Finite Group Databasebeta

← D32×Dic3⋊C4 #13170701

Subgroups — D32×Dic3⋊C4 #13170701

Order 1728.

1974 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×D32C211yesmaximal, characteristic
2C2×D32×Dic3C211yesmaximal, characteristic
3C2×D32×Dic3C211yesmaximal, characteristic
4#11723682C211yesmaximal, characteristic, complemented
5C3⋊D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
6D3×#3750C212yesmaximal, complemented
7C3×D3×Dic3⋊C4C212yesmaximal, complemented
8#11722911C211yesmaximal, characteristic, complemented
9#11722910C211yesmaximal, characteristic, complemented
10D3×#3724C212yesmaximal, complemented
11D3×Dic3⋊Dic3C212yesmaximal, complemented
12C2×D3×Dic3⋊C4—32nomaximal
13D32×C4⋊C4—31nomaximal
14C22×C3×D32C2211yescharacteristic
15C2×C3×C4×C3⋊D3C2211yescharacteristic
16C2×C32×C4×D3C2212yes—
17C2×#6294C2211yescharacteristic
18C2×#6294C2211yescharacteristic
19C2×Dic3×C3⋊D3C2211yescharacteristic
20C2×Dic3×C3⋊D3C2211yescharacteristic
21C2×D3×C3⋊Dic3C2212yes—
22C2×D3×C3⋊Dic3C2212yes—
23C2×C3×#624C2211yescharacteristic
24C2×C3×D3×Dic3C2212yes—
25C2×C3×D3×Dic3C2212yes—
26C2×C3×D3×Dic3C2212yes—
27C3×C4×D32—24no—
28D32×Dic3—24no—
29D32×Dic3C418yescomplemented
30#88857C2211yescharacteristic, complemented
31C3×#3750C2212yescomplemented
32C32×Dic3⋊C4C2211yescharacteristic, complemented
33#88815C2212yescomplemented
34#88807C2212yescomplemented
35#88806C2211yescharacteristic, complemented
36#88806C2212yescomplemented
37Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
38C3×#3724C2212yescomplemented
39C3×Dic3⋊Dic3C2212yescomplemented
40C22×C3×C4×D3—32no—
41C22×D3×Dic3—32no—
42C22×D3×Dic3—32no—
43C2×C4×D32—31no—
44C2×C4×D32—31no—
45C2×C4×D32D311yescharacteristic
46C2×#3750—32no—
47C4⋊C4×C3⋊D3—31no—
48C2×C3×Dic3⋊C4—32no—
49C3×D3×C4⋊C4—32no—
50C2×#3724—32no—
51C2×Dic3⋊Dic3—32no—
52#63900—31no—
53D3×C4⋊Dic3—32no—
54#63883—31no—
55#63883—31no—
56D3×Dic3⋊C4—32no—
57D3×Dic3⋊C4—32no—
58D3×Dic3⋊C4—32no—
59D3×Dic3⋊C4—32no—
60D3×Dic3⋊C4—32no—
61D3×Dic3⋊C4—32no—
62D3×Dic3⋊C4—32no—
63D3×Dic3⋊C4—32no—
64D3×Dic3⋊C4—32no—
65D3×Dic3⋊C4—62no—
66D3×Dic3⋊C4—61no—
67D3×Dic3⋊C4D312yesdirect product factor
68C22×C3×C3⋊D3C2311yescharacteristic
69C22×C32×D3C2312yes—
70C2×C3×D32C2×C414yes—
71C2×C3×D32D414yes—
72C2×C3×D32Q814yes—
73C2×C33×C4C2311yescharacteristic
74C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
75C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
76C2×C3×C3⋊Dic3C2312yes—
77C2×C3×C3⋊Dic3C2311yescharacteristic
78C2×C3×C3⋊Dic3C2312yes—
79C3×C4×C3⋊D3—22no—
80C2×C32×Dic3C2311yescharacteristic
81C2×C32×Dic3C2312yes—
82C2×C32×Dic3C2311yescharacteristic
83C32×C4×D3—24no—
84#6294—22no—
85#6294C2×C414yescomplemented
86Dic3×C3⋊D3—22no—
87Dic3×C3⋊D3C2×C414yescomplemented
88D3×C3⋊Dic3—24no—
89D3×C3⋊Dic3C2×C418yescomplemented
90C3×#624—22no—
91C3×D3×Dic3—24no—
92C3×D3×Dic3—24no—
93C3×D3×Dic3C2×C418yescomplemented
94C22×Dic3⋊C4—91no—
95C2×D3×C4⋊C4—92no—
96C23×C3×D3—32no—
97C22×D32C2×D311yescharacteristic
98C22×C32×C4—32no—
99C22×C3⋊Dic3—32no—
100C22×C3⋊Dic3—32no—
101C2×C4×C3⋊D3—31no—
102C2×C4×C3⋊D3—31no—
103C2×C4×C3⋊D3C2×D311yescharacteristic
104C22×C3×Dic3—32no—
105C22×C3×Dic3—32no—
106C22×C3×Dic3—32no—
107C2×C3×C4×D3—22no—
108C2×C3×C4×D3—32no—
109C2×C3×C4×D3—32no—
110C2×C3×C4×D3—32no—
111C2×C3×C4×D3—32no—
112C2×C3×C4×D3—32no—
113C2×C3×C4×D3—68no—
114C2×C3×C4×D3—61no—
115C2×C3×C4×D3C2×D312yes—
116C2×C3×C4×D3C2×D312yes—
117C2×#624—31no—
118C2×#624—31no—
119C2×#624C2×D311yescharacteristic
120C2×D3×Dic3—32no—
121C2×D3×Dic3—32no—
122C2×D3×Dic3—32no—
123C2×D3×Dic3—32no—
124C2×D3×Dic3—316no—
125C2×D3×Dic3—32no—
126C2×D3×Dic3—32no—
127C2×D3×Dic3—32no—
128C2×D3×Dic3—32no—
129C2×D3×Dic3—68no—
130C2×D3×Dic3—61no—
131C2×D3×Dic3—62no—
132C2×D3×Dic3—61no—
133C2×D3×Dic3—62no—
134C2×D3×Dic3C2×D312yes—
135C2×D3×Dic3C2×D312yes—
136C2×D3×Dic3C2×D312yes—
137C4×D32—24no—
138C4×D32—38no—
139C4×D32—64no—
140C32×C4⋊C4—31no—
141C4⋊(C3⋊Dic3)—31no—
142#3750—31no—
143#3750—32no—
144#3750—31no—
145#3750—32no—
146#3750—32no—
147#3750—61no—
148#3750—62no—
149#3750—121no—
150#3750C2×D312yescomplemented
151C3×C4⋊Dic3—32no—
152C3×Dic3⋊C4—21no—
153C3×Dic3⋊C4—32no—
154C3×Dic3⋊C4—32no—
155C3×Dic3⋊C4—32no—
156C3×Dic3⋊C4—32no—
157C3×Dic3⋊C4—32no—
158C3×Dic3⋊C4—62no—
159C3×Dic3⋊C4C2×D312yescomplemented
160#3724—32no—
161#3724—32no—
162#3724—32no—
163#3724—32no—
164#3724—62no—
165#3724—61no—
166#3724C2×D312yescomplemented
167Dic3⋊Dic3—32no—
168Dic3⋊Dic3—32no—
169Dic3⋊Dic3—32no—
170Dic3⋊Dic3—32no—
171Dic3⋊Dic3—32no—
172Dic3⋊Dic3—61no—
173Dic3⋊Dic3—62no—
174Dic3⋊Dic3C2×D312yescomplemented
175C22×C33C2411yescharacteristic
176C2×C3×C3⋊D3C22×C412yes—
177C2×C3×C3⋊D3C2×D412yes—
178C2×C3×C3⋊D3C2×Q812yes—
179C2×C32×D3C22×C414yes—
180C2×C32×D3C2×D414yes—
181C2×C32×D3C2×Q814yes—
182C3×D32C4⋊C4116yescomplemented
183C33×C4—21no—
184C3⋊(C3⋊Dic3)—21no—
185C3⋊(C3⋊Dic3)C22×C412yescomplemented
186C3×C3⋊Dic3—21no—
187C3×C3⋊Dic3—22no—
188C3×C3⋊Dic3C22×C414yescomplemented
189C32×Dic3—21no—
190C32×Dic3—22no—
191C32×Dic3C22×C412yescomplemented
192C23×C3×C4—91no—
193C23×Dic3—91no—
194C23×Dic3—91no—
195C22×C4×D3—32no—
196C22×C4×D3—92no—
197C22×C4×D3—92no—
198C2×C3×C4⋊C4—92no—
199C2×C4⋊Dic3—92no—
200C2×Dic3⋊C4—32no—
201C2×Dic3⋊C4—91no—
202C2×Dic3⋊C4—91no—
203C2×Dic3⋊C4—91no—
204C2×Dic3⋊C4—92no—
205C2×Dic3⋊C4—92no—
206C2×Dic3⋊C4—92no—
207C2×Dic3⋊C4—92no—
208C2×Dic3⋊C4—92no—
209C2×Dic3⋊C4—91no—
210C2×Dic3⋊C4—182no—
211D3×C4⋊C4—32no—
212D3×C4⋊C4—92no—
213D3×C4⋊C4—92no—
214D3×C4⋊C4—92no—
215D3×C4⋊C4—92no—
216D3×C4⋊C4—92no—
217D3×C4⋊C4—92no—
218D3×C4⋊C4—92no—
219D3×C4⋊C4—181no—
220C23×C32—32no—
221C22×C3⋊D3C22×D311yescharacteristic
222C22×C3×D3—22no—
223C22×C3×D3—32no—
224C22×C3×D3—38no—
225C22×C3×D3—38no—
226C22×C3×D3—38no—
227C22×C3×D3—61no—
228C22×C3×D3C22×D312yes—
229C22×C3×D3C22×D312yes—
230C2×D32Dic614yes—
231C2×D32C4×D314yes—
232C2×D32#6714yes—
233C2×C32×C4—21no—
234C2×C32×C4—22no—
235C2×C32×C4—31no—
236C2×C32×C4—32no—
237C2×C32×C4—31no—
238C2×C32×C4—41no—
239C2×C32×C4—64no—
240C2×C32×C4C22×D311yescharacteristic
241C2×C32×C4C22×D312yes—
242C2×C3⋊Dic3—31no—
243C2×C3⋊Dic3—32no—
244C2×C3⋊Dic3—38no—
245C2×C3⋊Dic3—32no—
246C2×C3⋊Dic3—31no—
247C2×C3⋊Dic3—62no—
248C2×C3⋊Dic3—61no—
249C2×C3⋊Dic3—61no—
250C2×C3⋊Dic3—62no—
251C2×C3⋊Dic3—64no—
252C2×C3⋊Dic3—121no—
253C2×C3⋊Dic3—121no—
254C2×C3⋊Dic3C22×D311yescharacteristic
255C2×C3⋊Dic3C22×D312yes—
256C2×C3⋊Dic3C22×D312yes—
257C4×C3⋊D3—22no—
258C4×C3⋊D3—34no—
259C4×C3⋊D3—62no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—22no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—32no—
264C2×C3×Dic3—32no—
265C2×C3×Dic3—38no—
266C2×C3×Dic3—32no—
267C2×C3×Dic3—32no—
268C2×C3×Dic3—32no—
269C2×C3×Dic3—62no—
270C2×C3×Dic3—61no—
271C2×C3×Dic3—62no—
272C2×C3×Dic3—64no—
273C2×C3×Dic3—64no—
274C2×C3×Dic3C22×D312yes—
275C2×C3×Dic3C22×D312yes—
276C2×C3×Dic3C22×D312yes—
277C2×C3×Dic3C22×D312yes—
278C3×C4×D3—24no—
279C3×C4×D3—24no—
280C3×C4×D3—38no—
281C3×C4×D3—44no—
282C3×C4×D3—64no—
283C3×C4×D3—64no—
284C3×C4×D3—64no—
285C3×C4×D3—64no—
286C3×C4×D3—122no—
287#624—22no—
288#624—34no—
289#624—62no—
290D3×Dic3—24no—
291D3×Dic3—24no—
292D3×Dic3—38no—
293D3×Dic3—38no—
294D3×Dic3—38no—
295D3×Dic3—38no—
296D3×Dic3—68no—
297D3×Dic3—64no—
298D3×Dic3—64no—
299D3×Dic3—64no—
300D3×Dic3—64no—
301D3×Dic3—64no—
302D3×Dic3—124no—
303D3×Dic3—122no—
304D3×Dic3C4×D318yescomplemented
305C22×C4⋊C4—271noSylow
306C2×C33C23×C411yescharacteristic
307C2×C33C22×D411yescharacteristic
308C2×C33C22×Q811yescharacteristic
309C3×C3⋊D3C2×C4⋊C414yescomplemented
310C32×D3C2×C4⋊C418yescomplemented
311C24×C3—91no—
312C23×D3—32no—
313C22×C3×C4—32no—
314C22×C3×C4—32no—
315C22×C3×C4—62no—
316C22×C3×C4—91no—
317C22×C3×C4—92no—
318C22×C3×C4—92no—
319C22×C3×C4—92no—
320C22×C3×C4—91no—
321C22×C3×C4—184no—
322C22×Dic3—32no—
323C22×Dic3—32no—
324C22×Dic3—32no—
325C22×Dic3—91no—
326C22×Dic3—98no—
327C22×Dic3—91no—
328C22×Dic3—92no—
329C22×Dic3—92no—
330C22×Dic3—92no—
331C22×Dic3—92no—
332C22×Dic3—91no—
333C22×Dic3—91no—
334C22×Dic3—182no—
335C22×Dic3—182no—
336C22×Dic3—184no—
337C2×C4×D3—32no—
338C2×C4×D3—32no—
339C2×C4×D3—32no—
340C2×C4×D3—32no—
341C2×C4×D3—32no—
342C2×C4×D3—61no—
343C2×C4×D3—68no—
344C2×C4×D3—916no—
345C2×C4×D3—92no—
346C2×C4×D3—92no—
347C2×C4×D3—92no—
348C2×C4×D3—92no—
349C2×C4×D3—92no—
350C2×C4×D3—92no—
351C2×C4×D3—181no—
352C2×C4×D3—181no—
353C2×C4×D3—188no—
354C2×C4×D3D3212yes—
355C3×C4⋊C4—32no—
356C3×C4⋊C4—61no—
357C3×C4⋊C4—92no—
358C3×C4⋊C4—92no—
359C3×C4⋊C4—92no—
360C4⋊Dic3—32no—
361C4⋊Dic3—92no—
362C4⋊Dic3—92no—
363C4⋊Dic3—92no—
364C4⋊Dic3—181no—
365Dic3⋊C4—32no—
366Dic3⋊C4—32no—
367Dic3⋊C4—32no—
368Dic3⋊C4—32no—
369Dic3⋊C4—32no—
370Dic3⋊C4—62no—
371Dic3⋊C4—92no—
372Dic3⋊C4—92no—
373Dic3⋊C4—92no—
374Dic3⋊C4—92no—
375Dic3⋊C4—92no—
376Dic3⋊C4—92no—
377Dic3⋊C4—92no—
378Dic3⋊C4—92no—
379Dic3⋊C4—91no—
380Dic3⋊C4—92no—
381Dic3⋊C4—91no—
382Dic3⋊C4—91no—
383Dic3⋊C4—181no—
384Dic3⋊C4—182no—
385Dic3⋊C4—182no—
386Dic3⋊C4—181no—
387Dic3⋊C4—182no—
388Dic3⋊C4—361no—
389Dic3⋊C4D3211yescharacteristic, direct product factor
390C22×C32—21no—
391C22×C32—22no—
392C22×C32—34no—
393C22×C32—34no—
394C22×C32—34no—
395C22×C32—41no—
396C22×C32C23×D311yescharacteristic
397C22×C32C23×D312yes—
398C2×C3⋊D3C2×Dic612yes—
399C2×C3⋊D3C2×C4×D312yes—
400C2×C3⋊D3C2×#6712yes—
401C2×C3×D3—24no—
402C2×C3×D3—24no—
403C2×C3×D3—24no—
404C2×C3×D3—34no—
405C2×C3×D3—34no—
406C2×C3×D3—34no—
407C2×C3×D3—332no—
408C2×C3×D3—62no—
409C2×C3×D3—62no—
410C2×C3×D3—62no—
411C2×C3×D3C2×Dic614yes—
412C2×C3×D3C2×C4×D314yes—
413C2×C3×D3C2×C4×D314yes—
414C2×C3×D3D3×D414yes—
415C2×C3×D3D3×Q814yes—
416C2×C3×D3C2×#6714yes—
417D32Dic3⋊C4116yesdirect product factor
418C32×C4—22no—
419C32×C4—21no—
420C32×C4—32no—
421C32×C4—42no—
422C32×C4—41no—
423C32×C4—62no—
424C32×C4—61no—
425C32×C4—81no—
426C3⋊Dic3—22no—
427C3⋊Dic3—21no—
428C3⋊Dic3—32no—
429C3⋊Dic3—34no—
430C3⋊Dic3—64no—
431C3⋊Dic3—62no—
432C3⋊Dic3—62no—
433C3⋊Dic3—61no—
434C3⋊Dic3—122no—
435C3⋊Dic3—121no—
436C3⋊Dic3—122no—
437C3⋊Dic3—241no—
438C3⋊Dic3C2×C4×D314yescomplemented
439C3×Dic3—22no—
440C3×Dic3—22no—
441C3×Dic3—22no—
442C3×Dic3—22no—
443C3×Dic3—34no—
444C3×Dic3—34no—
445C3×Dic3—41no—
446C3×Dic3—42no—
447C3×Dic3—64no—
448C3×Dic3—62no—
449C3×Dic3—62no—
450C3×Dic3—62no—
451C3×Dic3—122no—
452C3×Dic3—121no—
453C3×Dic3C2×C4×D314yescomplemented
454C23×C4—91no—
455C23×C4—271no—
456C23×C4—271no—
457C2×C4⋊C4—92no—
458C2×C4⋊C4—271no—
459C2×C4⋊C4—271no—
460C2×C4⋊C4—271no—
461C2×C4⋊C4—271no—
462C2×C4⋊C4—272no—
463C2×C4⋊C4—272no—
464C2×C4⋊C4—272no—
465C33C22×C4⋊C411yescharacteristic, complemented, Sylow
466C23×C3—32no—
467C23×C3—32no—
468C23×C3—62no—
469C23×C3—94no—
470C23×C3—94no—
471C23×C3—94no—
472C23×C3—91no—
473C22×D3—32no—
474C22×D3—38no—
475C22×D3—38no—
476C22×D3—38no—
477C22×D3—61no—
478C22×D3C2×D3212yes—
479C2×C3×C4—22no—
480C2×C3×C4—21no—
481C2×C3×C4—32no—
482C2×C3×C4—32no—
483C2×C3×C4—32no—
484C2×C3×C4—32no—
485C2×C3×C4—41no—
486C2×C3×C4—61no—
487C2×C3×C4—62no—
488C2×C3×C4—61no—
489C2×C3×C4—64no—
490C2×C3×C4—64no—
491C2×C3×C4—98no—
492C2×C3×C4—92no—
493C2×C3×C4—91no—
494C2×C3×C4—92no—
495C2×C3×C4—124no—
496C2×C3×C4—182no—
497C2×C3×C4—182no—
498C2×C3×C4—184no—
499C2×C3×C4—184no—
500C2×C3×C4C2×D3211yescharacteristic
501C2×C3×C4C2×D3212yes—
502C2×Dic3—32no—
503C2×Dic3—32no—
504C2×Dic3—38no—
505C2×Dic3—32no—
506C2×Dic3—32no—
507C2×Dic3—32no—
508C2×Dic3—62no—
509C2×Dic3—62no—
510C2×Dic3—61no—
511C2×Dic3—64no—
512C2×Dic3—64no—
513C2×Dic3—94no—
514C2×Dic3—98no—
515C2×Dic3—98no—
516C2×Dic3—92no—
517C2×Dic3—91no—
518C2×Dic3—94no—
519C2×Dic3—91no—
520C2×Dic3—92no—
521C2×Dic3—188no—
522C2×Dic3—181no—
523C2×Dic3—182no—
524C2×Dic3—182no—
525C2×Dic3—181no—
526C2×Dic3—182no—
527C2×Dic3—182no—
528C2×Dic3—184no—
529C2×Dic3—184no—
530C2×Dic3—361no—
531C2×Dic3—361no—
532C2×Dic3—364no—
533C2×Dic3C2×D3211yescharacteristic
534C2×Dic3C2×D3212yes—
535C2×Dic3C2×D3211yescharacteristic
536C4×D3—24no—
537C4×D3—38no—
538C4×D3—64no—
539C4×D3—64no—
540C4×D3—64no—
541C4×D3—64no—
542C4×D3—98no—
543C4×D3—98no—
544C4×D3—98no—
545C4×D3—122no—
546C4×D3—184no—
547C4×D3—184no—
548C4×D3—184no—
549C4×D3—184no—
550C4×D3—362no—
551C2×C32—22no—
552C2×C32—21no—
553C2×C32—22no—
554C2×C32—21no—
555C2×C32—21no—
556C2×C32—22no—
557C2×C32—38no—
558C2×C32—41no—
559C2×C32—41no—
560C2×C32—41no—
561C2×C32C22×Dic611yescharacteristic
562C2×C32C22×C4×D312yes—
563C2×C32C22×C4×D311yescharacteristic
564C2×C32C2×D3×D412yes—
565C2×C32C2×D3×Q812yes—
566C2×C32C22×#6711yescharacteristic
567C3⋊D3C2×Dic3⋊C414yescomplemented
568C3×D3—28no—
569C3×D3—38no—
570C3×D3—64no—
571C3×D3D3×C4⋊C418yescomplemented
572C3×D3C2×Dic3⋊C418yescomplemented
573C24—91no—
574C22×C4—32no—
575C22×C4—91no—
576C22×C4—92no—
577C22×C4—92no—
578C22×C4—92no—
579C22×C4—91no—
580C22×C4—184no—
581C22×C4—271no—
582C22×C4—271no—
583C22×C4—271no—
584C22×C4—278no—
585C22×C4—271no—
586C22×C4—272no—
587C22×C4—272no—
588C22×C4—544no—
589C4⋊C4—31no—
590C4⋊C4—92no—
591C4⋊C4—92no—
592C4⋊C4—92no—
593C4⋊C4—271no—
594C4⋊C4—272no—
595C4⋊C4—272no—
596C4⋊C4—271no—
597C4⋊C4—272no—
598C4⋊C4—271no—
599C22×C3—22no—
600C22×C3—21no—
601C22×C3—34no—
602C22×C3—34no—
603C22×C3—34no—
604C22×C3—34no—
605C22×C3—34no—
606C22×C3—34no—
607C22×C3—41no—
608C22×C3—64no—
609C22×C3—64no—
610C22×C3—64no—
611C22×C3—916no—
612C22×C3—92no—
613C22×C3—92no—
614C22×C3—92no—
615C22×C3C22×D3212yes—
616C22×C3C22×D3211yescharacteristic
617C2×D3—34no—
618C2×D3—34no—
619C2×D3—34no—
620C2×D3—332no—
621C2×D3—62no—
622C2×D3—62no—
623C2×D3—62no—
624C2×D3D3×Dic614yes—
625C2×D3C4×D3214yes—
626C2×D3D3×#6714yes—
627C3×C4—21no—
628C3×C4—22no—
629C3×C4—34no—
630C3×C4—41no—
631C3×C4—42no—
632C3×C4—62no—
633C3×C4—62no—
634C3×C4—62no—
635C3×C4—62no—
636C3×C4—81no—
637C3×C4—94no—
638C3×C4—121no—
639C3×C4—122no—
640C3×C4—181no—
641C3×C4—182no—
642Dic3—21no—
643Dic3—22no—
644Dic3—34no—
645Dic3—34no—
646Dic3—64no—
647Dic3—62no—
648Dic3—62no—
649Dic3—62no—
650Dic3—94no—
651Dic3—92no—
652Dic3—121no—
653Dic3—122no—
654Dic3—182no—
655Dic3—184no—
656Dic3—181no—
657Dic3—182no—
658Dic3—362no—
659Dic3—361no—
660Dic3—362no—
661Dic3—721no—
662Dic3C4×D3212yescomplemented
663C32—21no—
664C32—22no—
665C32—41no—
666C32C2×D3×C4⋊C412yescomplemented
667C32C22×Dic3⋊C411yescharacteristic, complemented
668C23—32no—
669C23—94no—
670C23—94no—
671C23—94no—
672C23—91no—
673C2×C4—31no—
674C2×C4—31no—
675C2×C4—32no—
676C2×C4—64no—
677C2×C4—98no—
678C2×C4—92no—
679C2×C4—92no—
680C2×C4—91no—
681C2×C4—182no—
682C2×C4—182no—
683C2×C4—184no—
684C2×C4—184no—
685C2×C4—274no—
686C2×C4—274no—
687C2×C4—278no—
688C2×C4—271no—
689C2×C4—271no—
690C2×C4—542no—
691C2×C4—542no—
692C2×C4—544no—
693C2×C4D3311yescharacteristic
694C2×C3—21no—
695C2×C3—22no—
696C2×C3—22no—
697C2×C3—21no—
698C2×C3—21no—
699C2×C3—22no—
700C2×C3—38no—
701C2×C3—38no—
702C2×C3—41no—
703C2×C3—41no—
704C2×C3—41no—
705C2×C3—68no—
706C2×C3—94no—
707C2×C3C2×D3×Dic612yes—
708C2×C3C2×C4×D3211yescharacteristic
709C2×C3C2×C4×D3212yes—
710C2×C3D32×D411yescharacteristic
711C2×C3D32×Q811yescharacteristic
712C2×C3C2×D3×#6712yes—
713D3—38no—
714D3—64no—
715D3D3×Dic3⋊C418yesdirect product factor
716C22—34no—
717C22—34no—
718C22—34no—
719C22—916no—
720C22—92no—
721C22—92no—
722C22—92no—
723C22C2×D3311yescharacteristic
724C4—21no—
725C4—32no—
726C4—62no—
727C4—61no—
728C4—94no—
729C4—181no—
730C4—182no—
731C4—272no—
732C4—541no—
733C3—21no—
734C3—22no—
735C3—41no—
736C3D32×C4⋊C411yescharacteristic, complemented
737C3C2×D3×Dic3⋊C412yescomplemented
738C2—38no—
739C2—94no—
740C2D32×Dic611yescharacteristic
741C2C4×D3311yescharacteristic
742C2D32×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutatorC2×C33C23×C4
FittingC2×C33×C4C23
socle, cosocleC22×C33C24
prime radicalC22×C3×D32C22
hypercenterC2×C4D33
hypocenterC33C22×C4⋊C4
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
4. #11723682C2semidirect
5. C3⋊D3×Dic3⋊C4C2semidirect
6. D3×#3750C2semidirect
7. C3×D3×Dic3⋊C4C2semidirect
8. #11722911C2semidirect
9. #11722910C2semidirect
10. D3×#3724C2semidirect
11. D3×Dic3⋊Dic3C2semidirect
29. D32×Dic3C4semidirect
30. #88857C22semidirect
31. C3×#3750C22semidirect
32. C32×Dic3⋊C4C22semidirect
33. #88815C22semidirect
34. #88807C22semidirect
35. #88806C22semidirect
36. #88806C22semidirect
37. Dic3⋊(C3⋊Dic3)C22semidirect
38. C3×#3724C22semidirect
39. C3×Dic3⋊Dic3C22semidirect
67. D3×Dic3⋊C4D3direct (N × H)
85. #6294C2×C4semidirect
87. Dic3×C3⋊D3C2×C4semidirect
89. D3×C3⋊Dic3C2×C4semidirect
93. C3×D3×Dic3C2×C4semidirect
150. #3750C2×D3semidirect
159. C3×Dic3⋊C4C2×D3semidirect
166. #3724C2×D3semidirect
174. Dic3⋊Dic3C2×D3semidirect
182. C3×D32C4⋊C4semidirect
185. C3⋊(C3⋊Dic3)C22×C4semidirect
188. C3×C3⋊Dic3C22×C4semidirect
191. C32×Dic3C22×C4semidirect
304. D3×Dic3C4×D3semidirect
309. C3×C3⋊D3C2×C4⋊C4semidirect
310. C32×D3C2×C4⋊C4semidirect
389. Dic3⋊C4D32direct (N × H)
417. D32Dic3⋊C4direct (N × H)
438. C3⋊Dic3C2×C4×D3semidirect
453. C3×Dic3C2×C4×D3semidirect
465. C33C22×C4⋊C4semidirect
567. C3⋊D3C2×Dic3⋊C4semidirect
571. C3×D3D3×C4⋊C4semidirect
572. C3×D3C2×Dic3⋊C4semidirect
662. Dic3C4×D32semidirect
666. C32C2×D3×C4⋊C4semidirect
667. C32C22×Dic3⋊C4semidirect
715. D3D3×Dic3⋊C4direct (N × H)
736. C3D32×C4⋊C4semidirect
737. C3C2×D3×Dic3⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×D322
C2×D32×Dic32
#117236822
C3⋊D3×Dic3⋊C42
D3×#37502
C3×D3×Dic3⋊C42
#117229112
#117229102
D3×#37242
D3×Dic3⋊Dic32
C2×D3×Dic3⋊C43
D32×C4⋊C43