Finite Group Databasebeta

← D3×#63883 #13170708

Subgroups — D3×#63883 #13170708

Order 1728.

2146 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D3×C3⋊D3C211yesmaximal, characteristic
2C2×D3×#624C211yesmaximal, characteristic
3C2×D3×#624C211yesmaximal, characteristic
4#11723682C211yesmaximal, characteristic, complemented
5#11723470C212yesmaximal, complemented
6C3×#63883C211yesmaximal, characteristic, complemented
7C3×D3×Dic3⋊C4C212yesmaximal, complemented
8#11722912C212yesmaximal, complemented
9#11722910C211yesmaximal, characteristic, complemented
10#11722908C211yesmaximal, characteristic, complemented
11D3×Dic3⋊Dic3C212yesmaximal, complemented
12C2×#63883—31nomaximal
13D32×C4⋊C4—32nomaximal
14C22×D3×C3⋊D3C2211yescharacteristic
15C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
16C2×C3×C4×C3⋊D3C2211yescharacteristic
17C2×C32×C4×D3C2211yescharacteristic
18C2×#6294C2211yescharacteristic
19C2×#6294C2211yescharacteristic
20C2×#6289C2211yescharacteristic
21C2×#6289C2212yes—
22C2×#6289C2212yes—
23C2×Dic3×C3⋊D3C2211yescharacteristic
24C2×D3×C3⋊Dic3C2211yescharacteristic
25C4×D3×C3⋊D3—24no—
26C2×C3×#624C2211yescharacteristic
27C2×C3×#624C2211yescharacteristic
28C2×C3×D3×Dic3C2212yes—
29C2×C3×D3×Dic3C2212yes—
30D3×#624—24no—
31D3×#624C418yescomplemented
32C3×#3750C2212yescomplemented
33C32×Dic3⋊C4C2212yescomplemented
34#88815C2212yescomplemented
35#88807C2212yescomplemented
36Dic3⋊(C3⋊Dic3)C2212yescomplemented
37C3×#3724C2212yescomplemented
38C3×Dic3⋊Dic3C2212yescomplemented
39C3×Dic3⋊Dic3C2212yescomplemented
40C22×C4×C3⋊D3—31no—
41C22×#624—31no—
42C22×#624—31no—
43C2×C4×D32—32no—
44C2×C4×D32—32no—
45C2×C4×D32—32no—
46C2×C4×D32—61no—
47C4⋊C4×C3⋊D3—32no—
48C2×C3×Dic3⋊C4—32no—
49C3×D3×C4⋊C4—32no—
50C3×D3×C4⋊C4—32no—
51C2×Dic3⋊Dic3—32no—
52#63900—32no—
53D3×C4⋊Dic3—32no—
54D3×C4⋊Dic3—32no—
55#63883—31no—
56#63883—31no—
57#63883—31no—
58#63883—32no—
59#63883—32no—
60#63883—32no—
61#63883—32no—
62#63883—62no—
63#63883D311yescharacteristic, direct product factor
64D3×Dic3⋊C4—32no—
65D3×Dic3⋊C4—32no—
66D3×Dic3⋊C4—32no—
67D3×Dic3⋊C4D312yescomplemented
68C22×C3⋊(C3⋊D3)C2311yescharacteristic
69C22×C3×C3⋊D3C2311yescharacteristic
70C22×C32×D3C2311yescharacteristic
71C2×D3×C3⋊D3C2×C414yes—
72C2×D3×C3⋊D3D414yes—
73C2×D3×C3⋊D3Q814yes—
74C2×C33×C4C2311yescharacteristic
75C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
76C4×C3⋊(C3⋊D3)—22no—
77C2×C3×C3⋊Dic3C2312yes—
78C2×C3×C3⋊Dic3C2311yescharacteristic
79C2×C3×C3⋊Dic3C2312yes—
80C3×C4×C3⋊D3—22no—
81C2×C32×Dic3C2312yes—
82C2×C32×Dic3C2311yescharacteristic
83C2×C32×Dic3C2312yes—
84C32×C4×D3—22no—
85#6294—22no—
86#6294C2×C414yescomplemented
87#6289—22no—
88#6289—24no—
89#6289C2×C418yescomplemented
90Dic3×C3⋊D3—22no—
91D3×C3⋊Dic3—22no—
92C3×#624—22no—
93C3×#624C2×C414yescomplemented
94C3×D3×Dic3—24no—
95C3×D3×Dic3C2×C418yescomplemented
96C2×D3×C4⋊C4—91no—
97C2×D3×C4⋊C4—92no—
98C23×C3⋊D3—31no—
99C22×D32—32no—
100C22×D32—61no—
101C22×C32×C4—31no—
102C22×C3⋊Dic3—31no—
103C2×C4×C3⋊D3—32no—
104C2×C4×C3⋊D3—31no—
105C2×C4×C3⋊D3—32no—
106C2×C4×C3⋊D3—31no—
107C2×C4×C3⋊D3—32no—
108C2×C4×C3⋊D3—31no—
109C2×C4×C3⋊D3—64no—
110C2×C4×C3⋊D3—61no—
111C2×C4×C3⋊D3—62no—
112C2×C4×C3⋊D3—121no—
113C2×C4×C3⋊D3C2×D311yescharacteristic
114C22×C3×Dic3—32no—
115C22×C3×Dic3—32no—
116C2×C3×C4×D3—21no—
117C2×C3×C4×D3—32no—
118C2×C3×C4×D3—32no—
119C2×C3×C4×D3—32no—
120C2×C3×C4×D3—32no—
121C2×C3×C4×D3—32no—
122C2×C3×C4×D3—61no—
123C2×C3×C4×D3C2×D312yes—
124C2×#624—31no—
125C2×#624—32no—
126C2×#624—32no—
127C2×#624—38no—
128C2×#624—31no—
129C2×#624—32no—
130C2×#624—32no—
131C2×#624—32no—
132C2×#624—64no—
133C2×#624—61no—
134C2×#624—62no—
135C2×#624—62no—
136C2×#624C2×D311yescharacteristic
137C2×#624C2×D311yescharacteristic
138C2×D3×Dic3—32no—
139C2×D3×Dic3—32no—
140C2×D3×Dic3—32no—
141C2×D3×Dic3—32no—
142C2×D3×Dic3—61no—
143C2×D3×Dic3—61no—
144C2×D3×Dic3C2×D312yes—
145C2×D3×Dic3C2×D312yes—
146C4×D32—316no—
147C4×D32—68no—
148C4×D32—68no—
149C4×D32—68no—
150C32×C4⋊C4—32no—
151C4⋊(C3⋊Dic3)—32no—
152#3750—32no—
153#3750C2×D312yescomplemented
154C3×C4⋊Dic3—32no—
155C3×C4⋊Dic3—32no—
156C3×Dic3⋊C4—22no—
157C3×Dic3⋊C4—32no—
158C3×Dic3⋊C4—32no—
159C3×Dic3⋊C4—32no—
160C3×Dic3⋊C4—32no—
161C3×Dic3⋊C4—32no—
162C3×Dic3⋊C4—32no—
163C3×Dic3⋊C4—62no—
164C3×Dic3⋊C4C2×D312yescomplemented
165C3×Dic3⋊C4C2×D312yescomplemented
166#3724—32no—
167#3724C2×D312yescomplemented
168Dic3⋊Dic3—32no—
169Dic3⋊Dic3—32no—
170Dic3⋊Dic3—32no—
171Dic3⋊Dic3—32no—
172Dic3⋊Dic3—32no—
173Dic3⋊Dic3—32no—
174Dic3⋊Dic3—62no—
175Dic3⋊Dic3—62no—
176Dic3⋊Dic3C2×D312yescomplemented
177Dic3⋊Dic3C2×D312yescomplemented
178C22×C33C2411yescharacteristic
179C2×C3⋊(C3⋊D3)C22×C412yes—
180C2×C3⋊(C3⋊D3)C2×D412yes—
181C2×C3⋊(C3⋊D3)C2×Q812yes—
182C2×C3×C3⋊D3C22×C412yes—
183C2×C3×C3⋊D3C2×D412yes—
184C2×C3×C3⋊D3C2×Q812yes—
185C2×C32×D3C22×C412yes—
186C2×C32×D3C2×D412yes—
187C2×C32×D3C2×Q812yes—
188D3×C3⋊D3C4⋊C4116yescomplemented
189C33×C4—21no—
190C3⋊(C3⋊Dic3)—21no—
191C3×C3⋊Dic3—21no—
192C3×C3⋊Dic3—22no—
193C3×C3⋊Dic3C22×C414yescomplemented
194C32×Dic3—21no—
195C32×Dic3—22no—
196C32×Dic3C22×C414yescomplemented
197C22×C4×D3—91no—
198C22×C4×D3—91no—
199C22×C4×D3—92no—
200C22×C4×D3—92no—
201C22×C4×D3—92no—
202C22×C4×D3—91no—
203C22×C4×D3—181no—
204C2×C3×C4⋊C4—91no—
205C2×C3×C4⋊C4—92no—
206C2×C4⋊Dic3—91no—
207C2×C4⋊Dic3—92no—
208C2×Dic3⋊C4—32no—
209C2×Dic3⋊C4—91no—
210C2×Dic3⋊C4—91no—
211C2×Dic3⋊C4—92no—
212D3×C4⋊C4—32no—
213D3×C4⋊C4—32no—
214D3×C4⋊C4—92no—
215D3×C4⋊C4—92no—
216D3×C4⋊C4—92no—
217D3×C4⋊C4—92no—
218D3×C4⋊C4—92no—
219D3×C4⋊C4—92no—
220D3×C4⋊C4—92no—
221D3×C4⋊C4—92no—
222D3×C4⋊C4—92no—
223D3×C4⋊C4—92no—
224D3×C4⋊C4—182no—
225C23×C32—31no—
226C22×C3⋊D3—32no—
227C22×C3⋊D3—31no—
228C22×C3⋊D3—34no—
229C22×C3⋊D3—34no—
230C22×C3⋊D3—34no—
231C22×C3⋊D3—61no—
232C22×C3⋊D3—62no—
233C22×C3⋊D3—121no—
234C22×C3⋊D3C22×D311yescharacteristic
235C22×C3×D3—21no—
236C22×C3×D3—32no—
237C22×C3×D3—61no—
238C22×C3×D3C22×D312yes—
239C2×D32—38no—
240C2×D32—38no—
241C2×D32—38no—
242C2×D32—64no—
243C2×D32—64no—
244C2×D32—64no—
245C2×C32×C4—21no—
246C2×C32×C4—22no—
247C2×C32×C4—32no—
248C2×C32×C4—31no—
249C2×C32×C4—32no—
250C2×C32×C4—41no—
251C2×C32×C4—62no—
252C2×C32×C4C22×D311yescharacteristic
253C2×C32×C4C22×D312yes—
254C2×C3⋊Dic3—31no—
255C2×C3⋊Dic3—32no—
256C2×C3⋊Dic3—61no—
257C2×C3⋊Dic3—62no—
258C2×C3⋊Dic3—62no—
259C2×C3⋊Dic3—121no—
260C2×C3⋊Dic3C22×D311yescharacteristic
261C2×C3⋊Dic3C22×D312yes—
262C2×C3⋊Dic3C22×D312yes—
263C4×C3⋊D3—22no—
264C4×C3⋊D3—38no—
265C4×C3⋊D3—62no—
266C4×C3⋊D3—62no—
267C4×C3⋊D3—62no—
268C4×C3⋊D3—64no—
269C4×C3⋊D3—64no—
270C4×C3⋊D3—64no—
271C4×C3⋊D3—124no—
272C4×C3⋊D3—124no—
273C2×C3×Dic3—22no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—22no—
276C2×C3×Dic3—32no—
277C2×C3×Dic3—32no—
278C2×C3×Dic3—38no—
279C2×C3×Dic3—32no—
280C2×C3×Dic3—32no—
281C2×C3×Dic3—32no—
282C2×C3×Dic3—62no—
283C2×C3×Dic3—61no—
284C2×C3×Dic3—62no—
285C2×C3×Dic3—64no—
286C2×C3×Dic3C22×D312yes—
287C2×C3×Dic3C22×D312yes—
288C2×C3×Dic3C22×D312yes—
289C2×C3×Dic3C22×D312yes—
290C2×C3×Dic3C22×D312yes—
291C3×C4×D3—24no—
292C3×C4×D3—24no—
293C3×C4×D3—38no—
294C3×C4×D3—38no—
295C3×C4×D3—64no—
296C3×C4×D3—64no—
297C3×C4×D3—64no—
298C3×C4×D3—64no—
299#624—22no—
300#624—34no—
301#624—38no—
302#624—38no—
303#624—68no—
304#624—64no—
305#624—64no—
306#624—64no—
307#624—64no—
308#624—62no—
309#624—124no—
310#624C4×D314yescomplemented
311D3×Dic3—24no—
312D3×Dic3—38no—
313D3×Dic3—64no—
314D3×Dic3—64no—
315D3×Dic3—64no—
316D3×Dic3—64no—
317D3×Dic3—64no—
318D3×Dic3C4×D318yescomplemented
319C22×C4⋊C4—271noSylow
320C2×C33C23×C411yescharacteristic
321C2×C33C22×D411yescharacteristic
322C2×C33C22×Q811yescharacteristic
323C3⋊(C3⋊D3)C2×C4⋊C414yescomplemented
324C3×C3⋊D3C2×C4⋊C414yescomplemented
325C32×D3C2×C4⋊C414yescomplemented
326C23×D3—92no—
327C23×D3—91no—
328C23×D3—181no—
329C22×C3×C4—32no—
330C22×C3×C4—61no—
331C22×C3×C4—91no—
332C22×C3×C4—91no—
333C22×C3×C4—92no—
334C22×C3×C4—92no—
335C22×C3×C4—91no—
336C22×Dic3—32no—
337C22×Dic3—32no—
338C22×Dic3—91no—
339C22×Dic3—91no—
340C22×Dic3—92no—
341C22×Dic3—91no—
342C22×Dic3—181no—
343C2×C4×D3—32no—
344C2×C4×D3—32no—
345C2×C4×D3—32no—
346C2×C4×D3—32no—
347C2×C4×D3—32no—
348C2×C4×D3—61no—
349C2×C4×D3—98no—
350C2×C4×D3—916no—
351C2×C4×D3—92no—
352C2×C4×D3—92no—
353C2×C4×D3—92no—
354C2×C4×D3—92no—
355C2×C4×D3—92no—
356C2×C4×D3—92no—
357C2×C4×D3—92no—
358C2×C4×D3—92no—
359C2×C4×D3—92no—
360C2×C4×D3—91no—
361C2×C4×D3—91no—
362C2×C4×D3—92no—
363C2×C4×D3—91no—
364C2×C4×D3—92no—
365C2×C4×D3—182no—
366C2×C4×D3—181no—
367C2×C4×D3—181no—
368C2×C4×D3—181no—
369C2×C4×D3—182no—
370C2×C4×D3—182no—
371C2×C4×D3—184no—
372C2×C4×D3—184no—
373C2×C4×D3—188no—
374C2×C4×D3—188no—
375C2×C4×D3—188no—
376C2×C4×D3—361no—
377C2×C4×D3D3211yescharacteristic
378C3×C4⋊C4—32no—
379C3×C4⋊C4—32no—
380C3×C4⋊C4—62no—
381C3×C4⋊C4—92no—
382C3×C4⋊C4—92no—
383C3×C4⋊C4—92no—
384C3×C4⋊C4—92no—
385C4⋊Dic3—32no—
386C4⋊Dic3—32no—
387C4⋊Dic3—92no—
388C4⋊Dic3—92no—
389C4⋊Dic3—92no—
390C4⋊Dic3—92no—
391C4⋊Dic3—182no—
392Dic3⋊C4—32no—
393Dic3⋊C4—32no—
394Dic3⋊C4—32no—
395Dic3⋊C4—32no—
396Dic3⋊C4—32no—
397Dic3⋊C4—32no—
398Dic3⋊C4—62no—
399Dic3⋊C4—92no—
400Dic3⋊C4—92no—
401Dic3⋊C4—92no—
402Dic3⋊C4—92no—
403Dic3⋊C4—92no—
404Dic3⋊C4—182no—
405Dic3⋊C4D3212yescomplemented
406C22×C32—22no—
407C22×C32—21no—
408C22×C32—32no—
409C22×C32—32no—
410C22×C32—32no—
411C22×C32—41no—
412C22×C32C23×D311yescharacteristic
413C22×C32C23×D312yes—
414C2×C3⋊D3—32no—
415C2×C3⋊D3—34no—
416C2×C3⋊D3—34no—
417C2×C3⋊D3—32no—
418C2×C3⋊D3—34no—
419C2×C3⋊D3—32no—
420C2×C3⋊D3—316no—
421C2×C3⋊D3—64no—
422C2×C3⋊D3—62no—
423C2×C3⋊D3—62no—
424C2×C3⋊D3—64no—
425C2×C3⋊D3—62no—
426C2×C3⋊D3—64no—
427C2×C3⋊D3—122no—
428C2×C3⋊D3—122no—
429C2×C3⋊D3—122no—
430C2×C3⋊D3C2×C4×D312yes—
431C2×C3⋊D3D3×D412yes—
432C2×C3⋊D3D3×Q812yes—
433C2×C3×D3—22no—
434C2×C3×D3—22no—
435C2×C3×D3—22no—
436C2×C3×D3—34no—
437C2×C3×D3—34no—
438C2×C3×D3—34no—
439C2×C3×D3—62no—
440C2×C3×D3—62no—
441C2×C3×D3—62no—
442C2×C3×D3C2×C4×D314yes—
443C2×C3×D3D3×D414yes—
444C2×C3×D3D3×Q814yes—
445D32—332no—
446D32—616no—
447C32×C4—21no—
448C32×C4—22no—
449C32×C4—22no—
450C32×C4—34no—
451C32×C4—42no—
452C32×C4—42no—
453C32×C4—61no—
454C32×C4—62no—
455C3⋊Dic3—21no—
456C3⋊Dic3—22no—
457C3⋊Dic3—61no—
458C3⋊Dic3—62no—
459C3⋊Dic3—62no—
460C3⋊Dic3—122no—
461C3⋊Dic3—122no—
462C3⋊Dic3C2×C4×D314yescomplemented
463C3×Dic3—22no—
464C3×Dic3—22no—
465C3×Dic3—22no—
466C3×Dic3—22no—
467C3×Dic3—24no—
468C3×Dic3—34no—
469C3×Dic3—34no—
470C3×Dic3—42no—
471C3×Dic3—64no—
472C3×Dic3—62no—
473C3×Dic3—62no—
474C3×Dic3—62no—
475C3×Dic3—62no—
476C3×Dic3—122no—
477C3×Dic3C2×C4×D314yescomplemented
478C3×Dic3C2×C4×D314yescomplemented
479C23×C4—271no—
480C23×C4—271no—
481C23×C4—271no—
482C2×C4⋊C4—91no—
483C2×C4⋊C4—92no—
484C2×C4⋊C4—272no—
485C2×C4⋊C4—272no—
486C2×C4⋊C4—271no—
487C2×C4⋊C4—271no—
488C2×C4⋊C4—271no—
489C2×C4⋊C4—272no—
490C33C22×C4⋊C411yescharacteristic, complemented, Sylow
491C23×C3—32no—
492C23×C3—61no—
493C23×C3—91no—
494C22×D3—32no—
495C22×D3—61no—
496C22×D3—98no—
497C22×D3—98no—
498C22×D3—98no—
499C22×D3—91no—
500C22×D3—92no—
501C22×D3—94no—
502C22×D3—94no—
503C22×D3—94no—
504C22×D3—184no—
505C22×D3—184no—
506C22×D3—184no—
507C22×D3—182no—
508C22×D3—181no—
509C22×D3—361no—
510C22×D3C2×D3211yescharacteristic
511C2×C3×C4—21no—
512C2×C3×C4—22no—
513C2×C3×C4—32no—
514C2×C3×C4—32no—
515C2×C3×C4—32no—
516C2×C3×C4—32no—
517C2×C3×C4—32no—
518C2×C3×C4—41no—
519C2×C3×C4—62no—
520C2×C3×C4—61no—
521C2×C3×C4—62no—
522C2×C3×C4—64no—
523C2×C3×C4—64no—
524C2×C3×C4—94no—
525C2×C3×C4—98no—
526C2×C3×C4—92no—
527C2×C3×C4—92no—
528C2×C3×C4—91no—
529C2×C3×C4—182no—
530C2×C3×C4—182no—
531C2×C3×C4—184no—
532C2×C3×C4C2×D3211yescharacteristic
533C2×C3×C4C2×D3212yes—
534C2×Dic3—32no—
535C2×Dic3—32no—
536C2×Dic3—38no—
537C2×Dic3—32no—
538C2×Dic3—32no—
539C2×Dic3—32no—
540C2×Dic3—62no—
541C2×Dic3—61no—
542C2×Dic3—62no—
543C2×Dic3—64no—
544C2×Dic3—94no—
545C2×Dic3—92no—
546C2×Dic3—91no—
547C2×Dic3—181no—
548C2×Dic3—182no—
549C2×Dic3—182no—
550C2×Dic3—182no—
551C2×Dic3—184no—
552C2×Dic3—184no—
553C2×Dic3—361no—
554C2×Dic3C2×D3211yescharacteristic
555C2×Dic3C2×D3212yes—
556C2×Dic3C2×D3212yes—
557C4×D3—22no—
558C4×D3—38no—
559C4×D3—38no—
560C4×D3—64no—
561C4×D3—64no—
562C4×D3—64no—
563C4×D3—64no—
564C4×D3—98no—
565C4×D3—98no—
566C4×D3—98no—
567C4×D3—98no—
568C4×D3—188no—
569C4×D3—182no—
570C4×D3—184no—
571C4×D3—184no—
572C4×D3—184no—
573C4×D3—184no—
574C4×D3—184no—
575C4×D3—184no—
576C4×D3—182no—
577C4×D3—184no—
578C4×D3—184no—
579C4×D3—184no—
580C4×D3—184no—
581C4×D3—182no—
582C4×D3—364no—
583C4×D3—364no—
584C4×D3—364no—
585C2×C32—21no—
586C2×C32—22no—
587C2×C32—21no—
588C2×C32—22no—
589C2×C32—22no—
590C2×C32—21no—
591C2×C32—34no—
592C2×C32—41no—
593C2×C32—41no—
594C2×C32—41no—
595C2×C32C22×C4×D311yescharacteristic
596C2×C32C22×C4×D312yes—
597C2×C32C2×D3×D411yescharacteristic
598C2×C32C2×D3×D412yes—
599C2×C32C2×D3×Q812yes—
600C2×C32C2×D3×Q811yescharacteristic
601C3⋊D3—38no—
602C3⋊D3—34no—
603C3⋊D3—64no—
604C3⋊D3—68no—
605C3⋊D3—124no—
606C3⋊D3D3×C4⋊C414yescomplemented
607C3×D3—24no—
608C3×D3—38no—
609C3×D3—64no—
610C3×D3D3×C4⋊C418yescomplemented
611C24—271no—
612C22×C4—31no—
613C22×C4—91no—
614C22×C4—91no—
615C22×C4—92no—
616C22×C4—92no—
617C22×C4—91no—
618C22×C4—272no—
619C22×C4—272no—
620C22×C4—271no—
621C22×C4—271no—
622C22×C4—278no—
623C22×C4—271no—
624C22×C4—271no—
625C22×C4—271no—
626C22×C4—271no—
627C22×C4—544no—
628C22×C4—544no—
629C4⋊C4—32no—
630C4⋊C4—92no—
631C4⋊C4—92no—
632C4⋊C4—92no—
633C4⋊C4—92no—
634C4⋊C4—272no—
635C4⋊C4—272no—
636C4⋊C4—272no—
637C22×C3—22no—
638C22×C3—21no—
639C22×C3—34no—
640C22×C3—34no—
641C22×C3—34no—
642C22×C3—41no—
643C22×C3—62no—
644C22×C3—62no—
645C22×C3—62no—
646C22×C3—92no—
647C22×C3—92no—
648C22×C3—92no—
649C22×C3C22×D3211yescharacteristic
650C22×C3C22×D3212yes—
651C2×D3—34no—
652C2×D3—34no—
653C2×D3—34no—
654C2×D3—62no—
655C2×D3—62no—
656C2×D3—62no—
657C2×D3—932no—
658C2×D3—92no—
659C2×D3—94no—
660C2×D3—92no—
661C2×D3—94no—
662C2×D3—94no—
663C2×D3—92no—
664C2×D3—916no—
665C2×D3—1816no—
666C2×D3—182no—
667C2×D3—184no—
668C2×D3—184no—
669C2×D3—182no—
670C2×D3—182no—
671C2×D3—184no—
672C2×D3—362no—
673C2×D3—362no—
674C2×D3—362no—
675C2×D3#379712yes—
676C2×D3C4×D3212yes—
677C2×D3#381112yes—
678C3×C4—22no—
679C3×C4—22no—
680C3×C4—21no—
681C3×C4—34no—
682C3×C4—34no—
683C3×C4—42no—
684C3×C4—42no—
685C3×C4—64no—
686C3×C4—62no—
687C3×C4—62no—
688C3×C4—62no—
689C3×C4—62no—
690C3×C4—94no—
691C3×C4—122no—
692C3×C4—182no—
693C3×C4—181no—
694Dic3—22no—
695Dic3—21no—
696Dic3—34no—
697Dic3—34no—
698Dic3—64no—
699Dic3—62no—
700Dic3—62no—
701Dic3—62no—
702Dic3—62no—
703Dic3—122no—
704Dic3—182no—
705Dic3—182no—
706Dic3—181no—
707Dic3—362no—
708Dic3—362no—
709Dic3C4×D3214yescomplemented
710C32—22no—
711C32—21no—
712C32—41no—
713C32C2×D3×C4⋊C411yescharacteristic, complemented
714C32C2×D3×C4⋊C412yescomplemented
715C23—31no—
716C23—91no—
717C23—274no—
718C23—274no—
719C23—274no—
720C23—271no—
721C2×C4—32no—
722C2×C4—32no—
723C2×C4—31no—
724C2×C4—62no—
725C2×C4—94no—
726C2×C4—98no—
727C2×C4—92no—
728C2×C4—91no—
729C2×C4—92no—
730C2×C4—182no—
731C2×C4—182no—
732C2×C4—184no—
733C2×C4—278no—
734C2×C4—274no—
735C2×C4—271no—
736C2×C4—542no—
737C2×C4—542no—
738C2×C4—544no—
739C2×C4—542no—
740C2×C4—542no—
741C2×C4—542no—
742C2×C4D3311yescharacteristic
743C2×C3—21no—
744C2×C3—22no—
745C2×C3—22no—
746C2×C3—21no—
747C2×C3—21no—
748C2×C3—22no—
749C2×C3—38no—
750C2×C3—41no—
751C2×C3—41no—
752C2×C3—41no—
753C2×C3—64no—
754C2×C3—94no—
755C2×C3C2×#379711yescharacteristic
756C2×C3C2×C4×D3212yes—
757C2×C3C2×C4×D3211yescharacteristic
758C2×C3D32×D412yes—
759C2×C3D32×Q812yes—
760C2×C3C2×#381111yescharacteristic
761D3—38no—
762D3—64no—
763D3—98no—
764D3—94no—
765D3—184no—
766D3—188no—
767D3—364no—
768D3#6388314yesdirect product factor
769C22—32no—
770C22—32no—
771C22—32no—
772C22—92no—
773C22—92no—
774C22—92no—
775C22—2716no—
776C22—272no—
777C22—272no—
778C22—272no—
779C22C2×D3311yescharacteristic
780C4—21no—
781C4—34no—
782C4—61no—
783C4—62no—
784C4—94no—
785C4—181no—
786C4—182no—
787C4—541no—
788C3—21no—
789C3—22no—
790C3—41no—
791C3D32×C4⋊C412yescomplemented
792C3C2×#6388311yescharacteristic, complemented
793C2—34no—
794C2—94no—
795C2—274no—
796C2D3×#379711yescharacteristic
797C2C4×D3311yescharacteristic
798C2D3×#381111yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutatorC2×C33C23×C4
FittingC2×C33×C4C23
socle, cosocleC22×C33C24
prime radicalC22×D3×C3⋊D3C22
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. #11723470C2semidirect
6. C3×#63883C2semidirect
7. C3×D3×Dic3⋊C4C2semidirect
8. #11722912C2semidirect
9. #11722910C2semidirect
10. #11722908C2semidirect
11. D3×Dic3⋊Dic3C2semidirect
31. D3×#624C4semidirect
32. C3×#3750C22semidirect
33. C32×Dic3⋊C4C22semidirect
34. #88815C22semidirect
35. #88807C22semidirect
36. Dic3⋊(C3⋊Dic3)C22semidirect
37. C3×#3724C22semidirect
38. C3×Dic3⋊Dic3C22semidirect
39. C3×Dic3⋊Dic3C22semidirect
63. #63883D3direct (N × H)
67. D3×Dic3⋊C4D3semidirect
86. #6294C2×C4semidirect
89. #6289C2×C4semidirect
93. C3×#624C2×C4semidirect
95. C3×D3×Dic3C2×C4semidirect
153. #3750C2×D3semidirect
164. C3×Dic3⋊C4C2×D3semidirect
165. C3×Dic3⋊C4C2×D3semidirect
167. #3724C2×D3semidirect
176. Dic3⋊Dic3C2×D3semidirect
177. Dic3⋊Dic3C2×D3semidirect
188. D3×C3⋊D3C4⋊C4semidirect
193. C3×C3⋊Dic3C22×C4semidirect
196. C32×Dic3C22×C4semidirect
310. #624C4×D3semidirect
318. D3×Dic3C4×D3semidirect
323. C3⋊(C3⋊D3)C2×C4⋊C4semidirect
324. C3×C3⋊D3C2×C4⋊C4semidirect
325. C32×D3C2×C4⋊C4semidirect
405. Dic3⋊C4D32semidirect
462. C3⋊Dic3C2×C4×D3semidirect
477. C3×Dic3C2×C4×D3semidirect
478. C3×Dic3C2×C4×D3semidirect
490. C33C22×C4⋊C4semidirect
606. C3⋊D3D3×C4⋊C4semidirect
610. C3×D3D3×C4⋊C4semidirect
709. Dic3C4×D32semidirect
713. C32C2×D3×C4⋊C4semidirect
714. C32C2×D3×C4⋊C4semidirect
768. D3#63883direct (N × H)
791. C3D32×C4⋊C4semidirect
792. C3C2×#63883semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D3×C3⋊D32
C2×D3×#6242
#117236822
#117234702
C3×#638832
C3×D3×Dic3⋊C42
#117229122
#117229102
#117229082
D3×Dic3⋊Dic32
C2×#638833
D32×C4⋊C43