Finite Group Databasebeta

← #11885749

Subgroups — #11885749

Order 1152.

1339 conjugacy classes of subgroups.

The subgroup lattice has 1015 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5609C211yesmaximal, characteristic, complemented
2C2×D3×#213C211yesmaximal, characteristic, complemented
3#10595074C211yesmaximal, characteristic, complemented
4C22×#3714C211yesmaximal, characteristic, complemented
5#10592735C211yesmaximal, characteristic, complemented
6C3×#5038C211yesmaximal, characteristic, complemented
7#10591482C211yesmaximal, characteristic, complemented
8#10591448C211yesmaximal, characteristic, complemented
9#10591429C211yesmaximal, characteristic, complemented
10#10591160C211yesmaximal, characteristic, complemented
11C3⋊C8×#67C211yesmaximal, characteristic, complemented
12#10590595C211yesmaximal, characteristic, complemented
13#10590576C211yesmaximal, characteristic, complemented
14#10590547C211yesmaximal, characteristic, complemented
15#10590456C211yesmaximal, characteristic, complemented
16D4×#213—31nomaximal
17#80729—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
19C2×C3×D3×D4—21no—
20C2×C3×D3×D4C2211yescharacteristic, complemented
21C22×C3×D12C2211yescharacteristic, complemented
22C2×#3811—21no—
23C2×D3×D12C2211yescharacteristic, complemented
24C32×#121C2211yescharacteristic, complemented
25C2×#3753C2211yescharacteristic, complemented
26C2×#3753C2211yescharacteristic, complemented
27C3×#940C2211yescharacteristic, complemented
28C3×#937—21no—
29C2×C3×#213C2211yescharacteristic, complemented
30C3×#930C2211yescharacteristic, complemented
31C3×C4×#67C2211yescharacteristic
32C22×C3×C3⋊C8C2211yescharacteristic, complemented
33C3×#895C2211yescharacteristic, complemented
34C3×#893C2211yescharacteristic, complemented
35C3×#884—21no—
36C3×#882—21no—
37#63981—21no—
38D3×#213—24no—
39#63923—21no—
40#63911C2211yescharacteristic, complemented
41#63910—21no—
42#63909C2211yescharacteristic, complemented
43#63894C2211yescharacteristic, complemented
44C2×#3714—24no—
45C2×#3714C2211yescharacteristic
46C2×#3714C2211yescharacteristic, complemented
47C2×#3714C2211yescharacteristic, complemented
48C2×#3714C2211yescharacteristic, complemented
49C2×#3713C2211yescharacteristic, complemented
50C2×#3713C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52#63657C2211yescharacteristic, complemented
53#63636C2211yescharacteristic, complemented
54#63636C2211yescharacteristic, complemented
55C3×#832C2211yescharacteristic, complemented
56C3×#809C2211yescharacteristic, complemented
57C3×#807C2211yescharacteristic, complemented
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63562C2211yescharacteristic, complemented
60#63562C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62Dic3×C3⋊C8C2211yescharacteristic, complemented
63C3×D42—31no—
64C22×#213—31no—
65C22×#213—31no—
66C2×D3×D8—31no—
67C22×D24—31no—
68#5609—31no—
69#5609D311yescharacteristic, complemented
70D4×D12—31no—
71C3×#466—31no—
72#5217—31no—
73#5217—31no—
74#5151—31no—
75C8×#67—31no—
76#5073—31no—
77#5072—31no—
78#5038—31no—
79#5038D311yescharacteristic, complemented
80#5036—31no—
81#5036—31no—
82#5036—31no—
83#5036—31no—
84#5036—61no—
85#5015—31no—
86C4×#213—31no—
87D4×C3⋊C8—31no—
88#4883—31no—
89#4872—31no—
90#4786—31no—
91#4786—31no—
92#4773—31no—
93#4773—31no—
94C23×C3⋊D3—21no—
95C23×C3×D3—21no—
96C23×C3×D3—21no—
97C22×D32—21no—
98C2×C32×D4—21no—
99C2×C32×D4C2311yescharacteristic
100C22×C32×C4C2311yescharacteristic
101C2×C4⋊(C3⋊D3)—22no—
102C2×C4⋊(C3⋊D3)—21no—
103C2×C4⋊(C3⋊D3)—41no—
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C4⋊(C3⋊D3)C2311yescharacteristic
106C2×C3×#67—21no—
107C2×C3×#67—21no—
108C2×C3×#67—21no—
109C2×C3×#67—21no—
110C2×C3×#67D411yescharacteristic
111C3×D3×D4—22no—
112C3×D3×D4—41no—
113C3×D3×D4—44no—
114C2×C3×D12—22no—
115C2×C3×D12—21no—
116C2×C3×D12—21no—
117C2×C3×D12—41no—
118C2×C3×D12C2311yescharacteristic
119C2×C3×D12C2311yescharacteristic
120C2×C3×D12C2311yescharacteristic
121C2×C3×C4×D3—21no—
122C2×C3×C4×D3C2311yescharacteristic
123#3811—44no—
124C2×#626—21no—
125C2×#626—21no—
126C2×#626—21no—
127C2×#626—21no—
128C2×#624—21no—
129D3×D12—22no—
130D3×D12—41no—
131C32×C4⋊C4C2311yescharacteristic
132C32×C22⋊C4—21no—
133#3753—22no—
134#3753—41no—
135C2×C3⋊(C3⋊C8)C2311yescharacteristic
136C2×C3⋊(C3⋊C8)C2311yescharacteristic
137C3×#217D411yescharacteristic
138C3×#213—22no—
139C3×(C2×D3)⋊C4—21no—
140C3×(C2×D3)⋊C4—21no—
141C3×(C2×D3)⋊C4—21no—
142C3×(C2×D3)⋊C4D411yescharacteristic
143C3×C4⋊Dic3C2311yescharacteristic
144C3×Dic3⋊C4D411yescharacteristic
145C3×C4×Dic3C2311yescharacteristic
146C2×C3×C3⋊C8—22no—
147C2×C3×C3⋊C8C2311yescharacteristic
148C2×C3×C3⋊C8C2311yescharacteristic
149#3722—21no—
150#3722—21no—
151#3714—22no—
152#3714—22no—
153#3714—22no—
154#3714D414yescomplemented
155#3713—22no—
156#3713—41no—
157D3×C3⋊C8—22no—
158D4×D8—91noSylow
159C22×C3×D4—31no—
160C22×C3×D4—31no—
161C22×C3×D4—61no—
162C2×D3×D4—21no—
163C2×D3×D4—31no—
164C2×D3×D4—61no—
165C2×D3×D4—61no—
166C2×D3×D4C2×D311yescharacteristic, complemented
167C22×D12—31no—
168C22×D12—31no—
169C22×D12—31no—
170C22×D12—61no—
171C22×D12C2×D311yescharacteristic, complemented
172C2×C3×D8—31no—
173C22×C3×C8—31no—
174C3×#127—31no—
175C3×#121—21no—
176C3×#121—31no—
177C3×#121—31no—
178C3×#121—61no—
179C3×#121C2×D311yescharacteristic, complemented
180C3×#121C2×D311yescharacteristic, complemented
181C3×#120—61no—
182C3×#120—61no—
183C3×C4×D4—31no—
184C3×C4×D4—31no—
185#940—31no—
186#940C2×D311yescharacteristic, complemented
187#937—21no—
188#937—61no—
189C2×#213—31no—
190C2×#213—31no—
191C2×#213—31no—
192C2×#213—31no—
193C2×#213—31no—
194C2×#213—31no—
195C2×#213—31no—
196C2×#213—31no—
197C2×#213—31no—
198C2×#213—31no—
199C2×#213—31no—
200C2×#213—31no—
201C2×#213—61no—
202C2×#213—61no—
203C2×#213—64no—
204C2×#213—64no—
205C2×#213C2×D311yescharacteristic, complemented
206#930—31no—
207#930C2×D311yescharacteristic, complemented
208C4×#67C2×D311yescharacteristic
209C22×C3⋊C8—31no—
210C22×C3⋊C8C2×D311yescharacteristic, complemented
211D3×D8—64no—
212C2×D24—31no—
213C2×D24—31no—
214C2×D24—31no—
215C2×D24—31no—
216C2×D24—64no—
217C2×D3×C8—31no—
218#895—31no—
219#895—61no—
220#895C2×D311yescharacteristic, complemented
221#893—31no—
222#893C2×D311yescharacteristic, complemented
223#884—21no—
224#884—61no—
225#882—21no—
226#882—61no—
227#882—61no—
228#882—61no—
229#874—31no—
230C4×D12—31no—
231C3×#107—31no—
232C3×#102—31no—
233C3×#102—31no—
234#832—31no—
235#832—31no—
236#832C2×D311yescharacteristic, complemented
237#830—31no—
238#830—31no—
239#830—31no—
240#830—61no—
241(C2×D3)⋊C8—31no—
242Dic3⋊C8—31no—
243C8×Dic3—31no—
244#809—31no—
245#809—31no—
246#809—31no—
247#809—31no—
248#809—31no—
249#809—31no—
250#809—61no—
251#809—61no—
252#809C2×D311yescharacteristic, complemented
253#807C2×D311yescharacteristic, complemented
254C4⋊(C3⋊C8)—31no—
255C4×C3⋊C8—31no—
256C23×C32—21no—
257C23×C32C2×D411yescharacteristic
258C22×C3⋊D3—21no—
259C22×C3⋊D3—21no—
260C22×C3⋊D3—42no—
261C22×C3⋊D3—42no—
262C22×C3⋊D3—81no—
263C22×C3×D3—21no—
264C22×C3×D3—21no—
265C22×C3×D3—21no—
266C22×C3×D3—42no—
267C22×C3×D3—42no—
268C22×C3×D3—42no—
269C22×C3×D3—42no—
270C22×C3×D3—81no—
271C22×C3×D3—81no—
272C22×C3×D3C2×D411yescharacteristic
273C2×D32—42no—
274C2×D32—42no—
275C2×D32—81no—
276C32×D4—21no—
277C32×D4—21no—
278C32×D4—42no—
279C2×C32×C4—21no—
280C2×C32×C4—21no—
281C2×C32×C4—21no—
282C2×C32×C4C2×D411yescharacteristic
283C2×C32×C4C2411yescharacteristic
284C4⋊(C3⋊D3)—21no—
285C4⋊(C3⋊D3)—21no—
286C4⋊(C3⋊D3)—21no—
287C4⋊(C3⋊D3)—42no—
288C4⋊(C3⋊D3)C2×D412yescomplemented
289C3×#67—42no—
290C3×#67—42no—
291C3×#67—42no—
292C3×#67—81no—
293C3×#67D814yescomplemented
294C2×C3×Dic3—21no—
295C2×C3×Dic3C2×D411yescharacteristic
296C2×C3×Dic3C2×D411yescharacteristic
297C2×C3×Dic3C2×D411yescharacteristic
298C3×D12—21no—
299C3×D12—21no—
300C3×D12—21no—
301C3×D12—21no—
302C3×D12—21no—
303C3×D12—42no—
304C3×D12—42no—
305C3×D12C2×D412yescomplemented
306C3×C4×D3—21no—
307C3×C4×D3—21no—
308C3×C4×D3—42no—
309#626—42no—
310#626—42no—
311#626—42no—
312#626—81no—
313#624—42no—
314C3⋊(C3⋊C8)—21no—
315C3⋊(C3⋊C8)—21no—
316C3×C3⋊C8—21no—
317C3×C3⋊C8C2×D412yescomplemented
318C22×D8—91no—
319C22×D8—91no—
320D42—31no—
321D42—91no—
322#493—91no—
323#466—31no—
324#466—91no—
325#459—91no—
326#459—91no—
327#447—91no—
328#447—91no—
329#447—91no—
330#447—91no—
331C4×D8—91no—
332C8×D4—91no—
333C24×C3—61no—
334C24×C3—61no—
335C23×D3—21no—
336C23×D3—21no—
337C23×D3—61no—
338C23×D3—61no—
339C23×D3—61no—
340C23×D3—61no—
341C23×D3—121no—
342C2×C3×D4—21no—
343C2×C3×D4—21no—
344C2×C3×D4—21no—
345C2×C3×D4—31no—
346C2×C3×D4—31no—
347C2×C3×D4—31no—
348C2×C3×D4—31no—
349C2×C3×D4—41no—
350C2×C3×D4—62no—
351C2×C3×D4—61no—
352C2×C3×D4—61no—
353C2×C3×D4—61no—
354C2×C3×D4—61no—
355C2×C3×D4—62no—
356C2×C3×D4—61no—
357C2×C3×D4—61no—
358C2×C3×D4—121no—
359C2×C3×D4—121no—
360C2×C3×D4—124no—
361C2×C3×D4C22×D311yescharacteristic
362C2×C3×D4C22×D311yescharacteristic
363C22×C3×C4—21no—
364C22×C3×C4—31no—
365C22×C3×C4—61no—
366C22×C3×C4C22×D311yescharacteristic
367C22×C3×C4C22×D311yescharacteristic
368C2×#67—21no—
369C2×#67—21no—
370C2×#67—21no—
371C2×#67—21no—
372C2×#67—61no—
373C2×#67—61no—
374C2×#67—61no—
375C2×#67—61no—
376C2×#67#6711yescharacteristic
377D3×D4—22no—
378D3×D4—41no—
379D3×D4—44no—
380D3×D4—62no—
381D3×D4—121no—
382D3×D4—124no—
383D3×D4—124no—
384C2×D12—22no—
385C2×D12—21no—
386C2×D12—21no—
387C2×D12—31no—
388C2×D12—31no—
389C2×D12—31no—
390C2×D12—31no—
391C2×D12—41no—
392C2×D12—61no—
393C2×D12—61no—
394C2×D12—62no—
395C2×D12—62no—
396C2×D12—62no—
397C2×D12—61no—
398C2×D12—61no—
399C2×D12—61no—
400C2×D12—61no—
401C2×D12—61no—
402C2×D12—61no—
403C2×D12—122no—
404C2×D12—121no—
405C2×D12—121no—
406C2×D12—121no—
407C2×D12—121no—
408C2×D12—122no—
409C2×D12C22×D311yescharacteristic
410C2×D12C22×D311yescharacteristic
411C2×D12C22×D311yescharacteristic
412C2×C4×D3—21no—
413C2×C4×D3—61no—
414C2×C4×D3—61no—
415C2×C4×D3C22×D311yescharacteristic
416C3×D8—62no—
417C2×C3×C8—31no—
418C2×C3×C8—31no—
419C2×C3×C8—62no—
420C3×C4⋊C4—21no—
421C3×C4⋊C4—31no—
422C3×C4⋊C4—31no—
423C3×C4⋊C4C22×D311yescharacteristic
424C3×C4⋊C4C22×D311yescharacteristic
425C3×C22⋊C4—21no—
426C3×C22⋊C4—21no—
427C3×C22⋊C4—31no—
428C3×C22⋊C4—31no—
429C3×C22⋊C4—41no—
430C3×C22⋊C4—61no—
431C3×C22⋊C4—61no—
432C3×C22⋊C4—61no—
433C3×C42—31no—
434#217#6711yescharacteristic
435#213—22no—
436#213—34no—
437#213—62no—
438#213—62no—
439#213—62no—
440#213—62no—
441#213—62no—
442#213—62no—
443#213—62no—
444#213—122no—
445#213—121no—
446#213—121no—
447#213—121no—
448#213—121no—
449#213—122no—
450(C2×D3)⋊C4—21no—
451(C2×D3)⋊C4—21no—
452(C2×D3)⋊C4—21no—
453(C2×D3)⋊C4—61no—
454(C2×D3)⋊C4—61no—
455(C2×D3)⋊C4—61no—
456(C2×D3)⋊C4—61no—
457(C2×D3)⋊C4#6711yescharacteristic
458C4⋊Dic3C22×D311yescharacteristic
459Dic3⋊C4#6711yescharacteristic
460C4×Dic3C22×D311yescharacteristic
461C2×C3⋊C8—22no—
462C2×C3⋊C8—31no—
463C2×C3⋊C8—31no—
464C2×C3⋊C8—31no—
465C2×C3⋊C8—31no—
466C2×C3⋊C8—61no—
467C2×C3⋊C8—61no—
468C2×C3⋊C8—62no—
469C2×C3⋊C8C22×D311yescharacteristic
470C2×C3⋊C8C22×D311yescharacteristic
471D24—34no—
472D24—62no—
473D24—62no—
474D24—62no—
475D3×C8—62no—
476C22×C32—21no—
477C22×C32—21no—
478C22×C32—41no—
479C22×C32—41no—
480C22×C32—41no—
481C22×C32C2×D812yescomplemented
482C22×C32C22×D411yescharacteristic
483C2×C3⋊D3—22no—
484C2×C3⋊D3—41no—
485C2×C3⋊D3—41no—
486C2×C3⋊D3—41no—
487C2×C3⋊D3—41no—
488C2×C3⋊D3—41no—
489C2×C3⋊D3—84no—
490C2×C3×D3—21no—
491C2×C3×D3—21no—
492C2×C3×D3—22no—
493C2×C3×D3—41no—
494C2×C3×D3—41no—
495C2×C3×D3—41no—
496C2×C3×D3—41no—
497C2×C3×D3—41no—
498C2×C3×D3—41no—
499C2×C3×D3—41no—
500C2×C3×D3—41no—
501C2×C3×D3—84no—
502C2×C3×D3—84no—
503C2×C3×D3C2×D812yescomplemented
504D32—84no—
505C32×C4—21no—
506C32×C4—41no—
507C32×C4C22×D411yescharacteristic
508C32×C4H(5,𝔽2)11yescharacteristic
509C3×Dic3—21no—
510C3×Dic3—21no—
511C3×Dic3—41no—
512C3×Dic3C2×D812yescomplemented
513C22×D4—31no—
514C22×D4—31no—
515C22×D4—61no—
516C22×D4—91no—
517C22×D4—91no—
518C22×D4—181no—
519C2×D8—31no—
520C2×D8—91no—
521C2×D8—91no—
522C2×D8—91no—
523C2×D8—91no—
524C2×D8—91no—
525C2×D8—91no—
526C2×D8—91no—
527C2×D8—91no—
528C2×D8—184no—
529C2×D8—184no—
530C22×C8—31no—
531C22×C8—91no—
532#127—31no—
533#127—91no—
534#121—31no—
535#121—31no—
536#121—61no—
537#121—91no—
538#121—181no—
539#121D3211yescharacteristic, complemented
540#120—61no—
541#120—61no—
542#120—181no—
543#120—181no—
544C4×D4—31no—
545C4×D4—31no—
546C4×D4—91no—
547#107—31no—
548C4⋊C8—91no—
549#102—31no—
550#102—31no—
551#102—91no—
552#102—91no—
553#102—91no—
554#102—91no—
555C22⋊C8—91no—
556C22⋊C8—91no—
557C4×C8—91no—
558C23×C3—21no—
559C23×C3—21no—
560C23×C3—21no—
561C23×C3—31no—
562C23×C3—41no—
563C23×C3—61no—
564C23×C3—61no—
565C23×C3—61no—
566C23×C3—122no—
567C23×C3—122no—
568C23×C3—122no—
569C23×C3—122no—
570C23×C3—241no—
571C23×C3—241no—
572C23×C3D3×D411yescharacteristic
573C23×C3C2×#6711yescharacteristic
574C22×D3—21no—
575C22×D3—21no—
576C22×D3—21no—
577C22×D3—42no—
578C22×D3—42no—
579C22×D3—42no—
580C22×D3—42no—
581C22×D3—61no—
582C22×D3—61no—
583C22×D3—61no—
584C22×D3—61no—
585C22×D3—81no—
586C22×D3—81no—
587C22×D3—121no—
588C22×D3—121no—
589C22×D3—122no—
590C22×D3—122no—
591C22×D3—122no—
592C22×D3—122no—
593C22×D3—122no—
594C22×D3—124no—
595C22×D3—122no—
596C22×D3—122no—
597C22×D3—122no—
598C22×D3—242no—
599C22×D3—241no—
600C22×D3—241no—
601C22×D3—241no—
602C22×D3—241no—
603C22×D3—242no—
604C22×D3C2×#6711yescharacteristic
605C3×D4—21no—
606C3×D4—21no—
607C3×D4—21no—
608C3×D4—21no—
609C3×D4—34no—
610C3×D4—32no—
611C3×D4—41no—
612C3×D4—41no—
613C3×D4—42no—
614C3×D4—42no—
615C3×D4—61no—
616C3×D4—61no—
617C3×D4—61no—
618C3×D4—61no—
619C3×D4—61no—
620C3×D4—82no—
621C3×D4—122no—
622C3×D4—122no—
623C3×D4—122no—
624C3×D4—122no—
625C3×D4—122no—
626C3×D4—241no—
627C2×C3×C4—21no—
628C2×C3×C4—21no—
629C2×C3×C4—21no—
630C2×C3×C4—21no—
631C2×C3×C4—21no—
632C2×C3×C4—21no—
633C2×C3×C4—21no—
634C2×C3×C4—21no—
635C2×C3×C4—31no—
636C2×C3×C4—31no—
637C2×C3×C4—31no—
638C2×C3×C4—41no—
639C2×C3×C4—41no—
640C2×C3×C4—41no—
641C2×C3×C4—61no—
642C2×C3×C4—61no—
643C2×C3×C4—61no—
644C2×C3×C4—122no—
645C2×C3×C4D3×D411yescharacteristic
646C2×C3×C4C2×#6711yescharacteristic
647C2×C3×C4C23×D311yescharacteristic
648C2×C3×C4C23×D311yescharacteristic
649#67—42no—
650#67—42no—
651#67—42no—
652#67—81no—
653#67—122no—
654#67—122no—
655#67—122no—
656#67—241no—
657#67#21314yescomplemented
658C2×Dic3—21no—
659C2×Dic3C2×#6711yescharacteristic
660C2×Dic3C2×#6711yescharacteristic
661C2×Dic3C2×#6711yescharacteristic
662D12—21no—
663D12—21no—
664D12—21no—
665D12—21no—
666D12—21no—
667D12—32no—
668D12—32no—
669D12—42no—
670D12—42no—
671D12—62no—
672D12—62no—
673D12—61no—
674D12—61no—
675D12—61no—
676D12—61no—
677D12—61no—
678D12—61no—
679D12—121no—
680D12—121no—
681D12—122no—
682D12—122no—
683D12—122no—
684D12—124no—
685D12—122no—
686D12—122no—
687D12—241no—
688D12D3×D412yescomplemented
689C4×D3—21no—
690C4×D3—21no—
691C4×D3—42no—
692C4×D3—122no—
693C4×D3—122no—
694C3×C8—32no—
695C3×C8—61no—
696C3⋊C8—21no—
697C3⋊C8—61no—
698C3⋊C8—61no—
699C3⋊C8—61no—
700C3⋊C8—61no—
701C3⋊C8—121no—
702C3⋊C8—121no—
703C3⋊C8D3×D412yescomplemented
704C2×C32—22no—
705C2×C32—81no—
706C2×C32D4211yescharacteristic
707C2×C32C22×D811yescharacteristic
708C2×C32#57611yescharacteristic
709C3⋊D3—42no—
710C3⋊D3—81no—
711C3×D3—22no—
712C3×D3—42no—
713C3×D3—81no—
714C3×D3—81no—
715C24—61no—
716C24—61no—
717C24—181no—
718C24—181no—
719C2×D4—21no—
720C2×D4—31no—
721C2×D4—31no—
722C2×D4—31no—
723C2×D4—31no—
724C2×D4—62no—
725C2×D4—61no—
726C2×D4—61no—
727C2×D4—61no—
728C2×D4—61no—
729C2×D4—62no—
730C2×D4—61no—
731C2×D4—61no—
732C2×D4—91no—
733C2×D4—91no—
734C2×D4—121no—
735C2×D4—121no—
736C2×D4—124no—
737C2×D4—182no—
738C2×D4—181no—
739C2×D4—181no—
740C2×D4—181no—
741C2×D4—182no—
742C2×D4—181no—
743C2×D4—181no—
744C2×D4—361no—
745C2×D4—361no—
746C2×D4—364no—
747C2×D4C2×D3211yescharacteristic
748C22×C4—31no—
749C22×C4—61no—
750C22×C4—181no—
751C22×C4C2×D3211yescharacteristic
752D8—62no—
753D8—94no—
754D8—182no—
755D8—182no—
756D8—182no—
757D8—182no—
758D8—182no—
759D8—361no—
760D8—361no—
761C2×C8—31no—
762C2×C8—31no—
763C2×C8—62no—
764C2×C8—91no—
765C2×C8—91no—
766C2×C8—182no—
767C4⋊C4—31no—
768C4⋊C4—31no—
769C4⋊C4C2×D3211yescharacteristic
770C22⋊C4—21no—
771C22⋊C4—31no—
772C22⋊C4—31no—
773C22⋊C4—61no—
774C22⋊C4—61no—
775C22⋊C4—61no—
776C22⋊C4—181no—
777C22⋊C4—181no—
778C42—31no—
779C22×C3—21no—
780C22×C3—21no—
781C22×C3—21no—
782C22×C3—21no—
783C22×C3—21no—
784C22×C3—22no—
785C22×C3—32no—
786C22×C3—41no—
787C22×C3—41no—
788C22×C3—41no—
789C22×C3—41no—
790C22×C3—41no—
791C22×C3—41no—
792C22×C3—41no—
793C22×C3—41no—
794C22×C3—61no—
795C22×C3—61no—
796C22×C3—62no—
797C22×C3—81no—
798C22×C3—81no—
799C22×C3—81no—
800C22×C3—121no—
801C22×C3—121no—
802C22×C3—121no—
803C22×C3—121no—
804C22×C3—121no—
805C22×C3—121no—
806C22×C3—121no—
807C22×C3—121no—
808C22×C3—244no—
809C22×C3—244no—
810C22×C3D3×D812yescomplemented
811C22×C3C2×#21312yescomplemented
812C22×C3C2×D3×D411yescharacteristic
813C22×C3C22×#6711yescharacteristic
814C2×D3—21no—
815C2×D3—21no—
816C2×D3—22no—
817C2×D3—41no—
818C2×D3—41no—
819C2×D3—41no—
820C2×D3—41no—
821C2×D3—41no—
822C2×D3—41no—
823C2×D3—41no—
824C2×D3—41no—
825C2×D3—62no—
826C2×D3—62no—
827C2×D3—84no—
828C2×D3—84no—
829C2×D3—122no—
830C2×D3—121no—
831C2×D3—121no—
832C2×D3—121no—
833C2×D3—121no—
834C2×D3—122no—
835C2×D3—121no—
836C2×D3—121no—
837C2×D3—121no—
838C2×D3—121no—
839C2×D3—121no—
840C2×D3—121no—
841C2×D3—241no—
842C2×D3—241no—
843C2×D3—241no—
844C2×D3—241no—
845C2×D3—244no—
846C2×D3—244no—
847C2×D3—244no—
848C2×D3—244no—
849C2×D3—248no—
850C2×D3C2×#21312yescomplemented
851C3×C4—21no—
852C3×C4—21no—
853C3×C4—21no—
854C3×C4—21no—
855C3×C4—32no—
856C3×C4—41no—
857C3×C4—41no—
858C3×C4—41no—
859C3×C4—61no—
860C3×C4—61no—
861C3×C4—81no—
862C3×C4—121no—
863C3×C4C2×D3×D411yescharacteristic
864C3×C4C2×D3×D411yescharacteristic
865C3×C4#100411yescharacteristic
866C3×C4#100911yescharacteristic
867Dic3—21no—
868Dic3—21no—
869Dic3—41no—
870Dic3C2×#21312yescomplemented
871C32D4×D811yescharacteristic, complemented, Sylow
872C23—21no—
873C23—31no—
874C23—61no—
875C23—61no—
876C23—61no—
877C23—122no—
878C23—122no—
879C23—122no—
880C23—122no—
881C23—181no—
882C23—181no—
883C23—241no—
884C23—241no—
885C23—362no—
886C23—362no—
887C23—362no—
888C23—362no—
889C23—721no—
890C23—721no—
891C23D3×#6711yescharacteristic
892D4—21no—
893D4—21no—
894D4—34no—
895D4—32no—
896D4—42no—
897D4—61no—
898D4—61no—
899D4—61no—
900D4—61no—
901D4—61no—
902D4—92no—
903D4—122no—
904D4—122no—
905D4—122no—
906D4—122no—
907D4—122no—
908D4—181no—
909D4—181no—
910D4—181no—
911D4—241no—
912D4—362no—
913D4—362no—
914D4—362no—
915D4—362no—
916D4—721no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—31no—
921C2×C4—31no—
922C2×C4—31no—
923C2×C4—61no—
924C2×C4—61no—
925C2×C4—61no—
926C2×C4—122no—
927C2×C4—362no—
928C2×C4D3×#6711yescharacteristic
929C2×C4C22×D3211yescharacteristic
930C8—32no—
931C8—61no—
932C8—181no—
933C8—181no—
934C2×C3—22no—
935C2×C3—22no—
936C2×C3—21no—
937C2×C3—21no—
938C2×C3—21no—
939C2×C3—42no—
940C2×C3—62no—
941C2×C3—81no—
942C2×C3—81no—
943C2×C3—122no—
944C2×C3—161no—
945C2×C3—241no—
946C2×C3—241no—
947C2×C3#560911yescharacteristic
948C2×C3C2×D3×D811yescharacteristic
949C2×C3#576911yescharacteristic
950C2×C3C22×#21311yescharacteristic
951C2×C3D4×#6711yescharacteristic
952C2×C3#583511yescharacteristic
953D3—22no—
954D3—42no—
955D3—81no—
956D3—81no—
957D3—122no—
958D3—122no—
959D3—242no—
960D3—242no—
961D3—241no—
962D3—241no—
963C22—21no—
964C22—21no—
965C22—32no—
966C22—41no—
967C22—41no—
968C22—41no—
969C22—61no—
970C22—61no—
971C22—62no—
972C22—121no—
973C22—121no—
974C22—121no—
975C22—121no—
976C22—121no—
977C22—121no—
978C22—121no—
979C22—121no—
980C22—182no—
981C22—244no—
982C22—244no—
983C22—361no—
984C22—361no—
985C22—361no—
986C22—361no—
987C22—361no—
988C22—724no—
989C22—724no—
990C22D3×#21312yescomplemented
991C22C2×D3×#6711yescharacteristic
992C4—21no—
993C4—32no—
994C4—41no—
995C4—61no—
996C4—61no—
997C4—121no—
998C4D32×D411yescharacteristic
999C4#6431411yescharacteristic
1000C3—21no—
1001C3#8072911yescharacteristic, complemented
1002C3D4×#21311yescharacteristic, complemented
1003C2—22no—
1004C2—62no—
1005C2—81no—
1006C2—122no—
1007C2—241no—
1008C2—241no—
1009C2—362no—
1010C2—721no—
1011C2C2×D3×#21311yescharacteristic
1012C2#1059529111yescharacteristic
1013C2#1059545611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
hypercenter#121D32
hypocenterC32D4×D8
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C3×#5609C2semidirect
2. C2×D3×#213C2semidirect
3. #10595074C2semidirect
4. C22×#3714C2semidirect
5. #10592735C2semidirect
6. C3×#5038C2semidirect
7. #10591482C2semidirect
8. #10591448C2semidirect
9. #10591429C2semidirect
10. #10591160C2semidirect
11. C3⋊C8×#67C2semidirect
12. #10590595C2semidirect
13. #10590576C2semidirect
14. #10590547C2semidirect
15. #10590456C2semidirect
18. C22×C4⋊(C3⋊D3)C22semidirect
20. C2×C3×D3×D4C22semidirect
21. C22×C3×D12C22semidirect
23. C2×D3×D12C22semidirect
24. C32×#121C22semidirect
25. C2×#3753C22semidirect
26. C2×#3753C22semidirect
27. C3×#940C22semidirect
29. C2×C3×#213C22semidirect
30. C3×#930C22semidirect
32. C22×C3×C3⋊C8C22semidirect
33. C3×#895C22semidirect
34. C3×#893C22semidirect
40. #63911C22semidirect
42. #63909C22semidirect
43. #63894C22semidirect
46. C2×#3714C22semidirect
47. C2×#3714C22semidirect
48. C2×#3714C22semidirect
49. C2×#3713C22semidirect
50. C2×#3713C22semidirect
51. C2×D3×C3⋊C8C22semidirect
52. #63657C22semidirect
53. #63636C22semidirect
54. #63636C22semidirect
55. C3×#832C22semidirect
56. C3×#809C22semidirect
57. C3×#807C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
59. #63562C22semidirect
60. #63562C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. Dic3×C3⋊C8C22semidirect
69. #5609D3semidirect
79. #5038D3semidirect
154. #3714D4semidirect
166. C2×D3×D4C2×D3semidirect
171. C22×D12C2×D3semidirect
179. C3×#121C2×D3semidirect
180. C3×#121C2×D3semidirect
186. #940C2×D3semidirect
205. C2×#213C2×D3semidirect
207. #930C2×D3semidirect
210. C22×C3⋊C8C2×D3semidirect
220. #895C2×D3semidirect
222. #893C2×D3semidirect
236. #832C2×D3semidirect
252. #809C2×D3semidirect
253. #807C2×D3semidirect
288. C4⋊(C3⋊D3)C2×D4semidirect
293. C3×#67D8semidirect
305. C3×D12C2×D4semidirect
317. C3×C3⋊C8C2×D4semidirect
481. C22×C32C2×D8semidirect
503. C2×C3×D3C2×D8semidirect
512. C3×Dic3C2×D8semidirect
539. #121D32semidirect
657. #67#213semidirect
688. D12D3×D4semidirect
703. C3⋊C8D3×D4semidirect
810. C22×C3D3×D8semidirect
811. C22×C3C2×#213semidirect
850. C2×D3C2×#213semidirect
870. Dic3C2×#213semidirect
871. C32D4×D8semidirect
990. C22D3×#213semidirect
1001. C3#80729semidirect
1002. C3D4×#213semidirect

Maximal subgroups

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

subgroupindex
C3×#56092
C2×D3×#2132
#105950742
C22×#37142
#105927352
C3×#50382
#105914822
#105914482
#105914292
#105911602
C3⋊C8×#672
#105905952
#105905762
#105905472
#105904562
D4×#2133
#807293