Finite Group Databasebeta

← C3×#10595225 #13174772

Subgroups — C3×#10595225 #13174772

Order 1728.

1744 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#625C211yesmaximal, characteristic, complemented
2C2×C3×#3805C211yesmaximal, characteristic, complemented
3C3×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
4C32×#937C212yesmaximal, complemented
5C3×#63982C211yesmaximal, characteristic, complemented
6C3×#63980C211yesmaximal, characteristic, complemented
7C3×#63970C212yesmaximal, complemented
8C3×D3×#217C212yesmaximal, complemented
9C3×#63915C211yesmaximal, characteristic, complemented
10C3×#63902C211yesmaximal, characteristic, complemented
11C3×#63891C212yesmaximal, complemented
12C3×#5591—32nomaximal
13#10595225C311yesmaximal, characteristic, direct product factor
14C23×C32×D3C2212yes—
15C2×C33×D4C2211yescharacteristic
16C22×C3×C3⋊Dic3C2211yescharacteristic
17C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
18C2×C32×#67C2212yescomplemented
19C2×C32×#67C2212yescomplemented
20C2×C3×#627C2211yescharacteristic, complemented
21C2×C3×#625—24no—
22C2×C3×#625C2212yes—
23C2×C3×#625C2211yescharacteristic
24C2×C3×#625C2211yescharacteristic
25C3×#3805—24no—
26C2×C3×D3×Dic3C2212yescomplemented
27C2×C3×D3×Dic3C2212yescomplemented
28C3×#3757C2211yescharacteristic
29C3×#3757C2211yescharacteristic, complemented
30C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
31C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
32C32×#217C2212yes—
33C32×(C2×D3)⋊C4C2212yescomplemented
34C32×(C2×D3)⋊C4C2212yescomplemented
35C3×#3724C2211yescharacteristic, complemented
36C3×Dic3⋊Dic3C2212yescomplemented
37C3×(C2×D3)⋊Dic3C2212yescomplemented
38C3×(C2×D3)⋊Dic3C2212yescomplemented
39C22×C3×#67—32no—
40C2×C3×#237—32no—
41C22×#625C2×C311yescharacteristic, complemented
42C2×#3805C2×C311yescharacteristic, complemented
43C32×#120—32no—
44D4×C3⋊Dic3C2×C311yescharacteristic, complemented
45C2×C3×#217—32no—
46C3×#939—32no—
47C3×#939—32no—
48C3×#938—32no—
49C3×#937—22no—
50C3×#937D312yescomplemented
51C3×#937C2×C312yescomplemented
52C3×D4×Dic3—32no—
53C3×D4×Dic3—61no—
54C3×#886—32no—
55C3×#885—32no—
56C3×#883—32no—
57C3×#67⋊C4—32no—
58C3×D3×C22⋊C4—32no—
59C3×#878—32no—
60#63982C2×C311yescharacteristic, complemented
61#63980C2×C311yescharacteristic, complemented
62#63970C2×C312yescomplemented
63D3×#217C2×C312yescomplemented
64#63915C2×C311yescharacteristic, complemented
65#63902C2×C311yescharacteristic, complemented
66#63891C2×C312yescomplemented
67C23×C33C2311yescharacteristic
68C23×C33C2311yescharacteristic
69C22×C32×D3—24no—
70C22×C32×D3—24no—
71C22×C32×D3—42no—
72C22×C32×D3C2312yes—
73C22×C32×D3C2312yes—
74C33×D4—22no—
75C2×C33×C4C2311yescharacteristic
76C2×C3×C3⋊Dic3—22no—
77C2×C3×C3⋊Dic3—22no—
78C2×C3×C3⋊Dic3C2311yescharacteristic
79C2×C3×C3⋊Dic3C2311yescharacteristic
80C2×C3×C3⋊Dic3C2311yescharacteristic
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C32×#67—24no—
83C32×#67—42no—
84C2×C32×Dic3C2312yes—
85C2×C32×Dic3C2312yes—
86C3×#627—22no—
87C3×#625—24no—
88C3×#625—22no—
89C3×#625D414yescomplemented
90C3×D3×Dic3—24no—
91C3×D3×Dic3—42no—
92C3×#546—91no—
93#5591—32no—
94C24×C32—32no—
95C23×C3×D3—22no—
96C23×C3×D3C2×D312yes—
97C23×C3×D3C22×C312yes—
98C2×C32×D4—21no—
99C2×C32×D4—22no—
100C2×C32×D4—32no—
101C2×C32×D4—32no—
102C2×C32×D4—41no—
103C2×C32×D4C2×D312yes—
104C2×C32×D4C22×C311yescharacteristic
105C22×C3⋊Dic3C22×C311yescharacteristic
106C22×C3⋊Dic3C22×C311yescharacteristic, complemented
107C2×C3×#67—22no—
108C2×C3×#67—22no—
109C2×C3×#67—32no—
110C2×C3×#67—32no—
111C2×C3×#67—32no—
112C2×C3×#67—32no—
113C2×C3×#67—68no—
114C2×C3×#67C2×D312yescomplemented
115C2×C3×#67C2×D312yescomplemented
116C2×C3×#67C22×C312yescomplemented
117C2×C3×#67C22×C312yescomplemented
118C22×C3×Dic3—32no—
119C22×C3×Dic3—32no—
120C22×C3×Dic3—32no—
121C22×C3×Dic3—32no—
122C22×C3×Dic3—61no—
123C22×C3×Dic3—61no—
124C3×#237—68no—
125C2×C3×C4×D3—32no—
126C2×C3×C4×D3—32no—
127C2×C3×Dic6—32no—
128C2×#627C22×C311yescharacteristic, complemented
129C2×#625—24no—
130C2×#625C22×C312yes—
131C2×#625C22×C311yescharacteristic
132C2×#625C22×C311yescharacteristic
133#3805—24no—
134C2×D3×Dic3C22×C312yescomplemented
135C2×D3×Dic3C22×C312yescomplemented
136C32×C22⋊C4—32no—
137C32×C22⋊C4—32no—
138C32×C22⋊C4—32no—
139#3757C22×C311yescharacteristic
140#3757C22×C311yescharacteristic, complemented
141C4⋊(C3⋊Dic3)C22×C311yescharacteristic, complemented
142C4×C3⋊Dic3C22×C311yescharacteristic, complemented
143C3×#217—22no—
144C3×#217—32no—
145C3×#217—32no—
146C3×#217—32no—
147C3×#217—32no—
148C3×#217—61no—
149C3×#217—61no—
150C3×#217C2×D312yes—
151C3×#217C22×C312yes—
152C3×(C2×D3)⋊C4—22no—
153C3×(C2×D3)⋊C4—22no—
154C3×(C2×D3)⋊C4—32no—
155C3×(C2×D3)⋊C4—32no—
156C3×(C2×D3)⋊C4C2×D312yescomplemented
157C3×(C2×D3)⋊C4C2×D312yescomplemented
158C3×(C2×D3)⋊C4C22×C312yescomplemented
159C3×(C2×D3)⋊C4C22×C312yescomplemented
160C3×C4⋊Dic3—32no—
161C3×C4⋊Dic3—32no—
162C3×C4⋊Dic3—61no—
163C3×Dic3⋊C4—32no—
164C3×Dic3⋊C4—32no—
165C3×C4×Dic3—32no—
166C3×C4×Dic3—61no—
167#3724C22×C311yescharacteristic, complemented
168Dic3⋊Dic3C22×C312yescomplemented
169(C2×D3)⋊Dic3C22×C312yescomplemented
170(C2×D3)⋊Dic3C22×C312yescomplemented
171C22×C33—21no—
172C22×C33—21no—
173C22×C33—21no—
174C22×C33—21no—
175C22×C33—21no—
176C22×C33#4112yescomplemented
177C22×C33C2411yescharacteristic
178C2×C32×D3—22no—
179C2×C32×D3—22no—
180C2×C32×D3—22no—
181C2×C32×D3—22no—
182C2×C32×D3—22no—
183C2×C32×D3—48no—
184C2×C32×D3C2×D414yes—
185C33×C4—21no—
186C3×C3⋊Dic3—21no—
187C3×C3⋊Dic3—21no—
188C3×C3⋊Dic3—21no—
189C3×C3⋊Dic3C2×D412yes—
190C32×Dic3—22no—
191C32×Dic3—22no—
192C2×C3×#41—91no—
193C22×C3×D4—91no—
194C22×#67—32no—
195C2×#237—32no—
196C3×#124—91no—
197C3×#123—92no—
198C3×C22⋊Q8—91no—
199C3×#121—92no—
200C3×#121—91no—
201C3×#120—32no—
202C3×#120—32no—
203C3×#120—62no—
204C3×C4×D4—91no—
205C3×C4×D4—91no—
206C2×C3×C22⋊C4—92no—
207C2×#217—32no—
208#939—32no—
209#939—32no—
210#938—32no—
211#937C3×D312yescomplemented
212D4×Dic3—32no—
213D4×Dic3—61no—
214#886—32no—
215#885—32no—
216#883—32no—
217#67⋊C4—32no—
218D3×C22⋊C4—32no—
219#878—32no—
220C23×C32—21no—
221C23×C32—21no—
222C23×C32—22no—
223C23×C32—22no—
224C23×C32—32no—
225C23×C32—32no—
226C23×C32—41no—
227C23×C32—41no—
228C23×C32—64no—
229C23×C32—64no—
230C23×C32—122no—
231C23×C32C22×D312yes—
232C23×C32C22×D312yes—
233C23×C32C23×C311yescharacteristic
234C23×C32C23×C311yescharacteristic
235C22×C3×D3—24no—
236C22×C3×D3—24no—
237C22×C3×D3—24no—
238C22×C3×D3—24no—
239C22×C3×D3—22no—
240C22×C3×D3—22no—
241C22×C3×D3—44no—
242C22×C3×D3—44no—
243C22×C3×D3—42no—
244C22×C3×D3—42no—
245C22×C3×D3—44no—
246C22×C3×D3C22×D312yes—
247C22×C3×D3C22×D312yes—
248C22×C3×D3C23×C312yes—
249C22×C3×D3C23×C312yes—
250C32×D4—22no—
251C32×D4—24no—
252C32×D4—24no—
253C32×D4—44no—
254C32×D4—44no—
255C32×D4—64no—
256C32×D4—122no—
257C2×C32×C4—21no—
258C2×C32×C4—22no—
259C2×C32×C4—32no—
260C2×C32×C4—32no—
261C2×C32×C4—41no—
262C2×C32×C4C22×D312yes—
263C2×C32×C4C23×C311yescharacteristic
264C2×C3⋊Dic3—22no—
265C2×C3⋊Dic3—22no—
266C2×C3⋊Dic3C23×C311yescharacteristic
267C2×C3⋊Dic3C23×C311yescharacteristic
268C2×C3⋊Dic3C23×C311yescharacteristic
269C2×C3⋊Dic3C23×C311yescharacteristic
270C3×#67—24no—
271C3×#67—24no—
272C3×#67—38no—
273C3×#67—44no—
274C3×#67—42no—
275C3×#67—42no—
276C3×#67—44no—
277C3×#67—64no—
278C3×#67—64no—
279C3×#67—64no—
280C2×C3×Dic3—22no—
281C2×C3×Dic3—22no—
282C2×C3×Dic3—32no—
283C2×C3×Dic3—32no—
284C2×C3×Dic3—32no—
285C2×C3×Dic3—32no—
286C2×C3×Dic3—61no—
287C2×C3×Dic3—61no—
288C2×C3×Dic3—61no—
289C2×C3×Dic3—61no—
290C2×C3×Dic3—64no—
291C2×C3×Dic3—64no—
292C2×C3×Dic3—64no—
293C2×C3×Dic3—122no—
294C2×C3×Dic3—122no—
295C2×C3×Dic3—122no—
296C2×C3×Dic3C22×D312yes—
297C2×C3×Dic3C22×D312yes—
298C2×C3×Dic3C23×C312yes—
299C2×C3×Dic3C23×C312yes—
300C3×C4×D3—64no—
301C3×C4×D3—122no—
302C3×Dic6—64no—
303#627—22no—
304#625—24no—
305#625—22no—
306#625C3×D414yescomplemented
307D3×Dic3—24no—
308D3×Dic3—42no—
309#546—91noSylow
310C2×C33—22no—
311C2×C33—41no—
312C2×C33C22×D411yescharacteristic
313C2×C33C2×#4111yescharacteristic
314C2×C33H(5,𝔽2)11yescharacteristic
315C32×D3—24no—
316C32×D3—42no—
317C24×C3—32no—
318C24×C3—32no—
319C24×C3—62no—
320C23×D3C2×C3×D312yes—
321C3×#41—184no—
322C2×C3×Q8—91no—
323C2×C3×D4—21no—
324C2×C3×D4—22no—
325C2×C3×D4—32no—
326C2×C3×D4—32no—
327C2×C3×D4—32no—
328C2×C3×D4—32no—
329C2×C3×D4—41no—
330C2×C3×D4—62no—
331C2×C3×D4—62no—
332C2×C3×D4—91no—
333C2×C3×D4—92no—
334C2×C3×D4—91no—
335C2×C3×D4—184no—
336C2×C3×D4D3211yescharacteristic
337C2×C3×D4C2×C3×D312yes—
338C22×C3×C4—92no—
339C22×C3×C4—92no—
340C22×C3×C4—91no—
341C22×C3×C4—91no—
342C2×#67—32no—
343C2×#67—32no—
344C2×#67—32no—
345C2×#67—32no—
346C2×#67—68no—
347C2×#67C2×C3×D312yescomplemented
348C2×#67C2×C3×D312yescomplemented
349C22×Dic3—32no—
350C22×Dic3—32no—
351C22×Dic3—32no—
352C22×Dic3—32no—
353C22×Dic3—61no—
354C22×Dic3—61no—
355#237—68no—
356C2×C4×D3—32no—
357C2×C4×D3—32no—
358C2×Dic6—32no—
359C3×C4⋊C4—91no—
360C3×C4⋊C4—92no—
361C3×C4⋊C4—91no—
362C3×C22⋊C4—32no—
363C3×C22⋊C4—32no—
364C3×C22⋊C4—32no—
365C3×C22⋊C4—32no—
366C3×C22⋊C4—32no—
367C3×C22⋊C4—32no—
368C3×C22⋊C4—62no—
369C3×C22⋊C4—62no—
370C3×C22⋊C4—62no—
371C3×C22⋊C4—92no—
372C3×C22⋊C4—92no—
373C3×C22⋊C4—91no—
374C3×C22⋊C4—91no—
375C3×C42—91no—
376#217—32no—
377#217—32no—
378#217—32no—
379#217—32no—
380#217—61no—
381#217—61no—
382#217C2×C3×D312yes—
383(C2×D3)⋊C4—32no—
384(C2×D3)⋊C4—32no—
385(C2×D3)⋊C4C2×C3×D312yescomplemented
386(C2×D3)⋊C4C2×C3×D312yescomplemented
387C4⋊Dic3—32no—
388C4⋊Dic3—32no—
389C4⋊Dic3—61no—
390Dic3⋊C4—32no—
391Dic3⋊C4—32no—
392C4×Dic3—32no—
393C4×Dic3—61no—
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—34no—
410C22×C32—41no—
411C22×C32—42no—
412C22×C32—42no—
413C22×C32—42no—
414C22×C32—41no—
415C22×C32—41no—
416C22×C32—42no—
417C22×C32—42no—
418C22×C32—41no—
419C22×C32—41no—
420C22×C32—42no—
421C22×C32—42no—
422C22×C32—62no—
423C22×C32—62no—
424C22×C32—62no—
425C22×C32—62no—
426C22×C32—62no—
427C22×C32—81no—
428C22×C32—81no—
429C22×C32—81no—
430C22×C32—81no—
431C22×C32—128no—
432C22×C32#23714yescomplemented
433C22×C32C3×#4112yescomplemented
434C22×C32C23×D312yes—
435C22×C32C24×C311yescharacteristic
436C2×C3×D3—22no—
437C2×C3×D3—22no—
438C2×C3×D3—22no—
439C2×C3×D3—22no—
440C2×C3×D3—24no—
441C2×C3×D3—22no—
442C2×C3×D3—22no—
443C2×C3×D3—22no—
444C2×C3×D3—22no—
445C2×C3×D3—22no—
446C2×C3×D3—22no—
447C2×C3×D3—24no—
448C2×C3×D3—42no—
449C2×C3×D3—42no—
450C2×C3×D3—42no—
451C2×C3×D3—42no—
452C2×C3×D3—48no—
453C2×C3×D3—48no—
454C2×C3×D3—416no—
455C2×C3×D3D3×D414yes—
456C2×C3×D3C2×C3×D414yes—
457C32×C4—21no—
458C32×C4—22no—
459C32×C4—22no—
460C32×C4—42no—
461C32×C4—42no—
462C32×C4—62no—
463C32×C4—62no—
464C3⋊Dic3—21no—
465C3⋊Dic3—21no—
466C3⋊Dic3—21no—
467C3⋊Dic3C2×C3×D412yes—
468C3×Dic3—22no—
469C3×Dic3—22no—
470C3×Dic3—22no—
471C3×Dic3—22no—
472C3×Dic3—34no—
473C3×Dic3—42no—
474C3×Dic3—42no—
475C3×Dic3—62no—
476C3×Dic3—62no—
477C3×Dic3—62no—
478C3×Dic3—62no—
479C3×Dic3—121no—
480C3×Dic3—121no—
481C3×Dic3—121no—
482C2×#41—91no—
483C22×D4—91no—
484#124—91no—
485#123—92no—
486C22⋊Q8—91no—
487#121—92no—
488#121—91no—
489#120—32no—
490C4×D4—91no—
491C4×D4—91no—
492C2×C22⋊C4—92no—
493C33#54611yescharacteristic, complemented, Sylow
494C23×C3—22no—
495C23×C3—21no—
496C23×C3—21no—
497C23×C3—22no—
498C23×C3—32no—
499C23×C3—32no—
500C23×C3—32no—
501C23×C3—32no—
502C23×C3—41no—
503C23×C3—41no—
504C23×C3—62no—
505C23×C3—62no—
506C23×C3—64no—
507C23×C3—64no—
508C23×C3—64no—
509C23×C3—64no—
510C23×C3—124no—
511C23×C3—124no—
512C23×C3—122no—
513C23×C3—122no—
514C23×C3—124no—
515C23×C3C2×D3211yescharacteristic
516C23×C3C2×D3211yescharacteristic
517C23×C3C22×C3×D312yes—
518C23×C3C22×C3×D312yes—
519C22×D3—24no—
520C22×D3—24no—
521C22×D3—42no—
522C22×D3C22×C3×D312yes—
523C22×D3C22×C3×D312yes—
524C3×Q8—182no—
525C3×D4—24no—
526C3×D4—22no—
527C3×D4—24no—
528C3×D4—44no—
529C3×D4—44no—
530C3×D4—64no—
531C3×D4—64no—
532C3×D4—94no—
533C3×D4—124no—
534C3×D4—122no—
535C3×D4—122no—
536C3×D4—124no—
537C3×D4—182no—
538C3×D4—184no—
539C2×C3×C4—21no—
540C2×C3×C4—22no—
541C2×C3×C4—32no—
542C2×C3×C4—32no—
543C2×C3×C4—32no—
544C2×C3×C4—32no—
545C2×C3×C4—41no—
546C2×C3×C4—62no—
547C2×C3×C4—62no—
548C2×C3×C4—91no—
549C2×C3×C4—91no—
550C2×C3×C4—91no—
551C2×C3×C4—91no—
552C2×C3×C4—184no—
553C2×C3×C4—182no—
554C2×C3×C4—182no—
555C2×C3×C4—362no—
556C2×C3×C4C2×D3211yescharacteristic
557C2×C3×C4C22×C3×D312yes—
558#67—24no—
559#67—38no—
560#67—42no—
561#67—64no—
562#67—64no—
563#67—64no—
564C2×Dic3—32no—
565C2×Dic3—32no—
566C2×Dic3—32no—
567C2×Dic3—32no—
568C2×Dic3—61no—
569C2×Dic3—61no—
570C2×Dic3—61no—
571C2×Dic3—61no—
572C2×Dic3—64no—
573C2×Dic3—64no—
574C2×Dic3—64no—
575C2×Dic3—122no—
576C2×Dic3—122no—
577C2×Dic3—122no—
578C2×Dic3C22×C3×D312yes—
579C2×Dic3C22×C3×D312yes—
580C4×D3—64no—
581C4×D3—122no—
582Dic6—64no—
583C2×C32—24no—
584C2×C32—22no—
585C2×C32—21no—
586C2×C32—21no—
587C2×C32—21no—
588C2×C32—22no—
589C2×C32—22no—
590C2×C32—22no—
591C2×C32—41no—
592C2×C32—41no—
593C2×C32—41no—
594C2×C32—44no—
595C2×C32—42no—
596C2×C32—41no—
597C2×C32—42no—
598C2×C32—42no—
599C2×C32—64no—
600C2×C32—82no—
601C2×C32—82no—
602C2×C32—82no—
603C2×C32—122no—
604C2×C32C2×D3×D412yes—
605C2×C32C2×#23712yes—
606C2×C32#100412yes—
607C2×C32C22×C3×D411yescharacteristic
608C2×C32C2×C3×#4111yescharacteristic
609C2×C32C3×H(5,𝔽2)11yescharacteristic
610C3×D3—24no—
611C3×D3—24no—
612C3×D3—44no—
613C3×D3—44no—
614C3×D3—42no—
615C3×D3—42no—
616C24—32no—
617#41—184no—
618C2×Q8—91no—
619C2×D4—32no—
620C2×D4—32no—
621C2×D4—91no—
622C2×D4—92no—
623C2×D4—91no—
624C2×D4—184no—
625C2×D4C3×D3211yescharacteristic
626C22×C4—92no—
627C22×C4—92no—
628C22×C4—91no—
629C22×C4—91no—
630C4⋊C4—91no—
631C4⋊C4—92no—
632C4⋊C4—91no—
633C22⋊C4—32no—
634C22⋊C4—32no—
635C22⋊C4—32no—
636C22⋊C4—92no—
637C22⋊C4—92no—
638C22⋊C4—91no—
639C22⋊C4—91no—
640C42—91no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—22no—
644C22×C3—22no—
645C22×C3—22no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—22no—
650C22×C3—22no—
651C22×C3—22no—
652C22×C3—21no—
653C22×C3—22no—
654C22×C3—22no—
655C22×C3—24no—
656C22×C3—34no—
657C22×C3—34no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3—42no—
661C22×C3—42no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3—42no—
665C22×C3—42no—
666C22×C3—42no—
667C22×C3—42no—
668C22×C3—41no—
669C22×C3—42no—
670C22×C3—64no—
671C22×C3—64no—
672C22×C3—62no—
673C22×C3—62no—
674C22×C3—62no—
675C22×C3—62no—
676C22×C3—62no—
677C22×C3—62no—
678C22×C3—62no—
679C22×C3—62no—
680C22×C3—62no—
681C22×C3—62no—
682C22×C3—81no—
683C22×C3—81no—
684C22×C3—81no—
685C22×C3—81no—
686C22×C3—122no—
687C22×C3—122no—
688C22×C3—122no—
689C22×C3—122no—
690C22×C3—128no—
691C22×C3—128no—
692C22×C3—1216no—
693C22×C3#380512yescomplemented
694C22×C3C3×#23714yescomplemented
695C22×C3C22×D3211yescharacteristic
696C22×C3C23×C3×D312yes—
697C2×D3—22no—
698C2×D3—22no—
699C2×D3—22no—
700C2×D3—22no—
701C2×D3—22no—
702C2×D3—48no—
703C2×D3C3×D3×D414yes—
704C3×C4—22no—
705C3×C4—21no—
706C3×C4—22no—
707C3×C4—42no—
708C3×C4—42no—
709C3×C4—62no—
710C3×C4—62no—
711C3×C4—62no—
712C3×C4—62no—
713C3×C4—92no—
714C3×C4—122no—
715C3×C4—122no—
716C3×C4—181no—
717C3×C4—181no—
718C3×C4—181no—
719Dic3—22no—
720Dic3—22no—
721Dic3—34no—
722Dic3—62no—
723Dic3—62no—
724Dic3—62no—
725Dic3—62no—
726Dic3—121no—
727Dic3—121no—
728Dic3—121no—
729C32—22no—
730C32—21no—
731C32—41no—
732C32#559112yescomplemented
733C32C3×#54611yescharacteristic, complemented
734C23—32no—
735C23—32no—
736C23—64no—
737C23—64no—
738C23—122no—
739C23C2×C3×D3211yescharacteristic
740C23C2×C3×D3211yescharacteristic
741Q8—182no—
742D4—22no—
743D4—64no—
744D4—94no—
745D4—122no—
746D4—182no—
747D4—184no—
748C2×C4—32no—
749C2×C4—32no—
750C2×C4—91no—
751C2×C4—91no—
752C2×C4—91no—
753C2×C4—91no—
754C2×C4—184no—
755C2×C4—182no—
756C2×C4—182no—
757C2×C4—362no—
758C2×C4C2×C3×D3211yescharacteristic
759C2×C3—24no—
760C2×C3—22no—
761C2×C3—21no—
762C2×C3—22no—
763C2×C3—21no—
764C2×C3—22no—
765C2×C3—21no—
766C2×C3—22no—
767C2×C3—44no—
768C2×C3—42no—
769C2×C3—42no—
770C2×C3—42no—
771C2×C3—41no—
772C2×C3—41no—
773C2×C3—41no—
774C2×C3—41no—
775C2×C3—64no—
776C2×C3—64no—
777C2×C3—82no—
778C2×C3—82no—
779C2×C3—82no—
780C2×C3—124no—
781C2×C3—124no—
782C2×C3—122no—
783C2×C3—122no—
784C2×C3D32×D411yescharacteristic
785C2×C3#6431311yescharacteristic
786C2×C3C2×#380511yescharacteristic
787C2×C3C2×C3×D3×D412yes—
788C2×C3C2×C3×#23712yes—
789C2×C3C3×#100412yes—
790D3—24no—
791D3—42no—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—21no—
796C22—21no—
797C22—34no—
798C22—62no—
799C22—62no—
800C22—62no—
801C22—62no—
802C22—62no—
803C22—128no—
804C22C3×#380512yescomplemented
805C22C22×C3×D3211yescharacteristic
806C4—21no—
807C4—62no—
808C4—62no—
809C4—92no—
810C4—181no—
811C4—181no—
812C4—181no—
813C3—21no—
814C3—22no—
815C3—41no—
816C3#1059522511yescharacteristic, direct product factor
817C3C3×#559112yescomplemented
818C2—22no—
819C2—41no—
820C2—64no—
821C2—122no—
822C2C3×D32×D411yescharacteristic
823C2C3×#6431311yescharacteristic
824C2C2×C3×#380511yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC2×C33×D4C22
socleC22×C33C24
hypercenterC2×C3×D4D32
hypocenterC32C3×#546
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. C22×C3×#625C2semidirect
2. C2×C3×#3805C2semidirect
3. C3×D4×C3⋊Dic3C2semidirect
4. C32×#937C2semidirect
5. C3×#63982C2semidirect
6. C3×#63980C2semidirect
7. C3×#63970C2semidirect
8. C3×D3×#217C2semidirect
9. C3×#63915C2semidirect
10. C3×#63902C2semidirect
11. C3×#63891C2semidirect
13. #10595225C3direct (N × H)
17. C22×C3×C3⋊Dic3C22semidirect
18. C2×C32×#67C22semidirect
19. C2×C32×#67C22semidirect
20. C2×C3×#627C22semidirect
26. C2×C3×D3×Dic3C22semidirect
27. C2×C3×D3×Dic3C22semidirect
29. C3×#3757C22semidirect
30. C3×C4⋊(C3⋊Dic3)C22semidirect
31. C3×C4×C3⋊Dic3C22semidirect
33. C32×(C2×D3)⋊C4C22semidirect
34. C32×(C2×D3)⋊C4C22semidirect
35. C3×#3724C22semidirect
36. C3×Dic3⋊Dic3C22semidirect
37. C3×(C2×D3)⋊Dic3C22semidirect
38. C3×(C2×D3)⋊Dic3C22semidirect
41. C22×#625C2×C3semidirect
42. C2×#3805C2×C3semidirect
44. D4×C3⋊Dic3C2×C3semidirect
50. C3×#937D3semidirect
51. C3×#937C2×C3semidirect
60. #63982C2×C3semidirect
61. #63980C2×C3semidirect
62. #63970C2×C3semidirect
63. D3×#217C2×C3semidirect
64. #63915C2×C3semidirect
65. #63902C2×C3semidirect
66. #63891C2×C3semidirect
89. C3×#625D4semidirect
106. C22×C3⋊Dic3C22×C3semidirect
114. C2×C3×#67C2×D3semidirect
115. C2×C3×#67C2×D3semidirect
116. C2×C3×#67C22×C3semidirect
117. C2×C3×#67C22×C3semidirect
128. C2×#627C22×C3semidirect
134. C2×D3×Dic3C22×C3semidirect
135. C2×D3×Dic3C22×C3semidirect
140. #3757C22×C3semidirect
141. C4⋊(C3⋊Dic3)C22×C3semidirect
142. C4×C3⋊Dic3C22×C3semidirect
156. C3×(C2×D3)⋊C4C2×D3semidirect
157. C3×(C2×D3)⋊C4C2×D3semidirect
158. C3×(C2×D3)⋊C4C22×C3semidirect
159. C3×(C2×D3)⋊C4C22×C3semidirect
167. #3724C22×C3semidirect
168. Dic3⋊Dic3C22×C3semidirect
169. (C2×D3)⋊Dic3C22×C3semidirect
170. (C2×D3)⋊Dic3C22×C3semidirect
176. C22×C33#41semidirect
211. #937C3×D3semidirect
306. #625C3×D4semidirect
347. C2×#67C2×C3×D3semidirect
348. C2×#67C2×C3×D3semidirect
385. (C2×D3)⋊C4C2×C3×D3semidirect
386. (C2×D3)⋊C4C2×C3×D3semidirect
432. C22×C32#237semidirect
433. C22×C32C3×#41semidirect
493. C33#546semidirect
693. C22×C3#3805semidirect
694. C22×C3C3×#237semidirect
732. C32#5591semidirect
733. C32C3×#546semidirect
804. C22C3×#3805semidirect
816. C3#10595225direct (N × H)
817. C3C3×#5591semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#6252
C2×C3×#38052
C3×D4×C3⋊Dic32
C32×#9372
C3×#639822
C3×#639802
C3×#639702
C3×D3×#2172
C3×#639152
C3×#639022
C3×#638912
C3×#55913
#105952253