—241no—
561C2×C3×C4C23×D311yescharacteristic
562C2×C3×C4C23×D311yescharacteristic
563#67—24no—
564C2×Dic3—21no—
565C2×Dic3—21no—
566C2×Dic3—31no—
567C2×Dic3—31no—
568C2×Dic3—31no—
569C2×Dic3—31no—
570C2×Dic3—61no—
571C2×Dic3—61no—
572C2×Dic3—61no—
573C2×Dic3—61no—
574C2×Dic3—61no—
575C2×Dic3—61no—
576C2×Dic3—81no—
577C2×Dic3—121no—
578C2×Dic3—121no—
579C2×Dic3—122no—
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—21no—
590D12—21no—
591D12—42no—
592D12C2×#6712yes—
593C4×D3—42no—
594C4×D3—122no—
595C4×D3—241no—
596C4×D3—241no—
597C4×D3#23712yes—
598C4×D3C2×#6712yes—
599Dic6—21no—
600Dic6—21no—
601Dic6—61no—
602Dic6—61no—
603Dic6—61no—
604Dic6—61no—
605Dic6—121no—
606Dic6—121no—
607Dic6—122no—
608Dic6—122no—
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—22no—
624C3×D3—42no—
625C3×D3—81no—
626C24—61no—
627#41—62no—
628#41—62no—
629C2×Q8—31no—
630C2×Q8—91no—
631C2×Q8—181no—
632C2×Q8—182no—
633C2×Q8—182no—
634C2×Q8C2×D3211yescharacteristic
635C2×D4—34no—
636C2×D4—31no—
637C2×D4—31no—
638C2×D4—61no—
639C2×D4—62no—
640C2×D4—61no—
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—182no—
653SD16—182no—
654SD16—182no—
655D8—62no—
656D8—62no—
657M16—62no—
658C2×C8—31no—
659C2×C8—31no—
660C2×C8—91no—
661C2×C8—182no—
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—121no—
702C22×C3—121no—
703C22×C3—121no—
704C22×C3—244no—
705C22×C3C2×D3×D411yescharacteristic
706C22×C3C2×D3×D411yescharacteristic
707C2×D3—21no—
708C2×D3—21no—
709C2×D3—22no—
710C2×D3—41no—
711C2×D3—41no—
712C2×D3—41no—
713C2×D3—41no—
714C2×D3—41no—
715C2×D3—84no—
716C2×D3#93912yes—
717C3×C4—21no—
718C3×C4—21no—
719C3×C4—32no—
720C3×C4—41no—
721C3×C4—41no—
722C3×C4—61no—
723C3×C4—61no—
724C3×C4—81no—
725C3×C4—121no—
726C3×C4—121no—
727C3×C4C2×D3×D411yescharacteristic
728C3×C4C2×#23711yescharacteristic
729C3×C4D3×#4111yescharacteristic
730C3×C4C22×#6711yescharacteristic
731Dic3—21no—
732Dic3—21no—
733Dic3—41no—
734Dic3—41no—
735Dic3—62no—
736Dic3—61no—
737Dic3—61no—
738Dic3—61no—
739Dic3—61no—
740Dic3—121no—
741Dic3—121no—
742Dic3—121no—
743Dic3—121no—
744Dic3—121no—
745Dic3—241no—
746Dic3—241no—
747Dic3#93912yes—
748C32#304211yescharacteristic, complemented, Sylow
749C23—21no—
750C23—31no—
751C23—64no—
752C23—61no—
753C23—61no—
754C23—241no—
755C23—241no—
756Q8—21no—
757Q8—21no—
758Q8—61no—
759Q8—61no—
760Q8—181no—
761Q8—181no—
762Q8—362no—
763D4—21no—
764D4—32no—
765D4—64no—
766D4—61no—
767D4—61no—
768D4—61no—
769D4—122no—
770D4D3×#6712yes—
771C2×C4—21no—
772C2×C4—31no—
773C2×C4—32no—
774C2×C4—32no—
775C2×C4—31no—
776C2×C4—31no—
777C2×C4—61no—
778C2×C4—61no—
779C2×C4—91no—
780C2×C4—91no—
781C2×C4—122no—
782C2×C4—181no—
783C2×C4—181no—
784C2×C4—241no—
785C2×C4—362no—
786C2×C4—721no—
787C2×C4—721no—
788C2×C4—721no—
789C2×C4C22×D3211yescharacteristic
790C8—21no—
791C8—61no—
792C8—61no—
793C8—181no—
794C2×C3—21no—
795C2×C3—21no—
796C2×C3—21no—
797C2×C3—42no—
798C2×C3—42no—
799C2×C3—62no—
800C2×C3—82no—
801C2×C3—122no—
802C2×C3—241no—
803C2×C3D3×#12111yescharacteristic
804C2×C3#576211yescharacteristic
805C2×C3#577511yescharacteristic
806C2×C3#577511yescharacteristic
807C2×C3#577811yescharacteristic
808C2×C3C2×#93911yescharacteristic
809D3—22no—
810D3—42no—
811D3—81no—
812C22—22no—
813C22—32no—
814C22—41no—
815C22—41no—
816C22—61no—
817C22—61no—
818C22—62no—
819C22—121no—
820C22—121no—
821C22—121no—
822C22—121no—
823C22—121no—
824C22—244no—
825C22D32×D411yescharacteristic
826C4—32no—
827C4—41no—
828C4—61no—
829C4—61no—
830C4—121no—
831C4—121no—
832C4—181no—
833C4—181no—
834C4—361no—
835C4—361no—
836C4D3×#23711yescharacteristic
837C4C2×D3×#6711yescharacteristic
838C3—21no—
839C3#8043011yescharacteristic, complemented
840C3#8393511yescharacteristic, complemented
841C2—42no—
842C2—62no—
843C2—122no—
844C2—241no—
845C2#1059474911yescharacteristic
846C2#1059475411yescharacteristic
847C2D3×#93911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
prime radicalC2×C3×#914C2
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
2. #10595356C2semidirect
3. #10595215C2semidirect
4. C2×D3×#214C2semidirect
5. #10592861C2semidirect
6. C3×#5162C2semidirect
7. #10591569C2semidirect
8. #10591564C2semidirect
9. #10591556C2semidirect
10. #10591476C2semidirect
11. #10591468C2semidirect
12. #10590948C2semidirect
13. #10590755C2semidirect
14. #10590751C2semidirect
15. #10590695C2semidirect
22. #64153C22semidirect
25. C3×#944C22semidirect
42. #63863C22semidirect
43. #63860C22semidirect
51. #63662C22semidirect
52. #63643C22semidirect
53. #63641C22semidirect
54. C3×#835C22semidirect
55. C3×#816C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. #63572C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
59. #63567C22semidirect
60. #63566C22semidirect
61. #63563C22semidirect
62. #63562C22semidirect
79. #5162D3semidirect
177. #944C2×D3semidirect
231. #835C2×D3semidirect
240. #816C2×D3semidirect
247. Dic3⋊C8C2×D3semidirect
748. C32#3042semidirect
839. C3#80430semidirect
840. C3#83935semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9142
#105953562
#105952152
C2×D3×#2142
#105928612
C3×#51622
#105915692
#105915642
#105915562
#105914762
#105914682
#105909482
#105907552
#105907512
#105906952
#839353
#804303