Finite Group Databasebeta

← C3×#10591456 #13158465

Subgroups — C3×#10591456 #13158465

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×C3×D4×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×C32×#213C211yesmaximal, characteristic, complemented
3C3×#63916C211yesmaximal, characteristic, complemented
4C2×C3×#3714C211yesmaximal, characteristic, complemented
5C32×#832C211yesmaximal, characteristic, complemented
6C3×#63564C211yesmaximal, characteristic, complemented
7C3×#63557C211yesmaximal, characteristic, complemented
8C3×#5156—31nomaximal
9C3×#4773—31nomaximal
10#10591456C311yesmaximal, characteristic, direct product factor
11C23×C3×C3⋊D3—21no—
12C2×C33×D4C2211yescharacteristic
13C2×C3×#638—21no—
14C3×D4×C3⋊D3—22no—
15C3×D4×C3⋊D3—22no—
16C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
17C2×C3×C4×C3⋊D3C2211yescharacteristic
18C2×C32×D12C2211yescharacteristic, complemented
19C2×C3×#626—21no—
20C32×#213—22no—
21C32×C4⋊Dic3C2211yescharacteristic, complemented
22C2×C32×C3⋊C8C2211yescharacteristic, complemented
23C2×C32×C3⋊C8C2211yescharacteristic, complemented
24C3×(C2×D3)⋊Dic3—21no—
25C3×#3714—22no—
26C2×D4×C3⋊D3C2×C311yescharacteristic, complemented
27C2×C3×D3×D4—31no—
28C2×C3×D3×D4—31no—
29C2×C3×D3×D4—61no—
30C2×C32×D8—31no—
31C3×#938—31no—
32C2×C3×#213—21no—
33C2×C3×#213—31no—
34C2×C3×#213D311yescharacteristic, complemented
35C2×C3×#213C2×C311yescharacteristic, complemented
36C2×C3×D24—31no—
37C3×#895—31no—
38#63916C2×C311yescharacteristic, complemented
39C2×#3714C2×C311yescharacteristic, complemented
40C32×#102—31no—
41C3×#832—21no—
42C3×#832D311yescharacteristic, complemented
43C3×#832C2×C311yescharacteristic, complemented
44C3×#821—31no—
45C3×(C2×D3)⋊C8—31no—
46C3×(C2×D3)⋊C8—31no—
47C3×#809—31no—
48#63564C2×C311yescharacteristic, complemented
49#63557C2×C311yescharacteristic, complemented
50C23×C33—21no—
51C22×C3×C3⋊D3—24no—
52C22×C3×C3⋊D3—21no—
53C22×C3×C3⋊D3—42no—
54C22×C3×C3⋊D3—42no—
55C22×C3×C3⋊D3D411yescharacteristic
56C22×C32×D3—21no—
57C33×D4—21no—
58C33×D4D412yescomplemented
59C2×C33×C4C2311yescharacteristic
60C3×#638—24no—
61C2×C3×C3⋊Dic3D411yescharacteristic
62C3×C4⋊(C3⋊D3)—21no—
63C3×C4⋊(C3⋊D3)D412yescomplemented
64C3×C4×C3⋊D3—21no—
65C3×C4×C3⋊D3—21no—
66C2×C32×Dic3—21no—
67C32×D12—21no—
68C32×D12—21no—
69C3×#626—42no—
70C32×C3⋊C8—21no—
71C32×C3⋊C8—21no—
72C3×#447—91no—
73#5156—31no—
74#4773—31no—
75C23×C3⋊D3—21no—
76C23×C3×D3—61no—
77C23×C3×D3—61no—
78C23×C3×D3—62no—
79C2×C32×D4—21no—
80C2×C32×D4—21no—
81C2×C32×D4—21no—
82C2×C32×D4—31no—
83C2×C32×D4—41no—
84C2×C32×D4C2×D311yescharacteristic
85C2×C32×D4C2×D311yescharacteristic
86C2×C32×D4C22×C311yescharacteristic
87C2×#638—21no—
88D4×C3⋊D3—22no—
89D4×C3⋊D3—22no—
90C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
91C2×C4×C3⋊D3C22×C311yescharacteristic
92C2×C3×#67—61no—
93C2×C3×#67—61no—
94C2×C3×#67—61no—
95C2×C3×#67—62no—
96C3×D3×D4—62no—
97C3×D3×D4—62no—
98C3×D3×D4—64no—
99C3×D3×D4—64no—
100C3×D3×D4—62no—
101C3×D3×D4—62no—
102C2×C3×D12—21no—
103C2×C3×D12—31no—
104C2×C3×D12—31no—
105C2×C3×D12—61no—
106C2×C3×D12—61no—
107C2×C3×D12C2×D311yescharacteristic, complemented
108C2×C3×D12C22×C311yescharacteristic, complemented
109C2×C3×C4×D3—31no—
110C2×C3×C4×D3—31no—
111C2×C3×C4×D3—61no—
112C2×#626—21no—
113C32×D8—62no—
114C2×C32×C8—31no—
115C2×C32×C8—31no—
116C32×C4⋊C4—31no—
117C3×#217—61no—
118C3×#213—24no—
119C3×#213—22no—
120C3×#213—22no—
121C3×#213—62no—
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—21no—
128C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
129C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
130C2×C3×C3⋊C8C22×C311yescharacteristic, complemented
131C2×C3×C3⋊C8C22×C311yescharacteristic, complemented
132C3×D24—62no—
133(C2×D3)⋊Dic3—21no—
134#3714—22no—
135C22×C33—22no—
136C22×C33—41no—
137C22×C33—41no—
138C22×C33C2×D411yescharacteristic
139C2×C3×C3⋊D3—21no—
140C2×C3×C3⋊D3—21no—
141C2×C3×C3⋊D3—22no—
142C2×C3×C3⋊D3—48no—
143C2×C3×C3⋊D3—41no—
144C2×C3×C3⋊D3—41no—
145C2×C3×C3⋊D3D812yescomplemented
146C2×C32×D3—41no—
147C2×C32×D3—41no—
148C2×C32×D3—41no—
149C33×C4C2×D411yescharacteristic
150C33×C4C2×D411yescharacteristic
151C3×C3⋊Dic3—21no—
152C32×Dic3—41no—
153C22×C3×D4—91no—
154C2×D3×D4—31no—
155C2×D3×D4—31no—
156C2×D3×D4—61no—
157C2×C3×D8—31no—
158C2×C3×D8—31no—
159C2×C3×D8—61no—
160C2×C3×D8—91no—
161C3×#121—91no—
162#938—31no—
163C2×#213—31no—
164C2×#213C3×D311yescharacteristic, complemented
165C2×D24—31no—
166#895—31no—
167C3×#102—31no—
168C3×#102—31no—
169C3×#102—61no—
170C3×#102—91no—
171C3×C22⋊C8—91no—
172#832C3×D311yescharacteristic, complemented
173#821—31no—
174(C2×D3)⋊C8—31no—
175(C2×D3)⋊C8—31no—
176#809—31no—
177C23×C32—21no—
178C23×C32—22no—
179C23×C32—21no—
180C23×C32—21no—
181C23×C32—41no—
182C23×C32—41no—
183C23×C32—42no—
184C23×C32—61no—
185C22×C3⋊D3—24no—
186C22×C3⋊D3—21no—
187C22×C3⋊D3—42no—
188C22×C3⋊D3—42no—
189C22×C3⋊D3C3×D411yescharacteristic
190C22×C3×D3—21no—
191C22×C3×D3—21no—
192C22×C3×D3—31no—
193C22×C3×D3—31no—
194C22×C3×D3—41no—
195C22×C3×D3—61no—
196C22×C3×D3—62no—
197C22×C3×D3—68no—
198C22×C3×D3—64no—
199C22×C3×D3—64no—
200C22×C3×D3—61no—
201C22×C3×D3—61no—
202C22×C3×D3—122no—
203C22×C3×D3—122no—
204C22×C3×D3—124no—
205C22×C3×D3—124no—
206C22×C3×D3—122no—
207C22×C3×D3—122no—
208C32×D4—21no—
209C32×D4—22no—
210C32×D4—21no—
211C32×D4—21no—
212C32×D4—22no—
213C32×D4—22no—
214C32×D4—22no—
215C32×D4—42no—
216C32×D4—41no—
217C32×D4—41no—
218C32×D4—42no—
219C32×D4—61no—
220C32×D4—61no—
221C32×D4D1212yescomplemented
222C32×D4#6712yescomplemented
223C32×D4C3×D412yescomplemented
224C2×C32×C4—21no—
225C2×C32×C4—21no—
226C2×C32×C4—21no—
227C2×C32×C4—41no—
228C2×C32×C4—61no—
229C2×C32×C4C22×D311yescharacteristic
230C2×C32×C4C22×D311yescharacteristic
231C2×C32×C4C23×C311yescharacteristic
232#638—24no—
233C2×C3⋊Dic3C3×D411yescharacteristic
234C4⋊(C3⋊D3)—21no—
235C4⋊(C3⋊D3)C3×D412yescomplemented
236C4×C3⋊D3—21no—
237C4×C3⋊D3—21no—
238C3×#67—68no—
239C3×#67—64no—
240C3×#67—64no—
241C3×#67—122no—
242C2×C3×Dic3—21no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—31no—
245C2×C3×Dic3—31no—
246C2×C3×Dic3—41no—
247C2×C3×Dic3—61no—
248C3×D12—22no—
249C3×D12—21no—
250C3×D12—21no—
251C3×D12—21no—
252C3×D12—21no—
253C3×D12—32no—
254C3×D12—32no—
255C3×D12—41no—
256C3×D12—62no—
257C3×D12—62no—
258C3×D12—61no—
259C3×D12—61no—
260C3×D12—122no—
261C3×C4×D3—62no—
262C3×C4×D3—62no—
263C3×C4×D3—61no—
264C3×C4×D3—61no—
265C3×C4×D3—61no—
266C3×C4×D3—61no—
267#626—42no—
268C32×C8—61no—
269C32×C8—61no—
270C3×C3⋊C8—22no—
271C3×C3⋊C8—21no—
272C3×C3⋊C8—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—41no—
276#447—91noSylow
277C2×C33—42no—
278C2×C33#12011yescharacteristic
279C2×C33C2×D811yescharacteristic
280C2×C33AGL(1,ℤ/8)11yescharacteristic
281C3×C3⋊D3—22no—
282C3×C3⋊D3—42no—
283C32×D3—81no—
284C24×C3—181no—
285C23×D3—61no—
286C23×D3—61no—
287C23×D3—62no—
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—91no—
296C2×C3×D4—181no—
297C2×C3×D4—181no—
298C2×C3×D4—182no—
299C2×C3×D4—182no—
300C2×C3×D4D3211yescharacteristic
301C2×C3×D4C2×C3×D311yescharacteristic
302C2×C3×D4C2×C3×D311yescharacteristic
303C22×C3×C4—91no—
304C2×#67—61no—
305C2×#67—61no—
306C2×#67—61no—
307C2×#67—62no—
308D3×D4—62no—
309D3×D4—62no—
310D3×D4—64no—
311D3×D4—64no—
312D3×D4—62no—
313D3×D4—62no—
314C2×D12—31no—
315C2×D12—31no—
316C2×D12—61no—
317C2×D12—61no—
318C2×D12C2×C3×D311yescharacteristic, complemented
319C2×C4×D3—31no—
320C2×C4×D3—31no—
321C2×C4×D3—61no—
322C3×D8—64no—
323C3×D8—62no—
324C3×D8—62no—
325C3×D8—182no—
326C2×C3×C8—31no—
327C2×C3×C8—31no—
328C2×C3×C8—31no—
329C2×C3×C8—31no—
330C2×C3×C8—61no—
331C2×C3×C8—61no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4—31no—
334C3×C4⋊C4—61no—
335C3×C22⋊C4—181no—
336#217—61no—
337#213—22no—
338#213—62no—
339(C2×D3)⋊C4—61no—
340C4⋊Dic3C2×C3×D311yescharacteristic, complemented
341C2×C3⋊C8C2×C3×D311yescharacteristic, complemented
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—41no—
352C22×C32—42no—
353C22×C32—42no—
354C22×C32—44no—
355C22×C32—41no—
356C22×C32—41no—
357C22×C32—42no—
358C22×C32—42no—
359C22×C32—41no—
360C22×C32—41no—
361C22×C32—41no—
362C22×C32—41no—
363C22×C32—81no—
364C22×C32—81no—
365C22×C32—81no—
366C22×C32—81no—
367C22×C32—82no—
368C22×C32—82no—
369C22×C32—121no—
370C22×C32—121no—
371C22×C32—121no—
372C22×C32D3×D411yescharacteristic
373C22×C32D3×D411yescharacteristic
374C22×C32C2×C3×D411yescharacteristic
375C2×C3⋊D3—21no—
376C2×C3⋊D3—21no—
377C2×C3⋊D3—22no—
378C2×C3⋊D3—48no—
379C2×C3⋊D3—41no—
380C2×C3⋊D3—41no—
381C2×C3⋊D3C3×D812yescomplemented
382C2×C3×D3—32no—
383C2×C3×D3—32no—
384C2×C3×D3—42no—
385C2×C3×D3—41no—
386C2×C3×D3—41no—
387C2×C3×D3—41no—
388C2×C3×D3—41no—
389C2×C3×D3—41no—
390C2×C3×D3—41no—
391C2×C3×D3—62no—
392C2×C3×D3—62no—
393C2×C3×D3—62no—
394C2×C3×D3—61no—
395C2×C3×D3—61no—
396C2×C3×D3—61no—
397C2×C3×D3—61no—
398C2×C3×D3—64no—
399C2×C3×D3—62no—
400C2×C3×D3—62no—
401C2×C3×D3—81no—
402C2×C3×D3—81no—
403C2×C3×D3—1216no—
404C2×C3×D3—128no—
405C2×C3×D3—128no—
406C2×C3×D3—122no—
407C2×C3×D3—122no—
408C2×C3×D3—121no—
409C2×C3×D3—121no—
410C2×C3×D3—121no—
411C2×C3×D3—121no—
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—121no—
421C32×C4C2×D1211yescharacteristic
422C32×C4D3×D411yescharacteristic
423C32×C4D3×D411yescharacteristic
424C32×C4C2×#6711yescharacteristic
425C32×C4C2×C3×D411yescharacteristic
426C32×C4C2×C3×D411yescharacteristic
427C3⋊Dic3—21no—
428C3×Dic3—41no—
429C3×Dic3—41no—
430C3×Dic3—62no—
431C3×Dic3—61no—
432C3×Dic3—61no—
433C3×Dic3—81no—
434C22×D4—91no—
435C2×D8—31no—
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—41no—
447C23×C3—41no—
448C23×C3—42no—
449C23×C3—61no—
450C23×C3—61no—
451C23×C3—91no—
452C23×C3—121no—
453C23×C3—184no—
454C23×C3—181no—
455C23×C3—362no—
456C23×C3—362no—
457C22×D3—21no—
458C22×D3—31no—
459C22×D3—31no—
460C22×D3—61no—
461C22×D3—62no—
462C22×D3—68no—
463C22×D3—64no—
464C22×D3—64no—
465C22×D3—61no—
466C22×D3—61no—
467C22×D3—122no—
468C22×D3—122no—
469C22×D3—124no—
470C22×D3—124no—
471C22×D3—122no—
472C22×D3—122no—
473C3×D4—22no—
474C3×D4—21no—
475C3×D4—21no—
476C3×D4—21no—
477C3×D4—22no—
478C3×D4—22no—
479C3×D4—22no—
480C3×D4—41no—
481C3×D4—41no—
482C3×D4—42no—
483C3×D4—42no—
484C3×D4—62no—
485C3×D4—61no—
486C3×D4—61no—
487C3×D4—61no—
488C3×D4—61no—
489C3×D4—92no—
490C3×D4—121no—
491C3×D4—184no—
492C3×D4—181no—
493C3×D4—362no—
494C3×D4#62612yescomplemented
495C3×D4C3×D1212yescomplemented
496C3×D4C3×#6712yescomplemented
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—41no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—91no—
504C2×C3×C4—121no—
505C2×C3×C4—181no—
506C2×C3×C4—181no—
507C2×C3×C4C2×D3211yescharacteristic
508C2×C3×C4C22×C3×D311yescharacteristic
509C2×C3×C4C22×C3×D311yescharacteristic
510#67—68no—
511#67—64no—
512#67—64no—
513#67—122no—
514C2×Dic3—21no—
515C2×Dic3—31no—
516C2×Dic3—31no—
517C2×Dic3—61no—
518D12—21no—
519D12—21no—
520D12—32no—
521D12—32no—
522D12—62no—
523D12—62no—
524D12—61no—
525D12—61no—
526D12—122no—
527C4×D3—62no—
528C4×D3—62no—
529C4×D3—61no—
530C4×D3—61no—
531C4×D3—61no—
532C4×D3—61no—
533C3×C8—62no—
534C3×C8—61no—
535C3×C8—61no—
536C3×C8—61no—
537C3×C8—61no—
538C3×C8—121no—
539C3⋊C8—21no—
540C3⋊C8—21no—
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—82no—
558C2×C32—82no—
559C2×C32—84no—
560C2×C32—241no—
561C2×C32#88211yescharacteristic
562C2×C32D3×D811yescharacteristic
563C2×C32D3×D811yescharacteristic
564C2×C32#91111yescharacteristic
565C2×C32#91411yescharacteristic
566C2×C32#93711yescharacteristic
567C2×C32C3×#12011yescharacteristic
568C2×C32C2×C3×D811yescharacteristic
569C2×C32C3×AGL(1,ℤ/8)11yescharacteristic
570C3⋊D3—22no—
571C3⋊D3—42no—
572C3×D3—64no—
573C3×D3—62no—
574C3×D3—62no—
575C3×D3—82no—
576C3×D3—81no—
577C3×D3—81no—
578C3×D3—124no—
579C3×D3—122no—
580C3×D3—122no—
581C24—181no—
582C2×D4—31no—
583C2×D4—91no—
584C2×D4—181no—
585C2×D4—181no—
586C2×D4—182no—
587C2×D4—182no—
588C2×D4C3×D3211yescharacteristic
589C22×C4—91no—
590D8—62no—
591D8—182no—
592C2×C8—31no—
593C2×C8—31no—
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—42no—
604C22×C3—42no—
605C22×C3—44no—
606C22×C3—42no—
607C22×C3—42no—
608C22×C3—41no—
609C22×C3—41no—
610C22×C3—41no—
611C22×C3—41no—
612C22×C3—41no—
613C22×C3—41no—
614C22×C3—41no—
615C22×C3—81no—
616C22×C3—81no—
617C22×C3—81no—
618C22×C3—81no—
619C22×C3—82no—
620C22×C3—82no—
621C22×C3—92no—
622C22×C3—122no—
623C22×C3—121no—
624C22×C3—121no—
625C22×C3—121no—
626C22×C3—121no—
627C22×C3—121no—
628C22×C3—121no—
629C22×C3—181no—
630C22×C3—181no—
631C22×C3—182no—
632C22×C3—241no—
633C22×C3—241no—
634C22×C3—368no—
635C22×C3—361no—
636C22×C3—361no—
637C22×C3#381111yescharacteristic
638C22×C3C3×D3×D411yescharacteristic
639C22×C3C3×D3×D411yescharacteristic
640C2×D3—32no—
641C2×D3—32no—
642C2×D3—41no—
643C2×D3—41no—
644C2×D3—41no—
645C2×D3—62no—
646C2×D3—62no—
647C2×D3—62no—
648C2×D3—61no—
649C2×D3—61no—
650C2×D3—61no—
651C2×D3—61no—
652C2×D3—64no—
653C2×D3—62no—
654C2×D3—62no—
655C2×D3—1216no—
656C2×D3—128no—
657C2×D3—128no—
658C2×D3—122no—
659C2×D3—122no—
660C2×D3—121no—
661C2×D3—121no—
662C2×D3—121no—
663C2×D3—121no—
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—121no—
673C3×C4—121no—
674C3×C4—181no—
675C3×C4—241no—
676C3×C4C2×#62611yescharacteristic
677C3×C4#381111yescharacteristic
678C3×C4C2×C3×D1211yescharacteristic
679C3×C4C3×D3×D411yescharacteristic
680C3×C4C3×D3×D411yescharacteristic
681C3×C4C2×C3×#6711yescharacteristic
682Dic3—41no—
683Dic3—62no—
684Dic3—61no—
685Dic3—61no—
686C32—21no—
687C32—21no—
688C32—21no—
689C32—41no—
690C32#477311yescharacteristic, complemented
691C32#515611yescharacteristic, complemented
692C32C3×#44711yescharacteristic, complemented
693C23—21no—
694C23—61no—
695C23—91no—
696C23—184no—
697C23—181no—
698C23—362no—
699C23—362no—
700D4—21no—
701D4—61no—
702D4—61no—
703D4—92no—
704D4—184no—
705D4—181no—
706D4—362no—
707D4C3×#62612yescomplemented
708C2×C4—61no—
709C2×C4—91no—
710C2×C4—181no—
711C2×C4—181no—
712C2×C4C2×C3×D3211yescharacteristic
713C8—61no—
714C8—61no—
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—82no—
732C2×C3—82no—
733C2×C3—84no—
734C2×C3—182no—
735C2×C3—242no—
736C2×C3—241no—
737C2×C3—241no—
738C2×C3—362no—
739C2×C3#6392611yescharacteristic
740C2×C3#6393711yescharacteristic
741C2×C3#6398111yescharacteristic
742C2×C3C3×#88211yescharacteristic
743C2×C3C3×D3×D811yescharacteristic
744C2×C3C3×D3×D811yescharacteristic
745C2×C3C3×#91111yescharacteristic
746C2×C3C3×#91411yescharacteristic
747C2×C3C3×#93711yescharacteristic
748D3—64no—
749D3—62no—
750D3—62no—
751D3—81no—
752D3—124no—
753D3—122no—
754D3—122no—
755C22—22no—
756C22—41no—
757C22—41no—
758C22—92no—
759C22—121no—
760C22—121no—
761C22—121no—
762C22—181no—
763C22—181no—
764C22—182no—
765C22—368no—
766C22—361no—
767C22—361no—
768C22C3×#381111yescharacteristic
769C4—121no—
770C4—181no—
771C4C2×C3×#62611yescharacteristic
772C4C3×#381111yescharacteristic
773C3—21no—
774C3—21no—
775C3—21no—
776C3—41no—
777C3#1059145611yescharacteristic, direct product factor
778C3C3×#477311yescharacteristic, complemented
779C3C3×#515611yescharacteristic, complemented
780C2—42no—
781C2—182no—
782C2—241no—
783C2—362no—
784C2C3×#6392611yescharacteristic
785C2C3×#6393711yescharacteristic
786C2C3×#6398111yescharacteristic
subgroupG/H
centerC22×C3#3811
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×D4×C3⋊D3C2semidirect
2. C2×C32×#213C2semidirect
3. C3×#63916C2semidirect
4. C2×C3×#3714C2semidirect
5. C32×#832C2semidirect
6. C3×#63564C2semidirect
7. C3×#63557C2semidirect
10. #10591456C3direct (N × H)
18. C2×C32×D12C22semidirect
21. C32×C4⋊Dic3C22semidirect
22. C2×C32×C3⋊C8C22semidirect
23. C2×C32×C3⋊C8C22semidirect
26. C2×D4×C3⋊D3C2×C3semidirect
34. C2×C3×#213D3semidirect
35. C2×C3×#213C2×C3semidirect
38. #63916C2×C3semidirect
39. C2×#3714C2×C3semidirect
42. C3×#832D3semidirect
43. C3×#832C2×C3semidirect
48. #63564C2×C3semidirect
49. #63557C2×C3semidirect
58. C33×D4D4semidirect
63. C3×C4⋊(C3⋊D3)D4semidirect
107. C2×C3×D12C2×D3semidirect
108. C2×C3×D12C22×C3semidirect
124. C3×C4⋊Dic3C2×D3semidirect
125. C3×C4⋊Dic3C22×C3semidirect
128. C2×C3×C3⋊C8C2×D3semidirect
129. C2×C3×C3⋊C8C2×D3semidirect
130. C2×C3×C3⋊C8C22×C3semidirect
131. C2×C3×C3⋊C8C22×C3semidirect
145. C2×C3×C3⋊D3D8semidirect
164. C2×#213C3×D3semidirect
172. #832C3×D3semidirect
221. C32×D4D12semidirect
222. C32×D4#67semidirect
223. C32×D4C3×D4semidirect
235. C4⋊(C3⋊D3)C3×D4semidirect
318. C2×D12C2×C3×D3semidirect
340. C4⋊Dic3C2×C3×D3semidirect
341. C2×C3⋊C8C2×C3×D3semidirect
342. C2×C3⋊C8C2×C3×D3semidirect
381. C2×C3⋊D3C3×D8semidirect
441. C33#447semidirect
494. C3×D4#626semidirect
495. C3×D4C3×D12semidirect
496. C3×D4C3×#67semidirect
690. C32#4773semidirect
691. C32#5156semidirect
692. C32C3×#447semidirect
707. D4C3×#626semidirect
777. C3#10591456direct (N × H)
778. C3C3×#4773semidirect
779. C3C3×#5156semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×C3⋊D32
C2×C32×#2132
C3×#639162
C2×C3×#37142
C32×#8322
C3×#635642
C3×#635572
C3×#51563
C3×#47733
#105914563