Finite Group Databasebeta

← C2×C3×#63978 #13175108

Subgroups — C2×C3×#63978 #13175108

Order 1728.

2546 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#638C211yesmaximal, characteristic, complemented
2C22×C32×#67C211yesmaximal, characteristic, complemented
3C23×C32×Dic3C211yesmaximal, characteristic, complemented
4C22×C3×#626C211yesmaximal, characteristic, complemented
5C3×#63978C218yesmaximal, direct product factor
6C2×C3×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
7C2×C3×#3722C211yesmaximal, characteristic, complemented
8C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
9C2×C3×#939—31nomaximal
10C2×C3×#930—31nomaximal
11C2×#63978C311yesmaximal, characteristic, direct product factor
12C24×C33C2211yescharacteristic
13C23×C3×C3⋊D3C2211yescharacteristic
14C23×C32×D3C2211yescharacteristic
15C2×C3×#638—24no—
16C2×C3×#638C2214yescomplemented
17C22×C3×C3⋊Dic3C2211yescharacteristic
18C2×C32×#67—24no—
19C2×C32×#67C2214yescomplemented
20C22×C32×Dic3—24no—
21C22×C32×Dic3C2211yescharacteristic
22C22×C32×Dic3C2211yescharacteristic
23C22×C32×Dic3C2211yescharacteristic
24C22×C32×Dic3C2214yescomplemented
25C2×C3×#626—24no—
26C2×C3×#626C2214yescomplemented
27C3×Dic3⋊Dic3C2214yescomplemented
28C3×#3722C2214yescomplemented
29C3×(C2×D3)⋊Dic3C2214yescomplemented
30C22×C32×D4—31no—
31C23×C32×C4—31no—
32C22×#638C2×C311yescharacteristic, complemented
33C22×C3×#67—21no—
34C22×C3×#67—31no—
35C22×C3×#67—31no—
36C22×C3×#67—31no—
37C22×C3×#67—61no—
38C22×C3×#67D311yescharacteristic, complemented
39C22×C3×#67C2×C311yescharacteristic, complemented
40C23×C3×Dic3—21no—
41C23×C3×Dic3D311yescharacteristic, complemented
42C23×C3×Dic3C2×C311yescharacteristic, complemented
43C22×C3×D12—31no—
44C22×#626C2×C311yescharacteristic, complemented
45C2×C3×#217—31no—
46C3×#939—38no—
47C3×#930—38no—
48C2×C3×(C2×D3)⋊C4—31no—
49C2×C3×(C2×D3)⋊C4—31no—
50C2×C3×(C2×D3)⋊C4—31no—
51C2×C3×C4⋊Dic3—31no—
52C2×C3×Dic3⋊C4—31no—
53#63978C2×C318yesdirect product factor
54C2×Dic3⋊Dic3C2×C311yescharacteristic, complemented
55C2×#3722C2×C311yescharacteristic, complemented
56C2×(C2×D3)⋊Dic3C2×C311yescharacteristic, complemented
57C23×C33—22no—
58C23×C33—22no—
59C23×C33D414yescomplemented
60C23×C33C2312yes—
61C23×C33C2311yescharacteristic
62C22×C3×C3⋊D3—22no—
63C22×C3×C3⋊D3—22no—
64C22×C3×C3⋊D3—22no—
65C22×C3×C3⋊D3C2312yes—
66C22×C32×D3—22no—
67C22×C32×D3—22no—
68C22×C32×D3—22no—
69C22×C32×D3C2312yes—
70C3×#638—28no—
71C2×C3×C3⋊Dic3—22no—
72C2×C3×C3⋊Dic3C2312yes—
73C32×#67—28no—
74C2×C32×Dic3—22no—
75C2×C32×Dic3—22no—
76C2×C32×Dic3—28no—
77C2×C32×Dic3D414yescomplemented
78C2×C32×Dic3C2312yes—
79C2×C32×Dic3C2312yes—
80C2×C32×Dic3C2312yes—
81C3×#626—28no—
82C2×C3×#121—91no—
83C2×#939—31no—
84C2×#930—31no—
85C24×C32—21no—
86C24×C32—21no—
87C24×C32—21no—
88C24×C32—31no—
89C24×C32—41no—
90C24×C32C2×D311yescharacteristic
91C24×C32C2×D311yescharacteristic
92C24×C32C22×C311yescharacteristic
93C23×C3⋊D3C22×C311yescharacteristic
94C23×C3×D3—21no—
95C23×C3×D3—31no—
96C23×C3×D3—31no—
97C23×C3×D3—61no—
98C23×C3×D3C2×D311yescharacteristic
99C23×C3×D3C22×C311yescharacteristic
100C2×C32×D4—34no—
101C2×C32×D4—64no—
102C22×C32×C4—31no—
103C22×C32×C4—31no—
104C22×C32×C4—31no—
105C22×C32×C4—34no—
106C22×C32×C4—64no—
107C2×#638—24no—
108C2×#638C22×C314yescomplemented
109C22×C3⋊Dic3C22×C311yescharacteristic
110C2×C3×#67—28no—
111C2×C3×#67—24no—
112C2×C3×#67—24no—
113C2×C3×#67—24no—
114C2×C3×#67—34no—
115C2×C3×#67—34no—
116C2×C3×#67—34no—
117C2×C3×#67—64no—
118C2×C3×#67—68no—
119C2×C3×#67—64no—
120C2×C3×#67—64no—
121C2×C3×#67—64no—
122C2×C3×#67C2×D314yescomplemented
123C2×C3×#67C22×C314yescomplemented
124C22×C3×Dic3—28no—
125C22×C3×Dic3—21no—
126C22×C3×Dic3—21no—
127C22×C3×Dic3—21no—
128C22×C3×Dic3—24no—
129C22×C3×Dic3—24no—
130C22×C3×Dic3—24no—
131C22×C3×Dic3—31no—
132C22×C3×Dic3—31no—
133C22×C3×Dic3—61no—
134C22×C3×Dic3C2×D311yescharacteristic
135C22×C3×Dic3C2×D311yescharacteristic
136C22×C3×Dic3C2×D311yescharacteristic
137C22×C3×Dic3C2×D314yescomplemented
138C22×C3×Dic3C22×C311yescharacteristic
139C22×C3×Dic3C22×C311yescharacteristic
140C22×C3×Dic3C22×C311yescharacteristic
141C22×C3×Dic3C22×C314yescomplemented
142C2×C3×D12—34no—
143C2×C3×D12—64no—
144C2×#626—24no—
145C2×#626C22×C314yescomplemented
146C3×#217—34no—
147C3×(C2×D3)⋊C4—34no—
148C3×(C2×D3)⋊C4—34no—
149C3×(C2×D3)⋊C4—34no—
150C3×C4⋊Dic3—34no—
151C3×Dic3⋊C4—34no—
152Dic3⋊Dic3C22×C314yescomplemented
153#3722C22×C314yescomplemented
154(C2×D3)⋊Dic3C22×C314yescomplemented
155C22×C33—28no—
156C22×C33—22no—
157C22×C33—22no—
158C22×C33C2×D412yes—
159C22×C33C2×D412yes—
160C22×C33C2×D414yescomplemented
161C22×C33#4112yes—
162C22×C33C2411yescharacteristic
163C2×C3×C3⋊D3—22no—
164C2×C3×C3⋊D3—22no—
165C2×C3×C3⋊D3—22no—
166C2×C3×C3⋊D3—44no—
167C2×C32×D3—22no—
168C2×C32×D3—22no—
169C2×C32×D3—22no—
170C2×C32×D3—44no—
171C3×C3⋊Dic3—22no—
172C32×Dic3—22no—
173C32×Dic3—22no—
174C32×Dic3C2×D414yescomplemented
175C22×C3×D4—31no—
176C22×C3×D4—31no—
177C22×C3×D4—61no—
178C22×C3×D4—91no—
179C22×C3×D4—91no—
180C23×C3×C4—31no—
181C23×C3×C4—31no—
182C23×C3×C4—61no—
183C22×#67—31no—
184C22×#67—31no—
185C22×#67—31no—
186C22×#67—61no—
187C22×#67C3×D311yescharacteristic, complemented
188C23×Dic3C3×D311yescharacteristic, complemented
189C22×D12—31no—
190C3×#121—98no—
191C2×C3×C4⋊C4—91no—
192C2×C3×C22⋊C4—91no—
193C2×C3×C22⋊C4—91no—
194C2×#217—31no—
195#939—38no—
196#930—38no—
197C2×(C2×D3)⋊C4—31no—
198C2×(C2×D3)⋊C4—31no—
199C2×(C2×D3)⋊C4—31no—
200C2×C4⋊Dic3—31no—
201C2×Dic3⋊C4—31no—
202C23×C32—22no—
203C23×C32—22no—
204C23×C32—24no—
205C23×C32—24no—
206C23×C32—22no—
207C23×C32—22no—
208C23×C32—22no—
209C23×C32—22no—
210C23×C32—24no—
211C23×C32—24no—
212C23×C32—24no—
213C23×C32—22no—
214C23×C32—21no—
215C23×C32—21no—
216C23×C32—22no—
217C23×C32—21no—
218C23×C32—22no—
219C23×C32—32no—
220C23×C32—44no—
221C23×C32—41no—
222C23×C32—42no—
223C23×C32—42no—
224C23×C32—42no—
225C23×C32—42no—
226C23×C32—42no—
227C23×C32—44no—
228C23×C32—44no—
229C23×C32—62no—
230C23×C32—62no—
231C23×C32—62no—
232C23×C32D1214yescomplemented
233C23×C32#6714yescomplemented
234C23×C32C3×D414yescomplemented
235C23×C32C22×D312yes—
236C23×C32C22×D312yes—
237C23×C32C22×D311yescharacteristic
238C23×C32C22×D311yescharacteristic
239C23×C32C23×C312yes—
240C23×C32C23×C311yescharacteristic
241C22×C3⋊D3—22no—
242C22×C3⋊D3—22no—
243C22×C3⋊D3—22no—
244C22×C3⋊D3C23×C312yes—
245C22×C3×D3—24no—
246C22×C3×D3—22no—
247C22×C3×D3—22no—
248C22×C3×D3—22no—
249C22×C3×D3—22no—
250C22×C3×D3—22no—
251C22×C3×D3—22no—
252C22×C3×D3—22no—
253C22×C3×D3—32no—
254C22×C3×D3—32no—
255C22×C3×D3—42no—
256C22×C3×D3—42no—
257C22×C3×D3—62no—
258C22×C3×D3—64no—
259C22×C3×D3—62no—
260C22×C3×D3—62no—
261C22×C3×D3—62no—
262C22×C3×D3—62no—
263C22×C3×D3—62no—
264C22×C3×D3—62no—
265C22×C3×D3—122no—
266C22×C3×D3—122no—
267C22×C3×D3C22×D312yes—
268C22×C3×D3C23×C312yes—
269C32×D4—68no—
270C2×C32×C4—34no—
271C2×C32×C4—32no—
272C2×C32×C4—32no—
273C2×C32×C4—32no—
274C2×C32×C4—68no—
275C2×C32×C4—62no—
276C2×C32×C4—62no—
277#638—28no—
278C2×C3⋊Dic3—22no—
279C2×C3⋊Dic3C23×C312yes—
280C3×#67—216no—
281C3×#67—28no—
282C3×#67—28no—
283C3×#67—616no—
284C3×#67—68no—
285C3×#67—68no—
286C3×#67—68no—
287C2×C3×Dic3—24no—
288C2×C3×Dic3—216no—
289C2×C3×Dic3—24no—
290C2×C3×Dic3—22no—
291C2×C3×Dic3—22no—
292C2×C3×Dic3—22no—
293C2×C3×Dic3—22no—
294C2×C3×Dic3—28no—
295C2×C3×Dic3—28no—
296C2×C3×Dic3—24no—
297C2×C3×Dic3—22no—
298C2×C3×Dic3—22no—
299C2×C3×Dic3—22no—
300C2×C3×Dic3—32no—
301C2×C3×Dic3—32no—
302C2×C3×Dic3—62no—
303C2×C3×Dic3—64no—
304C2×C3×Dic3—62no—
305C2×C3×Dic3—62no—
306C2×C3×Dic3#6714yescomplemented
307C2×C3×Dic3C3×D414yescomplemented
308C2×C3×Dic3C22×D312yes—
309C2×C3×Dic3C22×D312yes—
310C2×C3×Dic3C22×D312yes—
311C2×C3×Dic3C23×C312yes—
312C2×C3×Dic3C23×C312yes—
313C2×C3×Dic3C23×C312yes—
314C3×D12—68no—
315#626—28no—
316C2×#121—91noSylow
317C2×C33—24no—
318C2×C33#12114yescomplemented
319C2×C33C22×D411yescharacteristic
320C2×C33C22×D411yescharacteristic
321C2×C33C2×#4111yescharacteristic
322C3×C3⋊D3—42no—
323C32×D3—42no—
324C24×C3—21no—
325C24×C3—21no—
326C24×C3—21no—
327C24×C3—31no—
328C24×C3—31no—
329C24×C3—41no—
330C24×C3—61no—
331C24×C3—91no—
332C24×C3D3211yescharacteristic
333C24×C3C2×C3×D311yescharacteristic
334C24×C3C2×C3×D311yescharacteristic
335C23×D3—31no—
336C23×D3—31no—
337C23×D3—61no—
338C23×D3C2×C3×D311yescharacteristic
339C2×C3×D4—34no—
340C2×C3×D4—34no—
341C2×C3×D4—64no—
342C2×C3×D4—68no—
343C2×C3×D4—64no—
344C2×C3×D4—64no—
345C2×C3×D4—94no—
346C2×C3×D4—94no—
347C2×C3×D4—184no—
348C2×C3×D4—184no—
349C22×C3×C4—31no—
350C22×C3×C4—31no—
351C22×C3×C4—34no—
352C22×C3×C4—31no—
353C22×C3×C4—31no—
354C22×C3×C4—31no—
355C22×C3×C4—31no—
356C22×C3×C4—34no—
357C22×C3×C4—61no—
358C22×C3×C4—61no—
359C22×C3×C4—64no—
360C22×C3×C4—61no—
361C22×C3×C4—64no—
362C22×C3×C4—64no—
363C22×C3×C4—68no—
364C22×C3×C4—91no—
365C2×#67—24no—
366C2×#67—34no—
367C2×#67—34no—
368C2×#67—34no—
369C2×#67—64no—
370C2×#67—68no—
371C2×#67—64no—
372C2×#67—64no—
373C2×#67—64no—
374C2×#67C2×C3×D314yescomplemented
375C22×Dic3—24no—
376C22×Dic3—31no—
377C22×Dic3—31no—
378C22×Dic3—61no—
379C22×Dic3C2×C3×D311yescharacteristic
380C22×Dic3C2×C3×D311yescharacteristic
381C22×Dic3C2×C3×D311yescharacteristic
382C22×Dic3C2×C3×D314yescomplemented
383C2×D12—34no—
384C2×D12—64no—
385C3×C4⋊C4—94no—
386C3×C22⋊C4—94no—
387C3×C22⋊C4—94no—
388#217—34no—
389(C2×D3)⋊C4—34no—
390(C2×D3)⋊C4—34no—
391(C2×D3)⋊C4—34no—
392C4⋊Dic3—34no—
393Dic3⋊C4—34no—
394C22×C32—28no—
395C22×C32—22no—
396C22×C32—22no—
397C22×C32—24no—
398C22×C32—216no—
399C22×C32—24no—
400C22×C32—28no—
401C22×C32—28no—
402C22×C32—22no—
403C22×C32—22no—
404C22×C32—22no—
405C22×C32—22no—
406C22×C32—21no—
407C22×C32—21no—
408C22×C32—21no—
409C22×C32—22no—
410C22×C32—22no—
411C22×C32—24no—
412C22×C32—22no—
413C22×C32—22no—
414C22×C32—24no—
415C22×C32—22no—
416C22×C32—22no—
417C22×C32—22no—
418C22×C32—22no—
419C22×C32—22no—
420C22×C32—24no—
421C22×C32—42no—
422C22×C32—42no—
423C22×C32—44no—
424C22×C32—42no—
425C22×C32—41no—
426C22×C32—48no—
427C22×C32—42no—
428C22×C32—42no—
429C22×C32—42no—
430C22×C32—42no—
431C22×C32—48no—
432C22×C32—44no—
433C22×C32—416no—
434C22×C32—44no—
435C22×C32—62no—
436C22×C32—62no—
437C22×C32—62no—
438C22×C32—124no—
439C22×C32C2×D1212yes—
440C22×C32C2×D1214yescomplemented
441C22×C32#23512yes—
442C22×C32D3×D412yes—
443C22×C32#23712yes—
444C22×C32C2×#6712yes—
445C22×C32C2×#6712yes—
446C22×C32C2×#6714yescomplemented
447C22×C32C2×C3×D412yes—
448C22×C32C2×C3×D412yes—
449C22×C32C2×C3×D414yescomplemented
450C22×C32C3×#4112yes—
451C22×C32C23×D311yescharacteristic
452C22×C32C23×D311yescharacteristic
453C22×C32C24×C311yescharacteristic
454C2×C3⋊D3—22no—
455C2×C3⋊D3—22no—
456C2×C3⋊D3—22no—
457C2×C3⋊D3—44no—
458C2×C3×D3—24no—
459C2×C3×D3—22no—
460C2×C3×D3—22no—
461C2×C3×D3—22no—
462C2×C3×D3—22no—
463C2×C3×D3—22no—
464C2×C3×D3—22no—
465C2×C3×D3—42no—
466C2×C3×D3—42no—
467C2×C3×D3—48no—
468C2×C3×D3—44no—
469C2×C3×D3—44no—
470C2×C3×D3—64no—
471C2×C3×D3—62no—
472C2×C3×D3—62no—
473C2×C3×D3—62no—
474C2×C3×D3—62no—
475C2×C3×D3—62no—
476C2×C3×D3—62no—
477C2×C3×D3—122no—
478C2×C3×D3—122no—
479C2×C3×D3—128no—
480C2×C3×D3—124no—
481C2×C3×D3—124no—
482C32×C4—34no—
483C32×C4—62no—
484C32×C4—62no—
485C3⋊Dic3—22no—
486C3×Dic3—24no—
487C3×Dic3—24no—
488C3×Dic3—22no—
489C3×Dic3—22no—
490C3×Dic3—22no—
491C3×Dic3—22no—
492C3×Dic3—24no—
493C3×Dic3—64no—
494C3×Dic3—62no—
495C3×Dic3—62no—
496C3×Dic3C2×#6714yescomplemented
497C3×Dic3C2×C3×D414yescomplemented
498C22×D4—31no—
499C22×D4—91no—
500C22×D4—91no—
501C23×C4—31no—
502#121—98no—
503C2×C4⋊C4—91no—
504C2×C22⋊C4—91no—
505C2×C22⋊C4—91no—
506C33C2×#12111yescharacteristic, complemented, Sylow
507C23×C3—24no—
508C23×C3—24no—
509C23×C3—22no—
510C23×C3—22no—
511C23×C3—22no—
512C23×C3—22no—
513C23×C3—22no—
514C23×C3—22no—
515C23×C3—24no—
516C23×C3—24no—
517C23×C3—24no—
518C23×C3—22no—
519C23×C3—21no—
520C23×C3—21no—
521C23×C3—21no—
522C23×C3—22no—
523C23×C3—22no—
524C23×C3—32no—
525C23×C3—32no—
526C23×C3—42no—
527C23×C3—42no—
528C23×C3—42no—
529C23×C3—42no—
530C23×C3—44no—
531C23×C3—44no—
532C23×C3—44no—
533C23×C3—42no—
534C23×C3—41no—
535C23×C3—62no—
536C23×C3—64no—
537C23×C3—62no—
538C23×C3—62no—
539C23×C3—62no—
540C23×C3—62no—
541C23×C3—62no—
542C23×C3—62no—
543C23×C3—92no—
544C23×C3—122no—
545C23×C3—122no—
546C23×C3—182no—
547C23×C3—182no—
548C23×C3—182no—
549C23×C3#62614yescomplemented
550C23×C3C3×D1214yescomplemented
551C23×C3C3×#6714yescomplemented
552C23×C3C2×D3212yes—
553C23×C3C2×D3211yescharacteristic
554C23×C3C22×C3×D312yes—
555C23×C3C22×C3×D312yes—
556C23×C3C22×C3×D311yescharacteristic
557C23×C3C22×C3×D311yescharacteristic
558C22×D3—22no—
559C22×D3—22no—
560C22×D3—22no—
561C22×D3—32no—
562C22×D3—32no—
563C22×D3—62no—
564C22×D3—64no—
565C22×D3—62no—
566C22×D3—62no—
567C22×D3—62no—
568C22×D3—62no—
569C22×D3—62no—
570C22×D3—62no—
571C22×D3—122no—
572C22×D3—122no—
573C22×D3C22×C3×D312yes—
574C3×D4—616no—
575C3×D4—68no—
576C3×D4—68no—
577C3×D4—188no—
578C3×D4—188no—
579C2×C3×C4—32no—
580C2×C3×C4—32no—
581C2×C3×C4—34no—
582C2×C3×C4—34no—
583C2×C3×C4—32no—
584C2×C3×C4—32no—
585C2×C3×C4—32no—
586C2×C3×C4—32no—
587C2×C3×C4—62no—
588C2×C3×C4—64no—
589C2×C3×C4—62no—
590C2×C3×C4—62no—
591C2×C3×C4—68no—
592C2×C3×C4—68no—
593C2×C3×C4—616no—
594C2×C3×C4—64no—
595C2×C3×C4—64no—
596C2×C3×C4—62no—
597C2×C3×C4—62no—
598C2×C3×C4—62no—
599C2×C3×C4—62no—
600C2×C3×C4—92no—
601C2×C3×C4—182no—
602#67—28no—
603#67—616no—
604#67—68no—
605#67—68no—
606#67—68no—
607C2×Dic3—22no—
608C2×Dic3—22no—
609C2×Dic3—28no—
610C2×Dic3—32no—
611C2×Dic3—32no—
612C2×Dic3—62no—
613C2×Dic3—64no—
614C2×Dic3—62no—
615C2×Dic3—62no—
616C2×Dic3C3×#6714yescomplemented
617C2×Dic3C22×C3×D312yes—
618C2×Dic3C22×C3×D312yes—
619C2×Dic3C22×C3×D312yes—
620D12—68no—
621C2×C32—24no—
622C2×C32—28no—
623C2×C32—24no—
624C2×C32—24no—
625C2×C32—24no—
626C2×C32—24no—
627C2×C32—21no—
628C2×C32—21no—
629C2×C32—21no—
630C2×C32—21no—
631C2×C32—21no—
632C2×C32—21no—
633C2×C32—21no—
634C2×C32—21no—
635C2×C32—21no—
636C2×C32—24no—
637C2×C32—44no—
638C2×C32—41no—
639C2×C32—41no—
640C2×C32—41no—
641C2×C32—44no—
642C2×C32—44no—
643C2×C32—48no—
644C2×C32—122no—
645C2×C32#93014yescomplemented
646C2×C32#93914yescomplemented
647C2×C32C3×#12114yescomplemented
648C2×C32C22×D1211yescharacteristic
649C2×C32C2×#23511yescharacteristic
650C2×C32C2×D3×D411yescharacteristic
651C2×C32C2×#23711yescharacteristic
652C2×C32C22×#6711yescharacteristic
653C2×C32C22×#6711yescharacteristic
654C2×C32C22×C3×D411yescharacteristic
655C2×C32C22×C3×D411yescharacteristic
656C2×C32C2×C3×#4111yescharacteristic
657C3⋊D3—42no—
658C3×D3—44no—
659C3×D3—42no—
660C3×D3—42no—
661C3×D3—124no—
662C3×D3—122no—
663C3×D3—122no—
664C24—31no—
665C24—91no—
666C24C3×D3211yescharacteristic
667C2×D4—34no—
668C2×D4—64no—
669C2×D4—94no—
670C2×D4—94no—
671C2×D4—184no—
672C2×D4—184no—
673C22×C4—31no—
674C22×C4—31no—
675C22×C4—31no—
676C22×C4—34no—
677C22×C4—64no—
678C22×C4—91no—
679C4⋊C4—94no—
680C22⋊C4—94no—
681C22⋊C4—94no—
682C22×C3—24no—
683C22×C3—24no—
684C22×C3—216no—
685C22×C3—28no—
686C22×C3—28no—
687C22×C3—22no—
688C22×C3—22no—
689C22×C3—22no—
690C22×C3—22no—
691C22×C3—22no—
692C22×C3—22no—
693C22×C3—28no—
694C22×C3—21no—
695C22×C3—21no—
696C22×C3—21no—
697C22×C3—22no—
698C22×C3—22no—
699C22×C3—22no—
700C22×C3—22no—
701C22×C3—22no—
702C22×C3—22no—
703C22×C3—24no—
704C22×C3—24no—
705C22×C3—24no—
706C22×C3—22no—
707C22×C3—22no—
708C22×C3—22no—
709C22×C3—42no—
710C22×C3—42no—
711C22×C3—42no—
712C22×C3—42no—
713C22×C3—48no—
714C22×C3—48no—
715C22×C3—44no—
716C22×C3—44no—
717C22×C3—416no—
718C22×C3—41no—
719C22×C3—42no—
720C22×C3—42no—
721C22×C3—44no—
722C22×C3—42no—
723C22×C3—64no—
724C22×C3—62no—
725C22×C3—62no—
726C22×C3—62no—
727C22×C3—62no—
728C22×C3—62no—
729C22×C3—62no—
730C22×C3—122no—
731C22×C3—122no—
732C22×C3—128no—
733C22×C3—124no—
734C22×C3—124no—
735C22×C3—182no—
736C22×C3—182no—
737C22×C3—182no—
738C22×C3—364no—
739C22×C3#380412yes—
740C22×C3C2×#62612yes—
741C22×C3C2×#62614yescomplemented
742C22×C3D3×#6712yes—
743C22×C3C2×C3×D1212yes—
744C22×C3C2×C3×D1214yescomplemented
745C22×C3C3×#23512yes—
746C22×C3C3×D3×D412yes—
747C22×C3C3×#23712yes—
748C22×C3C2×C3×#6712yes—
749C22×C3C2×C3×#6712yes—
750C22×C3C2×C3×#6714yescomplemented
751C22×C3C22×D3211yescharacteristic
752C22×C3C23×C3×D311yescharacteristic
753C22×C3C23×C3×D311yescharacteristic
754C2×D3—22no—
755C2×D3—22no—
756C2×D3—22no—
757C2×D3—44no—
758C2×D3—64no—
759C2×D3—62no—
760C2×D3—62no—
761C2×D3—62no—
762C2×D3—62no—
763C2×D3—62no—
764C2×D3—62no—
765C2×D3—122no—
766C2×D3—122no—
767C2×D3—128no—
768C2×D3—124no—
769C2×D3—124no—
770C3×C4—34no—
771C3×C4—34no—
772C3×C4—64no—
773C3×C4—64no—
774C3×C4—64no—
775C3×C4—62no—
776C3×C4—62no—
777C3×C4—62no—
778C3×C4—62no—
779C3×C4—182no—
780Dic3—22no—
781Dic3—22no—
782Dic3—64no—
783Dic3—62no—
784Dic3—62no—
785Dic3C2×C3×#6714yescomplemented
786C32—21no—
787C32—21no—
788C32—21no—
789C32—41no—
790C32C2×#93011yescharacteristic, complemented
791C32C2×#93911yescharacteristic, complemented
792C32C2×C3×#12111yescharacteristic, complemented
793C23—22no—
794C23—22no—
795C23—32no—
796C23—62no—
797C23—62no—
798C23—62no—
799C23—92no—
800C23—182no—
801C23—182no—
802C23—182no—
803C23C3×#62614yescomplemented
804C23C2×C3×D3212yes—
805C23C2×C3×D3211yescharacteristic
806D4—68no—
807D4—188no—
808D4—188no—
809C2×C4—32no—
810C2×C4—34no—
811C2×C4—32no—
812C2×C4—32no—
813C2×C4—68no—
814C2×C4—62no—
815C2×C4—62no—
816C2×C4—92no—
817C2×C4—182no—
818C2×C3—28no—
819C2×C3—24no—
820C2×C3—24no—
821C2×C3—24no—
822C2×C3—21no—
823C2×C3—21no—
824C2×C3—21no—
825C2×C3—21no—
826C2×C3—21no—
827C2×C3—21no—
828C2×C3—21no—
829C2×C3—21no—
830C2×C3—21no—
831C2×C3—24no—
832C2×C3—24no—
833C2×C3—24no—
834C2×C3—44no—
835C2×C3—44no—
836C2×C3—48no—
837C2×C3—41no—
838C2×C3—41no—
839C2×C3—41no—
840C2×C3—44no—
841C2×C3—124no—
842C2×C3—122no—
843C2×C3—122no—
844C2×C3—362no—
845C2×C3#6397814yesdirect product factor
846C2×C3C3×#93014yescomplemented
847C2×C3C3×#93914yescomplemented
848C2×C3C2×#380411yescharacteristic
849C2×C3C22×#62611yescharacteristic
850C2×C3C2×D3×#6711yescharacteristic
851C2×C3C22×C3×D1211yescharacteristic
852C2×C3C2×C3×#23511yescharacteristic
853C2×C3C2×C3×D3×D411yescharacteristic
854C2×C3C2×C3×#23711yescharacteristic
855C2×C3C22×C3×#6711yescharacteristic
856C2×C3C22×C3×#6711yescharacteristic
857D3—42no—
858D3—124no—
859D3—122no—
860D3—122no—
861C22—22no—
862C22—22no—
863C22—28no—
864C22—62no—
865C22—62no—
866C22—62no—
867C22—124no—
868C22—182no—
869C22—182no—
870C22—182no—
871C22—364no—
872C22C3×#380412yes—
873C22C2×C3×#62612yes—
874C22C2×C3×#62614yescomplemented
875C22C3×D3×#6712yes—
876C22C22×C3×D3211yescharacteristic
877C4—34no—
878C4—62no—
879C4—62no—
880C4—182no—
881C3—21no—
882C3—21no—
883C3—21no—
884C3—41no—
885C3C2×#6397811yescharacteristic, direct product factor
886C3C2×C3×#93011yescharacteristic, complemented
887C3C2×C3×#93911yescharacteristic, complemented
888C2—24no—
889C2—122no—
890C2—362no—
891C2C3×#6397814yesdirect product factor
892C2C2×C3×#380411yescharacteristic
893C2C22×C3×#62611yescharacteristic
894C2C2×C3×D3×#6711yescharacteristic
subgroupG/H
centerC23×C3C2×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC24×C33C22
socleC23×C33C23
hypercenterC24×C3D32
hypocenterC32C2×C3×#121
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23×C3 ◁ C24×C3

Complements

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

NH ≅ G/Ntype
1. C22×C3×#638C2semidirect
2. C22×C32×#67C2semidirect
3. C23×C32×Dic3C2semidirect
4. C22×C3×#626C2semidirect
5. C3×#63978C2direct (N × H)
6. C2×C3×Dic3⋊Dic3C2semidirect
7. C2×C3×#3722C2semidirect
8. C2×C3×(C2×D3)⋊Dic3C2semidirect
11. C2×#63978C3direct (N × H)
16. C2×C3×#638C22semidirect
19. C2×C32×#67C22semidirect
24. C22×C32×Dic3C22semidirect
26. C2×C3×#626C22semidirect
27. C3×Dic3⋊Dic3C22semidirect
28. C3×#3722C22semidirect
29. C3×(C2×D3)⋊Dic3C22semidirect
32. C22×#638C2×C3semidirect
38. C22×C3×#67D3semidirect
39. C22×C3×#67C2×C3semidirect
41. C23×C3×Dic3D3semidirect
42. C23×C3×Dic3C2×C3semidirect
44. C22×#626C2×C3semidirect
53. #63978C2×C3direct (N × H)
54. C2×Dic3⋊Dic3C2×C3semidirect
55. C2×#3722C2×C3semidirect
56. C2×(C2×D3)⋊Dic3C2×C3semidirect
59. C23×C33D4semidirect
77. C2×C32×Dic3D4semidirect
108. C2×#638C22×C3semidirect
122. C2×C3×#67C2×D3semidirect
123. C2×C3×#67C22×C3semidirect
137. C22×C3×Dic3C2×D3semidirect
141. C22×C3×Dic3C22×C3semidirect
145. C2×#626C22×C3semidirect
152. Dic3⋊Dic3C22×C3semidirect
153. #3722C22×C3semidirect
154. (C2×D3)⋊Dic3C22×C3semidirect
160. C22×C33C2×D4semidirect
174. C32×Dic3C2×D4semidirect
187. C22×#67C3×D3semidirect
188. C23×Dic3C3×D3semidirect
232. C23×C32D12semidirect
233. C23×C32#67semidirect
234. C23×C32C3×D4semidirect
306. C2×C3×Dic3#67semidirect
307. C2×C3×Dic3C3×D4semidirect
318. C2×C33#121semidirect
374. C2×#67C2×C3×D3semidirect
382. C22×Dic3C2×C3×D3semidirect
440. C22×C32C2×D12semidirect
446. C22×C32C2×#67semidirect
449. C22×C32C2×C3×D4semidirect
496. C3×Dic3C2×#67semidirect
497. C3×Dic3C2×C3×D4semidirect
506. C33C2×#121semidirect
549. C23×C3#626semidirect
550. C23×C3C3×D12semidirect
551. C23×C3C3×#67semidirect
616. C2×Dic3C3×#67semidirect
645. C2×C32#930semidirect
646. C2×C32#939semidirect
647. C2×C32C3×#121semidirect
741. C22×C3C2×#626semidirect
744. C22×C3C2×C3×D12semidirect
750. C22×C3C2×C3×#67semidirect
785. Dic3C2×C3×#67semidirect
790. C32C2×#930semidirect
791. C32C2×#939semidirect
792. C32C2×C3×#121semidirect
803. C23C3×#626semidirect
845. C2×C3#63978direct (N × H)
846. C2×C3C3×#930semidirect
847. C2×C3C3×#939semidirect
874. C22C2×C3×#626semidirect
885. C3C2×#63978direct (N × H)
886. C3C2×C3×#930semidirect
887. C3C2×C3×#939semidirect
891. C2C3×#63978direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#6382
C22×C32×#672
C23×C32×Dic32
C22×C3×#6262
C3×#639782
C2×C3×Dic3⋊Dic32
C2×C3×#37222
C2×C3×(C2×D3)⋊Dic32
C2×C3×#9393
C2×C3×#9303
C2×#639783