Finite Group Databasebeta

← #11885751

Subgroups — #11885751

Order 1152.

1307 conjugacy classes of subgroups.

The subgroup lattice has 1004 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
3D12×#67C211yesmaximal, characteristic, complemented
4C22×#3713C211yesmaximal, characteristic, complemented
5#10592737C211yesmaximal, characteristic, complemented
6C3×#5036C211yesmaximal, characteristic, complemented
7#10591482C211yesmaximal, characteristic, complemented
8#10591447C211yesmaximal, characteristic, complemented
9#10591428C211yesmaximal, characteristic, complemented
10#10591162C211yesmaximal, characteristic, complemented
11#67⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
12#10590595C211yesmaximal, characteristic, complemented
13#10590547C211yesmaximal, characteristic, complemented
14#10590499C211yesmaximal, characteristic, complemented
15#10590452C211yesmaximal, characteristic, complemented
16D4×#213—31nomaximal
17#80024—31nomaximal
18C2×C3×D3×D4—21no—
19C2×C3×D3×D4C2211yescharacteristic, complemented
20C22×C3×D12C2211yescharacteristic, complemented
21C22×C3×D12C2211yescharacteristic, complemented
22C2×D3×#67—21no—
23C2×D3×D12C2211yescharacteristic, complemented
24C32×#121C2211yescharacteristic, complemented
25C2×#3753C2211yescharacteristic, complemented
26#64139C2211yescharacteristic, complemented
27C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
28C3×#940C2211yescharacteristic, complemented
29C3×#937—21no—
30C2×C3×#213C2211yescharacteristic, complemented
31C2×C3×#213C2211yescharacteristic, complemented
32C3×C4×#67C2211yescharacteristic
33C3×#895C2211yescharacteristic, complemented
34C3×#893C2211yescharacteristic, complemented
35C3×#884—21no—
36C3×#882—21no—
37#63977—21no—
38D3×#213—24no—
39#63922—21no—
40#63911C2211yescharacteristic, complemented
41#63908C2211yescharacteristic, complemented
42Dic3×D12C2211yescharacteristic, complemented
43#63886—21no—
44C2×#3714C2211yescharacteristic, complemented
45C2×#3714C2211yescharacteristic, complemented
46C2×#3713—24no—
47C2×#3713C2211yescharacteristic
48C2×#3713C2211yescharacteristic, complemented
49C2×#3713C2211yescharacteristic, complemented
50C2×#3713C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52#63659C2211yescharacteristic, complemented
53#63636C2211yescharacteristic, complemented
54#63634C2211yescharacteristic, complemented
55C3×#830C2211yescharacteristic, complemented
56C3×#809C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic, complemented
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63563C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62Dic3×C3⋊C8C2211yescharacteristic, complemented
63C3×D42—31no—
64D4×#67—31no—
65C22×#213—31no—
66C22×#213—31no—
67C22×#213—31no—
68C2×D3×D8—31no—
69#5609D311yescharacteristic, complemented
70D4×D12—31no—
71C3×#447—31no—
72#5217—31no—
73#5217—31no—
74#5156—31no—
75#5151—31no—
76#5150—31no—
77#5073—31no—
78#5072—31no—
79#5038—31no—
80#5038—31no—
81#5038—31no—
82#5038—61no—
83#5036—31no—
84#5036D311yescharacteristic, complemented
85#5015—31no—
86C4×#213—31no—
87D4×C3⋊C8—31no—
88#4786—31no—
89#4775—31no—
90#4773—31no—
91#4756—31no—
92#4732—31no—
93#67⋊C8—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×#638—21no—
102C2×C4⋊(C3⋊D3)C2311yescharacteristic
103C2×C3×#67—21no—
104C2×C3×#67—21no—
105C2×C3×#67—21no—
106C2×C3×#67D411yescharacteristic
107C3×D3×D4—22no—
108C3×D3×D4—41no—
109C3×D3×D4—44no—
110C2×C3×D12—22no—
111C2×C3×D12—22no—
112C2×C3×D12—21no—
113C2×C3×D12—21no—
114C2×C3×D12—21no—
115C2×C3×D12—41no—
116C2×C3×D12—41no—
117C2×C3×D12C2311yescharacteristic
118C2×C3×D12C2311yescharacteristic
119C2×C3×D12C2311yescharacteristic
120C2×C3×D12C2311yescharacteristic
121C2×C3×C4×D3—21no—
122C2×C3×C4×D3C2311yescharacteristic
123D3×#67—44no—
124C2×#626—21no—
125C2×#626—21no—
126C2×#626—21no—
127C2×#625—21no—
128C2×D3×Dic3—21no—
129D3×D12—22no—
130D3×D12—41no—
131C32×C4⋊C4C2311yescharacteristic
132C32×C22⋊C4—21no—
133#3753—22no—
134#3752—21no—
135C4⋊(C3⋊Dic3)C2311yescharacteristic
136C2×C3⋊(C3⋊C8)—22no—
137C2×C3⋊(C3⋊C8)C2311yescharacteristic
138C2×C3⋊(C3⋊C8)C2311yescharacteristic
139C3×#217D411yescharacteristic
140C3×#213—22no—
141C3×#213—41no—
142C3×(C2×D3)⋊C4—21no—
143C3×(C2×D3)⋊C4—21no—
144C3×(C2×D3)⋊C4D411yescharacteristic
145C3×Dic3⋊C4D411yescharacteristic
146C3×C4×Dic3C2311yescharacteristic
147C2×C3×C3⋊C8C2311yescharacteristic
148C2×C3×C3⋊C8C2311yescharacteristic
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151#3714—22no—
152#3714—41no—
153#3713—22no—
154#3713—22no—
155#3713—22no—
156#3713D414yescomplemented
157D3×C3⋊C8—22no—
158D4×D8—91noSylow
159C22×C3×D4—31no—
160C22×C3×D4—31no—
161C22×C3×D4—31no—
162C22×C3×D4—61no—
163C22×#67—61no—
164C2×D3×D4—21no—
165C2×D3×D4—31no—
166C2×D3×D4—61no—
167C2×D3×D4C2×D311yescharacteristic, complemented
168C22×D12—31no—
169C22×D12C2×D311yescharacteristic, complemented
170C22×D12C2×D311yescharacteristic, complemented
171C2×C3×D8—31no—
172C2×C3×D8—31no—
173C3×#127—31no—
174C3×#121—21no—
175C3×#121—31no—
176C3×#121—61no—
177C3×#121C2×D311yescharacteristic, complemented
178C3×#121C2×D311yescharacteristic, complemented
179C3×#120—61no—
180C3×#120—61no—
181C3×C4×D4—31no—
182C3×C4×D4—31no—
183#953—61no—
184#940—31no—
185#940C2×D311yescharacteristic, complemented
186#939—61no—
187#938—31no—
188#937—21no—
189#937—61no—
190D4×Dic3—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—31no—
202C2×#213—31no—
203C2×#213—61no—
204C2×#213—64no—
205C2×#213—64no—
206C2×#213—64no—
207C2×#213C2×D311yescharacteristic, complemented
208C2×#213C2×D311yescharacteristic, complemented
209#930—31no—
210#930—31no—
211#930—31no—
212#930—61no—
213C4×#67C2×D311yescharacteristic
214C22×C3⋊C8—31no—
215C22×C3⋊C8—31no—
216C22×C3⋊C8—31no—
217C22×C3⋊C8—61no—
218D3×D8—64no—
219C2×D24—31no—
220C2×D24—31no—
221C2×D3×C8—31no—
222#895—61no—
223#895C2×D311yescharacteristic, complemented
224#893C2×D311yescharacteristic, complemented
225#884—21no—
226#882—21no—
227#882—61no—
228#882—61no—
229#874—31no—
230C4×D12—31no—
231C3×#102—31no—
232C3×#102—31no—
233C3×C22⋊C8—31no—
234#832—31no—
235#832—31no—
236#832—31no—
237#832—31no—
238#832—61no—
239#830—31no—
240#830C2×D311yescharacteristic, complemented
241#821—31no—
242#821—31no—
243(C2×D3)⋊C8—31no—
244Dic3⋊C8—31no—
245C8×Dic3—31no—
246#809—31no—
247#809—31no—
248#809—61no—
249#809C2×D311yescharacteristic, complemented
250#809C2×D311yescharacteristic, complemented
251#807—31no—
252#807—31no—
253#807—61no—
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—21no—
261C22×C3×D3—21no—
262C22×C3×D3—21no—
263C22×C3×D3—42no—
264C22×C3×D3—42no—
265C22×C3×D3—42no—
266C22×C3×D3—42no—
267C22×C3×D3—42no—
268C22×C3×D3—42no—
269C22×C3×D3—81no—
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
284#638—42no—
285C2×C3⋊Dic3—21no—
286C4⋊(C3⋊D3)—21no—
287C4⋊(C3⋊D3)—21no—
288C3×#67—42no—
289C3×#67—42no—
290C3×#67—81no—
291C3×#67D814yescomplemented
292C2×C3×Dic3C2×D411yescharacteristic
293C2×C3×Dic3C2×D411yescharacteristic
294C2×C3×Dic3C2×D411yescharacteristic
295C3×D12—21no—
296C3×D12—21no—
297C3×D12—21no—
298C3×D12—21no—
299C3×D12—21no—
300C3×D12—21no—
301C3×D12—42no—
302C3×D12—42no—
303C3×D12—42no—
304C3×D12C2×D412yescomplemented
305C3×D12C2×D412yescomplemented
306C3×C4×D3—21no—
307C3×C4×D3—21no—
308C3×C4×D3—42no—
309#626—42no—
310#626—42no—
311#626—81no—
312#625—42no—
313D3×Dic3—42no—
314C3⋊(C3⋊C8)—21no—
315C3⋊(C3⋊C8)C2×D412yescomplemented
316C3×C3⋊C8—21no—
317C3×C3⋊C8—21no—
318C22×D8—91no—
319C22×D8—91no—
320D42—31no—
321D42—91no—
322#493—91no—
323#466—91no—
324#466—91no—
325#459—91no—
326#459—91no—
327#447—31no—
328#447—91no—
329#447—91no—
330#447—91no—
331C4×D8—91no—
332C8×D4—91no—
333C24×C3—61no—
334C24×C3—61no—
335C24×C3—61no—
336C23×D3—21no—
337C23×D3—21no—
338C23×D3—21no—
339C23×D3—61no—
340C23×D3—61no—
341C2×C3×D4—21no—
342C2×C3×D4—21no—
343C2×C3×D4—21no—
344C2×C3×D4—31no—
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—62no—
352C2×C3×D4—61no—
353C2×C3×D4—61no—
354C2×C3×D4—61no—
355C2×C3×D4—61no—
356C2×C3×D4—62no—
357C2×C3×D4—61no—
358C2×C3×D4—61no—
359C2×C3×D4—121no—
360C2×C3×D4—121no—
361C2×C3×D4—121no—
362C2×C3×D4—124no—
363C2×C3×D4C22×D311yescharacteristic
364C2×C3×D4C22×D311yescharacteristic
365C22×C3×C4—21no—
366C22×C3×C4—31no—
367C22×C3×C4—61no—
368C22×C3×C4C22×D311yescharacteristic
369C22×C3×C4C22×D311yescharacteristic
370C2×#67—21no—
371C2×#67—21no—
372C2×#67—21no—
373C2×#67—61no—
374C2×#67—61no—
375C2×#67—61no—
376C2×#67—61no—
377C2×#67—61no—
378C2×#67—61no—
379C2×#67—61no—
380C2×#67—121no—
381C2×#67—124no—
382C2×#67#6711yescharacteristic
383C22×Dic3—61no—
384D3×D4—22no—
385D3×D4—41no—
386D3×D4—44no—
387D3×D4—62no—
388D3×D4—121no—
389D3×D4—124no—
390C2×D12—22no—
391C2×D12—22no—
392C2×D12—21no—
393C2×D12—21no—
394C2×D12—21no—
395C2×D12—31no—
396C2×D12—31no—
397C2×D12—41no—
398C2×D12—41no—
399C2×D12—61no—
400C2×D12—62no—
401C2×D12—61no—
402C2×D12—61no—
403C2×D12—61no—
404C2×D12—121no—
405C2×D12C22×D311yescharacteristic
406C2×D12C22×D311yescharacteristic
407C2×D12C22×D311yescharacteristic
408C2×D12C22×D311yescharacteristic
409C2×C4×D3—21no—
410C2×C4×D3—61no—
411C2×C4×D3C22×D311yescharacteristic
412C3×D8—62no—
413C3×D8—121no—
414C2×C3×C8—31no—
415C2×C3×C8—31no—
416C3×C4⋊C4—21no—
417C3×C4⋊C4—31no—
418C3×C4⋊C4C22×D311yescharacteristic
419C3×C4⋊C4C22×D311yescharacteristic
420C3×C22⋊C4—21no—
421C3×C22⋊C4—21no—
422C3×C22⋊C4—31no—
423C3×C22⋊C4—31no—
424C3×C22⋊C4—41no—
425C3×C22⋊C4—61no—
426C3×C22⋊C4—61no—
427C3×C42—31no—
428#217—61no—
429#217—61no—
430#217#6711yescharacteristic
431#213—22no—
432#213—34no—
433#213—34no—
434#213—41no—
435#213—62no—
436#213—62no—
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(C2×D3)⋊C4—21no—
447(C2×D3)⋊C4—21no—
448(C2×D3)⋊C4—61no—
449(C2×D3)⋊C4—61no—
450(C2×D3)⋊C4—61no—
451(C2×D3)⋊C4—61no—
452(C2×D3)⋊C4—121no—
453(C2×D3)⋊C4#6711yescharacteristic
454C4⋊Dic3—31no—
455C4⋊Dic3—31no—
456C4⋊Dic3—61no—
457Dic3⋊C4#6711yescharacteristic
458C4×Dic3C22×D311yescharacteristic
459C2×C3⋊C8—31no—
460C2×C3⋊C8—31no—
461C2×C3⋊C8—31no—
462C2×C3⋊C8—31no—
463C2×C3⋊C8—61no—
464C2×C3⋊C8—61no—
465C2×C3⋊C8—62no—
466C2×C3⋊C8—62no—
467C2×C3⋊C8—62no—
468C2×C3⋊C8—122no—
469C2×C3⋊C8C22×D311yescharacteristic
470C2×C3⋊C8C22×D311yescharacteristic
471D24—62no—
472D24—121no—
473D3×C8—62no—
474C22×C32—21no—
475C22×C32—21no—
476C22×C32—41no—
477C22×C32—41no—
478C22×C32—41no—
479C22×C32C2×D812yescomplemented
480C22×C32C22×D411yescharacteristic
481C2×C3⋊D3—41no—
482C2×C3⋊D3—41no—
483C2×C3⋊D3—41no—
484C2×C3×D3—21no—
485C2×C3×D3—21no—
486C2×C3×D3—22no—
487C2×C3×D3—22no—
488C2×C3×D3—41no—
489C2×C3×D3—41no—
490C2×C3×D3—41no—
491C2×C3×D3—41no—
492C2×C3×D3—41no—
493C2×C3×D3—41no—
494C2×C3×D3—41no—
495C2×C3×D3—41no—
496C2×C3×D3—41no—
497C2×C3×D3—41no—
498C2×C3×D3—84no—
499C2×C3×D3—84no—
500C2×C3×D3—84no—
501C2×C3×D3C2×D812yescomplemented
502D32—84no—
503C32×C4—21no—
504C32×C4—41no—
505C32×C4C22×D411yescharacteristic
506C32×C4H(5,𝔽2)11yescharacteristic
507C3⋊Dic3—41no—
508C3×Dic3—21no—
509C3×Dic3—21no—
510C3×Dic3C2×D812yescomplemented
511C22×D4—31no—
512C22×D4—31no—
513C22×D4—31no—
514C22×D4—61no—
515C22×D4—91no—
516C22×D4—181no—
517C2×D8—31no—
518C2×D8—31no—
519C2×D8—91no—
520C2×D8—91no—
521C2×D8—91no—
522C2×D8—91no—
523C2×D8—91no—
524C2×D8—91no—
525C2×D8—91no—
526C2×D8—184no—
527C2×D8—184no—
528C22×C8—91no—
529C22×C8—91no—
530#127—31no—
531#127—91no—
532#121—31no—
533#121—61no—
534#121—91no—
535#121—91no—
536#121—181no—
537#121D3211yescharacteristic, complemented
538#120—61no—
539#120—61no—
540#120—181no—
541#120—181no—
542C4×D4—31no—
543C4×D4—31no—
544C4×D4—91no—
545#107—91no—
546C4⋊C8—91no—
547#102—31no—
548#102—31no—
549#102—91no—
550#102—91no—
551#102—91no—
552#102—91no—
553C22⋊C8—31no—
554C22⋊C8—91no—
555C4×C8—91no—
556C23×C3—21no—
557C23×C3—21no—
558C23×C3—21no—
559C23×C3—31no—
560C23×C3—41no—
561C23×C3—61no—
562C23×C3—61no—
563C23×C3—61no—
564C23×C3—61no—
565C23×C3—122no—
566C23×C3—122no—
567C23×C3—122no—
568C23×C3—122no—
569C23×C3—122no—
570C23×C3—122no—
571C23×C3—241no—
572C23×C3—241no—
573C23×C3—241no—
574C23×C3D3×D411yescharacteristic
575C23×C3C2×#6711yescharacteristic
576C22×D3—21no—
577C22×D3—21no—
578C22×D3—21no—
579C22×D3—21no—
580C22×D3—42no—
581C22×D3—42no—
582C22×D3—42no—
583C22×D3—42no—
584C22×D3—42no—
585C22×D3—42no—
586C22×D3—61no—
587C22×D3—61no—
588C22×D3—81no—
589C22×D3—81no—
590C22×D3—81no—
591C22×D3—121no—
592C22×D3—122no—
593C22×D3—122no—
594C22×D3—122no—
595C22×D3—122no—
596C22×D3—241no—
597C22×D3—241no—
598C22×D3C2×#6711yescharacteristic
599C3×D4—21no—
600C3×D4—21no—
601C3×D4—21no—
602C3×D4—21no—
603C3×D4—34no—
604C3×D4—32no—
605C3×D4—32no—
606C3×D4—41no—
607C3×D4—41no—
608C3×D4—42no—
609C3×D4—42no—
610C3×D4—61no—
611C3×D4—61no—
612C3×D4—61no—
613C3×D4—61no—
614C3×D4—61no—
615C3×D4—61no—
616C3×D4—82no—
617C3×D4—122no—
618C3×D4—122no—
619C3×D4—122no—
620C3×D4—122no—
621C3×D4—122no—
622C3×D4—241no—
623C2×C3×C4—21no—
624C2×C3×C4—21no—
625C2×C3×C4—21no—
626C2×C3×C4—21no—
627C2×C3×C4—21no—
628C2×C3×C4—21no—
629C2×C3×C4—21no—
630C2×C3×C4—21no—
631C2×C3×C4—31no—
632C2×C3×C4—31no—
633C2×C3×C4—31no—
634C2×C3×C4—41no—
635C2×C3×C4—41no—
636C2×C3×C4—41no—
637C2×C3×C4—61no—
638C2×C3×C4—61no—
639C2×C3×C4—122no—
640C2×C3×C4D3×D411yescharacteristic
641C2×C3×C4C2×#6711yescharacteristic
642C2×C3×C4C23×D311yescharacteristic
643C2×C3×C4C23×D311yescharacteristic
644#67—42no—
645#67—42no—
646#67—81no—
647#67—122no—
648#67—122no—
649#67—122no—
650#67—122no—
651#67—122no—
652#67—122no—
653#67—242no—
654#67—241no—
655#67#21314yescomplemented
656C2×Dic3—61no—
657C2×Dic3—61no—
658C2×Dic3—121no—
659C2×Dic3—122no—
660C2×Dic3C2×#6711yescharacteristic
661C2×Dic3C2×#6711yescharacteristic
662C2×Dic3C2×#6711yescharacteristic
663D12—21no—
664D12—21no—
665D12—21no—
666D12—21no—
667D12—21no—
668D12—21no—
669D12—42no—
670D12—42no—
671D12—42no—
672D12—61no—
673D12—61no—
674D12—61no—
675D12—61no—
676D12—121no—
677D12—121no—
678D12—122no—
679D12—122no—
680D12—241no—
681D12D3×D412yescomplemented
682D12D3×D412yescomplemented
683C4×D3—21no—
684C4×D3—21no—
685C4×D3—42no—
686C4×D3—122no—
687C3×C8—61no—
688C3×C8—61no—
689C3⋊C8—21no—
690C3⋊C8—21no—
691C3⋊C8—32no—
692C3⋊C8—32no—
693C3⋊C8—62no—
694C3⋊C8—61no—
695C3⋊C8—61no—
696C3⋊C8—121no—
697C2×C32—22no—
698C2×C32—81no—
699C2×C32D4211yescharacteristic
700C2×C32C22×D811yescharacteristic
701C2×C32#57611yescharacteristic
702C3⋊D3—81no—
703C3×D3—22no—
704C3×D3—42no—
705C3×D3—42no—
706C3×D3—81no—
707C3×D3—81no—
708C24—61no—
709C24—61no—
710C24—61no—
711C24—181no—
712C2×D4—21no—
713C2×D4—31no—
714C2×D4—31no—
715C2×D4—31no—
716C2×D4—31no—
717C2×D4—31no—
718C2×D4—62no—
719C2×D4—62no—
720C2×D4—61no—
721C2×D4—61no—
722C2×D4—61no—
723C2×D4—61no—
724C2×D4—62no—
725C2×D4—61no—
726C2×D4—61no—
727C2×D4—91no—
728C2×D4—121no—
729C2×D4—121no—
730C2×D4—121no—
731C2×D4—124no—
732C2×D4—181no—
733C2×D4—181no—
734C2×D4—181no—
735C2×D4—182no—
736C2×D4—181no—
737C2×D4—181no—
738C2×D4—361no—
739C2×D4—364no—
740C2×D4C2×D3211yescharacteristic
741C22×C4—31no—
742C22×C4—61no—
743C22×C4—181no—
744C22×C4C2×D3211yescharacteristic
745D8—62no—
746D8—94no—
747D8—121no—
748D8—182no—
749D8—182no—
750D8—182no—
751D8—182no—
752D8—182no—
753D8—361no—
754C2×C8—31no—
755C2×C8—31no—
756C2×C8—91no—
757C2×C8—91no—
758C2×C8—182no—
759C2×C8—182no—
760C4⋊C4—31no—
761C4⋊C4—91no—
762C4⋊C4C2×D3211yescharacteristic
763C22⋊C4—21no—
764C22⋊C4—31no—
765C22⋊C4—31no—
766C22⋊C4—61no—
767C22⋊C4—61no—
768C22⋊C4—181no—
769C22⋊C4—181no—
770C22⋊C4—181no—
771C42—31no—
772C22×C3—21no—
773C22×C3—21no—
774C22×C3—21no—
775C22×C3—21no—
776C22×C3—21no—
777C22×C3—22no—
778C22×C3—32no—
779C22×C3—41no—
780C22×C3—41no—
781C22×C3—41no—
782C22×C3—41no—
783C22×C3—41no—
784C22×C3—41no—
785C22×C3—41no—
786C22×C3—41no—
787C22×C3—61no—
788C22×C3—61no—
789C22×C3—62no—
790C22×C3—62no—
791C22×C3—81no—
792C22×C3—81no—
793C22×C3—81no—
794C22×C3—121no—
795C22×C3—121no—
796C22×C3—121no—
797C22×C3—121no—
798C22×C3—121no—
799C22×C3—121no—
800C22×C3—121no—
801C22×C3—121no—
802C22×C3—121no—
803C22×C3—121no—
804C22×C3—244no—
805C22×C3—244no—
806C22×C3—244no—
807C22×C3D3×D812yescomplemented
808C22×C3C2×#21312yescomplemented
809C22×C3C2×D3×D411yescharacteristic
810C22×C3C22×#6711yescharacteristic
811C2×D3—21no—
812C2×D3—21no—
813C2×D3—22no—
814C2×D3—22no—
815C2×D3—41no—
816C2×D3—41no—
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—84no—
826C2×D3—84no—
827C2×D3—84no—
828C2×D3—121no—
829C2×D3—121no—
830C2×D3—121no—
831C2×D3—121no—
832C2×D3—121no—
833C2×D3—121no—
834C2×D3—241no—
835C2×D3—241no—
836C2×D3—241no—
837C2×D3—244no—
838C2×D3—244no—
839C2×D3C2×#21312yescomplemented
840C3×C4—21no—
841C3×C4—21no—
842C3×C4—21no—
843C3×C4—21no—
844C3×C4—32no—
845C3×C4—41no—
846C3×C4—41no—
847C3×C4—41no—
848C3×C4—61no—
849C3×C4—61no—
850C3×C4—81no—
851C3×C4C2×D3×D411yescharacteristic
852C3×C4C2×D3×D411yescharacteristic
853C3×C4#100411yescharacteristic
854C3×C4#100411yescharacteristic
855Dic3—21no—
856Dic3—21no—
857Dic3—121no—
858Dic3—121no—
859Dic3—241no—
860Dic3C2×#21312yescomplemented
861C32D4×D811yescharacteristic, complemented, Sylow
862C23—21no—
863C23—31no—
864C23—61no—
865C23—61no—
866C23—61no—
867C23—61no—
868C23—122no—
869C23—122no—
870C23—122no—
871C23—122no—
872C23—122no—
873C23—122no—
874C23—181no—
875C23—241no—
876C23—241no—
877C23—241no—
878C23—362no—
879C23—362no—
880C23—721no—
881C23D3×#6711yescharacteristic
882D4—21no—
883D4—21no—
884D4—34no—
885D4—32no—
886D4—32no—
887D4—42no—
888D4—61no—
889D4—61no—
890D4—61no—
891D4—61no—
892D4—61no—
893D4—61no—
894D4—122no—
895D4—122no—
896D4—122no—
897D4—122no—
898D4—122no—
899D4—181no—
900D4—181no—
901D4—241no—
902D4—362no—
903D4—362no—
904D4—362no—
905D4—362no—
906D4—721no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—31no—
911C2×C4—31no—
912C2×C4—31no—
913C2×C4—61no—
914C2×C4—61no—
915C2×C4—122no—
916C2×C4—181no—
917C2×C4—362no—
918C2×C4D3×#6711yescharacteristic
919C2×C4C22×D3211yescharacteristic
920C8—61no—
921C8—61no—
922C8—92no—
923C8—181no—
924C2×C3—22no—
925C2×C3—22no—
926C2×C3—21no—
927C2×C3—21no—
928C2×C3—21no—
929C2×C3—42no—
930C2×C3—62no—
931C2×C3—81no—
932C2×C3—81no—
933C2×C3—122no—
934C2×C3—122no—
935C2×C3—161no—
936C2×C3—241no—
937C2×C3—241no—
938C2×C3#559011yescharacteristic
939C2×C3C2×D3×D811yescharacteristic
940C2×C3#577411yescharacteristic
941C2×C3C22×#21311yescharacteristic
942C2×C3D4×#6711yescharacteristic
943C2×C3#583511yescharacteristic
944D3—22no—
945D3—42no—
946D3—42no—
947D3—81no—
948D3—81no—
949D3—241no—
950D3—241no—
951D3—481no—
952C22—21no—
953C22—21no—
954C22—32no—
955C22—41no—
956C22—41no—
957C22—41no—
958C22—61no—
959C22—61no—
960C22—62no—
961C22—62no—
962C22—121no—
963C22—121no—
964C22—121no—
965C22—121no—
966C22—121no—
967C22—121no—
968C22—121no—
969C22—121no—
970C22—121no—
971C22—121no—
972C22—244no—
973C22—244no—
974C22—244no—
975C22—361no—
976C22—361no—
977C22—361no—
978C22—724no—
979C22D3×#21312yescomplemented
980C22C2×D3×#6711yescharacteristic
981C4—21no—
982C4—32no—
983C4—41no—
984C4—61no—
985C4—61no—
986C4—361no—
987C4D32×D411yescharacteristic
988C4#6431311yescharacteristic
989C3—21no—
990C3#8002411yescharacteristic, complemented
991C3D4×#21311yescharacteristic, complemented
992C2—22no—
993C2—62no—
994C2—81no—
995C2—122no—
996C2—122no—
997C2—241no—
998C2—241no—
999C2—721no—
1000C2C2×D3×#21311yescharacteristic
1001C2#1059528711yescharacteristic
1002C2#1059545411yescharacteristic
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. D12×#67C2semidirect
4. C22×#3713C2semidirect
5. #10592737C2semidirect
6. C3×#5036C2semidirect
7. #10591482C2semidirect
8. #10591447C2semidirect
9. #10591428C2semidirect
10. #10591162C2semidirect
11. #67⋊(C3⋊C8)C2semidirect
12. #10590595C2semidirect
13. #10590547C2semidirect
14. #10590499C2semidirect
15. #10590452C2semidirect
19. C2×C3×D3×D4C22semidirect
20. C22×C3×D12C22semidirect
21. C22×C3×D12C22semidirect
23. C2×D3×D12C22semidirect
24. C32×#121C22semidirect
25. C2×#3753C22semidirect
26. #64139C22semidirect
27. C22×C3⋊(C3⋊C8)C22semidirect
28. C3×#940C22semidirect
30. C2×C3×#213C22semidirect
31. C2×C3×#213C22semidirect
33. C3×#895C22semidirect
34. C3×#893C22semidirect
40. #63911C22semidirect
41. #63908C22semidirect
42. Dic3×D12C22semidirect
44. C2×#3714C22semidirect
45. C2×#3714C22semidirect
48. C2×#3713C22semidirect
49. C2×#3713C22semidirect
50. C2×#3713C22semidirect
51. C2×D3×C3⋊C8C22semidirect
52. #63659C22semidirect
53. #63636C22semidirect
54. #63634C22semidirect
55. C3×#830C22semidirect
56. C3×#809C22semidirect
57. C3×#809C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
59. #63563C22semidirect
60. #63563C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. Dic3×C3⋊C8C22semidirect
69. #5609D3semidirect
84. #5036D3semidirect
156. #3713D4semidirect
167. C2×D3×D4C2×D3semidirect
169. C22×D12C2×D3semidirect
170. C22×D12C2×D3semidirect
177. C3×#121C2×D3semidirect
178. C3×#121C2×D3semidirect
185. #940C2×D3semidirect
207. C2×#213C2×D3semidirect
208. C2×#213C2×D3semidirect
223. #895C2×D3semidirect
224. #893C2×D3semidirect
240. #830C2×D3semidirect
249. #809C2×D3semidirect
250. #809C2×D3semidirect
291. C3×#67D8semidirect
304. C3×D12C2×D4semidirect
305. C3×D12C2×D4semidirect
315. C3⋊(C3⋊C8)C2×D4semidirect
479. C22×C32C2×D8semidirect
501. C2×C3×D3C2×D8semidirect
510. C3×Dic3C2×D8semidirect
537. #121D32semidirect
655. #67#213semidirect
681. D12D3×D4semidirect
682. D12D3×D4semidirect
807. C22×C3D3×D8semidirect
808. C22×C3C2×#213semidirect
839. C2×D3C2×#213semidirect
860. Dic3C2×#213semidirect
861. C32D4×D8semidirect
979. C22D3×#213semidirect
990. C3#80024semidirect
991. 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
D12×#672
C22×#37132
#105927372
C3×#50362
#105914822
#105914472
#105914282
#105911622
#67⋊(C3⋊C8)2
#105905952
#105905472
#105904992
#105904522
D4×#2133
#800243