Finite Group Databasebeta

← #11866181

Subgroups — #11866181

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
1C3×#5715C211yesmaximal, characteristic, complemented
2C2×#63925C211yesmaximal, characteristic, complemented
3C2×D3×#213C211yesmaximal, characteristic, complemented
4#10593994C211yesmaximal, characteristic, complemented
5#10592771C211yesmaximal, characteristic, complemented
6C3×#5072C211yesmaximal, characteristic, complemented
7#10591432C211yesmaximal, characteristic, complemented
8#10591431C211yesmaximal, characteristic, complemented
9#10591429C211yesmaximal, characteristic, complemented
10#10591428C211yesmaximal, characteristic, complemented
11#10591421C211yesmaximal, characteristic, complemented
12#10591420C211yesmaximal, characteristic, complemented
13#10590356C211yesmaximal, characteristic, complemented
14#10590348C211yesmaximal, characteristic, complemented
15#10590324C211yesmaximal, characteristic, complemented
16#83384—31nomaximal
17#80334—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C2×D3×D12C2211yescharacteristic
21C32×#127C2211yescharacteristic, complemented
22C2×#3753C2211yescharacteristic
23C2×#3753C2211yescharacteristic, complemented
24C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
25C3×#940C2211yescharacteristic, complemented
26C3×#939—21no—
27C3×#939—21no—
28C3×#937—21no—
29C3×#937—21no—
30C3×#936C2211yescharacteristic, complemented
31C2×C3×#213C2211yescharacteristic
32C2×C3×#213C2211yescharacteristic, complemented
33C3×#875C2211yescharacteristic, complemented
34C3×C4×D12C2211yescharacteristic, complemented
35C3×#872C2211yescharacteristic
36#63925—24no—
37D3×#213—24no—
38#63921—21no—
39D3×(C2×D3)⋊C4—21no—
40#63904—21no—
41#63894C2211yescharacteristic, complemented
42Dic3×D12C2211yescharacteristic, complemented
43#63881—21no—
44#63841C2211yescharacteristic
45C2×#3717C2211yescharacteristic, complemented
46C2×#3715C2211yescharacteristic, complemented
47C2×#3714C2211yescharacteristic
48C2×#3713C2211yescharacteristic
49C2×#3711C2211yescharacteristic
50C2×D3×C3⋊C8C2211yescharacteristic
51#63659C2211yescharacteristic, complemented
52#63659C2211yescharacteristic, complemented
53C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
54C3×#832C2211yescharacteristic, complemented
55C3×#832C2211yescharacteristic, complemented
56C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
57Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63565C2211yescharacteristic, complemented
61#63563C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63C3×#535—31no—
64C2×#949—31no—
65C22×#213—31no—
66C2×#911—31no—
67C2×D3×D8—31no—
68#5715D311yescharacteristic, complemented
69#5545—31no—
70#5521—31no—
71C3×#459—31no—
72#5233—31no—
73#5215—31no—
74#5153—31no—
75#5150—31no—
76#5072—31no—
77#5072—31no—
78#5072—31no—
79#5072—31no—
80#5072—61no—
81#5072D311yescharacteristic, complemented
82#5057—31no—
83#5057—31no—
84#5057—31no—
85#5057—31no—
86#5016—31no—
87#4999—31no—
88#4844—31no—
89#4839—31no—
90#4787—31no—
91#4786—31no—
92#4772—31no—
93#4770—31no—
94C23×C3×D3—21no—
95C22×D32—21no—
96C2×C32×D4—21no—
97C2×C32×D4—21no—
98C2×C32×D4C2311yescharacteristic
99C2×C32×D4C2311yescharacteristic
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C4×C3⋊D3—21no—
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C2×C3×#67—21no—
105C2×C3×#67—21no—
106C22×C3×Dic3—21no—
107C3×#237—22no—
108C3×#237—22no—
109C3×D3×D4—22no—
110C3×D3×D4—22no—
111C2×C3×D12C2311yescharacteristic
112C2×C3×D12C2311yescharacteristic
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3C2311yescharacteristic
115C2×C3×Dic6C2311yescharacteristic
116C2×#626—21no—
117C2×#624—21no—
118C2×D3×Dic3—21no—
119D3×D12—22no—
120D3×D12D414yescomplemented
121C32×C42C2311yescharacteristic
122#3753—22no—
123#3753—22no—
124#3752—21no—
125C4⋊(C3⋊Dic3)C2311yescharacteristic
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128C3×#217—21no—
129C3×#217—21no—
130C3×#213—22no—
131C3×#213—22no—
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4D411yescharacteristic
136C3×(C2×D3)⋊C4D411yescharacteristic
137C3×C4⋊Dic3C2311yescharacteristic
138C3×Dic3⋊C4D411yescharacteristic
139C3×Dic3⋊C4D411yescharacteristic
140C3×C4×Dic3C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143#3722—21no—
144(C2×D3)⋊Dic3—21no—
145(C2×D3)⋊Dic3—21no—
146Dic32—21no—
147#3717—22no—
148#3715—22no—
149#3714—22no—
150#3713—22no—
151#3711—22no—
152D3×C3⋊C8—22no—
153#3041—91noSylow
154C2×C3×#41—31no—
155C22×C3×D4—31no—
156C2×#237C2×D311yescharacteristic
157C2×D3×D4—31no—
158C2×D3×D4C2×D311yescharacteristic
159C22×D12—31no—
160C2×C3×D8—31no—
161C2×C3×D8—31no—
162C3×#127—21no—
163C3×#127—31no—
164C3×#127C2×D311yescharacteristic, complemented
165C3×#127C2×D311yescharacteristic, complemented
166C3×#124—31no—
167C3×#124—31no—
168C3×#121—61no—
169C3×#121—61no—
170C3×#120—61no—
171C3×#120—61no—
172C3×C4×D4—31no—
173C3×#117—31no—
174#949—64no—
175C2×#215—31no—
176C2×#215—31no—
177#940C2×D311yescharacteristic, complemented
178#939—21no—
179#939—21no—
180#937—21no—
181#937—21no—
182#936C2×D311yescharacteristic, complemented
183D4×Dic3—31no—
184C2×#214—31no—
185C2×#213—31no—
186C2×#213—31no—
187C2×#213—31no—
188C2×#213—31no—
189C2×#213—31no—
190C2×#213—31no—
191C2×#213—31no—
192C2×#213—61no—
193C2×#213—61no—
194C2×#213—64no—
195C2×#213C2×D311yescharacteristic
196C2×#213C2×D311yescharacteristic, complemented
197C4×#67—61no—
198C2×(C2×D3)⋊C4—61no—
199#926—31no—
200C2×#208—31no—
201C22×C3⋊C8—31no—
202#911—64no—
203D3×D8—64no—
204C2×D24—31no—
205C2×#204—31no—
206C2×ΓL(1,𝔽25)—31no—
207C2×D3×C8—31no—
208#893—31no—
209#893—61no—
210#893—61no—
211#892—31no—
212#67⋊C4—61no—
213D3×C22⋊C4—61no—
214D3×C22⋊C4—61no—
215D3×C22⋊C4—61no—
216#875C2×D311yescharacteristic, complemented
217C4×D12—31no—
218C4×D12—31no—
219C4×D12—31no—
220C4×D12—31no—
221C4×D12—61no—
222C4×D12C2×D311yescharacteristic, complemented
223#872C2×D311yescharacteristic
224C3×C4⋊C8—31no—
225C3×#102—31no—
226C3×#102—31no—
227#835—31no—
228#835—31no—
229#832—31no—
230#832—31no—
231#832—31no—
232#832—31no—
233#832—31no—
234#832—31no—
235#832—61no—
236#832—61no—
237#832C2×D311yescharacteristic, complemented
238#832C2×D311yescharacteristic, complemented
239#821—31no—
240#816—31no—
241Dic3⋊C8—31no—
242Dic3⋊C8—31no—
243#810—31no—
244#809—31no—
245C4⋊(C3⋊C8)—31no—
246C4⋊(C3⋊C8)—31no—
247C4⋊(C3⋊C8)—31no—
248C4⋊(C3⋊C8)—31no—
249C4⋊(C3⋊C8)—61no—
250C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
251C23×C32—21no—
252C23×C32—21no—
253C22×C3⋊D3—21no—
254C22×C3×D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3—42no—
257C22×C3×D3—81no—
258C22×C3×D3—81no—
259C22×C3×D3C2×D411yescharacteristic
260C2×D32—24no—
261C2×D32—81no—
262C2×D32—81no—
263C32×D4—21no—
264C32×D4—21no—
265C32×D4—21no—
266C32×D4—21no—
267C32×D4—81no—
268C32×D4—81no—
269C2×C32×C4C2×D411yescharacteristic
270C2×C32×C4C2×D411yescharacteristic
271C2×C32×C4C2411yescharacteristic
272C2×C3⋊Dic3—21no—
273C4⋊(C3⋊D3)—21no—
274C4⋊(C3⋊D3)C2×D412yes—
275C4×C3⋊D3—81no—
276C3×#67—42no—
277C3×#67—42no—
278C3×#67—81no—
279C3×#67—81no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—42no—
283C2×C3×Dic3C2×D411yescharacteristic
284C2×C3×Dic3C2×D411yescharacteristic
285C2×C3×Dic3C2×D411yescharacteristic
286C3×D12—21no—
287C3×D12—21no—
288C3×D12—21no—
289C3×D12C2×D412yes—
290C3×C4×D3—81no—
291C3×C4×D3C2×D412yes—
292C3×C4×D3#4112yes—
293C3×Dic6—21no—
294C3×Dic6—21no—
295#626—24no—
296#624—81no—
297D3×Dic3—81no—
298C3⋊(C3⋊C8)—21no—
299C3⋊(C3⋊C8)—21no—
300C3×C3⋊C8—21no—
301C3×C3⋊C8—21no—
302C2×AGL(1,ℤ/8)—91no—
303C22×D8—91no—
304#535—31no—
305#518—91no—
306#463—91no—
307#463—91no—
308#463—91no—
309#463—91no—
310#459—31no—
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—31no—
324C2×C3×D4—21no—
325C2×C3×D4—21no—
326C2×C3×D4—21no—
327C2×C3×D4—21no—
328C2×C3×D4—21no—
329C2×C3×D4—21no—
330C2×C3×D4—31no—
331C2×C3×D4—31no—
332C2×C3×D4—41no—
333C2×C3×D4—41no—
334C2×C3×D4—62no—
335C2×C3×D4—62no—
336C2×C3×D4—61no—
337C2×C3×D4—61no—
338C2×C3×D4—61no—
339C2×C3×D4—61no—
340C2×C3×D4C22×D311yescharacteristic
341C2×C3×D4C22×D311yescharacteristic
342C2×C3×D4C22×D311yescharacteristic
343C2×C3×D4C22×D311yescharacteristic
344C22×C3×C4—31no—
345C22×C3×C4—61no—
346C22×C3×C4—61no—
347C2×#67—21no—
348C2×#67—21no—
349C2×#67—21no—
350C2×#67—21no—
351C2×#67—61no—
352C22×Dic3—21no—
353C22×Dic3—61no—
354#237—22no—
355#237—22no—
356D3×D4—22no—
357D3×D4—22no—
358D3×D4—34no—
359D3×D4—62no—
360C2×D12—31no—
361C2×D12—31no—
362C2×D12—34no—
363C2×D12—61no—
364C2×D12—62no—
365C2×D12—61no—
366C2×D12C22×D311yescharacteristic
367C2×D12C22×D311yescharacteristic
368C2×C4×D3—21no—
369C2×C4×D3—61no—
370C2×C4×D3—61no—
371C2×C4×D3—61no—
372C2×C4×D3—61no—
373C2×C4×D3—61no—
374C2×C4×D3—121no—
375C2×C4×D3C22×D311yescharacteristic
376C2×Dic6C22×D311yescharacteristic
377C3×D8—62no—
378C3×D8—62no—
379C2×C3×C8—31no—
380C2×C3×C8—31no—
381C3×C4⋊C4—31no—
382C3×C4⋊C4—31no—
383C3×C4⋊C4—31no—
384C3×C22⋊C4—31no—
385C3×C22⋊C4—31no—
386C3×C22⋊C4—61no—
387C3×C22⋊C4—61no—
388C3×C22⋊C4—61no—
389C3×C22⋊C4—61no—
390C3×C22⋊C4—61no—
391C3×C42—21no—
392C3×C42—31no—
393C3×C42C22×D311yescharacteristic
394C3×C42C22×D311yescharacteristic
395#217—21no—
396#217—21no—
397#217—61no—
398#217—61no—
399#215—62no—
400#215—62no—
401#214—62no—
402#213—22no—
403#213—22no—
404#213—62no—
405#213—62no—
406#213—62no—
407#213—62no—
408#213—62no—
409#213—62no—
410#213—62no—
411#213—122no—
412#213—122no—
413(C2×D3)⋊C4—21no—
414(C2×D3)⋊C4—21no—
415(C2×D3)⋊C4—21no—
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#6711yescharacteristic
424(C2×D3)⋊C4#6711yescharacteristic
425C4⋊Dic3—31no—
426C4⋊Dic3—31no—
427C4⋊Dic3—61no—
428C4⋊Dic3C22×D311yescharacteristic
429Dic3⋊C4#6711yescharacteristic
430Dic3⋊C4#6711yescharacteristic
431C4×Dic3—61no—
432C4×Dic3—61no—
433C4×Dic3C22×D311yescharacteristic
434#208—62no—
435C2×C3⋊C8—31no—
436C2×C3⋊C8—31no—
437C2×C3⋊C8—31no—
438C2×C3⋊C8—31no—
439C2×C3⋊C8—61no—
440C2×C3⋊C8—61no—
441C2×C3⋊C8—62no—
442C2×C3⋊C8C22×D311yescharacteristic
443C2×C3⋊C8C22×D311yescharacteristic
444D24—62no—
445#204—62no—
446ΓL(1,𝔽25)—62no—
447D3×C8—62no—
448C22×C32—41no—
449C22×C32—41no—
450C22×C32—41no—
451C22×C32—41no—
452C22×C32—41no—
453C22×C32—41no—
454C22×C32C22×D411yescharacteristic
455C2×C3⋊D3—22no—
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#12112yes—
468D32—84no—
469C32×C4—21no—
470C32×C4—21no—
471C32×C4C22×D411yescharacteristic
472C32×C4C2×#4111yescharacteristic
473C3⋊Dic3—41no—
474C3×Dic3—21no—
475C3×Dic3—21no—
476C3×Dic3—41no—
477C3×Dic3—41no—
478C3×Dic3#12112yes—
479C2×#41—31no—
480C22×D4—31no—
481C22×D4—91no—
482AGL(1,ℤ/8)—184no—
483C2×SD16—91no—
484C2×SD16—91no—
485C2×D8—31no—
486C2×D8—31no—
487C2×D8—91no—
488C2×D8—91no—
489C2×D8—91no—
490C2×D8—91no—
491C2×D8—184no—
492C2×M16—91no—
493C22×C8—91no—
494#127—31no—
495#127D3211yescharacteristic, complemented
496#124—31no—
497#124—31no—
498#121—61no—
499#121—61no—
500#120—61no—
501#120—61no—
502C4×D4—31no—
503C4×D4—91no—
504C4×D4—91no—
505C4×D4—91no—
506C4×D4—181no—
507C4×D4—181no—
508#117—31no—
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—91no—
517#103—91no—
518#102—31no—
519#102—31no—
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—61no—
532C23×C3—61no—
533C23×C3—122no—
534C23×C3—241no—
535C23×C3—241no—
536C22×D3—21no—
537C22×D3—21no—
538C22×D3—42no—
539C22×D3—64no—
540C22×D3—61no—
541C22×D3—61no—
542C22×D3—64no—
543C22×D3—81no—
544C22×D3—81no—
545C22×D3—121no—
546C22×D3—241no—
547C22×D3—241no—
548C22×D3—241no—
549C22×D3—241no—
550C22×D3C2×#6711yescharacteristic
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—21no—
560C3×D4—21no—
561C3×D4—32no—
562C3×D4—41no—
563C3×D4—41no—
564C3×D4—41no—
565C3×D4—41no—
566C3×D4—61no—
567C3×D4—61no—
568C3×D4—61no—
569C3×D4—81no—
570C3×D4—81no—
571C3×D4—81no—
572C3×D4—81no—
573C3×D4—82no—
574C3×D4—82no—
575C3×D4—122no—
576C3×D4—122no—
577C3×D4—241no—
578C3×D4—241no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—31no—
583C2×C3×C4—32no—
584C2×C3×C4—32no—
585C2×C3×C4—31no—
586C2×C3×C4—31no—
587C2×C3×C4—61no—
588C2×C3×C4—61no—
589C2×C3×C4—122no—
590C2×C3×C4—241no—
591C2×C3×C4D3×D411yescharacteristic
592C2×C3×C4D3×D411yescharacteristic
593C2×C3×C4C2×#6711yescharacteristic
594C2×C3×C4C2×#6711yescharacteristic
595C2×C3×C4C23×D311yescharacteristic
596C2×C3×C4C23×D311yescharacteristic
597#67—42no—
598#67—42no—
599#67—64no—
600#67—81no—
601#67—81no—
602C2×Dic3—21no—
603C2×Dic3—21no—
604C2×Dic3—42no—
605C2×Dic3—61no—
606C2×Dic3—61no—
607C2×Dic3—121no—
608C2×Dic3—241no—
609C2×Dic3C2×#6711yescharacteristic
610C2×Dic3C2×#6711yescharacteristic
611C2×Dic3C2×#6711yescharacteristic
612D12—21no—
613D12—21no—
614D12—21no—
615D12—32no—
616D12—32no—
617D12—62no—
618D12—64no—
619D12—61no—
620D12—61no—
621D12—121no—
622D12D3×D412yes—
623C4×D3—81no—
624C4×D3—241no—
625C4×D3—241no—
626C4×D3—241no—
627C4×D3—241no—
628C4×D3—241no—
629C4×D3—242no—
630C4×D3D3×D412yes—
631C4×D3#23712yes—
632Dic6—21no—
633Dic6—21no—
634C3×C8—61no—
635C3×C8—61no—
636C3⋊C8—21no—
637C3⋊C8—21no—
638C3⋊C8—61no—
639C3⋊C8—61no—
640C3⋊C8—61no—
641C3⋊C8—61no—
642C3⋊C8—121no—
643C3⋊C8—121no—
644C2×C32—81no—
645C2×C32—81no—
646C2×C32C2×#12111yescharacteristic
647C2×C32#57611yescharacteristic
648C2×C32#57611yescharacteristic
649C3⋊D3—42no—
650C3×D3—22no—
651C3×D3—42no—
652C3×D3—81no—
653C24—61no—
654C24—181no—
655#41—62no—
656#41—62no—
657C2×Q8—31no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—31no—
661C2×D4—31no—
662C2×D4—62no—
663C2×D4—62no—
664C2×D4—61no—
665C2×D4—61no—
666C2×D4—61no—
667C2×D4—61no—
668C2×D4—94no—
669C2×D4—91no—
670C2×D4—182no—
671C2×D4—181no—
672C2×D4C2×D3211yescharacteristic
673C2×D4C2×D3211yescharacteristic
674C22×C4—31no—
675C22×C4—61no—
676C22×C4—61no—
677C22×C4—181no—
678C22×C4—181no—
679C22×C4—181no—
680SD16—182no—
681SD16—182no—
682D8—62no—
683D8—62no—
684D8—182no—
685D8—182no—
686D8—182no—
687D8—182no—
688M16—182no—
689C2×C8—31no—
690C2×C8—31no—
691C2×C8—91no—
692C2×C8—91no—
693C2×C8—182no—
694C4⋊C4—31no—
695C4⋊C4—31no—
696C4⋊C4—31no—
697C4⋊C4—91no—
698C22⋊C4—31no—
699C22⋊C4—31no—
700C22⋊C4—61no—
701C22⋊C4—61no—
702C22⋊C4—61no—
703C22⋊C4—61no—
704C22⋊C4—61no—
705C22⋊C4—181no—
706C22⋊C4—181no—
707C22⋊C4—181no—
708C22⋊C4—181no—
709C42—31no—
710C42—181no—
711C42C2×D3211yescharacteristic
712C22×C3—21no—
713C22×C3—32no—
714C22×C3—41no—
715C22×C3—41no—
716C22×C3—41no—
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—61no—
727C22×C3—61no—
728C22×C3—62no—
729C22×C3—81no—
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×C3C2×D3×D411yescharacteristic
742C22×C3C22×#6711yescharacteristic
743C2×D3—21no—
744C2×D3—21no—
745C2×D3—22no—
746C2×D3—41no—
747C2×D3—41no—
748C2×D3—41no—
749C2×D3—41no—
750C2×D3—41no—
751C2×D3—62no—
752C2×D3—62no—
753C2×D3—84no—
754C2×D3—122no—
755C2×D3—121no—
756C2×D3—121no—
757C2×D3—121no—
758C2×D3—121no—
759C2×D3—241no—
760C2×D3—241no—
761C2×D3—244no—
762C2×D3—244no—
763C2×D3#93812yes—
764C3×C4—22no—
765C3×C4—21no—
766C3×C4—21no—
767C3×C4—21no—
768C3×C4—21no—
769C3×C4—21no—
770C3×C4—21no—
771C3×C4—32no—
772C3×C4—41no—
773C3×C4—61no—
774C3×C4—61no—
775C3×C4—121no—
776C3×C4—121no—
777C3×C4C2×D3×D411yescharacteristic
778C3×C4C2×D3×D411yescharacteristic
779C3×C4C2×#23711yescharacteristic
780C3×C4D3×#4111yescharacteristic
781Dic3—21no—
782Dic3—21no—
783Dic3—41no—
784Dic3—41no—
785Dic3—121no—
786Dic3—121no—
787Dic3—241no—
788Dic3#93812yes—
789C32#304111yescharacteristic, complemented, Sylow
790C23—21no—
791C23—21no—
792C23—31no—
793C23—61no—
794C23—61no—
795C23—122no—
796C23—184no—
797C23—181no—
798C23—241no—
799C23—241no—
800C23—721no—
801C23—721no—
802Q8—61no—
803Q8—61no—
804D4—21no—
805D4—21no—
806D4—21no—
807D4—21no—
808D4—32no—
809D4—61no—
810D4—61no—
811D4—61no—
812D4—81no—
813D4—81no—
814D4—92no—
815D4—122no—
816D4—122no—
817D4—184no—
818D4—181no—
819D4—241no—
820D4—241no—
821C2×C4—31no—
822C2×C4—32no—
823C2×C4—32no—
824C2×C4—31no—
825C2×C4—31no—
826C2×C4—61no—
827C2×C4—61no—
828C2×C4—122no—
829C2×C4—181no—
830C2×C4—241no—
831C2×C4—721no—
832C2×C4—721no—
833C2×C4—721no—
834C2×C4D3×#6711yescharacteristic
835C2×C4D3×#6711yescharacteristic
836C2×C4C22×D3211yescharacteristic
837C8—61no—
838C8—61no—
839C8—181no—
840C8—181no—
841C2×C3—21no—
842C2×C3—21no—
843C2×C3—21no—
844C2×C3—62no—
845C2×C3—81no—
846C2×C3—81no—
847C2×C3—81no—
848C2×C3—81no—
849C2×C3—122no—
850C2×C3—161no—
851C2×C3—161no—
852C2×C3—241no—
853C2×C3D3×#12111yescharacteristic
854C2×C3#575711yescharacteristic
855C2×C3#577411yescharacteristic
856C2×C3C2×#93811yescharacteristic
857C2×C3#583511yescharacteristic
858C2×C3#583511yescharacteristic
859D3—22no—
860D3—42no—
861D3—81no—
862D3—122no—
863D3—122no—
864D3—242no—
865C22—32no—
866C22—41no—
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—182no—
881C22—244no—
882C22—361no—
883C22—361no—
884C22—724no—
885C22C2×D3×#6711yescharacteristic
886C4—21no—
887C4—21no—
888C4—32no—
889C4—61no—
890C4—61no—
891C4—121no—
892C4—121no—
893C4—361no—
894C4D32×D411yescharacteristic
895C4D3×#23711yescharacteristic
896C3—21no—
897C3#8033411yescharacteristic, complemented
898C3#8338411yescharacteristic, complemented
899C2—62no—
900C2—81no—
901C2—81no—
902C2—122no—
903C2—241no—
904C2—362no—
905C2#1059509611yescharacteristic
906C2#1059509711yescharacteristic
907C2D3×#93811yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#127C22
socleC22×C32C22×D4
hypercenter#127D32
hypocenterC32#3041
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. C3×#5715C2semidirect
2. C2×#63925C2semidirect
3. C2×D3×#213C2semidirect
4. #10593994C2semidirect
5. #10592771C2semidirect
6. C3×#5072C2semidirect
7. #10591432C2semidirect
8. #10591431C2semidirect
9. #10591429C2semidirect
10. #10591428C2semidirect
11. #10591421C2semidirect
12. #10591420C2semidirect
13. #10590356C2semidirect
14. #10590348C2semidirect
15. #10590324C2semidirect
21. C32×#127C22semidirect
23. C2×#3753C22semidirect
24. C4×C4⋊(C3⋊D3)C22semidirect
25. C3×#940C22semidirect
30. C3×#936C22semidirect
32. C2×C3×#213C22semidirect
33. C3×#875C22semidirect
34. C3×C4×D12C22semidirect
41. #63894C22semidirect
42. Dic3×D12C22semidirect
45. C2×#3717C22semidirect
46. C2×#3715C22semidirect
51. #63659C22semidirect
52. #63659C22semidirect
53. C4⋊(C3⋊(C3⋊C8))C22semidirect
54. C3×#832C22semidirect
55. C3×#832C22semidirect
56. C3×C4⋊(C3⋊C8)C22semidirect
57. Dic3⋊(C3⋊C8)C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
59. #63566C22semidirect
60. #63565C22semidirect
61. #63563C22semidirect
62. #63562C22semidirect
68. #5715D3semidirect
81. #5072D3semidirect
120. D3×D12D4semidirect
164. C3×#127C2×D3semidirect
165. C3×#127C2×D3semidirect
177. #940C2×D3semidirect
182. #936C2×D3semidirect
196. C2×#213C2×D3semidirect
216. #875C2×D3semidirect
222. C4×D12C2×D3semidirect
237. #832C2×D3semidirect
238. #832C2×D3semidirect
250. C4⋊(C3⋊C8)C2×D3semidirect
495. #127D32semidirect
789. C32#3041semidirect
897. C3#80334semidirect
898. C3#83384semidirect

Maximal subgroups

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

subgroupindex
C3×#57152
C2×#639252
C2×D3×#2132
#105939942
#105927712
C3×#50722
#105914322
#105914312
#105914292
#105914282
#105914212
#105914202
#105903562
#105903482
#105903242
#833843
#803343