Finite Group Databasebeta

← #11867196

Subgroups — #11867196

Order 1152.

1161 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×M16C211yesmaximal, characteristic, complemented
2D3×#930C211yesmaximal, characteristic, complemented
3#10595005C211yesmaximal, characteristic, complemented
4C2×#63794C211yesmaximal, characteristic, complemented
5#10592834C211yesmaximal, characteristic, complemented
6C3×#5134C211yesmaximal, characteristic, complemented
7#10591178C211yesmaximal, characteristic, complemented
8#10591165C211yesmaximal, characteristic, complemented
9#10590939C211yesmaximal, characteristic, complemented
10#10590847C211yesmaximal, characteristic, complemented
11#10590832C211yesmaximal, characteristic, complemented
12#10590829C211yesmaximal, characteristic, complemented
13#10590826C211yesmaximal, characteristic, complemented
14#10590683C211yesmaximal, characteristic, complemented
15#10590671C211yesmaximal, characteristic, complemented
16#83772—31nomaximal
17#80805—31nomaximal
18C22×C3×C4×D3C2211yescharacteristic
19C2×D3×#67—21no—
20C2×D3×D12C2211yescharacteristic
21C2×#3799C2211yescharacteristic
22C2×C32×M16C2211yescharacteristic, complemented
23#64139C2211yescharacteristic
24#64139C2211yescharacteristic, complemented
25C2×#3745C2211yescharacteristic, complemented
26C3×#930C2211yescharacteristic
27C3×#924C2211yescharacteristic, complemented
28C2×C3×#208C2211yescharacteristic, complemented
29C3×D3×M16—24no—
30C2×C3×#204C2211yescharacteristic, complemented
31C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
32C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
33C2×C3×D3×C8C2211yescharacteristic, complemented
34C2×C3×D3×C8C2211yescharacteristic, complemented
35#63978—21no—
36#63977—21no—
37#63952—21no—
38D3×(C2×D3)⋊C4—21no—
39#63909C2211yescharacteristic
40#63909C2211yescharacteristic, complemented
41#63908C2211yescharacteristic
42#63906—21no—
43#63904—21no—
44D3×C4⋊Dic3C2211yescharacteristic
45#63856C2211yescharacteristic, complemented
46#63850—21no—
47#63841C2211yescharacteristic
48C2×#3717C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic, complemented
50#63794—24no—
51#63648C2211yescharacteristic, complemented
52#63648C2211yescharacteristic, complemented
53#63644C2211yescharacteristic, complemented
54C3×#821C2211yescharacteristic, complemented
55C3×#818C2211yescharacteristic, complemented
56C3×#816C2211yescharacteristic, complemented
57#63575C2211yescharacteristic, complemented
58#63573C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63564C2211yescharacteristic, complemented
61#63564C2211yescharacteristic, complemented
62#63563C2211yescharacteristic, complemented
63C22×C3×M16—31no—
64#5791—31no—
65C2×#930—31no—
66C2×#914—31no—
67C2×#908—31no—
68C2×D3×M16D311yescharacteristic, complemented
69#5627—31no—
70D3×#121—31no—
71C3×#468—31no—
72#5171—31no—
73#5135—31no—
74#5135—31no—
75#5135—31no—
76#5135—61no—
77#5134—31no—
78#5134D311yescharacteristic, complemented
79#5133—31no—
80#5131—31no—
81#5121—31no—
82#5115—31no—
83#5115—31no—
84#5114—31no—
85#5114—31no—
86#5049—31no—
87#5039—31no—
88#4883—31no—
89#4881—31no—
90#4807—31no—
91#4803—31no—
92#4775—31no—
93#4770—31no—
94C23×C3×D3D411yescharacteristic
95C22×D32—21no—
96C22×C32×C4C2311yescharacteristic
97C2×#638—21no—
98C2×#638—21no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C3×#67—21no—
102C22×C3×Dic3D411yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—22no—
105C2×C3×C4×D3—22no—
106C2×C3×C4×D3D411yescharacteristic
107C2×C3×C4×D3D411yescharacteristic
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×Dic6C2311yescharacteristic
111D3×#67—44no—
112C2×#626—21no—
113C2×#626—21no—
114C2×#626—21no—
115C2×#626—21no—
116C2×#625—21no—
117C2×#624—21no—
118C2×D3×Dic3—21no—
119D3×D12—22no—
120D3×D12—22no—
121#3799—22no—
122#3799—22no—
123C32×M16—22no—
124C2×C32×C8C2311yescharacteristic
125C2×C32×C8C2311yescharacteristic
126#3752—21no—
127#3752—21no—
128C4⋊(C3⋊Dic3)C2311yescharacteristic
129C4⋊(C3⋊Dic3)C2311yescharacteristic
130#3745—22no—
131C3×#217—21no—
132C3×(C2×D3)⋊C4—21no—
133C3×C4⋊Dic3C2311yescharacteristic
134C3×C4⋊Dic3C2311yescharacteristic
135C3×Dic3⋊C4—21no—
136C3×#208—22no—
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C3×#204—22no—
140C3×ΓL(1,𝔽25)—22no—
141C3×ΓL(1,𝔽25)D414yescomplemented
142C3×D3×C8—22no—
143C3×D3×C8—22no—
144#3724—21no—
145Dic3⋊Dic3—21no—
146#3722—21no—
147#3722—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151Dic32—21no—
152#3717—22no—
153#3714—22no—
154#3055—91noSylow
155C23×C3×C4—31no—
156C22×#67—61no—
157C2×#239—31no—
158C2×D3×D4—31no—
159C2×D3×D4—61no—
160C2×#235—31no—
161C22×D12—31no—
162C22×C4×D3C2×D311yescharacteristic
163C2×C3×SD16—31no—
164C2×C3×M16—21no—
165C2×C3×M16—31no—
166C2×C3×M16—31no—
167C2×C3×M16—31no—
168C2×C3×M16—64no—
169C2×C3×M16C2×D311yescharacteristic, complemented
170C2×C3×M16C2×D311yescharacteristic, complemented
171C22×C3×C8—31no—
172C22×C3×C8—31no—
173C3×C22⋊Q8—31no—
174C3×#121—31no—
175#953—61no—
176#946—31no—
177C2×#215—31no—
178#939—61no—
179#938—31no—
180C2×#213—31no—
181#930—31no—
182#930—31no—
183#930—31no—
184#930—31no—
185#930—31no—
186#930—31no—
187#930—31no—
188#930—61no—
189#930—61no—
190#930—61no—
191#930—61no—
192#930C2×D311yescharacteristic
193#929—61no—
194C4×#67—61no—
195C4×#67—61no—
196C2×(C2×D3)⋊C4—61no—
197#926—31no—
198C2×C4⋊Dic3—31no—
199#924—31no—
200#924C2×D311yescharacteristic, complemented
201C2×#208C2×D311yescharacteristic, complemented
202#914—64no—
203#908—64no—
204D3×M16—24no—
205C2×D24—31no—
206C2×D24—31no—
207C2×D24—31no—
208C2×D24—61no—
209C2×#204—31no—
210C2×#204C2×D311yescharacteristic, complemented
211C2×ΓL(1,𝔽25)C2×D311yescharacteristic
212C2×ΓL(1,𝔽25)C2×D311yescharacteristic
213C2×D3×C8C2×D311yescharacteristic, complemented
214C2×D3×C8C2×D311yescharacteristic, complemented
215#895—31no—
216#895—31no—
217#894—61no—
218#893—61no—
219#892—31no—
220D3×C4⋊C4—31no—
221#884—61no—
222#882—61no—
223#67⋊C4—61no—
224D3×C22⋊C4—61no—
225C3×#107—31no—
226C3×#103—31no—
227C3×#102—31no—
228#835—31no—
229#832—31no—
230#821—31no—
231#821—31no—
232#821—31no—
233#821—31no—
234#821—31no—
235#821—31no—
236#821—31no—
237#821—61no—
238#821—61no—
239#821C2×D311yescharacteristic, complemented
240#818—31no—
241#818C2×D311yescharacteristic, complemented
242#817—31no—
243#817—31no—
244#817—31no—
245#817—61no—
246#816—31no—
247#816C2×D311yescharacteristic, complemented
248#809—31no—
249#809—31no—
250#808—31no—
251#807—31no—
252C23×C32C2×D411yescharacteristic
253C22×C3⋊D3—21no—
254C22×C3⋊D3—21no—
255C22×C3×D3—22no—
256C22×C3×D3—22no—
257C22×C3×D3—21no—
258C22×C3×D3—41no—
259C22×C3×D3C2×D411yescharacteristic
260C22×C3×D3C2×D411yescharacteristic
261C2×D32—42no—
262C2×D32—42no—
263C2×D32—42no—
264C2×C32×C4—21no—
265C2×C32×C4—21no—
266C2×C32×C4C2×D411yescharacteristic
267C2×C32×C4C2411yescharacteristic
268#638—42no—
269#638—42no—
270C2×C3⋊Dic3—21no—
271C2×C3⋊Dic3—21no—
272C4⋊(C3⋊D3)—21no—
273C4⋊(C3⋊D3)—21no—
274C4⋊(C3⋊D3)—21no—
275C4⋊(C3⋊D3)—21no—
276C3×#67—42no—
277C2×C3×Dic3—22no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3C2×D411yescharacteristic
282C2×C3×Dic3C2×D411yescharacteristic
283C3×D12—21no—
284C3×D12—21no—
285C3×C4×D3—22no—
286C3×C4×D3—21no—
287C3×C4×D3—21no—
288C3×C4×D3—22no—
289C3×C4×D3C2×D412yes—
290C3×C4×D3#4112yes—
291C3×Dic6—21no—
292C3×Dic6—21no—
293#626—42no—
294#626—42no—
295#626—42no—
296#626—42no—
297#625—42no—
298#624—42no—
299D3×Dic3—42no—
300C32×C8—21no—
301C32×C8C2×D412yescomplemented
302C3×C3⋊C8—21no—
303C3×C3⋊C8C2×D412yescomplemented
304C2×AGL(1,ℤ/8)—91no—
305C22×M16—31no—
306#525—91no—
307C2×#121—91no—
308#469—91no—
309#469—91no—
310#468—31no—
311#468—91no—
312#466—91no—
313#466—91no—
314#465—91no—
315#465—91no—
316#428—91no—
317#418—91no—
318#417—91no—
319C24×C3—31no—
320C23×D3—61no—
321C23×D3—61no—
322C23×D3D1211yescharacteristic
323C2×C3×Q8—31no—
324C2×C3×D4—31no—
325C2×C3×D4—61no—
326C22×C3×C4—21no—
327C22×C3×C4—31no—
328C22×C3×C4—31no—
329C22×C3×C4—31no—
330C22×C3×C4—31no—
331C22×C3×C4—31no—
332C22×C3×C4—62no—
333C22×C3×C4—62no—
334C22×C3×C4C22×D311yescharacteristic
335C22×C3×C4C22×D311yescharacteristic
336C2×#67—21no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—121no—
348C2×#67—121no—
349C2×#67—124no—
350C22×Dic3—61no—
351C22×Dic3D1211yescharacteristic
352#239—62no—
353#239—62no—
354D3×D4—62no—
355D3×D4—62no—
356D3×D4—124no—
357#235—62no—
358#235—62no—
359C2×D12—31no—
360C2×D12—31no—
361C2×D12—31no—
362C2×D12—31no—
363C2×D12—61no—
364C2×D12—61no—
365C2×D12—62no—
366C2×D12—62no—
367C2×D12—61no—
368C2×D12—61no—
369C2×D12—61no—
370C2×D12—61no—
371C2×D12C22×D311yescharacteristic
372C2×C4×D3—22no—
373C2×C4×D3—22no—
374C2×C4×D3—61no—
375C2×C4×D3—61no—
376C2×C4×D3—61no—
377C2×C4×D3D1211yescharacteristic
378C2×C4×D3D1211yescharacteristic
379C2×C4×D3C22×D311yescharacteristic
380C2×C4×D3C22×D311yescharacteristic
381C2×Dic6C22×D311yescharacteristic
382C3×SD16—62no—
383C3×M16—22no—
384C3×M16—22no—
385C3×M16—34no—
386C3×M16—42no—
387C3×M16—62no—
388C3×M16—62no—
389C2×C3×C8—21no—
390C2×C3×C8—21no—
391C2×C3×C8—31no—
392C2×C3×C8—31no—
393C2×C3×C8—62no—
394C2×C3×C8—62no—
395C2×C3×C8C22×D311yescharacteristic
396C2×C3×C8C22×D311yescharacteristic
397C2×C3×C8C22×D311yescharacteristic
398C2×C3×C8C22×D311yescharacteristic
399C3×C4⋊C4—31no—
400C3×C4⋊C4—31no—
401C3×C4⋊C4—61no—
402C3×C22⋊C4—61no—
403C3×C22⋊C4—61no—
404#217—21no—
405#217—61no—
406#217—61no—
407#217—61no—
408#215—62no—
409#213—62no—
410(C2×D3)⋊C4—21no—
411(C2×D3)⋊C4—61no—
412(C2×D3)⋊C4—61no—
413(C2×D3)⋊C4—61no—
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—31no—
427C4⋊Dic3—31no—
428C4⋊Dic3—61no—
429C4⋊Dic3—61no—
430C4⋊Dic3—61no—
431C4⋊Dic3C22×D311yescharacteristic
432C4⋊Dic3C22×D311yescharacteristic
433Dic3⋊C4—21no—
434Dic3⋊C4—61no—
435Dic3⋊C4—61no—
436Dic3⋊C4—61no—
437C4×Dic3—61no—
438C4×Dic3—61no—
439#208—22no—
440C2×C3⋊C8C22×D311yescharacteristic
441C2×C3⋊C8C22×D311yescharacteristic
442D24—62no—
443D24—62no—
444D24—62no—
445D24—122no—
446#204—22no—
447#204—62no—
448ΓL(1,𝔽25)—22no—
449ΓL(1,𝔽25)#6714yescomplemented
450D3×C8—22no—
451D3×C8—22no—
452C22×C32—21no—
453C22×C32—21no—
454C22×C32—21no—
455C22×C32C22×D411yescharacteristic
456C2×C3⋊D3—41no—
457C2×C3⋊D3—41no—
458C2×C3⋊D3—41no—
459C2×C3⋊D3—41no—
460C2×C3⋊D3—41no—
461C2×C3⋊D3—41no—
462C2×C3×D3—21no—
463C2×C3×D3—21no—
464C2×C3×D3—21no—
465C2×C3×D3—21no—
466C2×C3×D3—44no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
469C2×C3×D3—41no—
470C2×C3×D3#12112yes—
471C2×C3×D3AGL(1,ℤ/8)12yescomplemented
472D32—84no—
473C32×C4—21no—
474C32×C4C22×D411yescharacteristic
475C32×C4C2×#4111yescharacteristic
476C3⋊Dic3—41no—
477C3⋊Dic3—41no—
478C3×Dic3—21no—
479C3×Dic3—41no—
480C3×Dic3—41no—
481C3×Dic3—41no—
482C3×Dic3#12112yes—
483C2×#41—91no—
484C22×D4—91no—
485C22×D4—181no—
486C23×C4—31no—
487AGL(1,ℤ/8)—184no—
488C2×SD16—31no—
489C2×SD16—91no—
490C2×D8—91no—
491C2×D8—91no—
492C2×M16—31no—
493C2×M16—31no—
494C2×M16—31no—
495C2×M16—64no—
496C2×M16D3211yescharacteristic, complemented
497C22×C8—31no—
498C22×C8—31no—
499#123—181no—
500C22⋊Q8—31no—
501C22⋊Q8—91no—
502#121—31no—
503#121—91no—
504#121—91no—
505#121—91no—
506#121—91no—
507#121—91no—
508#121—181no—
509#121—181no—
510#120—181no—
511C4×D4—181no—
512C4×D4—181no—
513#117—91no—
514C2×C4⋊C4—91no—
515C2×C22⋊C4—181no—
516#107—31no—
517#107—91no—
518#106—91no—
519#106—91no—
520#103—31no—
521#103—91no—
522#102—31no—
523#102—91no—
524#102—91no—
525#102—91no—
526#102—91no—
527#102—91no—
528C23×C3—21no—
529C23×C3—31no—
530C23×C3—31no—
531C23×C3—62no—
532C23×C3—62no—
533C23×C3—61no—
534C23×C3—121no—
535C23×C3C2×D1211yescharacteristic
536C23×C3D3×D411yescharacteristic
537C22×D3—22no—
538C22×D3—22no—
539C22×D3—21no—
540C22×D3—41no—
541C22×D3—61no—
542C22×D3—61no—
543C22×D3—61no—
544C22×D3—61no—
545C22×D3—121no—
546C22×D3—121no—
547C22×D3—122no—
548C22×D3—122no—
549C22×D3—122no—
550C22×D3—122no—
551C22×D3—122no—
552C22×D3—122no—
553C22×D3C2×D1211yescharacteristic
554C22×D3C2×D1211yescharacteristic
555C3×Q8—61no—
556C3×Q8—61no—
557C3×D4—61no—
558C3×D4—61no—
559C3×D4—122no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—31no—
567C2×C3×C4—32no—
568C2×C3×C4—32no—
569C2×C3×C4—31no—
570C2×C3×C4—41no—
571C2×C3×C4—41no—
572C2×C3×C4—62no—
573C2×C3×C4—62no—
574C2×C3×C4—62no—
575C2×C3×C4—61no—
576C2×C3×C4—61no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4—61no—
580C2×C3×C4C2×D1211yescharacteristic
581C2×C3×C4D3×D411yescharacteristic
582C2×C3×C4C23×D311yescharacteristic
583C2×C3×C4C23×D311yescharacteristic
584#67—42no—
585#67—122no—
586#67—122no—
587#67—122no—
588#67—122no—
589#67—122no—
590#67—122no—
591#67—122no—
592#67—122no—
593#67—122no—
594#67—122no—
595#67—242no—
596#67—242no—
597C2×Dic3—22no—
598C2×Dic3—21no—
599C2×Dic3—21no—
600C2×Dic3—21no—
601C2×Dic3—61no—
602C2×Dic3—61no—
603C2×Dic3—61no—
604C2×Dic3—61no—
605C2×Dic3—121no—
606C2×Dic3—121no—
607C2×Dic3—122no—
608C2×Dic3C2×D1211yescharacteristic
609C2×Dic3C2×D1211yescharacteristic
610D12—21no—
611D12—21no—
612D12—61no—
613D12—61no—
614D12—61no—
615D12—61no—
616D12—61no—
617D12—61no—
618D12—61no—
619D12—61no—
620D12—121no—
621D12—121no—
622D12—121no—
623D12—121no—
624D12—122no—
625D12—122no—
626D12—122no—
627D12—122no—
628C4×D3—22no—
629C4×D3—21no—
630C4×D3—21no—
631C4×D3—22no—
632C4×D3—122no—
633C4×D3—122no—
634C4×D3—122no—
635C4×D3#23512yes—
636C4×D3C2×#6712yes—
637Dic6—21no—
638Dic6—21no—
639C3×C8—21no—
640C3×C8—21no—
641C3×C8—22no—
642C3×C8—32no—
643C3×C8—41no—
644C3×C8—61no—
645C3×C8D3×D412yescomplemented
646C3×C8C2×#6712yescomplemented
647C3⋊C8—21no—
648C3⋊C8C2×#6712yescomplemented
649C2×C32—41no—
650C2×C32C2×#12111yescharacteristic
651C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
652C2×C32#57511yescharacteristic
653C3⋊D3—81no—
654C3⋊D3—81no—
655C3×D3—22no—
656C3×D3—22no—
657C3×D3—81no—
658C24—31no—
659C24—181no—
660#41—182no—
661#41—182no—
662C2×Q8—31no—
663C2×D4—31no—
664C2×D4—61no—
665C2×D4—91no—
666C2×D4—91no—
667C2×D4—182no—
668C2×D4—182no—
669C2×D4—181no—
670C2×D4—181no—
671C2×D4—181no—
672C2×D4—181no—
673C2×D4—181no—
674C2×D4—181no—
675C2×D4—181no—
676C2×D4—364no—
677C22×C4—31no—
678C22×C4—31no—
679C22×C4—31no—
680C22×C4—31no—
681C22×C4—31no—
682C22×C4—62no—
683C22×C4—62no—
684C22×C4—181no—
685C22×C4—181no—
686C22×C4C2×D3211yescharacteristic
687SD16—62no—
688SD16—182no—
689D8—182no—
690D8—182no—
691M16—22no—
692M16—34no—
693M16—62no—
694M16—62no—
695C2×C8—31no—
696C2×C8—31no—
697C2×C8—62no—
698C2×C8—62no—
699C2×C8C2×D3211yescharacteristic
700C2×C8C2×D3211yescharacteristic
701C4⋊C4—31no—
702C4⋊C4—31no—
703C4⋊C4—61no—
704C4⋊C4—91no—
705C4⋊C4—91no—
706C4⋊C4—181no—
707C4⋊C4—181no—
708C22⋊C4—61no—
709C22⋊C4—61no—
710C22⋊C4—181no—
711C22⋊C4—181no—
712C22⋊C4—181no—
713C22⋊C4—181no—
714C22⋊C4—181no—
715C22⋊C4—181no—
716C22⋊C4—181no—
717C42—181no—
718C22×C3—21no—
719C22×C3—21no—
720C22×C3—21no—
721C22×C3—21no—
722C22×C3—21no—
723C22×C3—21no—
724C22×C3—21no—
725C22×C3—32no—
726C22×C3—32no—
727C22×C3—41no—
728C22×C3—41no—
729C22×C3—41no—
730C22×C3—61no—
731C22×C3—61no—
732C22×C3—61no—
733C22×C3—61no—
734C22×C3—124no—
735C22×C3—121no—
736C22×C3—121no—
737C22×C3—121no—
738C22×C3C22×D1211yescharacteristic
739C22×C3C2×D3×D411yescharacteristic
740C2×D3—21no—
741C2×D3—21no—
742C2×D3—21no—
743C2×D3—21no—
744C2×D3—44no—
745C2×D3—41no—
746C2×D3—41no—
747C2×D3—41no—
748C2×D3—121no—
749C2×D3—121no—
750C2×D3—121no—
751C2×D3—121no—
752C2×D3—121no—
753C2×D3—121no—
754C2×D3—121no—
755C2×D3—121no—
756C2×D3—121no—
757C2×D3—121no—
758C2×D3—121no—
759C2×D3—121no—
760C2×D3—241no—
761C2×D3—241no—
762C2×D3—241no—
763C2×D3—241no—
764C2×D3—241no—
765C2×D3—241no—
766C2×D3—244no—
767C2×D3—244no—
768C2×D3#90812yescomplemented
769C2×D3#93012yes—
770C3×C4—21no—
771C3×C4—21no—
772C3×C4—21no—
773C3×C4—21no—
774C3×C4—32no—
775C3×C4—41no—
776C3×C4—61no—
777C3×C4—121no—
778C3×C4—121no—
779C3×C4—121no—
780C3×C4C2×#23511yescharacteristic
781C3×C4C2×D3×D411yescharacteristic
782C3×C4D3×#4111yescharacteristic
783C3×C4C22×#6711yescharacteristic
784Dic3—21no—
785Dic3—41no—
786Dic3—41no—
787Dic3—41no—
788Dic3—121no—
789Dic3—121no—
790Dic3—121no—
791Dic3—121no—
792Dic3—241no—
793Dic3—241no—
794Dic3#93012yes—
795C32#305511yescharacteristic, complemented, Sylow
796C23—31no—
797C23—31no—
798C23—62no—
799C23—62no—
800C23—61no—
801C23—121no—
802C23—181no—
803C23—181no—
804C23—362no—
805C23—362no—
806C23—362no—
807C23D3×D1211yescharacteristic
808Q8—61no—
809Q8—61no—
810D4—61no—
811D4—61no—
812D4—122no—
813D4—181no—
814D4—181no—
815D4—181no—
816D4—181no—
817D4—362no—
818D4—362no—
819D4—362no—
820D4—362no—
821D4—362no—
822D4—362no—
823D4—362no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—31no—
827C2×C4—32no—
828C2×C4—32no—
829C2×C4—31no—
830C2×C4—62no—
831C2×C4—62no—
832C2×C4—62no—
833C2×C4—61no—
834C2×C4—61no—
835C2×C4—61no—
836C2×C4—61no—
837C2×C4—61no—
838C2×C4—181no—
839C2×C4—181no—
840C2×C4—362no—
841C2×C4—362no—
842C2×C4D3×D1211yescharacteristic
843C2×C4C22×D3211yescharacteristic
844C8—21no—
845C8—32no—
846C8—61no—
847C8D3×#6712yescomplemented
848C2×C3—21no—
849C2×C3—21no—
850C2×C3—21no—
851C2×C3—41no—
852C2×C3—41no—
853C2×C3—62no—
854C2×C3—62no—
855C2×C3—81no—
856C2×C3—241no—
857C2×C3D3×#12111yescharacteristic
858C2×C3C2×#90811yescharacteristic
859C2×C3#574811yescharacteristic
860C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
861C2×C3#577711yescharacteristic
862C2×C3C2×#93011yescharacteristic
863D3—22no—
864D3—22no—
865D3—81no—
866D3—241no—
867D3—241no—
868D3—241no—
869D3—241no—
870D3—481no—
871D3—481no—
872C22—21no—
873C22—21no—
874C22—21no—
875C22—32no—
876C22—32no—
877C22—61no—
878C22—61no—
879C22—61no—
880C22—61no—
881C22—124no—
882C22—121no—
883C22—121no—
884C22—121no—
885C22—361no—
886C22—361no—
887C22—361no—
888C22—361no—
889C22—361no—
890C22—361no—
891C22—724no—
892C22C2×D3×D1211yescharacteristic
893C4—21no—
894C4—32no—
895C4—61no—
896C4—121no—
897C4—121no—
898C4—121no—
899C4—361no—
900C4—361no—
901C4D3×#23511yescharacteristic
902C4C2×D3×#6711yescharacteristic
903C3—21no—
904C3#8080511yescharacteristic, complemented
905C3#8377211yescharacteristic, complemented
906C2—41no—
907C2—62no—
908C2—62no—
909C2—241no—
910C2—721no—
911C2—721no—
912C2D3×#90811yescharacteristic
913C2#1059471111yescharacteristic
914C2D3×#93011yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
hypercenterC2×M16D32
hypocenterC32#3055
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×C3×D3×M16C2semidirect
2. D3×#930C2semidirect
3. #10595005C2semidirect
4. C2×#63794C2semidirect
5. #10592834C2semidirect
6. C3×#5134C2semidirect
7. #10591178C2semidirect
8. #10591165C2semidirect
9. #10590939C2semidirect
10. #10590847C2semidirect
11. #10590832C2semidirect
12. #10590829C2semidirect
13. #10590826C2semidirect
14. #10590683C2semidirect
15. #10590671C2semidirect
22. C2×C32×M16C22semidirect
24. #64139C22semidirect
25. C2×#3745C22semidirect
27. C3×#924C22semidirect
28. C2×C3×#208C22semidirect
30. C2×C3×#204C22semidirect
33. C2×C3×D3×C8C22semidirect
34. C2×C3×D3×C8C22semidirect
40. #63909C22semidirect
45. #63856C22semidirect
48. C2×#3717C22semidirect
49. C2×#3714C22semidirect
51. #63648C22semidirect
52. #63648C22semidirect
53. #63644C22semidirect
54. C3×#821C22semidirect
55. C3×#818C22semidirect
56. C3×#816C22semidirect
57. #63575C22semidirect
58. #63573C22semidirect
59. #63566C22semidirect
60. #63564C22semidirect
61. #63564C22semidirect
62. #63563C22semidirect
68. C2×D3×M16D3semidirect
78. #5134D3semidirect
141. C3×ΓL(1,𝔽25)D4semidirect
169. C2×C3×M16C2×D3semidirect
170. C2×C3×M16C2×D3semidirect
200. #924C2×D3semidirect
201. C2×#208C2×D3semidirect
210. C2×#204C2×D3semidirect
213. C2×D3×C8C2×D3semidirect
214. C2×D3×C8C2×D3semidirect
239. #821C2×D3semidirect
241. #818C2×D3semidirect
247. #816C2×D3semidirect
301. C32×C8C2×D4semidirect
303. C3×C3⋊C8C2×D4semidirect
449. ΓL(1,𝔽25)#67semidirect
471. C2×C3×D3AGL(1,ℤ/8)semidirect
496. C2×M16D32semidirect
645. C3×C8D3×D4semidirect
646. C3×C8C2×#67semidirect
648. C3⋊C8C2×#67semidirect
768. C2×D3#908semidirect
795. C32#3055semidirect
847. C8D3×#67semidirect
904. C3#80805semidirect
905. C3#83772semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×M162
D3×#9302
#105950052
C2×#637942
#105928342
C3×#51342
#105911782
#105911652
#105909392
#105908472
#105908322
#105908292
#105908262
#105906832
#105906712
#837723
#808053