Finite Group Databasebeta

← C2×C3×#67⋊Dic3 #13175091

Subgroups — C2×C3×#67⋊Dic3 #13175091

Order 1728.

2442 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C22×C32×#67C211yesmaximal, characteristic
3C22×C3×D3×Dic3C211yesmaximal, characteristic, complemented
4C2×C32×#217C211yesmaximal, characteristic, complemented
5C3×#67⋊Dic3C218yesmaximal, direct product factor
6C2×C3×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
7C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
8C2×C3×Dic32C211yesmaximal, characteristic, complemented
9C2×C3×D4×Dic3—31nomaximal
10C2×C3×#67⋊C4—31nomaximal
11C2×#67⋊Dic3C311yesmaximal, characteristic, direct product factor
12C24×C33C2211yescharacteristic
13C23×C32×D3C2211yescharacteristic
14C22×C3×C3⋊Dic3—24no—
15C22×C3×C3⋊Dic3C2211yescharacteristic
16C22×C3×C3⋊Dic3C2211yescharacteristic
17C22×C3×C3⋊Dic3C2214yescomplemented
18C2×C32×#67C418yescomplemented
19C2×C32×#67C2214yes—
20C22×C32×Dic3C2211yescharacteristic
21C22×C32×Dic3C2211yescharacteristic
22C22×C32×Dic3C2211yescharacteristic
23C2×C3×D3×Dic3—24no—
24C2×C3×D3×Dic3C2214yescomplemented
25C32×#217C2214yescomplemented
26C3×Dic3⋊Dic3C2214yescomplemented
27C3×(C2×D3)⋊Dic3C2214yescomplemented
28C3×Dic32C2214yescomplemented
29C22×C32×D4—31no—
30C23×C3⋊Dic3C2×C311yescharacteristic, complemented
31C22×C3×#67—21no—
32C22×C3×#67D311yescharacteristic
33C22×C3×#67C2×C311yescharacteristic
34C23×C3×Dic3—31no—
35C23×C3×Dic3—31no—
36C23×C3×Dic3—31no—
37C23×C3×Dic3—61no—
38C22×C3×C4×D3—31no—
39C22×D3×Dic3C2×C311yescharacteristic, complemented
40C2×C32×C22⋊C4—31no—
41C2×C3×#217—21no—
42C2×C3×#217—31no—
43C2×C3×#217D311yescharacteristic, complemented
44C2×C3×#217C2×C311yescharacteristic, complemented
45C3×D4×Dic3—38no—
46C2×C3×(C2×D3)⋊C4—31no—
47C2×C3×C4⋊Dic3—31no—
48C2×C3×Dic3⋊C4—31no—
49C2×C3×C4×Dic3—31no—
50C2×C3×C4×Dic3—31no—
51C3×#67⋊C4—38no—
52#67⋊Dic3C2×C318yesdirect product factor
53C2×Dic3⋊Dic3C2×C311yescharacteristic, complemented
54C2×(C2×D3)⋊Dic3C2×C311yescharacteristic, complemented
55C2×Dic32C2×C311yescharacteristic, complemented
56C23×C33—22no—
57C23×C33—22no—
58C23×C33C2×C414yescomplemented
59C23×C33C2312yes—
60C23×C33C2311yescharacteristic
61C22×C32×D3—22no—
62C22×C32×D3—22no—
63C22×C32×D3C2×C414yescomplemented
64C22×C32×D3C2312yes—
65C2×C3×C3⋊Dic3—22no—
66C2×C3×C3⋊Dic3—28no—
67C2×C3×C3⋊Dic3D414yescomplemented
68C2×C3×C3⋊Dic3C2312yes—
69C2×C3×C3⋊Dic3C2312yes—
70C32×#67C2×C4116yescomplemented
71C2×C32×Dic3—22no—
72C2×C32×Dic3—22no—
73C2×C32×Dic3C2×C414yescomplemented
74C2×C32×Dic3C2312yes—
75C2×C32×Dic3C2312yes—
76C2×C32×Dic3C2312yes—
77C3×D3×Dic3—28no—
78C2×C3×C4×D4—91no—
79C2×D4×Dic3—31no—
80C2×#67⋊C4—31no—
81C24×C32—21no—
82C24×C32—21no—
83C24×C32—21no—
84C24×C32—31no—
85C24×C32—41no—
86C24×C32C2×D311yescharacteristic
87C24×C32C2×D311yescharacteristic
88C24×C32C22×C311yescharacteristic
89C23×C3×D3—21no—
90C23×C3×D3C2×D311yescharacteristic
91C23×C3×D3C22×C311yescharacteristic
92C2×C32×D4—38no—
93C2×C32×D4—34no—
94C22×C32×C4—31no—
95C22×C32×C4—31no—
96C22×C32×C4—31no—
97C22×C3⋊Dic3—24no—
98C22×C3⋊Dic3C22×C311yescharacteristic
99C22×C3⋊Dic3C22×C311yescharacteristic
100C22×C3⋊Dic3C22×C314yescomplemented
101C2×C3×#67—28no—
102C2×C3×#67—24no—
103C2×C3×#67Dic318yescomplemented
104C2×C3×#67C3×C418yescomplemented
105C2×C3×#67C2×D314yes—
106C2×C3×#67C22×C314yes—
107C22×C3×Dic3—21no—
108C22×C3×Dic3—21no—
109C22×C3×Dic3—21no—
110C22×C3×Dic3—31no—
111C22×C3×Dic3—31no—
112C22×C3×Dic3—34no—
113C22×C3×Dic3—31no—
114C22×C3×Dic3—31no—
115C22×C3×Dic3—34no—
116C22×C3×Dic3—34no—
117C22×C3×Dic3—64no—
118C22×C3×Dic3—64no—
119C22×C3×Dic3—64no—
120C22×C3×Dic3—61no—
121C22×C3×Dic3—61no—
122C22×C3×Dic3—64no—
123C22×C3×Dic3—68no—
124C22×C3×Dic3C2×D311yescharacteristic
125C22×C3×Dic3C2×D311yescharacteristic
126C22×C3×Dic3C2×D311yescharacteristic
127C22×C3×Dic3C22×C311yescharacteristic
128C22×C3×Dic3C22×C311yescharacteristic
129C22×C3×Dic3C22×C311yescharacteristic
130C2×C3×C4×D3—34no—
131C2×C3×C4×D3—64no—
132C2×D3×Dic3—24no—
133C2×D3×Dic3C22×C314yescomplemented
134C32×C22⋊C4—34no—
135C3×#217—24no—
136C3×#217—34no—
137C3×#217C2×D314yescomplemented
138C3×#217C22×C314yescomplemented
139C3×(C2×D3)⋊C4—34no—
140C3×C4⋊Dic3—34no—
141C3×Dic3⋊C4—34no—
142C3×C4×Dic3—34no—
143C3×C4×Dic3—34no—
144Dic3⋊Dic3C22×C314yescomplemented
145(C2×D3)⋊Dic3C22×C314yescomplemented
146Dic32C22×C314yescomplemented
147C22×C33—28no—
148C22×C33—22no—
149C22×C33—22no—
150C22×C33C22×C412yes—
151C22×C33C22×C414yescomplemented
152C22×C33C2×D412yes—
153C22×C33#4112yes—
154C22×C33C2411yescharacteristic
155C2×C32×D3—28no—
156C2×C32×D3—22no—
157C2×C32×D3—22no—
158C2×C32×D3C22×C414yescomplemented
159C3×C3⋊Dic3—22no—
160C3×C3⋊Dic3C2×D414yescomplemented
161C32×Dic3—22no—
162C32×Dic3—22no—
163C32×Dic3C22×C414yescomplemented
164C22×C3×D4—31no—
165C22×C3×D4—31no—
166C22×C3×D4—61no—
167C23×C3×C4—91no—
168C23×C3×C4—91no—
169C22×#67C3×D311yescharacteristic
170C23×Dic3—31no—
171C23×Dic3—31no—
172C23×Dic3—31no—
173C23×Dic3—61no—
174C22×C4×D3—31no—
175C3×C4×D4—98no—
176C2×C3×C4⋊C4—91no—
177C2×C3×C22⋊C4—31no—
178C2×C3×C22⋊C4—31no—
179C2×C3×C22⋊C4—61no—
180C2×C3×C22⋊C4—91no—
181C2×C3×C42—91no—
182C2×#217—31no—
183C2×#217C3×D311yescharacteristic, complemented
184D4×Dic3—38no—
185C2×(C2×D3)⋊C4—31no—
186C2×C4⋊Dic3—31no—
187C2×Dic3⋊C4—31no—
188C2×C4×Dic3—31no—
189C2×C4×Dic3—31no—
190#67⋊C4—38no—
191C23×C32—22no—
192C23×C32—22no—
193C23×C32—24no—
194C23×C32—24no—
195C23×C32—22no—
196C23×C32—22no—
197C23×C32—22no—
198C23×C32—22no—
199C23×C32—24no—
200C23×C32—24no—
201C23×C32—24no—
202C23×C32—22no—
203C23×C32—21no—
204C23×C32—21no—
205C23×C32—21no—
206C23×C32—22no—
207C23×C32—22no—
208C23×C32—34no—
209C23×C32—32no—
210C23×C32—44no—
211C23×C32—41no—
212C23×C32—42no—
213C23×C32—42no—
214C23×C32—42no—
215C23×C32—42no—
216C23×C32—42no—
217C23×C32—44no—
218C23×C32—44no—
219C23×C32—62no—
220C23×C32—62no—
221C23×C32C4×D314yescomplemented
222C23×C32C2×Dic314yescomplemented
223C23×C32C2×C3×C414yescomplemented
224C23×C32C22×D312yes—
225C23×C32C22×D312yes—
226C23×C32C22×D311yescharacteristic
227C23×C32C22×D311yescharacteristic
228C23×C32C23×C312yes—
229C23×C32C23×C311yescharacteristic
230C22×C3×D3—22no—
231C22×C3×D3—22no—
232C22×C3×D3—22no—
233C22×C3×D3—22no—
234C22×C3×D3—24no—
235C22×C3×D3—22no—
236C22×C3×D3—42no—
237C22×C3×D3—42no—
238C22×C3×D3C2×Dic314yescomplemented
239C22×C3×D3C2×C3×C414yescomplemented
240C22×C3×D3C22×D312yes—
241C22×C3×D3C23×C312yes—
242C32×D4—316no—
243C2×C32×C4—34no—
244C2×C32×C4—32no—
245C2×C32×C4—32no—
246C2×C32×C4—32no—
247C2×C32×C4—62no—
248C2×C32×C4—62no—
249C2×C3⋊Dic3—22no—
250C2×C3⋊Dic3—28no—
251C2×C3⋊Dic3C3×D414yescomplemented
252C2×C3⋊Dic3C23×C312yes—
253C2×C3⋊Dic3C23×C312yes—
254C3×#67—216no—
255C3×#67C2×Dic3116yescomplemented
256C3×#67C2×C3×C4116yescomplemented
257C2×C3×Dic3—22no—
258C2×C3×Dic3—22no—
259C2×C3×Dic3—22no—
260C2×C3×Dic3—22no—
261C2×C3×Dic3—24no—
262C2×C3×Dic3—22no—
263C2×C3×Dic3—22no—
264C2×C3×Dic3—22no—
265C2×C3×Dic3—34no—
266C2×C3×Dic3—34no—
267C2×C3×Dic3—32no—
268C2×C3×Dic3—32no—
269C2×C3×Dic3—32no—
270C2×C3×Dic3—32no—
271C2×C3×Dic3—42no—
272C2×C3×Dic3—42no—
273C2×C3×Dic3—64no—
274C2×C3×Dic3—62no—
275C2×C3×Dic3—62no—
276C2×C3×Dic3—68no—
277C2×C3×Dic3—68no—
278C2×C3×Dic3—68no—
279C2×C3×Dic3—616no—
280C2×C3×Dic3—64no—
281C2×C3×Dic3—62no—
282C2×C3×Dic3—62no—
283C2×C3×Dic3C2×Dic314yescomplemented
284C2×C3×Dic3C2×C3×C414yescomplemented
285C2×C3×Dic3C22×D312yes—
286C2×C3×Dic3C22×D312yes—
287C2×C3×Dic3C22×D312yes—
288C2×C3×Dic3C23×C312yes—
289C2×C3×Dic3C23×C312yes—
290C2×C3×Dic3C23×C312yes—
291C3×C4×D3—68no—
292D3×Dic3—28no—
293C2×C4×D4—91noSylow
294C2×C33—24no—
295C2×C33C4×D414yescomplemented
296C2×C33C23×C411yescharacteristic
297C2×C33C22×D411yescharacteristic
298C2×C33C2×#4111yescharacteristic
299C32×D3—24no—
300C24×C3—21no—
301C24×C3—21no—
302C24×C3—21no—
303C24×C3—31no—
304C24×C3—31no—
305C24×C3—41no—
306C24×C3—61no—
307C24×C3D3211yescharacteristic
308C24×C3C2×C3×D311yescharacteristic
309C24×C3C2×C3×D311yescharacteristic
310C23×D3C2×C3×D311yescharacteristic
311C2×C3×D4—38no—
312C2×C3×D4—38no—
313C2×C3×D4—34no—
314C2×C3×D4—34no—
315C2×C3×D4—68no—
316C2×C3×D4—64no—
317C22×C3×C4—31no—
318C22×C3×C4—31no—
319C22×C3×C4—31no—
320C22×C3×C4—31no—
321C22×C3×C4—31no—
322C22×C3×C4—31no—
323C22×C3×C4—61no—
324C22×C3×C4—61no—
325C22×C3×C4—61no—
326C22×C3×C4—94no—
327C22×C3×C4—91no—
328C22×C3×C4—94no—
329C22×C3×C4—91no—
330C22×C3×C4—184no—
331C22×C3×C4—184no—
332C2×#67C3×Dic318yescomplemented
333C2×#67C2×C3×D314yes—
334C22×Dic3—31no—
335C22×Dic3—31no—
336C22×Dic3—34no—
337C22×Dic3—31no—
338C22×Dic3—31no—
339C22×Dic3—34no—
340C22×Dic3—34no—
341C22×Dic3—61no—
342C22×Dic3—61no—
343C22×Dic3—64no—
344C22×Dic3—64no—
345C22×Dic3—64no—
346C22×Dic3—64no—
347C22×Dic3—68no—
348C22×Dic3C2×C3×D311yescharacteristic
349C22×Dic3C2×C3×D311yescharacteristic
350C22×Dic3C2×C3×D311yescharacteristic
351C2×C4×D3—34no—
352C2×C4×D3—64no—
353C3×C4⋊C4—94no—
354C3×C22⋊C4—34no—
355C3×C22⋊C4—34no—
356C3×C22⋊C4—64no—
357C3×C22⋊C4—94no—
358C3×C42—94no—
359#217—34no—
360#217C2×C3×D314yescomplemented
361(C2×D3)⋊C4—34no—
362C4⋊Dic3—34no—
363Dic3⋊C4—34no—
364C4×Dic3—34no—
365C4×Dic3—34no—
366C22×C32—28no—
367C22×C32—22no—
368C22×C32—22no—
369C22×C32—24no—
370C22×C32—24no—
371C22×C32—216no—
372C22×C32—28no—
373C22×C32—28no—
374C22×C32—22no—
375C22×C32—22no—
376C22×C32—22no—
377C22×C32—22no—
378C22×C32—21no—
379C22×C32—21no—
380C22×C32—21no—
381C22×C32—22no—
382C22×C32—24no—
383C22×C32—22no—
384C22×C32—22no—
385C22×C32—22no—
386C22×C32—24no—
387C22×C32—22no—
388C22×C32—22no—
389C22×C32—22no—
390C22×C32—22no—
391C22×C32—22no—
392C22×C32—24no—
393C22×C32—34no—
394C22×C32—42no—
395C22×C32—44no—
396C22×C32—42no—
397C22×C32—42no—
398C22×C32—41no—
399C22×C32—48no—
400C22×C32—48no—
401C22×C32—42no—
402C22×C32—42no—
403C22×C32—42no—
404C22×C32—42no—
405C22×C32—44no—
406C22×C32—416no—
407C22×C32—44no—
408C22×C32—68no—
409C22×C32—62no—
410C22×C32—62no—
411C22×C32C2×C4×D312yes—
412C22×C32C2×C4×D314yescomplemented
413C22×C32D3×D412yes—
414C22×C32D3×D412yes—
415C22×C32#23712yes—
416C22×C32#23712yes—
417C22×C32C22×Dic312yes—
418C22×C32C22×Dic314yescomplemented
419C22×C32C22×C3×C412yes—
420C22×C32C22×C3×C414yescomplemented
421C22×C32C2×C3×D412yes—
422C22×C32C3×#4112yes—
423C22×C32C23×D311yescharacteristic
424C22×C32C23×D311yescharacteristic
425C22×C32C24×C311yescharacteristic
426C2×C3×D3—28no—
427C2×C3×D3—28no—
428C2×C3×D3—22no—
429C2×C3×D3—22no—
430C2×C3×D3—22no—
431C2×C3×D3—22no—
432C2×C3×D3—24no—
433C2×C3×D3—48no—
434C2×C3×D3—42no—
435C2×C3×D3—42no—
436C2×C3×D3C22×Dic314yescomplemented
437C2×C3×D3C22×C3×C414yescomplemented
438C32×C4—34no—
439C32×C4—62no—
440C32×C4—62no—
441C3⋊Dic3—22no—
442C3⋊Dic3C2×C3×D414yescomplemented
443C3×Dic3—22no—
444C3×Dic3—22no—
445C3×Dic3—22no—
446C3×Dic3—22no—
447C3×Dic3—24no—
448C3×Dic3—34no—
449C3×Dic3—34no—
450C3×Dic3—42no—
451C3×Dic3—42no—
452C3×Dic3—64no—
453C3×Dic3—64no—
454C3×Dic3—62no—
455C3×Dic3—62no—
456C3×Dic3C22×Dic314yescomplemented
457C3×Dic3C22×C3×C414yescomplemented
458C22×D4—31no—
459C23×C4—91no—
460C23×C4—91no—
461C4×D4—98no—
462C2×C4⋊C4—91no—
463C2×C22⋊C4—31no—
464C2×C22⋊C4—91no—
465C2×C42—91no—
466C33C2×C4×D411yescharacteristic, complemented, Sylow
467C23×C3—24no—
468C23×C3—24no—
469C23×C3—22no—
470C23×C3—22no—
471C23×C3—22no—
472C23×C3—22no—
473C23×C3—22no—
474C23×C3—22no—
475C23×C3—24no—
476C23×C3—24no—
477C23×C3—24no—
478C23×C3—21no—
479C23×C3—21no—
480C23×C3—22no—
481C23×C3—21no—
482C23×C3—22no—
483C23×C3—22no—
484C23×C3—32no—
485C23×C3—32no—
486C23×C3—34no—
487C23×C3—34no—
488C23×C3—42no—
489C23×C3—42no—
490C23×C3—42no—
491C23×C3—42no—
492C23×C3—44no—
493C23×C3—44no—
494C23×C3—44no—
495C23×C3—42no—
496C23×C3—41no—
497C23×C3—62no—
498C23×C3—64no—
499C23×C3—62no—
500C23×C3—62no—
501C23×C3—62no—
502C23×C3—62no—
503C23×C3—122no—
504C23×C3—122no—
505C23×C3D3×Dic314yescomplemented
506C23×C3C3×C4×D314yescomplemented
507C23×C3C2×C3×Dic314yescomplemented
508C23×C3C2×D3212yes—
509C23×C3C2×D3211yescharacteristic
510C23×C3C22×C3×D312yes—
511C23×C3C22×C3×D312yes—
512C23×C3C22×C3×D311yescharacteristic
513C23×C3C22×C3×D311yescharacteristic
514C22×D3—22no—
515C22×D3—22no—
516C22×D3C2×C3×Dic314yescomplemented
517C22×D3C22×C3×D312yes—
518C3×D4—316no—
519C3×D4—316no—
520C3×D4—616no—
521C2×C3×C4—32no—
522C2×C3×C4—32no—
523C2×C3×C4—34no—
524C2×C3×C4—34no—
525C2×C3×C4—32no—
526C2×C3×C4—32no—
527C2×C3×C4—32no—
528C2×C3×C4—32no—
529C2×C3×C4—62no—
530C2×C3×C4—64no—
531C2×C3×C4—62no—
532C2×C3×C4—62no—
533C2×C3×C4—62no—
534C2×C3×C4—62no—
535C2×C3×C4—62no—
536C2×C3×C4—62no—
537C2×C3×C4—92no—
538C2×C3×C4—94no—
539C2×C3×C4—92no—
540C2×C3×C4—122no—
541C2×C3×C4—122no—
542C2×C3×C4—188no—
543C2×C3×C4—188no—
544C2×C3×C4—182no—
545#67C2×C3×Dic3116yescomplemented
546C2×Dic3—22no—
547C2×Dic3—22no—
548C2×Dic3—32no—
549C2×Dic3—32no—
550C2×Dic3—34no—
551C2×Dic3—34no—
552C2×Dic3—32no—
553C2×Dic3—32no—
554C2×Dic3—64no—
555C2×Dic3—62no—
556C2×Dic3—62no—
557C2×Dic3—68no—
558C2×Dic3—68no—
559C2×Dic3—68no—
560C2×Dic3—616no—
561C2×Dic3—64no—
562C2×Dic3—62no—
563C2×Dic3—62no—
564C2×Dic3C2×C3×Dic314yescomplemented
565C2×Dic3C22×C3×D312yes—
566C2×Dic3C22×C3×D312yes—
567C2×Dic3C22×C3×D312yes—
568C4×D3—68no—
569C2×C32—24no—
570C2×C32—28no—
571C2×C32—24no—
572C2×C32—24no—
573C2×C32—24no—
574C2×C32—24no—
575C2×C32—21no—
576C2×C32—21no—
577C2×C32—21no—
578C2×C32—21no—
579C2×C32—21no—
580C2×C32—21no—
581C2×C32—21no—
582C2×C32—21no—
583C2×C32—21no—
584C2×C32—24no—
585C2×C32—44no—
586C2×C32—41no—
587C2×C32—41no—
588C2×C32—41no—
589C2×C32—44no—
590C2×C32—44no—
591C2×C32—48no—
592C2×C32—64no—
593C2×C32#67⋊C414yescomplemented
594C2×C32D4×Dic314yescomplemented
595C2×C32C3×C4×D414yescomplemented
596C2×C32C22×C4×D311yescharacteristic
597C2×C32C2×D3×D411yescharacteristic
598C2×C32C2×D3×D411yescharacteristic
599C2×C32C2×#23711yescharacteristic
600C2×C32C2×#23711yescharacteristic
601C2×C32C23×Dic311yescharacteristic
602C2×C32C23×C3×C411yescharacteristic
603C2×C32C22×C3×D411yescharacteristic
604C2×C32C2×C3×#4111yescharacteristic
605C3×D3—24no—
606C3×D3—24no—
607C3×D3—44no—
608C24—31no—
609C24C3×D3211yescharacteristic
610C2×D4—38no—
611C2×D4—34no—
612C22×C4—31no—
613C22×C4—31no—
614C22×C4—31no—
615C22×C4—94no—
616C22×C4—91no—
617C22×C4—91no—
618C22×C4—94no—
619C22×C4—184no—
620C22×C4—184no—
621C4⋊C4—94no—
622C22⋊C4—34no—
623C22⋊C4—94no—
624C42—94no—
625C22×C3—24no—
626C22×C3—24no—
627C22×C3—216no—
628C22×C3—28no—
629C22×C3—28no—
630C22×C3—22no—
631C22×C3—22no—
632C22×C3—22no—
633C22×C3—22no—
634C22×C3—22no—
635C22×C3—22no—
636C22×C3—28no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—22no—
641C22×C3—22no—
642C22×C3—22no—
643C22×C3—24no—
644C22×C3—24no—
645C22×C3—24no—
646C22×C3—22no—
647C22×C3—22no—
648C22×C3—22no—
649C22×C3—22no—
650C22×C3—22no—
651C22×C3—22no—
652C22×C3—34no—
653C22×C3—34no—
654C22×C3—42no—
655C22×C3—42no—
656C22×C3—42no—
657C22×C3—42no—
658C22×C3—48no—
659C22×C3—48no—
660C22×C3—44no—
661C22×C3—44no—
662C22×C3—416no—
663C22×C3—41no—
664C22×C3—42no—
665C22×C3—44no—
666C22×C3—42no—
667C22×C3—42no—
668C22×C3—64no—
669C22×C3—68no—
670C22×C3—62no—
671C22×C3—62no—
672C22×C3—62no—
673C22×C3—62no—
674C22×C3—68no—
675C22×C3—122no—
676C22×C3—122no—
677C22×C3—128no—
678C22×C3C2×D3×Dic312yes—
679C22×C3C2×D3×Dic314yescomplemented
680C22×C3#380512yes—
681C22×C3#381112yes—
682C22×C3C2×C3×C4×D312yes—
683C22×C3C2×C3×C4×D314yescomplemented
684C22×C3C3×D3×D412yes—
685C22×C3C3×D3×D412yes—
686C22×C3C3×#23712yes—
687C22×C3C3×#23712yes—
688C22×C3C22×C3×Dic312yes—
689C22×C3C22×C3×Dic314yescomplemented
690C22×C3C22×D3211yescharacteristic
691C22×C3C23×C3×D311yescharacteristic
692C22×C3C23×C3×D311yescharacteristic
693C2×D3—28no—
694C2×D3—22no—
695C2×D3—22no—
696C2×D3C22×C3×Dic314yescomplemented
697C3×C4—34no—
698C3×C4—34no—
699C3×C4—64no—
700C3×C4—62no—
701C3×C4—62no—
702C3×C4—62no—
703C3×C4—62no—
704C3×C4—94no—
705C3×C4—122no—
706C3×C4—122no—
707C3×C4—182no—
708Dic3—22no—
709Dic3—22no—
710Dic3—34no—
711Dic3—34no—
712Dic3—64no—
713Dic3—64no—
714Dic3—62no—
715Dic3—62no—
716Dic3C22×C3×Dic314yescomplemented
717C32—21no—
718C32—21no—
719C32—21no—
720C32—41no—
721C32C2×#67⋊C411yescharacteristic, complemented
722C32C2×D4×Dic311yescharacteristic, complemented
723C32C2×C3×C4×D411yescharacteristic, complemented
724C23—22no—
725C23—22no—
726C23—32no—
727C23—34no—
728C23—62no—
729C23—62no—
730C23C3×D3×Dic314yescomplemented
731C23C2×C3×D3212yes—
732C23C2×C3×D3211yescharacteristic
733D4—316no—
734C2×C4—32no—
735C2×C4—34no—
736C2×C4—32no—
737C2×C4—32no—
738C2×C4—62no—
739C2×C4—62no—
740C2×C4—92no—
741C2×C4—94no—
742C2×C4—92no—
743C2×C4—188no—
744C2×C4—188no—
745C2×C4—182no—
746C2×C3—28no—
747C2×C3—24no—
748C2×C3—24no—
749C2×C3—24no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—21no—
755C2×C3—21no—
756C2×C3—21no—
757C2×C3—21no—
758C2×C3—21no—
759C2×C3—24no—
760C2×C3—24no—
761C2×C3—24no—
762C2×C3—44no—
763C2×C3—44no—
764C2×C3—48no—
765C2×C3—41no—
766C2×C3—41no—
767C2×C3—41no—
768C2×C3—44no—
769C2×C3—64no—
770C2×C3—64no—
771C2×C3—124no—
772C2×C3#67⋊Dic314yesdirect product factor
773C2×C3C3×#67⋊C414yescomplemented
774C2×C3C3×D4×Dic314yescomplemented
775C2×C3C22×D3×Dic311yescharacteristic
776C2×C3C2×#380511yescharacteristic
777C2×C3C2×#381111yescharacteristic
778C2×C3C22×C3×C4×D311yescharacteristic
779C2×C3C2×C3×D3×D411yescharacteristic
780C2×C3C2×C3×D3×D411yescharacteristic
781C2×C3C2×C3×#23711yescharacteristic
782C2×C3C2×C3×#23711yescharacteristic
783C2×C3C23×C3×Dic311yescharacteristic
784D3—24no—
785C22—22no—
786C22—22no—
787C22—28no—
788C22—34no—
789C22—62no—
790C22—62no—
791C22—68no—
792C22C2×C3×D3×Dic312yes—
793C22C2×C3×D3×Dic314yescomplemented
794C22C3×#380512yes—
795C22C3×#381112yes—
796C22C22×C3×D3211yescharacteristic
797C4—34no—
798C4—62no—
799C4—62no—
800C4—94no—
801C4—182no—
802C3—21no—
803C3—21no—
804C3—21no—
805C3—41no—
806C3C2×#67⋊Dic311yescharacteristic, direct product factor
807C3C2×C3×#67⋊C411yescharacteristic, complemented
808C3C2×C3×D4×Dic311yescharacteristic, complemented
809C2—24no—
810C2—64no—
811C2C3×#67⋊Dic314yesdirect product factor
812C2C22×C3×D3×Dic311yescharacteristic
813C2C2×C3×#380511yescharacteristic
814C2C2×C3×#381111yescharacteristic
subgroupG/H
centerC23×C3C2×D32
commutatorC2×C32C23×C3×C4
FrattiniC22C22×C3×D32
FittingC24×C33C22
socleC23×C33C23
prime radicalC22×C32×#67C2
cosocleC22×C32C24×C3
hypercenterC24×C3D32
hypocenterC32C2×C3×C4×D4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C23×C3 ◁ C24×C3

Complements

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

NH ≅ G/Ntype
1. C23×C3×C3⋊Dic3C2semidirect
3. C22×C3×D3×Dic3C2semidirect
4. C2×C32×#217C2semidirect
5. C3×#67⋊Dic3C2direct (N × H)
6. C2×C3×Dic3⋊Dic3C2semidirect
7. C2×C3×(C2×D3)⋊Dic3C2semidirect
8. C2×C3×Dic32C2semidirect
11. C2×#67⋊Dic3C3direct (N × H)
17. C22×C3×C3⋊Dic3C22semidirect
18. C2×C32×#67C4semidirect
24. C2×C3×D3×Dic3C22semidirect
25. C32×#217C22semidirect
26. C3×Dic3⋊Dic3C22semidirect
27. C3×(C2×D3)⋊Dic3C22semidirect
28. C3×Dic32C22semidirect
30. C23×C3⋊Dic3C2×C3semidirect
39. C22×D3×Dic3C2×C3semidirect
43. C2×C3×#217D3semidirect
44. C2×C3×#217C2×C3semidirect
52. #67⋊Dic3C2×C3direct (N × H)
53. C2×Dic3⋊Dic3C2×C3semidirect
54. C2×(C2×D3)⋊Dic3C2×C3semidirect
55. C2×Dic32C2×C3semidirect
58. C23×C33C2×C4semidirect
63. C22×C32×D3C2×C4semidirect
67. C2×C3×C3⋊Dic3D4semidirect
70. C32×#67C2×C4semidirect
73. C2×C32×Dic3C2×C4semidirect
100. C22×C3⋊Dic3C22×C3semidirect
103. C2×C3×#67Dic3semidirect
104. C2×C3×#67C3×C4semidirect
133. C2×D3×Dic3C22×C3semidirect
137. C3×#217C2×D3semidirect
138. C3×#217C22×C3semidirect
144. Dic3⋊Dic3C22×C3semidirect
145. (C2×D3)⋊Dic3C22×C3semidirect
146. Dic32C22×C3semidirect
151. C22×C33C22×C4semidirect
158. C2×C32×D3C22×C4semidirect
160. C3×C3⋊Dic3C2×D4semidirect
163. C32×Dic3C22×C4semidirect
183. C2×#217C3×D3semidirect
221. C23×C32C4×D3semidirect
222. C23×C32C2×Dic3semidirect
223. C23×C32C2×C3×C4semidirect
238. C22×C3×D3C2×Dic3semidirect
239. C22×C3×D3C2×C3×C4semidirect
251. C2×C3⋊Dic3C3×D4semidirect
255. C3×#67C2×Dic3semidirect
256. C3×#67C2×C3×C4semidirect
283. C2×C3×Dic3C2×Dic3semidirect
284. C2×C3×Dic3C2×C3×C4semidirect
295. C2×C33C4×D4semidirect
332. C2×#67C3×Dic3semidirect
360. #217C2×C3×D3semidirect
412. C22×C32C2×C4×D3semidirect
418. C22×C32C22×Dic3semidirect
420. C22×C32C22×C3×C4semidirect
436. C2×C3×D3C22×Dic3semidirect
437. C2×C3×D3C22×C3×C4semidirect
442. C3⋊Dic3C2×C3×D4semidirect
456. C3×Dic3C22×Dic3semidirect
457. C3×Dic3C22×C3×C4semidirect
466. C33C2×C4×D4semidirect
505. C23×C3D3×Dic3semidirect
506. C23×C3C3×C4×D3semidirect
507. C23×C3C2×C3×Dic3semidirect
516. C22×D3C2×C3×Dic3semidirect
545. #67C2×C3×Dic3semidirect
564. C2×Dic3C2×C3×Dic3semidirect
593. C2×C32#67⋊C4semidirect
594. C2×C32D4×Dic3semidirect
595. C2×C32C3×C4×D4semidirect
679. C22×C3C2×D3×Dic3semidirect
683. C22×C3C2×C3×C4×D3semidirect
689. C22×C3C22×C3×Dic3semidirect
696. C2×D3C22×C3×Dic3semidirect
716. Dic3C22×C3×Dic3semidirect
721. C32C2×#67⋊C4semidirect
722. C32C2×D4×Dic3semidirect
723. C32C2×C3×C4×D4semidirect
730. C23C3×D3×Dic3semidirect
772. C2×C3#67⋊Dic3direct (N × H)
773. C2×C3C3×#67⋊C4semidirect
774. C2×C3C3×D4×Dic3semidirect
793. C22C2×C3×D3×Dic3semidirect
806. C3C2×#67⋊Dic3direct (N × H)
807. C3C2×C3×#67⋊C4semidirect
808. C3C2×C3×D4×Dic3semidirect
811. C2C3×#67⋊Dic3direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×C3⋊Dic32
C22×C32×#672
C22×C3×D3×Dic32
C2×C32×#2172
C3×#67⋊Dic32
C2×C3×Dic3⋊Dic32
C2×C3×(C2×D3)⋊Dic32
C2×C3×Dic322
C2×C3×D4×Dic33
C2×C3×#67⋊C43
C2×#67⋊Dic33