Finite Group Databasebeta

← C2×C3×#63969 #13175083

Subgroups — C2×C3×#63969 #13175083

Order 1728.

2002 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×#67C211yesmaximal, characteristic
2C22×C3×D3×Dic3C211yesmaximal, characteristic, complemented
3C2×C3×#3757C211yesmaximal, characteristic, complemented
4C2×C32×#217C211yesmaximal, characteristic, complemented
5C3×#63969C218yesmaximal, direct product factor
6C2×C3×#3724C211yesmaximal, characteristic, complemented
7C2×C3×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
8C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
9C2×C3×#935—31nomaximal
10C2×C3×#883—31nomaximal
11C2×#63969C311yesmaximal, characteristic, direct product factor
12C24×C33C2211yescharacteristic
13C23×C32×D3C2211yescharacteristic
14C22×C3×C3⋊Dic3C2211yescharacteristic
15C22×C3×C3⋊Dic3C2211yescharacteristic
16C2×C32×#67—24no—
17C2×C32×#67C2214yes—
18C22×C32×Dic3C2211yescharacteristic
19C22×C32×Dic3C2211yescharacteristic
20C22×C32×Dic3C2211yescharacteristic
21C2×C3×D3×Dic3—24no—
22C2×C3×D3×Dic3C2214yescomplemented
23C3×#3757C2214yescomplemented
24C32×#217C2214yescomplemented
25C3×#3724C2214yescomplemented
26C3×Dic3⋊Dic3C2214yescomplemented
27C3×(C2×D3)⋊Dic3C2214yescomplemented
28C22×C32×D4—31no—
29C22×C3×#67—21no—
30C22×C3×#67D311yescharacteristic
31C22×C3×#67C2×C311yescharacteristic
32C23×C3×Dic3—31no—
33C22×C3×C4×D3—31no—
34C22×D3×Dic3C2×C311yescharacteristic, complemented
35C2×C32×C22⋊C4—31no—
36C2×#3757C2×C311yescharacteristic, complemented
37C2×C3×#217—21no—
38C2×C3×#217—31no—
39C2×C3×#217—31no—
40C2×C3×#217—31no—
41C2×C3×#217—61no—
42C2×C3×#217D311yescharacteristic, complemented
43C2×C3×#217C2×C311yescharacteristic, complemented
44C3×#935—38no—
45C2×C3×(C2×D3)⋊C4—31no—
46C2×C3×C4⋊Dic3—31no—
47C2×C3×Dic3⋊C4—31no—
48C2×C3×Dic3⋊C4—31no—
49C2×C3×Dic3⋊C4—31no—
50C3×#883—38no—
51#63969C2×C318yesdirect product factor
52C2×#3724C2×C311yescharacteristic, complemented
53C2×Dic3⋊Dic3C2×C311yescharacteristic, complemented
54C2×(C2×D3)⋊Dic3C2×C311yescharacteristic, complemented
55C23×C33—22no—
56C23×C33—22no—
57C23×C33—22no—
58C23×C33C2312yes—
59C23×C33C2311yescharacteristic
60C22×C32×D3—22no—
61C22×C32×D3—22no—
62C22×C32×D3D414yes—
63C22×C32×D3C2312yes—
64C2×C3×C3⋊Dic3—22no—
65C2×C3×C3⋊Dic3—22no—
66C2×C3×C3⋊Dic3C2312yes—
67C2×C3×C3⋊Dic3C2312yes—
68C32×#67—28no—
69C2×C32×Dic3—22no—
70C2×C32×Dic3—22no—
71C2×C32×Dic3—22no—
72C2×C32×Dic3C2312yes—
73C2×C32×Dic3C2312yes—
74C2×C32×Dic3C2312yes—
75C3×D3×Dic3—28no—
76C2×C3×#123—91no—
77C2×#935—31no—
78C2×#883—31no—
79C24×C32—21no—
80C24×C32—21no—
81C24×C32—21no—
82C24×C32—31no—
83C24×C32—41no—
84C24×C32C2×D311yescharacteristic
85C24×C32C2×D311yescharacteristic
86C24×C32C22×C311yescharacteristic
87C23×C3×D3—21no—
88C23×C3×D3C2×D311yescharacteristic
89C23×C3×D3C22×C311yescharacteristic
90C2×C32×D4—34no—
91C2×C32×D4—64no—
92C22×C32×C4—31no—
93C22×C32×C4—31no—
94C22×C32×C4—31no—
95C22×C3⋊Dic3C22×C311yescharacteristic
96C22×C3⋊Dic3C22×C311yescharacteristic
97C2×C3×#67—28no—
98C2×C3×#67—24no—
99C2×C3×#67—24no—
100C2×C3×#67—24no—
101C2×C3×#67C2×D314yes—
102C2×C3×#67C22×C314yes—
103C22×C3×Dic3—21no—
104C22×C3×Dic3—21no—
105C22×C3×Dic3—21no—
106C22×C3×Dic3—31no—
107C22×C3×Dic3—31no—
108C22×C3×Dic3—31no—
109C22×C3×Dic3—31no—
110C22×C3×Dic3—34no—
111C22×C3×Dic3—64no—
112C22×C3×Dic3—61no—
113C22×C3×Dic3—61no—
114C22×C3×Dic3C2×D311yescharacteristic
115C22×C3×Dic3C2×D311yescharacteristic
116C22×C3×Dic3C2×D311yescharacteristic
117C22×C3×Dic3C22×C311yescharacteristic
118C22×C3×Dic3C22×C311yescharacteristic
119C22×C3×Dic3C22×C311yescharacteristic
120C2×C3×C4×D3—34no—
121C2×C3×C4×D3—64no—
122C2×D3×Dic3—24no—
123C2×D3×Dic3C22×C314yescomplemented
124C32×C22⋊C4—34no—
125#3757C22×C314yescomplemented
126C3×#217—24no—
127C3×#217—34no—
128C3×#217—34no—
129C3×#217—34no—
130C3×#217—64no—
131C3×#217C2×D314yescomplemented
132C3×#217C22×C314yescomplemented
133C3×(C2×D3)⋊C4—34no—
134C3×C4⋊Dic3—34no—
135C3×Dic3⋊C4—34no—
136C3×Dic3⋊C4—34no—
137C3×Dic3⋊C4—34no—
138#3724C22×C314yescomplemented
139Dic3⋊Dic3C22×C314yescomplemented
140(C2×D3)⋊Dic3C22×C314yescomplemented
141C22×C33—22no—
142C22×C33—22no—
143C22×C33—22no—
144C22×C33—44no—
145C22×C33C2×D412yes—
146C22×C33#4112yes—
147C22×C33#4112yes—
148C22×C33C2411yescharacteristic
149C2×C32×D3—28no—
150C2×C32×D3—22no—
151C2×C32×D3—22no—
152C2×C32×D3C2×D414yes—
153C3×C3⋊Dic3—22no—
154C3×C3⋊Dic3—22no—
155C32×Dic3—22no—
156C32×Dic3—22no—
157C32×Dic3—22no—
158C22×C3×D4—31no—
159C22×C3×D4—31no—
160C22×C3×D4—61no—
161C23×C3×C4—91no—
162C22×#67C3×D311yescharacteristic
163C23×Dic3—31no—
164C22×C4×D3—31no—
165C3×#123—98no—
166C2×C3×C4⋊C4—91no—
167C2×C3×C4⋊C4—91no—
168C2×C3×C22⋊C4—31no—
169C2×C3×C22⋊C4—31no—
170C2×C3×C22⋊C4—61no—
171C2×C3×C22⋊C4—91no—
172C2×C3×C22⋊C4—91no—
173C2×#217—31no—
174C2×#217—31no—
175C2×#217—31no—
176C2×#217—61no—
177C2×#217C3×D311yescharacteristic, complemented
178#935—38no—
179C2×(C2×D3)⋊C4—31no—
180C2×C4⋊Dic3—31no—
181C2×Dic3⋊C4—31no—
182C2×Dic3⋊C4—31no—
183C2×Dic3⋊C4—31no—
184#883—38no—
185C23×C32—22no—
186C23×C32—22no—
187C23×C32—22no—
188C23×C32—24no—
189C23×C32—24no—
190C23×C32—24no—
191C23×C32—22no—
192C23×C32—22no—
193C23×C32—22no—
194C23×C32—22no—
195C23×C32—22no—
196C23×C32—22no—
197C23×C32—22no—
198C23×C32—21no—
199C23×C32—21no—
200C23×C32—21no—
201C23×C32—22no—
202C23×C32—22no—
203C23×C32—34no—
204C23×C32—32no—
205C23×C32—41no—
206C23×C32—42no—
207C23×C32—42no—
208C23×C32—42no—
209C23×C32—42no—
210C23×C32—42no—
211C23×C32—42no—
212C23×C32—42no—
213C23×C32—44no—
214C23×C32—44no—
215C23×C32—44no—
216C23×C32—62no—
217C23×C32—62no—
218C23×C32C22×D312yes—
219C23×C32C22×D312yes—
220C23×C32C22×D311yescharacteristic
221C23×C32C22×D311yescharacteristic
222C23×C32C23×C312yes—
223C23×C32C23×C311yescharacteristic
224C22×C3×D3—22no—
225C22×C3×D3—22no—
226C22×C3×D3—22no—
227C22×C3×D3—22no—
228C22×C3×D3—24no—
229C22×C3×D3—22no—
230C22×C3×D3—42no—
231C22×C3×D3—42no—
232C22×C3×D3#6714yes—
233C22×C3×D3C3×D414yes—
234C22×C3×D3C22×D312yes—
235C22×C3×D3C23×C312yes—
236C32×D4—68no—
237C2×C32×C4—32no—
238C2×C32×C4—32no—
239C2×C32×C4—32no—
240C2×C32×C4—62no—
241C2×C32×C4—62no—
242C2×C32×C4—62no—
243C2×C3⋊Dic3—22no—
244C2×C3⋊Dic3—22no—
245C2×C3⋊Dic3C23×C312yes—
246C2×C3⋊Dic3C23×C312yes—
247C3×#67—216no—
248C3×#67—28no—
249C3×#67—28no—
250C2×C3×Dic3—24no—
251C2×C3×Dic3—22no—
252C2×C3×Dic3—22no—
253C2×C3×Dic3—22no—
254C2×C3×Dic3—22no—
255C2×C3×Dic3—22no—
256C2×C3×Dic3—22no—
257C2×C3×Dic3—22no—
258C2×C3×Dic3—22no—
259C2×C3×Dic3—22no—
260C2×C3×Dic3—32no—
261C2×C3×Dic3—32no—
262C2×C3×Dic3—32no—
263C2×C3×Dic3—32no—
264C2×C3×Dic3—42no—
265C2×C3×Dic3—42no—
266C2×C3×Dic3—62no—
267C2×C3×Dic3—62no—
268C2×C3×Dic3—68no—
269C2×C3×Dic3—62no—
270C2×C3×Dic3—62no—
271C2×C3×Dic3—62no—
272C2×C3×Dic3—62no—
273C2×C3×Dic3—122no—
274C2×C3×Dic3—122no—
275C2×C3×Dic3C22×D312yes—
276C2×C3×Dic3C22×D312yes—
277C2×C3×Dic3C22×D312yes—
278C2×C3×Dic3C23×C312yes—
279C2×C3×Dic3C23×C312yes—
280C2×C3×Dic3C23×C312yes—
281C3×C4×D3—68no—
282D3×Dic3—28no—
283C2×#123—91noSylow
284C2×C33—42no—
285C2×C33#12314yescomplemented
286C2×C33C22×D411yescharacteristic
287C2×C33C2×#4111yescharacteristic
288C2×C33C2×#4111yescharacteristic
289C32×D3—24no—
290C24×C3—21no—
291C24×C3—21no—
292C24×C3—21no—
293C24×C3—31no—
294C24×C3—31no—
295C24×C3—41no—
296C24×C3—61no—
297C24×C3D3211yescharacteristic
298C24×C3C2×C3×D311yescharacteristic
299C24×C3C2×C3×D311yescharacteristic
300C23×D3C2×C3×D311yescharacteristic
301C2×C3×D4—34no—
302C2×C3×D4—34no—
303C2×C3×D4—64no—
304C2×C3×D4—64no—
305C2×C3×D4—64no—
306C2×C3×D4—68no—
307C22×C3×C4—31no—
308C22×C3×C4—31no—
309C22×C3×C4—31no—
310C22×C3×C4—31no—
311C22×C3×C4—31no—
312C22×C3×C4—31no—
313C22×C3×C4—61no—
314C22×C3×C4—61no—
315C22×C3×C4—61no—
316C22×C3×C4—94no—
317C22×C3×C4—91no—
318C22×C3×C4—91no—
319C22×C3×C4—184no—
320C2×#67—24no—
321C2×#67C2×C3×D314yes—
322C22×Dic3—31no—
323C22×Dic3—31no—
324C22×Dic3—31no—
325C22×Dic3—31no—
326C22×Dic3—34no—
327C22×Dic3—61no—
328C22×Dic3—61no—
329C22×Dic3—64no—
330C22×Dic3C2×C3×D311yescharacteristic
331C22×Dic3C2×C3×D311yescharacteristic
332C22×Dic3C2×C3×D311yescharacteristic
333C2×C4×D3—34no—
334C2×C4×D3—64no—
335C3×C4⋊C4—94no—
336C3×C4⋊C4—94no—
337C3×C22⋊C4—34no—
338C3×C22⋊C4—34no—
339C3×C22⋊C4—64no—
340C3×C22⋊C4—94no—
341C3×C22⋊C4—94no—
342#217—34no—
343#217—34no—
344#217—34no—
345#217—64no—
346#217C2×C3×D314yescomplemented
347(C2×D3)⋊C4—34no—
348C4⋊Dic3—34no—
349Dic3⋊C4—34no—
350Dic3⋊C4—34no—
351Dic3⋊C4—34no—
352C22×C32—22no—
353C22×C32—22no—
354C22×C32—22no—
355C22×C32—24no—
356C22×C32—24no—
357C22×C32—24no—
358C22×C32—22no—
359C22×C32—22no—
360C22×C32—22no—
361C22×C32—22no—
362C22×C32—22no—
363C22×C32—22no—
364C22×C32—21no—
365C22×C32—21no—
366C22×C32—21no—
367C22×C32—22no—
368C22×C32—22no—
369C22×C32—22no—
370C22×C32—22no—
371C22×C32—22no—
372C22×C32—22no—
373C22×C32—22no—
374C22×C32—22no—
375C22×C32—22no—
376C22×C32—34no—
377C22×C32—42no—
378C22×C32—42no—
379C22×C32—42no—
380C22×C32—41no—
381C22×C32—42no—
382C22×C32—42no—
383C22×C32—42no—
384C22×C32—42no—
385C22×C32—42no—
386C22×C32—42no—
387C22×C32—44no—
388C22×C32—44no—
389C22×C32—44no—
390C22×C32—48no—
391C22×C32—48no—
392C22×C32—48no—
393C22×C32—416no—
394C22×C32—44no—
395C22×C32—44no—
396C22×C32—44no—
397C22×C32—68no—
398C22×C32—62no—
399C22×C32—62no—
400C22×C32#23512yes—
401C22×C32D3×D412yes—
402C22×C32#23712yes—
403C22×C32#23712yes—
404C22×C32#23712yes—
405C22×C32C2×#6712yes—
406C22×C32C2×C3×D412yes—
407C22×C32C3×#4112yes—
408C22×C32C3×#4112yes—
409C22×C32C23×D311yescharacteristic
410C22×C32C23×D311yescharacteristic
411C22×C32C24×C311yescharacteristic
412C2×C3×D3—28no—
413C2×C3×D3—28no—
414C2×C3×D3—22no—
415C2×C3×D3—22no—
416C2×C3×D3—22no—
417C2×C3×D3—22no—
418C2×C3×D3—24no—
419C2×C3×D3—48no—
420C2×C3×D3—42no—
421C2×C3×D3—42no—
422C2×C3×D3C2×#6714yes—
423C2×C3×D3C2×C3×D414yes—
424C32×C4—62no—
425C32×C4—62no—
426C32×C4—62no—
427C3⋊Dic3—22no—
428C3⋊Dic3—22no—
429C3×Dic3—24no—
430C3×Dic3—22no—
431C3×Dic3—22no—
432C3×Dic3—22no—
433C3×Dic3—22no—
434C3×Dic3—22no—
435C3×Dic3—22no—
436C3×Dic3—42no—
437C3×Dic3—42no—
438C3×Dic3—62no—
439C3×Dic3—62no—
440C3×Dic3—62no—
441C3×Dic3—62no—
442C3×Dic3—122no—
443C3×Dic3—122no—
444C22×D4—31no—
445C23×C4—91no—
446#123—98no—
447C2×C4⋊C4—91no—
448C2×C4⋊C4—91no—
449C2×C22⋊C4—31no—
450C2×C22⋊C4—91no—
451C2×C22⋊C4—91no—
452C33C2×#12311yescharacteristic, complemented, Sylow
453C23×C3—24no—
454C23×C3—24no—
455C23×C3—24no—
456C23×C3—22no—
457C23×C3—22no—
458C23×C3—22no—
459C23×C3—22no—
460C23×C3—22no—
461C23×C3—22no—
462C23×C3—22no—
463C23×C3—22no—
464C23×C3—22no—
465C23×C3—21no—
466C23×C3—21no—
467C23×C3—21no—
468C23×C3—22no—
469C23×C3—22no—
470C23×C3—22no—
471C23×C3—32no—
472C23×C3—32no—
473C23×C3—34no—
474C23×C3—34no—
475C23×C3—42no—
476C23×C3—42no—
477C23×C3—42no—
478C23×C3—42no—
479C23×C3—42no—
480C23×C3—42no—
481C23×C3—44no—
482C23×C3—44no—
483C23×C3—44no—
484C23×C3—42no—
485C23×C3—41no—
486C23×C3—62no—
487C23×C3—64no—
488C23×C3—62no—
489C23×C3—62no—
490C23×C3—62no—
491C23×C3—62no—
492C23×C3—122no—
493C23×C3—122no—
494C23×C3C2×D3212yes—
495C23×C3C2×D3211yescharacteristic
496C23×C3C22×C3×D312yes—
497C23×C3C22×C3×D312yes—
498C23×C3C22×C3×D311yescharacteristic
499C23×C3C22×C3×D311yescharacteristic
500C22×D3—22no—
501C22×D3—22no—
502C22×D3C3×#6714yes—
503C22×D3C22×C3×D312yes—
504C3×D4—68no—
505C3×D4—68no—
506C3×D4—616no—
507C2×C3×C4—32no—
508C2×C3×C4—32no—
509C2×C3×C4—32no—
510C2×C3×C4—32no—
511C2×C3×C4—32no—
512C2×C3×C4—32no—
513C2×C3×C4—62no—
514C2×C3×C4—62no—
515C2×C3×C4—62no—
516C2×C3×C4—64no—
517C2×C3×C4—62no—
518C2×C3×C4—62no—
519C2×C3×C4—62no—
520C2×C3×C4—62no—
521C2×C3×C4—62no—
522C2×C3×C4—62no—
523C2×C3×C4—92no—
524C2×C3×C4—92no—
525C2×C3×C4—122no—
526C2×C3×C4—122no—
527C2×C3×C4—188no—
528C2×C3×C4—182no—
529C2×C3×C4—182no—
530#67—28no—
531C2×Dic3—22no—
532C2×Dic3—22no—
533C2×Dic3—22no—
534C2×Dic3—32no—
535C2×Dic3—32no—
536C2×Dic3—32no—
537C2×Dic3—32no—
538C2×Dic3—62no—
539C2×Dic3—62no—
540C2×Dic3—68no—
541C2×Dic3—62no—
542C2×Dic3—62no—
543C2×Dic3—62no—
544C2×Dic3—62no—
545C2×Dic3—122no—
546C2×Dic3—122no—
547C2×Dic3C22×C3×D312yes—
548C2×Dic3C22×C3×D312yes—
549C2×Dic3C22×C3×D312yes—
550C4×D3—68no—
551C2×C32—24no—
552C2×C32—24no—
553C2×C32—21no—
554C2×C32—21no—
555C2×C32—21no—
556C2×C32—21no—
557C2×C32—21no—
558C2×C32—21no—
559C2×C32—21no—
560C2×C32—21no—
561C2×C32—21no—
562C2×C32—24no—
563C2×C32—44no—
564C2×C32—41no—
565C2×C32—41no—
566C2×C32—41no—
567C2×C32—44no—
568C2×C32—44no—
569C2×C32—44no—
570C2×C32—48no—
571C2×C32—42no—
572C2×C32—42no—
573C2×C32—42no—
574C2×C32—64no—
575C2×C32#88314yescomplemented
576C2×C32#93514yescomplemented
577C2×C32C3×#12314yescomplemented
578C2×C32C2×#23511yescharacteristic
579C2×C32C2×D3×D411yescharacteristic
580C2×C32C2×#23711yescharacteristic
581C2×C32C2×#23711yescharacteristic
582C2×C32C2×#23711yescharacteristic
583C2×C32C22×#6711yescharacteristic
584C2×C32C22×C3×D411yescharacteristic
585C2×C32C2×C3×#4111yescharacteristic
586C2×C32C2×C3×#4111yescharacteristic
587C3×D3—24no—
588C3×D3—24no—
589C3×D3—44no—
590C24—31no—
591C24C3×D3211yescharacteristic
592C2×D4—34no—
593C2×D4—64no—
594C22×C4—31no—
595C22×C4—31no—
596C22×C4—31no—
597C22×C4—94no—
598C22×C4—91no—
599C22×C4—91no—
600C22×C4—184no—
601C4⋊C4—94no—
602C4⋊C4—94no—
603C22⋊C4—34no—
604C22⋊C4—94no—
605C22⋊C4—94no—
606C22×C3—24no—
607C22×C3—24no—
608C22×C3—24no—
609C22×C3—22no—
610C22×C3—22no—
611C22×C3—22no—
612C22×C3—22no—
613C22×C3—22no—
614C22×C3—22no—
615C22×C3—22no—
616C22×C3—22no—
617C22×C3—22no—
618C22×C3—21no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—22no—
622C22×C3—22no—
623C22×C3—22no—
624C22×C3—22no—
625C22×C3—22no—
626C22×C3—22no—
627C22×C3—22no—
628C22×C3—22no—
629C22×C3—22no—
630C22×C3—34no—
631C22×C3—34no—
632C22×C3—42no—
633C22×C3—42no—
634C22×C3—42no—
635C22×C3—42no—
636C22×C3—42no—
637C22×C3—42no—
638C22×C3—44no—
639C22×C3—44no—
640C22×C3—44no—
641C22×C3—48no—
642C22×C3—48no—
643C22×C3—48no—
644C22×C3—416no—
645C22×C3—44no—
646C22×C3—44no—
647C22×C3—44no—
648C22×C3—41no—
649C22×C3—42no—
650C22×C3—42no—
651C22×C3—42no—
652C22×C3—64no—
653C22×C3—68no—
654C22×C3—62no—
655C22×C3—62no—
656C22×C3—62no—
657C22×C3—62no—
658C22×C3—68no—
659C22×C3—122no—
660C22×C3—122no—
661C22×C3—128no—
662C22×C3#380412yes—
663C22×C3#380512yes—
664C22×C3D3×#6712yes—
665C22×C3C3×#23512yes—
666C22×C3C3×D3×D412yes—
667C22×C3C3×#23712yes—
668C22×C3C3×#23712yes—
669C22×C3C3×#23712yes—
670C22×C3C2×C3×#6712yes—
671C22×C3C22×D3211yescharacteristic
672C22×C3C23×C3×D311yescharacteristic
673C22×C3C23×C3×D311yescharacteristic
674C2×D3—28no—
675C2×D3—22no—
676C2×D3—22no—
677C2×D3C2×C3×#6714yes—
678C3×C4—64no—
679C3×C4—62no—
680C3×C4—62no—
681C3×C4—62no—
682C3×C4—62no—
683C3×C4—62no—
684C3×C4—62no—
685C3×C4—122no—
686C3×C4—122no—
687C3×C4—182no—
688C3×C4—182no—
689Dic3—22no—
690Dic3—22no—
691Dic3—22no—
692Dic3—62no—
693Dic3—62no—
694Dic3—62no—
695Dic3—62no—
696Dic3—122no—
697Dic3—122no—
698C32—21no—
699C32—21no—
700C32—21no—
701C32—41no—
702C32C2×#88311yescharacteristic, complemented
703C32C2×#93511yescharacteristic, complemented
704C32C2×C3×#12311yescharacteristic, complemented
705C23—22no—
706C23—22no—
707C23—22no—
708C23—32no—
709C23—34no—
710C23—62no—
711C23—62no—
712C23C2×C3×D3212yes—
713C23C2×C3×D3211yescharacteristic
714D4—68no—
715C2×C4—32no—
716C2×C4—32no—
717C2×C4—32no—
718C2×C4—62no—
719C2×C4—62no—
720C2×C4—62no—
721C2×C4—92no—
722C2×C4—92no—
723C2×C4—188no—
724C2×C4—182no—
725C2×C4—182no—
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—21no—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—21no—
732C2×C3—21no—
733C2×C3—21no—
734C2×C3—21no—
735C2×C3—24no—
736C2×C3—24no—
737C2×C3—24no—
738C2×C3—44no—
739C2×C3—44no—
740C2×C3—44no—
741C2×C3—48no—
742C2×C3—42no—
743C2×C3—42no—
744C2×C3—42no—
745C2×C3—41no—
746C2×C3—41no—
747C2×C3—41no—
748C2×C3—44no—
749C2×C3—64no—
750C2×C3—64no—
751C2×C3—124no—
752C2×C3#6396914yesdirect product factor
753C2×C3C3×#88314yescomplemented
754C2×C3C3×#93514yescomplemented
755C2×C3C2×#380411yescharacteristic
756C2×C3C2×#380511yescharacteristic
757C2×C3C2×D3×#6711yescharacteristic
758C2×C3C2×C3×#23511yescharacteristic
759C2×C3C2×C3×D3×D411yescharacteristic
760C2×C3C2×C3×#23711yescharacteristic
761C2×C3C2×C3×#23711yescharacteristic
762C2×C3C2×C3×#23711yescharacteristic
763C2×C3C22×C3×#6711yescharacteristic
764D3—24no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—34no—
769C22—44no—
770C22—62no—
771C22—62no—
772C22—68no—
773C22C3×#380412yes—
774C22C3×#380512yes—
775C22C3×D3×#6712yes—
776C22C22×C3×D3211yescharacteristic
777C4—62no—
778C4—62no—
779C4—62no—
780C4—182no—
781C4—182no—
782C3—21no—
783C3—21no—
784C3—21no—
785C3—41no—
786C3C2×#6396911yescharacteristic, direct product factor
787C3C2×C3×#88311yescharacteristic, complemented
788C3C2×C3×#93511yescharacteristic, complemented
789C2—42no—
790C2—64no—
791C2C3×#6396914yesdirect product factor
792C2C2×C3×#380411yescharacteristic
793C2C2×C3×#380511yescharacteristic
794C2C2×C3×D3×#6711yescharacteristic
subgroupG/H
centerC23×C3C2×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC24×C33C22
socleC23×C33C23
prime radicalC22×C32×#67C2
hypercenterC24×C3D32
hypocenterC32C2×C3×#123
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23×C3 ◁ C24×C3

Complements

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

NH ≅ G/Ntype
2. C22×C3×D3×Dic3C2semidirect
3. C2×C3×#3757C2semidirect
4. C2×C32×#217C2semidirect
5. C3×#63969C2direct (N × H)
6. C2×C3×#3724C2semidirect
7. C2×C3×Dic3⋊Dic3C2semidirect
8. C2×C3×(C2×D3)⋊Dic3C2semidirect
11. C2×#63969C3direct (N × H)
22. C2×C3×D3×Dic3C22semidirect
23. C3×#3757C22semidirect
24. C32×#217C22semidirect
25. C3×#3724C22semidirect
26. C3×Dic3⋊Dic3C22semidirect
27. C3×(C2×D3)⋊Dic3C22semidirect
34. C22×D3×Dic3C2×C3semidirect
36. C2×#3757C2×C3semidirect
42. C2×C3×#217D3semidirect
43. C2×C3×#217C2×C3semidirect
51. #63969C2×C3direct (N × H)
52. C2×#3724C2×C3semidirect
53. C2×Dic3⋊Dic3C2×C3semidirect
54. C2×(C2×D3)⋊Dic3C2×C3semidirect
123. C2×D3×Dic3C22×C3semidirect
125. #3757C22×C3semidirect
131. C3×#217C2×D3semidirect
132. C3×#217C22×C3semidirect
138. #3724C22×C3semidirect
139. Dic3⋊Dic3C22×C3semidirect
140. (C2×D3)⋊Dic3C22×C3semidirect
177. C2×#217C3×D3semidirect
285. C2×C33#123semidirect
346. #217C2×C3×D3semidirect
452. C33C2×#123semidirect
575. C2×C32#883semidirect
576. C2×C32#935semidirect
577. C2×C32C3×#123semidirect
702. C32C2×#883semidirect
703. C32C2×#935semidirect
704. C32C2×C3×#123semidirect
752. C2×C3#63969direct (N × H)
753. C2×C3C3×#883semidirect
754. C2×C3C3×#935semidirect
786. C3C2×#63969direct (N × H)
787. C3C2×C3×#883semidirect
788. C3C2×C3×#935semidirect
791. C2C3×#63969direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C32×#672
C22×C3×D3×Dic32
C2×C3×#37572
C2×C32×#2172
C3×#639692
C2×C3×#37242
C2×C3×Dic3⋊Dic32
C2×C3×(C2×D3)⋊Dic32
C2×C3×#9353
C2×C3×#8833
C2×#639693