Finite Group Databasebeta

← C3×#10590595 #13157612

Subgroups — C3×#10590595 #13157612

Order 1728.

1012 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×D12C211yesmaximal, characteristic, complemented
2C32×#895C211yesmaximal, characteristic, complemented
3C2×C3×#3714C211yesmaximal, characteristic, complemented
4C2×C3×#3713C211yesmaximal, characteristic, complemented
5C3×#63636C211yesmaximal, characteristic, complemented
6C32×#809C211yesmaximal, characteristic, complemented
7C3×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8C3×#5036—31nomaximal
9C3×#4773—31nomaximal
10#10590595C311yesmaximal, characteristic, direct product factor
11C22×C3×D32—21no—
12C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
13C2×C32×D12—21no—
14C2×C32×D12C2211yescharacteristic
15C2×C32×D12C2211yescharacteristic, complemented
16C2×C32×C4×D3C2211yescharacteristic
17C2×C3×#626—21no—
18C3×D3×D12—22no—
19C3×D3×D12—22no—
20C33×C4⋊C4C2211yescharacteristic, complemented
21C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
22C32×(C2×D3)⋊C4—21no—
23C2×C32×C3⋊C8C2211yescharacteristic, complemented
24C3×#3714—22no—
25C3×#3713—22no—
26C2×C3×D3×D4—31no—
27C22×C3×D12—31no—
28C2×D3×D12C2×C311yescharacteristic, complemented
29C32×#121—31no—
30C2×C3×#213—31no—
31C2×C3×#213—31no—
32C2×C3×#213—31no—
33C2×C3×D24—31no—
34C3×#895—21no—
35C3×#895D311yescharacteristic, complemented
36C3×#895C2×C311yescharacteristic, complemented
37C2×#3714C2×C311yescharacteristic, complemented
38C2×#3713C2×C311yescharacteristic, complemented
39C32×#102—31no—
40#63636C2×C311yescharacteristic, complemented
41C3×#830—31no—
42C3×(C2×D3)⋊C8—31no—
43C3×#809—21no—
44C3×#809—31no—
45C3×#809—31no—
46C3×#809—61no—
47C3×#809D311yescharacteristic, complemented
48C3×#809C2×C311yescharacteristic, complemented
49(C2×D3)⋊(C3⋊C8)C2×C311yescharacteristic, complemented
50C22×C3×C3⋊D3—21no—
51C22×C32×D3—21no—
52C22×C32×D3—21no—
53C22×C32×D3D411yescharacteristic
54C2×C3×D32—24no—
55C2×C3×D32—42no—
56C2×C3×D32—42no—
57C2×C33×C4—21no—
58C2×C33×C4C2311yescharacteristic
59C3×C4⋊(C3⋊D3)—21no—
60C3×C4⋊(C3⋊D3)D412yescomplemented
61C2×C32×Dic3D411yescharacteristic
62C32×D12—21no—
63C32×D12—21no—
64C32×D12—21no—
65C32×D12—42no—
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#5036—31no—
74#4773—31no—
75C23×C3×D3—61no—
76C23×C3×D3—61no—
77C22×D32—21no—
78C2×C32×D4—31no—
79C2×C32×D4—31no—
80C2×C32×D4—61no—
81C22×C32×C4—31no—
82C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
83C2×C3×#67—61no—
84C3×D3×D4—62no—
85C3×D3×D4—62no—
86C2×C3×D12—21no—
87C2×C3×D12—22no—
88C2×C3×D12—21no—
89C2×C3×D12—21no—
90C2×C3×D12—21no—
91C2×C3×D12—31no—
92C2×C3×D12—31no—
93C2×C3×D12—62no—
94C2×C3×D12—61no—
95C2×C3×D12—62no—
96C2×C3×D12—61no—
97C2×C3×D12C2×D311yescharacteristic
98C2×C3×D12C2×D311yescharacteristic, complemented
99C2×C3×D12C22×C311yescharacteristic
100C2×C3×D12C22×C311yescharacteristic, complemented
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3C2×D311yescharacteristic
103C2×C3×C4×D3C22×C311yescharacteristic
104C2×#626—21no—
105D3×D12—22no—
106D3×D12—22no—
107C2×C32×C8—31no—
108C32×C4⋊C4—21no—
109C32×C4⋊C4—21no—
110C32×C4⋊C4—21no—
111C32×C4⋊C4—41no—
112C32×C4⋊C4C2×D311yescharacteristic, complemented
113C32×C4⋊C4C2×D311yescharacteristic, complemented
114C32×C4⋊C4C22×C311yescharacteristic, complemented
115C32×C22⋊C4—61no—
116C2×C3⋊(C3⋊C8)C22×C311yescharacteristic, complemented
117C3×#213—62no—
118C3×#213—62no—
119C3×#213—62no—
120C3×(C2×D3)⋊C4—22no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C2×C3×C3⋊C8—21no—
124C2×C3×C3⋊C8—31no—
125C2×C3×C3⋊C8—31no—
126C2×C3×C3⋊C8—61no—
127C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
128C2×C3×C3⋊C8C22×C311yescharacteristic, complemented
129C3×D24—62no—
130#3714—22no—
131#3713—22no—
132C22×C33C2×D411yescharacteristic
133C2×C3×C3⋊D3—22no—
134C2×C3×C3⋊D3—41no—
135C2×C3×C3⋊D3—41no—
136C2×C32×D3—21no—
137C2×C32×D3—21no—
138C2×C32×D3—22no—
139C2×C32×D3—41no—
140C2×C32×D3—41no—
141C2×C32×D3—41no—
142C2×C32×D3—41no—
143C2×C32×D3—41no—
144C2×C32×D3D812yescomplemented
145C3×D32—48no—
146C33×C4—41no—
147C33×C4C2×D411yescharacteristic
148C33×C4C2×D411yescharacteristic
149C32×Dic3—21no—
150C22×C3×D4—91no—
151C2×D3×D4—31no—
152C22×D12—31no—
153C2×C3×D8—91no—
154C2×C3×D8—91no—
155C3×#121—31no—
156C3×#121—31no—
157C3×#121—61no—
158C2×#213—31no—
159C2×#213—31no—
160C2×#213—31no—
161C2×D24—31no—
162#895C3×D311yescharacteristic, complemented
163C3×#102—31no—
164C3×#102—31no—
165C3×#102—61no—
166C3×#102—91no—
167C3×C22⋊C8—91no—
168#830—31no—
169(C2×D3)⋊C8—31no—
170#809—31no—
171#809—31no—
172#809—61no—
173#809C3×D311yescharacteristic, complemented
174C23×C32—31no—
175C23×C32—61no—
176C23×C32—61no—
177C22×C3⋊D3—21no—
178C22×C3×D3—21no—
179C22×C3×D3—21no—
180C22×C3×D3—22no—
181C22×C3×D3—21no—
182C22×C3×D3—21no—
183C22×C3×D3—21no—
184C22×C3×D3—41no—
185C22×C3×D3—64no—
186C22×C3×D3—64no—
187C22×C3×D3—61no—
188C22×C3×D3—61no—
189C22×C3×D3—121no—
190C22×C3×D3—122no—
191C22×C3×D3—122no—
192C22×C3×D3—122no—
193C22×C3×D3—122no—
194C22×C3×D3#6711yescharacteristic
195C22×C3×D3C3×D411yescharacteristic
196C2×D32—24no—
197C2×D32—42no—
198C2×D32—42no—
199C32×D4—32no—
200C32×D4—61no—
201C32×D4—61no—
202C32×D4—61no—
203C32×D4—122no—
204C2×C32×C4—21no—
205C2×C32×C4—22no—
206C2×C32×C4—21no—
207C2×C32×C4—21no—
208C2×C32×C4—21no—
209C2×C32×C4—21no—
210C2×C32×C4—21no—
211C2×C32×C4—31no—
212C2×C32×C4—41no—
213C2×C32×C4—41no—
214C2×C32×C4—41no—
215C2×C32×C4—42no—
216C2×C32×C4—61no—
217C2×C32×C4—61no—
218C2×C32×C4C22×D311yescharacteristic
219C2×C32×C4C22×D311yescharacteristic
220C2×C32×C4C23×C311yescharacteristic
221C4⋊(C3⋊D3)—21no—
222C4⋊(C3⋊D3)C3×D412yescomplemented
223C3×#67—64no—
224C2×C3×Dic3—21no—
225C2×C3×Dic3#6711yescharacteristic
226C2×C3×Dic3C3×D411yescharacteristic
227C3×D12—21no—
228C3×D12—21no—
229C3×D12—21no—
230C3×D12—21no—
231C3×D12—21no—
232C3×D12—21no—
233C3×D12—22no—
234C3×D12—32no—
235C3×D12—32no—
236C3×D12—41no—
237C3×D12—41no—
238C3×D12—41no—
239C3×D12—44no—
240C3×D12—42no—
241C3×D12—42no—
242C3×D12—62no—
243C3×D12—64no—
244C3×D12—61no—
245C3×D12—61no—
246C3×D12—121no—
247C3×D12D1212yescomplemented
248C3×D12C3×D412yescomplemented
249C3×C4×D3—21no—
250C3×C4×D3—21no—
251C3×C4×D3—21no—
252C3×C4×D3—21no—
253C3×C4×D3—41no—
254C3×C4×D3—41no—
255#626—24no—
256C32×C8—61no—
257C3⋊(C3⋊C8)—21no—
258C3×C3⋊C8—21no—
259C3×C3⋊C8—21no—
260C3×C3⋊C8—41no—
261C3×C3⋊C8—61no—
262C3×C3⋊C8—61no—
263C3×C3⋊C8—121no—
264#447—91noSylow
265C2×C33#12011yescharacteristic
266C2×C33C2×D811yescharacteristic
267C2×C33AGL(1,ℤ/8)11yescharacteristic
268C3×C3⋊D3—42no—
269C32×D3—22no—
270C32×D3—42no—
271C32×D3—81no—
272C24×C3—181no—
273C23×D3—61no—
274C23×D3—61no—
275C2×C3×D4—31no—
276C2×C3×D4—31no—
277C2×C3×D4—31no—
278C2×C3×D4—31no—
279C2×C3×D4—61no—
280C2×C3×D4—61no—
281C2×C3×D4—61no—
282C2×C3×D4—61no—
283C2×C3×D4—62no—
284C2×C3×D4—91no—
285C2×C3×D4—181no—
286C2×C3×D4—182no—
287C2×C3×D4—182no—
288C22×C3×C4—31no—
289C22×C3×C4—31no—
290C22×C3×C4—61no—
291C2×#67—61no—
292D3×D4—62no—
293D3×D4—62no—
294C2×D12—21no—
295C2×D12—31no—
296C2×D12—31no—
297C2×D12—61no—
298C2×D12—62no—
299C2×D12—61no—
300C2×D12—62no—
301C2×D12C2×C3×D311yescharacteristic
302C2×D12C2×C3×D311yescharacteristic, complemented
303C2×C4×D3C2×C3×D311yescharacteristic
304C3×D8—182no—
305C3×D8—182no—
306C2×C3×C8—31no—
307C2×C3×C8—31no—
308C2×C3×C8—61no—
309C2×C3×C8—91no—
310C3×C4⋊C4—21no—
311C3×C4⋊C4—21no—
312C3×C4⋊C4—21no—
313C3×C4⋊C4—41no—
314C3×C4⋊C4D3211yescharacteristic, complemented
315C3×C4⋊C4C2×C3×D311yescharacteristic, complemented
316C3×C4⋊C4C2×C3×D311yescharacteristic, complemented
317C3×C22⋊C4—61no—
318C3×C22⋊C4—61no—
319C3×C22⋊C4—62no—
320#213—62no—
321#213—62no—
322#213—62no—
323(C2×D3)⋊C4—21no—
324C2×C3⋊C8—31no—
325C2×C3⋊C8—31no—
326C2×C3⋊C8—61no—
327C2×C3⋊C8C2×C3×D311yescharacteristic, complemented
328D24—62no—
329C22×C32—21no—
330C22×C32—21no—
331C22×C32—21no—
332C22×C32—32no—
333C22×C32—41no—
334C22×C32—61no—
335C22×C32—61no—
336C22×C32—62no—
337C22×C32—121no—
338C22×C32—121no—
339C22×C32—121no—
340C22×C32—121no—
341C22×C32—121no—
342C22×C32D3×D411yescharacteristic
343C22×C32C2×#6711yescharacteristic
344C22×C32C2×C3×D411yescharacteristic
345C2×C3⋊D3—22no—
346C2×C3⋊D3—41no—
347C2×C3⋊D3—41no—
348C2×C3×D3—21no—
349C2×C3×D3—21no—
350C2×C3×D3—21no—
351C2×C3×D3—21no—
352C2×C3×D3—22no—
353C2×C3×D3—22no—
354C2×C3×D3—22no—
355C2×C3×D3—41no—
356C2×C3×D3—41no—
357C2×C3×D3—42no—
358C2×C3×D3—41no—
359C2×C3×D3—41no—
360C2×C3×D3—41no—
361C2×C3×D3—41no—
362C2×C3×D3—42no—
363C2×C3×D3—42no—
364C2×C3×D3—42no—
365C2×C3×D3—41no—
366C2×C3×D3—41no—
367C2×C3×D3—41no—
368C2×C3×D3—41no—
369C2×C3×D3—41no—
370C2×C3×D3—41no—
371C2×C3×D3—62no—
372C2×C3×D3—62no—
373C2×C3×D3—81no—
374C2×C3×D3—81no—
375C2×C3×D3—122no—
376C2×C3×D3—128no—
377C2×C3×D3—128no—
378C2×C3×D3—121no—
379C2×C3×D3—121no—
380C2×C3×D3—121no—
381C2×C3×D3—121no—
382C2×C3×D3—241no—
383C2×C3×D3—241no—
384C2×C3×D3#21312yescomplemented
385C2×C3×D3C3×D812yescomplemented
386D32—48no—
387C32×C4—21no—
388C32×C4—21no—
389C32×C4—21no—
390C32×C4—21no—
391C32×C4—21no—
392C32×C4—21no—
393C32×C4—41no—
394C32×C4—41no—
395C32×C4—41no—
396C32×C4—42no—
397C32×C4—41no—
398C32×C4—41no—
399C32×C4—61no—
400C32×C4—81no—
401C32×C4—81no—
402C32×C4—82no—
403C32×C4C2×D1211yescharacteristic
404C32×C4D3×D411yescharacteristic
405C32×C4D3×D411yescharacteristic
406C32×C4D3×D411yescharacteristic
407C32×C4C2×C3×D411yescharacteristic
408C32×C4C2×C3×D411yescharacteristic
409C3×Dic3—21no—
410C3×Dic3—21no—
411C3×Dic3—41no—
412C22×D4—91no—
413C2×D8—91no—
414C2×D8—91no—
415#121—31no—
416#102—31no—
417#102—91no—
418C22⋊C8—91no—
419C33#44711yescharacteristic, complemented, Sylow
420C23×C3—31no—
421C23×C3—31no—
422C23×C3—61no—
423C23×C3—62no—
424C23×C3—61no—
425C23×C3—61no—
426C23×C3—61no—
427C23×C3—61no—
428C23×C3—121no—
429C23×C3—184no—
430C23×C3—181no—
431C23×C3—362no—
432C23×C3—362no—
433C22×D3—21no—
434C22×D3—21no—
435C22×D3—64no—
436C22×D3—64no—
437C22×D3—61no—
438C22×D3—61no—
439C22×D3—121no—
440C22×D3—122no—
441C22×D3—122no—
442C22×D3—122no—
443C22×D3—122no—
444C22×D3C3×#6711yescharacteristic
445C3×D4—32no—
446C3×D4—32no—
447C3×D4—62no—
448C3×D4—61no—
449C3×D4—61no—
450C3×D4—61no—
451C3×D4—61no—
452C3×D4—61no—
453C3×D4—61no—
454C3×D4—92no—
455C3×D4—121no—
456C3×D4—121no—
457C3×D4—121no—
458C3×D4—122no—
459C3×D4—122no—
460C3×D4—124no—
461C3×D4—184no—
462C3×D4—181no—
463C2×C3×C4—22no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—31no—
471C2×C3×C4—31no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—42no—
475C2×C3×C4—41no—
476C2×C3×C4—61no—
477C2×C3×C4—61no—
478C2×C3×C4—61no—
479C2×C3×C4—61no—
480C2×C3×C4—61no—
481C2×C3×C4—121no—
482C2×C3×C4—121no—
483C2×C3×C4C2×D3211yescharacteristic
484C2×C3×C4C22×C3×D311yescharacteristic
485C2×C3×C4C22×C3×D311yescharacteristic
486#67—64no—
487C2×Dic3C3×#6711yescharacteristic
488D12—21no—
489D12—21no—
490D12—21no—
491D12—32no—
492D12—32no—
493D12—42no—
494D12—62no—
495D12—64no—
496D12—61no—
497D12—61no—
498D12—121no—
499D12C3×D1212yescomplemented
500C4×D3—21no—
501C4×D3—21no—
502C3×C8—61no—
503C3×C8—61no—
504C3×C8—121no—
505C3×C8—181no—
506C3⋊C8—21no—
507C3⋊C8—61no—
508C3⋊C8—61no—
509C3⋊C8—121no—
510C2×C32—21no—
511C2×C32—21no—
512C2×C32—21no—
513C2×C32—21no—
514C2×C32—21no—
515C2×C32—21no—
516C2×C32—21no—
517C2×C32—21no—
518C2×C32—21no—
519C2×C32—41no—
520C2×C32—41no—
521C2×C32—41no—
522C2×C32—62no—
523C2×C32—122no—
524C2×C32—241no—
525C2×C32#88211yescharacteristic
526C2×C32D3×D811yescharacteristic
527C2×C32#91411yescharacteristic
528C2×C32C2×#21311yescharacteristic
529C2×C32#93711yescharacteristic
530C2×C32#94911yescharacteristic
531C2×C32C3×#12011yescharacteristic
532C2×C32C2×C3×D811yescharacteristic
533C2×C32C3×AGL(1,ℤ/8)11yescharacteristic
534C3⋊D3—42no—
535C3×D3—22no—
536C3×D3—22no—
537C3×D3—42no—
538C3×D3—42no—
539C3×D3—42no—
540C3×D3—82no—
541C3×D3—82no—
542C3×D3—81no—
543C3×D3—81no—
544C3×D3—122no—
545C3×D3—122no—
546C3×D3—242no—
547C24—181no—
548C2×D4—31no—
549C2×D4—31no—
550C2×D4—61no—
551C2×D4—91no—
552C2×D4—181no—
553C2×D4—182no—
554C2×D4—182no—
555C22×C4—31no—
556D8—182no—
557D8—182no—
558C2×C8—31no—
559C2×C8—91no—
560C4⋊C4C3×D3211yescharacteristic, complemented
561C22⋊C4—61no—
562C22×C3—21no—
563C22×C3—21no—
564C22×C3—21no—
565C22×C3—32no—
566C22×C3—32no—
567C22×C3—41no—
568C22×C3—62no—
569C22×C3—61no—
570C22×C3—61no—
571C22×C3—61no—
572C22×C3—61no—
573C22×C3—62no—
574C22×C3—62no—
575C22×C3—121no—
576C22×C3—121no—
577C22×C3—122no—
578C22×C3—122no—
579C22×C3—122no—
580C22×C3—122no—
581C22×C3—121no—
582C22×C3—121no—
583C22×C3—121no—
584C22×C3—121no—
585C22×C3—121no—
586C22×C3—121no—
587C22×C3—121no—
588C22×C3—121no—
589C22×C3—121no—
590C22×C3—121no—
591C22×C3—182no—
592C22×C3—241no—
593C22×C3—241no—
594C22×C3—368no—
595C22×C3—361no—
596C22×C3—361no—
597C22×C3D3×#6711yescharacteristic
598C22×C3C3×D3×D411yescharacteristic
599C22×C3C2×C3×#6711yescharacteristic
600C2×D3—21no—
601C2×D3—21no—
602C2×D3—22no—
603C2×D3—41no—
604C2×D3—41no—
605C2×D3—41no—
606C2×D3—41no—
607C2×D3—41no—
608C2×D3—62no—
609C2×D3—62no—
610C2×D3—122no—
611C2×D3—128no—
612C2×D3—128no—
613C2×D3—121no—
614C2×D3—121no—
615C2×D3—121no—
616C2×D3—121no—
617C2×D3—241no—
618C2×D3—241no—
619C2×D3C3×#21312yescomplemented
620C3×C4—21no—
621C3×C4—21no—
622C3×C4—21no—
623C3×C4—21no—
624C3×C4—21no—
625C3×C4—21no—
626C3×C4—42no—
627C3×C4—41no—
628C3×C4—41no—
629C3×C4—41no—
630C3×C4—41no—
631C3×C4—41no—
632C3×C4—61no—
633C3×C4—61no—
634C3×C4—81no—
635C3×C4—81no—
636C3×C4—82no—
637C3×C4—121no—
638C3×C4D3×D1211yescharacteristic
639C3×C4#380211yescharacteristic
640C3×C4C2×C3×D1211yescharacteristic
641C3×C4C3×D3×D411yescharacteristic
642C3×C4C3×D3×D411yescharacteristic
643C3×C4C3×D3×D411yescharacteristic
644Dic3—21no—
645C32—21no—
646C32—21no—
647C32—21no—
648C32—41no—
649C32#477311yescharacteristic, complemented
650C32#503611yescharacteristic, complemented
651C32C3×#44711yescharacteristic, complemented
652C23—31no—
653C23—61no—
654C23—61no—
655C23—184no—
656C23—181no—
657C23—362no—
658C23—362no—
659D4—32no—
660D4—61no—
661D4—61no—
662D4—61no—
663D4—92no—
664D4—122no—
665D4—184no—
666D4—181no—
667C2×C4—21no—
668C2×C4—31no—
669C2×C4—61no—
670C2×C4—61no—
671C2×C4C2×C3×D3211yescharacteristic
672C8—61no—
673C8—181no—
674C2×C3—21no—
675C2×C3—21no—
676C2×C3—21no—
677C2×C3—21no—
678C2×C3—21no—
679C2×C3—21no—
680C2×C3—21no—
681C2×C3—21no—
682C2×C3—21no—
683C2×C3—41no—
684C2×C3—41no—
685C2×C3—41no—
686C2×C3—62no—
687C2×C3—62no—
688C2×C3—122no—
689C2×C3—122no—
690C2×C3—122no—
691C2×C3—242no—
692C2×C3—242no—
693C2×C3—241no—
694C2×C3—241no—
695C2×C3—362no—
696C2×C3#6392211yescharacteristic
697C2×C3D3×#21311yescharacteristic
698C2×C3#6393911yescharacteristic
699C2×C3C3×#88211yescharacteristic
700C2×C3C3×D3×D811yescharacteristic
701C2×C3C3×#91411yescharacteristic
702C2×C3C2×C3×#21311yescharacteristic
703C2×C3C3×#93711yescharacteristic
704C2×C3C3×#94911yescharacteristic
705D3—22no—
706D3—42no—
707D3—81no—
708D3—122no—
709D3—122no—
710D3—242no—
711C22—32no—
712C22—61no—
713C22—61no—
714C22—62no—
715C22—121no—
716C22—121no—
717C22—121no—
718C22—121no—
719C22—121no—
720C22—182no—
721C22—368no—
722C22—361no—
723C22—361no—
724C22C3×D3×#6711yescharacteristic
725C4—41no—
726C4—61no—
727C4C3×D3×D1211yescharacteristic
728C4C3×#380211yescharacteristic
729C3—21no—
730C3—21no—
731C3—21no—
732C3—41no—
733C3#1059059511yescharacteristic, direct product factor
734C3C3×#477311yescharacteristic, complemented
735C3C3×#503611yescharacteristic, complemented
736C2—62no—
737C2—122no—
738C2—241no—
739C2—362no—
740C2C3×#6392211yescharacteristic
741C2C3×D3×#21311yescharacteristic
742C2C3×#6393911yescharacteristic
subgroupG/H
centerC22×C3D3×#67
commutator, cosocleC2×C32×C4C23×C3
FrattiniC2×C4C2×C3×D32
FittingC33×C4⋊C4C22
socleC22×C33C2×D4
hypercenterC3×C4⋊C4D32
hypocenterC32C3×#447
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×D12C2semidirect
2. C32×#895C2semidirect
3. C2×C3×#3714C2semidirect
4. C2×C3×#3713C2semidirect
5. C3×#63636C2semidirect
6. C32×#809C2semidirect
7. C3×(C2×D3)⋊(C3⋊C8)C2semidirect
10. #10590595C3direct (N × H)
15. C2×C32×D12C22semidirect
20. C33×C4⋊C4C22semidirect
21. C2×C3×C3⋊(C3⋊C8)C22semidirect
23. C2×C32×C3⋊C8C22semidirect
28. C2×D3×D12C2×C3semidirect
35. C3×#895D3semidirect
36. C3×#895C2×C3semidirect
37. C2×#3714C2×C3semidirect
38. C2×#3713C2×C3semidirect
40. #63636C2×C3semidirect
47. C3×#809D3semidirect
48. C3×#809C2×C3semidirect
49. (C2×D3)⋊(C3⋊C8)C2×C3semidirect
60. C3×C4⋊(C3⋊D3)D4semidirect
66. C32×D12D4semidirect
98. C2×C3×D12C2×D3semidirect
100. C2×C3×D12C22×C3semidirect
112. C32×C4⋊C4C2×D3semidirect
113. C32×C4⋊C4C2×D3semidirect
114. C32×C4⋊C4C22×C3semidirect
116. C2×C3⋊(C3⋊C8)C22×C3semidirect
127. C2×C3×C3⋊C8C2×D3semidirect
128. C2×C3×C3⋊C8C22×C3semidirect
144. C2×C32×D3D8semidirect
162. #895C3×D3semidirect
173. #809C3×D3semidirect
222. C4⋊(C3⋊D3)C3×D4semidirect
247. C3×D12D12semidirect
248. C3×D12C3×D4semidirect
302. C2×D12C2×C3×D3semidirect
314. C3×C4⋊C4D32semidirect
315. C3×C4⋊C4C2×C3×D3semidirect
316. C3×C4⋊C4C2×C3×D3semidirect
327. C2×C3⋊C8C2×C3×D3semidirect
384. C2×C3×D3#213semidirect
385. C2×C3×D3C3×D8semidirect
419. C33#447semidirect
499. D12C3×D12semidirect
560. C4⋊C4C3×D32semidirect
619. C2×D3C3×#213semidirect
649. C32#4773semidirect
650. C32#5036semidirect
651. C32C3×#447semidirect
733. C3#10590595direct (N × H)
734. C3C3×#4773semidirect
735. C3C3×#5036semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×D122
C32×#8952
C2×C3×#37142
C2×C3×#37132
C3×#636362
C32×#8092
C3×(C2×D3)⋊(C3⋊C8)2
C3×#50363
C3×#47733
#105905953