Finite Group Databasebeta

← C2×D3×#3714 #13170528

Subgroups — C2×D3×#3714 #13170528

Order 1728.

1794 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
2C2×C3×D3×D12C211yesmaximal, characteristic, complemented
3C2×#88810C211yesmaximal, characteristic, complemented
4C2×#88791C211yesmaximal, characteristic, complemented
5C2×#88790C211yesmaximal, characteristic, complemented
6C2×C3×#3714C211yesmaximal, characteristic, complemented
7C2×C3×D3×C3⋊C8C211yesmaximal, characteristic, complemented
8D3×#3714C218yesmaximal, direct product factor
9C2×D3×#213—31nomaximal
10C22×#3714—31nomaximal
11C2×D3×D24—31nomaximal
12C22×D3×C3⋊D3—21no—
13C22×C3×D32—21no—
14C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic, complemented
15C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
16C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
17C2×C32×D12C2211yescharacteristic, complemented
18C2×C32×C4×D3C2211yescharacteristic
19C2×#6292—21no—
20D3×C4⋊(C3⋊D3)—22no—
21D3×C4⋊(C3⋊D3)C2214yescomplemented
22C2×C3×#626—21no—
23C3×D3×D12—22no—
24C3×D3×D12C2214yescomplemented
25C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
26C2×C32×C3⋊C8C2211yescharacteristic, complemented
27#88810C2214yescomplemented
28#88791C2214yescomplemented
29#88790C2214yescomplemented
30C3×#3714C2214yescomplemented
31C3×D3×C3⋊C8C2214yescomplemented
32C22×C4⋊(C3⋊D3)—31no—
33C2×C3×D3×D4—31no—
34C22×C3×D12—31no—
35C2×D3×D12—31no—
36C2×D3×D12—31no—
37C2×D3×D12—61no—
38C2×D3×D12D311yescharacteristic, complemented
39C2×#3753—31no—
40C2×#3745—31no—
41C2×C3×#213—31no—
42C22×C3×C3⋊C8—31no—
43C2×C3×D24—31no—
44C2×C3×D3×C8—31no—
45D3×#213—38no—
46C2×#3714—31no—
47C2×#3714—31no—
48C2×#3714—31no—
49C2×#3714—31no—
50C2×#3714—31no—
51C2×#3714—31no—
52C2×#3714—38no—
53C2×#3714—61no—
54C2×#3714—61no—
55C2×#3714D311yescharacteristic, direct product factor
56C2×#3713—31no—
57C2×D3×C3⋊C8D311yescharacteristic, complemented
58D3×D24—38no—
59C22×C3⋊(C3⋊D3)—21no—
60C22×C3×C3⋊D3—21no—
61C22×C3×C3⋊D3—21no—
62C22×C32×D3—21no—
63C22×C32×D3D411yescharacteristic
64C2×D3×C3⋊D3—24no—
65C2×D3×C3⋊D3—44no—
66C2×C3×D32—24no—
67C2×C3×D32—44no—
68C2×C33×C4C2311yescharacteristic
69C4⋊(C3⋊(C3⋊D3))—21no—
70C4⋊(C3⋊(C3⋊D3))C2312yescomplemented
71C3×C4⋊(C3⋊D3)—21no—
72C3×C4⋊(C3⋊D3)—21no—
73C3×C4⋊(C3⋊D3)C2312yescomplemented
74C3×C4⋊(C3⋊D3)C2312yescomplemented
75C2×C32×Dic3D411yescharacteristic
76C32×D12—21no—
77C32×D12C2312yescomplemented
78C32×C4×D3D412yes—
79C32×C4×D3C2312yes—
80#6292—24no—
81C3×#626—24no—
82C3×C3⋊(C3⋊C8)C2312yescomplemented
83C32×C3⋊C8C2312yescomplemented
84C22×#213—91no—
85C2×D3×D8—91no—
86C22×D24—91no—
87C23×C3⋊D3—61no—
88C23×C3×D3—61no—
89C23×C3×D3—61no—
90C22×D32—21no—
91C22×D32—62no—
92C22×D32—61no—
93C22×D32—61no—
94C2×C32×D4—31no—
95C22×C32×C4—31no—
96C2×C4⋊(C3⋊D3)—31no—
97C2×C4⋊(C3⋊D3)—31no—
98C2×C4⋊(C3⋊D3)—31no—
99C2×C4⋊(C3⋊D3)—34no—
100C2×C4⋊(C3⋊D3)—62no—
101C2×C4⋊(C3⋊D3)—61no—
102C2×C4⋊(C3⋊D3)—61no—
103C2×C4⋊(C3⋊D3)—61no—
104C2×C4⋊(C3⋊D3)—61no—
105C2×C4⋊(C3⋊D3)—121no—
106C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
107C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
108C2×C3×#67—61no—
109C3×D3×D4—34no—
110C3×D3×D4—62no—
111C2×C3×D12—21no—
112C2×C3×D12—31no—
113C2×C3×D12—31no—
114C2×C3×D12—31no—
115C2×C3×D12—31no—
116C2×C3×D12—34no—
117C2×C3×D12—62no—
118C2×C3×D12—61no—
119C2×C3×D12—61no—
120C2×C3×D12—61no—
121C2×C3×D12C2×D311yescharacteristic, complemented
122C2×C3×D12C2×D311yescharacteristic, complemented
123C2×C3×C4×D3—21no—
124C2×C3×C4×D3C2×D311yescharacteristic
125C2×C3×C4×D3C2×D311yescharacteristic
126C2×#626—21no—
127C2×#626—62no—
128C2×#626—61no—
129C2×#626—61no—
130D3×D12—22no—
131D3×D12—34no—
132D3×D12—34no—
133D3×D12—64no—
134D3×D12—64no—
135D3×D12—62no—
136D3×D12—62no—
137D3×D12C2×D314yescomplemented
138C2×C32×C8—31no—
139#3753—34no—
140C2×C3⋊(C3⋊C8)C2×D311yescharacteristic, complemented
141#3745—34no—
142C3×#213—34no—
143C2×C3×C3⋊C8—21no—
144C2×C3×C3⋊C8—31no—
145C2×C3×C3⋊C8—31no—
146C2×C3×C3⋊C8—34no—
147C2×C3×C3⋊C8—61no—
148C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
149C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
150C3×D24—34no—
151C3×D3×C8—34no—
152#3714—34no—
153#3714—34no—
154#3714—34no—
155#3714—34no—
156#3714—34no—
157#3714—34no—
158#3714—64no—
159#3714—64no—
160#3714C2×D314yesdirect product factor
161#3713—34no—
162D3×C3⋊C8C2×D314yescomplemented
163C22×C33C2×D411yescharacteristic
164C2×C3⋊(C3⋊D3)—22no—
165C2×C3⋊(C3⋊D3)—42no—
166C2×C3×C3⋊D3—22no—
167C2×C3×C3⋊D3—22no—
168C2×C3×C3⋊D3—42no—
169C2×C3×C3⋊D3—42no—
170C2×C32×D3—22no—
171C2×C32×D3—42no—
172C2×C32×D3D814yescomplemented
173C2×C32×D3C2×D412yes—
174D3×C3⋊D3—48no—
175C3×D32—48no—
176C33×C4C2×D411yescharacteristic
177C33×C4C2411yescharacteristic
178C32×Dic3C2×D412yes—
179C22×C3×D4—91no—
180C2×D3×D4—31no—
181C2×D3×D4—91no—
182C22×D12—31no—
183C22×D12—91no—
184C22×D12—91no—
185C22×D12—181no—
186C2×C3×D8—91no—
187C22×C3×C8—91no—
188C2×#213—31no—
189C2×#213—98no—
190C2×#213—91no—
191C2×#213—91no—
192C2×#213—91no—
193C2×#213—91no—
194C2×#213—91no—
195C2×#213—181no—
196C22×C3⋊C8—31no—
197D3×D8—98no—
198C2×D24—31no—
199C2×D24—98no—
200C2×D24—91no—
201C2×D24—91no—
202C2×D24—91no—
203C2×D24—91no—
204C2×D24—181no—
205C2×D3×C8—31no—
206C23×C32—31no—
207C23×C32—61no—
208C22×C3⋊D3—21no—
209C22×C3⋊D3—21no—
210C22×C3⋊D3—64no—
211C22×C3⋊D3—61no—
212C22×C3⋊D3—62no—
213C22×C3⋊D3—61no—
214C22×C3⋊D3—61no—
215C22×C3⋊D3—121no—
216C22×C3⋊D3—121no—
217C22×C3⋊D3—122no—
218C22×C3⋊D3—124no—
219C22×C3×D3—21no—
220C22×C3×D3—21no—
221C22×C3×D3—21no—
222C22×C3×D3—41no—
223C22×C3×D3—64no—
224C22×C3×D3—62no—
225C22×C3×D3—61no—
226C22×C3×D3—61no—
227C22×C3×D3—61no—
228C22×C3×D3—61no—
229C22×C3×D3—64no—
230C22×C3×D3—121no—
231C22×C3×D3—124no—
232C22×C3×D3—124no—
233C22×C3×D3D1211yescharacteristic
234C22×C3×D3#6711yescharacteristic
235C2×D32—24no—
236C2×D32—44no—
237C2×D32—68no—
238C2×D32—64no—
239C2×D32—64no—
240C2×D32—128no—
241C2×D32—124no—
242C2×D32—124no—
243C32×D4—32no—
244C32×D4—61no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—31no—
249C2×C32×C4—32no—
250C2×C32×C4—32no—
251C2×C32×C4—41no—
252C2×C32×C4C22×D311yescharacteristic
253C2×C32×C4C22×D311yescharacteristic
254C2×C32×C4C22×D311yescharacteristic
255C4⋊(C3⋊D3)—21no—
256C4⋊(C3⋊D3)—21no—
257C4⋊(C3⋊D3)—32no—
258C4⋊(C3⋊D3)—32no—
259C4⋊(C3⋊D3)—32no—
260C4⋊(C3⋊D3)—62no—
261C4⋊(C3⋊D3)—62no—
262C4⋊(C3⋊D3)—62no—
263C4⋊(C3⋊D3)—64no—
264C4⋊(C3⋊D3)—61no—
265C4⋊(C3⋊D3)—62no—
266C4⋊(C3⋊D3)—61no—
267C4⋊(C3⋊D3)—61no—
268C4⋊(C3⋊D3)—122no—
269C4⋊(C3⋊D3)—121no—
270C4⋊(C3⋊D3)—121no—
271C4⋊(C3⋊D3)—122no—
272C4⋊(C3⋊D3)C22×D312yescomplemented
273C4⋊(C3⋊D3)C22×D312yescomplemented
274C3×#67—64no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3D1211yescharacteristic
277C2×C3×Dic3#6711yescharacteristic
278C3×D12—21no—
279C3×D12—21no—
280C3×D12—22no—
281C3×D12—32no—
282C3×D12—32no—
283C3×D12—32no—
284C3×D12—32no—
285C3×D12—41no—
286C3×D12—62no—
287C3×D12—62no—
288C3×D12—62no—
289C3×D12—64no—
290C3×D12—61no—
291C3×D12—61no—
292C3×D12—61no—
293C3×D12—61no—
294C3×D12—121no—
295C3×D12C22×D312yescomplemented
296C3×D12C22×D312yescomplemented
297C3×C4×D3—22no—
298C3×C4×D3—22no—
299C3×C4×D3D1212yes—
300C3×C4×D3#6712yes—
301C3×C4×D3C22×D312yes—
302C3×C4×D3C22×D312yes—
303#626—24no—
304#626—68no—
305#626—64no—
306#626—64no—
307C32×C8—32no—
308C3⋊(C3⋊C8)C22×D312yescomplemented
309C3×C3⋊C8—22no—
310C3×C3⋊C8—32no—
311C3×C3⋊C8—32no—
312C3×C3⋊C8—62no—
313C3×C3⋊C8C22×D312yescomplemented
314C3×C3⋊C8C22×D312yescomplemented
315C22×D8—271noSylow
316C2×C33C2×D812yescomplemented
317C2×C33C22×D411yescharacteristic
318C3⋊(C3⋊D3)—42no—
319C3×C3⋊D3—42no—
320C3×C3⋊D3—42no—
321C32×D3—42no—
322C32×D3C2×D814yescomplemented
323C24×C3—181no—
324C23×D3—61no—
325C23×D3—61no—
326C23×D3—181no—
327C23×D3—181no—
328C23×D3—182no—
329C23×D3—181no—
330C2×C3×D4—31no—
331C2×C3×D4—31no—
332C2×C3×D4—61no—
333C2×C3×D4—94no—
334C2×C3×D4—91no—
335C2×C3×D4—91no—
336C2×C3×D4—182no—
337C2×C3×D4—181no—
338C22×C3×C4—31no—
339C22×C3×C4—31no—
340C22×C3×C4—61no—
341C2×#67—61no—
342C2×#67—181no—
343D3×D4—34no—
344D3×D4—62no—
345D3×D4—94no—
346D3×D4—182no—
347C2×D12—31no—
348C2×D12—31no—
349C2×D12—31no—
350C2×D12—31no—
351C2×D12—34no—
352C2×D12—61no—
353C2×D12—61no—
354C2×D12—62no—
355C2×D12—61no—
356C2×D12—94no—
357C2×D12—94no—
358C2×D12—91no—
359C2×D12—91no—
360C2×D12—91no—
361C2×D12—184no—
362C2×D12—181no—
363C2×D12—181no—
364C2×D12—181no—
365C2×D12—182no—
366C2×D12—182no—
367C2×D12—184no—
368C2×D12—181no—
369C2×D12—181no—
370C2×D12—182no—
371C2×D12—361no—
372C2×D12D3211yescharacteristic, complemented
373C2×C4×D3D3211yescharacteristic
374C3×D8—94no—
375C2×C3×C8—31no—
376C2×C3×C8—31no—
377C2×C3×C8—61no—
378C2×C3×C8—94no—
379C2×C3×C8—91no—
380#213—34no—
381#213—94no—
382#213—94no—
383#213—94no—
384#213—94no—
385#213—94no—
386#213—184no—
387C2×C3⋊C8—31no—
388C2×C3⋊C8—31no—
389C2×C3⋊C8—34no—
390C2×C3⋊C8—61no—
391C2×C3⋊C8D3211yescharacteristic, complemented
392D24—34no—
393D24—94no—
394D24—94no—
395D24—94no—
396D24—94no—
397D24—184no—
398D3×C8—34no—
399C22×C32—21no—
400C22×C32—21no—
401C22×C32—21no—
402C22×C32—34no—
403C22×C32—32no—
404C22×C32—41no—
405C22×C32—62no—
406C22×C32—122no—
407C22×C32C2×D1211yescharacteristic
408C22×C32D3×D411yescharacteristic
409C22×C32C2×#6711yescharacteristic
410C2×C3⋊D3—22no—
411C2×C3⋊D3—22no—
412C2×C3⋊D3—42no—
413C2×C3⋊D3—42no—
414C2×C3⋊D3—62no—
415C2×C3⋊D3—64no—
416C2×C3⋊D3—62no—
417C2×C3⋊D3—62no—
418C2×C3⋊D3—122no—
419C2×C3⋊D3—122no—
420C2×C3⋊D3—124no—
421C2×C3⋊D3—128no—
422C2×C3⋊D3—122no—
423C2×C3⋊D3—124no—
424C2×C3⋊D3—122no—
425C2×C3⋊D3—122no—
426C2×C3⋊D3—242no—
427C2×C3⋊D3—242no—
428C2×C3⋊D3—244no—
429C2×C3×D3—22no—
430C2×C3×D3—22no—
431C2×C3×D3—24no—
432C2×C3×D3—22no—
433C2×C3×D3—42no—
434C2×C3×D3—42no—
435C2×C3×D3—42no—
436C2×C3×D3—64no—
437C2×C3×D3—62no—
438C2×C3×D3—62no—
439C2×C3×D3—62no—
440C2×C3×D3—62no—
441C2×C3×D3—82no—
442C2×C3×D3—122no—
443C2×C3×D3—128no—
444C2×C3×D3—124no—
445C2×C3×D3—122no—
446C2×C3×D3—122no—
447C2×C3×D3—122no—
448C2×C3×D3—122no—
449C2×C3×D3—128no—
450C2×C3×D3—242no—
451C2×C3×D3D2414yescomplemented
452C2×C3×D3#21314yescomplemented
453C2×C3×D3C2×D1212yes—
454C2×C3×D3C2×#6712yes—
455D32—48no—
456D32—1216no—
457D32—128no—
458D32—128no—
459C32×C4—21no—
460C32×C4—21no—
461C32×C4—21no—
462C32×C4—21no—
463C32×C4—21no—
464C32×C4—21no—
465C32×C4—32no—
466C32×C4—41no—
467C32×C4—41no—
468C32×C4C2×D1211yescharacteristic
469C32×C4D3×D411yescharacteristic
470C32×C4C2×#6711yescharacteristic
471C32×C4C23×D311yescharacteristic
472C32×C4C23×D311yescharacteristic
473C32×C4C23×D311yescharacteristic
474C3×Dic3—22no—
475C3×Dic3C2×D1212yes—
476C3×Dic3C2×#6712yes—
477C22×D4—91no—
478C22×D4—271no—
479C2×D8—91no—
480C2×D8—271no—
481C2×D8—278no—
482C2×D8—271no—
483C2×D8—271no—
484C22×C8—91no—
485C33C22×D811yescharacteristic, complemented, Sylow
486C23×C3—31no—
487C23×C3—31no—
488C23×C3—61no—
489C23×C3—61no—
490C23×C3—61no—
491C23×C3—121no—
492C23×C3—184no—
493C23×C3—181no—
494C23×C3—181no—
495C23×C3—364no—
496C22×D3—21no—
497C22×D3—64no—
498C22×D3—62no—
499C22×D3—61no—
500C22×D3—61no—
501C22×D3—61no—
502C22×D3—61no—
503C22×D3—64no—
504C22×D3—121no—
505C22×D3—124no—
506C22×D3—124no—
507C22×D3—184no—
508C22×D3—184no—
509C22×D3—188no—
510C22×D3—182no—
511C22×D3—181no—
512C22×D3—181no—
513C22×D3—181no—
514C22×D3—184no—
515C22×D3—361no—
516C22×D3—361no—
517C22×D3—362no—
518C22×D3—364no—
519C22×D3—364no—
520C22×D3—368no—
521C22×D3—364no—
522C22×D3#62611yescharacteristic
523C3×D4—32no—
524C3×D4—32no—
525C3×D4—62no—
526C3×D4—61no—
527C3×D4—61no—
528C3×D4—92no—
529C3×D4—92no—
530C3×D4—121no—
531C3×D4—184no—
532C3×D4—181no—
533C3×D4—181no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—31no—
538C2×C3×C4—31no—
539C2×C3×C4—32no—
540C2×C3×C4—32no—
541C2×C3×C4—32no—
542C2×C3×C4—32no—
543C2×C3×C4—41no—
544C2×C3×C4—62no—
545C2×C3×C4—62no—
546C2×C3×C4—61no—
547C2×C3×C4C2×D3211yescharacteristic
548C2×C3×C4C2×D3211yescharacteristic
549C2×C3×C4C2×D3211yescharacteristic
550#67—64no—
551#67—184no—
552C2×Dic3#62611yescharacteristic
553D12—21no—
554D12—32no—
555D12—32no—
556D12—32no—
557D12—32no—
558D12—62no—
559D12—62no—
560D12—62no—
561D12—64no—
562D12—61no—
563D12—61no—
564D12—61no—
565D12—61no—
566D12—92no—
567D12—92no—
568D12—92no—
569D12—121no—
570D12—182no—
571D12—182no—
572D12—182no—
573D12—182no—
574D12—184no—
575D12—184no—
576D12—188no—
577D12—181no—
578D12—181no—
579D12—181no—
580D12—362no—
581D12—361no—
582D12—361no—
583D12—362no—
584D12C2×D3212yescomplemented
585C4×D3#62612yes—
586C4×D3C2×D3212yes—
587C3×C8—32no—
588C3×C8—32no—
589C3×C8—62no—
590C3×C8—92no—
591C3⋊C8—32no—
592C3⋊C8—32no—
593C3⋊C8—62no—
594C3⋊C8C2×D3212yescomplemented
595C2×C32—21no—
596C2×C32—22no—
597C2×C32—21no—
598C2×C32—21no—
599C2×C32—22no—
600C2×C32—22no—
601C2×C32—34no—
602C2×C32—42no—
603C2×C32—41no—
604C2×C32—122no—
605C2×C32C2×D2412yescomplemented
606C2×C32D3×D812yescomplemented
607C2×C32C2×#21312yescomplemented
608C2×C32C22×D1211yescharacteristic
609C2×C32C2×D3×D411yescharacteristic
610C2×C32C22×#6711yescharacteristic
611C3⋊D3—42no—
612C3⋊D3—42no—
613C3⋊D3—122no—
614C3⋊D3—124no—
615C3⋊D3—122no—
616C3⋊D3—122no—
617C3⋊D3—242no—
618C3⋊D3—242no—
619C3⋊D3—244no—
620C3×D3—24no—
621C3×D3—42no—
622C3×D3—42no—
623C3×D3—82no—
624C3×D3—124no—
625C3×D3—122no—
626C3×D3—122no—
627C3×D3—122no—
628C3×D3—122no—
629C3×D3—242no—
630C3×D3C2×D2414yescomplemented
631C3×D3C2×#21314yescomplemented
632C24—181no—
633C24—541no—
634C2×D4—31no—
635C2×D4—94no—
636C2×D4—91no—
637C2×D4—91no—
638C2×D4—182no—
639C2×D4—181no—
640C2×D4—274no—
641C2×D4—271no—
642C2×D4—542no—
643C2×D4—541no—
644C22×C4—31no—
645D8—94no—
646D8—274no—
647D8—274no—
648D8—274no—
649C2×C8—31no—
650C2×C8—94no—
651C2×C8—91no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—32no—
656C22×C3—34no—
657C22×C3—32no—
658C22×C3—34no—
659C22×C3—41no—
660C22×C3—62no—
661C22×C3—64no—
662C22×C3—62no—
663C22×C3—62no—
664C22×C3—122no—
665C22×C3—122no—
666C22×C3—122no—
667C22×C3—182no—
668C22×C3—182no—
669C22×C3—242no—
670C22×C3—368no—
671C22×C3—362no—
672C22×C3—362no—
673C22×C3D3×D1211yescharacteristic
674C22×C3C2×#62611yescharacteristic
675C22×C3D3×#6711yescharacteristic
676C2×D3—22no—
677C2×D3—42no—
678C2×D3—64no—
679C2×D3—62no—
680C2×D3—62no—
681C2×D3—62no—
682C2×D3—62no—
683C2×D3—122no—
684C2×D3—128no—
685C2×D3—124no—
686C2×D3—122no—
687C2×D3—122no—
688C2×D3—122no—
689C2×D3—122no—
690C2×D3—128no—
691C2×D3—184no—
692C2×D3—182no—
693C2×D3—182no—
694C2×D3—182no—
695C2×D3—242no—
696C2×D3—362no—
697C2×D3—362no—
698C2×D3—364no—
699C2×D3—368no—
700C2×D3—368no—
701C2×D3—3616no—
702C2×D3—364no—
703C2×D3—362no—
704C2×D3—362no—
705C2×D3—362no—
706C2×D3—368no—
707C2×D3—722no—
708C2×D3—722no—
709C2×D3—724no—
710C2×D3#371414yesdirect product factor
711C2×D3C2×#62612yes—
712C3×C4—21no—
713C3×C4—21no—
714C3×C4—21no—
715C3×C4—21no—
716C3×C4—21no—
717C3×C4—21no—
718C3×C4—32no—
719C3×C4—32no—
720C3×C4—41no—
721C3×C4—41no—
722C3×C4—62no—
723C3×C4D3×D1211yescharacteristic
724C3×C4C2×#62611yescharacteristic
725C3×C4D3×#6711yescharacteristic
726C3×C4C22×D3211yescharacteristic
727C3×C4C22×D3211yescharacteristic
728C3×C4C22×D3211yescharacteristic
729Dic3C2×#62612yes—
730C32—21no—
731C32—21no—
732C32—21no—
733C32—41no—
734C32C22×D2411yescharacteristic, complemented
735C32C2×D3×D811yescharacteristic, complemented
736C32C22×#21311yescharacteristic, complemented
737C23—31no—
738C23—61no—
739C23—184no—
740C23—181no—
741C23—181no—
742C23—364no—
743C23—544no—
744C23—541no—
745C23—1084no—
746D4—32no—
747D4—61no—
748D4—92no—
749D4—92no—
750D4—184no—
751D4—181no—
752D4—181no—
753D4—272no—
754D4—544no—
755D4—541no—
756C2×C4—31no—
757C2×C4—32no—
758C2×C4—32no—
759C2×C4D3311yescharacteristic
760C8—32no—
761C8—92no—
762C2×C3—22no—
763C2×C3—22no—
764C2×C3—22no—
765C2×C3—21no—
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—34no—
769C2×C3—34no—
770C2×C3—42no—
771C2×C3—41no—
772C2×C3—64no—
773C2×C3—122no—
774C2×C3—122no—
775C2×C3—242no—
776C2×C3—362no—
777C2×C3—362no—
778C2×C3D3×D2412yescomplemented
779C2×C3C2×#371412yescomplemented
780C2×C3D3×#21312yescomplemented
781C2×C3C2×D3×D1211yescharacteristic
782C2×C3C22×#62611yescharacteristic
783C2×C3C2×D3×#6711yescharacteristic
784D3—42no—
785D3—124no—
786D3—122no—
787D3—122no—
788D3—122no—
789D3—122no—
790D3—242no—
791D3—364no—
792D3—362no—
793D3—362no—
794D3—362no—
795D3—722no—
796D3—722no—
797D3—724no—
798D3C2×#371414yesdirect product factor
799C22—34no—
800C22—32no—
801C22—62no—
802C22—122no—
803C22—182no—
804C22—182no—
805C22—368no—
806C22—362no—
807C22—362no—
808C22—542no—
809C22—1088no—
810C22—1082no—
811C22D3×#62611yescharacteristic
812C4—32no—
813C4D3×#62611yescharacteristic
814C4C2×D3311yescharacteristic
815C3—21no—
816C3—21no—
817C3—21no—
818C3—41no—
819C3C2×D3×D2411yescharacteristic, complemented
820C3C22×#371411yescharacteristic, complemented
821C3C2×D3×#21311yescharacteristic, complemented
822C2—34no—
823C2—122no—
824C2—362no—
825C2—362no—
826C2—1082no—
827C2D3×#371412yesdirect product factor
828C2C2×D3×#62611yescharacteristic
subgroupG/H
centerC22D3×#626
commutator, cosocleC33×C4C24
FrattiniC4C2×D33
FittingC2×C33×C4C23
socleC22×C33C2×D4
hypercenterC2×C4D33
hypocenterC33C22×D8
LCSG ▷ C33×C4 ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×D3×C4⋊(C3⋊D3)C2semidirect
2. C2×C3×D3×D12C2semidirect
3. C2×#88810C2semidirect
4. C2×#88791C2semidirect
5. C2×#88790C2semidirect
6. C2×C3×#3714C2semidirect
7. C2×C3×D3×C3⋊C8C2semidirect
8. D3×#3714C2direct (N × H)
14. C2×C4⋊(C3⋊(C3⋊D3))C22semidirect
15. C2×C3×C4⋊(C3⋊D3)C22semidirect
16. C2×C3×C4⋊(C3⋊D3)C22semidirect
17. C2×C32×D12C22semidirect
21. D3×C4⋊(C3⋊D3)C22semidirect
24. C3×D3×D12C22semidirect
25. C2×C3×C3⋊(C3⋊C8)C22semidirect
26. C2×C32×C3⋊C8C22semidirect
27. #88810C22semidirect
28. #88791C22semidirect
29. #88790C22semidirect
30. C3×#3714C22semidirect
31. C3×D3×C3⋊C8C22semidirect
38. C2×D3×D12D3semidirect
55. C2×#3714D3direct (N × H)
57. C2×D3×C3⋊C8D3semidirect
70. C4⋊(C3⋊(C3⋊D3))C23semidirect
73. C3×C4⋊(C3⋊D3)C23semidirect
74. C3×C4⋊(C3⋊D3)C23semidirect
77. C32×D12C23semidirect
82. C3×C3⋊(C3⋊C8)C23semidirect
83. C32×C3⋊C8C23semidirect
106. C2×C4⋊(C3⋊D3)C2×D3semidirect
107. C2×C4⋊(C3⋊D3)C2×D3semidirect
121. C2×C3×D12C2×D3semidirect
122. C2×C3×D12C2×D3semidirect
137. D3×D12C2×D3semidirect
140. C2×C3⋊(C3⋊C8)C2×D3semidirect
148. C2×C3×C3⋊C8C2×D3semidirect
149. C2×C3×C3⋊C8C2×D3semidirect
160. #3714C2×D3direct (N × H)
162. D3×C3⋊C8C2×D3semidirect
172. C2×C32×D3D8semidirect
272. C4⋊(C3⋊D3)C22×D3semidirect
273. C4⋊(C3⋊D3)C22×D3semidirect
295. C3×D12C22×D3semidirect
296. C3×D12C22×D3semidirect
308. C3⋊(C3⋊C8)C22×D3semidirect
313. C3×C3⋊C8C22×D3semidirect
314. C3×C3⋊C8C22×D3semidirect
316. C2×C33C2×D8semidirect
322. C32×D3C2×D8semidirect
372. C2×D12D32semidirect
391. C2×C3⋊C8D32semidirect
451. C2×C3×D3D24semidirect
452. C2×C3×D3#213semidirect
485. C33C22×D8semidirect
584. D12C2×D32semidirect
594. C3⋊C8C2×D32semidirect
605. C2×C32C2×D24semidirect
606. C2×C32D3×D8semidirect
607. C2×C32C2×#213semidirect
630. C3×D3C2×D24semidirect
631. C3×D3C2×#213semidirect
710. C2×D3#3714direct (N × H)
734. C32C22×D24semidirect
735. C32C2×D3×D8semidirect
736. C32C22×#213semidirect
778. C2×C3D3×D24semidirect
779. C2×C3C2×#3714semidirect
780. C2×C3D3×#213semidirect
798. D3C2×#3714direct (N × H)
819. C3C2×D3×D24semidirect
820. C3C22×#3714semidirect
821. C3C2×D3×#213semidirect
827. C2D3×#3714direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D3×C4⋊(C3⋊D3)2
C2×C3×D3×D122
C2×#888102
C2×#887912
C2×#887902
C2×C3×#37142
C2×C3×D3×C3⋊C82
D3×#37142
C2×D3×#2133
C22×#37143
C2×D3×D243