Finite Group Databasebeta

← C3×#10591515 #13158542

Subgroups — C3×#10591515 #13158542

Order 1728.

1092 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×D12C211yesmaximal, characteristic, complemented
2C2×C3×#3753C211yesmaximal, characteristic, complemented
3C32×#938C211yesmaximal, characteristic, complemented
4C2×C32×#213C211yesmaximal, characteristic, complemented
5C3×#63564C211yesmaximal, characteristic, complemented
6C3×#63562C211yesmaximal, characteristic, complemented
7C3×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8C3×#5156—31nomaximal
9C3×#5036—31nomaximal
10#10591515C311yesmaximal, characteristic, direct product factor
11C22×C3×D32—21no—
12C2×C33×D4C2211yescharacteristic, complemented
13C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
14C2×C32×#67—21no—
15C2×C32×D12C2211yescharacteristic
16C2×C32×C4×D3C2211yescharacteristic
17C2×C3×#626—21no—
18C3×D3×D12—22no—
19C3×D3×D12—22no—
20C3×#3753—22no—
21C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
22C32×#217—21no—
23C32×#213—22no—
24C32×C4⋊Dic3C2211yescharacteristic, complemented
25C2×C32×C3⋊C8C2211yescharacteristic, complemented
26C2×C3×D3×D4—31no—
27C22×C3×D12—31no—
28C2×D3×D12C2×C311yescharacteristic, complemented
29C2×C32×D8—31no—
30C32×#121—31no—
31C2×#3753C2×C311yescharacteristic, complemented
32C3×#938—21no—
33C3×#938D311yescharacteristic, complemented
34C3×#938C2×C311yescharacteristic, complemented
35C2×C3×#213—21no—
36C2×C3×#213—31no—
37C2×C3×#213—31no—
38C2×C3×#213—61no—
39C2×C3×#213D311yescharacteristic, complemented
40C2×C3×#213C2×C311yescharacteristic, complemented
41C3×#832—31no—
42C3×#830—31no—
43C3×#821—31no—
44C3×(C2×D3)⋊C8—31no—
45C3×#809—31no—
46C3×#809—31no—
47#63564C2×C311yescharacteristic, complemented
48#63562C2×C311yescharacteristic, complemented
49(C2×D3)⋊(C3⋊C8)C2×C311yescharacteristic, complemented
50C23×C33—21no—
51C22×C3×C3⋊D3—21no—
52C22×C32×D3—21no—
53C22×C32×D3D411yescharacteristic
54C2×C3×D32—24no—
55C2×C3×D32—42no—
56C2×C3×D32—42no—
57C33×D4—21no—
58C33×D4—21no—
59C2×C33×C4C2311yescharacteristic
60C3×C4⋊(C3⋊D3)—21no—
61C3×C4⋊(C3⋊D3)D412yescomplemented
62C32×#67—42no—
63C2×C32×Dic3—21no—
64C2×C32×Dic3D411yescharacteristic
65C32×D12—21no—
66C32×D12D412yescomplemented
67C32×C4×D3—21no—
68C32×C4×D3—21no—
69C3×#626—24no—
70C3×C3⋊(C3⋊C8)—21no—
71C32×C3⋊C8—21no—
72C3×#447—91no—
73#5156—31no—
74#5036—31no—
75C23×C3×D3—61no—
76C23×C3×D3—61no—
77C22×D32—21no—
78C2×C32×D4—21no—
79C2×C32×D4—21no—
80C2×C32×D4—21no—
81C2×C32×D4—31no—
82C2×C32×D4—41no—
83C2×C32×D4—61no—
84C2×C32×D4C2×D311yescharacteristic, complemented
85C2×C32×D4C2×D311yescharacteristic, complemented
86C2×C32×D4C22×C311yescharacteristic, complemented
87C22×C32×C4—31no—
88C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
89C2×C3×#67—22no—
90C2×C3×#67—21no—
91C2×C3×#67—21no—
92C2×C3×#67—61no—
93C3×D3×D4—62no—
94C3×D3×D4—62no—
95C2×C3×D12—21no—
96C2×C3×D12—31no—
97C2×C3×D12—31no—
98C2×C3×D12—62no—
99C2×C3×D12—61no—
100C2×C3×D12—62no—
101C2×C3×D12—61no—
102C2×C3×D12C2×D311yescharacteristic
103C2×C3×D12C22×C311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3C2×D311yescharacteristic
106C2×C3×C4×D3C22×C311yescharacteristic
107C2×#626—21no—
108D3×D12—22no—
109D3×D12—22no—
110C32×D8—62no—
111C2×C32×C8—31no—
112C32×C4⋊C4—31no—
113C32×C22⋊C4—61no—
114#3753—22no—
115C2×C3⋊(C3⋊C8)C22×C311yescharacteristic, complemented
116C3×#217—22no—
117C3×#217—21no—
118C3×#217—21no—
119C3×#213—24no—
120C3×#213—22no—
121C3×#213—22no—
122C3×#213—62no—
123C3×#213—62no—
124C3×#213—64no—
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3C2×D311yescharacteristic, complemented
127C3×C4⋊Dic3C22×C311yescharacteristic, complemented
128C2×C3×C3⋊C8—21no—
129C2×C3×C3⋊C8—31no—
130C2×C3×C3⋊C8—31no—
131C2×C3×C3⋊C8—61no—
132C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
133C2×C3×C3⋊C8C22×C311yescharacteristic, complemented
134C22×C33—41no—
135C22×C33—41no—
136C22×C33—41no—
137C22×C33C2×D411yescharacteristic
138C2×C3×C3⋊D3—22no—
139C2×C3×C3⋊D3—41no—
140C2×C3×C3⋊D3—41no—
141C2×C32×D3—21no—
142C2×C32×D3—21no—
143C2×C32×D3—22no—
144C2×C32×D3—41no—
145C2×C32×D3—41no—
146C2×C32×D3D812yescomplemented
147C3×D32—48no—
148C33×C4C2×D411yescharacteristic
149C33×C4C2×D411yescharacteristic
150C32×Dic3—21no—
151C32×Dic3—41no—
152C22×C3×D4—91no—
153C2×D3×D4—31no—
154C22×D12—31no—
155C2×C3×D8—31no—
156C2×C3×D8—31no—
157C2×C3×D8—61no—
158C2×C3×D8—91no—
159C3×#121—31no—
160C3×#121—31no—
161C3×#121—61no—
162#938C3×D311yescharacteristic, complemented
163C2×#213—31no—
164C2×#213—31no—
165C2×#213—61no—
166C2×#213C3×D311yescharacteristic, complemented
167C3×#102—91no—
168C3×#102—91no—
169C3×C22⋊C8—91no—
170#832—31no—
171#830—31no—
172#821—31no—
173(C2×D3)⋊C8—31no—
174#809—31no—
175#809—31no—
176C23×C32—21no—
177C23×C32—22no—
178C23×C32—21no—
179C23×C32—21no—
180C23×C32—31no—
181C23×C32—41no—
182C23×C32—41no—
183C23×C32—42no—
184C23×C32—61no—
185C22×C3⋊D3—21no—
186C22×C3×D3—21no—
187C22×C3×D3—21no—
188C22×C3×D3—21no—
189C22×C3×D3—41no—
190C22×C3×D3—64no—
191C22×C3×D3—64no—
192C22×C3×D3—61no—
193C22×C3×D3—61no—
194C22×C3×D3—121no—
195C22×C3×D3—122no—
196C22×C3×D3—122no—
197C22×C3×D3—122no—
198C22×C3×D3—122no—
199C22×C3×D3#6711yescharacteristic
200C22×C3×D3C3×D411yescharacteristic
201C2×D32—24no—
202C2×D32—42no—
203C2×D32—42no—
204C32×D4—21no—
205C32×D4—21no—
206C32×D4—22no—
207C32×D4—22no—
208C32×D4—21no—
209C32×D4—21no—
210C32×D4—21no—
211C32×D4—21no—
212C32×D4—32no—
213C32×D4—41no—
214C32×D4—41no—
215C32×D4—41no—
216C32×D4—41no—
217C32×D4—42no—
218C32×D4—42no—
219C32×D4—61no—
220C32×D4—122no—
221C2×C32×C4—21no—
222C2×C32×C4—21no—
223C2×C32×C4—21no—
224C2×C32×C4—31no—
225C2×C32×C4—41no—
226C2×C32×C4—61no—
227C2×C32×C4—61no—
228C2×C32×C4—61no—
229C2×C32×C4C22×D311yescharacteristic
230C2×C32×C4C22×D311yescharacteristic
231C2×C32×C4C23×C311yescharacteristic
232C4⋊(C3⋊D3)—21no—
233C4⋊(C3⋊D3)C3×D412yescomplemented
234C3×#67—44no—
235C3×#67—42no—
236C3×#67—42no—
237C3×#67—64no—
238C2×C3×Dic3—22no—
239C2×C3×Dic3—21no—
240C2×C3×Dic3—21no—
241C2×C3×Dic3—21no—
242C2×C3×Dic3#6711yescharacteristic
243C2×C3×Dic3C3×D411yescharacteristic
244C3×D12—21no—
245C3×D12—21no—
246C3×D12—22no—
247C3×D12—32no—
248C3×D12—32no—
249C3×D12—41no—
250C3×D12—62no—
251C3×D12—64no—
252C3×D12—61no—
253C3×D12—61no—
254C3×D12—121no—
255C3×D12#6712yescomplemented
256C3×D12C3×D412yescomplemented
257C3×C4×D3—21no—
258C3×C4×D3—21no—
259C3×C4×D3—21no—
260C3×C4×D3—21no—
261C3×C4×D3—41no—
262C3×C4×D3—41no—
263#626—24no—
264C32×C8—61no—
265C3⋊(C3⋊C8)—21no—
266C3×C3⋊C8—22no—
267C3×C3⋊C8—21no—
268C3×C3⋊C8—21no—
269C3×C3⋊C8—62no—
270C3×C3⋊C8—61no—
271C3×C3⋊C8—61no—
272#447—91noSylow
273C2×C33—81no—
274C2×C33#12011yescharacteristic
275C2×C33C2×D811yescharacteristic
276C2×C33AGL(1,ℤ/8)11yescharacteristic
277C3×C3⋊D3—42no—
278C32×D3—22no—
279C32×D3—42no—
280C24×C3—181no—
281C23×D3—61no—
282C23×D3—61no—
283C2×C3×D4—21no—
284C2×C3×D4—21no—
285C2×C3×D4—21no—
286C2×C3×D4—31no—
287C2×C3×D4—31no—
288C2×C3×D4—41no—
289C2×C3×D4—61no—
290C2×C3×D4—61no—
291C2×C3×D4—61no—
292C2×C3×D4—62no—
293C2×C3×D4—91no—
294C2×C3×D4—181no—
295C2×C3×D4—182no—
296C2×C3×D4—182no—
297C2×C3×D4D3211yescharacteristic, complemented
298C2×C3×D4C2×C3×D311yescharacteristic, complemented
299C2×C3×D4C2×C3×D311yescharacteristic, complemented
300C22×C3×C4—31no—
301C22×C3×C4—31no—
302C22×C3×C4—61no—
303C2×#67—21no—
304C2×#67—61no—
305D3×D4—62no—
306D3×D4—62no—
307C2×D12—31no—
308C2×D12—31no—
309C2×D12—61no—
310C2×D12—62no—
311C2×D12—61no—
312C2×D12—62no—
313C2×D12C2×C3×D311yescharacteristic
314C2×C4×D3C2×C3×D311yescharacteristic
315C3×D8—62no—
316C3×D8—62no—
317C3×D8—64no—
318C3×D8—182no—
319C2×C3×C8—31no—
320C2×C3×C8—31no—
321C2×C3×C8—61no—
322C2×C3×C8—91no—
323C3×C4⋊C4—31no—
324C3×C4⋊C4—31no—
325C3×C4⋊C4—61no—
326C3×C22⋊C4—61no—
327C3×C22⋊C4—61no—
328C3×C22⋊C4—62no—
329#217—21no—
330#213—22no—
331#213—62no—
332#213—62no—
333#213—64no—
334C4⋊Dic3C2×C3×D311yescharacteristic, complemented
335C2×C3⋊C8—31no—
336C2×C3⋊C8—31no—
337C2×C3⋊C8—61no—
338C2×C3⋊C8C2×C3×D311yescharacteristic, complemented
339C22×C32—21no—
340C22×C32—21no—
341C22×C32—21no—
342C22×C32—32no—
343C22×C32—41no—
344C22×C32—42no—
345C22×C32—42no—
346C22×C32—42no—
347C22×C32—44no—
348C22×C32—41no—
349C22×C32—41no—
350C22×C32—41no—
351C22×C32—41no—
352C22×C32—41no—
353C22×C32—42no—
354C22×C32—42no—
355C22×C32—41no—
356C22×C32—41no—
357C22×C32—41no—
358C22×C32—41no—
359C22×C32—61no—
360C22×C32—61no—
361C22×C32—62no—
362C22×C32—81no—
363C22×C32—81no—
364C22×C32—81no—
365C22×C32—81no—
366C22×C32—82no—
367C22×C32—82no—
368C22×C32—121no—
369C22×C32—121no—
370C22×C32D3×D411yescharacteristic
371C22×C32C2×#6711yescharacteristic
372C22×C32C2×C3×D411yescharacteristic
373C2×C3⋊D3—22no—
374C2×C3⋊D3—41no—
375C2×C3⋊D3—41no—
376C2×C3×D3—21no—
377C2×C3×D3—21no—
378C2×C3×D3—21no—
379C2×C3×D3—21no—
380C2×C3×D3—22no—
381C2×C3×D3—22no—
382C2×C3×D3—22no—
383C2×C3×D3—41no—
384C2×C3×D3—41no—
385C2×C3×D3—42no—
386C2×C3×D3—41no—
387C2×C3×D3—41no—
388C2×C3×D3—41no—
389C2×C3×D3—41no—
390C2×C3×D3—62no—
391C2×C3×D3—62no—
392C2×C3×D3—81no—
393C2×C3×D3—81no—
394C2×C3×D3—122no—
395C2×C3×D3—128no—
396C2×C3×D3—128no—
397C2×C3×D3—121no—
398C2×C3×D3—121no—
399C2×C3×D3—121no—
400C2×C3×D3—121no—
401C2×C3×D3—241no—
402C2×C3×D3—241no—
403C2×C3×D3#21312yescomplemented
404C2×C3×D3C3×D812yescomplemented
405D32—48no—
406C32×C4—21no—
407C32×C4—21no—
408C32×C4—21no—
409C32×C4—21no—
410C32×C4—21no—
411C32×C4—21no—
412C32×C4—41no—
413C32×C4—41no—
414C32×C4—61no—
415C32×C4—121no—
416C32×C4D3×D411yescharacteristic
417C32×C4D3×D411yescharacteristic
418C32×C4D3×D411yescharacteristic
419C32×C4C2×#6711yescharacteristic
420C32×C4C2×C3×D411yescharacteristic
421C32×C4C2×C3×D411yescharacteristic
422C3×Dic3—21no—
423C3×Dic3—21no—
424C3×Dic3—41no—
425C3×Dic3—42no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C22×D4—91no—
429C2×D8—31no—
430C2×D8—91no—
431#121—31no—
432#102—91no—
433#102—91no—
434C22⋊C8—91no—
435C33#44711yescharacteristic, complemented, Sylow
436C23×C3—22no—
437C23×C3—21no—
438C23×C3—21no—
439C23×C3—21no—
440C23×C3—31no—
441C23×C3—31no—
442C23×C3—41no—
443C23×C3—41no—
444C23×C3—42no—
445C23×C3—61no—
446C23×C3—61no—
447C23×C3—61no—
448C23×C3—121no—
449C23×C3—184no—
450C23×C3—181no—
451C23×C3—362no—
452C23×C3—362no—
453C22×D3—21no—
454C22×D3—64no—
455C22×D3—64no—
456C22×D3—61no—
457C22×D3—61no—
458C22×D3—121no—
459C22×D3—122no—
460C22×D3—122no—
461C22×D3—122no—
462C22×D3—122no—
463C22×D3C3×#6711yescharacteristic
464C3×D4—22no—
465C3×D4—22no—
466C3×D4—21no—
467C3×D4—21no—
468C3×D4—21no—
469C3×D4—21no—
470C3×D4—21no—
471C3×D4—21no—
472C3×D4—32no—
473C3×D4—32no—
474C3×D4—41no—
475C3×D4—41no—
476C3×D4—41no—
477C3×D4—41no—
478C3×D4—42no—
479C3×D4—42no—
480C3×D4—62no—
481C3×D4—61no—
482C3×D4—61no—
483C3×D4—92no—
484C3×D4—121no—
485C3×D4—122no—
486C3×D4—122no—
487C3×D4—124no—
488C3×D4—184no—
489C3×D4—181no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—31no—
494C2×C3×C4—31no—
495C2×C3×C4—41no—
496C2×C3×C4—61no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—62no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—121no—
505C2×C3×C4—121no—
506C2×C3×C4C2×D3211yescharacteristic
507C2×C3×C4C22×C3×D311yescharacteristic
508C2×C3×C4C22×C3×D311yescharacteristic
509#67—42no—
510#67—64no—
511C2×Dic3—21no—
512C2×Dic3C3×#6711yescharacteristic
513D12—21no—
514D12—32no—
515D12—32no—
516D12—62no—
517D12—64no—
518D12—61no—
519D12—61no—
520D12—121no—
521D12C3×#6712yescomplemented
522C4×D3—21no—
523C4×D3—21no—
524C3×C8—62no—
525C3×C8—61no—
526C3×C8—61no—
527C3×C8—181no—
528C3⋊C8—21no—
529C3⋊C8—62no—
530C3⋊C8—61no—
531C3⋊C8—61no—
532C2×C32—21no—
533C2×C32—21no—
534C2×C32—21no—
535C2×C32—21no—
536C2×C32—21no—
537C2×C32—21no—
538C2×C32—21no—
539C2×C32—21no—
540C2×C32—21no—
541C2×C32—41no—
542C2×C32—41no—
543C2×C32—41no—
544C2×C32—62no—
545C2×C32—82no—
546C2×C32—82no—
547C2×C32—82no—
548C2×C32—84no—
549C2×C32—81no—
550C2×C32—81no—
551C2×C32—81no—
552C2×C32—122no—
553C2×C32D3×D811yescharacteristic
554C2×C32#91111yescharacteristic
555C2×C32C2×#21311yescharacteristic
556C2×C32#93711yescharacteristic
557C2×C32#93711yescharacteristic
558C2×C32#94911yescharacteristic
559C2×C32C3×#12011yescharacteristic
560C2×C32C2×C3×D811yescharacteristic
561C2×C32C3×AGL(1,ℤ/8)11yescharacteristic
562C3⋊D3—42no—
563C3×D3—22no—
564C3×D3—22no—
565C3×D3—42no—
566C3×D3—42no—
567C3×D3—42no—
568C3×D3—82no—
569C3×D3—122no—
570C3×D3—122no—
571C3×D3—242no—
572C24—181no—
573C2×D4—31no—
574C2×D4—61no—
575C2×D4—91no—
576C2×D4—181no—
577C2×D4—182no—
578C2×D4—182no—
579C2×D4C3×D3211yescharacteristic, complemented
580C22×C4—31no—
581D8—62no—
582D8—182no—
583C2×C8—31no—
584C2×C8—91no—
585C4⋊C4—31no—
586C22⋊C4—61no—
587C22×C3—21no—
588C22×C3—21no—
589C22×C3—21no—
590C22×C3—32no—
591C22×C3—32no—
592C22×C3—42no—
593C22×C3—42no—
594C22×C3—42no—
595C22×C3—42no—
596C22×C3—42no—
597C22×C3—44no—
598C22×C3—41no—
599C22×C3—41no—
600C22×C3—41no—
601C22×C3—41no—
602C22×C3—41no—
603C22×C3—41no—
604C22×C3—41no—
605C22×C3—41no—
606C22×C3—41no—
607C22×C3—41no—
608C22×C3—62no—
609C22×C3—61no—
610C22×C3—61no—
611C22×C3—61no—
612C22×C3—61no—
613C22×C3—62no—
614C22×C3—62no—
615C22×C3—81no—
616C22×C3—81no—
617C22×C3—81no—
618C22×C3—81no—
619C22×C3—82no—
620C22×C3—82no—
621C22×C3—121no—
622C22×C3—121no—
623C22×C3—122no—
624C22×C3—121no—
625C22×C3—121no—
626C22×C3—121no—
627C22×C3—121no—
628C22×C3—182no—
629C22×C3—241no—
630C22×C3—241no—
631C22×C3—368no—
632C22×C3—361no—
633C22×C3—361no—
634C22×C3D3×#6711yescharacteristic
635C22×C3C3×D3×D411yescharacteristic
636C22×C3C2×C3×#6711yescharacteristic
637C2×D3—21no—
638C2×D3—21no—
639C2×D3—22no—
640C2×D3—41no—
641C2×D3—41no—
642C2×D3—62no—
643C2×D3—62no—
644C2×D3—122no—
645C2×D3—128no—
646C2×D3—128no—
647C2×D3—121no—
648C2×D3—121no—
649C2×D3—121no—
650C2×D3—121no—
651C2×D3—241no—
652C2×D3—241no—
653C2×D3C3×#21312yescomplemented
654C3×C4—21no—
655C3×C4—21no—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—41no—
661C3×C4—41no—
662C3×C4—61no—
663C3×C4—61no—
664C3×C4—121no—
665C3×C4—122no—
666C3×C4—121no—
667C3×C4—121no—
668C3×C4D3×#6711yescharacteristic
669C3×C4#381111yescharacteristic
670C3×C4C3×D3×D411yescharacteristic
671C3×C4C3×D3×D411yescharacteristic
672C3×C4C3×D3×D411yescharacteristic
673C3×C4C2×C3×#6711yescharacteristic
674Dic3—21no—
675Dic3—41no—
676C32—21no—
677C32—21no—
678C32—21no—
679C32—41no—
680C32#503611yescharacteristic, complemented
681C32#515611yescharacteristic, complemented
682C32C3×#44711yescharacteristic, complemented
683C23—21no—
684C23—31no—
685C23—61no—
686C23—184no—
687C23—181no—
688C23—362no—
689C23—362no—
690D4—21no—
691D4—21no—
692D4—32no—
693D4—61no—
694D4—92no—
695D4—122no—
696D4—184no—
697D4—181no—
698C2×C4—31no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4C2×C3×D3211yescharacteristic
703C8—61no—
704C8—181no—
705C2×C3—21no—
706C2×C3—21no—
707C2×C3—21no—
708C2×C3—21no—
709C2×C3—21no—
710C2×C3—21no—
711C2×C3—21no—
712C2×C3—21no—
713C2×C3—21no—
714C2×C3—41no—
715C2×C3—41no—
716C2×C3—41no—
717C2×C3—62no—
718C2×C3—62no—
719C2×C3—82no—
720C2×C3—82no—
721C2×C3—82no—
722C2×C3—84no—
723C2×C3—81no—
724C2×C3—81no—
725C2×C3—81no—
726C2×C3—122no—
727C2×C3—122no—
728C2×C3—122no—
729C2×C3—242no—
730C2×C3—362no—
731C2×C3D3×#21311yescharacteristic
732C2×C3#6392511yescharacteristic
733C2×C3#6398311yescharacteristic
734C2×C3C3×D3×D811yescharacteristic
735C2×C3C3×#91111yescharacteristic
736C2×C3C2×C3×#21311yescharacteristic
737C2×C3C3×#93711yescharacteristic
738C2×C3C3×#93711yescharacteristic
739C2×C3C3×#94911yescharacteristic
740D3—22no—
741D3—42no—
742D3—122no—
743D3—122no—
744D3—242no—
745C22—32no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—61no—
750C22—61no—
751C22—62no—
752C22—121no—
753C22—121no—
754C22—182no—
755C22—368no—
756C22—361no—
757C22—361no—
758C22C3×D3×#6711yescharacteristic
759C4—61no—
760C4—121no—
761C4C3×D3×#6711yescharacteristic
762C4C3×#381111yescharacteristic
763C3—21no—
764C3—21no—
765C3—21no—
766C3—41no—
767C3#1059151511yescharacteristic, direct product factor
768C3C3×#503611yescharacteristic, complemented
769C3C3×#515611yescharacteristic, complemented
770C2—62no—
771C2—81no—
772C2—122no—
773C2—362no—
774C2C3×D3×#21311yescharacteristic
775C2C3×#6392511yescharacteristic
776C2C3×#6398311yescharacteristic
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×C3×D3×D12C2semidirect
2. C2×C3×#3753C2semidirect
3. C32×#938C2semidirect
4. C2×C32×#213C2semidirect
5. C3×#63564C2semidirect
6. C3×#63562C2semidirect
7. C3×(C2×D3)⋊(C3⋊C8)C2semidirect
10. #10591515C3direct (N × H)
12. C2×C33×D4C22semidirect
21. C2×C3×C3⋊(C3⋊C8)C22semidirect
24. C32×C4⋊Dic3C22semidirect
25. C2×C32×C3⋊C8C22semidirect
28. C2×D3×D12C2×C3semidirect
31. C2×#3753C2×C3semidirect
33. C3×#938D3semidirect
34. C3×#938C2×C3semidirect
39. C2×C3×#213D3semidirect
40. C2×C3×#213C2×C3semidirect
47. #63564C2×C3semidirect
48. #63562C2×C3semidirect
49. (C2×D3)⋊(C3⋊C8)C2×C3semidirect
61. C3×C4⋊(C3⋊D3)D4semidirect
66. C32×D12D4semidirect
84. C2×C32×D4C2×D3semidirect
85. C2×C32×D4C2×D3semidirect
86. C2×C32×D4C22×C3semidirect
115. C2×C3⋊(C3⋊C8)C22×C3semidirect
126. C3×C4⋊Dic3C2×D3semidirect
127. C3×C4⋊Dic3C22×C3semidirect
132. C2×C3×C3⋊C8C2×D3semidirect
133. C2×C3×C3⋊C8C22×C3semidirect
146. C2×C32×D3D8semidirect
162. #938C3×D3semidirect
166. C2×#213C3×D3semidirect
233. C4⋊(C3⋊D3)C3×D4semidirect
255. C3×D12#67semidirect
256. C3×D12C3×D4semidirect
297. C2×C3×D4D32semidirect
298. C2×C3×D4C2×C3×D3semidirect
299. C2×C3×D4C2×C3×D3semidirect
334. C4⋊Dic3C2×C3×D3semidirect
338. C2×C3⋊C8C2×C3×D3semidirect
403. C2×C3×D3#213semidirect
404. C2×C3×D3C3×D8semidirect
435. C33#447semidirect
521. D12C3×#67semidirect
579. C2×D4C3×D32semidirect
653. C2×D3C3×#213semidirect
680. C32#5036semidirect
681. C32#5156semidirect
682. C32C3×#447semidirect
767. C3#10591515direct (N × H)
768. C3C3×#5036semidirect
769. C3C3×#5156semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×D122
C2×C3×#37532
C32×#9382
C2×C32×#2132
C3×#635642
C3×#635622
C3×(C2×D3)⋊(C3⋊C8)2
C3×#51563
C3×#50363
#105915153