Finite Group Databasebeta

← #11866186

Subgroups — #11866186

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
1C3×#5674C211yesmaximal, characteristic, complemented
2C2×#63939C211yesmaximal, characteristic, complemented
3C2×D3×#213C211yesmaximal, characteristic, complemented
4#10593994C211yesmaximal, characteristic, complemented
5#10592756C211yesmaximal, characteristic, complemented
6C3×#5057C211yesmaximal, characteristic, complemented
7#10591568C211yesmaximal, characteristic, complemented
8#10591567C211yesmaximal, characteristic, complemented
9#10591556C211yesmaximal, characteristic, complemented
10#10591429C211yesmaximal, characteristic, complemented
11#10591428C211yesmaximal, characteristic, complemented
12#10591421C211yesmaximal, characteristic, complemented
13#10590355C211yesmaximal, characteristic, complemented
14#10590347C211yesmaximal, characteristic, complemented
15#10590324C211yesmaximal, characteristic, complemented
16#83384—31nomaximal
17#80536—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C2×D3×D12C2211yescharacteristic
21C32×#124C2211yescharacteristic, complemented
22C2×#3755C2211yescharacteristic, complemented
23C2×#3753C2211yescharacteristic
24C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
25C3×#947C2211yescharacteristic, complemented
26C2×C3×#215C2211yescharacteristic, complemented
27C3×#940C2211yescharacteristic, complemented
28C2×C3×#213C2211yescharacteristic
29C3×#884—21no—
30C3×#884—21no—
31C3×#882—21no—
32C3×#882—21no—
33C3×#874C2211yescharacteristic, complemented
34C3×C4×D12C2211yescharacteristic, complemented
35C3×#872C2211yescharacteristic
36#63939—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×#3714C2211yescharacteristic
46C2×#3714C2211yescharacteristic, complemented
47C2×#3713C2211yescharacteristic
48C2×#3713C2211yescharacteristic, complemented
49C2×#3711C2211yescharacteristic
50C2×D3×C3⋊C8C2211yescharacteristic
51#63662C2211yescharacteristic, complemented
52#63659C2211yescharacteristic, complemented
53C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
54C3×#835C2211yescharacteristic, complemented
55C3×#832C2211yescharacteristic, complemented
56C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
57Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63563C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61#63562C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63C3×#535—31no—
64C2×#949—31no—
65C22×#213—31no—
66C2×#914—31no—
67C2×D3×D8—31no—
68#5674D311yescharacteristic, complemented
69#5545—31no—
70#5521—31no—
71C3×#463—31no—
72#5233—31no—
73#5215—31no—
74#5165—31no—
75#5150—31no—
76#5072—31no—
77#5072—31no—
78#5072—31no—
79#5072—31no—
80#5057—31no—
81#5057—31no—
82#5057—31no—
83#5057—31no—
84#5057—61no—
85#5057D311yescharacteristic, complemented
86#5015—31no—
87#4999—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
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4×C3⋊D3—21no—
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C3×#239—22no—
104C3×#239—22no—
105C3×D3×D4—22no—
106C3×D3×D4—22no—
107C2×C3×D12—21no—
108C2×C3×D12—21no—
109C2×C3×D12—21no—
110C2×C3×D12C2311yescharacteristic
111C2×C3×D12C2311yescharacteristic
112C2×C3×D12C2311yescharacteristic
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3—21no—
115C2×C3×C4×D3C2311yescharacteristic
116C2×#626—21no—
117C2×#624—21no—
118C2×D3×Dic3—21no—
119D3×D12—22no—
120D3×D12D414yescomplemented
121C32×C22⋊C4—21no—
122C32×C22⋊C4—21no—
123C32×C42C2311yescharacteristic
124#3755—22no—
125#3753—22no—
126#3752—21no—
127C4⋊(C3⋊Dic3)C2311yescharacteristic
128C2×C3⋊(C3⋊C8)C2311yescharacteristic
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130C3×#215—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#3714—22no—
148#3714—22no—
149#3713—22no—
150#3713—22no—
151#3711—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—
160C2×C3×SD16—31no—
161C2×C3×D8—31no—
162C3×#127—31no—
163C3×#127—31no—
164C3×#124—21no—
165C3×#124—31no—
166C3×#124C2×D311yescharacteristic, complemented
167C3×#124C2×D311yescharacteristic, complemented
168C3×#121—61no—
169C3×#121—61no—
170C3×#120—61no—
171C3×#120—61no—
172C3×C4×D4—31no—
173C3×#117—31no—
174#949—64no—
175#947C2×D311yescharacteristic, complemented
176C2×#215—31no—
177C2×#215—31no—
178C2×#215—61no—
179C2×#215C2×D311yescharacteristic, complemented
180#940C2×D311yescharacteristic, complemented
181D4×Dic3—31no—
182C2×#213—31no—
183C2×#213—31no—
184C2×#213—31no—
185C2×#213—31no—
186C2×#213—31no—
187C2×#213—31no—
188C2×#213—31no—
189C2×#213—31no—
190C2×#213—61no—
191C2×#213—64no—
192C2×#213C2×D311yescharacteristic
193C4×#67—61no—
194C2×(C2×D3)⋊C4—61no—
195#926—31no—
196C2×#208—31no—
197C22×C3⋊C8—31no—
198#914—64no—
199D3×D8—64no—
200C2×D24—31no—
201C2×D24—31no—
202C2×ΓL(1,𝔽25)—31no—
203C2×D3×C8—31no—
204#893—31no—
205#893—61no—
206#893—61no—
207#892—31no—
208#884—21no—
209#884—21no—
210#882—21no—
211#882—21no—
212#67⋊C4—61no—
213D3×C22⋊C4—61no—
214D3×C22⋊C4—61no—
215D3×C22⋊C4—61no—
216#874C2×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×#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#832—31no—
235#832—31no—
236#832—31no—
237#832—61no—
238#832C2×D311yescharacteristic, complemented
239#821—31no—
240#821—31no—
241Dic3⋊C8—31no—
242Dic3⋊C8—31no—
243#809—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—
252C22×C3⋊D3—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×Q8—21no—
264C32×Q8—21no—
265C32×D4—21no—
266C32×D4—21no—
267C2×C32×C4—21no—
268C2×C32×C4C2×D411yescharacteristic
269C2×C32×C4C2×D411yescharacteristic
270C2×C32×C4C2411yescharacteristic
271C2×C3⋊Dic3—21no—
272C4⋊(C3⋊D3)—21no—
273C4⋊(C3⋊D3)C2×D412yes—
274C4×C3⋊D3—81no—
275C3×#67—42no—
276C3×#67—81no—
277C3×#67—81no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3C2×D411yescharacteristic
280C2×C3×Dic3C2×D411yescharacteristic
281C2×C3×Dic3C2×D411yescharacteristic
282C3×D12—21no—
283C3×D12—21no—
284C3×D12—21no—
285C3×D12—21no—
286C3×D12—21no—
287C3×D12—42no—
288C3×D12—81no—
289C3×D12—81no—
290C3×D12C2×D412yes—
291C3×C4×D3—42no—
292C3×C4×D3—81no—
293C3×C4×D3C2×D412yes—
294C3×C4×D3#4112yes—
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—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—31no—
328C2×C3×D4—31no—
329C2×C3×D4—31no—
330C2×C3×D4—61no—
331C2×C3×D4—62no—
332C2×C3×D4—62no—
333C2×C3×D4—61no—
334C2×C3×D4—61no—
335C2×C3×D4—61no—
336C2×C3×D4—61no—
337C2×C3×D4—61no—
338C2×C3×D4C22×D311yescharacteristic
339C2×C3×D4C22×D311yescharacteristic
340C22×C3×C4—31no—
341C22×C3×C4—61no—
342C22×C3×C4—61no—
343C2×#67—21no—
344C2×#67—21no—
345C2×#67—21no—
346C2×#67—61no—
347C22×Dic3—61no—
348#239—22no—
349#239—22no—
350D3×D4—22no—
351D3×D4—22no—
352D3×D4—34no—
353D3×D4—62no—
354C2×D12—21no—
355C2×D12—21no—
356C2×D12—21no—
357C2×D12—31no—
358C2×D12—31no—
359C2×D12—34no—
360C2×D12—61no—
361C2×D12—62no—
362C2×D12—61no—
363C2×D12C22×D311yescharacteristic
364C2×D12C22×D311yescharacteristic
365C2×D12C22×D311yescharacteristic
366C2×C4×D3—21no—
367C2×C4×D3—21no—
368C2×C4×D3—61no—
369C2×C4×D3—61no—
370C2×C4×D3—61no—
371C2×C4×D3—61no—
372C2×C4×D3—61no—
373C2×C4×D3—121no—
374C2×C4×D3C22×D311yescharacteristic
375C3×SD16—62no—
376C3×D8—62no—
377C2×C3×C8—31no—
378C2×C3×C8—31no—
379C3×C4⋊C4—31no—
380C3×C4⋊C4—31no—
381C3×C4⋊C4—31no—
382C3×C22⋊C4—21no—
383C3×C22⋊C4—21no—
384C3×C22⋊C4—21no—
385C3×C22⋊C4—21no—
386C3×C22⋊C4—31no—
387C3×C22⋊C4—31no—
388C3×C22⋊C4—41no—
389C3×C22⋊C4—41no—
390C3×C22⋊C4—61no—
391C3×C22⋊C4—61no—
392C3×C22⋊C4—61no—
393C3×C42—21no—
394C3×C42—31no—
395C3×C42C22×D311yescharacteristic
396C3×C42C22×D311yescharacteristic
397#217—61no—
398#217—61no—
399#215—22no—
400#215—62no—
401#215—62no—
402#215—122no—
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—62no—
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—
445D24—62no—
446ΓL(1,𝔽25)—62no—
447D3×C8—62no—
448C22×C32—41no—
449C22×C32—41no—
450C22×C32—41no—
451C22×C32C22×D411yescharacteristic
452C2×C3⋊D3—22no—
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—21no—
470C32×C4—21no—
471C32×C4—41no—
472C32×C4C22×D411yescharacteristic
473C32×C4C2×#4111yescharacteristic
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)—184no—
483C2×SD16—31no—
484C2×SD16—91no—
485C2×D8—31no—
486C2×D8—91no—
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#127—31no—
496#124—31no—
497#124D3211yescharacteristic, complemented
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—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—61no—
529C23×C3—61no—
530C23×C3—61no—
531C23×C3—122no—
532C23×C3—241no—
533C23×C3—241no—
534C22×D3—21no—
535C22×D3—21no—
536C22×D3—21no—
537C22×D3—42no—
538C22×D3—64no—
539C22×D3—61no—
540C22×D3—61no—
541C22×D3—64no—
542C22×D3—81no—
543C22×D3—81no—
544C22×D3—121no—
545C22×D3—241no—
546C22×D3—241no—
547C22×D3—241no—
548C22×D3—241no—
549C22×D3C2×#6711yescharacteristic
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—21no—
559C3×D4—21no—
560C3×D4—32no—
561C3×D4—41no—
562C3×D4—41no—
563C3×D4—61no—
564C3×D4—61no—
565C3×D4—61no—
566C3×D4—61no—
567C3×D4—61no—
568C3×D4—122no—
569C3×D4—122no—
570C3×D4—241no—
571C3×D4—241no—
572C3×D4—241no—
573C3×D4—241no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—31no—
580C2×C3×C4—32no—
581C2×C3×C4—32no—
582C2×C3×C4—31no—
583C2×C3×C4—31no—
584C2×C3×C4—41no—
585C2×C3×C4—61no—
586C2×C3×C4—122no—
587C2×C3×C4—241no—
588C2×C3×C4D3×D411yescharacteristic
589C2×C3×C4D3×D411yescharacteristic
590C2×C3×C4C2×#6711yescharacteristic
591C2×C3×C4C2×#6711yescharacteristic
592C2×C3×C4C23×D311yescharacteristic
593C2×C3×C4C23×D311yescharacteristic
594#67—42no—
595#67—64no—
596#67—81no—
597#67—81no—
598C2×Dic3—21no—
599C2×Dic3—61no—
600C2×Dic3—61no—
601C2×Dic3—121no—
602C2×Dic3—241no—
603C2×Dic3C2×#6711yescharacteristic
604C2×Dic3C2×#6711yescharacteristic
605C2×Dic3C2×#6711yescharacteristic
606D12—21no—
607D12—21no—
608D12—21no—
609D12—21no—
610D12—21no—
611D12—32no—
612D12—32no—
613D12—42no—
614D12—62no—
615D12—64no—
616D12—61no—
617D12—61no—
618D12—81no—
619D12—81no—
620D12—121no—
621D12D3×D412yes—
622C4×D3—42no—
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—
632C3×C8—61no—
633C3×C8—61no—
634C3⋊C8—21no—
635C3⋊C8—21no—
636C3⋊C8—61no—
637C3⋊C8—61no—
638C3⋊C8—61no—
639C3⋊C8—61no—
640C3⋊C8—121no—
641C3⋊C8—121no—
642C2×C32—81no—
643C2×C32C2×#12111yescharacteristic
644C2×C32#57611yescharacteristic
645C2×C32#57611yescharacteristic
646C3⋊D3—42no—
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—31no—
657C2×D4—31no—
658C2×D4—31no—
659C2×D4—61no—
660C2×D4—62no—
661C2×D4—62no—
662C2×D4—61no—
663C2×D4—61no—
664C2×D4—61no—
665C2×D4—61no—
666C2×D4—61no—
667C2×D4—94no—
668C2×D4—91no—
669C2×D4—182no—
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—62no—
679SD16—182no—
680D8—62no—
681D8—182no—
682D8—182no—
683D8—182no—
684D8—182no—
685D8—182no—
686M16—182no—
687C2×C8—31no—
688C2×C8—31no—
689C2×C8—91no—
690C2×C8—91no—
691C2×C8—182no—
692C4⋊C4—31no—
693C4⋊C4—31no—
694C4⋊C4—31no—
695C4⋊C4—91no—
696C22⋊C4—21no—
697C22⋊C4—21no—
698C22⋊C4—31no—
699C22⋊C4—31no—
700C22⋊C4—61no—
701C22⋊C4—61no—
702C22⋊C4—61no—
703C22⋊C4—181no—
704C22⋊C4—181no—
705C22⋊C4—181no—
706C22⋊C4—181no—
707C42—31no—
708C42—181no—
709C42C2×D3211yescharacteristic
710C22×C3—21no—
711C22×C3—32no—
712C22×C3—41no—
713C22×C3—41no—
714C22×C3—41no—
715C22×C3—41no—
716C22×C3—41no—
717C22×C3—41no—
718C22×C3—61no—
719C22×C3—61no—
720C22×C3—62no—
721C22×C3—81no—
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×C3C22×#6711yescharacteristic
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—62no—
747C2×D3—62no—
748C2×D3—84no—
749C2×D3—122no—
750C2×D3—121no—
751C2×D3—121no—
752C2×D3—121no—
753C2×D3—121no—
754C2×D3—241no—
755C2×D3—241no—
756C2×D3—244no—
757C2×D3—244no—
758C2×D3#93812yes—
759C3×C4—21no—
760C3×C4—21no—
761C3×C4—21no—
762C3×C4—21no—
763C3×C4—21no—
764C3×C4—21no—
765C3×C4—32no—
766C3×C4—41no—
767C3×C4—41no—
768C3×C4—41no—
769C3×C4—41no—
770C3×C4—61no—
771C3×C4—61no—
772C3×C4—81no—
773C3×C4—121no—
774C3×C4C2×D3×D411yescharacteristic
775C3×C4C2×D3×D411yescharacteristic
776C3×C4C2×#23711yescharacteristic
777C3×C4D3×#4111yescharacteristic
778Dic3—21no—
779Dic3—21no—
780Dic3—41no—
781Dic3—121no—
782Dic3—121no—
783Dic3—241no—
784Dic3#93812yes—
785C32#304111yescharacteristic, complemented, Sylow
786C23—21no—
787C23—31no—
788C23—61no—
789C23—61no—
790C23—61no—
791C23—122no—
792C23—184no—
793C23—181no—
794C23—241no—
795C23—241no—
796C23—721no—
797C23—721no—
798Q8—21no—
799Q8—21no—
800D4—21no—
801D4—21no—
802D4—32no—
803D4—61no—
804D4—61no—
805D4—61no—
806D4—61no—
807D4—61no—
808D4—92no—
809D4—122no—
810D4—122no—
811D4—184no—
812D4—181no—
813D4—241no—
814D4—241no—
815D4—241no—
816D4—241no—
817C2×C4—21no—
818C2×C4—31no—
819C2×C4—32no—
820C2×C4—32no—
821C2×C4—31no—
822C2×C4—31no—
823C2×C4—61no—
824C2×C4—122no—
825C2×C4—181no—
826C2×C4—241no—
827C2×C4—721no—
828C2×C4—721no—
829C2×C4—721no—
830C2×C4D3×#6711yescharacteristic
831C2×C4D3×#6711yescharacteristic
832C2×C4C22×D3211yescharacteristic
833C8—61no—
834C8—61no—
835C8—181no—
836C8—181no—
837C2×C3—21no—
838C2×C3—21no—
839C2×C3—21no—
840C2×C3—62no—
841C2×C3—81no—
842C2×C3—81no—
843C2×C3—122no—
844C2×C3—161no—
845C2×C3—241no—
846C2×C3—241no—
847C2×C3D3×#12111yescharacteristic
848C2×C3#576911yescharacteristic
849C2×C3#577411yescharacteristic
850C2×C3C2×#93811yescharacteristic
851C2×C3#583511yescharacteristic
852C2×C3#583511yescharacteristic
853D3—22no—
854D3—42no—
855D3—81no—
856D3—81no—
857D3—122no—
858D3—122no—
859D3—242no—
860C22—32no—
861C22—41no—
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—182no—
876C22—244no—
877C22—361no—
878C22—361no—
879C22—724no—
880C22C2×D3×#6711yescharacteristic
881C4—21no—
882C4—21no—
883C4—32no—
884C4—41no—
885C4—61no—
886C4—61no—
887C4—121no—
888C4—361no—
889C4D32×D411yescharacteristic
890C4D3×#23711yescharacteristic
891C3—21no—
892C3#8053611yescharacteristic, complemented
893C3#8338411yescharacteristic, complemented
894C2—62no—
895C2—81no—
896C2—122no—
897C2—241no—
898C2—241no—
899C2—362no—
900C2D3×#93811yescharacteristic
901C2#1059545411yescharacteristic
902C2#1059545611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#124C22
socleC22×C32C22×D4
hypercenter#124D32
hypocenterC32#3041
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. C3×#5674C2semidirect
2. C2×#63939C2semidirect
3. C2×D3×#213C2semidirect
4. #10593994C2semidirect
5. #10592756C2semidirect
6. C3×#5057C2semidirect
7. #10591568C2semidirect
8. #10591567C2semidirect
9. #10591556C2semidirect
10. #10591429C2semidirect
11. #10591428C2semidirect
12. #10591421C2semidirect
13. #10590355C2semidirect
14. #10590347C2semidirect
15. #10590324C2semidirect
21. C32×#124C22semidirect
22. C2×#3755C22semidirect
24. C4×C4⋊(C3⋊D3)C22semidirect
25. C3×#947C22semidirect
26. C2×C3×#215C22semidirect
27. C3×#940C22semidirect
33. C3×#874C22semidirect
34. C3×C4×D12C22semidirect
41. #63894C22semidirect
42. Dic3×D12C22semidirect
46. C2×#3714C22semidirect
48. C2×#3713C22semidirect
51. #63662C22semidirect
52. #63659C22semidirect
53. C4⋊(C3⋊(C3⋊C8))C22semidirect
54. C3×#835C22semidirect
55. C3×#832C22semidirect
56. C3×C4⋊(C3⋊C8)C22semidirect
57. Dic3⋊(C3⋊C8)C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
59. #63563C22semidirect
60. #63563C22semidirect
61. #63562C22semidirect
62. #63562C22semidirect
68. #5674D3semidirect
85. #5057D3semidirect
120. D3×D12D4semidirect
166. C3×#124C2×D3semidirect
167. C3×#124C2×D3semidirect
175. #947C2×D3semidirect
179. C2×#215C2×D3semidirect
180. #940C2×D3semidirect
216. #874C2×D3semidirect
222. C4×D12C2×D3semidirect
230. #835C2×D3semidirect
238. #832C2×D3semidirect
250. C4⋊(C3⋊C8)C2×D3semidirect
497. #124D32semidirect
785. C32#3041semidirect
892. C3#80536semidirect
893. C3#83384semidirect

Maximal subgroups

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

subgroupindex
C3×#56742
C2×#639392
C2×D3×#2132
#105939942
#105927562
C3×#50572
#105915682
#105915672
#105915562
#105914292
#105914282
#105914212
#105903552
#105903472
#105903242
#833843
#805363