Finite Group Databasebeta

← #11866196

Subgroups — #11866196

Order 1152.

1114 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#914C211yesmaximal, characteristic, complemented
2#10595426C211yesmaximal, characteristic, complemented
3#10595215C211yesmaximal, characteristic, complemented
4C2×D3×#213C211yesmaximal, characteristic, complemented
5#10592864C211yesmaximal, characteristic, complemented
6C3×#5165C211yesmaximal, characteristic, complemented
7#10591570C211yesmaximal, characteristic, complemented
8#10591567C211yesmaximal, characteristic, complemented
9#10591556C211yesmaximal, characteristic, complemented
10#10591486C211yesmaximal, characteristic, complemented
11#10591481C211yesmaximal, characteristic, complemented
12#10590939C211yesmaximal, characteristic, complemented
13#10590753C211yesmaximal, characteristic, complemented
14#10590749C211yesmaximal, characteristic, complemented
15#10590695C211yesmaximal, characteristic, complemented
16#83934—31nomaximal
17#80536—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C2×D3×D12C2211yescharacteristic
21C2×C32×SD16C2211yescharacteristic, complemented
22#64156C2211yescharacteristic, complemented
23D4×C3⋊Dic3C2211yescharacteristic, complemented
24C2×#3753C2211yescharacteristic
25C3×#947C2211yescharacteristic, complemented
26C2×C3×#215C2211yescharacteristic, complemented
27C3×D4×Dic3C2211yescharacteristic, complemented
28C2×C3×#213C2211yescharacteristic
29C2×C3×#213C2211yescharacteristic, complemented
30C3×#914—24no—
31C2×C3×D24C2211yescharacteristic, complemented
32C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
33#67⋊Dic3—21no—
34Dic3×#67—21no—
35D3×#217—21no—
36C2×(C2×D3)⋊Dic3—21no—
37D3×#213—24no—
38#63922—21no—
39#63922—21no—
40#63914C2211yescharacteristic, complemented
41#63911C2211yescharacteristic, complemented
42#63906—21no—
43#63906—21no—
44#63898C2211yescharacteristic, complemented
45Dic3×D12C2211yescharacteristic, complemented
46#63855C2211yescharacteristic
47#63841C2211yescharacteristic
48C2×#3714C2211yescharacteristic
49C2×#3713C2211yescharacteristic
50C2×D3×C3⋊C8C2211yescharacteristic
51#63662C2211yescharacteristic, complemented
52#63648C2211yescharacteristic, complemented
53#63641C2211yescharacteristic, complemented
54C3×#835C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57#63572C2211yescharacteristic, complemented
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63564C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61#63563C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63C2×C3×AGL(1,ℤ/8)—31no—
64#5830—31no—
65#5798—31no—
66C22×#213—31no—
67C2×#914D311yescharacteristic, complemented
68C2×D3×D8—31no—
69#5674—31no—
70#5545—31no—
71C3×#463—31no—
72#5233—31no—
73#5165—31no—
74#5165—31no—
75#5165—31no—
76#5165—31no—
77#5165—61no—
78#5165D311yescharacteristic, complemented
79#5150—31no—
80#5150—31no—
81#5150—31no—
82#5150—31no—
83#5150—31no—
84#5131—31no—
85#5119—31no—
86#5057—31no—
87#5015—31no—
88#4843—31no—
89#4839—31no—
90#4819—31no—
91#4804—31no—
92#4786—31no—
93#4770—31no—
94C23×C3×D3—21no—
95C22×D32—21no—
96C2×C32×Q8C2311yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C22×C3⋊Dic3—21no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C3×#67—21no—
101C22×C3×Dic3—21no—
102C3×#239—22no—
103C3×#239—22no—
104C3×D3×D4—22no—
105C3×D3×D4D414yescomplemented
106C2×C3×D12—21no—
107C2×C3×D12C2311yescharacteristic
108C2×C3×D12C2311yescharacteristic
109C2×C3×D12C2311yescharacteristic
110C2×C3×C4×D3—21no—
111C2×C3×C4×D3C2311yescharacteristic
112C2×#626—21no—
113C2×#626—21no—
114C2×#626—21no—
115C2×#625—21no—
116C2×#625—21no—
117C2×D3×Dic3—21no—
118C2×D3×Dic3—21no—
119D3×D12—22no—
120D3×D12—22no—
121C32×SD16—22no—
122C2×C32×C8C2311yescharacteristic
123#3757—21no—
124#3753—22no—
125#3752—21no—
126#3752—21no—
127C4⋊(C3⋊Dic3)C2311yescharacteristic
128C4×C3⋊Dic3C2311yescharacteristic
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130C3×#217—21no—
131C3×#215—22no—
132C3×#213—22no—
133C3×#213—22no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×C4⋊Dic3C2311yescharacteristic
137C3×C4×Dic3C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C3×D24—22no—
141C3×ΓL(1,𝔽25)—22no—
142Dic3⋊Dic3D411yescharacteristic
143Dic3⋊Dic3D411yescharacteristic
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#3714—22no—
151#3713—22no—
152D3×C3⋊C8—22no—
153#3041—91noSylow
154C2×C3×#41—31no—
155C22×C3×D4—31no—
156C2×#239C2×D311yescharacteristic
157C2×D3×D4—31no—
158C2×D3×D4C2×D311yescharacteristic
159C22×D12—31no—
160C3×AGL(1,ℤ/8)—64no—
161C2×C3×SD16—21no—
162C2×C3×SD16—31no—
163C2×C3×SD16C2×D311yescharacteristic, complemented
164C2×C3×SD16C2×D311yescharacteristic, complemented
165C2×C3×D8—31no—
166C2×C3×D8—31no—
167C2×C3×D8—31no—
168C2×C3×M16—31no—
169C3×#124—31no—
170C3×C4×D4—31no—
171C2×#217—61no—
172C2×#217—61no—
173#947—31no—
174#947—31no—
175#947—61no—
176#947C2×D311yescharacteristic, complemented
177C2×#215C2×D311yescharacteristic, complemented
178#940—31no—
179#940—31no—
180#940—31no—
181#937—61no—
182#937—61no—
183D4×Dic3—31no—
184D4×Dic3—31no—
185D4×Dic3—31no—
186D4×Dic3—31no—
187D4×Dic3—61no—
188D4×Dic3—61no—
189D4×Dic3—61no—
190D4×Dic3C2×D311yescharacteristic, complemented
191C2×#213—31no—
192C2×#213—31no—
193C2×#213—31no—
194C2×#213—31no—
195C2×#213—31no—
196C2×#213—61no—
197C2×#213—64no—
198C2×#213C2×D311yescharacteristic
199C2×#213C2×D311yescharacteristic, complemented
200#930—61no—
201#930—61no—
202C4×#67—61no—
203C2×(C2×D3)⋊C4—61no—
204#926—31no—
205#926—31no—
206C22×C3⋊C8—31no—
207#914—24no—
208D3×D8—64no—
209C2×D24—31no—
210C2×D24C2×D311yescharacteristic, complemented
211C2×ΓL(1,𝔽25)C2×D311yescharacteristic
212C2×D3×C8—31no—
213#893—31no—
214#892—31no—
215#884—61no—
216#884—61no—
217#882—61no—
218#882—61no—
219#67⋊C4—61no—
220D3×C22⋊C4—61no—
221#874—31no—
222C4×D12—31no—
223#872—31no—
224C3×C4⋊C8—31no—
225C3×#103—31no—
226C3×#102—31no—
227#835—31no—
228#835—31no—
229#835—61no—
230#835C2×D311yescharacteristic, complemented
231#832—31no—
232#832—31no—
233#832—31no—
234#821—31no—
235#821—31no—
236#821—31no—
237#821—31no—
238#821—31no—
239#821—61no—
240#821C2×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#809—31no—
249#809—31no—
250C4⋊(C3⋊C8)—31no—
251C23×C32—21no—
252C22×C3⋊D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3—24no—
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—81no—
258C22×C3×D3—81no—
259C22×C3×D3C2×D411yescharacteristic
260C2×D32—42no—
261C2×D32—81no—
262C2×D32—81no—
263C32×Q8—21no—
264C32×Q8—21no—
265C32×D4—21no—
266C32×D4C2×D412yes—
267C2×C32×C4—21no—
268C2×C32×C4C2411yescharacteristic
269C2×C3⋊Dic3—21no—
270C2×C3⋊Dic3—81no—
271C2×C3⋊Dic3C2×D411yescharacteristic
272C2×C3⋊Dic3C2×D411yescharacteristic
273C4⋊(C3⋊D3)—21no—
274C4⋊(C3⋊D3)—21no—
275C3×#67—24no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—81no—
278C2×C3×Dic3C2×D411yescharacteristic
279C2×C3×Dic3C2×D411yescharacteristic
280C2×C3×Dic3C2×D411yescharacteristic
281C3×D12—21no—
282C3×D12—21no—
283C3×D12—21no—
284C3×D12—21no—
285C3×D12—21no—
286C3×D12—42no—
287C3×D12C2×D412yes—
288C3×C4×D3—42no—
289C3×C4×D3C2×D412yes—
290C3×C4×D3#4112yes—
291#626—42no—
292#626—81no—
293#626—81no—
294#625—81no—
295#625—81no—
296D3×Dic3—81no—
297D3×Dic3—81no—
298C32×C8—21no—
299C3⋊(C3⋊C8)—21no—
300C3×C3⋊C8—21no—
301C3×C3⋊C8—21no—
302C2×AGL(1,ℤ/8)—31no—
303C22×D8—91no—
304#535—91no—
305#518—91no—
306#463—31no—
307#463—91no—
308#463—91no—
309#463—91no—
310#459—91no—
311#459—91no—
312#459—91no—
313#459—91no—
314#424—91no—
315#418—91no—
316#416—91no—
317C24×C3—61no—
318C23×D3—21no—
319C23×D3—61no—
320C23×D3—61no—
321C3×#41—62no—
322C3×#41—62no—
323C2×C3×Q8—21no—
324C2×C3×Q8C22×D311yescharacteristic
325C2×C3×Q8C22×D311yescharacteristic
326C2×C3×D4—21no—
327C2×C3×D4—34no—
328C2×C3×D4—31no—
329C2×C3×D4—31no—
330C2×C3×D4—31no—
331C2×C3×D4—61no—
332C2×C3×D4—62no—
333C2×C3×D4—61no—
334C2×C3×D4C22×D311yescharacteristic
335C2×C3×D4C22×D311yescharacteristic
336C22×C3×C4—31no—
337C22×C3×C4—61no—
338C22×C3×C4—61no—
339C2×#67—21no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—61no—
347C22×Dic3—21no—
348C22×Dic3—61no—
349C22×Dic3—61no—
350C22×Dic3—61no—
351C22×Dic3—61no—
352C22×Dic3—121no—
353#239—22no—
354#239—22no—
355D3×D4—22no—
356D3×D4—62no—
357D3×D4—62no—
358D3×D4#6714yescomplemented
359C2×D12—21no—
360C2×D12—31no—
361C2×D12—31no—
362C2×D12—61no—
363C2×D12—62no—
364C2×D12—62no—
365C2×D12—61no—
366C2×D12—61no—
367C2×D12—61no—
368C2×D12C22×D311yescharacteristic
369C2×D12C22×D311yescharacteristic
370C2×D12C22×D311yescharacteristic
371C2×C4×D3—21no—
372C2×C4×D3—61no—
373C2×C4×D3—61no—
374C2×C4×D3C22×D311yescharacteristic
375C3×SD16—22no—
376C3×SD16—22no—
377C3×SD16—42no—
378C3×SD16—62no—
379C3×D8—62no—
380C3×D8—62no—
381C3×D8—62no—
382C3×M16—62no—
383C2×C3×C8—21no—
384C2×C3×C8—31no—
385C2×C3×C8—31no—
386C2×C3×C8C22×D311yescharacteristic
387C2×C3×C8C22×D311yescharacteristic
388C3×C4⋊C4—31no—
389C3×C22⋊C4—61no—
390C3×C22⋊C4—61no—
391C3×C22⋊C4—61no—
392C3×C42—31no—
393#217—21no—
394#217—31no—
395#217—31no—
396#217—61no—
397#217—61no—
398#217—61no—
399#217—61no—
400#217—61no—
401#217—121no—
402#215—22no—
403#213—22no—
404#213—22no—
405#213—62no—
406#213—62no—
407#213—62no—
408#213—62no—
409#213—62no—
410#213—122no—
411(C2×D3)⋊C4—21no—
412(C2×D3)⋊C4—21no—
413(C2×D3)⋊C4—31no—
414(C2×D3)⋊C4—31no—
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⋊Dic3C22×D311yescharacteristic
430Dic3⋊C4—31no—
431Dic3⋊C4—31no—
432C4×Dic3—31no—
433C4×Dic3—31no—
434C4×Dic3—61no—
435C4×Dic3—61no—
436C4×Dic3—61no—
437C4×Dic3C22×D311yescharacteristic
438C2×C3⋊C8—31no—
439C2×C3⋊C8—31no—
440C2×C3⋊C8—61no—
441C2×C3⋊C8—62no—
442C2×C3⋊C8C22×D311yescharacteristic
443C2×C3⋊C8C22×D311yescharacteristic
444D24—22no—
445D24—62no—
446ΓL(1,𝔽25)—22no—
447D3×C8—62no—
448C22×C32—22no—
449C22×C32—41no—
450C22×C32—41no—
451C22×C32C22×D411yescharacteristic
452C2×C3⋊D3—41no—
453C2×C3⋊D3—41no—
454C2×C3⋊D3—41no—
455C2×C3×D3—21no—
456C2×C3×D3—21no—
457C2×C3×D3—22no—
458C2×C3×D3—41no—
459C2×C3×D3—41no—
460C2×C3×D3—41no—
461C2×C3×D3—41no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3—84no—
467C2×C3×D3#12112yes—
468D32—84no—
469C32×C4—41no—
470C32×C4C22×D411yescharacteristic
471C32×C4C2×#4111yescharacteristic
472C3⋊Dic3—21no—
473C3⋊Dic3—21no—
474C3⋊Dic3—41no—
475C3×Dic3—21no—
476C3×Dic3—21no—
477C3×Dic3—41no—
478C3×Dic3#12112yes—
479C2×#41—31no—
480C22×D4—31no—
481C22×D4—91no—
482AGL(1,ℤ/8)—64no—
483C2×SD16—31no—
484C2×SD16D3211yescharacteristic, complemented
485C2×D8—31no—
486C2×D8—31no—
487C2×D8—31no—
488C2×D8—91no—
489C2×D8—91no—
490C2×D8—91no—
491C2×D8—184no—
492C2×M16—31no—
493C22×C8—91no—
494#127—91no—
495#127—91no—
496#124—31no—
497#124—91no—
498#121—181no—
499#121—181no—
500#120—181no—
501#120—181no—
502C4×D4—31no—
503C4×D4—91no—
504C4×D4—91no—
505C4×D4—91no—
506C4×D4—181no—
507C4×D4—181no—
508#117—91no—
509#117—91no—
510C2×C22⋊C4—181no—
511C2×C22⋊C4—181no—
512C4⋊C8—31no—
513C4⋊C8—91no—
514C4⋊C8—91no—
515C4⋊C8—91no—
516#103—31no—
517#103—91no—
518#102—31no—
519#102—91no—
520#102—91no—
521#102—91no—
522#102—91no—
523#102—91no—
524C23×C3—21no—
525C23×C3—21no—
526C23×C3—31no—
527C23×C3—41no—
528C23×C3—64no—
529C23×C3—61no—
530C23×C3—61no—
531C23×C3—61no—
532C23×C3—241no—
533C23×C3—241no—
534C22×D3—21no—
535C22×D3—24no—
536C22×D3—21no—
537C22×D3—21no—
538C22×D3—61no—
539C22×D3—61no—
540C22×D3—81no—
541C22×D3—81no—
542C22×D3—121no—
543C22×D3—122no—
544C22×D3—122no—
545C22×D3—241no—
546C22×D3—241no—
547C22×D3—241no—
548C22×D3—241no—
549C22×D3D3×D411yescharacteristic
550C3×Q8—21no—
551C3×Q8—21no—
552C3×Q8—21no—
553C3×Q8—21no—
554C3×Q8—41no—
555C3×Q8—41no—
556C3×D4—21no—
557C3×D4—21no—
558C3×D4—22no—
559C3×D4—32no—
560C3×D4—41no—
561C3×D4—64no—
562C3×D4—61no—
563C3×D4—61no—
564C3×D4—61no—
565C3×D4—61no—
566C3×D4—61no—
567C3×D4—122no—
568C3×D4D3×D412yes—
569C3×D4C2×#6712yes—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—31no—
574C2×C3×C4—32no—
575C2×C3×C4—32no—
576C2×C3×C4—31no—
577C2×C3×C4—31no—
578C2×C3×C4—41no—
579C2×C3×C4—61no—
580C2×C3×C4—122no—
581C2×C3×C4—241no—
582C2×C3×C4C23×D311yescharacteristic
583C2×C3×C4C23×D311yescharacteristic
584#67—24no—
585#67—122no—
586#67—241no—
587#67—241no—
588#67—241no—
589#67—241no—
590#67—241no—
591#67—241no—
592C2×Dic3—21no—
593C2×Dic3—31no—
594C2×Dic3—31no—
595C2×Dic3—31no—
596C2×Dic3—31no—
597C2×Dic3—61no—
598C2×Dic3—61no—
599C2×Dic3—61no—
600C2×Dic3—61no—
601C2×Dic3—81no—
602C2×Dic3—121no—
603C2×Dic3—241no—
604C2×Dic3—241no—
605C2×Dic3—241no—
606C2×Dic3—241no—
607C2×Dic3—242no—
608C2×Dic3D3×D411yescharacteristic
609C2×Dic3D3×D411yescharacteristic
610C2×Dic3D3×D411yescharacteristic
611D12—21no—
612D12—21no—
613D12—21no—
614D12—21no—
615D12—21no—
616D12—42no—
617D12—61no—
618D12—61no—
619D12—61no—
620D12—61no—
621D12—121no—
622D12—121no—
623D12—122no—
624D12—241no—
625D12—241no—
626D12C2×#6712yes—
627C4×D3—42no—
628C4×D3—241no—
629C4×D3—241no—
630C4×D3#23712yes—
631C4×D3C2×#6712yes—
632C3×C8—21no—
633C3×C8—21no—
634C3×C8—41no—
635C3×C8—61no—
636C3×C8—61no—
637C3⋊C8—21no—
638C3⋊C8—21no—
639C3⋊C8—61no—
640C3⋊C8—61no—
641C3⋊C8—121no—
642C2×C32—42no—
643C2×C32C2×#12111yescharacteristic
644C2×C32#57611yescharacteristic
645C2×C32#57611yescharacteristic
646C3⋊D3—81no—
647C3×D3—22no—
648C3×D3—42no—
649C3×D3—81no—
650C3×D3—81no—
651C24—61no—
652C24—181no—
653#41—62no—
654#41—62no—
655C2×Q8C2×D3211yescharacteristic
656C2×D4—34no—
657C2×D4—31no—
658C2×D4—31no—
659C2×D4—31no—
660C2×D4—61no—
661C2×D4—62no—
662C2×D4—61no—
663C2×D4—91no—
664C2×D4—182no—
665C2×D4—182no—
666C2×D4—181no—
667C2×D4—181no—
668C2×D4—181no—
669C2×D4—181no—
670C2×D4—181no—
671C2×D4C2×D3211yescharacteristic
672C22×C4—31no—
673C22×C4—61no—
674C22×C4—61no—
675C22×C4—181no—
676C22×C4—181no—
677C22×C4—181no—
678SD16—22no—
679SD16—62no—
680D8—62no—
681D8—62no—
682D8—62no—
683D8—182no—
684D8—182no—
685D8—182no—
686M16—62no—
687C2×C8—31no—
688C2×C8—31no—
689C2×C8—91no—
690C2×C8—182no—
691C2×C8C2×D3211yescharacteristic
692C4⋊C4—31no—
693C4⋊C4—91no—
694C4⋊C4—91no—
695C4⋊C4—91no—
696C22⋊C4—61no—
697C22⋊C4—61no—
698C22⋊C4—61no—
699C22⋊C4—91no—
700C22⋊C4—91no—
701C22⋊C4—181no—
702C22⋊C4—181no—
703C22⋊C4—181no—
704C22⋊C4—181no—
705C22⋊C4—181no—
706C22⋊C4—181no—
707C42—31no—
708C42—91no—
709C42—181no—
710C22×C3—22no—
711C22×C3—22no—
712C22×C3—21no—
713C22×C3—32no—
714C22×C3—42no—
715C22×C3—41no—
716C22×C3—41no—
717C22×C3—41no—
718C22×C3—41no—
719C22×C3—61no—
720C22×C3—61no—
721C22×C3—62no—
722C22×C3—81no—
723C22×C3—81no—
724C22×C3—121no—
725C22×C3—121no—
726C22×C3—121no—
727C22×C3—121no—
728C22×C3—121no—
729C22×C3—121no—
730C22×C3—121no—
731C22×C3—121no—
732C22×C3—244no—
733C22×C3C2×D3×D411yescharacteristic
734C22×C3C2×D3×D411yescharacteristic
735C2×D3—21no—
736C2×D3—21no—
737C2×D3—22no—
738C2×D3—41no—
739C2×D3—41no—
740C2×D3—41no—
741C2×D3—41no—
742C2×D3—41no—
743C2×D3—41no—
744C2×D3—41no—
745C2×D3—41no—
746C2×D3—84no—
747C2×D3—121no—
748C2×D3—121no—
749C2×D3—121no—
750C2×D3—121no—
751C2×D3—121no—
752C2×D3—121no—
753C2×D3—241no—
754C2×D3—241no—
755C2×D3—241no—
756C2×D3—244no—
757C2×D3—244no—
758C2×D3#93912yes—
759C3×C4—21no—
760C3×C4—21no—
761C3×C4—32no—
762C3×C4—41no—
763C3×C4—41no—
764C3×C4—61no—
765C3×C4—61no—
766C3×C4—81no—
767C3×C4—121no—
768C3×C4C2×D3×D411yescharacteristic
769C3×C4C2×#23711yescharacteristic
770C3×C4D3×#4111yescharacteristic
771C3×C4C22×#6711yescharacteristic
772Dic3—21no—
773Dic3—21no—
774Dic3—41no—
775Dic3—61no—
776Dic3—61no—
777Dic3—61no—
778Dic3—61no—
779Dic3—121no—
780Dic3—121no—
781Dic3—121no—
782Dic3—121no—
783Dic3—241no—
784Dic3#93912yes—
785C32#304111yescharacteristic, complemented, Sylow
786C23—21no—
787C23—31no—
788C23—64no—
789C23—61no—
790C23—61no—
791C23—61no—
792C23—181no—
793C23—241no—
794C23—241no—
795C23—362no—
796C23—721no—
797C23—721no—
798Q8—21no—
799Q8—21no—
800D4—21no—
801D4—32no—
802D4—64no—
803D4—61no—
804D4—61no—
805D4—61no—
806D4—61no—
807D4—61no—
808D4—122no—
809D4—181no—
810D4—181no—
811D4—362no—
812D4—721no—
813D4—721no—
814D4—721no—
815D4—721no—
816D4D3×#6712yes—
817C2×C4—21no—
818C2×C4—31no—
819C2×C4—32no—
820C2×C4—32no—
821C2×C4—31no—
822C2×C4—31no—
823C2×C4—61no—
824C2×C4—91no—
825C2×C4—91no—
826C2×C4—122no—
827C2×C4—181no—
828C2×C4—241no—
829C2×C4—721no—
830C2×C4—721no—
831C2×C4—721no—
832C2×C4C22×D3211yescharacteristic
833C8—21no—
834C8—61no—
835C8—61no—
836C8—181no—
837C2×C3—21no—
838C2×C3—21no—
839C2×C3—21no—
840C2×C3—42no—
841C2×C3—42no—
842C2×C3—62no—
843C2×C3—82no—
844C2×C3—122no—
845C2×C3—241no—
846C2×C3—241no—
847C2×C3D3×#12111yescharacteristic
848C2×C3#576911yescharacteristic
849C2×C3#577411yescharacteristic
850C2×C3#577411yescharacteristic
851C2×C3#577411yescharacteristic
852C2×C3C2×#93911yescharacteristic
853D3—22no—
854D3—42no—
855D3—81no—
856D3—81no—
857D3—241no—
858D3—241no—
859D3—481no—
860C22—22no—
861C22—32no—
862C22—41no—
863C22—41no—
864C22—61no—
865C22—61no—
866C22—62no—
867C22—121no—
868C22—121no—
869C22—121no—
870C22—121no—
871C22—121no—
872C22—121no—
873C22—121no—
874C22—121no—
875C22—244no—
876C22—361no—
877C22—361no—
878C22—361no—
879C22—724no—
880C22D32×D411yescharacteristic
881C4—32no—
882C4—41no—
883C4—61no—
884C4—61no—
885C4—121no—
886C4—181no—
887C4—181no—
888C4—361no—
889C4D3×#23711yescharacteristic
890C4C2×D3×#6711yescharacteristic
891C3—21no—
892C3#8053611yescharacteristic, complemented
893C3#8393411yescharacteristic, complemented
894C2—42no—
895C2—62no—
896C2—122no—
897C2—241no—
898C2—241no—
899C2—721no—
900C2#1059475011yescharacteristic
901C2#1059475511yescharacteristic
902C2D3×#93911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
hypercenterC2×SD16D32
hypocenterC32#3041
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×#914C2semidirect
2. #10595426C2semidirect
3. #10595215C2semidirect
4. C2×D3×#213C2semidirect
5. #10592864C2semidirect
6. C3×#5165C2semidirect
7. #10591570C2semidirect
8. #10591567C2semidirect
9. #10591556C2semidirect
10. #10591486C2semidirect
11. #10591481C2semidirect
12. #10590939C2semidirect
13. #10590753C2semidirect
14. #10590749C2semidirect
15. #10590695C2semidirect
21. C2×C32×SD16C22semidirect
22. #64156C22semidirect
23. D4×C3⋊Dic3C22semidirect
25. C3×#947C22semidirect
26. C2×C3×#215C22semidirect
27. C3×D4×Dic3C22semidirect
29. C2×C3×#213C22semidirect
31. C2×C3×D24C22semidirect
40. #63914C22semidirect
41. #63911C22semidirect
44. #63898C22semidirect
45. Dic3×D12C22semidirect
51. #63662C22semidirect
52. #63648C22semidirect
53. #63641C22semidirect
54. C3×#835C22semidirect
55. C3×#821C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. #63572C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
59. #63564C22semidirect
60. #63563C22semidirect
61. #63563C22semidirect
62. #63562C22semidirect
67. C2×#914D3semidirect
78. #5165D3semidirect
105. C3×D3×D4D4semidirect
163. C2×C3×SD16C2×D3semidirect
164. C2×C3×SD16C2×D3semidirect
176. #947C2×D3semidirect
177. C2×#215C2×D3semidirect
190. D4×Dic3C2×D3semidirect
199. C2×#213C2×D3semidirect
210. C2×D24C2×D3semidirect
230. #835C2×D3semidirect
240. #821C2×D3semidirect
247. Dic3⋊C8C2×D3semidirect
358. D3×D4#67semidirect
484. C2×SD16D32semidirect
785. C32#3041semidirect
892. C3#80536semidirect
893. C3#83934semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9142
#105954262
#105952152
C2×D3×#2132
#105928642
C3×#51652
#105915702
#105915672
#105915562
#105914862
#105914812
#105909392
#105907532
#105907492
#105906952
#839343
#805363