Finite Group Databasebeta

← C3×#10595166 #13174729

Subgroups — C3×#10595166 #13174729

Order 1728.

1582 conjugacy classes of subgroups.

The subgroup lattice has 810 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×#63982C211yesmaximal, characteristic, complemented
5C3×#63980C211yesmaximal, characteristic, complemented
6C3×#63978C212yesmaximal, complemented
7C3×#63971C212yesmaximal, complemented
8C2×C3×#3724C211yesmaximal, characteristic, complemented
9C3×#63912C211yesmaximal, characteristic, complemented
10C3×#63896C212yesmaximal, complemented
11C3×#63865C211yesmaximal, characteristic, complemented
12C3×#5597—32nomaximal
13#10595166C311yesmaximal, 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×#3724C2212yes—
34C3×#3724C2211yescharacteristic
35C3×#3724C2211yescharacteristic
36C3×Dic3⋊Dic3C2212yes—
37C3×#3722C2212yes—
38C3×(C2×D3)⋊Dic3C2212yes—
39C2×#3830C2×C311yescharacteristic, complemented
40C2×C3×#237—32no—
41C2×C3×#237—32no—
42C2×C3×#237—61no—
43C2×#3805C2×C311yescharacteristic, complemented
44C32×#121—32no—
45C3×#939—22no—
46C3×#939—32no—
47C3×#939—32no—
48C3×#939—32no—
49C3×#939D312yescomplemented
50C3×#939C2×C312yescomplemented
51C3×#930—32no—
52C2×C3×Dic3⋊C4—32no—
53C3×#896—32no—
54C3×#896—32no—
55C3×#884—32no—
56C3×#884—32no—
57C3×#878—32no—
58C3×#878—32no—
59#63982C2×C311yescharacteristic, complemented
60#63980C2×C311yescharacteristic, complemented
61#63978C2×C312yescomplemented
62#63971C2×C312yescomplemented
63C2×#3724C2×C311yescharacteristic, complemented
64#63912C2×C311yescharacteristic, complemented
65#63896C2×C312yescomplemented
66#63865C2×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—42no—
84C2×C32×Dic3—42no—
85C2×C32×Dic3C2312yes—
86C2×C32×Dic3C2312yes—
87C2×C32×Dic3C2312yes—
88C3×#627—22no—
89C3×#626—42no—
90C3×#625—22no—
91C3×D3×Dic3—24no—
92C3×#537—91no—
93#5597—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⋊C4—32no—
161C3×Dic3⋊C4—32no—
162C3×Dic3⋊C4—32no—
163C3×Dic3⋊C4—32no—
164C3×Dic3⋊C4C2×D312yes—
165C3×Dic3⋊C4C22×C312yes—
166#3724C22×C311yescharacteristic
167#3724C22×C312yes—
168#3724C22×C311yescharacteristic
169Dic3⋊Dic3C22×C312yes—
170#3722C22×C312yes—
171(C2×D3)⋊Dic3C22×C312yes—
172C22×C33—21no—
173C22×C33—21no—
174C22×C33—21no—
175C22×C33—21no—
176C22×C33—21no—
177C22×C33C2×D412yes—
178C22×C33C2411yescharacteristic
179C2×C3×C3⋊D3—21no—
180C2×C3×C3⋊D3—21no—
181C2×C3×C3⋊D3—21no—
182C2×C32×D3—22no—
183C2×C32×D3—22no—
184C2×C32×D3—22no—
185C33×C4—21no—
186C3×C3⋊Dic3—21no—
187C3×C3⋊Dic3C2×D412yes—
188C3×C3⋊Dic3C2×D412yes—
189C32×Dic3—22no—
190C32×Dic3—22no—
191C32×Dic3—22no—
192C2×C3×#41—91no—
193C2×C3×#41—91no—
194C2×#237—32no—
195C2×#237—32no—
196C2×#237—61no—
197C3×C22⋊Q8—91no—
198C3×C22⋊Q8—92no—
199C3×C22⋊Q8—91no—
200C3×#121—32no—
201C3×#121—32no—
202C3×#121—62no—
203C3×#121—91no—
204C3×#121—92no—
205C3×#121—92no—
206C3×#121—91no—
207C2×C3×C4⋊C4—91no—
208#939—32no—
209#939—32no—
210#939—32no—
211#939C3×D312yescomplemented
212#930—32no—
213C2×Dic3⋊C4—32no—
214#896—32no—
215#896—32no—
216#884—32no—
217#884—32no—
218#878—32no—
219#878—32no—
220C23×C32—21no—
221C23×C32—21no—
222C23×C32—22no—
223C23×C32—22no—
224C23×C32—32no—
225C23×C32—41no—
226C23×C32—41no—
227C23×C32C22×D312yes—
228C23×C32C22×D312yes—
229C23×C32C23×C311yescharacteristic
230C23×C32C23×C311yescharacteristic
231C22×C3⋊D3C23×C311yescharacteristic
232C22×C3×D3—22no—
233C22×C3×D3—32no—
234C22×C3×D3—61no—
235C22×C3×D3C22×D312yes—
236C22×C3×D3C23×C312yes—
237C32×D4—22no—
238C32×D4—24no—
239C32×D4—24no—
240C32×D4—44no—
241C32×D4—44no—
242C32×D4—64no—
243C32×D4—122no—
244C2×C32×C4—21no—
245C2×C32×C4—22no—
246C2×C32×C4—32no—
247C2×C32×C4—32no—
248C2×C32×C4—32no—
249C2×C32×C4—41no—
250C2×C32×C4—122no—
251C2×C32×C4C22×D312yes—
252C2×C32×C4C23×C311yescharacteristic
253#638—22no—
254#638—22no—
255C2×C3⋊Dic3—22no—
256C2×C3⋊Dic3C3×D414yescomplemented
257C2×C3⋊Dic3C23×C311yescharacteristic
258C2×C3⋊Dic3C23×C311yescharacteristic
259C2×C3⋊Dic3C23×C311yescharacteristic
260C4×C3⋊D3—22no—
261#634—22no—
262C3×#67—24no—
263C3×#67—24no—
264C3×#67—44no—
265C3×#67—42no—
266C3×#67—42no—
267C3×#67—44no—
268C3×#67—64no—
269C3×#67—64no—
270C3×#67—64no—
271C3×#67—64no—
272C3×#67—64no—
273C3×#67—122no—
274C2×C3×Dic3—22no—
275C2×C3×Dic3—22no—
276C2×C3×Dic3—22no—
277C2×C3×Dic3—38no—
278C2×C3×Dic3—32no—
279C2×C3×Dic3—32no—
280C2×C3×Dic3—32no—
281C2×C3×Dic3—42no—
282C2×C3×Dic3—42no—
283C2×C3×Dic3—44no—
284C2×C3×Dic3—64no—
285C2×C3×Dic3—61no—
286C2×C3×Dic3—61no—
287C2×C3×Dic3—61no—
288C2×C3×Dic3—64no—
289C2×C3×Dic3—64no—
290C2×C3×Dic3—64no—
291C2×C3×Dic3C22×D312yes—
292C2×C3×Dic3C22×D312yes—
293C2×C3×Dic3C22×D312yes—
294C2×C3×Dic3C23×C312yes—
295C2×C3×Dic3C23×C312yes—
296C2×C3×Dic3C23×C312yes—
297C3×D12—122no—
298C3×C4×D3—64no—
299C3×C4×D3—64no—
300C3×C4×D3—64no—
301C3×Dic6—64no—
302C3×Dic6—64no—
303C3×Dic6—64no—
304#627—22no—
305#626—42no—
306#625—22no—
307D3×Dic3—24no—
308#537—91noSylow
309C2×C33—22no—
310C2×C33—41no—
311C2×C33C22×D411yescharacteristic
312C2×C33H(5,𝔽2)11yescharacteristic
313C2×C332−1+411yescharacteristic
314C3×C3⋊D3—41no—
315C32×D3—42no—
316C3×#41—184no—
317C3×#41—184no—
318C2×C3×Q8—91no—
319C2×C3×Q8—91no—
320C2×C3×D4—21no—
321C2×C3×D4—22no—
322C2×C3×D4—32no—
323C2×C3×D4—32no—
324C2×C3×D4—32no—
325C2×C3×D4—32no—
326C2×C3×D4—41no—
327C2×C3×D4—62no—
328C2×C3×D4—62no—
329C2×C3×D4—92no—
330C2×C3×D4—91no—
331C2×C3×D4—91no—
332C2×C3×D4—91no—
333C2×C3×D4D3211yescharacteristic
334C2×C3×D4C2×C3×D312yes—
335C22×C3×C4—32no—
336C22×C3×C4—32no—
337C22×C3×C4—62no—
338C22×C3×C4—92no—
339C22×C3×C4—91no—
340C22×C3×C4—91no—
341C22×C3×C4—91no—
342C2×#67—32no—
343C2×#67—32no—
344C2×#67—32no—
345C2×#67—32no—
346C2×#67—61no—
347C2×#67—61no—
348C2×#67C2×C3×D312yes—
349C2×#67C2×C3×D312yes—
350C22×Dic3—32no—
351C22×Dic3—32no—
352C22×Dic3—32no—
353C22×Dic3—61no—
354C22×Dic3—61no—
355C22×Dic3C2×C3×D312yes—
356#237—68no—
357#237—68no—
358#237—68no—
359C2×D12—32no—
360C2×C4×D3—32no—
361C2×C4×D3—32no—
362C2×C4×D3—61no—
363C2×Dic6—32no—
364C2×Dic6—32no—
365C2×Dic6—61no—
366C3×C4⋊C4—32no—
367C3×C4⋊C4—32no—
368C3×C4⋊C4—62no—
369C3×C4⋊C4—91no—
370C3×C4⋊C4—92no—
371C3×C4⋊C4—91no—
372C3×C4⋊C4—92no—
373C3×C22⋊C4—32no—
374C3×C22⋊C4—32no—
375C3×C22⋊C4—32no—
376C3×C22⋊C4—32no—
377C3×C22⋊C4—62no—
378C3×C22⋊C4—62no—
379C3×C22⋊C4—92no—
380C3×C22⋊C4—92no—
381#217—32no—
382#217C2×C3×D312yes—
383(C2×D3)⋊C4—32no—
384(C2×D3)⋊C4—32no—
385(C2×D3)⋊C4—32no—
386(C2×D3)⋊C4C2×C3×D312yes—
387C4⋊Dic3—32no—
388Dic3⋊C4—32no—
389Dic3⋊C4—32no—
390Dic3⋊C4—32no—
391Dic3⋊C4—32no—
392Dic3⋊C4—32no—
393Dic3⋊C4C2×C3×D312yes—
394C22×C32—21no—
395C22×C32—22no—
396C22×C32—22no—
397C22×C32—21no—
398C22×C32—21no—
399C22×C32—22no—
400C22×C32—22no—
401C22×C32—22no—
402C22×C32—22no—
403C22×C32—21no—
404C22×C32—21no—
405C22×C32—21no—
406C22×C32—22no—
407C22×C32—22no—
408C22×C32—24no—
409C22×C32—41no—
410C22×C32—42no—
411C22×C32—42no—
412C22×C32—42no—
413C22×C32—42no—
414C22×C32—41no—
415C22×C32—41no—
416C22×C32—42no—
417C22×C32—41no—
418C22×C32—41no—
419C22×C32—42no—
420C22×C32—42no—
421C22×C32—62no—
422C22×C32—62no—
423C22×C32—62no—
424C22×C32—81no—
425C22×C32—81no—
426C22×C32—81no—
427C22×C32—81no—
428C22×C32D3×D414yes—
429C22×C32C2×C3×D412yes—
430C22×C32C23×D312yes—
431C22×C32C24×C311yescharacteristic
432C2×C3⋊D3—21no—
433C2×C3⋊D3—21no—
434C2×C3⋊D3—21no—
435C2×C3×D3—22no—
436C2×C3×D3—22no—
437C2×C3×D3—22no—
438C2×C3×D3—22no—
439C2×C3×D3—22no—
440C2×C3×D3—22no—
441C2×C3×D3—42no—
442C2×C3×D3—42no—
443C2×C3×D3—42no—
444C2×C3×D3—62no—
445C2×C3×D3—62no—
446C2×C3×D3—62no—
447C2×C3×D3—62no—
448C2×C3×D3—121no—
449C2×C3×D3—121no—
450C32×C4—21no—
451C32×C4—22no—
452C32×C4—22no—
453C32×C4—42no—
454C32×C4—42no—
455C32×C4—62no—
456C32×C4—62no—
457C32×C4—62no—
458C3⋊Dic3—21no—
459C3⋊Dic3C2×C3×D412yes—
460C3⋊Dic3C2×C3×D412yes—
461C3×Dic3—24no—
462C3×Dic3—22no—
463C3×Dic3—22no—
464C3×Dic3—22no—
465C3×Dic3—22no—
466C3×Dic3—22no—
467C3×Dic3—22no—
468C3×Dic3—34no—
469C3×Dic3—34no—
470C3×Dic3—42no—
471C3×Dic3—42no—
472C3×Dic3—62no—
473C3×Dic3—62no—
474C3×Dic3—62no—
475C3×Dic3—62no—
476C2×#41—91no—
477C2×#41—91no—
478C22⋊Q8—91no—
479C22⋊Q8—92no—
480C22⋊Q8—91no—
481#121—32no—
482#121—91no—
483#121—92no—
484#121—92no—
485#121—91no—
486C2×C4⋊C4—91no—
487C33#53711yescharacteristic, complemented, Sylow
488C23×C3—22no—
489C23×C3—21no—
490C23×C3—21no—
491C23×C3—22no—
492C23×C3—32no—
493C23×C3—32no—
494C23×C3—41no—
495C23×C3—41no—
496C23×C3—62no—
497C23×C3—91no—
498C23×C3C2×D3211yescharacteristic
499C23×C3C2×D3211yescharacteristic
500C23×C3C22×C3×D312yes—
501C23×C3C22×C3×D312yes—
502C22×D3—32no—
503C22×D3—61no—
504C22×D3C22×C3×D312yes—
505C3×Q8—182no—
506C3×Q8—182no—
507C3×D4—24no—
508C3×D4—22no—
509C3×D4—24no—
510C3×D4—44no—
511C3×D4—44no—
512C3×D4—64no—
513C3×D4—64no—
514C3×D4—124no—
515C3×D4—122no—
516C3×D4—122no—
517C3×D4—124no—
518C3×D4—182no—
519C3×D4—182no—
520C3×D4—182no—
521C3×D4—362no—
522C2×C3×C4—21no—
523C2×C3×C4—22no—
524C2×C3×C4—32no—
525C2×C3×C4—32no—
526C2×C3×C4—32no—
527C2×C3×C4—32no—
528C2×C3×C4—32no—
529C2×C3×C4—32no—
530C2×C3×C4—41no—
531C2×C3×C4—62no—
532C2×C3×C4—62no—
533C2×C3×C4—62no—
534C2×C3×C4—91no—
535C2×C3×C4—91no—
536C2×C3×C4—94no—
537C2×C3×C4—91no—
538C2×C3×C4—122no—
539C2×C3×C4—122no—
540C2×C3×C4—124no—
541C2×C3×C4—182no—
542C2×C3×C4—184no—
543C2×C3×C4—182no—
544C2×C3×C4C2×D3211yescharacteristic
545C2×C3×C4C22×C3×D312yes—
546#67—24no—
547#67—42no—
548#67—64no—
549#67—64no—
550#67—64no—
551#67—64no—
552#67—64no—
553#67—122no—
554C2×Dic3—32no—
555C2×Dic3—32no—
556C2×Dic3—38no—
557C2×Dic3—32no—
558C2×Dic3—42no—
559C2×Dic3—64no—
560C2×Dic3—61no—
561C2×Dic3—61no—
562C2×Dic3—61no—
563C2×Dic3—64no—
564C2×Dic3—64no—
565C2×Dic3—64no—
566C2×Dic3C22×C3×D312yes—
567C2×Dic3C22×C3×D312yes—
568C2×Dic3C22×C3×D312yes—
569D12—122no—
570C4×D3—64no—
571C4×D3—64no—
572C4×D3—64no—
573Dic6—64no—
574Dic6—64no—
575Dic6—64no—
576C2×C32—24no—
577C2×C32—22no—
578C2×C32—21no—
579C2×C32—21no—
580C2×C32—21no—
581C2×C32—22no—
582C2×C32—22no—
583C2×C32—22no—
584C2×C32—41no—
585C2×C32—41no—
586C2×C32—41no—
587C2×C32—42no—
588C2×C32—44no—
589C2×C32—41no—
590C2×C32—42no—
591C2×C32—42no—
592C2×C32—82no—
593C2×C32—82no—
594C2×C32—82no—
595C2×C32—122no—
596C2×C32C2×D3×D412yes—
597C2×C32#100412yes—
598C2×C32#101012yes—
599C2×C32C22×C3×D411yescharacteristic
600C2×C32C3×H(5,𝔽2)11yescharacteristic
601C2×C32C3×2−1+411yescharacteristic
602C3⋊D3—41no—
603C3×D3—42no—
604C3×D3—42no—
605C3×D3—82no—
606C3×D3—122no—
607C3×D3—122no—
608#41—184no—
609#41—184no—
610C2×Q8—91no—
611C2×Q8—91no—
612C2×D4—32no—
613C2×D4—32no—
614C2×D4—92no—
615C2×D4—91no—
616C2×D4—91no—
617C2×D4—91no—
618C2×D4C3×D3211yescharacteristic
619C22×C4—32no—
620C22×C4—92no—
621C22×C4—91no—
622C22×C4—91no—
623C22×C4—91no—
624C4⋊C4—32no—
625C4⋊C4—91no—
626C4⋊C4—92no—
627C4⋊C4—91no—
628C4⋊C4—92no—
629C22⋊C4—32no—
630C22⋊C4—32no—
631C22⋊C4—92no—
632C22⋊C4—92no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—22no—
636C22×C3—22no—
637C22×C3—22no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—22no—
642C22×C3—22no—
643C22×C3—22no—
644C22×C3—21no—
645C22×C3—22no—
646C22×C3—22no—
647C22×C3—24no—
648C22×C3—42no—
649C22×C3—41no—
650C22×C3—42no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—41no—
654C22×C3—42no—
655C22×C3—42no—
656C22×C3—42no—
657C22×C3—42no—
658C22×C3—41no—
659C22×C3—42no—
660C22×C3—62no—
661C22×C3—62no—
662C22×C3—62no—
663C22×C3—62no—
664C22×C3—62no—
665C22×C3—62no—
666C22×C3—81no—
667C22×C3—81no—
668C22×C3—81no—
669C22×C3—81no—
670C22×C3—122no—
671C22×C3—122no—
672C22×C3—122no—
673C22×C3—181no—
674C22×C3—181no—
675C22×C3—181no—
676C22×C3#381112yes—
677C22×C3C3×D3×D414yes—
678C22×C3C22×D3211yescharacteristic
679C22×C3C23×C3×D312yes—
680C2×D3—22no—
681C2×D3—22no—
682C2×D3—22no—
683C2×D3—62no—
684C2×D3—62no—
685C2×D3—62no—
686C2×D3—62no—
687C2×D3—121no—
688C2×D3—121no—
689C3×C4—22no—
690C3×C4—21no—
691C3×C4—22no—
692C3×C4—42no—
693C3×C4—42no—
694C3×C4—64no—
695C3×C4—62no—
696C3×C4—62no—
697C3×C4—62no—
698C3×C4—62no—
699C3×C4—62no—
700C3×C4—62no—
701C3×C4—92no—
702C3×C4—92no—
703C3×C4—122no—
704C3×C4—122no—
705C3×C4—181no—
706Dic3—22no—
707Dic3—22no—
708Dic3—22no—
709Dic3—34no—
710Dic3—34no—
711Dic3—62no—
712Dic3—62no—
713Dic3—62no—
714Dic3—62no—
715C32—21no—
716C32—22no—
717C32—41no—
718C32#559712yescomplemented
719C32C3×#53711yescharacteristic, complemented
720C23—32no—
721C23—91no—
722C23C2×C3×D3211yescharacteristic
723C23C2×C3×D3211yescharacteristic
724Q8—182no—
725Q8—182no—
726D4—22no—
727D4—64no—
728D4—122no—
729D4—182no—
730D4—182no—
731D4—182no—
732D4—362no—
733C2×C4—32no—
734C2×C4—32no—
735C2×C4—32no—
736C2×C4—91no—
737C2×C4—91no—
738C2×C4—94no—
739C2×C4—91no—
740C2×C4—122no—
741C2×C4—182no—
742C2×C4—184no—
743C2×C4—182no—
744C2×C4C2×C3×D3211yescharacteristic
745C2×C3—22no—
746C2×C3—24no—
747C2×C3—21no—
748C2×C3—22no—
749C2×C3—21no—
750C2×C3—22no—
751C2×C3—22no—
752C2×C3—21no—
753C2×C3—42no—
754C2×C3—44no—
755C2×C3—42no—
756C2×C3—41no—
757C2×C3—42no—
758C2×C3—41no—
759C2×C3—41no—
760C2×C3—41no—
761C2×C3—82no—
762C2×C3—82no—
763C2×C3—82no—
764C2×C3—122no—
765C2×C3—122no—
766C2×C3—242no—
767C2×C3—361no—
768C2×C3#6430911yescharacteristic
769C2×C3#6431311yescharacteristic
770C2×C3C2×#381111yescharacteristic
771C2×C3C2×C3×D3×D412yes—
772C2×C3C3×#100412yes—
773C2×C3C3×#101012yes—
774D3—42no—
775D3—122no—
776D3—122no—
777C22—21no—
778C22—21no—
779C22—21no—
780C22—21no—
781C22—21no—
782C22—62no—
783C22—62no—
784C22—62no—
785C22—181no—
786C22—181no—
787C22—181no—
788C22C3×#381112yes—
789C22C22×C3×D3211yescharacteristic
790C4—21no—
791C4—62no—
792C4—62no—
793C4—62no—
794C4—92no—
795C4—92no—
796C4—181no—
797C3—21no—
798C3—22no—
799C3—41no—
800C3#1059516611yescharacteristic, direct product factor
801C3C3×#559712yescomplemented
802C2—22no—
803C2—41no—
804C2—122no—
805C2—361no—
806C2C3×#6430911yescharacteristic
807C2C3×#6431311yescharacteristic
808C2C2×C3×#381111yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC2×C33×D4C22
socleC22×C33C24
hypercenterC2×C3×D4D32
hypocenterC32C3×#537
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×#63982C2semidirect
5. C3×#63980C2semidirect
6. C3×#63978C2semidirect
7. C3×#63971C2semidirect
8. C2×C3×#3724C2semidirect
9. C3×#63912C2semidirect
10. C3×#63896C2semidirect
11. C3×#63865C2semidirect
13. #10595166C3direct (N × H)
39. C2×#3830C2×C3semidirect
43. C2×#3805C2×C3semidirect
49. C3×#939D3semidirect
50. C3×#939C2×C3semidirect
59. #63982C2×C3semidirect
60. #63980C2×C3semidirect
61. #63978C2×C3semidirect
62. #63971C2×C3semidirect
63. C2×#3724C2×C3semidirect
64. #63912C2×C3semidirect
65. #63896C2×C3semidirect
66. #63865C2×C3semidirect
76. C2×C3×C3⋊Dic3D4semidirect
211. #939C3×D3semidirect
256. C2×C3⋊Dic3C3×D4semidirect
487. C33#537semidirect
718. C32#5597semidirect
719. C32C3×#537semidirect
800. C3#10595166direct (N × H)
801. C3C3×#5597semidirect

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×#639822
C3×#639802
C3×#639782
C3×#639712
C2×C3×#37242
C3×#639122
C3×#638962
C3×#638652
C3×#55973
#105951663