Finite Group Databasebeta

← #11884015

Subgroups — #11884015

Order 1152.

1173 conjugacy classes of subgroups.

The subgroup lattice has 941 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×SD16C211yesmaximal, characteristic, complemented
2#10595342C211yesmaximal, characteristic, complemented
3C2×#63941C211yesmaximal, characteristic, complemented
4#10595293C211yesmaximal, characteristic, complemented
5#10592871C211yesmaximal, characteristic, complemented
6C3×#5163C211yesmaximal, characteristic, complemented
7#10591583C211yesmaximal, characteristic, complemented
8#10591566C211yesmaximal, characteristic, complemented
9#10591472C211yesmaximal, characteristic, complemented
10#10591464C211yesmaximal, characteristic, complemented
11#10591448C211yesmaximal, characteristic, complemented
12#10590943C211yesmaximal, characteristic, complemented
13#10590826C211yesmaximal, characteristic, complemented
14#10590754C211yesmaximal, characteristic, complemented
15#10590727C211yesmaximal, characteristic, complemented
16#83864—31nomaximal
17#80404—31nomaximal
18C2×#3832C2211yescharacteristic, complemented
19C2×C3×D3×Q8C2211yescharacteristic, complemented
20C2×C3×D3×D4C2211yescharacteristic
21C2×D3×#67—21no—
22C2×#3802C2211yescharacteristic
23C2×C32×SD16C2211yescharacteristic, complemented
24#64147C2211yescharacteristic
25C2×#3753C2211yescharacteristic, complemented
26C3×Q8×Dic3C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic
28C2×C3×#215C2211yescharacteristic, complemented
29C3×#940C2211yescharacteristic
30C2×C3×#214C2211yescharacteristic, complemented
31C3×D3×SD16—24no—
32C2×C3×#204C2211yescharacteristic
33C2×C3×D3×C8C2211yescharacteristic, complemented
34#63983—21no—
35#63976—21no—
36#63970—21no—
37#63941—24no—
38#63909—21no—
39#63909C2211yescharacteristic, complemented
40#63908C2211yescharacteristic
41C4×#626—21no—
42C4×#626C2211yescharacteristic
43Dic3×D12C2211yescharacteristic
44#63871—21no—
45#63871C2211yescharacteristic, complemented
46#63864—21no—
47#63864C2211yescharacteristic, complemented
48C2×#3715C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic
50C2×#3714C2211yescharacteristic, complemented
51C2×#3712C2211yescharacteristic, complemented
52#63662C2211yescharacteristic, complemented
53#63648C2211yescharacteristic, complemented
54#63647C2211yescharacteristic, complemented
55C3×#832C2211yescharacteristic, complemented
56C3×#821C2211yescharacteristic, complemented
57C3×Dic3⋊C8C2211yescharacteristic, complemented
58#63575C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63562C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62#63554C2211yescharacteristic, complemented
63C22×C3×SD16—31no—
64#5817—31no—
65D4×#67—31no—
66C2×#914—31no—
67C2×#914—31no—
68C2×D3×SD16D311yescharacteristic, complemented
69#5717—31no—
70#5576—31no—
71C3×#460—31no—
72#5227—31no—
73#5217—31no—
74#5176—31no—
75#5174—31no—
76#5172—31no—
77#5172—31no—
78#5172—61no—
79#5170—31no—
80#5169—31no—
81#5165—31no—
82#5164—31no—
83#5163D311yescharacteristic, complemented
84#5115—31no—
85#5111—31no—
86#5074—31no—
87#5026—31no—
88#4844—31no—
89#4836—31no—
90#4780—31no—
91#4776—31no—
92#4775—31no—
93#4773—31no—
94C23×C3×D3—21no—
95C22×D32—21no—
96C2×C32×Q8C2311yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C2×#638—21no—
99#3832—22no—
100#3832—41no—
101C2×C4⋊(C3⋊D3)—21no—
102C2×C4⋊(C3⋊D3)C2311yescharacteristic
103C2×C4×C3⋊D3—21no—
104C2×C4×C3⋊D3C2311yescharacteristic
105C2×C3×#67—21no—
106C2×C3×#67—21no—
107C2×C3×#67—21no—
108C3×D3×Q8—22no—
109C3×D3×Q8—41no—
110C3×D3×D4—22no—
111C3×D3×D4—41no—
112C2×C3×D12C2311yescharacteristic
113C2×C3×D12C2311yescharacteristic
114C2×C3×C4×D3—21no—
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×Dic6—21no—
117C2×C3×Dic6C2311yescharacteristic
118D3×#67—44no—
119C2×#626—21no—
120C2×#626D411yescharacteristic
121C2×#625—21no—
122C2×#625—21no—
123C2×D3×Dic3—21no—
124#3802—22no—
125#3802—41no—
126C32×SD16—22no—
127C2×C32×C8C2311yescharacteristic
128#3757—21no—
129#3753—41no—
130C4⋊(C3⋊Dic3)C2311yescharacteristic
131C2×C3⋊(C3⋊C8)C2311yescharacteristic
132C3×#215—22no—
133C3×#215D414yescomplemented
134C3×#214—22no—
135C3×C4⋊Dic3—21no—
136C3×C4⋊Dic3C2311yescharacteristic
137C3×C4×Dic3—21no—
138C3×C4×Dic3C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C3×#204—22no—
142C3×D3×C8—22no—
143Dic3⋊Dic3—21no—
144Dic3⋊Dic3D411yescharacteristic
145#3722—21no—
146#3722—21no—
147#3722—21no—
148#3722—21no—
149#3722D411yescharacteristic
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3—21no—
152(C2×D3)⋊Dic3D411yescharacteristic
153#3715—41no—
154#3714—22no—
155#3714—22no—
156#3712—22no—
157#3265—91noSylow
158C22×C3×Q8—31no—
159C22×C3×D4—31no—
160C22×#67—61no—
161C2×#239—31no—
162C2×#239—31no—
163C2×#239—61no—
164C2×D3×Q8C2×D311yescharacteristic, complemented
165C2×D3×D4—31no—
166C2×D3×D4—31no—
167C2×D3×D4—61no—
168C2×D3×D4C2×D311yescharacteristic
169C2×C3×SD16—21no—
170C2×C3×SD16—31no—
171C2×C3×SD16—31no—
172C2×C3×SD16—31no—
173C2×C3×SD16—31no—
174C2×C3×SD16—64no—
175C2×C3×SD16C2×D311yescharacteristic, complemented
176C2×C3×SD16C2×D311yescharacteristic, complemented
177C22×C3×C8—31no—
178C3×#127—31no—
179C3×C4×Q8—31no—
180#953—61no—
181#947—31no—
182#947—61no—
183#946—31no—
184#946—61no—
185Q8×Dic3C2×D311yescharacteristic, complemented
186C2×#215—31no—
187C2×#215C2×D311yescharacteristic
188C2×#215C2×D311yescharacteristic, complemented
189#940C2×D311yescharacteristic
190#939—61no—
191#938—31no—
192#938—31no—
193#938—31no—
194#938—61no—
195#938—61no—
196#937—61no—
197#937—61no—
198#937—61no—
199D4×Dic3—31no—
200C2×#214—31no—
201C2×#214C2×D311yescharacteristic, complemented
202C2×#213—31no—
203C2×#213—31no—
204C2×#213—31no—
205C2×#213—31no—
206C2×#213—61no—
207#930—31no—
208#930—31no—
209#930—61no—
210C4×#67—31no—
211C4×#67—61no—
212#914—64no—
213#914—64no—
214D3×SD16—24no—
215C2×D24—31no—
216C2×D24—31no—
217C2×#204C2×D311yescharacteristic
218C2×ΓL(1,𝔽25)—31no—
219C2×ΓL(1,𝔽25)—31no—
220C2×D3×C8C2×D311yescharacteristic, complemented
221#897—31no—
222#897—61no—
223#895—31no—
224#895—61no—
225#875—31no—
226#875—61no—
227C4×D12—31no—
228C4×D12—31no—
229C4×D12—61no—
230C3×C4⋊C8—31no—
231C3×#102—31no—
232C3×#102—31no—
233#835—31no—
234#835—31no—
235#835—31no—
236#835—61no—
237#832—31no—
238#832C2×D311yescharacteristic, complemented
239#830—31no—
240#821—31no—
241#821—31no—
242#821—61no—
243#821C2×D311yescharacteristic, complemented
244(C2×D3)⋊C8—31no—
245(C2×D3)⋊C8—31no—
246(C2×D3)⋊C8—31no—
247(C2×D3)⋊C8—61no—
248#818—31no—
249#816—31no—
250#815—31no—
251Dic3⋊C8C2×D311yescharacteristic, complemented
252#809—31no—
253#807—31no—
254#803—31no—
255C23×C32—21no—
256C22×C3⋊D3—21no—
257C22×C3⋊D3C2×D411yescharacteristic
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3—42no—
261C22×C3×D3—42no—
262C22×C3×D3—81no—
263C22×C3×D3C2×D411yescharacteristic
264C2×D32—42no—
265C2×D32—42no—
266C2×D32—81no—
267C32×Q8—21no—
268C32×Q8C2×D412yescomplemented
269C32×D4—21no—
270C32×D4—21no—
271C2×C32×C4—21no—
272C2×C32×C4C2411yescharacteristic
273#638—42no—
274C2×C3⋊Dic3—21no—
275C2×C3⋊Dic3C2×D411yescharacteristic
276C4⋊(C3⋊D3)—21no—
277C4⋊(C3⋊D3)—21no—
278C4⋊(C3⋊D3)—42no—
279C4×C3⋊D3—21no—
280C4×C3⋊D3—21no—
281C4×C3⋊D3—42no—
282C3×#67—42no—
283C3×#67—42no—
284C3×#67—81no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3C2×D411yescharacteristic
288C2×C3×Dic3C2×D411yescharacteristic
289C2×C3×Dic3C2×D411yescharacteristic
290C3×D12—21no—
291C3×D12—21no—
292C3×D12—21no—
293C3×D12C2×D412yes—
294C3×C4×D3—21no—
295C3×C4×D3—21no—
296C3×C4×D3—42no—
297C3×Dic6—21no—
298C3×Dic6—21no—
299C3×Dic6—42no—
300#626—22no—
301#626—42no—
302#625—42no—
303#625—42no—
304D3×Dic3—42no—
305C32×C8—21no—
306C3⋊(C3⋊C8)—21no—
307C3×C3⋊C8—21no—
308C3×C3⋊C8C2×D412yescomplemented
309C2×AGL(1,ℤ/8)—91no—
310C22×SD16—31no—
311#548—91no—
312D42—91no—
313#496—91no—
314#468—91no—
315#466—91no—
316#463—91no—
317#460—31no—
318#450—91no—
319#449—91no—
320#448—91no—
321#447—91no—
322#440—91no—
323#435—91no—
324C24×C3—61no—
325C23×D3—21no—
326C23×D3—61no—
327C23×D3—61no—
328C2×C3×Q8—21no—
329C2×C3×Q8—31no—
330C2×C3×Q8—61no—
331C2×C3×Q8—62no—
332C2×C3×Q8—121no—
333C2×C3×Q8C22×D311yescharacteristic
334C2×C3×Q8C22×D311yescharacteristic
335C2×C3×D4—21no—
336C2×C3×D4—31no—
337C2×C3×D4—31no—
338C2×C3×D4—61no—
339C2×C3×D4—61no—
340C2×C3×D4—61no—
341C2×C3×D4—62no—
342C2×C3×D4—121no—
343C2×C3×D4C22×D311yescharacteristic
344C2×C3×D4C22×D311yescharacteristic
345C22×C3×C4—31no—
346C22×C3×C4—61no—
347C2×#67—21no—
348C2×#67—21no—
349C2×#67—21no—
350C2×#67—31no—
351C2×#67—61no—
352C2×#67—61no—
353C2×#67—61no—
354C2×#67—61no—
355C2×#67—61no—
356C2×#67—61no—
357C2×#67—61no—
358C2×#67—121no—
359C2×#67—124no—
360C22×Dic3—61no—
361#239—62no—
362#239—62no—
363#239—122no—
364#239—121no—
365#239—121no—
366#239—122no—
367D3×Q8—22no—
368D3×Q8—41no—
369D3×D4—22no—
370D3×D4—41no—
371D3×D4—62no—
372D3×D4—62no—
373D3×D4—121no—
374D3×D4—121no—
375D3×D4—124no—
376C2×D12—31no—
377C2×D12—31no—
378C2×D12—31no—
379C2×D12—61no—
380C2×D12—61no—
381C2×D12—61no—
382C2×D12—61no—
383C2×D12—121no—
384C2×D12C22×D311yescharacteristic
385C2×D12C22×D311yescharacteristic
386C2×C4×D3—21no—
387C2×C4×D3—31no—
388C2×C4×D3—31no—
389C2×C4×D3—61no—
390C2×C4×D3—61no—
391C2×C4×D3—61no—
392C2×C4×D3—61no—
393C2×C4×D3—121no—
394C2×C4×D3C22×D311yescharacteristic
395C2×Dic6—21no—
396C2×Dic6C22×D311yescharacteristic
397C3×SD16—22no—
398C3×SD16—22no—
399C3×SD16—34no—
400C3×SD16—42no—
401C3×SD16—62no—
402C3×SD16—62no—
403C3×SD16—62no—
404C2×C3×C8—21no—
405C2×C3×C8—31no—
406C2×C3×C8—31no—
407C2×C3×C8—62no—
408C2×C3×C8C22×D311yescharacteristic
409C2×C3×C8C22×D311yescharacteristic
410C3×C4⋊C4—31no—
411C3×C4⋊C4—61no—
412C3×C42—31no—
413C3×C42—61no—
414#217—31no—
415#217—61no—
416#217—61no—
417#217—61no—
418#217—61no—
419#217—121no—
420#215—22no—
421#215—121no—
422#215#6714yescomplemented
423#214—22no—
424#214—121no—
425#213—62no—
426#213—62no—
427#213—121no—
428#213—121no—
429#213—122no—
430(C2×D3)⋊C4—31no—
431(C2×D3)⋊C4—31no—
432(C2×D3)⋊C4—31no—
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)⋊C4—61no—
442(C2×D3)⋊C4—61no—
443C4⋊Dic3—21no—
444C4⋊Dic3—31no—
445C4⋊Dic3—31no—
446C4⋊Dic3—31no—
447C4⋊Dic3—61no—
448C4⋊Dic3—61no—
449C4⋊Dic3C22×D311yescharacteristic
450Dic3⋊C4—31no—
451Dic3⋊C4—61no—
452C4×Dic3—21no—
453C4×Dic3C22×D311yescharacteristic
454C2×C3⋊C8—31no—
455C2×C3⋊C8—31no—
456C2×C3⋊C8—61no—
457C2×C3⋊C8C22×D311yescharacteristic
458C2×C3⋊C8C22×D311yescharacteristic
459D24—62no—
460D24—62no—
461#204—22no—
462ΓL(1,𝔽25)—62no—
463ΓL(1,𝔽25)—62no—
464D3×C8—22no—
465C22×C32—41no—
466C22×C32—41no—
467C22×C32—41no—
468C22×C32C22×D411yescharacteristic
469C2×C3⋊D3—21no—
470C2×C3⋊D3—21no—
471C2×C3⋊D3—21no—
472C2×C3⋊D3—41no—
473C2×C3⋊D3—41no—
474C2×C3⋊D3—41no—
475C2×C3×D3—21no—
476C2×C3×D3—21no—
477C2×C3×D3—22no—
478C2×C3×D3—41no—
479C2×C3×D3—41no—
480C2×C3×D3—41no—
481C2×C3×D3—41no—
482C2×C3×D3—41no—
483C2×C3×D3—84no—
484C2×C3×D3AGL(1,ℤ/8)12yescomplemented
485D32—84no—
486C32×C4—22no—
487C32×C4C22×D411yescharacteristic
488C32×C4H(5,𝔽2)11yescharacteristic
489C3⋊Dic3—21no—
490C3⋊Dic3—41no—
491C3×Dic3—21no—
492C3×Dic3—21no—
493C3×Dic3—21no—
494C3×Dic3—41no—
495C3×Dic3—41no—
496C2×#41—91no—
497C22×Q8—31no—
498C22×D4—31no—
499C22×D4—91no—
500C22×D4—181no—
501AGL(1,ℤ/8)—184no—
502C2×SD16—31no—
503C2×SD16—31no—
504C2×SD16—31no—
505C2×SD16—31no—
506C2×SD16—64no—
507C2×SD16—91no—
508C2×SD16D3211yescharacteristic, complemented
509C2×D8—91no—
510C2×D8—91no—
511C2×D8—91no—
512C2×M16—91no—
513C22×C8—31no—
514#127—31no—
515#124—91no—
516#124—181no—
517C22⋊Q8—91no—
518C22⋊Q8—181no—
519#121—91no—
520#121—91no—
521#121—91no—
522#121—181no—
523#121—181no—
524#120—181no—
525#120—181no—
526C4×Q8—31no—
527C4×D4—91no—
528C4×D4—91no—
529C4×D4—181no—
530#107—91no—
531C4⋊C8—31no—
532#103—91no—
533#103—91no—
534#102—31no—
535#102—31no—
536#102—91no—
537#102—91no—
538C22⋊C8—91no—
539C22⋊C8—91no—
540#97—91no—
541C23×C3—21no—
542C23×C3—21no—
543C23×C3—31no—
544C23×C3—41no—
545C23×C3—61no—
546C23×C3—61no—
547C23×C3—122no—
548C23×C3—122no—
549C23×C3—241no—
550C22×D3—21no—
551C22×D3—21no—
552C22×D3—31no—
553C22×D3—31no—
554C22×D3—42no—
555C22×D3—42no—
556C22×D3—61no—
557C22×D3—61no—
558C22×D3—61no—
559C22×D3—81no—
560C22×D3—121no—
561C22×D3—122no—
562C22×D3—122no—
563C22×D3—122no—
564C22×D3—122no—
565C22×D3—241no—
566C22×D3—241no—
567C22×D3D3×D411yescharacteristic
568C3×Q8—21no—
569C3×Q8—21no—
570C3×Q8—22no—
571C3×Q8—41no—
572C3×Q8—61no—
573C3×Q8—61no—
574C3×Q8—122no—
575C3×Q8D3×D412yescomplemented
576C3×Q8C2×#6712yescomplemented
577C3×D4—21no—
578C3×D4—21no—
579C3×D4—21no—
580C3×D4—21no—
581C3×D4—32no—
582C3×D4—41no—
583C3×D4—41no—
584C3×D4—61no—
585C3×D4—61no—
586C3×D4—61no—
587C3×D4—122no—
588C3×D4—122no—
589C3×D4—241no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—31no—
594C2×C3×C4—31no—
595C2×C3×C4—31no—
596C2×C3×C4—41no—
597C2×C3×C4—61no—
598C2×C3×C4—61no—
599C2×C3×C4—61no—
600C2×C3×C4—61no—
601C2×C3×C4—122no—
602C2×C3×C4C23×D311yescharacteristic
603C2×C3×C4C23×D311yescharacteristic
604#67—42no—
605#67—42no—
606#67—62no—
607#67—81no—
608#67—122no—
609#67—122no—
610#67—122no—
611#67—122no—
612#67—122no—
613#67—122no—
614#67—122no—
615#67—242no—
616C2×Dic3—21no—
617C2×Dic3—21no—
618C2×Dic3—31no—
619C2×Dic3—31no—
620C2×Dic3—61no—
621C2×Dic3—61no—
622C2×Dic3—61no—
623C2×Dic3—121no—
624C2×Dic3—122no—
625C2×Dic3D3×D411yescharacteristic
626C2×Dic3D3×D411yescharacteristic
627C2×Dic3D3×D411yescharacteristic
628D12—21no—
629D12—21no—
630D12—21no—
631D12—62no—
632D12—62no—
633D12—61no—
634D12—61no—
635D12—61no—
636D12—61no—
637D12—121no—
638D12—122no—
639D12—122no—
640D12—124no—
641D12—122no—
642D12C2×#6712yes—
643C4×D3—21no—
644C4×D3—21no—
645C4×D3—42no—
646C4×D3—61no—
647C4×D3—61no—
648C4×D3—61no—
649C4×D3—61no—
650C4×D3—121no—
651C4×D3—121no—
652C4×D3—122no—
653C4×D3—122no—
654C4×D3—124no—
655C4×D3—122no—
656Dic6—21no—
657Dic6—21no—
658Dic6—42no—
659C3×C8—21no—
660C3×C8—21no—
661C3×C8—32no—
662C3×C8—41no—
663C3×C8—61no—
664C3⋊C8—21no—
665C3⋊C8—61no—
666C3⋊C8—61no—
667C3⋊C8—121no—
668C3⋊C8C2×#6712yescomplemented
669C2×C32—81no—
670C2×C32D4211yescharacteristic
671C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
672C2×C32#57711yescharacteristic
673C3⋊D3—41no—
674C3⋊D3—81no—
675C3×D3—22no—
676C3×D3—42no—
677C3×D3—81no—
678C24—61no—
679C24—181no—
680#41—182no—
681#41—361no—
682C2×Q8—31no—
683C2×Q8—61no—
684C2×Q8—62no—
685C2×Q8—121no—
686C2×Q8C2×D3211yescharacteristic
687C2×D4—31no—
688C2×D4—31no—
689C2×D4—61no—
690C2×D4—61no—
691C2×D4—61no—
692C2×D4—62no—
693C2×D4—91no—
694C2×D4—91no—
695C2×D4—121no—
696C2×D4—181no—
697C2×D4—181no—
698C2×D4—181no—
699C2×D4—182no—
700C2×D4—181no—
701C2×D4—181no—
702C2×D4—361no—
703C2×D4—364no—
704C2×D4C2×D3211yescharacteristic
705C22×C4—31no—
706C22×C4—61no—
707C22×C4—91no—
708C22×C4—181no—
709C22×C4—181no—
710SD16—22no—
711SD16—34no—
712SD16—62no—
713SD16—62no—
714SD16—62no—
715SD16—361no—
716D8—182no—
717D8—182no—
718D8—361no—
719M16—182no—
720C2×C8—31no—
721C2×C8—31no—
722C2×C8—62no—
723C2×C8—91no—
724C2×C8C2×D3211yescharacteristic
725C4⋊C4—31no—
726C4⋊C4—61no—
727C4⋊C4—91no—
728C4⋊C4—91no—
729C4⋊C4—181no—
730C22⋊C4—91no—
731C22⋊C4—91no—
732C22⋊C4—181no—
733C22⋊C4—181no—
734C22⋊C4—181no—
735C22⋊C4—181no—
736C22⋊C4—181no—
737C22⋊C4—181no—
738C22⋊C4—181no—
739C42—31no—
740C42—61no—
741C22×C3—21no—
742C22×C3—32no—
743C22×C3—41no—
744C22×C3—41no—
745C22×C3—41no—
746C22×C3—41no—
747C22×C3—41no—
748C22×C3—41no—
749C22×C3—61no—
750C22×C3—61no—
751C22×C3—62no—
752C22×C3—81no—
753C22×C3—81no—
754C22×C3—81no—
755C22×C3—121no—
756C22×C3—121no—
757C22×C3—121no—
758C22×C3—121no—
759C22×C3—121no—
760C22×C3—244no—
761C22×C3C2×D3×D411yescharacteristic
762C22×C3C2×D3×D411yescharacteristic
763C2×D3—21no—
764C2×D3—21no—
765C2×D3—22no—
766C2×D3—41no—
767C2×D3—41no—
768C2×D3—41no—
769C2×D3—41no—
770C2×D3—41no—
771C2×D3—61no—
772C2×D3—61no—
773C2×D3—61no—
774C2×D3—61no—
775C2×D3—61no—
776C2×D3—61no—
777C2×D3—84no—
778C2×D3—121no—
779C2×D3—121no—
780C2×D3—121no—
781C2×D3—122no—
782C2×D3—121no—
783C2×D3—121no—
784C2×D3—121no—
785C2×D3—121no—
786C2×D3—121no—
787C2×D3—121no—
788C2×D3—241no—
789C2×D3—241no—
790C2×D3—244no—
791C2×D3—244no—
792C2×D3#91412yescomplemented
793C3×C4—22no—
794C3×C4—22no—
795C3×C4—21no—
796C3×C4—21no—
797C3×C4—42no—
798C3×C4—61no—
799C3×C4—61no—
800C3×C4—61no—
801C3×C4—121no—
802C3×C4—121no—
803C3×C4C2×D3×D411yescharacteristic
804C3×C4#100411yescharacteristic
805C3×C4#100911yescharacteristic
806C3×C4C22×#6711yescharacteristic
807Dic3—21no—
808Dic3—21no—
809Dic3—21no—
810Dic3—41no—
811Dic3—41no—
812Dic3—61no—
813Dic3—61no—
814Dic3—121no—
815Dic3—121no—
816Dic3—121no—
817Dic3—241no—
818C32#326511yescharacteristic, complemented, Sylow
819C23—21no—
820C23—31no—
821C23—61no—
822C23—61no—
823C23—91no—
824C23—122no—
825C23—122no—
826C23—181no—
827C23—241no—
828C23—362no—
829C23—362no—
830C23—721no—
831Q8—21no—
832Q8—61no—
833Q8—61no—
834Q8—122no—
835Q8D3×#6712yescomplemented
836D4—21no—
837D4—21no—
838D4—32no—
839D4—61no—
840D4—61no—
841D4—61no—
842D4—122no—
843D4—122no—
844D4—182no—
845D4—181no—
846D4—181no—
847D4—241no—
848D4—362no—
849D4—362no—
850D4—362no—
851D4—362no—
852D4—362no—
853C2×C4—21no—
854C2×C4—31no—
855C2×C4—31no—
856C2×C4—31no—
857C2×C4—61no—
858C2×C4—61no—
859C2×C4—61no—
860C2×C4—61no—
861C2×C4—91no—
862C2×C4—122no—
863C2×C4—181no—
864C2×C4—181no—
865C2×C4—181no—
866C2×C4—362no—
867C2×C4—362no—
868C2×C4C22×D3211yescharacteristic
869C8—21no—
870C8—32no—
871C8—61no—
872C8—181no—
873C2×C3—21no—
874C2×C3—21no—
875C2×C3—21no—
876C2×C3—62no—
877C2×C3—81no—
878C2×C3—81no—
879C2×C3—122no—
880C2×C3—161no—
881C2×C3—241no—
882C2×C3#560911yescharacteristic
883C2×C3C2×#91411yescharacteristic
884C2×C3#576211yescharacteristic
885C2×C3#576211yescharacteristic
886C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
887C2×C3D4×#6711yescharacteristic
888D3—22no—
889D3—42no—
890D3—81no—
891D3—121no—
892D3—121no—
893D3—241no—
894D3—242no—
895D3—241no—
896D3—241no—
897C22—32no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—61no—
902C22—61no—
903C22—62no—
904C22—121no—
905C22—121no—
906C22—121no—
907C22—121no—
908C22—121no—
909C22—181no—
910C22—181no—
911C22—181no—
912C22—244no—
913C22—361no—
914C22—361no—
915C22—361no—
916C22—724no—
917C22D32×D411yescharacteristic
918C4—22no—
919C4—61no—
920C4—61no—
921C4—61no—
922C4—121no—
923C4—121no—
924C4—181no—
925C4—361no—
926C4#6431411yescharacteristic
927C4C2×D3×#6711yescharacteristic
928C3—21no—
929C3#8040411yescharacteristic, complemented
930C3#8386411yescharacteristic, complemented
931C2—62no—
932C2—81no—
933C2—122no—
934C2—241no—
935C2—361no—
936C2—721no—
937C2D3×#91411yescharacteristic
938C2#1059474811yescharacteristic
939C2#1059529111yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
hypercenterC2×SD16D32
hypocenterC32#3265
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. #10595342C2semidirect
3. C2×#63941C2semidirect
4. #10595293C2semidirect
5. #10592871C2semidirect
6. C3×#5163C2semidirect
7. #10591583C2semidirect
8. #10591566C2semidirect
9. #10591472C2semidirect
10. #10591464C2semidirect
11. #10591448C2semidirect
12. #10590943C2semidirect
13. #10590826C2semidirect
14. #10590754C2semidirect
15. #10590727C2semidirect
18. C2×#3832C22semidirect
19. C2×C3×D3×Q8C22semidirect
23. C2×C32×SD16C22semidirect
25. C2×#3753C22semidirect
26. C3×Q8×Dic3C22semidirect
28. C2×C3×#215C22semidirect
30. C2×C3×#214C22semidirect
33. C2×C3×D3×C8C22semidirect
39. #63909C22semidirect
45. #63871C22semidirect
47. #63864C22semidirect
48. C2×#3715C22semidirect
50. C2×#3714C22semidirect
51. C2×#3712C22semidirect
52. #63662C22semidirect
53. #63648C22semidirect
54. #63647C22semidirect
55. C3×#832C22semidirect
56. C3×#821C22semidirect
57. C3×Dic3⋊C8C22semidirect
58. #63575C22semidirect
59. #63566C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #63554C22semidirect
68. C2×D3×SD16D3semidirect
83. #5163D3semidirect
133. C3×#215D4semidirect
164. C2×D3×Q8C2×D3semidirect
175. C2×C3×SD16C2×D3semidirect
176. C2×C3×SD16C2×D3semidirect
185. Q8×Dic3C2×D3semidirect
188. C2×#215C2×D3semidirect
201. C2×#214C2×D3semidirect
220. C2×D3×C8C2×D3semidirect
238. #832C2×D3semidirect
243. #821C2×D3semidirect
251. Dic3⋊C8C2×D3semidirect
268. C32×Q8C2×D4semidirect
308. C3×C3⋊C8C2×D4semidirect
422. #215#67semidirect
484. C2×C3×D3AGL(1,ℤ/8)semidirect
508. C2×SD16D32semidirect
575. C3×Q8D3×D4semidirect
576. C3×Q8C2×#67semidirect
668. C3⋊C8C2×#67semidirect
792. C2×D3#914semidirect
818. C32#3265semidirect
835. Q8D3×#67semidirect
929. C3#80404semidirect
930. C3#83864semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×SD162
#105953422
C2×#639412
#105952932
#105928712
C3×#51632
#105915832
#105915662
#105914722
#105914642
#105914482
#105909432
#105908262
#105907542
#105907272
#838643
#804043