Finite Group Databasebeta

← C3×#10595165 #13174728

Subgroups — C3×#10595165 #13174728

Order 1728.

1646 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3830C211yesmaximal, characteristic, complemented
2C2×C3×#3805C211yesmaximal, characteristic, complemented
3C32×#939C212yesmaximal, complemented
4C3×#63979C211yesmaximal, characteristic, complemented
5C3×#63978C212yesmaximal, complemented
6C3×#67⋊Dic3C212yesmaximal, complemented
7C2×C3×Dic32C211yesmaximal, characteristic, complemented
8C3×#63953C211yesmaximal, characteristic, complemented
9C3×#63913C211yesmaximal, characteristic, complemented
10C3×#63881C212yesmaximal, complemented
11C3×#63840C211yesmaximal, characteristic, complemented
12C3×#5596—32nomaximal
13#10595165C311yesmaximal, characteristic, direct product factor
14C2×C33×D4C2211yescharacteristic
15C2×C3×#638C2211yescharacteristic
16C2×C3×#638C2211yescharacteristic
17C22×C3×C3⋊Dic3C2211yescharacteristic
18C22×C3×C3⋊Dic3C2211yescharacteristic
19C3×#3830—24no—
20C2×C3×C4×C3⋊D3C2211yescharacteristic
21C2×C3×#634C2211yescharacteristic
22C2×C32×#67C2212yes—
23C2×C32×#67C2212yes—
24C22×C32×Dic3C2212yes—
25C2×C3×#627C2211yescharacteristic
26C2×C3×#626C2212yes—
27C2×C3×#625C2211yescharacteristic
28C3×#3805—24no—
29C2×C3×D3×Dic3C2212yes—
30C32×#217C2212yes—
31C32×(C2×D3)⋊C4C2212yes—
32C32×Dic3⋊C4C2212yes—
33C3×Dic3⋊Dic3C2212yes—
34C3×#3722C2212yes—
35C3×(C2×D3)⋊Dic3C2212yes—
36C3×Dic32C2211yescharacteristic
37C3×Dic32C2212yes—
38C3×Dic32C2211yescharacteristic
39C2×#3830C2×C311yescharacteristic, complemented
40C2×C3×#237—32no—
41C2×C3×#237—32no—
42C2×C3×#237—61no—
43C2×#3805C2×C311yescharacteristic, complemented
44C32×#121—32no—
45C3×#940—32no—
46C3×#939—22no—
47C3×#939—32no—
48C3×#939D312yescomplemented
49C3×#939C2×C312yescomplemented
50C3×D4×Dic3—32no—
51C3×#930—32no—
52C2×C3×C4×Dic3—32no—
53C3×#893—32no—
54C3×#888—32no—
55C3×#885—32no—
56C3×#885—32no—
57C3×#67⋊C4—32no—
58C3×#67⋊C4—32no—
59#63979C2×C311yescharacteristic, complemented
60#63978C2×C312yescomplemented
61#67⋊Dic3C2×C312yescomplemented
62C2×Dic32C2×C311yescharacteristic, complemented
63#63953C2×C311yescharacteristic, complemented
64#63913C2×C311yescharacteristic, complemented
65#63881C2×C312yescomplemented
66#63840C2×C311yescharacteristic, complemented
67C23×C33C2311yescharacteristic
68C23×C33C2311yescharacteristic
69C22×C3×C3⋊D3C2311yescharacteristic
70C22×C32×D3C2312yes—
71C33×D4—22no—
72C2×C33×C4C2311yescharacteristic
73C3×#638—22no—
74C3×#638—22no—
75C2×C3×C3⋊Dic3—22no—
76C2×C3×C3⋊Dic3D414yescomplemented
77C2×C3×C3⋊Dic3C2311yescharacteristic
78C2×C3×C3⋊Dic3C2311yescharacteristic
79C2×C3×C3⋊Dic3C2311yescharacteristic
80C3×C4×C3⋊D3—22no—
81C3×#634—22no—
82C32×#67—24no—
83C32×#67—24no—
84C2×C32×Dic3—24no—
85C2×C32×Dic3C2312yes—
86C2×C32×Dic3C2312yes—
87C2×C32×Dic3C2312yes—
88C3×#627—22no—
89C3×#626—24no—
90C3×#625—22no—
91C3×D3×Dic3—24no—
92C3×#532—91no—
93#5596—32no—
94C2×C32×D4—21no—
95C2×C32×D4—22no—
96C2×C32×D4—32no—
97C2×C32×D4—32no—
98C2×C32×D4—41no—
99C2×C32×D4C2×D312yes—
100C2×C32×D4C22×C311yescharacteristic
101C22×C32×C4—32no—
102C2×#638C22×C311yescharacteristic
103C2×#638C22×C311yescharacteristic
104C22×C3⋊Dic3C22×C311yescharacteristic
105C22×C3⋊Dic3C22×C311yescharacteristic
106#3830—24no—
107C2×C4×C3⋊D3C22×C311yescharacteristic
108C2×#634C22×C311yescharacteristic
109C2×C3×#67—22no—
110C2×C3×#67—22no—
111C2×C3×#67—32no—
112C2×C3×#67—32no—
113C2×C3×#67—32no—
114C2×C3×#67—32no—
115C2×C3×#67—61no—
116C2×C3×#67—61no—
117C2×C3×#67C2×D312yes—
118C2×C3×#67C2×D312yes—
119C2×C3×#67C22×C312yes—
120C2×C3×#67C22×C312yes—
121C22×C3×Dic3—22no—
122C22×C3×Dic3—32no—
123C22×C3×Dic3—32no—
124C22×C3×Dic3—32no—
125C22×C3×Dic3—61no—
126C22×C3×Dic3—61no—
127C22×C3×Dic3C2×D312yes—
128C22×C3×Dic3C22×C312yes—
129C3×#237—68no—
130C3×#237—68no—
131C3×#237—68no—
132C2×C3×D12—32no—
133C2×C3×C4×D3—32no—
134C2×C3×C4×D3—32no—
135C2×C3×C4×D3—61no—
136C2×C3×Dic6—32no—
137C2×C3×Dic6—32no—
138C2×C3×Dic6—61no—
139C2×#627C22×C311yescharacteristic
140C2×#626C22×C312yes—
141C2×#625C22×C311yescharacteristic
142#3805—24no—
143C2×D3×Dic3C22×C312yes—
144C32×C4⋊C4—32no—
145C32×C22⋊C4—32no—
146C32×C22⋊C4—32no—
147C3×#217—22no—
148C3×#217—32no—
149C3×#217C2×D312yes—
150C3×#217C22×C312yes—
151C3×(C2×D3)⋊C4—22no—
152C3×(C2×D3)⋊C4—32no—
153C3×(C2×D3)⋊C4—32no—
154C3×(C2×D3)⋊C4—32no—
155C3×(C2×D3)⋊C4C2×D312yes—
156C3×(C2×D3)⋊C4C22×C312yes—
157C3×C4⋊Dic3—32no—
158C3×Dic3⋊C4—22no—
159C3×Dic3⋊C4—32no—
160C3×Dic3⋊C4C2×D312yes—
161C3×Dic3⋊C4C22×C312yes—
162C3×C4×Dic3—32no—
163C3×C4×Dic3—32no—
164C3×C4×Dic3—32no—
165C3×C4×Dic3—32no—
166Dic3⋊Dic3C22×C312yes—
167#3722C22×C312yes—
168(C2×D3)⋊Dic3C22×C312yes—
169Dic32C22×C311yescharacteristic
170Dic32C22×C312yes—
171Dic32C22×C311yescharacteristic
172C22×C33—22no—
173C22×C33—21no—
174C22×C33—22no—
175C22×C33C2×D412yes—
176C22×C33C2411yescharacteristic
177C2×C3×C3⋊D3—21no—
178C2×C3×C3⋊D3—22no—
179C2×C32×D3—22no—
180C2×C32×D3—22no—
181C2×C32×D3—22no—
182C33×C4—21no—
183C3×C3⋊Dic3—21no—
184C3×C3⋊Dic3C2×D412yes—
185C3×C3⋊Dic3C2×D412yes—
186C32×Dic3—22no—
187C32×Dic3—22no—
188C32×Dic3#4114yescomplemented
189C2×C3×#41—91no—
190C2×C3×#41—91no—
191C2×#237—32no—
192C2×#237—32no—
193C2×#237—61no—
194C3×C4⋊Q8—91no—
195C3×#127—91no—
196C3×#124—91no—
197C3×#124—91no—
198C3×#121—32no—
199C3×#121—32no—
200C3×#121—62no—
201C3×#121—92no—
202C3×C4×D4—92no—
203C3×C4×D4—92no—
204C2×C3×C42—91no—
205#940—32no—
206#939—32no—
207#939C3×D312yescomplemented
208D4×Dic3—32no—
209#930—32no—
210C2×C4×Dic3—32no—
211#893—32no—
212#888—32no—
213#885—32no—
214#885—32no—
215#67⋊C4—32no—
216#67⋊C4—32no—
217C23×C32—21no—
218C23×C32—21no—
219C23×C32—22no—
220C23×C32—22no—
221C23×C32—32no—
222C23×C32—41no—
223C23×C32—41no—
224C23×C32C22×D312yes—
225C23×C32C22×D312yes—
226C23×C32C23×C311yescharacteristic
227C23×C32C23×C311yescharacteristic
228C22×C3⋊D3C23×C311yescharacteristic
229C22×C3×D3—22no—
230C22×C3×D3—32no—
231C22×C3×D3—61no—
232C22×C3×D3C22×D312yes—
233C22×C3×D3C23×C312yes—
234C32×D4—22no—
235C32×D4—24no—
236C32×D4—24no—
237C32×D4—44no—
238C32×D4—44no—
239C32×D4—64no—
240C32×D4—64no—
241C2×C32×C4—21no—
242C2×C32×C4—22no—
243C2×C32×C4—32no—
244C2×C32×C4—32no—
245C2×C32×C4—32no—
246C2×C32×C4—41no—
247C2×C32×C4—64no—
248C2×C32×C4C22×D312yes—
249C2×C32×C4C23×C311yescharacteristic
250#638—22no—
251#638—22no—
252C2×C3⋊Dic3—22no—
253C2×C3⋊Dic3C3×D414yescomplemented
254C2×C3⋊Dic3C23×C311yescharacteristic
255C2×C3⋊Dic3C23×C311yescharacteristic
256C2×C3⋊Dic3C23×C311yescharacteristic
257C4×C3⋊D3—22no—
258#634—22no—
259C3×#67—24no—
260C3×#67—24no—
261C3×#67—24no—
262C3×#67—24no—
263C3×#67—44no—
264C3×#67—44no—
265C3×#67—64no—
266C3×#67—64no—
267C3×#67—64no—
268C3×#67—64no—
269C3×#67—64no—
270C3×#67—64no—
271C2×C3×Dic3—24no—
272C2×C3×Dic3—24no—
273C2×C3×Dic3—22no—
274C2×C3×Dic3—22no—
275C2×C3×Dic3—22no—
276C2×C3×Dic3—38no—
277C2×C3×Dic3—32no—
278C2×C3×Dic3—32no—
279C2×C3×Dic3—32no—
280C2×C3×Dic3—44no—
281C2×C3×Dic3—64no—
282C2×C3×Dic3—61no—
283C2×C3×Dic3—61no—
284C2×C3×Dic3—61no—
285C2×C3×Dic3—64no—
286C2×C3×Dic3—64no—
287C2×C3×Dic3—64no—
288C2×C3×Dic3C22×D312yes—
289C2×C3×Dic3C22×D312yes—
290C2×C3×Dic3C22×D312yes—
291C2×C3×Dic3C23×C312yes—
292C2×C3×Dic3C23×C312yes—
293C2×C3×Dic3C23×C312yes—
294C3×D12—64no—
295C3×C4×D3—64no—
296C3×C4×D3—64no—
297C3×C4×D3—64no—
298C3×Dic6—64no—
299C3×Dic6—64no—
300C3×Dic6—64no—
301#627—22no—
302#626—24no—
303#625—22no—
304D3×Dic3—24no—
305#532—91noSylow
306C2×C33—22no—
307C2×C33—41no—
308C2×C33C22×D411yescharacteristic
309C2×C33C2×#4112yes—
310C3×C3⋊D3—41no—
311C32×D3—42no—
312C3×#41—184no—
313C3×#41—184no—
314C2×C3×Q8—91no—
315C2×C3×Q8—91no—
316C2×C3×D4—21no—
317C2×C3×D4—22no—
318C2×C3×D4—32no—
319C2×C3×D4—32no—
320C2×C3×D4—32no—
321C2×C3×D4—32no—
322C2×C3×D4—41no—
323C2×C3×D4—62no—
324C2×C3×D4—62no—
325C2×C3×D4—92no—
326C2×C3×D4—91no—
327C2×C3×D4—91no—
328C2×C3×D4—91no—
329C2×C3×D4D3211yescharacteristic
330C2×C3×D4C2×C3×D312yes—
331C22×C3×C4—32no—
332C22×C3×C4—32no—
333C22×C3×C4—62no—
334C22×C3×C4—92no—
335C22×C3×C4—91no—
336C22×C3×C4—91no—
337C22×C3×C4—91no—
338C2×#67—32no—
339C2×#67—32no—
340C2×#67—32no—
341C2×#67—32no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67C2×C3×D312yes—
345C2×#67C2×C3×D312yes—
346C22×Dic3—32no—
347C22×Dic3—32no—
348C22×Dic3—32no—
349C22×Dic3—61no—
350C22×Dic3—61no—
351C22×Dic3C2×C3×D312yes—
352#237—68no—
353#237—68no—
354#237—68no—
355C2×D12—32no—
356C2×C4×D3—32no—
357C2×C4×D3—32no—
358C2×C4×D3—61no—
359C2×Dic6—32no—
360C2×Dic6—32no—
361C2×Dic6—61no—
362C3×C4⋊C4—32no—
363C3×C4⋊C4—32no—
364C3×C4⋊C4—62no—
365C3×C4⋊C4—92no—
366C3×C22⋊C4—32no—
367C3×C22⋊C4—32no—
368C3×C22⋊C4—32no—
369C3×C22⋊C4—32no—
370C3×C22⋊C4—62no—
371C3×C22⋊C4—62no—
372C3×C22⋊C4—92no—
373C3×C22⋊C4—92no—
374C3×C42—92no—
375C3×C42—91no—
376C3×C42—91no—
377#217—32no—
378#217C2×C3×D312yes—
379(C2×D3)⋊C4—32no—
380(C2×D3)⋊C4—32no—
381(C2×D3)⋊C4—32no—
382(C2×D3)⋊C4C2×C3×D312yes—
383C4⋊Dic3—32no—
384Dic3⋊C4—32no—
385Dic3⋊C4C2×C3×D312yes—
386C4×Dic3—32no—
387C4×Dic3—32no—
388C4×Dic3—32no—
389C4×Dic3—32no—
390C22×C32—21no—
391C22×C32—22no—
392C22×C32—22no—
393C22×C32—22no—
394C22×C32—22no—
395C22×C32—22no—
396C22×C32—22no—
397C22×C32—22no—
398C22×C32—22no—
399C22×C32—21no—
400C22×C32—22no—
401C22×C32—22no—
402C22×C32—24no—
403C22×C32—41no—
404C22×C32—42no—
405C22×C32—42no—
406C22×C32—42no—
407C22×C32—42no—
408C22×C32—42no—
409C22×C32—42no—
410C22×C32—42no—
411C22×C32—42no—
412C22×C32—42no—
413C22×C32—62no—
414C22×C32—62no—
415C22×C32—62no—
416C22×C32—82no—
417C22×C32—82no—
418C22×C32D3×D414yes—
419C22×C32C2×C3×D412yes—
420C22×C32C23×D312yes—
421C22×C32C24×C311yescharacteristic
422C2×C3⋊D3—21no—
423C2×C3⋊D3—22no—
424C2×C3×D3—22no—
425C2×C3×D3—22no—
426C2×C3×D3—22no—
427C2×C3×D3—22no—
428C2×C3×D3—22no—
429C2×C3×D3—22no—
430C2×C3×D3—42no—
431C2×C3×D3—42no—
432C2×C3×D3—42no—
433C2×C3×D3—62no—
434C2×C3×D3—62no—
435C2×C3×D3—62no—
436C2×C3×D3—62no—
437C2×C3×D3—122no—
438C32×C4—21no—
439C32×C4—22no—
440C32×C4—22no—
441C32×C4—34no—
442C32×C4—42no—
443C32×C4—42no—
444C32×C4—62no—
445C32×C4—62no—
446C3⋊Dic3—21no—
447C3⋊Dic3C2×C3×D412yes—
448C3⋊Dic3C2×C3×D412yes—
449C3×Dic3—22no—
450C3×Dic3—22no—
451C3×Dic3—22no—
452C3×Dic3—22no—
453C3×Dic3—24no—
454C3×Dic3—34no—
455C3×Dic3—34no—
456C3×Dic3—42no—
457C3×Dic3—42no—
458C3×Dic3—62no—
459C3×Dic3—62no—
460C3×Dic3—62no—
461C3×Dic3—62no—
462C3×Dic3#23714yescomplemented
463C3×Dic3C3×#4114yescomplemented
464C2×#41—91no—
465C2×#41—91no—
466C4⋊Q8—91no—
467#127—91no—
468#124—91no—
469#124—91no—
470#121—32no—
471#121—92no—
472C4×D4—92no—
473C4×D4—92no—
474C2×C42—91no—
475C33#53211yescharacteristic, complemented, Sylow
476C23×C3—22no—
477C23×C3—21no—
478C23×C3—21no—
479C23×C3—22no—
480C23×C3—32no—
481C23×C3—32no—
482C23×C3—41no—
483C23×C3—41no—
484C23×C3—62no—
485C23×C3—91no—
486C23×C3C2×D3211yescharacteristic
487C23×C3C2×D3211yescharacteristic
488C23×C3C22×C3×D312yes—
489C23×C3C22×C3×D312yes—
490C22×D3—32no—
491C22×D3—61no—
492C22×D3C22×C3×D312yes—
493C3×Q8—182no—
494C3×Q8—182no—
495C3×D4—24no—
496C3×D4—22no—
497C3×D4—24no—
498C3×D4—44no—
499C3×D4—44no—
500C3×D4—64no—
501C3×D4—64no—
502C3×D4—64no—
503C3×D4—64no—
504C3×D4—124no—
505C3×D4—124no—
506C3×D4—184no—
507C3×D4—182no—
508C3×D4—182no—
509C3×D4—182no—
510C2×C3×C4—21no—
511C2×C3×C4—22no—
512C2×C3×C4—32no—
513C2×C3×C4—32no—
514C2×C3×C4—32no—
515C2×C3×C4—32no—
516C2×C3×C4—32no—
517C2×C3×C4—32no—
518C2×C3×C4—41no—
519C2×C3×C4—62no—
520C2×C3×C4—62no—
521C2×C3×C4—62no—
522C2×C3×C4—64no—
523C2×C3×C4—64no—
524C2×C3×C4—91no—
525C2×C3×C4—91no—
526C2×C3×C4—94no—
527C2×C3×C4—91no—
528C2×C3×C4—124no—
529C2×C3×C4—182no—
530C2×C3×C4—184no—
531C2×C3×C4—182no—
532C2×C3×C4C2×D3211yescharacteristic
533C2×C3×C4C22×C3×D312yes—
534#67—24no—
535#67—24no—
536#67—64no—
537#67—64no—
538#67—64no—
539#67—64no—
540#67—64no—
541#67—64no—
542C2×Dic3—24no—
543C2×Dic3—32no—
544C2×Dic3—32no—
545C2×Dic3—38no—
546C2×Dic3—32no—
547C2×Dic3—64no—
548C2×Dic3—61no—
549C2×Dic3—61no—
550C2×Dic3—61no—
551C2×Dic3—64no—
552C2×Dic3—64no—
553C2×Dic3—64no—
554C2×Dic3C22×C3×D312yes—
555C2×Dic3C22×C3×D312yes—
556C2×Dic3C22×C3×D312yes—
557D12—64no—
558C4×D3—64no—
559C4×D3—64no—
560C4×D3—64no—
561Dic6—64no—
562Dic6—64no—
563Dic6—64no—
564C2×C32—24no—
565C2×C32—22no—
566C2×C32—22no—
567C2×C32—21no—
568C2×C32—22no—
569C2×C32—22no—
570C2×C32—22no—
571C2×C32—41no—
572C2×C32—42no—
573C2×C32—42no—
574C2×C32—44no—
575C2×C32—41no—
576C2×C32—42no—
577C2×C32—42no—
578C2×C32—82no—
579C2×C32—82no—
580C2×C32—82no—
581C2×C32—122no—
582C2×C32C2×D3×D412yes—
583C2×C32C2×#23712yes—
584C2×C32D3×#4112yes—
585C2×C32C22×C3×D411yescharacteristic
586C2×C32C2×C3×#4112yes—
587C3⋊D3—41no—
588C3×D3—42no—
589C3×D3—42no—
590C3×D3—82no—
591C3×D3—122no—
592C3×D3—122no—
593#41—184no—
594#41—184no—
595C2×Q8—91no—
596C2×Q8—91no—
597C2×D4—32no—
598C2×D4—32no—
599C2×D4—92no—
600C2×D4—91no—
601C2×D4—91no—
602C2×D4—91no—
603C2×D4C3×D3211yescharacteristic
604C22×C4—32no—
605C22×C4—92no—
606C22×C4—91no—
607C22×C4—91no—
608C22×C4—91no—
609C4⋊C4—32no—
610C4⋊C4—92no—
611C22⋊C4—32no—
612C22⋊C4—32no—
613C22⋊C4—92no—
614C22⋊C4—92no—
615C42—92no—
616C42—91no—
617C42—91no—
618C22×C3—22no—
619C22×C3—22no—
620C22×C3—22no—
621C22×C3—22no—
622C22×C3—22no—
623C22×C3—21no—
624C22×C3—22no—
625C22×C3—22no—
626C22×C3—22no—
627C22×C3—21no—
628C22×C3—22no—
629C22×C3—22no—
630C22×C3—24no—
631C22×C3—42no—
632C22×C3—42no—
633C22×C3—42no—
634C22×C3—42no—
635C22×C3—42no—
636C22×C3—42no—
637C22×C3—42no—
638C22×C3—42no—
639C22×C3—41no—
640C22×C3—42no—
641C22×C3—62no—
642C22×C3—62no—
643C22×C3—62no—
644C22×C3—62no—
645C22×C3—62no—
646C22×C3—62no—
647C22×C3—82no—
648C22×C3—82no—
649C22×C3—122no—
650C22×C3—122no—
651C22×C3—122no—
652C22×C3—182no—
653C22×C3—181no—
654C22×C3#381112yes—
655C22×C3C3×D3×D414yes—
656C22×C3C22×D3211yescharacteristic
657C22×C3C23×C3×D312yes—
658C2×D3—22no—
659C2×D3—22no—
660C2×D3—22no—
661C2×D3—62no—
662C2×D3—62no—
663C2×D3—62no—
664C2×D3—62no—
665C2×D3—122no—
666C3×C4—22no—
667C3×C4—21no—
668C3×C4—22no—
669C3×C4—34no—
670C3×C4—34no—
671C3×C4—42no—
672C3×C4—42no—
673C3×C4—64no—
674C3×C4—62no—
675C3×C4—62no—
676C3×C4—62no—
677C3×C4—62no—
678C3×C4—92no—
679C3×C4—92no—
680C3×C4—122no—
681C3×C4—122no—
682C3×C4—181no—
683Dic3—22no—
684Dic3—22no—
685Dic3—34no—
686Dic3—34no—
687Dic3—62no—
688Dic3—62no—
689Dic3—62no—
690Dic3—62no—
691Dic3C3×#23714yescomplemented
692C32—21no—
693C32—22no—
694C32—41no—
695C32#559612yescomplemented
696C32C3×#53211yescharacteristic, complemented
697C23—32no—
698C23—91no—
699C23C2×C3×D3211yescharacteristic
700C23C2×C3×D3211yescharacteristic
701Q8—182no—
702Q8—182no—
703D4—22no—
704D4—64no—
705D4—64no—
706D4—184no—
707D4—182no—
708D4—182no—
709D4—182no—
710C2×C4—32no—
711C2×C4—32no—
712C2×C4—32no—
713C2×C4—64no—
714C2×C4—91no—
715C2×C4—91no—
716C2×C4—94no—
717C2×C4—91no—
718C2×C4—182no—
719C2×C4—184no—
720C2×C4—182no—
721C2×C4C2×C3×D3211yescharacteristic
722C2×C3—22no—
723C2×C3—24no—
724C2×C3—21no—
725C2×C3—22no—
726C2×C3—22no—
727C2×C3—22no—
728C2×C3—22no—
729C2×C3—42no—
730C2×C3—44no—
731C2×C3—42no—
732C2×C3—41no—
733C2×C3—42no—
734C2×C3—41no—
735C2×C3—42no—
736C2×C3—82no—
737C2×C3—82no—
738C2×C3—82no—
739C2×C3—122no—
740C2×C3—122no—
741C2×C3—242no—
742C2×C3—361no—
743C2×C3D3×#23712yes—
744C2×C3C2×#381111yescharacteristic
745C2×C3C2×C3×D3×D412yes—
746C2×C3C2×C3×#23712yes—
747C2×C3C3×D3×#4112yes—
748D3—42no—
749D3—122no—
750D3—122no—
751C22—22no—
752C22—21no—
753C22—22no—
754C22—62no—
755C22—62no—
756C22—62no—
757C22—181no—
758C22—182no—
759C22C3×#381112yes—
760C22C22×C3×D3211yescharacteristic
761C4—21no—
762C4—34no—
763C4—62no—
764C4—62no—
765C4—92no—
766C4—92no—
767C4—181no—
768C3—21no—
769C3—22no—
770C3—41no—
771C3#1059516511yescharacteristic, direct product factor
772C3C3×#559612yescomplemented
773C2—22no—
774C2—41no—
775C2—122no—
776C2—361no—
777C2C3×D3×#23712yes—
778C2C2×C3×#381111yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC2×C33×D4C22
socleC22×C33C24
hypercenterC2×C3×D4D32
hypocenterC32C3×#532
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3830C2semidirect
2. C2×C3×#3805C2semidirect
3. C32×#939C2semidirect
4. C3×#63979C2semidirect
5. C3×#63978C2semidirect
6. C3×#67⋊Dic3C2semidirect
7. C2×C3×Dic32C2semidirect
8. C3×#63953C2semidirect
9. C3×#63913C2semidirect
10. C3×#63881C2semidirect
11. C3×#63840C2semidirect
13. #10595165C3direct (N × H)
39. C2×#3830C2×C3semidirect
43. C2×#3805C2×C3semidirect
48. C3×#939D3semidirect
49. C3×#939C2×C3semidirect
59. #63979C2×C3semidirect
60. #63978C2×C3semidirect
61. #67⋊Dic3C2×C3semidirect
62. C2×Dic32C2×C3semidirect
63. #63953C2×C3semidirect
64. #63913C2×C3semidirect
65. #63881C2×C3semidirect
66. #63840C2×C3semidirect
76. C2×C3×C3⋊Dic3D4semidirect
188. C32×Dic3#41semidirect
207. #939C3×D3semidirect
253. C2×C3⋊Dic3C3×D4semidirect
462. C3×Dic3#237semidirect
463. C3×Dic3C3×#41semidirect
475. C33#532semidirect
691. Dic3C3×#237semidirect
695. C32#5596semidirect
696. C32C3×#532semidirect
771. C3#10595165direct (N × H)
772. C3C3×#5596semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#38302
C2×C3×#38052
C32×#9392
C3×#639792
C3×#639782
C3×#67⋊Dic32
C2×C3×Dic322
C3×#639532
C3×#639132
C3×#638812
C3×#638402
C3×#55963
#105951653