Finite Group Databasebeta

← #11866188

Subgroups — #11866188

Order 1152.

1122 conjugacy classes of subgroups.

The subgroup lattice has 909 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×D8C211yesmaximal, characteristic, complemented
2#10595235C211yesmaximal, characteristic, complemented
3#10595215C211yesmaximal, characteristic, complemented
4C2×#63934C211yesmaximal, characteristic, complemented
5#10592849C211yesmaximal, characteristic, complemented
6C3×#5153C211yesmaximal, characteristic, complemented
7#10591481C211yesmaximal, characteristic, complemented
8#10591476C211yesmaximal, characteristic, complemented
9#10591433C211yesmaximal, characteristic, complemented
10#10591431C211yesmaximal, characteristic, complemented
11#10591421C211yesmaximal, characteristic, complemented
12#10590753C211yesmaximal, characteristic, complemented
13#10590751C211yesmaximal, characteristic, complemented
14#10590694C211yesmaximal, characteristic, complemented
15#10590690C211yesmaximal, characteristic, complemented
16#83826—31nomaximal
17#80536—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C2×#3799C2211yescharacteristic
21C2×C32×D8C2211yescharacteristic
22#64149C2211yescharacteristic, complemented
23D4×C3⋊Dic3C2211yescharacteristic, complemented
24C2×#3753C2211yescharacteristic, complemented
25C3×#936C2211yescharacteristic, complemented
26C3×D4×Dic3C2211yescharacteristic, complemented
27C2×C3×#214C2211yescharacteristic, complemented
28C2×C3×#213C2211yescharacteristic
29C2×C3×#213C2211yescharacteristic
30C3×D3×D8—24no—
31C2×C3×D24C2211yescharacteristic
32C2×C3×D3×C8C2211yescharacteristic
33#63977—21no—
34#63977—21no—
35#67⋊Dic3—21no—
36Dic3×#67—21no—
37D3×#217—21no—
38C2×(C2×D3)⋊Dic3—21no—
39#63958—21no—
40#63958—21no—
41#63934—24no—
42#63911C2211yescharacteristic, complemented
43#63898C2211yescharacteristic, complemented
44Dic3×D12C2211yescharacteristic, complemented
45#63863C2211yescharacteristic, complemented
46#63855C2211yescharacteristic
47#63841C2211yescharacteristic
48C2×#3715C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic, complemented
50C2×#3711C2211yescharacteristic
51#63659C2211yescharacteristic, complemented
52#63648C2211yescharacteristic, complemented
53#63641C2211yescharacteristic, complemented
54C3×#832C2211yescharacteristic, complemented
55C3×#816C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57#63572C2211yescharacteristic, complemented
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63564C2211yescharacteristic, complemented
61#63563C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63C22×C3×D8—31no—
64#5805—31no—
65#5798—31no—
66C2×#932—31no—
67C2×#914—31no—
68C2×D3×D8D311yescharacteristic, complemented
69#5674—31no—
70#5545—31no—
71C3×#463—31no—
72#5215—31no—
73#5165—31no—
74#5153—31no—
75#5153—31no—
76#5153—31no—
77#5153D311yescharacteristic, complemented
78#5150—31no—
79#5150—31no—
80#5150—31no—
81#5150—31no—
82#5150—31no—
83#5150—61no—
84#5113—31no—
85#5102—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—
95C23×C3×D3—21no—
96C2×C32×D4C2311yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C2×#638—21no—
99C2×#638—21no—
100C22×C3⋊Dic3—21no—
101C2×C4⋊(C3⋊D3)C2311yescharacteristic
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C22×C3×Dic3—21no—
105C3×D3×D4—22no—
106C3×D3×D4—22no—
107C3×D3×D4—22no—
108C3×D3×D4D414yescomplemented
109C2×C3×D12C2311yescharacteristic
110C2×C3×D12C2311yescharacteristic
111C2×C3×C4×D3C2311yescharacteristic
112C2×C3×Dic6C2311yescharacteristic
113C2×#626—21no—
114C2×#626—21no—
115C2×#626—21no—
116C2×#624—21no—
117C2×D3×Dic3—21no—
118C2×D3×Dic3—21no—
119#3799—22no—
120#3799—22no—
121C32×D8—22no—
122C2×C32×C8C2311yescharacteristic
123#3757—21no—
124#3753—22no—
125C4⋊(C3⋊Dic3)C2311yescharacteristic
126C4×C3⋊Dic3C2311yescharacteristic
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128C3×#217—21no—
129C3×#217—21no—
130C3×#217—21no—
131C3×#214—22no—
132C3×#213—22no—
133C3×#213—22no—
134C3×C4⋊Dic3C2311yescharacteristic
135C3×C4×Dic3C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C3×D24—22no—
139C3×D3×C8—22no—
140Dic3⋊Dic3D411yescharacteristic
141Dic3⋊Dic3D411yescharacteristic
142(C2×D3)⋊Dic3—21no—
143(C2×D3)⋊Dic3—21no—
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#3715—22no—
151#3714—22no—
152#3711—22no—
153#3041—91noSylow
154C22×C3×D4—31no—
155C22×C3×D4—31no—
156C2×#239—31no—
157C2×D3×D4C2×D311yescharacteristic
158C2×D3×D4C2×D311yescharacteristic
159C2×#235—31no—
160C2×C3×SD16—31no—
161C2×C3×D8—21no—
162C2×C3×D8—31no—
163C2×C3×D8—31no—
164C2×C3×D8—31no—
165C2×C3×D8—64no—
166C2×C3×D8C2×D311yescharacteristic
167C2×C3×D8C2×D311yescharacteristic
168C22×C3×C8—31no—
169C3×#124—31no—
170C3×C4×D4—31no—
171#953—61no—
172#953—61no—
173C2×#217—61no—
174C2×#217—61no—
175#947—31no—
176C2×#215—31no—
177#940—31no—
178#940—31no—
179#940—31no—
180#940—61no—
181#938—61no—
182#938—61no—
183#936—31no—
184#936C2×D311yescharacteristic, complemented
185D4×Dic3—31no—
186D4×Dic3—31no—
187D4×Dic3—31no—
188D4×Dic3—31no—
189D4×Dic3—61no—
190D4×Dic3—61no—
191D4×Dic3—61no—
192D4×Dic3C2×D311yescharacteristic, complemented
193C2×#214—31no—
194C2×#214C2×D311yescharacteristic, complemented
195#932—64no—
196C2×#213—31no—
197C2×#213—31no—
198C2×#213—31no—
199C2×#213—61no—
200C2×#213C2×D311yescharacteristic
201C2×#213C2×D311yescharacteristic
202C4×#67—61no—
203C2×(C2×D3)⋊C4—61no—
204#926—31no—
205#926—31no—
206C2×#208—31no—
207#914—64no—
208D3×D8—24no—
209C2×D24—31no—
210C2×D24C2×D311yescharacteristic
211C2×ΓL(1,𝔽25)—31no—
212C2×D3×C8C2×D311yescharacteristic
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#832—31no—
229#832—31no—
230#832—31no—
231#832—31no—
232#832—61no—
233#832C2×D311yescharacteristic, complemented
234#821—31no—
235#821—31no—
236#821—31no—
237#821—31no—
238#821—61no—
239#816—31no—
240#816C2×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—
252C23×C32—21no—
253C22×C3⋊D3—21no—
254C22×C3×D3—21no—
255C22×C3×D3—24no—
256C22×C3×D3—21no—
257C22×C3×D3—42no—
258C22×C3×D3—81no—
259C22×C3×D3—81no—
260C22×C3×D3—81no—
261C22×C3×D3—81no—
262C22×C3×D3C2×D411yescharacteristic
263C32×D4—21no—
264C32×D4—21no—
265C32×D4—21no—
266C32×D4C2×D412yes—
267C2×C32×C4C2411yescharacteristic
268#638—81no—
269#638—81no—
270C2×C3⋊Dic3—21no—
271C2×C3⋊Dic3—81no—
272C2×C3⋊Dic3C2×D411yescharacteristic
273C2×C3⋊Dic3C2×D411yescharacteristic
274C4⋊(C3⋊D3)—21no—
275C4⋊(C3⋊D3)—21no—
276C3×#67—24no—
277C3×#67—42no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—81no—
281C2×C3×Dic3C2×D411yescharacteristic
282C2×C3×Dic3C2×D411yescharacteristic
283C2×C3×Dic3C2×D411yescharacteristic
284C3×D12—21no—
285C3×D12—21no—
286C3×D12—21no—
287C3×D12C2×D412yes—
288C3×C4×D3C2×D412yes—
289C3×C4×D3#4112yes—
290C3×Dic6—21no—
291C3×Dic6—21no—
292#626—42no—
293#626—81no—
294#626—81no—
295#624—42no—
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)—91no—
303C22×D8—31no—
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—
318C24×C3—61no—
319C23×D3—21no—
320C23×D3—21no—
321C2×C3×Q8—31no—
322C2×C3×D4—21no—
323C2×C3×D4—21no—
324C2×C3×D4—34no—
325C2×C3×D4—31no—
326C2×C3×D4—31no—
327C2×C3×D4—62no—
328C2×C3×D4—62no—
329C2×C3×D4—62no—
330C2×C3×D4—61no—
331C2×C3×D4—61no—
332C2×C3×D4C22×D311yescharacteristic
333C2×C3×D4C22×D311yescharacteristic
334C2×C3×D4C22×D311yescharacteristic
335C2×C3×D4C22×D311yescharacteristic
336C22×C3×C4—31no—
337C22×C3×C4—61no—
338C2×#67—21no—
339C2×#67—21no—
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—
349C22×Dic3—21no—
350C22×Dic3—61no—
351C22×Dic3—61no—
352C22×Dic3—61no—
353C22×Dic3—61no—
354C22×Dic3—121no—
355#239—62no—
356#239—62no—
357D3×D4—22no—
358D3×D4—22no—
359D3×D4—22no—
360D3×D4#6714yescomplemented
361#235—62no—
362#235—62no—
363C2×D12—31no—
364C2×D12—31no—
365C2×D12—61no—
366C2×D12—61no—
367C2×D12—61no—
368C2×D12—61no—
369C2×D12C22×D311yescharacteristic
370C2×D12C22×D311yescharacteristic
371C2×C4×D3—61no—
372C2×C4×D3—61no—
373C2×C4×D3—61no—
374C2×C4×D3—61no—
375C2×C4×D3C22×D311yescharacteristic
376C2×Dic6C22×D311yescharacteristic
377C3×SD16—62no—
378C3×D8—22no—
379C3×D8—22no—
380C3×D8—42no—
381C3×D8—62no—
382C3×D8—62no—
383C3×D8—62no—
384C2×C3×C8—21no—
385C2×C3×C8—31no—
386C2×C3×C8—31no—
387C2×C3×C8—62no—
388C2×C3×C8C22×D311yescharacteristic
389C2×C3×C8C22×D311yescharacteristic
390C3×C4⋊C4—31no—
391C3×C22⋊C4—61no—
392C3×C22⋊C4—61no—
393C3×C22⋊C4—61no—
394C3×C42—31no—
395#217—21no—
396#217—21no—
397#217—21no—
398#217—31no—
399#217—31no—
400#217—61no—
401#217—61no—
402#217—61no—
403#217—61no—
404#217—61no—
405#217—61no—
406#217—61no—
407#217—121no—
408#215—62no—
409#214—22no—
410#214—62no—
411#213—22no—
412#213—22no—
413#213—62no—
414#213—62no—
415#213—62no—
416#213—122no—
417(C2×D3)⋊C4—31no—
418(C2×D3)⋊C4—31no—
419(C2×D3)⋊C4—61no—
420(C2×D3)⋊C4—61no—
421(C2×D3)⋊C4—61no—
422(C2×D3)⋊C4—61no—
423(C2×D3)⋊C4—61no—
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
438#208—62no—
439C2×C3⋊C8—31no—
440C2×C3⋊C8—31no—
441C2×C3⋊C8—61no—
442C2×C3⋊C8C22×D311yescharacteristic
443C2×C3⋊C8C22×D311yescharacteristic
444D24—22no—
445D24—62no—
446ΓL(1,𝔽25)—62no—
447D3×C8—22no—
448C22×C32—22no—
449C22×C32—41no—
450C22×C32—41no—
451C22×C32—41no—
452C22×C32—41no—
453C22×C32—41no—
454C22×C32C22×D411yescharacteristic
455C2×C3⋊D3—41no—
456C2×C3⋊D3—41no—
457C2×C3⋊D3—41no—
458C2×C3×D3—21no—
459C2×C3×D3—21no—
460C2×C3×D3—22no—
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—84no—
468C2×C3×D3#12112yes—
469C32×C4C22×D411yescharacteristic
470C32×C4C2×#4111yescharacteristic
471C3⋊Dic3—21no—
472C3⋊Dic3—21no—
473C3⋊Dic3—41no—
474C3×Dic3—21no—
475C3×Dic3—21no—
476C3×Dic3—41no—
477C3×Dic3—41no—
478C3×Dic3#12112yes—
479C2×#41—91no—
480C22×D4—31no—
481C22×D4—31no—
482AGL(1,ℤ/8)—184no—
483C2×SD16—31no—
484C2×SD16—91no—
485C2×D8—31no—
486C2×D8—31no—
487C2×D8—31no—
488C2×D8—64no—
489C2×D8—91no—
490C2×D8—91no—
491C2×D8D3211yescharacteristic
492C2×M16—91no—
493C22×C8—31no—
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—21no—
527C23×C3—21no—
528C23×C3—31no—
529C23×C3—41no—
530C23×C3—41no—
531C23×C3—64no—
532C23×C3—61no—
533C23×C3—61no—
534C23×C3—122no—
535C23×C3—241no—
536C23×C3—241no—
537C23×C3—241no—
538C23×C3—241no—
539C22×D3—21no—
540C22×D3—24no—
541C22×D3—21no—
542C22×D3—42no—
543C22×D3—61no—
544C22×D3—61no—
545C22×D3—81no—
546C22×D3—81no—
547C22×D3—81no—
548C22×D3—81no—
549C22×D3—121no—
550C22×D3D3×D411yescharacteristic
551C3×Q8—61no—
552C3×Q8—61no—
553C3×D4—21no—
554C3×D4—21no—
555C3×D4—21no—
556C3×D4—21no—
557C3×D4—21no—
558C3×D4—21no—
559C3×D4—22no—
560C3×D4—32no—
561C3×D4—41no—
562C3×D4—41no—
563C3×D4—41no—
564C3×D4—64no—
565C3×D4—61no—
566C3×D4—61no—
567C3×D4—61no—
568C3×D4—122no—
569C3×D4D3×D412yes—
570C3×D4C2×#6712yes—
571C2×C3×C4—21no—
572C2×C3×C4—31no—
573C2×C3×C4—32no—
574C2×C3×C4—32no—
575C2×C3×C4—31no—
576C2×C3×C4—31no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4—241no—
580C2×C3×C4C23×D311yescharacteristic
581C2×C3×C4C23×D311yescharacteristic
582#67—24no—
583#67—42no—
584#67—122no—
585#67—241no—
586#67—241no—
587#67—241no—
588#67—241no—
589#67—241no—
590#67—241no—
591#67—242no—
592#67—242no—
593C2×Dic3—21no—
594C2×Dic3—21no—
595C2×Dic3—31no—
596C2×Dic3—31no—
597C2×Dic3—31no—
598C2×Dic3—31no—
599C2×Dic3—61no—
600C2×Dic3—61no—
601C2×Dic3—61no—
602C2×Dic3—61no—
603C2×Dic3—81no—
604C2×Dic3—121no—
605C2×Dic3—241no—
606C2×Dic3—241no—
607C2×Dic3—241no—
608C2×Dic3—241no—
609C2×Dic3—242no—
610C2×Dic3D3×D411yescharacteristic
611C2×Dic3D3×D411yescharacteristic
612C2×Dic3D3×D411yescharacteristic
613D12—21no—
614D12—21no—
615D12—21no—
616D12—61no—
617D12—61no—
618D12—61no—
619D12—61no—
620D12—121no—
621D12—121no—
622D12—122no—
623D12—241no—
624D12—241no—
625D12C2×#6712yes—
626C4×D3—122no—
627C4×D3—122no—
628C4×D3—241no—
629C4×D3—241no—
630C4×D3#23712yes—
631C4×D3C2×#6712yes—
632Dic6—21no—
633Dic6—21no—
634C3×C8—21no—
635C3×C8—21no—
636C3×C8—41no—
637C3×C8—61no—
638C3×C8—61no—
639C3⋊C8—21no—
640C3⋊C8—21no—
641C3⋊C8—61no—
642C3⋊C8—61no—
643C3⋊C8—121no—
644C2×C32—42no—
645C2×C32—81no—
646C2×C32C2×#12111yescharacteristic
647C2×C32#57611yescharacteristic
648C2×C32#57611yescharacteristic
649C3⋊D3—81no—
650C3×D3—22no—
651C3×D3—42no—
652C3×D3—81no—
653C24—61no—
654C24—61no—
655#41—182no—
656#41—182no—
657C2×Q8—31no—
658C2×D4—34no—
659C2×D4—31no—
660C2×D4—31no—
661C2×D4—62no—
662C2×D4—62no—
663C2×D4—62no—
664C2×D4—61no—
665C2×D4—61no—
666C2×D4—91no—
667C2×D4—181no—
668C2×D4—181no—
669C2×D4—181no—
670C2×D4—181no—
671C2×D4—181no—
672C2×D4C2×D3211yescharacteristic
673C2×D4C2×D3211yescharacteristic
674C22×C4—31no—
675C22×C4—61no—
676C22×C4—181no—
677C22×C4—181no—
678C22×C4—181no—
679C22×C4—181no—
680SD16—62no—
681SD16—182no—
682D8—22no—
683D8—62no—
684D8—62no—
685D8—62no—
686D8—182no—
687D8—182no—
688M16—182no—
689C2×C8—31no—
690C2×C8—31no—
691C2×C8—62no—
692C2×C8—91no—
693C2×C8C2×D3211yescharacteristic
694C4⋊C4—31no—
695C4⋊C4—91no—
696C4⋊C4—91no—
697C4⋊C4—91no—
698C22⋊C4—61no—
699C22⋊C4—61no—
700C22⋊C4—61no—
701C22⋊C4—91no—
702C22⋊C4—91no—
703C22⋊C4—181no—
704C22⋊C4—181no—
705C22⋊C4—181no—
706C22⋊C4—181no—
707C22⋊C4—181no—
708C22⋊C4—181no—
709C42—31no—
710C42—91no—
711C42—181no—
712C22×C3—22no—
713C22×C3—22no—
714C22×C3—21no—
715C22×C3—32no—
716C22×C3—42no—
717C22×C3—41no—
718C22×C3—41no—
719C22×C3—41no—
720C22×C3—41no—
721C22×C3—41no—
722C22×C3—41no—
723C22×C3—41no—
724C22×C3—41no—
725C22×C3—41no—
726C22×C3—41no—
727C22×C3—61no—
728C22×C3—61no—
729C22×C3—62no—
730C22×C3—81no—
731C22×C3—81no—
732C22×C3—81no—
733C22×C3—81no—
734C22×C3—81no—
735C22×C3—121no—
736C22×C3—121no—
737C22×C3—121no—
738C22×C3—121no—
739C22×C3—121no—
740C22×C3—244no—
741C22×C3—244no—
742C22×C3C2×D3×D411yescharacteristic
743C22×C3C2×D3×D411yescharacteristic
744C2×D3—21no—
745C2×D3—21no—
746C2×D3—22no—
747C2×D3—41no—
748C2×D3—41no—
749C2×D3—41no—
750C2×D3—41no—
751C2×D3—41no—
752C2×D3—84no—
753C2×D3—84no—
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#93912yes—
764C3×C4—21no—
765C3×C4—21no—
766C3×C4—32no—
767C3×C4—61no—
768C3×C4—61no—
769C3×C4—121no—
770C3×C4—121no—
771C3×C4C2×D3×D411yescharacteristic
772C3×C4C2×#23711yescharacteristic
773C3×C4D3×#4111yescharacteristic
774C3×C4C22×#6711yescharacteristic
775Dic3—21no—
776Dic3—21no—
777Dic3—41no—
778Dic3—41no—
779Dic3—62no—
780Dic3—61no—
781Dic3—61no—
782Dic3—61no—
783Dic3—61no—
784Dic3—121no—
785Dic3—121no—
786Dic3—121no—
787Dic3—241no—
788Dic3#93912yes—
789C32#304111yescharacteristic, complemented, Sylow
790C23—21no—
791C23—21no—
792C23—31no—
793C23—64no—
794C23—61no—
795C23—61no—
796C23—122no—
797C23—181no—
798C23—241no—
799C23—241no—
800C23—241no—
801C23—241no—
802Q8—61no—
803Q8—61no—
804D4—21no—
805D4—21no—
806D4—21no—
807D4—32no—
808D4—64no—
809D4—61no—
810D4—61no—
811D4—61no—
812D4—122no—
813D4—181no—
814D4—181no—
815D4—362no—
816D4—721no—
817D4—721no—
818D4—721no—
819D4—721no—
820D4D3×#6712yes—
821C2×C4—31no—
822C2×C4—32no—
823C2×C4—32no—
824C2×C4—31no—
825C2×C4—31no—
826C2×C4—61no—
827C2×C4—61no—
828C2×C4—91no—
829C2×C4—91no—
830C2×C4—181no—
831C2×C4—241no—
832C2×C4—362no—
833C2×C4—721no—
834C2×C4—721no—
835C2×C4—721no—
836C2×C4C22×D3211yescharacteristic
837C8—21no—
838C8—61no—
839C8—61no—
840C8—181no—
841C2×C3—21no—
842C2×C3—21no—
843C2×C3—21no—
844C2×C3—42no—
845C2×C3—42no—
846C2×C3—62no—
847C2×C3—82no—
848C2×C3—81no—
849C2×C3—81no—
850C2×C3—122no—
851C2×C3—161no—
852C2×C3—241no—
853C2×C3D3×#12111yescharacteristic
854C2×C3#575711yescharacteristic
855C2×C3#575711yescharacteristic
856C2×C3#576911yescharacteristic
857C2×C3#577411yescharacteristic
858C2×C3C2×#93911yescharacteristic
859D3—22no—
860D3—42no—
861D3—81no—
862D3—241no—
863D3—241no—
864D3—481no—
865C22—22no—
866C22—32no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22—61no—
873C22—61no—
874C22—62no—
875C22—121no—
876C22—121no—
877C22—121no—
878C22—121no—
879C22—121no—
880C22—244no—
881C22—244no—
882C22—361no—
883C22—361no—
884C22—361no—
885C22D32×D411yescharacteristic
886C4—32no—
887C4—61no—
888C4—61no—
889C4—121no—
890C4—121no—
891C4—181no—
892C4—181no—
893C4—361no—
894C4D3×#23711yescharacteristic
895C4C2×D3×#6711yescharacteristic
896C3—21no—
897C3#8053611yescharacteristic, complemented
898C3#8382611yescharacteristic, complemented
899C2—42no—
900C2—62no—
901C2—81no—
902C2—122no—
903C2—241no—
904C2—721no—
905C2#1059473211yescharacteristic
906C2#1059473411yescharacteristic
907C2D3×#93911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
hypercenterC2×D8D32
hypocenterC32#3041
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×D8C2semidirect
2. #10595235C2semidirect
3. #10595215C2semidirect
4. C2×#63934C2semidirect
5. #10592849C2semidirect
6. C3×#5153C2semidirect
7. #10591481C2semidirect
8. #10591476C2semidirect
9. #10591433C2semidirect
10. #10591431C2semidirect
11. #10591421C2semidirect
12. #10590753C2semidirect
13. #10590751C2semidirect
14. #10590694C2semidirect
15. #10590690C2semidirect
22. #64149C22semidirect
23. D4×C3⋊Dic3C22semidirect
24. C2×#3753C22semidirect
25. C3×#936C22semidirect
26. C3×D4×Dic3C22semidirect
27. C2×C3×#214C22semidirect
42. #63911C22semidirect
43. #63898C22semidirect
44. Dic3×D12C22semidirect
45. #63863C22semidirect
48. C2×#3715C22semidirect
49. C2×#3714C22semidirect
51. #63659C22semidirect
52. #63648C22semidirect
53. #63641C22semidirect
54. C3×#832C22semidirect
55. C3×#816C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. #63572C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
59. #63566C22semidirect
60. #63564C22semidirect
61. #63563C22semidirect
62. #63562C22semidirect
68. C2×D3×D8D3semidirect
77. #5153D3semidirect
108. C3×D3×D4D4semidirect
184. #936C2×D3semidirect
192. D4×Dic3C2×D3semidirect
194. C2×#214C2×D3semidirect
233. #832C2×D3semidirect
240. #816C2×D3semidirect
247. Dic3⋊C8C2×D3semidirect
360. D3×D4#67semidirect
789. C32#3041semidirect
897. C3#80536semidirect
898. C3#83826semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×D82
#105952352
#105952152
C2×#639342
#105928492
C3×#51532
#105914812
#105914762
#105914332
#105914312
#105914212
#105907532
#105907512
#105906942
#105906902
#838263
#805363