Finite Group Databasebeta

← D3×#63894 #13170739

Subgroups — D3×#63894 #13170739

Order 1728.

2182 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×C4⋊(C3⋊D3)C211yesmaximal, characteristic
2C2×D3×#624C212yesmaximal, complemented
3#11723691C211yesmaximal, characteristic, complemented
4#11723494C211yesmaximal, characteristic, complemented
5#11723484C211yesmaximal, characteristic, complemented
6C3×#63894C211yesmaximal, characteristic, complemented
7C3×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
8C3×C4×D3×Dic3C211yesmaximal, characteristic, complemented
9#11722937C212yesmaximal, complemented
10#11722933C212yesmaximal, complemented
11D3×#3722C212yesmaximal, complemented
12C2×#63894—31nomaximal
13D3×#893—31nomaximal
14C4×D3×D12—31nomaximal
15C22×D3×C3⋊D3C2212yes—
16C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
17C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
18C2×C32×C4×D3C2211yescharacteristic
19C2×#6294C2212yescomplemented
20C2×#6292C2212yes—
21C2×#6289C2212yescomplemented
22C2×#6289C2212yescomplemented
23D3×C4⋊(C3⋊D3)C418yescomplemented
24C2×C3×#624C2212yescomplemented
25C2×C3×D3×Dic3C2212yes—
26C2×C3×D3×Dic3C2211yescharacteristic
27C2×C3×D3×Dic3C2211yescharacteristic
28D3×#624—28no—
29C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
30C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
31C32×C4⋊Dic3C2211yescharacteristic, complemented
32C32×C4×Dic3C2211yescharacteristic, complemented
33#88814C2212yescomplemented
34#88804C2212yescomplemented
35#88804C2212yescomplemented
36C3×Dic3⋊Dic3C2212yescomplemented
37C3×#3722C2212yescomplemented
38C3×Dic32C2211yescharacteristic, complemented
39C3×Dic32C2211yescharacteristic, complemented
40C22×C4⋊(C3⋊D3)—31no—
41C22×#624—32no—
42C2×D3×D12—31no—
43C2×D3×D12—31no—
44C2×D3×D12—61no—
45C2×C4×D32—32no—
46C2×C4×D32—32no—
47#64102—31no—
48C4×C4⋊(C3⋊D3)—31no—
49C2×C3×C4⋊Dic3—31no—
50C2×C3×C4×Dic3—31no—
51C3×#893—31no—
52C3×D3×C4⋊C4—31no—
53C3×C4×D12—31no—
54C3×C42×D3—31no—
55C2×#3722—32no—
56D3×(C2×D3)⋊C4—32no—
57D3×(C2×D3)⋊C4—32no—
58#63904—32no—
59C4×#626—32no—
60#63898—31no—
61#63894—31no—
62#63894—32no—
63#63894—31no—
64#63894—31no—
65#63894—31no—
66#63894—31no—
67#63894—32no—
68#63894—61no—
69#63894—61no—
70#63894D311yescharacteristic, direct product factor
71Dic3×D12—31no—
72D3×C4⋊Dic3D311yescharacteristic, complemented
73#63881—32no—
74#63880—32no—
75C4×D3×Dic3D311yescharacteristic, complemented
76C22×C3⋊(C3⋊D3)C2312yes—
77C22×C3×C3⋊D3C2312yes—
78C22×C32×D3C2311yescharacteristic
79C2×D3×C3⋊D3—24no—
80C2×D3×C3⋊D3—24no—
81C2×D3×C3⋊D3C2×C418yescomplemented
82C2×C33×C4C2311yescharacteristic
83C4⋊(C3⋊(C3⋊D3))C2×C414yescomplemented
84C2×C3×C3⋊Dic3C2311yescharacteristic
85C2×C3×C3⋊Dic3C2312yes—
86C2×C3×C3⋊Dic3C2311yescharacteristic
87C3×C4⋊(C3⋊D3)C2×C414yescomplemented
88C2×C32×Dic3C2312yes—
89C2×C32×Dic3C2311yescharacteristic
90C2×C32×Dic3C2311yescharacteristic
91C2×C32×Dic3C2311yescharacteristic
92C32×C4×D3C2×C414yescomplemented
93#6294—24no—
94#6292C2×C418yescomplemented
95#6289—24no—
96#6289—24no—
97C3×#624—24no—
98C3×D3×Dic3—24no—
99C3×D3×Dic3—22no—
100C3×D3×Dic3D414yescomplemented
101C4×D3×D4—91no—
102C2×#893—91no—
103C2×C4×D12—91no—
104C23×C3⋊D3—32no—
105C22×D32—32no—
106C22×D32—32no—
107C22×D32—62no—
108C22×C32×C4—31no—
109C2×C4⋊(C3⋊D3)—32no—
110C2×C4⋊(C3⋊D3)—31no—
111C2×C4⋊(C3⋊D3)—31no—
112C2×C4⋊(C3⋊D3)—31no—
113C2×C4⋊(C3⋊D3)—38no—
114C2×C4⋊(C3⋊D3)—61no—
115C2×C4⋊(C3⋊D3)—61no—
116C2×C4⋊(C3⋊D3)—61no—
117C2×C4⋊(C3⋊D3)—121no—
118C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
119C2×C4×C3⋊D3—32no—
120C2×C4×C3⋊D3—32no—
121C22×C3×Dic3—31no—
122C22×C3×Dic3—31no—
123C22×C3×Dic3—32no—
124C2×C3×D12—31no—
125C2×C3×D12—31no—
126C2×C3×D12—61no—
127C2×C3×C4×D3—21no—
128C2×C3×C4×D3—31no—
129C2×C3×C4×D3—32no—
130C2×C3×C4×D3—31no—
131C2×C3×C4×D3—32no—
132C2×C3×C4×D3—32no—
133C2×C3×C4×D3C2×D311yescharacteristic
134C2×C3×C4×D3C2×D311yescharacteristic
135C2×#626—32no—
136C2×#626—32no—
137C2×#626—62no—
138C2×#624—32no—
139C2×#624—32no—
140C2×#624—32no—
141C2×#624—32no—
142C2×#624—32no—
143C2×#624—68no—
144C2×#624—62no—
145C2×#624—62no—
146C2×#624C2×D312yescomplemented
147C2×D3×Dic3—32no—
148C2×D3×Dic3—32no—
149C2×D3×Dic3C2×D312yes—
150C2×D3×Dic3C2×D311yescharacteristic
151C2×D3×Dic3C2×D311yescharacteristic
152D3×D12—38no—
153D3×D12—38no—
154D3×D12—68no—
155C4×D32—68no—
156C4×D32—68no—
157C32×C4⋊C4—31no—
158C32×C42—31no—
159#3752—32no—
160#3752—32no—
161C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
162C4×C3⋊Dic3C2×D311yescharacteristic, complemented
163C3×(C2×D3)⋊C4—32no—
164C3×(C2×D3)⋊C4—32no—
165C3×C4⋊Dic3—21no—
166C3×C4⋊Dic3—31no—
167C3×C4⋊Dic3—31no—
168C3×C4⋊Dic3—32no—
169C3×C4⋊Dic3—61no—
170C3×C4⋊Dic3C2×D311yescharacteristic, complemented
171C3×C4⋊Dic3C2×D311yescharacteristic, complemented
172C3×Dic3⋊C4—32no—
173C3×C4×Dic3—21no—
174C3×C4×Dic3—31no—
175C3×C4×Dic3—31no—
176C3×C4×Dic3—31no—
177C3×C4×Dic3—31no—
178C3×C4×Dic3—31no—
179C3×C4×Dic3—31no—
180C3×C4×Dic3—61no—
181C3×C4×Dic3C2×D311yescharacteristic, complemented
182C3×C4×Dic3C2×D311yescharacteristic, complemented
183Dic3⋊Dic3C2×D312yescomplemented
184#3722—32no—
185#3722—32no—
186#3722—32no—
187#3722—32no—
188#3722—32no—
189#3722—62no—
190#3722—62no—
191#3722C2×D312yescomplemented
192(C2×D3)⋊Dic3—32no—
193(C2×D3)⋊Dic3—32no—
194Dic32C2×D311yescharacteristic, complemented
195Dic32C2×D311yescharacteristic, complemented
196C22×C33C2411yescharacteristic
197C2×C3⋊(C3⋊D3)—22no—
198C2×C3⋊(C3⋊D3)—22no—
199C2×C3⋊(C3⋊D3)C22×C414yescomplemented
200C2×C3×C3⋊D3—22no—
201C2×C3×C3⋊D3—22no—
202C2×C3×C3⋊D3C22×C414yescomplemented
203C2×C32×D3C22×C412yes—
204C2×C32×D3C2×D412yes—
205C2×C32×D3#4112yes—
206D3×C3⋊D3—216no—
207C33×C4C22×C412yescomplemented
208C3×C3⋊Dic3—22no—
209C3×C3⋊Dic3—21no—
210C3×C3⋊Dic3C2×D412yescomplemented
211C32×Dic3—22no—
212C32×Dic3—21no—
213C32×Dic3C22×C412yescomplemented
214C32×Dic3C2×D412yescomplemented
215C2×D3×D4—91no—
216C22×D12—91no—
217C22×D12—91no—
218C22×D12—181no—
219C22×C4×D3—92no—
220C22×C4×D3—92no—
221C22×C4×D3—92no—
222C3×C4×D4—91no—
223C2×C3×C4⋊C4—91no—
224C2×C3×C42—91no—
225D4×Dic3—91no—
226C4×#67—92no—
227C2×(C2×D3)⋊C4—92no—
228C2×(C2×D3)⋊C4—92no—
229C2×C4⋊Dic3—31no—
230C2×C4×Dic3—31no—
231#893—31no—
232#893—92no—
233#893—91no—
234#893—91no—
235#893—92no—
236#893—91no—
237#893—91no—
238#893—181no—
239D3×C4⋊C4—31no—
240#67⋊C4—92no—
241D3×C22⋊C4—92no—
242C4×D12—31no—
243C4×D12—92no—
244C4×D12—91no—
245C4×D12—91no—
246C4×D12—92no—
247C4×D12—91no—
248C4×D12—91no—
249C4×D12—181no—
250C42×D3—31no—
251C23×C32—31no—
252C22×C3⋊D3—32no—
253C22×C3⋊D3—32no—
254C22×C3⋊D3—32no—
255C22×C3⋊D3—38no—
256C22×C3⋊D3—62no—
257C22×C3⋊D3—62no—
258C22×C3⋊D3—62no—
259C22×C3⋊D3—64no—
260C22×C3⋊D3—64no—
261C22×C3⋊D3—122no—
262C22×C3⋊D3C22×D312yes—
263C22×C3×D3—21no—
264C22×C3×D3—32no—
265C22×C3×D3—32no—
266C22×C3×D3—62no—
267C22×C3×D3C22×D311yescharacteristic
268C22×C3×D3C22×D311yescharacteristic
269C2×D32—38no—
270C2×D32—38no—
271C2×D32—68no—
272C2×D32—64no—
273C2×D32—64no—
274C2×D32—64no—
275C2×D32—64no—
276C2×D32—124no—
277C2×D32—124no—
278C2×C32×C4—21no—
279C2×C32×C4—21no—
280C2×C32×C4—21no—
281C2×C32×C4—31no—
282C2×C32×C4—31no—
283C2×C32×C4—34no—
284C2×C32×C4—31no—
285C2×C32×C4—32no—
286C2×C32×C4—41no—
287C2×C32×C4C22×D311yescharacteristic
288C2×C32×C4C22×D311yescharacteristic
289C2×C32×C4C22×D311yescharacteristic
290C2×C3⋊Dic3C22×D311yescharacteristic
291C2×C3⋊Dic3C22×D312yes—
292C2×C3⋊Dic3C22×D311yescharacteristic
293C4⋊(C3⋊D3)—38no—
294C4⋊(C3⋊D3)—34no—
295C4⋊(C3⋊D3)—34no—
296C4⋊(C3⋊D3)—34no—
297C4⋊(C3⋊D3)—64no—
298C4⋊(C3⋊D3)—64no—
299C4⋊(C3⋊D3)—64no—
300C4⋊(C3⋊D3)—124no—
301C4⋊(C3⋊D3)C4×D314yescomplemented
302C4×C3⋊D3—64no—
303C4×C3⋊D3—64no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3—21no—
307C2×C3×Dic3—22no—
308C2×C3×Dic3—31no—
309C2×C3×Dic3—31no—
310C2×C3×Dic3—34no—
311C2×C3×Dic3—31no—
312C2×C3×Dic3—32no—
313C2×C3×Dic3—31no—
314C2×C3×Dic3—32no—
315C2×C3×Dic3—61no—
316C2×C3×Dic3—61no—
317C2×C3×Dic3—62no—
318C2×C3×Dic3—64no—
319C2×C3×Dic3—62no—
320C2×C3×Dic3C22×D311yescharacteristic
321C2×C3×Dic3C22×D311yescharacteristic
322C2×C3×Dic3C22×D312yes—
323C2×C3×Dic3C22×D312yes—
324C2×C3×Dic3C22×D311yescharacteristic
325C2×C3×Dic3C22×D311yescharacteristic
326C2×C3×Dic3C22×D311yescharacteristic
327C2×C3×Dic3C22×D311yescharacteristic
328C3×D12—34no—
329C3×D12—34no—
330C3×D12—64no—
331C3×C4×D3—24no—
332C3×C4×D3—34no—
333C3×C4×D3—64no—
334C3×C4×D3—64no—
335C3×C4×D3—62no—
336C3×C4×D3—64no—
337C3×C4×D3C4×D314yescomplemented
338C3×C4×D3C4×D314yescomplemented
339#626—38no—
340#626—38no—
341#626—68no—
342#624—24no—
343#624—64no—
344#624—64no—
345#624—64no—
346#624—64no—
347#624—64no—
348#624—124no—
349#624—124no—
350D3×Dic3—22no—
351D3×Dic3—24no—
352D3×Dic3—64no—
353D3×Dic3—64no—
354D3×Dic3D1214yescomplemented
355C2×C4×D4—271noSylow
356C2×C33C23×C411yescharacteristic
357C2×C33C22×D411yescharacteristic
358C2×C33C2×#4111yescharacteristic
359C3⋊(C3⋊D3)—24no—
360C3×C3⋊D3—24no—
361C32×D3C4×D414yescomplemented
362C23×D3—92no—
363C23×D3—92no—
364C23×D3—92no—
365C23×D3—182no—
366C2×C3×D4—91no—
367C22×C3×C4—31no—
368C22×C3×C4—31no—
369C22×C3×C4—61no—
370C22×C3×C4—92no—
371C22×C3×C4—91no—
372C22×C3×C4—91no—
373C22×C3×C4—92no—
374C2×#67—92no—
375C22×Dic3—31no—
376C22×Dic3—31no—
377C22×Dic3—32no—
378C22×Dic3—92no—
379D3×D4—98no—
380C2×D12—31no—
381C2×D12—31no—
382C2×D12—61no—
383C2×D12—98no—
384C2×D12—98no—
385C2×D12—92no—
386C2×D12—92no—
387C2×D12—91no—
388C2×D12—91no—
389C2×D12—91no—
390C2×D12—188no—
391C2×D12—181no—
392C2×D12—181no—
393C2×D12—181no—
394C2×D12—182no—
395C2×D12—361no—
396C2×C4×D3—31no—
397C2×C4×D3—31no—
398C2×C4×D3—32no—
399C2×C4×D3—32no—
400C2×C4×D3—32no—
401C2×C4×D3—92no—
402C2×C4×D3—92no—
403C2×C4×D3—92no—
404C2×C4×D3—92no—
405C2×C4×D3—92no—
406C2×C4×D3—92no—
407C2×C4×D3—92no—
408C2×C4×D3—92no—
409C2×C4×D3—182no—
410C2×C4×D3—182no—
411C2×C4×D3—188no—
412C2×C4×D3—188no—
413C2×C4×D3—188no—
414C2×C4×D3D3211yescharacteristic
415C3×C4⋊C4—31no—
416C3×C4⋊C4—31no—
417C3×C4⋊C4—61no—
418C3×C4⋊C4—92no—
419C3×C4⋊C4—91no—
420C3×C22⋊C4—92no—
421C3×C42—31no—
422C3×C42—31no—
423C3×C42—61no—
424C3×C42—91no—
425C3×C42—91no—
426C3×C42—91no—
427#217—92no—
428(C2×D3)⋊C4—32no—
429(C2×D3)⋊C4—32no—
430(C2×D3)⋊C4—92no—
431(C2×D3)⋊C4—92no—
432(C2×D3)⋊C4—92no—
433(C2×D3)⋊C4—92no—
434(C2×D3)⋊C4—92no—
435(C2×D3)⋊C4—92no—
436(C2×D3)⋊C4—92no—
437(C2×D3)⋊C4—92no—
438(C2×D3)⋊C4—182no—
439(C2×D3)⋊C4—182no—
440C4⋊Dic3—31no—
441C4⋊Dic3—31no—
442C4⋊Dic3—32no—
443C4⋊Dic3—61no—
444C4⋊Dic3D3211yescharacteristic, complemented
445Dic3⋊C4—32no—
446C4×Dic3—31no—
447C4×Dic3—31no—
448C4×Dic3—31no—
449C4×Dic3—31no—
450C4×Dic3—31no—
451C4×Dic3—31no—
452C4×Dic3—61no—
453C4×Dic3D3211yescharacteristic, complemented
454C22×C32—21no—
455C22×C32—21no—
456C22×C32—21no—
457C22×C32—32no—
458C22×C32—32no—
459C22×C32—32no—
460C22×C32—41no—
461C22×C32C23×D311yescharacteristic
462C22×C32C23×D311yescharacteristic
463C22×C32C23×D311yescharacteristic
464C2×C3⋊D3—22no—
465C2×C3⋊D3—22no—
466C2×C3⋊D3—34no—
467C2×C3⋊D3—34no—
468C2×C3⋊D3—34no—
469C2×C3⋊D3—64no—
470C2×C3⋊D3—64no—
471C2×C3⋊D3—64no—
472C2×C3⋊D3—616no—
473C2×C3⋊D3—62no—
474C2×C3⋊D3—62no—
475C2×C3⋊D3—62no—
476C2×C3⋊D3—62no—
477C2×C3⋊D3—62no—
478C2×C3⋊D3—62no—
479C2×C3⋊D3—124no—
480C2×C3⋊D3—122no—
481C2×C3⋊D3—122no—
482C2×C3⋊D3—122no—
483C2×C3⋊D3—122no—
484C2×C3⋊D3—122no—
485C2×C3⋊D3—122no—
486C2×C3⋊D3—242no—
487C2×C3⋊D3—242no—
488C2×C3⋊D3C2×C4×D314yescomplemented
489C2×C3×D3—22no—
490C2×C3×D3—22no—
491C2×C3×D3—22no—
492C2×C3×D3—34no—
493C2×C3×D3—34no—
494C2×C3×D3—64no—
495C2×C3×D3—62no—
496C2×C3×D3—62no—
497C2×C3×D3—62no—
498C2×C3×D3—62no—
499C2×C3×D3—122no—
500C2×C3×D3—122no—
501C2×C3×D3C2×C4×D312yes—
502C2×C3×D3C2×C4×D312yes—
503C2×C3×D3C2×D1212yes—
504C2×C3×D3#23512yes—
505C2×C3×D3D3×D412yes—
506C2×C3×D3#23912yes—
507D32—616no—
508D32—616no—
509D32—1216no—
510C32×C4—22no—
511C32×C4—22no—
512C32×C4—22no—
513C32×C4—32no—
514C32×C4—32no—
515C32×C4—42no—
516C32×C4—62no—
517C32×C4—61no—
518C32×C4C2×C4×D312yescomplemented
519C32×C4C2×C4×D312yescomplemented
520C32×C4C2×C4×D312yescomplemented
521C3⋊Dic3—21no—
522C3⋊Dic3—22no—
523C3⋊Dic3C2×D1212yescomplemented
524C3×Dic3—21no—
525C3×Dic3—22no—
526C3×Dic3—22no—
527C3×Dic3—21no—
528C3×Dic3—22no—
529C3×Dic3—22no—
530C3×Dic3—32no—
531C3×Dic3—32no—
532C3×Dic3—42no—
533C3×Dic3—41no—
534C3×Dic3—62no—
535C3×Dic3—62no—
536C3×Dic3—62no—
537C3×Dic3—61no—
538C3×Dic3—61no—
539C3×Dic3—122no—
540C3×Dic3—121no—
541C3×Dic3C2×C4×D312yescomplemented
542C3×Dic3C2×C4×D312yescomplemented
543C3×Dic3C2×D1212yescomplemented
544C3×Dic3D3×D412yescomplemented
545C22×D4—271no—
546C23×C4—272no—
547C4×D4—91no—
548C4×D4—271no—
549C4×D4—272no—
550C4×D4—271no—
551C4×D4—272no—
552C4×D4—271no—
553C2×C4⋊C4—91no—
554C2×C22⋊C4—272no—
555C2×C42—91no—
556C33C2×C4×D411yescharacteristic, complemented, Sylow
557C23×C3—31no—
558C23×C3—31no—
559C23×C3—61no—
560C23×C3—92no—
561C22×D3—32no—
562C22×D3—32no—
563C22×D3—62no—
564C22×D3—98no—
565C22×D3—98no—
566C22×D3—92no—
567C22×D3—92no—
568C22×D3—92no—
569C22×D3—98no—
570C22×D3—188no—
571C22×D3—182no—
572C22×D3—182no—
573C22×D3—182no—
574C22×D3—184no—
575C22×D3—184no—
576C22×D3—184no—
577C22×D3—184no—
578C22×D3—184no—
579C22×D3—184no—
580C22×D3—362no—
581C22×D3—364no—
582C22×D3—364no—
583C22×D3C2×D3211yescharacteristic
584C3×D4—94no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—31no—
589C2×C3×C4—31no—
590C2×C3×C4—31no—
591C2×C3×C4—31no—
592C2×C3×C4—34no—
593C2×C3×C4—34no—
594C2×C3×C4—31no—
595C2×C3×C4—32no—
596C2×C3×C4—31no—
597C2×C3×C4—32no—
598C2×C3×C4—41no—
599C2×C3×C4—64no—
600C2×C3×C4—61no—
601C2×C3×C4—61no—
602C2×C3×C4—61no—
603C2×C3×C4—62no—
604C2×C3×C4—94no—
605C2×C3×C4—91no—
606C2×C3×C4—91no—
607C2×C3×C4—92no—
608C2×C3×C4—184no—
609C2×C3×C4—184no—
610C2×C3×C4—182no—
611C2×C3×C4C2×D3211yescharacteristic
612C2×C3×C4C2×D3211yescharacteristic
613C2×C3×C4C2×D3211yescharacteristic
614#67—98no—
615C2×Dic3—31no—
616C2×Dic3—31no—
617C2×Dic3—34no—
618C2×Dic3—31no—
619C2×Dic3—31no—
620C2×Dic3—32no—
621C2×Dic3—32no—
622C2×Dic3—61no—
623C2×Dic3—61no—
624C2×Dic3—62no—
625C2×Dic3—64no—
626C2×Dic3—62no—
627C2×Dic3—184no—
628C2×Dic3C2×D3211yescharacteristic
629C2×Dic3C2×D3212yes—
630C2×Dic3C2×D3211yescharacteristic
631C2×Dic3C2×D3211yescharacteristic
632D12—34no—
633D12—34no—
634D12—64no—
635D12—98no—
636D12—98no—
637D12—94no—
638D12—94no—
639D12—94no—
640D12—184no—
641D12—184no—
642D12—184no—
643D12—188no—
644D12—364no—
645C4×D3—34no—
646C4×D3—64no—
647C4×D3—62no—
648C4×D3—64no—
649C4×D3—64no—
650C4×D3—184no—
651C4×D3—184no—
652C4×D3—184no—
653C4×D3—184no—
654C4×D3—184no—
655C4×D3—184no—
656C4×D3—184no—
657C4×D3—184no—
658C4×D3—364no—
659C4×D3—364no—
660C4×D3#62414yescomplemented
661C2×C32—21no—
662C2×C32—21no—
663C2×C32—21no—
664C2×C32—21no—
665C2×C32—21no—
666C2×C32—21no—
667C2×C32—21no—
668C2×C32—21no—
669C2×C32—21no—
670C2×C32—34no—
671C2×C32—41no—
672C2×C32—41no—
673C2×C32—41no—
674C2×C32C22×C4×D311yescharacteristic
675C2×C32C22×C4×D311yescharacteristic
676C2×C32C22×C4×D311yescharacteristic
677C2×C32C22×D1211yescharacteristic
678C2×C32C2×#23511yescharacteristic
679C2×C32C2×D3×D411yescharacteristic
680C2×C32C2×D3×D411yescharacteristic
681C2×C32C2×#23911yescharacteristic
682C2×C32D3×#4111yescharacteristic
683C3⋊D3—24no—
684C3⋊D3—64no—
685C3⋊D3—64no—
686C3⋊D3—64no—
687C3⋊D3—124no—
688C3⋊D3—124no—
689C3⋊D3—124no—
690C3⋊D3—244no—
691C3×D3—24no—
692C3×D3—64no—
693C3×D3—64no—
694C3×D3—124no—
695C3×D3C4×D1214yescomplemented
696C3×D3#89314yescomplemented
697C24—272no—
698C2×D4—91no—
699C2×D4—278no—
700C2×D4—272no—
701C2×D4—271no—
702C22×C4—31no—
703C22×C4—92no—
704C22×C4—91no—
705C22×C4—91no—
706C22×C4—92no—
707C22×C4—272no—
708C22×C4—272no—
709C22×C4—272no—
710C22×C4—548no—
711C4⋊C4—31no—
712C4⋊C4—92no—
713C4⋊C4—91no—
714C22⋊C4—92no—
715C22⋊C4—272no—
716C22⋊C4—272no—
717C22⋊C4—272no—
718C42—31no—
719C42—91no—
720C42—91no—
721C42—91no—
722C22×C3—21no—
723C22×C3—21no—
724C22×C3—21no—
725C22×C3—32no—
726C22×C3—32no—
727C22×C3—32no—
728C22×C3—32no—
729C22×C3—32no—
730C22×C3—32no—
731C22×C3—41no—
732C22×C3—62no—
733C22×C3—62no—
734C22×C3—62no—
735C22×C3—94no—
736C22×C3—182no—
737C22×C3—182no—
738C22×C3C22×D3211yescharacteristic
739C22×C3C22×D3211yescharacteristic
740C22×C3C22×D3211yescharacteristic
741C2×D3—34no—
742C2×D3—34no—
743C2×D3—64no—
744C2×D3—62no—
745C2×D3—62no—
746C2×D3—62no—
747C2×D3—62no—
748C2×D3—94no—
749C2×D3—94no—
750C2×D3—94no—
751C2×D3—122no—
752C2×D3—122no—
753C2×D3—184no—
754C2×D3—184no—
755C2×D3—184no—
756C2×D3—1816no—
757C2×D3—1816no—
758C2×D3—182no—
759C2×D3—182no—
760C2×D3—182no—
761C2×D3—182no—
762C2×D3—182no—
763C2×D3—182no—
764C2×D3—1816no—
765C2×D3—364no—
766C2×D3—3616no—
767C2×D3—362no—
768C2×D3—362no—
769C2×D3—362no—
770C2×D3—362no—
771C2×D3—362no—
772C2×D3—362no—
773C2×D3—722no—
774C2×D3—722no—
775C2×D3#379912yes—
776C2×D3D3×D1212yes—
777C2×D3C2×#62412yes—
778C3×C4—22no—
779C3×C4—22no—
780C3×C4—22no—
781C3×C4—32no—
782C3×C4—32no—
783C3×C4—32no—
784C3×C4—32no—
785C3×C4—42no—
786C3×C4—62no—
787C3×C4—62no—
788C3×C4—61no—
789C3×C4—62no—
790C3×C4—62no—
791C3×C4—61no—
792C3×C4—92no—
793C3×C4—122no—
794C3×C4—121no—
795C3×C4—182no—
796C3×C4—181no—
797C3×C4C4×D3212yescomplemented
798C3×C4C4×D3212yescomplemented
799C3×C4C2×#62412yescomplemented
800Dic3—21no—
801Dic3—22no—
802Dic3—32no—
803Dic3—32no—
804Dic3—62no—
805Dic3—61no—
806Dic3—62no—
807Dic3—61no—
808Dic3—62no—
809Dic3—122no—
810Dic3—121no—
811Dic3D3×D1212yescomplemented
812Dic3C2×#62412yescomplemented
813C32—21no—
814C32—21no—
815C32—21no—
816C32—41no—
817C32C2×C4×D1211yescharacteristic, complemented
818C32C2×#89311yescharacteristic, complemented
819C32C4×D3×D411yescharacteristic, complemented
820C23—31no—
821C23—92no—
822C23—278no—
823C23—272no—
824C23—544no—
825C23—544no—
826D4—94no—
827D4—278no—
828D4—274no—
829C2×C4—31no—
830C2×C4—31no—
831C2×C4—34no—
832C2×C4—31no—
833C2×C4—32no—
834C2×C4—94no—
835C2×C4—91no—
836C2×C4—91no—
837C2×C4—92no—
838C2×C4—184no—
839C2×C4—184no—
840C2×C4—182no—
841C2×C4—544no—
842C2×C4—544no—
843C2×C4—544no—
844C2×C4D3311yescharacteristic
845C2×C3—21no—
846C2×C3—21no—
847C2×C3—21no—
848C2×C3—21no—
849C2×C3—21no—
850C2×C3—21no—
851C2×C3—21no—
852C2×C3—21no—
853C2×C3—21no—
854C2×C3—34no—
855C2×C3—34no—
856C2×C3—41no—
857C2×C3—41no—
858C2×C3—41no—
859C2×C3—64no—
860C2×C3—184no—
861C2×C3C2×#379911yescharacteristic
862C2×C3C2×C4×D3211yescharacteristic
863C2×C3C2×C4×D3211yescharacteristic
864C2×C3C2×D3×D1211yescharacteristic
865C2×C3C2×D3×D1211yescharacteristic
866C2×C3D3×#23511yescharacteristic
867C2×C3D32×D411yescharacteristic
868C2×C3D3×#23911yescharacteristic
869C2×C3C22×#62411yescharacteristic
870D3—64no—
871D3—64no—
872D3—124no—
873D3—184no—
874D3—184no—
875D3—184no—
876D3—364no—
877D3—364no—
878D3—364no—
879D3—724no—
880D3#6389414yesdirect product factor
881C22—32no—
882C22—32no—
883C22—32no—
884C22—94no—
885C22—182no—
886C22—182no—
887C22—274no—
888C22—5416no—
889C22—542no—
890C22—542no—
891C22C2×D3311yescharacteristic
892C4—32no—
893C4—32no—
894C4—61no—
895C4—62no—
896C4—92no—
897C4—181no—
898C4—182no—
899C4D3×#62412yescomplemented
900C3—21no—
901C3—21no—
902C3—21no—
903C3—41no—
904C3C4×D3×D1211yescharacteristic, complemented
905C3D3×#89311yescharacteristic, complemented
906C3C2×#6389411yescharacteristic, complemented
907C2—34no—
908C2—184no—
909C2—544no—
910C2D3×#379911yescharacteristic
911C2D32×D1211yescharacteristic
912C2C2×D3×#62411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutatorC2×C33C23×C4
FittingC2×C33×C4C23
socle, cosocleC22×C33C24
prime radicalC2×D3×C4⋊(C3⋊D3)C2
hypercenterC2×C4D33
hypocenterC33C2×C4×D4
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C2×D3×#624C2semidirect
3. #11723691C2semidirect
4. #11723494C2semidirect
5. #11723484C2semidirect
6. C3×#63894C2semidirect
7. C3×D3×C4⋊Dic3C2semidirect
8. C3×C4×D3×Dic3C2semidirect
9. #11722937C2semidirect
10. #11722933C2semidirect
11. D3×#3722C2semidirect
19. C2×#6294C22semidirect
21. C2×#6289C22semidirect
22. C2×#6289C22semidirect
23. D3×C4⋊(C3⋊D3)C4semidirect
24. C2×C3×#624C22semidirect
29. C3×C4⋊(C3⋊Dic3)C22semidirect
30. C3×C4×C3⋊Dic3C22semidirect
31. C32×C4⋊Dic3C22semidirect
32. C32×C4×Dic3C22semidirect
33. #88814C22semidirect
34. #88804C22semidirect
35. #88804C22semidirect
36. C3×Dic3⋊Dic3C22semidirect
37. C3×#3722C22semidirect
38. C3×Dic32C22semidirect
39. C3×Dic32C22semidirect
70. #63894D3direct (N × H)
72. D3×C4⋊Dic3D3semidirect
75. C4×D3×Dic3D3semidirect
81. C2×D3×C3⋊D3C2×C4semidirect
83. C4⋊(C3⋊(C3⋊D3))C2×C4semidirect
87. C3×C4⋊(C3⋊D3)C2×C4semidirect
92. C32×C4×D3C2×C4semidirect
94. #6292C2×C4semidirect
100. C3×D3×Dic3D4semidirect
146. C2×#624C2×D3semidirect
161. C4⋊(C3⋊Dic3)C2×D3semidirect
162. C4×C3⋊Dic3C2×D3semidirect
170. C3×C4⋊Dic3C2×D3semidirect
171. C3×C4⋊Dic3C2×D3semidirect
181. C3×C4×Dic3C2×D3semidirect
182. C3×C4×Dic3C2×D3semidirect
183. Dic3⋊Dic3C2×D3semidirect
191. #3722C2×D3semidirect
194. Dic32C2×D3semidirect
195. Dic32C2×D3semidirect
199. C2×C3⋊(C3⋊D3)C22×C4semidirect
202. C2×C3×C3⋊D3C22×C4semidirect
207. C33×C4C22×C4semidirect
210. C3×C3⋊Dic3C2×D4semidirect
213. C32×Dic3C22×C4semidirect
214. C32×Dic3C2×D4semidirect
301. C4⋊(C3⋊D3)C4×D3semidirect
337. C3×C4×D3C4×D3semidirect
338. C3×C4×D3C4×D3semidirect
354. D3×Dic3D12semidirect
361. C32×D3C4×D4semidirect
444. C4⋊Dic3D32semidirect
453. C4×Dic3D32semidirect
488. C2×C3⋊D3C2×C4×D3semidirect
518. C32×C4C2×C4×D3semidirect
519. C32×C4C2×C4×D3semidirect
520. C32×C4C2×C4×D3semidirect
523. C3⋊Dic3C2×D12semidirect
541. C3×Dic3C2×C4×D3semidirect
542. C3×Dic3C2×C4×D3semidirect
543. C3×Dic3C2×D12semidirect
544. C3×Dic3D3×D4semidirect
556. C33C2×C4×D4semidirect
660. C4×D3#624semidirect
695. C3×D3C4×D12semidirect
696. C3×D3#893semidirect
797. C3×C4C4×D32semidirect
798. C3×C4C4×D32semidirect
799. C3×C4C2×#624semidirect
811. Dic3D3×D12semidirect
812. Dic3C2×#624semidirect
817. C32C2×C4×D12semidirect
818. C32C2×#893semidirect
819. C32C4×D3×D4semidirect
880. D3#63894direct (N × H)
899. C4D3×#624semidirect
904. C3C4×D3×D12semidirect
905. C3D3×#893semidirect
906. C3C2×#63894semidirect

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×D3×#6242
#117236912
#117234942
#117234842
C3×#638942
C3×D3×C4⋊Dic32
C3×C4×D3×Dic32
#117229372
#117229332
D3×#37222
C2×#638943
D3×#8933
C4×D3×D123