Finite Group Databasebeta

← #11884013

Subgroups — #11884013

Order 1152.

1156 conjugacy classes of subgroups.

The subgroup lattice has 933 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×SD16C211yesmaximal, characteristic, complemented
2#10595409C211yesmaximal, characteristic, complemented
3C2×#63939C211yesmaximal, characteristic, complemented
4#10595288C211yesmaximal, characteristic, complemented
5#10592862C211yesmaximal, characteristic, complemented
6C3×#5172C211yesmaximal, characteristic, complemented
7#10591584C211yesmaximal, characteristic, complemented
8#10591572C211yesmaximal, characteristic, complemented
9#10591502C211yesmaximal, characteristic, complemented
10#10591475C211yesmaximal, characteristic, complemented
11#10591447C211yesmaximal, characteristic, complemented
12#10590942C211yesmaximal, characteristic, complemented
13#10590826C211yesmaximal, characteristic, complemented
14#10590750C211yesmaximal, characteristic, complemented
15#10590723C211yesmaximal, characteristic, complemented
16#83864—31nomaximal
17#80121—31nomaximal
18C2×C3×#239C2211yescharacteristic, complemented
19C2×C3×D3×Q8C2211yescharacteristic, complemented
20C2×C3×D3×D4C2211yescharacteristic
21C2×D3×#67—21no—
22C2×D3×D12C2211yescharacteristic
23C2×C32×SD16C2211yescharacteristic, complemented
24Q8×C3⋊Dic3C2211yescharacteristic, complemented
25C2×#3755C2211yescharacteristic, complemented
26#64149C2211yescharacteristic
27C2×C3×#215C2211yescharacteristic
28C3×#938C2211yescharacteristic
29C2×C3×#214C2211yescharacteristic, complemented
30C2×C3×#213C2211yescharacteristic, complemented
31C3×D3×SD16—24no—
32C2×C3×#204C2211yescharacteristic
33C2×C3×D3×C8C2211yescharacteristic, complemented
34#63983—21no—
35#63977—21no—
36#63971—21no—
37#63939—24no—
38#63909C2211yescharacteristic
39#63908—21no—
40#63908C2211yescharacteristic, complemented
41C4×#625—21no—
42C4×#625C2211yescharacteristic
43#63898C2211yescharacteristic
44#63863—21no—
45#63863C2211yescharacteristic, complemented
46#63856—21no—
47#63856C2211yescharacteristic, complemented
48C2×#3717C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic, complemented
50C2×#3713C2211yescharacteristic
51C2×#3711C2211yescharacteristic, complemented
52#63659C2211yescharacteristic, complemented
53#63648C2211yescharacteristic, complemented
54#63641C2211yescharacteristic, complemented
55C3×#835C2211yescharacteristic, complemented
56C3×#821C2211yescharacteristic, complemented
57C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
58#63575C2211yescharacteristic, complemented
59#63565C2211yescharacteristic, complemented
60#63563C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62#63555C2211yescharacteristic, complemented
63C22×C3×SD16—31no—
64#5831—31no—
65C2×#949—31no—
66#5817—31no—
67D4×#67—31no—
68C2×#914—31no—
69C2×D3×SD16D311yescharacteristic, complemented
70#5609—31no—
71C3×#449—31no—
72#5227—31no—
73#5217—31no—
74#5176—31no—
75#5174—31no—
76#5172D311yescharacteristic, complemented
77#5169—31no—
78#5165—31no—
79#5164—31no—
80#5163—31no—
81#5163—31no—
82#5163—61no—
83#5156—31no—
84#5154—31no—
85#5115—31no—
86#5111—31no—
87#5042—31no—
88#4817—31no—
89#4806—31no—
90#4787—31no—
91#4775—31no—
92#4731—31no—
93#4728—31no—
94C23×C3×D3—21no—
95C22×D32—21no—
96C2×C32×Q8C2311yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C2×#638—21no—
99C2×#638—21no—
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C3×#239—22no—
104C3×#239—41no—
105C3×D3×Q8—22no—
106C3×D3×Q8—41no—
107C3×D3×D4—22no—
108C3×D3×D4—41no—
109C2×C3×D12—21no—
110C2×C3×D12C2311yescharacteristic
111C2×C3×D12C2311yescharacteristic
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3C2311yescharacteristic
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×Dic6—21no—
117C2×C3×Dic6C2311yescharacteristic
118D3×#67—44no—
119C2×#626—21no—
120C2×#626—21no—
121C2×#625—21no—
122C2×#625D411yescharacteristic
123C2×D3×Dic3—21no—
124D3×D12—22no—
125D3×D12—41no—
126C32×SD16—22no—
127C2×C32×C8C2311yescharacteristic
128#3755—22no—
129C4⋊(C3⋊Dic3)—21no—
130C4⋊(C3⋊Dic3)C2311yescharacteristic
131C4×C3⋊Dic3—21no—
132C4×C3⋊Dic3C2311yescharacteristic
133C2×C3⋊(C3⋊C8)C2311yescharacteristic
134C3×#217—21no—
135C3×#215D414yescomplemented
136C3×#214—22no—
137C3×#213—41no—
138C3×C4⋊Dic3C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C3×#204—22no—
142C3×D3×C8—22no—
143#3724—21no—
144#3724D411yescharacteristic
145#3722—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3D411yescharacteristic
152(C2×D3)⋊Dic3D411yescharacteristic
153#3717—41no—
154#3714—22no—
155#3713—22no—
156#3711—22no—
157#3265—91noSylow
158C2×C3×#41—31no—
159C22×C3×Q8—31no—
160C22×C3×D4—31no—
161C22×#67—61no—
162C2×#239C2×D311yescharacteristic, complemented
163C2×D3×Q8C2×D311yescharacteristic, complemented
164C2×D3×D4—31no—
165C2×D3×D4—61no—
166C2×D3×D4C2×D311yescharacteristic
167C22×D12—31no—
168C2×C3×SD16—21no—
169C2×C3×SD16—31no—
170C2×C3×SD16—31no—
171C2×C3×SD16—31no—
172C2×C3×SD16—64no—
173C2×C3×SD16C2×D311yescharacteristic, complemented
174C2×C3×SD16C2×D311yescharacteristic, complemented
175C2×C3×D8—31no—
176C22×C3×C8—31no—
177C3×#121—31no—
178#953—61no—
179#949—64no—
180#947—31no—
181#947—61no—
182#946—31no—
183#946—61no—
184Q8×Dic3—31no—
185Q8×Dic3—31no—
186Q8×Dic3—61no—
187C2×#215—31no—
188C2×#215—31no—
189C2×#215—31no—
190C2×#215—61no—
191C2×#215C2×D311yescharacteristic
192#940—31no—
193#940—31no—
194#940—61no—
195#939—61no—
196#938—31no—
197#938—61no—
198#938C2×D311yescharacteristic
199#937—61no—
200#937—61no—
201#936—31no—
202#936—61no—
203D4×Dic3—31no—
204C2×#214C2×D311yescharacteristic, complemented
205C2×#213—31no—
206C2×#213—31no—
207C2×#213—31no—
208C2×#213C2×D311yescharacteristic, complemented
209#930—31no—
210#930—31no—
211#930—61no—
212C4×#67—31no—
213C4×#67—31no—
214C4×#67—61no—
215C4×#67—61no—
216#924—31no—
217#924—61no—
218C2×#208—31no—
219#914—64no—
220D3×SD16—24no—
221C2×D24—31no—
222C2×#204—31no—
223C2×#204C2×D311yescharacteristic
224C2×ΓL(1,𝔽25)—31no—
225C2×D3×C8C2×D311yescharacteristic, complemented
226#895—31no—
227#893—31no—
228#884—61no—
229#882—61no—
230C3×#103—31no—
231C3×#102—31no—
232C3×C22⋊C8—31no—
233#835—31no—
234#835C2×D311yescharacteristic, complemented
235#832—31no—
236#832—31no—
237#832—31no—
238#832—61no—
239#830—31no—
240#821—31no—
241#821—31no—
242#821—31no—
243#821—61no—
244#821C2×D311yescharacteristic, complemented
245(C2×D3)⋊C8—31no—
246(C2×D3)⋊C8C2×D311yescharacteristic, complemented
247#818—31no—
248#815—31no—
249#815—31no—
250Dic3⋊C8—31no—
251Dic3⋊C8—31no—
252Dic3⋊C8—61no—
253#810—31no—
254#807—31no—
255C23×C32—21no—
256C22×C3⋊D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—42no—
260C22×C3×D3—42no—
261C22×C3×D3—81no—
262C22×C3×D3C2×D411yescharacteristic
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—
274#638—81no—
275C2×C3⋊Dic3—21no—
276C2×C3⋊Dic3C2×D411yescharacteristic
277C2×C3⋊Dic3C2×D411yescharacteristic
278C4⋊(C3⋊D3)—21no—
279C4⋊(C3⋊D3)—21no—
280C3×#67—42no—
281C3×#67—42no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3C2×D411yescharacteristic
285C2×C3×Dic3C2×D411yescharacteristic
286C3×D12—21no—
287C3×D12—21no—
288C3×D12—21no—
289C3×D12—42no—
290C3×D12C2×D412yes—
291C3×C4×D3—21no—
292C3×C4×D3—21no—
293C3×C4×D3—21no—
294C3×C4×D3—21no—
295C3×C4×D3—42no—
296C3×C4×D3—42no—
297C3×Dic6—21no—
298C3×Dic6—21no—
299C3×Dic6—42no—
300#626—42no—
301#626—42no—
302#625—22no—
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—91no—
318#450—91no—
319#449—31no—
320#448—91no—
321#447—91no—
322#440—91no—
323#435—91no—
324C24×C3—61no—
325C23×D3—21no—
326C23×D3—61no—
327C23×D3—61no—
328C3×#41—62no—
329C3×#41—121no—
330C2×C3×Q8—21no—
331C2×C3×Q8—31no—
332C2×C3×Q8—61no—
333C2×C3×Q8—62no—
334C2×C3×Q8—121no—
335C2×C3×Q8C22×D311yescharacteristic
336C2×C3×Q8C22×D311yescharacteristic
337C2×C3×D4—21no—
338C2×C3×D4—31no—
339C2×C3×D4—31no—
340C2×C3×D4—61no—
341C2×C3×D4—61no—
342C2×C3×D4—62no—
343C2×C3×D4—61no—
344C2×C3×D4—121no—
345C2×C3×D4C22×D311yescharacteristic
346C2×C3×D4C22×D311yescharacteristic
347C22×C3×C4—31no—
348C22×C3×C4—31no—
349C22×C3×C4—61no—
350C22×C3×C4—61no—
351C2×#67—21no—
352C2×#67—21no—
353C2×#67—31no—
354C2×#67—31no—
355C2×#67—61no—
356C2×#67—61no—
357C2×#67—61no—
358C2×#67—61no—
359C2×#67—61no—
360C2×#67—61no—
361C2×#67—61no—
362C2×#67—61no—
363C2×#67—121no—
364C2×#67—121no—
365C2×#67—124no—
366C22×Dic3—61no—
367#239—22no—
368#239—41no—
369D3×Q8—22no—
370D3×Q8—41no—
371D3×D4—22no—
372D3×D4—41no—
373D3×D4—62no—
374D3×D4—121no—
375D3×D4—124no—
376C2×D12—21no—
377C2×D12—31no—
378C2×D12—31no—
379C2×D12—61no—
380C2×D12—62no—
381C2×D12—61no—
382C2×D12—61no—
383C2×D12—121no—
384C2×D12C22×D311yescharacteristic
385C2×D12C22×D311yescharacteristic
386C2×C4×D3—21no—
387C2×C4×D3—21no—
388C2×C4×D3—61no—
389C2×C4×D3C22×D311yescharacteristic
390C2×C4×D3C22×D311yescharacteristic
391C2×Dic6—21no—
392C2×Dic6C22×D311yescharacteristic
393C3×SD16—22no—
394C3×SD16—22no—
395C3×SD16—34no—
396C3×SD16—42no—
397C3×SD16—62no—
398C3×SD16—62no—
399C3×D8—121no—
400C2×C3×C8—21no—
401C2×C3×C8—31no—
402C2×C3×C8—31no—
403C2×C3×C8—62no—
404C2×C3×C8C22×D311yescharacteristic
405C2×C3×C8C22×D311yescharacteristic
406C3×C4⋊C4—31no—
407C3×C22⋊C4—61no—
408#217—21no—
409#217—31no—
410#217—31no—
411#217—61no—
412#217—61no—
413#217—61no—
414#217—61no—
415#217—61no—
416#215—62no—
417#215—62no—
418#215—122no—
419#215—121no—
420#215#6714yescomplemented
421#214—22no—
422#213—41no—
423#213—62no—
424#213—62no—
425#213—62no—
426(C2×D3)⋊C4—31no—
427(C2×D3)⋊C4—31no—
428(C2×D3)⋊C4—61no—
429(C2×D3)⋊C4—61no—
430(C2×D3)⋊C4—61no—
431(C2×D3)⋊C4—61no—
432(C2×D3)⋊C4—61no—
433(C2×D3)⋊C4—61no—
434(C2×D3)⋊C4—61no—
435C4⋊Dic3—31no—
436C4⋊Dic3—31no—
437C4⋊Dic3—61no—
438C4⋊Dic3—61no—
439C4⋊Dic3—61no—
440C4⋊Dic3—121no—
441C4⋊Dic3C22×D311yescharacteristic
442Dic3⋊C4—31no—
443Dic3⋊C4—31no—
444Dic3⋊C4—61no—
445Dic3⋊C4—61no—
446C4×Dic3—31no—
447C4×Dic3—31no—
448C4×Dic3—61no—
449C4×Dic3—61no—
450C4×Dic3—61no—
451C4×Dic3—121no—
452#208—62no—
453C2×C3⋊C8—31no—
454C2×C3⋊C8—31no—
455C2×C3⋊C8—61no—
456C2×C3⋊C8C22×D311yescharacteristic
457C2×C3⋊C8C22×D311yescharacteristic
458D24—62no—
459#204—22no—
460#204—121no—
461ΓL(1,𝔽25)—62no—
462D3×C8—22no—
463C22×C32—41no—
464C22×C32—41no—
465C22×C32—41no—
466C22×C32C22×D411yescharacteristic
467C2×C3⋊D3—41no—
468C2×C3⋊D3—41no—
469C2×C3⋊D3—41no—
470C2×C3×D3—21no—
471C2×C3×D3—21no—
472C2×C3×D3—22no—
473C2×C3×D3—21no—
474C2×C3×D3—21no—
475C2×C3×D3—21no—
476C2×C3×D3—41no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479C2×C3×D3—41no—
480C2×C3×D3—41no—
481C2×C3×D3—84no—
482C2×C3×D3AGL(1,ℤ/8)12yescomplemented
483D32—84no—
484C32×C4—22no—
485C32×C4C22×D411yescharacteristic
486C32×C4H(5,𝔽2)11yescharacteristic
487C3⋊Dic3—21no—
488C3⋊Dic3—21no—
489C3⋊Dic3—41no—
490C3×Dic3—21no—
491C3×Dic3—21no—
492C3×Dic3—41no—
493C3×Dic3—41no—
494C2×#41—31no—
495C22×Q8—31no—
496C22×D4—31no—
497C22×D4—91no—
498C22×D4—181no—
499AGL(1,ℤ/8)—184no—
500C2×SD16—31no—
501C2×SD16—31no—
502C2×SD16—31no—
503C2×SD16—64no—
504C2×SD16—91no—
505C2×SD16—91no—
506C2×SD16D3211yescharacteristic, complemented
507C2×D8—31no—
508C2×D8—91no—
509C2×D8—91no—
510C2×M16—91no—
511C22×C8—31no—
512#127—91no—
513#124—91no—
514#124—181no—
515C22⋊Q8—91no—
516C22⋊Q8—181no—
517#121—31no—
518#121—91no—
519#121—91no—
520#121—181no—
521#121—181no—
522#120—181no—
523#120—181no—
524C4×Q8—91no—
525C4×D4—91no—
526C4×D4—91no—
527C4×D4—181no—
528#107—91no—
529C4⋊C8—91no—
530#103—31no—
531#103—91no—
532#102—31no—
533#102—91no—
534#102—91no—
535#102—91no—
536C22⋊C8—31no—
537C22⋊C8—91no—
538#97—91no—
539C23×C3—21no—
540C23×C3—21no—
541C23×C3—31no—
542C23×C3—31no—
543C23×C3—41no—
544C23×C3—61no—
545C23×C3—61no—
546C23×C3—122no—
547C23×C3—122no—
548C23×C3—241no—
549C22×D3—21no—
550C22×D3—21no—
551C22×D3—42no—
552C22×D3—42no—
553C22×D3—61no—
554C22×D3—61no—
555C22×D3—81no—
556C22×D3—121no—
557C22×D3—122no—
558C22×D3—122no—
559C22×D3—122no—
560C22×D3—122no—
561C22×D3—241no—
562C22×D3—241no—
563C22×D3D3×D411yescharacteristic
564C22×D3D3×D411yescharacteristic
565C3×Q8—21no—
566C3×Q8—21no—
567C3×Q8—22no—
568C3×Q8—41no—
569C3×Q8—61no—
570C3×Q8—61no—
571C3×Q8—122no—
572C3×Q8D3×D412yescomplemented
573C3×Q8C2×#6712yescomplemented
574C3×D4—21no—
575C3×D4—21no—
576C3×D4—21no—
577C3×D4—21no—
578C3×D4—32no—
579C3×D4—41no—
580C3×D4—41no—
581C3×D4—61no—
582C3×D4—61no—
583C3×D4—61no—
584C3×D4—122no—
585C3×D4—122no—
586C3×D4—122no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—31no—
591C2×C3×C4—31no—
592C2×C3×C4—41no—
593C2×C3×C4—61no—
594C2×C3×C4—61no—
595C2×C3×C4—61no—
596C2×C3×C4—61no—
597C2×C3×C4—61no—
598C2×C3×C4—61no—
599C2×C3×C4—122no—
600C2×C3×C4—122no—
601C2×C3×C4C23×D311yescharacteristic
602C2×C3×C4C23×D311yescharacteristic
603#67—42no—
604#67—42no—
605#67—62no—
606#67—62no—
607#67—122no—
608#67—122no—
609#67—122no—
610#67—122no—
611#67—122no—
612#67—122no—
613#67—242no—
614#67—241no—
615#67—241no—
616#67—242no—
617C2×Dic3—21no—
618C2×Dic3—21no—
619C2×Dic3—31no—
620C2×Dic3—31no—
621C2×Dic3—31no—
622C2×Dic3—31no—
623C2×Dic3—61no—
624C2×Dic3—61no—
625C2×Dic3—61no—
626C2×Dic3—61no—
627C2×Dic3—121no—
628C2×Dic3—122no—
629C2×Dic3D3×D411yescharacteristic
630C2×Dic3D3×D411yescharacteristic
631D12—21no—
632D12—21no—
633D12—21no—
634D12—42no—
635D12—61no—
636D12—61no—
637D12—61no—
638D12—61no—
639D12—121no—
640D12—121no—
641D12—122no—
642D12—122no—
643D12C2×#6712yes—
644C4×D3—21no—
645C4×D3—21no—
646C4×D3—21no—
647C4×D3—21no—
648C4×D3—42no—
649C4×D3—42no—
650C4×D3—122no—
651Dic6—21no—
652Dic6—21no—
653Dic6—42no—
654C3×C8—21no—
655C3×C8—21no—
656C3×C8—32no—
657C3×C8—41no—
658C3×C8—61no—
659C3⋊C8—21no—
660C3⋊C8—61no—
661C3⋊C8—61no—
662C3⋊C8—121no—
663C3⋊C8C2×#6712yescomplemented
664C2×C32—81no—
665C2×C32D4211yescharacteristic
666C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
667C2×C32#57711yescharacteristic
668C3⋊D3—81no—
669C3×D3—22no—
670C3×D3—41no—
671C3×D3—42no—
672C3×D3—81no—
673C24—61no—
674C24—181no—
675#41—62no—
676#41—121no—
677C2×Q8—31no—
678C2×Q8—61no—
679C2×Q8—62no—
680C2×Q8—121no—
681C2×Q8C2×D3211yescharacteristic
682C2×D4—31no—
683C2×D4—31no—
684C2×D4—61no—
685C2×D4—61no—
686C2×D4—62no—
687C2×D4—61no—
688C2×D4—91no—
689C2×D4—91no—
690C2×D4—121no—
691C2×D4—181no—
692C2×D4—182no—
693C2×D4—181no—
694C2×D4—181no—
695C2×D4—181no—
696C2×D4—181no—
697C2×D4—361no—
698C2×D4—364no—
699C2×D4C2×D3211yescharacteristic
700C22×C4—31no—
701C22×C4—31no—
702C22×C4—61no—
703C22×C4—61no—
704C22×C4—181no—
705SD16—22no—
706SD16—34no—
707SD16—62no—
708SD16—62no—
709SD16—182no—
710SD16—361no—
711D8—121no—
712D8—182no—
713D8—182no—
714M16—182no—
715C2×C8—31no—
716C2×C8—31no—
717C2×C8—62no—
718C2×C8—91no—
719C2×C8C2×D3211yescharacteristic
720C4⋊C4—31no—
721C4⋊C4—91no—
722C4⋊C4—91no—
723C4⋊C4—181no—
724C4⋊C4—181no—
725C22⋊C4—61no—
726C22⋊C4—91no—
727C22⋊C4—91no—
728C22⋊C4—181no—
729C22⋊C4—181no—
730C22⋊C4—181no—
731C22⋊C4—181no—
732C22⋊C4—181no—
733C22⋊C4—181no—
734C42—91no—
735C42—181no—
736C22×C3—21no—
737C22×C3—32no—
738C22×C3—41no—
739C22×C3—41no—
740C22×C3—41no—
741C22×C3—41no—
742C22×C3—41no—
743C22×C3—41no—
744C22×C3—61no—
745C22×C3—61no—
746C22×C3—61no—
747C22×C3—61no—
748C22×C3—61no—
749C22×C3—62no—
750C22×C3—81no—
751C22×C3—81no—
752C22×C3—81no—
753C22×C3—121no—
754C22×C3—121no—
755C22×C3—121no—
756C22×C3—121no—
757C22×C3—121no—
758C22×C3—244no—
759C22×C3C2×D3×D411yescharacteristic
760C22×C3C2×D3×D411yescharacteristic
761C2×D3—21no—
762C2×D3—21no—
763C2×D3—21no—
764C2×D3—21no—
765C2×D3—22no—
766C2×D3—21no—
767C2×D3—41no—
768C2×D3—41no—
769C2×D3—41no—
770C2×D3—41no—
771C2×D3—41no—
772C2×D3—84no—
773C2×D3—121no—
774C2×D3—121no—
775C2×D3—121no—
776C2×D3—121no—
777C2×D3—121no—
778C2×D3—121no—
779C2×D3—241no—
780C2×D3—241no—
781C2×D3—241no—
782C2×D3—244no—
783C2×D3—244no—
784C2×D3#91412yescomplemented
785C3×C4—22no—
786C3×C4—22no—
787C3×C4—21no—
788C3×C4—21no—
789C3×C4—42no—
790C3×C4—61no—
791C3×C4—61no—
792C3×C4—121no—
793C3×C4—121no—
794C3×C4C2×D3×D411yescharacteristic
795C3×C4#100411yescharacteristic
796C3×C4#100411yescharacteristic
797C3×C4C22×#6711yescharacteristic
798Dic3—21no—
799Dic3—21no—
800Dic3—41no—
801Dic3—41no—
802Dic3—62no—
803Dic3—61no—
804Dic3—61no—
805Dic3—61no—
806Dic3—61no—
807Dic3—121no—
808Dic3—121no—
809Dic3—121no—
810Dic3—241no—
811C32#326511yescharacteristic, complemented, Sylow
812C23—21no—
813C23—31no—
814C23—31no—
815C23—61no—
816C23—61no—
817C23—122no—
818C23—122no—
819C23—181no—
820C23—241no—
821C23—362no—
822C23—362no—
823C23—721no—
824Q8—21no—
825Q8—61no—
826Q8—61no—
827Q8—122no—
828Q8D3×#6712yescomplemented
829D4—21no—
830D4—21no—
831D4—32no—
832D4—61no—
833D4—61no—
834D4—61no—
835D4—122no—
836D4—122no—
837D4—122no—
838D4—182no—
839D4—181no—
840D4—181no—
841D4—362no—
842D4—362no—
843D4—362no—
844D4—362no—
845D4—721no—
846C2×C4—21no—
847C2×C4—31no—
848C2×C4—31no—
849C2×C4—61no—
850C2×C4—61no—
851C2×C4—61no—
852C2×C4—61no—
853C2×C4—61no—
854C2×C4—61no—
855C2×C4—91no—
856C2×C4—91no—
857C2×C4—122no—
858C2×C4—122no—
859C2×C4—181no—
860C2×C4—362no—
861C2×C4C22×D3211yescharacteristic
862C8—21no—
863C8—32no—
864C8—61no—
865C8—181no—
866C2×C3—21no—
867C2×C3—21no—
868C2×C3—21no—
869C2×C3—62no—
870C2×C3—81no—
871C2×C3—81no—
872C2×C3—121no—
873C2×C3—122no—
874C2×C3—161no—
875C2×C3—241no—
876C2×C3#559011yescharacteristic
877C2×C3C2×#91411yescharacteristic
878C2×C3#576211yescharacteristic
879C2×C3#577011yescharacteristic
880C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
881C2×C3D4×#6711yescharacteristic
882D3—22no—
883D3—42no—
884D3—41no—
885D3—81no—
886D3—241no—
887D3—241no—
888D3—481no—
889C22—32no—
890C22—41no—
891C22—41no—
892C22—41no—
893C22—61no—
894C22—61no—
895C22—61no—
896C22—61no—
897C22—61no—
898C22—62no—
899C22—121no—
900C22—121no—
901C22—121no—
902C22—121no—
903C22—121no—
904C22—244no—
905C22—361no—
906C22—361no—
907C22—361no—
908C22—724no—
909C22D32×D411yescharacteristic
910C4—22no—
911C4—61no—
912C4—61no—
913C4—121no—
914C4—121no—
915C4—181no—
916C4—181no—
917C4—361no—
918C4#6431311yescharacteristic
919C4C2×D3×#6711yescharacteristic
920C3—21no—
921C3#8012111yescharacteristic, complemented
922C3#8386411yescharacteristic, complemented
923C2—62no—
924C2—81no—
925C2—121no—
926C2—122no—
927C2—241no—
928C2—721no—
929C2D3×#91411yescharacteristic
930C2#1059475311yescharacteristic
931C2#1059528711yescharacteristic
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. #10595409C2semidirect
3. C2×#63939C2semidirect
4. #10595288C2semidirect
5. #10592862C2semidirect
6. C3×#5172C2semidirect
7. #10591584C2semidirect
8. #10591572C2semidirect
9. #10591502C2semidirect
10. #10591475C2semidirect
11. #10591447C2semidirect
12. #10590942C2semidirect
13. #10590826C2semidirect
14. #10590750C2semidirect
15. #10590723C2semidirect
18. C2×C3×#239C22semidirect
19. C2×C3×D3×Q8C22semidirect
23. C2×C32×SD16C22semidirect
24. Q8×C3⋊Dic3C22semidirect
25. C2×#3755C22semidirect
29. C2×C3×#214C22semidirect
30. C2×C3×#213C22semidirect
33. C2×C3×D3×C8C22semidirect
40. #63908C22semidirect
45. #63863C22semidirect
47. #63856C22semidirect
48. C2×#3717C22semidirect
49. C2×#3714C22semidirect
51. C2×#3711C22semidirect
52. #63659C22semidirect
53. #63648C22semidirect
54. #63641C22semidirect
55. C3×#835C22semidirect
56. C3×#821C22semidirect
57. C3×(C2×D3)⋊C8C22semidirect
58. #63575C22semidirect
59. #63565C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #63555C22semidirect
69. C2×D3×SD16D3semidirect
76. #5172D3semidirect
135. C3×#215D4semidirect
162. C2×#239C2×D3semidirect
163. C2×D3×Q8C2×D3semidirect
173. C2×C3×SD16C2×D3semidirect
174. C2×C3×SD16C2×D3semidirect
204. C2×#214C2×D3semidirect
208. C2×#213C2×D3semidirect
225. C2×D3×C8C2×D3semidirect
234. #835C2×D3semidirect
244. #821C2×D3semidirect
246. (C2×D3)⋊C8C2×D3semidirect
268. C32×Q8C2×D4semidirect
308. C3×C3⋊C8C2×D4semidirect
420. #215#67semidirect
482. C2×C3×D3AGL(1,ℤ/8)semidirect
506. C2×SD16D32semidirect
572. C3×Q8D3×D4semidirect
573. C3×Q8C2×#67semidirect
663. C3⋊C8C2×#67semidirect
784. C2×D3#914semidirect
811. C32#3265semidirect
828. Q8D3×#67semidirect
921. C3#80121semidirect
922. 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
#105954092
C2×#639392
#105952882
#105928622
C3×#51722
#105915842
#105915722
#105915022
#105914752
#105914472
#105909422
#105908262
#105907502
#105907232
#838643
#801213