Finite Group Databasebeta

← #67×#213 #11885745

Subgroups — #67×#213 #11885745

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×D4×#67C211yesmaximal, characteristic, complemented
2C22×C3×#213C211yesmaximal, characteristic, complemented
3C2×D3×#213C211yesmaximal, characteristic, complemented
4D12×#67C211yesmaximal, characteristic, complemented
5#10592916C211yesmaximal, characteristic, complemented
6#10591515C211yesmaximal, characteristic, complemented
7#10591498C211yesmaximal, characteristic, complemented
8#10591482C211yesmaximal, characteristic, complemented
9#10591481C211yesmaximal, characteristic, complemented
10#10591447C211yesmaximal, characteristic, complemented
11#10591428C211yesmaximal, characteristic, complemented
12Dic3×#213C211yesmaximal, characteristic, complemented
13#10591164C211yesmaximal, characteristic, complemented
14#10591160C211yesmaximal, characteristic, complemented
15C3⋊C8×#67C211yesmaximal, characteristic, complemented
16D8×#67—31nomaximal
17D4×#213—31nomaximal
18C22×C32×D4C2211yescharacteristic, complemented
19C22×C3×#67—21no—
20C2×C3×D3×D4C2211yescharacteristic, complemented
21C22×C3×D12C2211yescharacteristic, complemented
22C2×D3×#67—21no—
23C2×D3×D12C2211yescharacteristic, complemented
24C2×#3753C2211yescharacteristic, complemented
25C2×#3753C2211yescharacteristic, complemented
26#64139C2211yescharacteristic, complemented
27C3×#953—21no—
28C3×#940C2211yescharacteristic, complemented
29C3×#939—21no—
30C3×#938C2211yescharacteristic, complemented
31C3×#937—21no—
32C3×D4×Dic3C2211yescharacteristic, complemented
33C2×C3×#213—24no—
34C2×C3×#213C2211yescharacteristic
35C2×C3×#213C2211yescharacteristic, complemented
36C2×C3×#213C2211yescharacteristic, complemented
37C2×C3×#213C2211yescharacteristic, complemented
38C3×#930C2211yescharacteristic, complemented
39C3×C4×#67C2211yescharacteristic
40C22×C3×C3⋊C8C2211yescharacteristic, complemented
41#63977—21no—
42D3×#213—24no—
43#63922—21no—
44#63911C2211yescharacteristic, complemented
45#63908C2211yescharacteristic, complemented
46Dic3×D12C2211yescharacteristic, complemented
47#63886—21no—
48C2×#3714C2211yescharacteristic, complemented
49C2×#3713C2211yescharacteristic, complemented
50C2×#3713C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52#63659C2211yescharacteristic, complemented
53#63659C2211yescharacteristic, complemented
54#63657C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63564C2211yescharacteristic, complemented
58#63563C2211yescharacteristic, complemented
59#63562C2211yescharacteristic, complemented
60#63562C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62Dic3×C3⋊C8C2211yescharacteristic, complemented
63C22×C3×D8—31no—
64C3×D42—31no—
65D4×#67—31no—
66D4×#67D311yescharacteristic, complemented
67C22×#213—31no—
68C22×#213D311yescharacteristic, complemented
69C2×D3×D8—31no—
70D4×D12—31no—
71#5217—31no—
72#5217—31no—
73#5217—31no—
74#5217—31no—
75#5217—61no—
76#5157—31no—
77#5156—31no—
78#5156—31no—
79#5151—31no—
80#5150—31no—
81#5150—31no—
82Dic3×D8—31no—
83#5115—31no—
84C8×#67—31no—
85#5073—31no—
86#5072—31no—
87#5038—31no—
88#5038—31no—
89#5036—31no—
90#5036—31no—
91#5015—31no—
92C4×#213—31no—
93D4×C3⋊C8—31no—
94C24×C32—21no—
95C23×C3×D3—21no—
96C23×C3×D3—21no—
97C22×D32—21no—
98C2×C32×D4—22no—
99C2×C32×D4—21no—
100C2×C32×D4—41no—
101C2×C32×D4C2311yescharacteristic
102C2×C32×D4C2311yescharacteristic
103C22×C32×C4C2311yescharacteristic
104C2×#638—21no—
105C2×C4⋊(C3⋊D3)C2311yescharacteristic
106C2×C3×#67—21no—
107C2×C3×#67—21no—
108C2×C3×#67—21no—
109C2×C3×#67—21no—
110C2×C3×#67—21no—
111C2×C3×#67—44no—
112C2×C3×#67D411yescharacteristic
113C22×C3×Dic3—21no—
114C3×D3×D4—22no—
115C3×D3×D4—41no—
116C2×C3×D12—22no—
117C2×C3×D12—21no—
118C2×C3×D12—41no—
119C2×C3×D12C2311yescharacteristic
120C2×C3×D12C2311yescharacteristic
121C2×C3×D12C2311yescharacteristic
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—
131#3753—22no—
132#3753—41no—
133#3752—21no—
134C4⋊(C3⋊Dic3)C2311yescharacteristic
135C2×C3⋊(C3⋊C8)C2311yescharacteristic
136C2×C3⋊(C3⋊C8)C2311yescharacteristic
137C3×#217—21no—
138C3×#217—21no—
139C3×#217D411yescharacteristic
140C3×#213—22no—
141C3×#213—22no—
142C3×#213—22no—
143C3×#213D414yescomplemented
144C3×(C2×D3)⋊C4—21no—
145C3×(C2×D3)⋊C4D411yescharacteristic
146C3×C4⋊Dic3C2311yescharacteristic
147C3×Dic3⋊C4D411yescharacteristic
148C3×C4×Dic3C2311yescharacteristic
149C2×C3×C3⋊C8—22no—
150C2×C3×C3⋊C8C2311yescharacteristic
151C2×C3×C3⋊C8C2311yescharacteristic
152(C2×D3)⋊Dic3—21no—
153(C2×D3)⋊Dic3—21no—
154#3714—22no—
155#3713—22no—
156#3713—41no—
157D3×C3⋊C8—22no—
158D4×D8—91noSylow
159C22×C3×D4—21no—
160C22×C3×D4—31no—
161C22×C3×D4—31no—
162C22×C3×D4—61no—
163C22×C3×D4C2×D311yescharacteristic, complemented
164C22×C3×D4C2×D311yescharacteristic, complemented
165C22×#67—21no—
166C22×#67—61no—
167C2×D3×D4—31no—
168C2×D3×D4—61no—
169C2×D3×D4C2×D311yescharacteristic, complemented
170C22×D12—31no—
171C22×D12C2×D311yescharacteristic, complemented
172C2×C3×D8—31no—
173C2×C3×D8—31no—
174C2×C3×D8—31no—
175C2×C3×D8—31no—
176C2×C3×D8—64no—
177C22×C3×C8—31no—
178C3×#127—31no—
179C3×#121—31no—
180C3×#121—31no—
181C3×#121—61no—
182C3×#120—61no—
183C3×#120—61no—
184C3×C4×D4—31no—
185C3×C4×D4—31no—
186#953—21no—
187#953—61no—
188#940—31no—
189#940C2×D311yescharacteristic, complemented
190#939—21no—
191#939—61no—
192#938—31no—
193#938C2×D311yescharacteristic, complemented
194#937—21no—
195#937—61no—
196D4×Dic3—31no—
197D4×Dic3C2×D311yescharacteristic, complemented
198C2×#213—24no—
199C2×#213—31no—
200C2×#213—31no—
201C2×#213—31no—
202C2×#213—31no—
203C2×#213—31no—
204C2×#213—31no—
205C2×#213—31no—
206C2×#213—31no—
207C2×#213—31no—
208C2×#213—61no—
209C2×#213—61no—
210C2×#213—64no—
211C2×#213C2×D311yescharacteristic
212C2×#213C2×D311yescharacteristic, complemented
213C2×#213C2×D311yescharacteristic, complemented
214C2×#213C2×D311yescharacteristic, complemented
215#930—31no—
216#930—31no—
217#930—31no—
218#930—61no—
219#930C2×D311yescharacteristic, complemented
220C4×#67C2×D311yescharacteristic
221C22×C3⋊C8—31no—
222C22×C3⋊C8C2×D311yescharacteristic, complemented
223D3×D8—64no—
224C2×D24—31no—
225C2×D3×C8—31no—
226#895—61no—
227#882—61no—
228#882—61no—
229#874—31no—
230C4×D12—31no—
231#832—31no—
232#832—31no—
233#832—31no—
234#832—31no—
235#832—31no—
236#832—31no—
237#832—31no—
238#832—61no—
239#832—61no—
240#830—31no—
241#830—31no—
242#830—31no—
243#830—61no—
244#821—31no—
245#821—31no—
246(C2×D3)⋊C8—31no—
247#818—31no—
248Dic3⋊C8—31no—
249C8×Dic3—31no—
250#809—31no—
251#809—31no—
252#809—31no—
253#807—31no—
254C4⋊(C3⋊C8)—31no—
255C4×C3⋊C8—31no—
256C23×C32—21no—
257C23×C32—21no—
258C23×C32—42no—
259C23×C32—42no—
260C23×C32—81no—
261C23×C32C2×D411yescharacteristic
262C22×C3⋊D3—21no—
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—21no—
279C32×D4—42no—
280C32×D4C2×D412yescomplemented
281C2×C32×C4—21no—
282C2×C32×C4—21no—
283C2×C32×C4C2×D411yescharacteristic
284C2×C32×C4C2411yescharacteristic
285#638—42no—
286C2×C3⋊Dic3—21no—
287C4⋊(C3⋊D3)—21no—
288C4⋊(C3⋊D3)—21no—
289C3×#67—42no—
290C3×#67—42no—
291C3×#67—42no—
292C3×#67—42no—
293C3×#67—81no—
294C3×#67D814yescomplemented
295C2×C3×Dic3—21no—
296C2×C3×Dic3—42no—
297C2×C3×Dic3C2×D411yescharacteristic
298C2×C3×Dic3C2×D411yescharacteristic
299C2×C3×Dic3C2×D411yescharacteristic
300C3×D12—21no—
301C3×D12—21no—
302C3×D12—21no—
303C3×D12—21no—
304C3×D12—21no—
305C3×D12—42no—
306C3×D12C2×D412yescomplemented
307C3×C4×D3—21no—
308C3×C4×D3—21no—
309#626—42no—
310#626—42no—
311#626—81no—
312#625—42no—
313D3×Dic3—42no—
314C3⋊(C3⋊C8)—21no—
315C3⋊(C3⋊C8)—21no—
316C3×C3⋊C8—21no—
317C3×C3⋊C8C2×D412yescomplemented
318C22×D8—31no—
319C22×D8—91no—
320D42—31no—
321D42—91no—
322#493—91no—
323#466—91no—
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—21no—
334C24×C3—21no—
335C24×C3—41no—
336C24×C3—61no—
337C24×C3—61no—
338C23×D3—21no—
339C23×D3—21no—
340C23×D3—61no—
341C23×D3—61no—
342C2×C3×D4—22no—
343C2×C3×D4—22no—
344C2×C3×D4—21no—
345C2×C3×D4—21no—
346C2×C3×D4—21no—
347C2×C3×D4—21no—
348C2×C3×D4—31no—
349C2×C3×D4—31no—
350C2×C3×D4—31no—
351C2×C3×D4—31no—
352C2×C3×D4—41no—
353C2×C3×D4—42no—
354C2×C3×D4—41no—
355C2×C3×D4—41no—
356C2×C3×D4—42no—
357C2×C3×D4—62no—
358C2×C3×D4—61no—
359C2×C3×D4—61no—
360C2×C3×D4—61no—
361C2×C3×D4—62no—
362C2×C3×D4—61no—
363C2×C3×D4—61no—
364C2×C3×D4—61no—
365C2×C3×D4—121no—
366C2×C3×D4—121no—
367C2×C3×D4—124no—
368C2×C3×D4C22×D311yescharacteristic
369C2×C3×D4C22×D311yescharacteristic
370C2×C3×D4C22×D311yescharacteristic
371C2×C3×D4C22×D311yescharacteristic
372C22×C3×C4—21no—
373C22×C3×C4—31no—
374C22×C3×C4—61no—
375C22×C3×C4C22×D311yescharacteristic
376C22×C3×C4C22×D311yescharacteristic
377C2×#67—21no—
378C2×#67—21no—
379C2×#67—21no—
380C2×#67—21no—
381C2×#67—21no—
382C2×#67—44no—
383C2×#67—61no—
384C2×#67—61no—
385C2×#67—61no—
386C2×#67—61no—
387C2×#67—61no—
388C2×#67—61no—
389C2×#67—61no—
390C2×#67—121no—
391C2×#67—124no—
392C2×#67#6711yescharacteristic
393C22×Dic3—21no—
394C22×Dic3—61no—
395D3×D4—22no—
396D3×D4—41no—
397D3×D4—62no—
398D3×D4—121no—
399D3×D4—124no—
400C2×D12—22no—
401C2×D12—21no—
402C2×D12—31no—
403C2×D12—31no—
404C2×D12—41no—
405C2×D12—61no—
406C2×D12—62no—
407C2×D12—61no—
408C2×D12—61no—
409C2×D12—61no—
410C2×D12—121no—
411C2×D12C22×D311yescharacteristic
412C2×D12C22×D311yescharacteristic
413C2×D12C22×D311yescharacteristic
414C2×C4×D3—61no—
415C2×C4×D3C22×D311yescharacteristic
416C3×D8—34no—
417C3×D8—62no—
418C3×D8—62no—
419C3×D8—62no—
420C2×C3×C8—31no—
421C2×C3×C8—31no—
422C2×C3×C8—62no—
423C3×C4⋊C4—31no—
424C3×C4⋊C4—31no—
425C3×C22⋊C4—31no—
426C3×C22⋊C4—31no—
427C3×C22⋊C4—61no—
428C3×C22⋊C4—61no—
429C3×C22⋊C4—61no—
430C3×C42—31no—
431#217—21no—
432#217—21no—
433#217—61no—
434#217—61no—
435#217#6711yescharacteristic
436#213—22no—
437#213—22no—
438#213—22no—
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#213#6714yesdirect product factor
451(C2×D3)⋊C4—21no—
452(C2×D3)⋊C4—61no—
453(C2×D3)⋊C4—61no—
454(C2×D3)⋊C4—61no—
455(C2×D3)⋊C4—61no—
456(C2×D3)⋊C4—121no—
457(C2×D3)⋊C4#6711yescharacteristic
458C4⋊Dic3—31no—
459C4⋊Dic3—31no—
460C4⋊Dic3—61no—
461C4⋊Dic3C22×D311yescharacteristic
462Dic3⋊C4#6711yescharacteristic
463C4×Dic3C22×D311yescharacteristic
464C2×C3⋊C8—22no—
465C2×C3⋊C8—31no—
466C2×C3⋊C8—31no—
467C2×C3⋊C8—31no—
468C2×C3⋊C8—31no—
469C2×C3⋊C8—61no—
470C2×C3⋊C8—61no—
471C2×C3⋊C8—62no—
472C2×C3⋊C8C22×D311yescharacteristic
473C2×C3⋊C8C22×D311yescharacteristic
474D24—62no—
475D3×C8—62no—
476C22×C32—21no—
477C22×C32—21no—
478C22×C32—22no—
479C22×C32—41no—
480C22×C32—41no—
481C22×C32—41no—
482C22×C32—41no—
483C22×C32—41no—
484C22×C32—84no—
485C22×C32C2×D812yescomplemented
486C22×C32C22×D411yescharacteristic
487C2×C3⋊D3—41no—
488C2×C3⋊D3—41no—
489C2×C3⋊D3—41no—
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×C4C22×D411yescharacteristic
507C32×C4H(5,𝔽2)11yescharacteristic
508C3⋊Dic3—41no—
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—181no—
518C22×D4D3211yescharacteristic, complemented
519C2×D8—31no—
520C2×D8—31no—
521C2×D8—31no—
522C2×D8—31no—
523C2×D8—64no—
524C2×D8—91no—
525C2×D8—91no—
526C2×D8—91no—
527C2×D8—91no—
528C2×D8—91no—
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—91no—
539#121—181no—
540#120—61no—
541#120—61no—
542#120—181no—
543#120—181no—
544C4×D4—31no—
545C4×D4—31no—
546C4×D4—91no—
547#107—91no—
548C4⋊C8—91no—
549#102—91no—
550#102—91no—
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—21no—
562C23×C3—21no—
563C23×C3—31no—
564C23×C3—41no—
565C23×C3—41no—
566C23×C3—42no—
567C23×C3—42no—
568C23×C3—44no—
569C23×C3—42no—
570C23×C3—42no—
571C23×C3—61no—
572C23×C3—61no—
573C23×C3—61no—
574C23×C3—82no—
575C23×C3—81no—
576C23×C3—81no—
577C23×C3—82no—
578C23×C3—122no—
579C23×C3—122no—
580C23×C3—122no—
581C23×C3—122no—
582C23×C3—241no—
583C23×C3—241no—
584C23×C3D3×D411yescharacteristic
585C23×C3C2×#6711yescharacteristic
586C22×D3—21no—
587C22×D3—21no—
588C22×D3—21no—
589C22×D3—42no—
590C22×D3—42no—
591C22×D3—42no—
592C22×D3—42no—
593C22×D3—61no—
594C22×D3—61no—
595C22×D3—81no—
596C22×D3—81no—
597C22×D3—121no—
598C22×D3—122no—
599C22×D3—122no—
600C22×D3—122no—
601C22×D3—122no—
602C22×D3—241no—
603C22×D3—241no—
604C22×D3C2×#6711yescharacteristic
605C3×D4—22no—
606C3×D4—21no—
607C3×D4—21no—
608C3×D4—21no—
609C3×D4—21no—
610C3×D4—21no—
611C3×D4—21no—
612C3×D4—22no—
613C3×D4—34no—
614C3×D4—32no—
615C3×D4—41no—
616C3×D4—41no—
617C3×D4—42no—
618C3×D4—42no—
619C3×D4—44no—
620C3×D4—61no—
621C3×D4—61no—
622C3×D4—61no—
623C3×D4—61no—
624C3×D4—61no—
625C3×D4—122no—
626C3×D4—122no—
627C3×D4—122no—
628C3×D4—122no—
629C3×D4—122no—
630C3×D4—241no—
631C3×D4D3×D412yescomplemented
632C3×D4C2×#6712yescomplemented
633C2×C3×C4—21no—
634C2×C3×C4—21no—
635C2×C3×C4—21no—
636C2×C3×C4—21no—
637C2×C3×C4—21no—
638C2×C3×C4—21no—
639C2×C3×C4—31no—
640C2×C3×C4—31no—
641C2×C3×C4—31no—
642C2×C3×C4—41no—
643C2×C3×C4—41no—
644C2×C3×C4—61no—
645C2×C3×C4—61no—
646C2×C3×C4—61no—
647C2×C3×C4—122no—
648C2×C3×C4D3×D411yescharacteristic
649C2×C3×C4C2×#6711yescharacteristic
650C2×C3×C4C23×D311yescharacteristic
651C2×C3×C4C23×D311yescharacteristic
652#67—42no—
653#67—42no—
654#67—42no—
655#67—42no—
656#67—81no—
657#67—122no—
658#67—122no—
659#67—122no—
660#67—122no—
661#67—122no—
662#67—122no—
663#67—242no—
664#67—241no—
665#67#21314yesdirect product factor
666C2×Dic3—21no—
667C2×Dic3—42no—
668C2×Dic3—61no—
669C2×Dic3—61no—
670C2×Dic3—121no—
671C2×Dic3—122no—
672C2×Dic3C2×#6711yescharacteristic
673C2×Dic3C2×#6711yescharacteristic
674C2×Dic3C2×#6711yescharacteristic
675D12—21no—
676D12—21no—
677D12—21no—
678D12—21no—
679D12—21no—
680D12—42no—
681D12—61no—
682D12—61no—
683D12—61no—
684D12—61no—
685D12—121no—
686D12—121no—
687D12—122no—
688D12—122no—
689D12—241no—
690D12C2×#6712yescomplemented
691C4×D3—21no—
692C4×D3—21no—
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⋊C8C2×#6712yescomplemented
704C2×C32—22no—
705C2×C32—42no—
706C2×C32—81no—
707C2×C32D4211yescharacteristic
708C2×C32C22×D811yescharacteristic
709C2×C32#57611yescharacteristic
710C3⋊D3—81no—
711C3×D3—22no—
712C3×D3—42no—
713C3×D3—81no—
714C3×D3—81no—
715C24—21no—
716C24—61no—
717C24—61no—
718C24—181no—
719C2×D4—22no—
720C2×D4—21no—
721C2×D4—31no—
722C2×D4—31no—
723C2×D4—31no—
724C2×D4—31no—
725C2×D4—41no—
726C2×D4—62no—
727C2×D4—61no—
728C2×D4—61no—
729C2×D4—61no—
730C2×D4—62no—
731C2×D4—61no—
732C2×D4—61no—
733C2×D4—61no—
734C2×D4—91no—
735C2×D4—121no—
736C2×D4—121no—
737C2×D4—124no—
738C2×D4—181no—
739C2×D4—181no—
740C2×D4—181no—
741C2×D4—182no—
742C2×D4—181no—
743C2×D4—181no—
744C2×D4—361no—
745C2×D4—364no—
746C2×D4C2×D3211yescharacteristic
747C2×D4C2×D3211yescharacteristic
748C22×C4—31no—
749C22×C4—61no—
750C22×C4—181no—
751C22×C4C2×D3211yescharacteristic
752D8—34no—
753D8—62no—
754D8—62no—
755D8—62no—
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⋊C4—91no—
770C22⋊C4—31no—
771C22⋊C4—31no—
772C22⋊C4—61no—
773C22⋊C4—61no—
774C22⋊C4—61no—
775C22⋊C4—181no—
776C22⋊C4—181no—
777C22⋊C4—181no—
778C42—31no—
779C22×C3—21no—
780C22×C3—21no—
781C22×C3—21no—
782C22×C3—21no—
783C22×C3—22no—
784C22×C3—22no—
785C22×C3—21no—
786C22×C3—22no—
787C22×C3—32no—
788C22×C3—41no—
789C22×C3—41no—
790C22×C3—42no—
791C22×C3—42no—
792C22×C3—41no—
793C22×C3—41no—
794C22×C3—41no—
795C22×C3—41no—
796C22×C3—41no—
797C22×C3—41no—
798C22×C3—41no—
799C22×C3—41no—
800C22×C3—41no—
801C22×C3—41no—
802C22×C3—61no—
803C22×C3—61no—
804C22×C3—62no—
805C22×C3—81no—
806C22×C3—81no—
807C22×C3—81no—
808C22×C3—81no—
809C22×C3—84no—
810C22×C3—84no—
811C22×C3—88no—
812C22×C3—121no—
813C22×C3—121no—
814C22×C3—121no—
815C22×C3—121no—
816C22×C3—121no—
817C22×C3—121no—
818C22×C3—121no—
819C22×C3—121no—
820C22×C3—244no—
821C22×C3—244no—
822C22×C3D3×D812yescomplemented
823C22×C3C2×#21312yescomplemented
824C22×C3C2×D3×D411yescharacteristic
825C22×C3C22×#6711yescharacteristic
826C2×D3—21no—
827C2×D3—21no—
828C2×D3—22no—
829C2×D3—41no—
830C2×D3—41no—
831C2×D3—41no—
832C2×D3—41no—
833C2×D3—41no—
834C2×D3—41no—
835C2×D3—41no—
836C2×D3—41no—
837C2×D3—84no—
838C2×D3—84no—
839C2×D3—121no—
840C2×D3—121no—
841C2×D3—121no—
842C2×D3—121no—
843C2×D3—121no—
844C2×D3—121no—
845C2×D3—241no—
846C2×D3—241no—
847C2×D3—241no—
848C2×D3—244no—
849C2×D3—244no—
850C2×D3C2×#21312yescomplemented
851C3×C4—21no—
852C3×C4—21no—
853C3×C4—21no—
854C3×C4—21no—
855C3×C4—32no—
856C3×C4—41no—
857C3×C4—61no—
858C3×C4—61no—
859C3×C4—121no—
860C3×C4C2×D3×D411yescharacteristic
861C3×C4#100411yescharacteristic
862C3×C4#100411yescharacteristic
863C3×C4C22×#6711yescharacteristic
864Dic3—21no—
865Dic3—21no—
866Dic3—41no—
867Dic3—121no—
868Dic3—121no—
869Dic3—241no—
870Dic3C2×#21312yescomplemented
871C32D4×D811yescharacteristic, complemented, Sylow
872C23—21no—
873C23—21no—
874C23—31no—
875C23—42no—
876C23—42no—
877C23—61no—
878C23—61no—
879C23—61no—
880C23—81no—
881C23—122no—
882C23—122no—
883C23—122no—
884C23—122no—
885C23—181no—
886C23—241no—
887C23—241no—
888C23—362no—
889C23—362no—
890C23—721no—
891C23D3×#6711yescharacteristic
892D4—21no—
893D4—21no—
894D4—21no—
895D4—34no—
896D4—32no—
897D4—42no—
898D4—61no—
899D4—61no—
900D4—61no—
901D4—61no—
902D4—61no—
903D4—122no—
904D4—122no—
905D4—122no—
906D4—122no—
907D4—122no—
908D4—181no—
909D4—181no—
910D4—241no—
911D4—362no—
912D4—362no—
913D4—362no—
914D4—362no—
915D4—721no—
916D4D3×#6712yescomplemented
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—31no—
920C2×C4—31no—
921C2×C4—31no—
922C2×C4—61no—
923C2×C4—61no—
924C2×C4—61no—
925C2×C4—122no—
926C2×C4—181no—
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—42no—
941C2×C3—42no—
942C2×C3—62no—
943C2×C3—82no—
944C2×C3—82no—
945C2×C3—81no—
946C2×C3—81no—
947C2×C3—122no—
948C2×C3—241no—
949C2×C3—241no—
950C2×C3C2×D3×D811yescharacteristic
951C2×C3#575711yescharacteristic
952C2×C3C22×#21311yescharacteristic
953C2×C3D4×#6711yescharacteristic
954C2×C3D4×#6711yescharacteristic
955C2×C3#583511yescharacteristic
956D3—22no—
957D3—42no—
958D3—81no—
959D3—81no—
960D3—241no—
961D3—241no—
962D3—481no—
963C22—21no—
964C22—21no—
965C22—22no—
966C22—32no—
967C22—41no—
968C22—41no—
969C22—41no—
970C22—41no—
971C22—41no—
972C22—61no—
973C22—61no—
974C22—62no—
975C22—84no—
976C22—121no—
977C22—121no—
978C22—121no—
979C22—121no—
980C22—121no—
981C22—121no—
982C22—121no—
983C22—121no—
984C22—244no—
985C22—244no—
986C22—361no—
987C22—361no—
988C22—361no—
989C22—724no—
990C22D3×#21312yescomplemented
991C22C2×D3×#6711yescharacteristic
992C4—21no—
993C4—32no—
994C4—61no—
995C4—61no—
996C4—121no—
997C4—361no—
998C4C2×D3×#6711yescharacteristic
999C4#6433011yescharacteristic
1000C3—21no—
1001C3D4×#21311yescharacteristic, complemented
1002C3D8×#6711yescharacteristic, complemented
1003C2—22no—
1004C2—42no—
1005C2—62no—
1006C2—81no—
1007C2—122no—
1008C2—241no—
1009C2—241no—
1010C2—721no—
1011C2C2×D3×#21311yescharacteristic
1012C2#1059509611yescharacteristic
1013C2#67211yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
hypercenterC22×D4D32
hypocenterC32D4×D8
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C3×D4×#67C2semidirect
2. C22×C3×#213C2semidirect
3. C2×D3×#213C2semidirect
4. D12×#67C2semidirect
5. #10592916C2semidirect
6. #10591515C2semidirect
7. #10591498C2semidirect
8. #10591482C2semidirect
9. #10591481C2semidirect
10. #10591447C2semidirect
11. #10591428C2semidirect
12. Dic3×#213C2semidirect
13. #10591164C2semidirect
14. #10591160C2semidirect
15. C3⋊C8×#67C2semidirect
18. C22×C32×D4C22semidirect
20. C2×C3×D3×D4C22semidirect
21. C22×C3×D12C22semidirect
23. C2×D3×D12C22semidirect
24. C2×#3753C22semidirect
25. C2×#3753C22semidirect
26. #64139C22semidirect
28. C3×#940C22semidirect
30. C3×#938C22semidirect
32. C3×D4×Dic3C22semidirect
35. C2×C3×#213C22semidirect
36. C2×C3×#213C22semidirect
37. C2×C3×#213C22semidirect
38. C3×#930C22semidirect
40. C22×C3×C3⋊C8C22semidirect
44. #63911C22semidirect
45. #63908C22semidirect
46. Dic3×D12C22semidirect
48. C2×#3714C22semidirect
49. C2×#3713C22semidirect
50. C2×#3713C22semidirect
51. C2×D3×C3⋊C8C22semidirect
52. #63659C22semidirect
53. #63659C22semidirect
54. #63657C22semidirect
55. #63575C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63564C22semidirect
58. #63563C22semidirect
59. #63562C22semidirect
60. #63562C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. Dic3×C3⋊C8C22semidirect
66. D4×#67D3semidirect
68. C22×#213D3semidirect
143. C3×#213D4semidirect
163. C22×C3×D4C2×D3semidirect
164. C22×C3×D4C2×D3semidirect
169. C2×D3×D4C2×D3semidirect
171. C22×D12C2×D3semidirect
189. #940C2×D3semidirect
193. #938C2×D3semidirect
197. D4×Dic3C2×D3semidirect
212. C2×#213C2×D3semidirect
213. C2×#213C2×D3semidirect
214. C2×#213C2×D3semidirect
219. #930C2×D3semidirect
222. C22×C3⋊C8C2×D3semidirect
280. C32×D4C2×D4semidirect
294. C3×#67D8semidirect
306. C3×D12C2×D4semidirect
317. C3×C3⋊C8C2×D4semidirect
450. #213#67direct (N × H)
485. C22×C32C2×D8semidirect
503. C2×C3×D3C2×D8semidirect
512. C3×Dic3C2×D8semidirect
518. C22×D4D32semidirect
631. C3×D4D3×D4semidirect
632. C3×D4C2×#67semidirect
665. #67#213direct (N × H)
690. D12C2×#67semidirect
703. C3⋊C8C2×#67semidirect
822. C22×C3D3×D8semidirect
823. C22×C3C2×#213semidirect
850. C2×D3C2×#213semidirect
870. Dic3C2×#213semidirect
871. C32D4×D8semidirect
916. D4D3×#67semidirect
990. C22D3×#213semidirect
1001. C3D4×#213semidirect
1002. C3D8×#67semidirect

Maximal subgroups

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

subgroupindex
C3×D4×#672
C22×C3×#2132
C2×D3×#2132
D12×#672
#105929162
#105915152
#105914982
#105914822
#105914812
#105914472
#105914282
Dic3×#2132
#105911642
#105911602
C3⋊C8×#672
D8×#673
D4×#2133