Finite Group Databasebeta

← C3×#10591458 #13158467

Subgroups — C3×#10591458 #13158467

Order 1728.

1160 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×D3×D4C211yesmaximal, characteristic
2C2×C32×#214C211yesmaximal, characteristic, complemented
3C3×#63856C211yesmaximal, characteristic, complemented
4C2×C3×#3715C211yesmaximal, characteristic, complemented
5C3×#63659C211yesmaximal, characteristic, complemented
6C3×#63563C211yesmaximal, characteristic, complemented
7C3×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8C3×#5218—31nomaximal
9C3×#5169—31nomaximal
10#10591458C311yesmaximal, characteristic, direct product factor
11C23×C32×D3—21no—
12C2×C33×D4C2211yescharacteristic
13C2×C32×#67—21no—
14C32×D3×D4—22no—
15C32×D3×D4—22no—
16C2×C32×D12C2211yescharacteristic
17C2×C32×C4×D3C2211yescharacteristic
18C2×C32×Dic6C2211yescharacteristic, complemented
19C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
20C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
21C32×#214—22no—
22C2×C32×C3⋊C8C2211yescharacteristic, complemented
23C3×#3724—21no—
24C3×(C2×D3)⋊Dic3—21no—
25C3×#3715—22no—
26C22×C32×D4—31no—
27C2×C3×D3×D4—21no—
28C2×C3×D3×D4D311yescharacteristic
29C2×C3×D3×D4C2×C311yescharacteristic
30C2×C32×SD16—31no—
31C3×#946—31no—
32C2×C3×#215—31no—
33C2×C3×#214—21no—
34C2×C3×#214—31no—
35C2×C3×#214D311yescharacteristic, complemented
36C2×C3×#214C2×C311yescharacteristic, complemented
37C3×#924—31no—
38#63856C2×C311yescharacteristic, complemented
39C2×#3715C2×C311yescharacteristic, complemented
40#63659C2×C311yescharacteristic, complemented
41C3×#832—31no—
42C3×#832—31no—
43C3×#832—31no—
44C3×#832—61no—
45C3×#830—31no—
46C3×#821—31no—
47C3×(C2×D3)⋊C8—31no—
48#63563C2×C311yescharacteristic, complemented
49(C2×D3)⋊(C3⋊C8)C2×C311yescharacteristic, complemented
50C23×C33—21no—
51C22×C32×D3—24no—
52C22×C32×D3—21no—
53C22×C32×D3—42no—
54C22×C32×D3—42no—
55C22×C32×D3D411yescharacteristic
56C33×D4—21no—
57C33×D4D412yes—
58C2×C33×C4C2311yescharacteristic
59C2×C3×C3⋊Dic3—21no—
60C32×#67—24no—
61C2×C32×Dic3—21no—
62C2×C32×Dic3D411yescharacteristic
63C32×D12—21no—
64C32×D12D412yes—
65C32×C4×D3—21no—
66C32×C4×D3—21no—
67C32×Dic6—21no—
68C32×Dic6—21no—
69C3×C3⋊(C3⋊C8)—21no—
70C32×C3⋊C8—21no—
71C3×#450—91no—
72#5218—31no—
73#5169—31no—
74C24×C32—61no—
75C23×C3×D3—22no—
76C23×C3×D3—21no—
77C23×C3×D3—21no—
78C2×C32×Q8—31no—
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×C3×#67—22no—
92C2×C3×#67—21no—
93C2×C3×#67—21no—
94C3×D3×D4—24no—
95C3×D3×D4—24no—
96C3×D3×D4—22no—
97C3×D3×D4—22no—
98C3×D3×D4—22no—
99C3×D3×D4—22no—
100C2×C3×D12—21no—
101C2×C3×D12C2×D311yescharacteristic
102C2×C3×D12C22×C311yescharacteristic
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3C2×D311yescharacteristic
105C2×C3×C4×D3C22×C311yescharacteristic
106C2×C3×Dic6—21no—
107C2×C3×Dic6C2×D311yescharacteristic, complemented
108C2×C3×Dic6C22×C311yescharacteristic, complemented
109C32×SD16—62no—
110C2×C32×C8—31no—
111C4⋊(C3⋊Dic3)C22×C311yescharacteristic, complemented
112C2×C3⋊(C3⋊C8)C22×C311yescharacteristic, complemented
113C3×#217—61no—
114C3×#215—62no—
115C3×#214—24no—
116C3×#214—22no—
117C3×#214—22no—
118C3×#214—62no—
119C3×(C2×D3)⋊C4—61no—
120C3×C4⋊Dic3—31no—
121C3×C4⋊Dic3—31no—
122C3×C4⋊Dic3—61no—
123C3×Dic3⋊C4—61no—
124C3×Dic3⋊C4—61no—
125C2×C3×C3⋊C8—21no—
126C2×C3×C3⋊C8—31no—
127C2×C3×C3⋊C8—31no—
128C2×C3×C3⋊C8—61no—
129C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
130C2×C3×C3⋊C8C22×C311yescharacteristic, complemented
131#3724—21no—
132(C2×D3)⋊Dic3—21no—
133#3715—22no—
134C22×C33—22no—
135C22×C33—41no—
136C22×C33—41no—
137C22×C33C2×D411yescharacteristic
138C2×C32×D3—21no—
139C2×C32×D3—21no—
140C2×C32×D3—22no—
141C2×C32×D3—48no—
142C2×C32×D3—41no—
143C2×C32×D3—41no—
144C2×C32×D3SD1612yescomplemented
145C33×C4C2×D411yescharacteristic
146C33×C4C2×D411yescharacteristic
147C3×C3⋊Dic3—41no—
148C32×Dic3—21no—
149C32×Dic3—41no—
150C22×C3×D4—31no—
151C22×C3×D4—31no—
152C22×C3×D4—61no—
153C2×D3×D4C3×D311yescharacteristic
154C2×C3×SD16—31no—
155C2×C3×SD16—31no—
156C2×C3×SD16—61no—
157C2×C3×SD16—91no—
158C3×C22⋊Q8—91no—
159#946—31no—
160C2×#215—31no—
161C2×#214—31no—
162C2×#214C3×D311yescharacteristic, complemented
163#924—31no—
164C3×#102—91no—
165C3×#102—91no—
166C3×C22⋊C8—91no—
167#832—31no—
168#832—31no—
169#832—31no—
170#832—61no—
171#830—31no—
172#821—31no—
173(C2×D3)⋊C8—31no—
174C23×C32—21no—
175C23×C32—22no—
176C23×C32—21no—
177C23×C32—21no—
178C23×C32—31no—
179C23×C32—41no—
180C23×C32—41no—
181C23×C32—42no—
182C23×C32—64no—
183C23×C32—61no—
184C23×C32—122no—
185C23×C32—122no—
186C22×C3×D3—22no—
187C22×C3×D3—28no—
188C22×C3×D3—24no—
189C22×C3×D3—24no—
190C22×C3×D3—21no—
191C22×C3×D3—21no—
192C22×C3×D3—21no—
193C22×C3×D3—44no—
194C22×C3×D3—42no—
195C22×C3×D3—42no—
196C22×C3×D3—44no—
197C22×C3×D3—42no—
198C22×C3×D3—42no—
199C22×C3×D3#6711yescharacteristic
200C22×C3×D3C3×D411yescharacteristic
201C32×Q8—61no—
202C32×Q8—61no—
203C32×D4—21no—
204C32×D4—22no—
205C32×D4—21no—
206C32×D4—21no—
207C32×D4—22no—
208C32×D4—22no—
209C32×D4—22no—
210C32×D4—32no—
211C32×D4—42no—
212C32×D4—41no—
213C32×D4—41no—
214C32×D4—42no—
215C32×D4—64no—
216C32×D4—61no—
217C32×D4#6712yes—
218C32×D4#6712yes—
219C32×D4C3×D412yes—
220C2×C32×C4—21no—
221C2×C32×C4—21no—
222C2×C32×C4—21no—
223C2×C32×C4—31no—
224C2×C32×C4—41no—
225C2×C32×C4—61no—
226C2×C32×C4—61no—
227C2×C32×C4—61no—
228C2×C32×C4C22×D311yescharacteristic
229C2×C32×C4C22×D311yescharacteristic
230C2×C32×C4C23×C311yescharacteristic
231C2×C3⋊Dic3—21no—
232C3×#67—28no—
233C3×#67—24no—
234C3×#67—24no—
235C2×C3×Dic3—21no—
236C2×C3×Dic3—21no—
237C2×C3×Dic3—21no—
238C2×C3×Dic3—41no—
239C2×C3×Dic3—61no—
240C2×C3×Dic3—61no—
241C2×C3×Dic3—121no—
242C2×C3×Dic3#6711yescharacteristic
243C2×C3×Dic3C3×D411yescharacteristic
244C3×D12—22no—
245C3×D12—21no—
246C3×D12—21no—
247C3×D12—22no—
248C3×D12#6712yes—
249C3×D12C3×D412yes—
250C3×C4×D3—22no—
251C3×C4×D3—22no—
252C3×C4×D3—21no—
253C3×C4×D3—21no—
254C3×C4×D3—21no—
255C3×C4×D3—21no—
256C3×Dic6—22no—
257C3×Dic6—21no—
258C3×Dic6—21no—
259C3×Dic6—21no—
260C3×Dic6—21no—
261C3×Dic6—41no—
262C32×C8—61no—
263C3⋊(C3⋊C8)—21no—
264C3×C3⋊C8—22no—
265C3×C3⋊C8—21no—
266C3×C3⋊C8—21no—
267C3×C3⋊C8—61no—
268C3×C3⋊C8—61no—
269C3×C3⋊C8—121no—
270#450—91noSylow
271C2×C33—42no—
272C2×C33#12011yescharacteristic
273C2×C33C2×SD1611yescharacteristic
274C2×C33AGL(1,ℤ/8)11yescharacteristic
275C32×D3—22no—
276C32×D3—42no—
277C24×C3—61no—
278C24×C3—61no—
279C24×C3—62no—
280C23×D3—21no—
281C2×C3×Q8—31no—
282C2×C3×Q8—31no—
283C2×C3×Q8—61no—
284C2×C3×D4—21no—
285C2×C3×D4—21no—
286C2×C3×D4—21no—
287C2×C3×D4—31no—
288C2×C3×D4—31no—
289C2×C3×D4—41no—
290C2×C3×D4—61no—
291C2×C3×D4—61no—
292C2×C3×D4—61no—
293C2×C3×D4—62no—
294C2×C3×D4—62no—
295C2×C3×D4—64no—
296C2×C3×D4—64no—
297C2×C3×D4—62no—
298C2×C3×D4—62no—
299C2×C3×D4—62no—
300C2×C3×D4D3211yescharacteristic
301C2×C3×D4C2×C3×D311yescharacteristic
302C2×C3×D4C2×C3×D311yescharacteristic
303C22×C3×C4—31no—
304C22×C3×C4—31no—
305C22×C3×C4—61no—
306C2×#67—21no—
307D3×D4—22no—
308D3×D4—22no—
309C2×D12C2×C3×D311yescharacteristic
310C2×C4×D3C2×C3×D311yescharacteristic
311C2×Dic6C2×C3×D311yescharacteristic, complemented
312C3×SD16—64no—
313C3×SD16—62no—
314C3×SD16—62no—
315C3×SD16—182no—
316C2×C3×C8—31no—
317C2×C3×C8—31no—
318C2×C3×C8—61no—
319C2×C3×C8—91no—
320C3×C4⋊C4—91no—
321C3×C4⋊C4—181no—
322C3×C22⋊C4—181no—
323#217—61no—
324#215—62no—
325#214—22no—
326#214—62no—
327(C2×D3)⋊C4—61no—
328C4⋊Dic3—31no—
329C4⋊Dic3—31no—
330C4⋊Dic3—61no—
331Dic3⋊C4—61no—
332Dic3⋊C4—61no—
333C2×C3⋊C8—31no—
334C2×C3⋊C8—31no—
335C2×C3⋊C8—61no—
336C2×C3⋊C8C2×C3×D311yescharacteristic, complemented
337C22×C32—22no—
338C22×C32—24no—
339C22×C32—22no—
340C22×C32—22no—
341C22×C32—21no—
342C22×C32—21no—
343C22×C32—21no—
344C22×C32—32no—
345C22×C32—41no—
346C22×C32—42no—
347C22×C32—42no—
348C22×C32—44no—
349C22×C32—41no—
350C22×C32—41no—
351C22×C32—42no—
352C22×C32—42no—
353C22×C32—41no—
354C22×C32—41no—
355C22×C32—41no—
356C22×C32—41no—
357C22×C32—61no—
358C22×C32—61no—
359C22×C32—62no—
360C22×C32—81no—
361C22×C32—81no—
362C22×C32—81no—
363C22×C32—81no—
364C22×C32—82no—
365C22×C32—82no—
366C22×C32—128no—
367C22×C32—121no—
368C22×C32—121no—
369C22×C32D3×D411yescharacteristic
370C22×C32C2×#6711yescharacteristic
371C22×C32C2×C3×D411yescharacteristic
372C2×C3×D3—22no—
373C2×C3×D3—22no—
374C2×C3×D3—21no—
375C2×C3×D3—21no—
376C2×C3×D3—21no—
377C2×C3×D3—21no—
378C2×C3×D3—24no—
379C2×C3×D3—22no—
380C2×C3×D3—22no—
381C2×C3×D3—22no—
382C2×C3×D3—416no—
383C2×C3×D3—48no—
384C2×C3×D3—48no—
385C2×C3×D3—42no—
386C2×C3×D3—42no—
387C2×C3×D3—41no—
388C2×C3×D3—41no—
389C2×C3×D3—41no—
390C2×C3×D3—41no—
391C2×C3×D3#21412yescomplemented
392C2×C3×D3C3×SD1612yescomplemented
393C32×C4—21no—
394C32×C4—21no—
395C32×C4—21no—
396C32×C4—21no—
397C32×C4—21no—
398C32×C4—21no—
399C32×C4—41no—
400C32×C4—41no—
401C32×C4—61no—
402C32×C4—121no—
403C32×C4D3×D411yescharacteristic
404C32×C4C2×#6711yescharacteristic
405C32×C4C2×#6711yescharacteristic
406C32×C4C2×#6711yescharacteristic
407C32×C4C2×C3×D411yescharacteristic
408C32×C4C2×C3×D411yescharacteristic
409C3⋊Dic3—41no—
410C3×Dic3—22no—
411C3×Dic3—21no—
412C3×Dic3—21no—
413C3×Dic3—42no—
414C3×Dic3—41no—
415C3×Dic3—41no—
416C3×Dic3—121no—
417C3×Dic3—121no—
418C3×Dic3—241no—
419C22×D4—31no—
420C2×SD16—31no—
421C2×SD16—91no—
422C22⋊Q8—91no—
423#102—91no—
424#102—91no—
425C22⋊C8—91no—
426C33#45011yescharacteristic, complemented, Sylow
427C23×C3—22no—
428C23×C3—21no—
429C23×C3—21no—
430C23×C3—21no—
431C23×C3—31no—
432C23×C3—31no—
433C23×C3—41no—
434C23×C3—41no—
435C23×C3—42no—
436C23×C3—61no—
437C23×C3—68no—
438C23×C3—64no—
439C23×C3—64no—
440C23×C3—62no—
441C23×C3—61no—
442C23×C3—61no—
443C23×C3—122no—
444C23×C3—122no—
445C23×C3—124no—
446C23×C3—124no—
447C23×C3—122no—
448C23×C3—122no—
449C22×D3—24no—
450C22×D3—21no—
451C22×D3—42no—
452C22×D3—42no—
453C22×D3C3×#6711yescharacteristic
454C3×Q8—62no—
455C3×Q8—61no—
456C3×Q8—61no—
457C3×Q8—61no—
458C3×Q8—61no—
459C3×Q8—121no—
460C3×D4—22no—
461C3×D4—21no—
462C3×D4—21no—
463C3×D4—21no—
464C3×D4—22no—
465C3×D4—22no—
466C3×D4—22no—
467C3×D4—32no—
468C3×D4—32no—
469C3×D4—41no—
470C3×D4—41no—
471C3×D4—42no—
472C3×D4—42no—
473C3×D4—62no—
474C3×D4—62no—
475C3×D4—68no—
476C3×D4—64no—
477C3×D4—64no—
478C3×D4—61no—
479C3×D4—61no—
480C3×D4#62512yes—
481C3×D4C3×#6712yes—
482C3×D4C3×#6712yes—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—31no—
487C2×C3×C4—31no—
488C2×C3×C4—41no—
489C2×C3×C4—61no—
490C2×C3×C4—62no—
491C2×C3×C4—62no—
492C2×C3×C4—61no—
493C2×C3×C4—61no—
494C2×C3×C4—61no—
495C2×C3×C4—61no—
496C2×C3×C4—61no—
497C2×C3×C4—61no—
498C2×C3×C4—121no—
499C2×C3×C4—181no—
500C2×C3×C4C2×D3211yescharacteristic
501C2×C3×C4C22×C3×D311yescharacteristic
502C2×C3×C4C22×C3×D311yescharacteristic
503#67—24no—
504C2×Dic3—21no—
505C2×Dic3—61no—
506C2×Dic3—61no—
507C2×Dic3—121no—
508C2×Dic3C3×#6711yescharacteristic
509D12—21no—
510D12C3×#6712yes—
511C4×D3—21no—
512C4×D3—21no—
513Dic6—21no—
514Dic6—21no—
515C3×C8—62no—
516C3×C8—61no—
517C3×C8—61no—
518C3×C8—181no—
519C3⋊C8—21no—
520C3⋊C8—61no—
521C3⋊C8—61no—
522C3⋊C8—121no—
523C2×C32—21no—
524C2×C32—21no—
525C2×C32—21no—
526C2×C32—21no—
527C2×C32—21no—
528C2×C32—21no—
529C2×C32—21no—
530C2×C32—21no—
531C2×C32—21no—
532C2×C32—41no—
533C2×C32—41no—
534C2×C32—41no—
535C2×C32—42no—
536C2×C32—44no—
537C2×C32—42no—
538C2×C32—42no—
539C2×C32—62no—
540C2×C32—82no—
541C2×C32—82no—
542C2×C32—84no—
543C2×C32—122no—
544C2×C32D3×SD1611yescharacteristic
545C2×C32#91411yescharacteristic
546C2×C32#93211yescharacteristic
547C2×C32C2×#21411yescharacteristic
548C2×C32#93711yescharacteristic
549C2×C32#95311yescharacteristic
550C2×C32C3×#12011yescharacteristic
551C2×C32C2×C3×SD1611yescharacteristic
552C2×C32C3×AGL(1,ℤ/8)11yescharacteristic
553C3×D3—24no—
554C3×D3—22no—
555C3×D3—22no—
556C3×D3—44no—
557C3×D3—42no—
558C3×D3—42no—
559C24—61no—
560C2×Q8—31no—
561C2×D4—31no—
562C2×D4—61no—
563C2×D4—62no—
564C2×D4—62no—
565C2×D4C3×D3211yescharacteristic
566C22×C4—31no—
567SD16—62no—
568SD16—182no—
569C2×C8—31no—
570C2×C8—91no—
571C4⋊C4—91no—
572C4⋊C4—181no—
573C22⋊C4—181no—
574C22×C3—24no—
575C22×C3—22no—
576C22×C3—22no—
577C22×C3—22no—
578C22×C3—21no—
579C22×C3—21no—
580C22×C3—21no—
581C22×C3—32no—
582C22×C3—32no—
583C22×C3—42no—
584C22×C3—42no—
585C22×C3—44no—
586C22×C3—42no—
587C22×C3—42no—
588C22×C3—41no—
589C22×C3—41no—
590C22×C3—41no—
591C22×C3—41no—
592C22×C3—41no—
593C22×C3—41no—
594C22×C3—41no—
595C22×C3—62no—
596C22×C3—62no—
597C22×C3—62no—
598C22×C3—64no—
599C22×C3—61no—
600C22×C3—61no—
601C22×C3—61no—
602C22×C3—61no—
603C22×C3—62no—
604C22×C3—62no—
605C22×C3—81no—
606C22×C3—81no—
607C22×C3—81no—
608C22×C3—81no—
609C22×C3—82no—
610C22×C3—82no—
611C22×C3—122no—
612C22×C3—122no—
613C22×C3—1216no—
614C22×C3—128no—
615C22×C3—128no—
616C22×C3—121no—
617C22×C3—121no—
618C22×C3—121no—
619C22×C3—121no—
620C22×C3D3×#6711yescharacteristic
621C22×C3C3×D3×D411yescharacteristic
622C22×C3C2×C3×#6711yescharacteristic
623C2×D3—21no—
624C2×D3—21no—
625C2×D3—22no—
626C2×D3—48no—
627C2×D3—41no—
628C2×D3—41no—
629C2×D3C3×#21412yescomplemented
630C3×C4—21no—
631C3×C4—21no—
632C3×C4—21no—
633C3×C4—21no—
634C3×C4—21no—
635C3×C4—21no—
636C3×C4—41no—
637C3×C4—41no—
638C3×C4—62no—
639C3×C4—61no—
640C3×C4—61no—
641C3×C4—122no—
642C3×C4—121no—
643C3×C4—121no—
644C3×C4—361no—
645C3×C4C2×#62511yescharacteristic
646C3×C4D3×#6711yescharacteristic
647C3×C4C3×D3×D411yescharacteristic
648C3×C4C2×C3×#6711yescharacteristic
649C3×C4C2×C3×#6711yescharacteristic
650C3×C4C2×C3×#6711yescharacteristic
651Dic3—21no—
652Dic3—41no—
653Dic3—121no—
654Dic3—121no—
655Dic3—241no—
656C32—21no—
657C32—21no—
658C32—21no—
659C32—41no—
660C32#516911yescharacteristic, complemented
661C32#521811yescharacteristic, complemented
662C32C3×#45011yescharacteristic, complemented
663C23—21no—
664C23—31no—
665C23—64no—
666C23—61no—
667C23—122no—
668C23—122no—
669Q8—61no—
670Q8—61no—
671D4—21no—
672D4—32no—
673D4—64no—
674D4—61no—
675D4C3×#62512yes—
676C2×C4—31no—
677C2×C4—61no—
678C2×C4—61no—
679C2×C4—61no—
680C2×C4—181no—
681C2×C4C2×C3×D3211yescharacteristic
682C8—61no—
683C8—181no—
684C2×C3—21no—
685C2×C3—21no—
686C2×C3—21no—
687C2×C3—21no—
688C2×C3—21no—
689C2×C3—21no—
690C2×C3—21no—
691C2×C3—21no—
692C2×C3—21no—
693C2×C3—44no—
694C2×C3—42no—
695C2×C3—42no—
696C2×C3—42no—
697C2×C3—41no—
698C2×C3—41no—
699C2×C3—41no—
700C2×C3—64no—
701C2×C3—62no—
702C2×C3—62no—
703C2×C3—82no—
704C2×C3—82no—
705C2×C3—84no—
706C2×C3—124no—
707C2×C3—122no—
708C2×C3—122no—
709C2×C3D3×#21411yescharacteristic
710C2×C3#6393411yescharacteristic
711C2×C3#6397611yescharacteristic
712C2×C3C3×D3×SD1611yescharacteristic
713C2×C3C3×#91411yescharacteristic
714C2×C3C3×#93211yescharacteristic
715C2×C3C2×C3×#21411yescharacteristic
716C2×C3C3×#93711yescharacteristic
717C2×C3C3×#95311yescharacteristic
718D3—22no—
719D3—42no—
720C22—22no—
721C22—32no—
722C22—41no—
723C22—41no—
724C22—61no—
725C22—61no—
726C22—62no—
727C22—128no—
728C22—121no—
729C22—121no—
730C22C3×D3×#6711yescharacteristic
731C4—61no—
732C4—121no—
733C4—361no—
734C4C2×C3×#62511yescharacteristic
735C4C3×D3×#6711yescharacteristic
736C3—21no—
737C3—21no—
738C3—21no—
739C3—41no—
740C3#1059145811yescharacteristic, direct product factor
741C3C3×#516911yescharacteristic, complemented
742C3C3×#521811yescharacteristic, complemented
743C2—42no—
744C2—62no—
745C2—122no—
746C2C3×D3×#21411yescharacteristic
747C2C3×#6393411yescharacteristic
748C2C3×#6397611yescharacteristic
subgroupG/H
centerC22×C3D3×#67
commutator, cosocleC2×C32×C4C23×C3
FrattiniC2×C4C2×C3×D32
FittingC2×C33×D4C22
socleC22×C33C2×D4
prime radicalC2×C32×D3×D4C2
hypercenterC2×C3×D4D32
hypocenterC32C3×#450
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
2. C2×C32×#214C2semidirect
3. C3×#63856C2semidirect
4. C2×C3×#3715C2semidirect
5. C3×#63659C2semidirect
6. C3×#63563C2semidirect
7. C3×(C2×D3)⋊(C3⋊C8)C2semidirect
10. #10591458C3direct (N × H)
18. C2×C32×Dic6C22semidirect
19. C3×C4⋊(C3⋊Dic3)C22semidirect
20. C2×C3×C3⋊(C3⋊C8)C22semidirect
22. C2×C32×C3⋊C8C22semidirect
35. C2×C3×#214D3semidirect
36. C2×C3×#214C2×C3semidirect
38. #63856C2×C3semidirect
39. C2×#3715C2×C3semidirect
40. #63659C2×C3semidirect
48. #63563C2×C3semidirect
49. (C2×D3)⋊(C3⋊C8)C2×C3semidirect
107. C2×C3×Dic6C2×D3semidirect
108. C2×C3×Dic6C22×C3semidirect
111. C4⋊(C3⋊Dic3)C22×C3semidirect
112. C2×C3⋊(C3⋊C8)C22×C3semidirect
129. C2×C3×C3⋊C8C2×D3semidirect
130. C2×C3×C3⋊C8C22×C3semidirect
144. C2×C32×D3SD16semidirect
162. C2×#214C3×D3semidirect
311. C2×Dic6C2×C3×D3semidirect
336. C2×C3⋊C8C2×C3×D3semidirect
391. C2×C3×D3#214semidirect
392. C2×C3×D3C3×SD16semidirect
426. C33#450semidirect
629. C2×D3C3×#214semidirect
660. C32#5169semidirect
661. C32#5218semidirect
662. C32C3×#450semidirect
740. C3#10591458direct (N × H)
741. C3C3×#5169semidirect
742. C3C3×#5218semidirect

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×C32×#2142
C3×#638562
C2×C3×#37152
C3×#636592
C3×#635632
C3×(C2×D3)⋊(C3⋊C8)2
C3×#52183
C3×#51693
#105914583