Finite Group Databasebeta

← #11884005

Subgroups — #11884005

Order 1152.

1241 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64117C211yesmaximal, characteristic, complemented
2#10595074C211yesmaximal, characteristic, complemented
3#10594916C211yesmaximal, characteristic, complemented
4C2×D3×#204C211yesmaximal, characteristic, complemented
5C3×#5134C211yesmaximal, characteristic, complemented
6C3×#5127C211yesmaximal, characteristic, complemented
7#10591183C211yesmaximal, characteristic, complemented
8#10591182C211yesmaximal, characteristic, complemented
9#10590951C211yesmaximal, characteristic, complemented
10#10590947C211yesmaximal, characteristic, complemented
11#10590881C211yesmaximal, characteristic, complemented
12#10590879C211yesmaximal, characteristic, complemented
13#10590832C211yesmaximal, characteristic, complemented
14#10590773C211yesmaximal, characteristic, complemented
15#10590770C211yesmaximal, characteristic, complemented
16#80834—31nomaximal
17#79494—31nomaximal
18C2×#3828C2211yescharacteristic, complemented
19C22×C4⋊(C3⋊D3)C2211yescharacteristic
20C2×#3811—21no—
21C2×D3×D12C2211yescharacteristic
22C2×D3×Dic6C2211yescharacteristic, complemented
23C2×C32×M16C2211yescharacteristic, complemented
24#64117—24no—
25C2×#3745C2211yescharacteristic
26C2×#3745C2211yescharacteristic, complemented
27C2×#3744C2211yescharacteristic
28C2×#3744C2211yescharacteristic, complemented
29C3×#930C2211yescharacteristic
30C3×C4×#67C2211yescharacteristic
31C3×#924C2211yescharacteristic, complemented
32C2×C3×#204C2211yescharacteristic, complemented
33C2×C3×D3×C8C2211yescharacteristic, complemented
34#63981—21no—
35#63971—21no—
36#63953—21no—
37#63923—21no—
38#63911C2211yescharacteristic
39#63910—21no—
40#63909C2211yescharacteristic
41#63909C2211yescharacteristic, complemented
42#63894C2211yescharacteristic
43#63881—21no—
44#63865—21no—
45#63864C2211yescharacteristic, complemented
46#63844C2211yescharacteristic, complemented
47C2×#3717C2211yescharacteristic
48C2×#3717C2211yescharacteristic, complemented
49C2×#3716C2211yescharacteristic, complemented
50C2×#3714C2211yescharacteristic, complemented
51D3×#204—24no—
52C3×#830C2211yescharacteristic, complemented
53C3×#821C2211yescharacteristic, complemented
54C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
55C3×#818C2211yescharacteristic, complemented
56C3×#816C2211yescharacteristic, complemented
57C3×#815C2211yescharacteristic, complemented
58C3×Dic3⋊C8C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63564C2211yescharacteristic
61#63564C2211yescharacteristic, complemented
62#63564C2211yescharacteristic, complemented
63C2×D3×SD16—31no—
64C2×#908—31no—
65C2×#908—31no—
66C2×#908—61no—
67C22×#204—31no—
68#5633—31no—
69#5609—31no—
70#5552—31no—
71D4×D12—31no—
72C3×#468—31no—
73C3×#435—31no—
74#5176—31no—
75#5134D311yescharacteristic, complemented
76#5127D311yescharacteristic, complemented
77#5115—31no—
78#5046—31no—
79#5037—31no—
80#4889—31no—
81#4883—31no—
82#4848—31no—
83#4844—31no—
84#4819—31no—
85#4806—31no—
86#4773—31no—
87#4762—31no—
88#4738—31no—
89#4734—31no—
90#4732—31no—
91#4731—31no—
92#4712—31no—
93#4710—31no—
94C23×C3⋊D3—21no—
95C22×D32—21no—
96C22×C32×C4C2311yescharacteristic
97C2×#638—21no—
98#3828—22no—
99#3828—41no—
100C2×C4⋊(C3⋊D3)—22no—
101C2×C4⋊(C3⋊D3)—21no—
102C2×C4⋊(C3⋊D3)—41no—
103C2×C4⋊(C3⋊D3)C2311yescharacteristic
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C4⋊(C3⋊D3)C2311yescharacteristic
106C2×C4×C3⋊D3—21no—
107C2×#634C2311yescharacteristic
108C2×C3×#67—21no—
109C2×C3×#67D411yescharacteristic
110C2×C3×D12C2311yescharacteristic
111C2×C3×C4×D3C2311yescharacteristic
112C2×C3×Dic6C2311yescharacteristic
113#3811—44no—
114C2×#627—21no—
115C2×#626—21no—
116C2×#626—21no—
117C2×#626—21no—
118C2×#626—21no—
119C2×#626—21no—
120C2×#624—21no—
121C2×D3×Dic3—21no—
122D3×D12—22no—
123D3×D12—41no—
124D3×Dic6—22no—
125D3×Dic6—41no—
126C32×M16—22no—
127C2×C32×C8C2311yescharacteristic
128C2×C32×C8C2311yescharacteristic
129#3745—22no—
130#3745—22no—
131#3744—22no—
132#3744D414yescomplemented
133C3×#217—21no—
134C3×#217D411yescharacteristic
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4D411yescharacteristic
137C3×C4⋊Dic3C2311yescharacteristic
138C3×C4⋊Dic3C2311yescharacteristic
139C3×Dic3⋊C4—21no—
140C3×Dic3⋊C4D411yescharacteristic
141C3×C4×Dic3C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144C3×#204—22no—
145C3×D3×C8—22no—
146#3724—21no—
147#3722—21no—
148#3722—21no—
149#3722—21no—
150#3722—21no—
151#3722—21no—
152Dic32—21no—
153#3717—22no—
154#3717—41no—
155#3716—22no—
156#3714—41no—
157#3265—91noSylow
158C2×D3×Q8—31no—
159C2×D3×D4—31no—
160C2×D3×D4—61no—
161C2×D3×D4—61no—
162C2×#235—31no—
163C2×#235—31no—
164C2×#235—61no—
165C22×D12—31no—
166C22×D12—31no—
167C22×D12—31no—
168C22×D12—61no—
169C22×Dic6—31no—
170C2×C3×SD16—31no—
171C2×C3×M16—21no—
172C2×C3×M16C2×D311yescharacteristic, complemented
173C2×C3×M16C2×D311yescharacteristic, complemented
174C22×C3×C8—31no—
175C3×C22⋊Q8—31no—
176C3×#121—31no—
177C3×C4×D4—31no—
178#947—31no—
179C2×#215—31no—
180C2×#215—31no—
181#940—31no—
182#939—61no—
183#937—61no—
184C2×#214—31no—
185C2×#213—31no—
186#930—31no—
187#930—31no—
188#930C2×D311yescharacteristic
189C4×#67C2×D311yescharacteristic
190#924C2×D311yescharacteristic, complemented
191D3×SD16—64no—
192#908—64no—
193#908—64no—
194#908—68no—
195C2×D24—31no—
196C2×D24—31no—
197C2×D24—31no—
198C2×D24—31no—
199C2×D24—31no—
200C2×D24—61no—
201C2×D24—61no—
202C2×#204—31no—
203C2×#204—31no—
204C2×#204—31no—
205C2×#204—31no—
206C2×#204—31no—
207C2×#204—31no—
208C2×#204—31no—
209C2×#204—61no—
210C2×#204—61no—
211C2×#204—64no—
212C2×#204C2×D311yescharacteristic, complemented
213C2×D3×C8C2×D311yescharacteristic, complemented
214#896—61no—
215#896—61no—
216#895—31no—
217#895—31no—
218#895—61no—
219#893—31no—
220#893—61no—
221#887—31no—
222#885—61no—
223#885—61no—
224#884—61no—
225#884—61no—
226#882—61no—
227#882—61no—
228#882—61no—
229#67⋊C4—61no—
230#875—31no—
231#874—31no—
232C4×D12—31no—
233C4×Dic6—31no—
234C3×#107—31no—
235C3×C4⋊C8—31no—
236C3×#103—31no—
237C3×#102—31no—
238C3×C22⋊C8—31no—
239C3×C22⋊C8—31no—
240C3×#97—31no—
241#830C2×D311yescharacteristic, complemented
242#821—31no—
243#821—31no—
244#821—31no—
245#821C2×D311yescharacteristic, complemented
246(C2×D3)⋊C8C2×D311yescharacteristic, complemented
247#818C2×D311yescharacteristic, complemented
248#816—31no—
249#816C2×D311yescharacteristic, complemented
250#815C2×D311yescharacteristic, complemented
251Dic3⋊C8C2×D311yescharacteristic, complemented
252#810—31no—
253#809—31no—
254#809—31no—
255#809—31no—
256C23×C32C2×D411yescharacteristic
257C22×C3⋊D3—21no—
258C22×C3⋊D3—21no—
259C22×C3⋊D3—21no—
260C22×C3⋊D3—42no—
261C22×C3⋊D3—42no—
262C22×C3⋊D3—81no—
263C22×C3×D3—21no—
264C22×C3×D3C2×D411yescharacteristic
265C2×D32—42no—
266C2×D32—42no—
267C2×D32—81no—
268C2×C32×C4—21no—
269C2×C32×C4—21no—
270C2×C32×C4C2×D411yescharacteristic
271C2×C32×C4C2411yescharacteristic
272#638—42no—
273C2×C3⋊Dic3—21no—
274C4⋊(C3⋊D3)—21no—
275C4⋊(C3⋊D3)—21no—
276C4⋊(C3⋊D3)—21no—
277C4⋊(C3⋊D3)—21no—
278C4⋊(C3⋊D3)—21no—
279C4⋊(C3⋊D3)—42no—
280C4⋊(C3⋊D3)C2×D412yes—
281C4×C3⋊D3—42no—
282#634—21no—
283#634C2×D412yescomplemented
284C3×#67—22no—
285C3×#67—42no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3—21no—
288C2×C3×Dic3—21no—
289C2×C3×Dic3C2×D411yescharacteristic
290C2×C3×Dic3C2×D411yescharacteristic
291C2×C3×Dic3C2×D411yescharacteristic
292C3×D12—21no—
293C3×D12—21no—
294C3×C4×D3—21no—
295C3×C4×D3—21no—
296C3×Dic6—21no—
297C3×Dic6—21no—
298#627—42no—
299#626—42no—
300#626—42no—
301#626—42no—
302#626—42no—
303#626—81no—
304#624—42no—
305D3×Dic3—42no—
306C32×C8—21no—
307C32×C8C2×D412yescomplemented
308C3×C3⋊C8—21no—
309C3×C3⋊C8—21no—
310C2×AGL(1,ℤ/8)—91no—
311C22×SD16—91no—
312#548—91no—
313D42—91no—
314#496—91no—
315#468—31no—
316#466—91no—
317#463—91no—
318#460—91no—
319#450—91no—
320#449—91no—
321#448—91no—
322#447—91no—
323#440—91no—
324#435—31no—
325C23×D3—61no—
326C23×D3—61no—
327C23×D3—61no—
328C23×D3—61no—
329C23×D3—121no—
330C2×C3×Q8—31no—
331C2×C3×D4—31no—
332C2×C3×D4—31no—
333C2×C3×D4—61no—
334C22×C3×C4—21no—
335C22×C3×C4—31no—
336C22×C3×C4C22×D311yescharacteristic
337C22×C3×C4C22×D311yescharacteristic
338C2×#67—21no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—121no—
347C2×#67D1211yescharacteristic
348C22×Dic3—61no—
349D3×Q8—62no—
350D3×Q8—121no—
351D3×D4—62no—
352D3×D4—121no—
353D3×D4—124no—
354D3×D4—124no—
355#235—62no—
356#235—62no—
357#235—64no—
358#235—121no—
359#235—121no—
360#235—122no—
361C2×D12—31no—
362C2×D12—31no—
363C2×D12—31no—
364C2×D12—31no—
365C2×D12—31no—
366C2×D12—31no—
367C2×D12—61no—
368C2×D12—61no—
369C2×D12—61no—
370C2×D12—62no—
371C2×D12—62no—
372C2×D12—62no—
373C2×D12—64no—
374C2×D12—61no—
375C2×D12—61no—
376C2×D12—61no—
377C2×D12—61no—
378C2×D12—61no—
379C2×D12—61no—
380C2×D12—61no—
381C2×D12—121no—
382C2×D12—121no—
383C2×D12—121no—
384C2×D12—121no—
385C2×D12—122no—
386C2×D12C22×D311yescharacteristic
387C2×C4×D3—61no—
388C2×C4×D3—61no—
389C2×C4×D3—61no—
390C2×C4×D3—61no—
391C2×C4×D3—61no—
392C2×C4×D3—121no—
393C2×C4×D3C22×D311yescharacteristic
394C2×Dic6—31no—
395C2×Dic6—31no—
396C2×Dic6—61no—
397C2×Dic6—62no—
398C2×Dic6—61no—
399C2×Dic6—61no—
400C2×Dic6—121no—
401C2×Dic6C22×D311yescharacteristic
402C3×SD16—62no—
403C3×M16—24no—
404C3×M16—22no—
405C3×M16—22no—
406C2×C3×C8—21no—
407C2×C3×C8—21no—
408C2×C3×C8—31no—
409C2×C3×C8—31no—
410C2×C3×C8—62no—
411C2×C3×C8C22×D311yescharacteristic
412C2×C3×C8C22×D311yescharacteristic
413C2×C3×C8C22×D311yescharacteristic
414C2×C3×C8C22×D311yescharacteristic
415C3×C4⋊C4—31no—
416C3×C4⋊C4—31no—
417C3×C4⋊C4—31no—
418C3×C4⋊C4—61no—
419C3×C22⋊C4—31no—
420C3×C22⋊C4—31no—
421C3×C22⋊C4—61no—
422C3×C22⋊C4—61no—
423C3×C42—31no—
424#217—21no—
425#217D1211yescharacteristic
426#215—62no—
427#215—121no—
428#214—62no—
429#213—121no—
430(C2×D3)⋊C4—21no—
431(C2×D3)⋊C4—61no—
432(C2×D3)⋊C4—61no—
433(C2×D3)⋊C4—61no—
434(C2×D3)⋊C4—61no—
435(C2×D3)⋊C4—61no—
436(C2×D3)⋊C4—61no—
437(C2×D3)⋊C4—61no—
438(C2×D3)⋊C4—61no—
439(C2×D3)⋊C4—61no—
440(C2×D3)⋊C4—61no—
441(C2×D3)⋊C4D1211yescharacteristic
442C4⋊Dic3C22×D311yescharacteristic
443C4⋊Dic3C22×D311yescharacteristic
444Dic3⋊C4—21no—
445Dic3⋊C4—61no—
446Dic3⋊C4—61no—
447Dic3⋊C4D1211yescharacteristic
448C4×Dic3—61no—
449C4×Dic3—61no—
450C4×Dic3C22×D311yescharacteristic
451C2×C3⋊C8C22×D311yescharacteristic
452C2×C3⋊C8C22×D311yescharacteristic
453D24—62no—
454D24—62no—
455D24—64no—
456D24—64no—
457D24—62no—
458D24—62no—
459D24—121no—
460#204—22no—
461#204—34no—
462#204—34no—
463#204—64no—
464#204—62no—
465#204—62no—
466#204—64no—
467#204—62no—
468#204—62no—
469#204—121no—
470D3×C8—22no—
471C22×C32—21no—
472C22×C32—21no—
473C22×C32—21no—
474C22×C32C22×D411yescharacteristic
475C2×C3⋊D3—22no—
476C2×C3⋊D3—41no—
477C2×C3⋊D3—41no—
478C2×C3⋊D3—41no—
479C2×C3⋊D3—41no—
480C2×C3⋊D3—41no—
481C2×C3⋊D3—41no—
482C2×C3⋊D3—41no—
483C2×C3⋊D3—41no—
484C2×C3⋊D3—84no—
485C2×C3×D3—21no—
486C2×C3×D3—21no—
487C2×C3×D3—41no—
488C2×C3×D3—41no—
489C2×C3×D3—41no—
490C2×C3×D3AGL(1,ℤ/8)12yescomplemented
491D32—84no—
492C32×C4—21no—
493C32×C4C22×D411yescharacteristic
494C32×C4H(5,𝔽2)11yescharacteristic
495C3⋊Dic3—22no—
496C3×Dic3—21no—
497C3×Dic3—21no—
498C3×Dic3—21no—
499C3×Dic3—41no—
500C3×Dic3—41no—
501C3×Dic3—41no—
502C2×#41—91no—
503C22×Q8—91no—
504C22×D4—91no—
505C22×D4—91no—
506C22×D4—181no—
507AGL(1,ℤ/8)—184no—
508C2×SD16—31no—
509C2×SD16—91no—
510C2×SD16—91no—
511C2×SD16—91no—
512C2×SD16—91no—
513C2×SD16—91no—
514C2×SD16—184no—
515C2×D8—91no—
516C2×D8—91no—
517C2×D8—91no—
518C2×M16D3211yescharacteristic, complemented
519C22×C8—31no—
520#127—91no—
521#124—91no—
522#124—181no—
523C22⋊Q8—31no—
524C22⋊Q8—181no—
525#121—31no—
526#121—91no—
527#121—91no—
528#121—181no—
529#121—181no—
530#120—181no—
531#120—181no—
532C4×Q8—91no—
533C4×D4—31no—
534C4×D4—91no—
535C4×D4—181no—
536#107—31no—
537C4⋊C8—31no—
538#103—31no—
539#103—91no—
540#102—31no—
541#102—91no—
542#102—91no—
543#102—91no—
544C22⋊C8—31no—
545C22⋊C8—31no—
546#97—31no—
547C23×C3—21no—
548C23×C3—31no—
549C23×C3—61no—
550C23×C3C2×D1211yescharacteristic
551C23×C3D3×D411yescharacteristic
552C22×D3—21no—
553C22×D3—61no—
554C22×D3—61no—
555C22×D3—61no—
556C22×D3—61no—
557C22×D3—61no—
558C22×D3—61no—
559C22×D3—121no—
560C22×D3—121no—
561C22×D3—121no—
562C22×D3—122no—
563C22×D3—122no—
564C22×D3—122no—
565C22×D3—122no—
566C22×D3—122no—
567C22×D3—124no—
568C22×D3—122no—
569C22×D3—122no—
570C22×D3—122no—
571C22×D3—242no—
572C22×D3—241no—
573C22×D3—241no—
574C22×D3—241no—
575C22×D3—241no—
576C22×D3—242no—
577C22×D3C2×D1211yescharacteristic
578C3×Q8—61no—
579C3×Q8—61no—
580C3×D4—62no—
581C3×D4—61no—
582C3×D4—61no—
583C3×D4—122no—
584C2×C3×C4—22no—
585C2×C3×C4—22no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—31no—
593C2×C3×C4—31no—
594C2×C3×C4—31no—
595C2×C3×C4—61no—
596C2×C3×C4—61no—
597C2×C3×C4—61no—
598C2×C3×C4—61no—
599C2×C3×C4—61no—
600C2×C3×C4C2×D1211yescharacteristic
601C2×C3×C4D3×D411yescharacteristic
602C2×C3×C4C23×D311yescharacteristic
603C2×C3×C4C23×D311yescharacteristic
604#67—22no—
605#67—42no—
606#67—122no—
607#67—122no—
608#67—122no—
609#67—122no—
610#67—122no—
611#67—122no—
612#67—124no—
613#67—241no—
614C2×Dic3—21no—
615C2×Dic3—21no—
616C2×Dic3—21no—
617C2×Dic3—61no—
618C2×Dic3—61no—
619C2×Dic3—121no—
620C2×Dic3—122no—
621C2×Dic3C2×D1211yescharacteristic
622C2×Dic3C2×D1211yescharacteristic
623C2×Dic3C2×D1211yescharacteristic
624D12—21no—
625D12—21no—
626D12—32no—
627D12—32no—
628D12—62no—
629D12—62no—
630D12—62no—
631D12—61no—
632D12—61no—
633D12—61no—
634D12—61no—
635D12—61no—
636D12—61no—
637D12—61no—
638D12—61no—
639D12—61no—
640D12—61no—
641D12—121no—
642D12—121no—
643D12—121no—
644D12—122no—
645D12—122no—
646D12—124no—
647D12—122no—
648D12—122no—
649D12—122no—
650D12—122no—
651D12—241no—
652C4×D3—21no—
653C4×D3—21no—
654C4×D3—122no—
655C4×D3—122no—
656C4×D3—122no—
657C4×D3—122no—
658C4×D3—122no—
659C4×D3—124no—
660Dic6—21no—
661Dic6—21no—
662Dic6—32no—
663Dic6—32no—
664Dic6—62no—
665Dic6—61no—
666Dic6—61no—
667Dic6—121no—
668Dic6—122no—
669Dic6—122no—
670C3×C8—22no—
671C3×C8—21no—
672C3×C8—21no—
673C3×C8—22no—
674C3×C8—61no—
675C3×C8—61no—
676C3×C8D3×D412yescomplemented
677C3×C8D3×D412yescomplemented
678C3⋊C8—21no—
679C3⋊C8—21no—
680C2×C32—41no—
681C2×C32D4211yescharacteristic
682C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
683C2×C32#57711yescharacteristic
684C3⋊D3—42no—
685C3⋊D3—81no—
686C3⋊D3—81no—
687C3×D3—22no—
688C3×D3—81no—
689C24—181no—
690C24—181no—
691#41—182no—
692#41—361no—
693C2×Q8—31no—
694C2×Q8—91no—
695C2×Q8—181no—
696C2×Q8—182no—
697C2×Q8—361no—
698C2×D4—31no—
699C2×D4—31no—
700C2×D4—61no—
701C2×D4—91no—
702C2×D4—91no—
703C2×D4—91no—
704C2×D4—182no—
705C2×D4—181no—
706C2×D4—181no—
707C2×D4—181no—
708C2×D4—182no—
709C2×D4—181no—
710C2×D4—181no—
711C2×D4—181no—
712C2×D4—181no—
713C2×D4—361no—
714C2×D4—361no—
715C2×D4—364no—
716C22×C4—31no—
717C22×C4—181no—
718C22×C4—181no—
719C22×C4—181no—
720C22×C4C2×D3211yescharacteristic
721SD16—62no—
722SD16—94no—
723SD16—182no—
724SD16—182no—
725SD16—182no—
726SD16—361no—
727D8—182no—
728D8—182no—
729D8—361no—
730M16—22no—
731C2×C8—31no—
732C2×C8—31no—
733C2×C8—62no—
734C2×C8C2×D3211yescharacteristic
735C2×C8C2×D3211yescharacteristic
736C4⋊C4—31no—
737C4⋊C4—31no—
738C4⋊C4—31no—
739C4⋊C4—61no—
740C4⋊C4—181no—
741C22⋊C4—31no—
742C22⋊C4—31no—
743C22⋊C4—61no—
744C22⋊C4—61no—
745C22⋊C4—181no—
746C22⋊C4—181no—
747C22⋊C4—181no—
748C22⋊C4—181no—
749C22⋊C4—181no—
750C42—31no—
751C42—181no—
752C22×C3—22no—
753C22×C3—21no—
754C22×C3—21no—
755C22×C3—21no—
756C22×C3—21no—
757C22×C3—21no—
758C22×C3—21no—
759C22×C3—21no—
760C22×C3—32no—
761C22×C3—41no—
762C22×C3—41no—
763C22×C3—61no—
764C22×C3—61no—
765C22×C3—121no—
766C22×C3—121no—
767C22×C3—121no—
768C22×C3C22×D1211yescharacteristic
769C22×C3C2×D3×D411yescharacteristic
770C2×D3—21no—
771C2×D3—21no—
772C2×D3—41no—
773C2×D3—41no—
774C2×D3—41no—
775C2×D3—62no—
776C2×D3—62no—
777C2×D3—122no—
778C2×D3—121no—
779C2×D3—121no—
780C2×D3—121no—
781C2×D3—121no—
782C2×D3—122no—
783C2×D3—122no—
784C2×D3—121no—
785C2×D3—121no—
786C2×D3—121no—
787C2×D3—121no—
788C2×D3—121no—
789C2×D3—121no—
790C2×D3—121no—
791C2×D3—121no—
792C2×D3—121no—
793C2×D3—121no—
794C2×D3—121no—
795C2×D3—121no—
796C2×D3—241no—
797C2×D3—241no—
798C2×D3—241no—
799C2×D3—241no—
800C2×D3—241no—
801C2×D3—241no—
802C2×D3—244no—
803C2×D3—244no—
804C2×D3—244no—
805C2×D3—244no—
806C2×D3—248no—
807C2×D3#90812yescomplemented
808C3×C4—22no—
809C3×C4—21no—
810C3×C4—21no—
811C3×C4—21no—
812C3×C4—21no—
813C3×C4—61no—
814C3×C4—61no—
815C3×C4—61no—
816C3×C4—121no—
817C3×C4—121no—
818C3×C4—121no—
819C3×C4C2×D3×D411yescharacteristic
820C3×C4C2×D3×D411yescharacteristic
821C3×C4#100911yescharacteristic
822C3×C4#100911yescharacteristic
823Dic3—21no—
824Dic3—21no—
825Dic3—21no—
826Dic3—41no—
827Dic3—41no—
828Dic3—41no—
829Dic3—62no—
830Dic3—62no—
831Dic3—122no—
832C32#326511yescharacteristic, complemented, Sylow
833C23—31no—
834C23—61no—
835C23—181no—
836C23—181no—
837C23—181no—
838C23—362no—
839C23—362no—
840C23—362no—
841C23—362no—
842C23—721no—
843C23—721no—
844C23D3×D1211yescharacteristic
845Q8—61no—
846Q8—61no—
847Q8—92no—
848Q8—181no—
849Q8—362no—
850D4—62no—
851D4—61no—
852D4—61no—
853D4—92no—
854D4—122no—
855D4—181no—
856D4—181no—
857D4—181no—
858D4—181no—
859D4—181no—
860D4—362no—
861D4—362no—
862D4—362no—
863D4—362no—
864D4—362no—
865D4—362no—
866D4—721no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—31no—
870C2×C4—31no—
871C2×C4—31no—
872C2×C4—61no—
873C2×C4—61no—
874C2×C4—61no—
875C2×C4—61no—
876C2×C4—61no—
877C2×C4—181no—
878C2×C4—362no—
879C2×C4—362no—
880C2×C4—362no—
881C2×C4D3×D1211yescharacteristic
882C2×C4C22×D3211yescharacteristic
883C8—21no—
884C8—61no—
885C8—61no—
886C8#381112yescomplemented
887C2×C3—21no—
888C2×C3—21no—
889C2×C3—21no—
890C2×C3—42no—
891C2×C3—41no—
892C2×C3—41no—
893C2×C3—62no—
894C2×C3—241no—
895C2×C3D4×D1211yescharacteristic
896C2×C3#560911yescharacteristic
897C2×C3C2×#90811yescharacteristic
898C2×C3#575111yescharacteristic
899C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
900C2×C3#577811yescharacteristic
901D3—22no—
902D3—81no—
903D3—122no—
904D3—122no—
905D3—242no—
906D3—242no—
907D3—242no—
908D3—241no—
909D3—241no—
910D3—241no—
911D3—241no—
912C22—21no—
913C22—21no—
914C22—21no—
915C22—32no—
916C22—61no—
917C22—61no—
918C22—121no—
919C22—121no—
920C22—121no—
921C22—182no—
922C22—361no—
923C22—361no—
924C22—361no—
925C22—361no—
926C22—361no—
927C22—361no—
928C22—361no—
929C22—361no—
930C22—724no—
931C22—724no—
932C22C2×D3×D1211yescharacteristic
933C4—21no—
934C4—61no—
935C4—61no—
936C4—61no—
937C4—121no—
938C4—121no—
939C4—121no—
940C4—182no—
941C4#6430811yescharacteristic
942C4C2×#381111yescharacteristic
943C3—21no—
944C3#7949411yescharacteristic, complemented
945C3#8083411yescharacteristic, complemented
946C2—41no—
947C2—62no—
948C2—241no—
949C2—362no—
950C2—721no—
951C2—721no—
952C2D3×#90811yescharacteristic
953C2#1059471511yescharacteristic
954C2#1059507411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
hypercenterC2×M16D32
hypocenterC32#3265
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×#64117C2semidirect
2. #10595074C2semidirect
3. #10594916C2semidirect
4. C2×D3×#204C2semidirect
5. C3×#5134C2semidirect
6. C3×#5127C2semidirect
7. #10591183C2semidirect
8. #10591182C2semidirect
9. #10590951C2semidirect
10. #10590947C2semidirect
11. #10590881C2semidirect
12. #10590879C2semidirect
13. #10590832C2semidirect
14. #10590773C2semidirect
15. #10590770C2semidirect
18. C2×#3828C22semidirect
22. C2×D3×Dic6C22semidirect
23. C2×C32×M16C22semidirect
26. C2×#3745C22semidirect
28. C2×#3744C22semidirect
31. C3×#924C22semidirect
32. C2×C3×#204C22semidirect
33. C2×C3×D3×C8C22semidirect
41. #63909C22semidirect
45. #63864C22semidirect
46. #63844C22semidirect
48. C2×#3717C22semidirect
49. C2×#3716C22semidirect
50. C2×#3714C22semidirect
52. C3×#830C22semidirect
53. C3×#821C22semidirect
54. C3×(C2×D3)⋊C8C22semidirect
55. C3×#818C22semidirect
56. C3×#816C22semidirect
57. C3×#815C22semidirect
58. C3×Dic3⋊C8C22semidirect
59. #63567C22semidirect
61. #63564C22semidirect
62. #63564C22semidirect
75. #5134D3semidirect
76. #5127D3semidirect
132. #3744D4semidirect
172. C2×C3×M16C2×D3semidirect
173. C2×C3×M16C2×D3semidirect
190. #924C2×D3semidirect
212. C2×#204C2×D3semidirect
213. C2×D3×C8C2×D3semidirect
241. #830C2×D3semidirect
245. #821C2×D3semidirect
246. (C2×D3)⋊C8C2×D3semidirect
247. #818C2×D3semidirect
249. #816C2×D3semidirect
250. #815C2×D3semidirect
251. Dic3⋊C8C2×D3semidirect
283. #634C2×D4semidirect
307. C32×C8C2×D4semidirect
490. C2×C3×D3AGL(1,ℤ/8)semidirect
518. C2×M16D32semidirect
676. C3×C8D3×D4semidirect
677. C3×C8D3×D4semidirect
807. C2×D3#908semidirect
832. C32#3265semidirect
886. C8#3811semidirect
944. C3#79494semidirect
945. C3#80834semidirect

Maximal subgroups

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

subgroupindex
C2×#641172
#105950742
#105949162
C2×D3×#2042
C3×#51342
C3×#51272
#105911832
#105911822
#105909512
#105909472
#105908812
#105908792
#105908322
#105907732
#105907702
#808343
#794943