Finite Group Databasebeta

← C3×#10591448 #13158459

Subgroups — C3×#10591448 #13158459

Order 1728.

1208 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×D3×D4C211yesmaximal, characteristic, complemented
2C2×C3×#3753C211yesmaximal, characteristic, complemented
3C3×#63909C211yesmaximal, characteristic, complemented
4C2×C3×#3714C211yesmaximal, characteristic, complemented
5C32×#832C211yesmaximal, characteristic, complemented
6C3×#63562C211yesmaximal, characteristic, complemented
7C3×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8C3×#5217—31nomaximal
9C3×#4773—31nomaximal
10#10591448C311yesmaximal, characteristic, direct product factor
11C23×C32×D3—21no—
12C2×C33×D4C2211yescharacteristic
13C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
14C2×C32×#67—21no—
15C32×D3×D4—22no—
16C32×D3×D4—22no—
17C2×C32×D12C2211yescharacteristic
18C2×C32×C4×D3C2211yescharacteristic
19C2×C3×#626—21no—
20C3×#3753—22no—
21C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
22C32×C4⋊Dic3C2211yescharacteristic, complemented
23C2×C32×C3⋊C8C2211yescharacteristic, complemented
24C3×#3722—21no—
25C3×#3714—22no—
26C22×C32×D4—31no—
27C2×C3×D3×D4—21no—
28C2×C3×D3×D4D311yescharacteristic, complemented
29C2×C3×D3×D4C2×C311yescharacteristic, complemented
30C2×#3753C2×C311yescharacteristic, complemented
31C2×C3×#213—31no—
32C2×C3×#213—31no—
33C2×C3×#213—31no—
34C2×C3×#213—61no—
35C3×#930—31no—
36C2×C3×D24—31no—
37C3×#895—31no—
38#63909C2×C311yescharacteristic, complemented
39C2×#3714C2×C311yescharacteristic, complemented
40C32×#102—31no—
41C3×#832—21no—
42C3×#832—31no—
43C3×#832D311yescharacteristic, complemented
44C3×#832C2×C311yescharacteristic, complemented
45C3×#830—31no—
46C3×(C2×D3)⋊C8—31no—
47C3×#809—31no—
48#63562C2×C311yescharacteristic, complemented
49(C2×D3)⋊(C3⋊C8)C2×C311yescharacteristic, complemented
50C23×C33—21no—
51C22×C3×C3⋊D3—21no—
52C22×C32×D3—24no—
53C22×C32×D3—21no—
54C22×C32×D3—42no—
55C22×C32×D3—42no—
56C22×C32×D3D411yescharacteristic
57C33×D4—21no—
58C33×D4D412yescomplemented
59C2×C33×C4C2311yescharacteristic
60C3×C4⋊(C3⋊D3)—21no—
61C3×C4⋊(C3⋊D3)—21no—
62C32×#67—24no—
63C2×C32×Dic3—21no—
64C2×C32×Dic3D411yescharacteristic
65C32×D12—21no—
66C32×D12D412yescomplemented
67C32×C4×D3—21no—
68C32×C4×D3—21no—
69C3×#626—42no—
70C3×C3⋊(C3⋊C8)—21no—
71C32×C3⋊C8—21no—
72C3×#447—91no—
73#5217—31no—
74#4773—31no—
75C24×C32—61no—
76C23×C3×D3—22no—
77C23×C3×D3—21no—
78C23×C3×D3—21no—
79C2×C32×D4—21no—
80C2×C32×D4—21no—
81C2×C32×D4—21no—
82C2×C32×D4—31no—
83C2×C32×D4—41no—
84C2×C32×D4—61no—
85C2×C32×D4—62no—
86C2×C32×D4—62no—
87C2×C32×D4C2×D311yescharacteristic
88C2×C32×D4C2×D311yescharacteristic
89C2×C32×D4C22×C311yescharacteristic
90C22×C32×C4—31no—
91C2×C4⋊(C3⋊D3)C22×C311yescharacteristic, complemented
92C2×C3×#67—22no—
93C2×C3×#67—21no—
94C2×C3×#67—21no—
95C2×C3×#67—61no—
96C3×D3×D4—24no—
97C3×D3×D4—24no—
98C3×D3×D4—22no—
99C3×D3×D4—22no—
100C3×D3×D4—22no—
101C3×D3×D4—22no—
102C2×C3×D12—21no—
103C2×C3×D12—31no—
104C2×C3×D12—31no—
105C2×C3×D12—61no—
106C2×C3×D12—61no—
107C2×C3×D12C2×D311yescharacteristic
108C2×C3×D12C22×C311yescharacteristic
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3C2×D311yescharacteristic
111C2×C3×C4×D3C22×C311yescharacteristic
112C2×#626—21no—
113C2×C32×C8—31no—
114C32×C4⋊C4—31no—
115#3753—22no—
116C2×C3⋊(C3⋊C8)C22×C311yescharacteristic, complemented
117C3×#213—62no—
118C3×#213—64no—
119C3×#213—62no—
120C3×#213—62no—
121C3×(C2×D3)⋊C4—61no—
122C3×(C2×D3)⋊C4—61no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3C2×D311yescharacteristic, complemented
125C3×C4⋊Dic3C22×C311yescharacteristic, complemented
126C2×C3×C3⋊C8—21no—
127C2×C3×C3⋊C8—31no—
128C2×C3×C3⋊C8—31no—
129C2×C3×C3⋊C8—61no—
130C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
131C2×C3×C3⋊C8C22×C311yescharacteristic, complemented
132C3×D24—62no—
133#3722—21no—
134#3714—22no—
135C22×C33—22no—
136C22×C33—41no—
137C22×C33—41no—
138C22×C33C2×D411yescharacteristic
139C2×C3×C3⋊D3—41no—
140C2×C3×C3⋊D3—41no—
141C2×C3×C3⋊D3—41no—
142C2×C32×D3—21no—
143C2×C32×D3—21no—
144C2×C32×D3—22no—
145C2×C32×D3—48no—
146C2×C32×D3—41no—
147C2×C32×D3—41no—
148C2×C32×D3D812yescomplemented
149C33×C4C2×D411yescharacteristic
150C33×C4C2×D411yescharacteristic
151C32×Dic3—21no—
152C32×Dic3—41no—
153C22×C3×D4—31no—
154C22×C3×D4—31no—
155C22×C3×D4—61no—
156C2×D3×D4C3×D311yescharacteristic, complemented
157C2×C3×D8—91no—
158C2×C3×D8—91no—
159C3×#121—91no—
160C2×#213—31no—
161C2×#213—31no—
162C2×#213—31no—
163C2×#213—61no—
164#930—31no—
165C2×D24—31no—
166#895—31no—
167C3×#102—31no—
168C3×#102—31no—
169C3×#102—61no—
170C3×#102—91no—
171C3×C22⋊C8—91no—
172#832—31no—
173#832C3×D311yescharacteristic, complemented
174#830—31no—
175(C2×D3)⋊C8—31no—
176#809—31no—
177C23×C32—21no—
178C23×C32—22no—
179C23×C32—21no—
180C23×C32—21no—
181C23×C32—31no—
182C23×C32—41no—
183C23×C32—41no—
184C23×C32—42no—
185C23×C32—64no—
186C23×C32—61no—
187C23×C32—122no—
188C23×C32—122no—
189C22×C3⋊D3—21no—
190C22×C3×D3—22no—
191C22×C3×D3—28no—
192C22×C3×D3—24no—
193C22×C3×D3—24no—
194C22×C3×D3—21no—
195C22×C3×D3—21no—
196C22×C3×D3—21no—
197C22×C3×D3—44no—
198C22×C3×D3—42no—
199C22×C3×D3—42no—
200C22×C3×D3—44no—
201C22×C3×D3—42no—
202C22×C3×D3—42no—
203C22×C3×D3—61no—
204C22×C3×D3—61no—
205C22×C3×D3—121no—
206C22×C3×D3#6711yescharacteristic
207C22×C3×D3C3×D411yescharacteristic
208C32×D4—21no—
209C32×D4—22no—
210C32×D4—21no—
211C32×D4—21no—
212C32×D4—22no—
213C32×D4—22no—
214C32×D4—22no—
215C32×D4—32no—
216C32×D4—42no—
217C32×D4—41no—
218C32×D4—41no—
219C32×D4—42no—
220C32×D4—64no—
221C32×D4—61no—
222C32×D4D1212yescomplemented
223C32×D4#6712yescomplemented
224C32×D4C3×D412yescomplemented
225C2×C32×C4—21no—
226C2×C32×C4—21no—
227C2×C32×C4—21no—
228C2×C32×C4—31no—
229C2×C32×C4—41no—
230C2×C32×C4—61no—
231C2×C32×C4—61no—
232C2×C32×C4—61no—
233C2×C32×C4C22×D311yescharacteristic
234C2×C32×C4C22×D311yescharacteristic
235C2×C32×C4C23×C311yescharacteristic
236C4⋊(C3⋊D3)—21no—
237C4⋊(C3⋊D3)—21no—
238C3×#67—28no—
239C3×#67—24no—
240C3×#67—24no—
241C3×#67—122no—
242C2×C3×Dic3—21no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—41no—
246C2×C3×Dic3#6711yescharacteristic
247C2×C3×Dic3C3×D411yescharacteristic
248C3×D12—22no—
249C3×D12—21no—
250C3×D12—21no—
251C3×D12—22no—
252C3×D12—62no—
253C3×D12—61no—
254C3×D12—61no—
255C3×D12—61no—
256C3×D12—61no—
257C3×D12—121no—
258C3×D12—122no—
259C3×D12#6712yescomplemented
260C3×D12C3×D412yescomplemented
261C3×C4×D3—22no—
262C3×C4×D3—22no—
263C3×C4×D3—21no—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267#626—42no—
268C32×C8—61no—
269C3⋊(C3⋊C8)—21no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272C3×C3⋊C8—41no—
273C3×C3⋊C8—62no—
274C3×C3⋊C8—61no—
275C3×C3⋊C8—61no—
276#447—91noSylow
277C2×C33—42no—
278C2×C33#12011yescharacteristic
279C2×C33C2×D811yescharacteristic
280C2×C33AGL(1,ℤ/8)11yescharacteristic
281C3×C3⋊D3—81no—
282C32×D3—22no—
283C32×D3—42no—
284C24×C3—61no—
285C24×C3—61no—
286C24×C3—62no—
287C23×D3—21no—
288C2×C3×D4—21no—
289C2×C3×D4—21no—
290C2×C3×D4—21no—
291C2×C3×D4—31no—
292C2×C3×D4—31no—
293C2×C3×D4—41no—
294C2×C3×D4—61no—
295C2×C3×D4—61no—
296C2×C3×D4—61no—
297C2×C3×D4—62no—
298C2×C3×D4—62no—
299C2×C3×D4—64no—
300C2×C3×D4—64no—
301C2×C3×D4—62no—
302C2×C3×D4—62no—
303C2×C3×D4—62no—
304C2×C3×D4—91no—
305C2×C3×D4—181no—
306C2×C3×D4D3211yescharacteristic
307C2×C3×D4C2×C3×D311yescharacteristic
308C2×C3×D4C2×C3×D311yescharacteristic
309C22×C3×C4—31no—
310C22×C3×C4—31no—
311C22×C3×C4—61no—
312C2×#67—21no—
313C2×#67—61no—
314D3×D4—22no—
315D3×D4—22no—
316C2×D12—31no—
317C2×D12—31no—
318C2×D12—61no—
319C2×D12—61no—
320C2×D12C2×C3×D311yescharacteristic
321C2×C4×D3C2×C3×D311yescharacteristic
322C3×D8—182no—
323C3×D8—182no—
324C2×C3×C8—31no—
325C2×C3×C8—31no—
326C2×C3×C8—61no—
327C2×C3×C8—91no—
328C3×C4⋊C4—31no—
329C3×C4⋊C4—31no—
330C3×C4⋊C4—61no—
331C3×C22⋊C4—181no—
332#213—62no—
333#213—64no—
334#213—62no—
335#213—62no—
336(C2×D3)⋊C4—61no—
337(C2×D3)⋊C4—61no—
338C4⋊Dic3C2×C3×D311yescharacteristic, complemented
339C2×C3⋊C8—31no—
340C2×C3⋊C8—31no—
341C2×C3⋊C8—61no—
342C2×C3⋊C8C2×C3×D311yescharacteristic, complemented
343D24—62no—
344C22×C32—22no—
345C22×C32—24no—
346C22×C32—22no—
347C22×C32—22no—
348C22×C32—21no—
349C22×C32—21no—
350C22×C32—21no—
351C22×C32—32no—
352C22×C32—41no—
353C22×C32—42no—
354C22×C32—42no—
355C22×C32—44no—
356C22×C32—41no—
357C22×C32—41no—
358C22×C32—42no—
359C22×C32—42no—
360C22×C32—41no—
361C22×C32—41no—
362C22×C32—41no—
363C22×C32—41no—
364C22×C32—61no—
365C22×C32—61no—
366C22×C32—62no—
367C22×C32—81no—
368C22×C32—81no—
369C22×C32—81no—
370C22×C32—81no—
371C22×C32—82no—
372C22×C32—82no—
373C22×C32—128no—
374C22×C32—121no—
375C22×C32—121no—
376C22×C32D3×D411yescharacteristic
377C22×C32C2×#6711yescharacteristic
378C22×C32C2×C3×D411yescharacteristic
379C2×C3⋊D3—41no—
380C2×C3⋊D3—41no—
381C2×C3⋊D3—41no—
382C2×C3×D3—22no—
383C2×C3×D3—22no—
384C2×C3×D3—21no—
385C2×C3×D3—21no—
386C2×C3×D3—21no—
387C2×C3×D3—21no—
388C2×C3×D3—24no—
389C2×C3×D3—22no—
390C2×C3×D3—22no—
391C2×C3×D3—22no—
392C2×C3×D3—416no—
393C2×C3×D3—48no—
394C2×C3×D3—48no—
395C2×C3×D3—42no—
396C2×C3×D3—42no—
397C2×C3×D3—41no—
398C2×C3×D3—41no—
399C2×C3×D3—41no—
400C2×C3×D3—41no—
401C2×C3×D3—122no—
402C2×C3×D3—121no—
403C2×C3×D3—121no—
404C2×C3×D3—121no—
405C2×C3×D3—121no—
406C2×C3×D3—121no—
407C2×C3×D3—121no—
408C2×C3×D3—241no—
409C2×C3×D3—241no—
410C2×C3×D3#21312yescomplemented
411C2×C3×D3C3×D812yescomplemented
412C32×C4—21no—
413C32×C4—21no—
414C32×C4—21no—
415C32×C4—21no—
416C32×C4—21no—
417C32×C4—21no—
418C32×C4—41no—
419C32×C4—41no—
420C32×C4—61no—
421C32×C4—121no—
422C32×C4C2×D1211yescharacteristic
423C32×C4D3×D411yescharacteristic
424C32×C4C2×#6711yescharacteristic
425C32×C4C2×#6711yescharacteristic
426C32×C4C2×C3×D411yescharacteristic
427C32×C4C2×C3×D411yescharacteristic
428C3×Dic3—22no—
429C3×Dic3—21no—
430C3×Dic3—21no—
431C3×Dic3—41no—
432C3×Dic3—41no—
433C3×Dic3—81no—
434C22×D4—31no—
435C2×D8—91no—
436C2×D8—91no—
437#121—91no—
438#102—31no—
439#102—91no—
440C22⋊C8—91no—
441C33#44711yescharacteristic, complemented, Sylow
442C23×C3—22no—
443C23×C3—21no—
444C23×C3—21no—
445C23×C3—21no—
446C23×C3—31no—
447C23×C3—31no—
448C23×C3—41no—
449C23×C3—41no—
450C23×C3—42no—
451C23×C3—61no—
452C23×C3—68no—
453C23×C3—64no—
454C23×C3—64no—
455C23×C3—62no—
456C23×C3—61no—
457C23×C3—61no—
458C23×C3—122no—
459C23×C3—122no—
460C23×C3—124no—
461C23×C3—124no—
462C23×C3—122no—
463C23×C3—122no—
464C23×C3—181no—
465C22×D3—24no—
466C22×D3—21no—
467C22×D3—42no—
468C22×D3—42no—
469C22×D3—61no—
470C22×D3—61no—
471C22×D3—121no—
472C22×D3C3×#6711yescharacteristic
473C3×D4—22no—
474C3×D4—21no—
475C3×D4—21no—
476C3×D4—21no—
477C3×D4—22no—
478C3×D4—22no—
479C3×D4—22no—
480C3×D4—32no—
481C3×D4—32no—
482C3×D4—41no—
483C3×D4—41no—
484C3×D4—42no—
485C3×D4—42no—
486C3×D4—62no—
487C3×D4—62no—
488C3×D4—68no—
489C3×D4—64no—
490C3×D4—64no—
491C3×D4—61no—
492C3×D4—61no—
493C3×D4—181no—
494C3×D4—181no—
495C3×D4—362no—
496C3×D4#62612yescomplemented
497C3×D4C3×D1212yescomplemented
498C3×D4C3×#6712yescomplemented
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—31no—
503C2×C3×C4—31no—
504C2×C3×C4—41no—
505C2×C3×C4—61no—
506C2×C3×C4—62no—
507C2×C3×C4—62no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—121no—
515C2×C3×C4C2×D3211yescharacteristic
516C2×C3×C4C22×C3×D311yescharacteristic
517C2×C3×C4C22×C3×D311yescharacteristic
518#67—24no—
519#67—122no—
520C2×Dic3—21no—
521C2×Dic3C3×#6711yescharacteristic
522D12—21no—
523D12—62no—
524D12—61no—
525D12—61no—
526D12—61no—
527D12—61no—
528D12—121no—
529D12—122no—
530D12C3×#6712yescomplemented
531C4×D3—21no—
532C4×D3—21no—
533C3×C8—61no—
534C3×C8—61no—
535C3×C8—121no—
536C3×C8—181no—
537C3⋊C8—21no—
538C3⋊C8—62no—
539C3⋊C8—61no—
540C3⋊C8—61no—
541C2×C32—21no—
542C2×C32—21no—
543C2×C32—21no—
544C2×C32—21no—
545C2×C32—21no—
546C2×C32—21no—
547C2×C32—21no—
548C2×C32—21no—
549C2×C32—21no—
550C2×C32—41no—
551C2×C32—41no—
552C2×C32—41no—
553C2×C32—42no—
554C2×C32—44no—
555C2×C32—42no—
556C2×C32—42no—
557C2×C32—62no—
558C2×C32—82no—
559C2×C32—82no—
560C2×C32—84no—
561C2×C32—122no—
562C2×C32#88211yescharacteristic
563C2×C32D3×D811yescharacteristic
564C2×C32#91411yescharacteristic
565C2×C32C2×#21311yescharacteristic
566C2×C32#93211yescharacteristic
567C2×C32#95311yescharacteristic
568C2×C32C3×#12011yescharacteristic
569C2×C32C2×C3×D811yescharacteristic
570C2×C32C3×AGL(1,ℤ/8)11yescharacteristic
571C3⋊D3—81no—
572C3×D3—24no—
573C3×D3—22no—
574C3×D3—22no—
575C3×D3—44no—
576C3×D3—42no—
577C3×D3—42no—
578C3×D3—242no—
579C3×D3—241no—
580C3×D3—241no—
581C24—61no—
582C2×D4—31no—
583C2×D4—61no—
584C2×D4—62no—
585C2×D4—62no—
586C2×D4—91no—
587C2×D4—181no—
588C2×D4C3×D3211yescharacteristic
589C22×C4—31no—
590D8—182no—
591D8—182no—
592C2×C8—31no—
593C2×C8—91no—
594C4⋊C4—31no—
595C22⋊C4—181no—
596C22×C3—24no—
597C22×C3—22no—
598C22×C3—22no—
599C22×C3—22no—
600C22×C3—21no—
601C22×C3—21no—
602C22×C3—21no—
603C22×C3—32no—
604C22×C3—32no—
605C22×C3—42no—
606C22×C3—42no—
607C22×C3—44no—
608C22×C3—42no—
609C22×C3—42no—
610C22×C3—41no—
611C22×C3—41no—
612C22×C3—41no—
613C22×C3—41no—
614C22×C3—41no—
615C22×C3—41no—
616C22×C3—41no—
617C22×C3—62no—
618C22×C3—62no—
619C22×C3—62no—
620C22×C3—64no—
621C22×C3—61no—
622C22×C3—61no—
623C22×C3—61no—
624C22×C3—61no—
625C22×C3—62no—
626C22×C3—62no—
627C22×C3—81no—
628C22×C3—81no—
629C22×C3—81no—
630C22×C3—81no—
631C22×C3—82no—
632C22×C3—82no—
633C22×C3—122no—
634C22×C3—122no—
635C22×C3—1216no—
636C22×C3—128no—
637C22×C3—128no—
638C22×C3—121no—
639C22×C3—121no—
640C22×C3—121no—
641C22×C3—121no—
642C22×C3—361no—
643C22×C3—361no—
644C22×C3—361no—
645C22×C3D3×#6711yescharacteristic
646C22×C3C3×D3×D411yescharacteristic
647C22×C3C2×C3×#6711yescharacteristic
648C2×D3—21no—
649C2×D3—21no—
650C2×D3—22no—
651C2×D3—48no—
652C2×D3—41no—
653C2×D3—41no—
654C2×D3—122no—
655C2×D3—121no—
656C2×D3—121no—
657C2×D3—121no—
658C2×D3—121no—
659C2×D3—121no—
660C2×D3—121no—
661C2×D3—241no—
662C2×D3—241no—
663C2×D3C3×#21312yescomplemented
664C3×C4—21no—
665C3×C4—21no—
666C3×C4—21no—
667C3×C4—21no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—41no—
671C3×C4—41no—
672C3×C4—62no—
673C3×C4—61no—
674C3×C4—61no—
675C3×C4—121no—
676C3×C4—121no—
677C3×C4—241no—
678C3×C4C2×#62611yescharacteristic
679C3×C4D3×#6711yescharacteristic
680C3×C4C2×C3×D1211yescharacteristic
681C3×C4C3×D3×D411yescharacteristic
682C3×C4C2×C3×#6711yescharacteristic
683C3×C4C2×C3×#6711yescharacteristic
684Dic3—21no—
685Dic3—41no—
686C32—21no—
687C32—21no—
688C32—21no—
689C32—41no—
690C32#477311yescharacteristic, complemented
691C32#521711yescharacteristic, complemented
692C32C3×#44711yescharacteristic, complemented
693C23—21no—
694C23—31no—
695C23—64no—
696C23—61no—
697C23—122no—
698C23—122no—
699C23—181no—
700D4—21no—
701D4—32no—
702D4—64no—
703D4—61no—
704D4—181no—
705D4—181no—
706D4—362no—
707D4C3×#62612yescomplemented
708C2×C4—31no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4C2×C3×D3211yescharacteristic
713C8—61no—
714C8—181no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—21no—
718C2×C3—21no—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3—21no—
722C2×C3—21no—
723C2×C3—21no—
724C2×C3—44no—
725C2×C3—42no—
726C2×C3—42no—
727C2×C3—42no—
728C2×C3—41no—
729C2×C3—41no—
730C2×C3—41no—
731C2×C3—64no—
732C2×C3—62no—
733C2×C3—62no—
734C2×C3—82no—
735C2×C3—82no—
736C2×C3—84no—
737C2×C3—124no—
738C2×C3—122no—
739C2×C3—122no—
740C2×C3—721no—
741C2×C3D3×#21311yescharacteristic
742C2×C3#6393411yescharacteristic
743C2×C3#6397711yescharacteristic
744C2×C3C3×#88211yescharacteristic
745C2×C3C3×D3×D811yescharacteristic
746C2×C3C3×#91411yescharacteristic
747C2×C3C2×C3×#21311yescharacteristic
748C2×C3C3×#93211yescharacteristic
749C2×C3C3×#95311yescharacteristic
750D3—22no—
751D3—42no—
752D3—242no—
753D3—241no—
754D3—241no—
755C22—22no—
756C22—32no—
757C22—41no—
758C22—41no—
759C22—61no—
760C22—61no—
761C22—62no—
762C22—128no—
763C22—121no—
764C22—121no—
765C22—361no—
766C22—361no—
767C22—361no—
768C22C3×D3×#6711yescharacteristic
769C4—61no—
770C4—121no—
771C4C2×C3×#62611yescharacteristic
772C4C3×D3×#6711yescharacteristic
773C3—21no—
774C3—21no—
775C3—21no—
776C3—41no—
777C3#1059144811yescharacteristic, direct product factor
778C3C3×#477311yescharacteristic, complemented
779C3C3×#521711yescharacteristic, complemented
780C2—42no—
781C2—62no—
782C2—122no—
783C2—721no—
784C2C3×D3×#21311yescharacteristic
785C2C3×#6393411yescharacteristic
786C2C3×#6397711yescharacteristic
subgroupG/H
centerC22×C3D3×#67
commutator, cosocleC2×C32×C4C23×C3
FrattiniC2×C4C2×C3×D32
FittingC2×C33×D4C22
socleC22×C33C2×D4
hypercenterC2×C3×D4D32
hypocenterC32C3×#447
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×D3×D4C2semidirect
2. C2×C3×#3753C2semidirect
3. C3×#63909C2semidirect
4. C2×C3×#3714C2semidirect
5. C32×#832C2semidirect
6. C3×#63562C2semidirect
7. C3×(C2×D3)⋊(C3⋊C8)C2semidirect
10. #10591448C3direct (N × H)
13. C2×C3×C4⋊(C3⋊D3)C22semidirect
21. C2×C3×C3⋊(C3⋊C8)C22semidirect
22. C32×C4⋊Dic3C22semidirect
23. C2×C32×C3⋊C8C22semidirect
28. C2×C3×D3×D4D3semidirect
29. C2×C3×D3×D4C2×C3semidirect
30. C2×#3753C2×C3semidirect
38. #63909C2×C3semidirect
39. C2×#3714C2×C3semidirect
43. C3×#832D3semidirect
44. C3×#832C2×C3semidirect
48. #63562C2×C3semidirect
49. (C2×D3)⋊(C3⋊C8)C2×C3semidirect
58. C33×D4D4semidirect
66. C32×D12D4semidirect
91. C2×C4⋊(C3⋊D3)C22×C3semidirect
116. C2×C3⋊(C3⋊C8)C22×C3semidirect
124. C3×C4⋊Dic3C2×D3semidirect
125. C3×C4⋊Dic3C22×C3semidirect
130. C2×C3×C3⋊C8C2×D3semidirect
131. C2×C3×C3⋊C8C22×C3semidirect
148. C2×C32×D3D8semidirect
156. C2×D3×D4C3×D3semidirect
173. #832C3×D3semidirect
222. C32×D4D12semidirect
223. C32×D4#67semidirect
224. C32×D4C3×D4semidirect
259. C3×D12#67semidirect
260. C3×D12C3×D4semidirect
338. C4⋊Dic3C2×C3×D3semidirect
342. C2×C3⋊C8C2×C3×D3semidirect
410. C2×C3×D3#213semidirect
411. C2×C3×D3C3×D8semidirect
441. C33#447semidirect
496. C3×D4#626semidirect
497. C3×D4C3×D12semidirect
498. C3×D4C3×#67semidirect
530. D12C3×#67semidirect
663. C2×D3C3×#213semidirect
690. C32#4773semidirect
691. C32#5217semidirect
692. C32C3×#447semidirect
707. D4C3×#626semidirect
777. C3#10591448direct (N × H)
778. C3C3×#4773semidirect
779. C3C3×#5217semidirect

Maximal subgroups

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

subgroupindex
C2×C32×D3×D42
C2×C3×#37532
C3×#639092
C2×C3×#37142
C32×#8322
C3×#635622
C3×(C2×D3)⋊(C3⋊C8)2
C3×#52173
C3×#47733
#105914483