Finite Group Databasebeta

← D3×#63877 #13170702

Subgroups — D3×#63877 #13170702

Order 1728.

1590 conjugacy classes of subgroups.

The subgroup lattice has 1094 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D32×Dic3C211yesmaximal, characteristic
2#11723683C211yesmaximal, characteristic, complemented
3#11723464C211yesmaximal, characteristic, complemented
4#11723459C211yesmaximal, characteristic, complemented
5D3×#3750C211yesmaximal, characteristic, complemented
6C3×D3×(C2×D3)⋊C4C211yesmaximal, characteristic
7C3×#63877C211yesmaximal, characteristic, complemented
8C3×C4×D3×Dic3C211yesmaximal, characteristic, complemented
9#11722922C211yesmaximal, characteristic, complemented
10#11722919C211yesmaximal, characteristic, complemented
11#11722916C211yesmaximal, characteristic, complemented
12#11722913C211yesmaximal, characteristic, complemented
13D3×#3724C211yesmaximal, characteristic, complemented
14D3×(C2×D3)⋊Dic3C211yesmaximal, characteristic
15D3×Dic32C211yesmaximal, characteristic, complemented
16C2×#63877—31nomaximal
17D3×#877—31nomaximal
18D3×#872—31nomaximal
19C22×C3×D32C2211yescharacteristic
20C2×C32×C4×D3C2211yescharacteristic
21C2×#6294C2211yescharacteristic
22C2×Dic3×C3⋊D3C2211yescharacteristic
23C2×D3×C3⋊Dic3C2211yescharacteristic
24C2×D3×C3⋊Dic3C2211yescharacteristic
25C2×D3×C3⋊Dic3C2211yescharacteristic
26C2×C3×D3×Dic3C2211yescharacteristic
27C2×C3×D3×Dic3C2211yescharacteristic
28C2×C3×D3×Dic3C2211yescharacteristic
29C2×C3×D3×Dic3C2211yescharacteristic
30D32×Dic3C418yescomplemented
31#88857C2211yescharacteristic, complemented
32C3×#3752C2211yescharacteristic
33C3×#3750C2211yescharacteristic, complemented
34C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
35C32×(C2×D3)⋊C4C2211yescharacteristic
36C32×C4×Dic3C2211yescharacteristic, complemented
37#88815C2211yescharacteristic, complemented
38#88814C2211yescharacteristic
39#88813C2211yescharacteristic, complemented
40#88807C2211yescharacteristic, complemented
41#88806C2211yescharacteristic, complemented
42#88806C2211yescharacteristic, complemented
43#88806C2211yescharacteristic, complemented
44#88803C2211yescharacteristic
45(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
46Dic3×C3⋊Dic3C2211yescharacteristic, complemented
47Dic3×C3⋊Dic3C2211yescharacteristic, complemented
48C3×#3724C2211yescharacteristic, complemented
49C3×#3722C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×Dic32C2211yescharacteristic, complemented
53C3×Dic32C2211yescharacteristic, complemented
54C3×Dic32C2211yescharacteristic, complemented
55C22×D3×Dic3—31no—
56C22×D3×Dic3—31no—
57C2×C4×D32—31no—
58C2×#3750—31no—
59#64086—31no—
60#64081—31no—
61C2×C3×(C2×D3)⋊C4—31no—
62C2×C3×C4×Dic3—31no—
63C3×D3×C22⋊C4—31no—
64C3×#877—31no—
65C3×#872—31no—
66C3×C42×D3—31no—
67D3×#217—31no—
68C2×#3724—31no—
69C2×(C2×D3)⋊Dic3—31no—
70#63957—31no—
71#63955—31no—
72C2×Dic32—31no—
73D3×(C2×D3)⋊C4—31no—
74D3×(C2×D3)⋊C4D311yescharacteristic
75#63878—31no—
76#63878—31no—
77#63877—31no—
78#63877—31no—
79#63877—31no—
80#63877—31no—
81#63877—31no—
82#63877—31no—
83#63877—31no—
84#63877—31no—
85#63877—31no—
86#63877—31no—
87#63877—31no—
88#63877—61no—
89#63877—61no—
90#63877D311yescharacteristic, direct product factor
91D3×Dic3⋊C4—31no—
92D3×Dic3⋊C4—31no—
93D3×Dic3⋊C4—31no—
94D3×Dic3⋊C4—31no—
95D3×Dic3⋊C4—61no—
96C4×D3×Dic3—31no—
97C4×D3×Dic3—31no—
98C4×D3×Dic3D311yescharacteristic, complemented
99#63874—31no—
100#63855—31no—
101#63836—31no—
102#63836—31no—
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C32×D3C2311yescharacteristic
105C22×C32×D3C2311yescharacteristic
106C2×C3×D32—22no—
107C2×C3×D32—22no—
108C2×C3×D32C2×C414yes—
109C2×C33×C4C2311yescharacteristic
110C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
111C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C32×C4×D3—22no—
122#6294C2×C414yescomplemented
123Dic3×C3⋊D3C2×C414yescomplemented
124D3×C3⋊Dic3—22no—
125D3×C3⋊Dic3C2×C414yes—
126D3×C3⋊Dic3C2×C414yescomplemented
127C3×D3×Dic3—22no—
128C3×D3×Dic3—22no—
129C3×D3×Dic3C2×C414yes—
130C3×D3×Dic3C2×C414yescomplemented
131D3×#117—91no—
132C2×#877—91no—
133C2×#872—91no—
134C23×C3×D3—31no—
135C23×C3×D3—31no—
136C22×D32C2×D311yescharacteristic
137C22×C32×C4—31no—
138C22×C3⋊Dic3—31no—
139C22×C3⋊Dic3—31no—
140C22×C3⋊Dic3—31no—
141C2×C4×C3⋊D3—31no—
142C22×C3×Dic3—31no—
143C22×C3×Dic3—31no—
144C22×C3×Dic3—31no—
145C22×C3×Dic3—31no—
146C2×C3×C4×D3—21no—
147C2×C3×C4×D3—31no—
148C2×C3×C4×D3—31no—
149C2×C3×C4×D3—31no—
150C2×C3×C4×D3—31no—
151C2×C3×C4×D3C2×D311yescharacteristic
152C2×C3×C4×D3C2×D311yescharacteristic
153C2×#624—31no—
154C2×D3×Dic3—31no—
155C2×D3×Dic3—31no—
156C2×D3×Dic3—31no—
157C2×D3×Dic3—31no—
158C2×D3×Dic3—31no—
159C2×D3×Dic3—31no—
160C2×D3×Dic3—31no—
161C2×D3×Dic3—31no—
162C2×D3×Dic3—38no—
163C2×D3×Dic3—38no—
164C2×D3×Dic3—31no—
165C2×D3×Dic3—31no—
166C2×D3×Dic3—61no—
167C2×D3×Dic3—61no—
168C2×D3×Dic3—61no—
169C2×D3×Dic3—61no—
170C2×D3×Dic3C2×D311yescharacteristic
171C2×D3×Dic3C2×D311yescharacteristic
172C2×D3×Dic3C2×D311yescharacteristic
173C2×D3×Dic3C2×D311yescharacteristic
174C4×D32—38no—
175C32×C22⋊C4—31no—
176C32×C42—31no—
177#3757—31no—
178#3752—31no—
179#3752C2×D311yescharacteristic
180#3750—31no—
181#3750—31no—
182#3750—31no—
183#3750—31no—
184#3750—31no—
185#3750—31no—
186#3750—31no—
187#3750—61no—
188#3750—61no—
189#3750—61no—
190#3750—121no—
191#3750C2×D311yescharacteristic, complemented
192C4×C3⋊Dic3—31no—
193C4×C3⋊Dic3—31no—
194C4×C3⋊Dic3C2×D311yescharacteristic, complemented
195C3×#217—31no—
196C3×#217—31no—
197C3×(C2×D3)⋊C4—21no—
198C3×(C2×D3)⋊C4—31no—
199C3×(C2×D3)⋊C4—31no—
200C3×(C2×D3)⋊C4—31no—
201C3×(C2×D3)⋊C4—31no—
202C3×(C2×D3)⋊C4—31no—
203C3×(C2×D3)⋊C4—31no—
204C3×(C2×D3)⋊C4—61no—
205C3×(C2×D3)⋊C4C2×D311yescharacteristic
206C3×(C2×D3)⋊C4C2×D311yescharacteristic
207C3×Dic3⋊C4—31no—
208C3×Dic3⋊C4—31no—
209C3×Dic3⋊C4—31no—
210C3×Dic3⋊C4—31no—
211C3×Dic3⋊C4—61no—
212C3×C4×Dic3—21no—
213C3×C4×Dic3—31no—
214C3×C4×Dic3—31no—
215C3×C4×Dic3—31no—
216C3×C4×Dic3—31no—
217C3×C4×Dic3—31no—
218C3×C4×Dic3—31no—
219C3×C4×Dic3—31no—
220C3×C4×Dic3—31no—
221C3×C4×Dic3—61no—
222C3×C4×Dic3C2×D311yescharacteristic, complemented
223C3×C4×Dic3C2×D311yescharacteristic, complemented
224#3724—31no—
225#3724—31no—
226#3724—31no—
227#3724—31no—
228#3724—31no—
229#3724—31no—
230#3724—31no—
231#3724—61no—
232#3724—61no—
233#3724—61no—
234#3724C2×D311yescharacteristic, complemented
235Dic3⋊Dic3—31no—
236Dic3⋊Dic3—31no—
237Dic3⋊Dic3—31no—
238Dic3⋊Dic3—31no—
239Dic3⋊Dic3—61no—
240#3722—31no—
241#3722C2×D311yescharacteristic
242(C2×D3)⋊Dic3—31no—
243(C2×D3)⋊Dic3—31no—
244(C2×D3)⋊Dic3—31no—
245(C2×D3)⋊Dic3—31no—
246(C2×D3)⋊Dic3—31no—
247(C2×D3)⋊Dic3—31no—
248(C2×D3)⋊Dic3—61no—
249(C2×D3)⋊Dic3—61no—
250(C2×D3)⋊Dic3C2×D311yescharacteristic
251(C2×D3)⋊Dic3C2×D311yescharacteristic
252Dic32—31no—
253Dic32—31no—
254Dic32—31no—
255Dic32—31no—
256Dic32—31no—
257Dic32—31no—
258Dic32—31no—
259Dic32—61no—
260Dic32—61no—
261Dic32C2×D311yescharacteristic, complemented
262Dic32C2×D311yescharacteristic, complemented
263Dic32C2×D311yescharacteristic, complemented
264C22×C33C2411yescharacteristic
265C2×C3×C3⋊D3—21no—
266C2×C3×C3⋊D3—21no—
267C2×C3×C3⋊D3C22×C412yes—
268C2×C32×D3—21no—
269C2×C32×D3—21no—
270C2×C32×D3C22×C412yes—
271C2×C32×D3C22×C412yes—
272C2×C32×D3#4112yes—
273C2×C32×D3#4112yes—
274C3×D32—28no—
275C33×C4—21no—
276C3⋊(C3⋊Dic3)—21no—
277C3⋊(C3⋊Dic3)C22×C412yes—
278C3×C3⋊Dic3—21no—
279C3×C3⋊Dic3—21no—
280C3×C3⋊Dic3—21no—
281C3×C3⋊Dic3C22×C412yes—
282C3×C3⋊Dic3C22×C412yes—
283C32×Dic3—21no—
284C32×Dic3—21no—
285C32×Dic3—21no—
286C32×Dic3C22×C412yes—
287C23×Dic3—91no—
288C22×C4×D3—91no—
289C22×C4×D3—91no—
290C3×#117—91no—
291C2×C3×C22⋊C4—91no—
292C2×C3×C42—91no—
293C2×#217—91no—
294C2×(C2×D3)⋊C4—31no—
295C2×(C2×D3)⋊C4—91no—
296#926—91no—
297C2×Dic3⋊C4—91no—
298C2×Dic3⋊C4—91no—
299C2×Dic3⋊C4—91no—
300C2×Dic3⋊C4—91no—
301C2×Dic3⋊C4—181no—
302C2×C4×Dic3—31no—
303C2×C4×Dic3—91no—
304C2×C4×Dic3—91no—
305#892—91no—
306#892—91no—
307D3×C4⋊C4—91no—
308D3×C4⋊C4—91no—
309D3×C22⋊C4—31no—
310D3×C22⋊C4—91no—
311#877—31no—
312#877—91no—
313#877—91no—
314#877—91no—
315#877—91no—
316#877—91no—
317#877—91no—
318#877—91no—
319#877—91no—
320#877—91no—
321#877—181no—
322#872—31no—
323#872—91no—
324#872—91no—
325#872—91no—
326#872—91no—
327#872—91no—
328#872—91no—
329#872—91no—
330#872—91no—
331#872—91no—
332#872—181no—
333C42×D3—31no—
334C42×D3—91no—
335C23×C32—31no—
336C23×C32—31no—
337C22×C3⋊D3C22×D311yescharacteristic
338C22×C3×D3—21no—
339C22×C3×D3—21no—
340C22×C3×D3—31no—
341C22×C3×D3—31no—
342C22×C3×D3—34no—
343C22×C3×D3—34no—
344C22×C3×D3—61no—
345C22×C3×D3—62no—
346C22×C3×D3—62no—
347C22×C3×D3—62no—
348C22×C3×D3—62no—
349C22×C3×D3C22×D311yescharacteristic
350C22×C3×D3C22×D311yescharacteristic
351C22×C3×D3C22×D311yescharacteristic
352C22×C3×D3C22×D311yescharacteristic
353C2×D32—22no—
354C2×D32—22no—
355C2×D32C4×D314yes—
356C2×C32×C4—21no—
357C2×C32×C4—21no—
358C2×C32×C4—21no—
359C2×C32×C4—31no—
360C2×C32×C4—31no—
361C2×C32×C4—31no—
362C2×C32×C4—31no—
363C2×C32×C4—41no—
364C2×C32×C4—62no—
365C2×C32×C4C22×D311yescharacteristic
366C2×C32×C4C22×D311yescharacteristic
367C2×C32×C4C22×D311yescharacteristic
368C2×C3⋊Dic3—31no—
369C2×C3⋊Dic3—31no—
370C2×C3⋊Dic3—31no—
371C2×C3⋊Dic3—34no—
372C2×C3⋊Dic3—34no—
373C2×C3⋊Dic3—31no—
374C2×C3⋊Dic3—31no—
375C2×C3⋊Dic3—31no—
376C2×C3⋊Dic3—61no—
377C2×C3⋊Dic3—61no—
378C2×C3⋊Dic3—61no—
379C2×C3⋊Dic3—61no—
380C2×C3⋊Dic3—61no—
381C2×C3⋊Dic3—61no—
382C2×C3⋊Dic3—62no—
383C2×C3⋊Dic3—121no—
384C2×C3⋊Dic3—121no—
385C2×C3⋊Dic3C22×D311yescharacteristic
386C2×C3⋊Dic3C22×D311yescharacteristic
387C2×C3⋊Dic3C22×D311yescharacteristic
388C2×C3⋊Dic3C22×D311yescharacteristic
389C2×C3⋊Dic3C22×D311yescharacteristic
390C4×C3⋊D3—34no—
391C2×C3×Dic3—21no—
392C2×C3×Dic3—21no—
393C2×C3×Dic3—21no—
394C2×C3×Dic3—21no—
395C2×C3×Dic3—31no—
396C2×C3×Dic3—31no—
397C2×C3×Dic3—31no—
398C2×C3×Dic3—31no—
399C2×C3×Dic3—34no—
400C2×C3×Dic3—34no—
401C2×C3×Dic3—31no—
402C2×C3×Dic3—31no—
403C2×C3×Dic3—31no—
404C2×C3×Dic3—31no—
405C2×C3×Dic3—31no—
406C2×C3×Dic3—31no—
407C2×C3×Dic3—61no—
408C2×C3×Dic3—61no—
409C2×C3×Dic3—61no—
410C2×C3×Dic3—61no—
411C2×C3×Dic3—61no—
412C2×C3×Dic3—62no—
413C2×C3×Dic3—62no—
414C2×C3×Dic3C22×D311yescharacteristic
415C2×C3×Dic3C22×D311yescharacteristic
416C2×C3×Dic3C22×D311yescharacteristic
417C2×C3×Dic3C22×D311yescharacteristic
418C2×C3×Dic3C22×D311yescharacteristic
419C2×C3×Dic3C22×D311yescharacteristic
420C2×C3×Dic3C22×D311yescharacteristic
421C2×C3×Dic3C22×D311yescharacteristic
422C3×C4×D3—22no—
423C3×C4×D3—22no—
424C3×C4×D3—34no—
425C3×C4×D3—34no—
426C3×C4×D3—42no—
427C3×C4×D3—62no—
428C3×C4×D3—62no—
429#624—34no—
430D3×Dic3—22no—
431D3×Dic3—22no—
432D3×Dic3—34no—
433D3×Dic3—34no—
434D3×Dic3—34no—
435D3×Dic3—34no—
436D3×Dic3—34no—
437D3×Dic3—34no—
438D3×Dic3—34no—
439D3×Dic3—34no—
440D3×Dic3—64no—
441D3×Dic3—64no—
442D3×Dic3—64no—
443D3×Dic3—62no—
444D3×Dic3—62no—
445D3×Dic3—122no—
446D3×Dic3C4×D314yes—
447D3×Dic3C4×D314yescomplemented
448C2×#117—271noSylow
449C2×C33C23×C411yescharacteristic
450C2×C33C2×#4111yescharacteristic
451C2×C33C2×#4111yescharacteristic
452C3×C3⋊D3—22no—
453C32×D3—22no—
454C32×D3#11714yescomplemented
455C24×C3—91no—
456C23×D3—31no—
457C23×D3—31no—
458C22×C3×C4—31no—
459C22×C3×C4—31no—
460C22×C3×C4—61no—
461C22×C3×C4—91no—
462C22×C3×C4—91no—
463C22×C3×C4—91no—
464C22×C3×C4—91no—
465C22×Dic3—31no—
466C22×Dic3—31no—
467C22×Dic3—31no—
468C22×Dic3—31no—
469C22×Dic3—91no—
470C22×Dic3—98no—
471C22×Dic3—91no—
472C22×Dic3—91no—
473C22×Dic3—91no—
474C22×Dic3—91no—
475C22×Dic3—91no—
476C22×Dic3—91no—
477C22×Dic3—91no—
478C22×Dic3—181no—
479C22×Dic3—181no—
480C22×Dic3—181no—
481C2×C4×D3—31no—
482C2×C4×D3—31no—
483C2×C4×D3—31no—
484C2×C4×D3—31no—
485C2×C4×D3—98no—
486C2×C4×D3—98no—
487C2×C4×D3—91no—
488C2×C4×D3—91no—
489C2×C4×D3—91no—
490C2×C4×D3—91no—
491C2×C4×D3—91no—
492C2×C4×D3—91no—
493C2×C4×D3—91no—
494C2×C4×D3—181no—
495C2×C4×D3D3211yescharacteristic
496C3×C4⋊C4—91no—
497C3×C4⋊C4—91no—
498C3×C22⋊C4—31no—
499C3×C22⋊C4—31no—
500C3×C22⋊C4—61no—
501C3×C22⋊C4—91no—
502C3×C22⋊C4—91no—
503C3×C22⋊C4—91no—
504C3×C22⋊C4—91no—
505C3×C42—31no—
506C3×C42—31no—
507C3×C42—61no—
508C3×C42—91no—
509C3×C42—91no—
510C3×C42—91no—
511C3×C42—91no—
512#217—31no—
513#217—31no—
514#217—91no—
515#217—91no—
516#217—91no—
517#217—91no—
518#217—181no—
519(C2×D3)⋊C4—31no—
520(C2×D3)⋊C4—31no—
521(C2×D3)⋊C4—31no—
522(C2×D3)⋊C4—31no—
523(C2×D3)⋊C4—31no—
524(C2×D3)⋊C4—31no—
525(C2×D3)⋊C4—61no—
526(C2×D3)⋊C4—91no—
527(C2×D3)⋊C4—91no—
528(C2×D3)⋊C4—91no—
529(C2×D3)⋊C4—91no—
530(C2×D3)⋊C4—91no—
531(C2×D3)⋊C4—181no—
532(C2×D3)⋊C4D3211yescharacteristic
533C4⋊Dic3—91no—
534C4⋊Dic3—91no—
535Dic3⋊C4—31no—
536Dic3⋊C4—31no—
537Dic3⋊C4—31no—
538Dic3⋊C4—31no—
539Dic3⋊C4—61no—
540Dic3⋊C4—91no—
541Dic3⋊C4—91no—
542Dic3⋊C4—91no—
543Dic3⋊C4—91no—
544Dic3⋊C4—91no—
545Dic3⋊C4—91no—
546Dic3⋊C4—91no—
547Dic3⋊C4—91no—
548Dic3⋊C4—91no—
549Dic3⋊C4—91no—
550Dic3⋊C4—91no—
551Dic3⋊C4—91no—
552Dic3⋊C4—91no—
553Dic3⋊C4—91no—
554Dic3⋊C4—91no—
555Dic3⋊C4—91no—
556Dic3⋊C4—181no—
557Dic3⋊C4—181no—
558Dic3⋊C4—181no—
559Dic3⋊C4—181no—
560Dic3⋊C4—181no—
561Dic3⋊C4—181no—
562Dic3⋊C4—181no—
563Dic3⋊C4—361no—
564C4×Dic3—31no—
565C4×Dic3—31no—
566C4×Dic3—31no—
567C4×Dic3—31no—
568C4×Dic3—31no—
569C4×Dic3—31no—
570C4×Dic3—31no—
571C4×Dic3—31no—
572C4×Dic3—61no—
573C4×Dic3—91no—
574C4×Dic3—91no—
575C4×Dic3—91no—
576C4×Dic3—91no—
577C4×Dic3—91no—
578C4×Dic3—91no—
579C4×Dic3—91no—
580C4×Dic3—91no—
581C4×Dic3—91no—
582C4×Dic3—181no—
583C4×Dic3—181no—
584C4×Dic3D3211yescharacteristic, complemented
585C22×C32—21no—
586C22×C32—21no—
587C22×C32—21no—
588C22×C32—32no—
589C22×C32—32no—
590C22×C32—32no—
591C22×C32—32no—
592C22×C32—41no—
593C22×C32—61no—
594C22×C32—61no—
595C22×C32C23×D311yescharacteristic
596C22×C32C23×D311yescharacteristic
597C22×C32C23×D311yescharacteristic
598C2×C3⋊D3—21no—
599C2×C3⋊D3—21no—
600C2×C3⋊D3C2×C4×D312yes—
601C2×C3×D3—21no—
602C2×C3×D3—21no—
603C2×C3×D3—21no—
604C2×C3×D3—21no—
605C2×C3×D3—22no—
606C2×C3×D3—22no—
607C2×C3×D3—22no—
608C2×C3×D3—22no—
609C2×C3×D3—32no—
610C2×C3×D3—32no—
611C2×C3×D3—41no—
612C2×C3×D3—41no—
613C2×C3×D3—62no—
614C2×C3×D3—68no—
615C2×C3×D3—61no—
616C2×C3×D3—61no—
617C2×C3×D3—61no—
618C2×C3×D3—61no—
619C2×C3×D3—68no—
620C2×C3×D3—121no—
621C2×C3×D3—121no—
622C2×C3×D3C2×C4×D312yes—
623C2×C3×D3C2×C4×D312yes—
624C2×C3×D3C2×C4×D312yes—
625C2×C3×D3C2×C4×D312yes—
626C2×C3×D3#23512yes—
627C2×C3×D3#23512yes—
628C2×C3×D3#23712yes—
629C2×C3×D3#23712yes—
630D32—28no—
631C32×C4—21no—
632C32×C4—21no—
633C32×C4—21no—
634C32×C4—32no—
635C32×C4—41no—
636C32×C4—41no—
637C32×C4—41no—
638C32×C4—61no—
639C32×C4—61no—
640C32×C4—61no—
641C32×C4—81no—
642C3⋊Dic3—21no—
643C3⋊Dic3—21no—
644C3⋊Dic3—21no—
645C3⋊Dic3—32no—
646C3⋊Dic3—32no—
647C3⋊Dic3—32no—
648C3⋊Dic3—62no—
649C3⋊Dic3—62no—
650C3⋊Dic3—62no—
651C3⋊Dic3—61no—
652C3⋊Dic3—61no—
653C3⋊Dic3—61no—
654C3⋊Dic3—122no—
655C3⋊Dic3—121no—
656C3⋊Dic3—121no—
657C3⋊Dic3—121no—
658C3⋊Dic3—241no—
659C3⋊Dic3C2×C4×D312yes—
660C3⋊Dic3C2×C4×D312yes—
661C3×Dic3—21no—
662C3×Dic3—21no—
663C3×Dic3—21no—
664C3×Dic3—21no—
665C3×Dic3—21no—
666C3×Dic3—21no—
667C3×Dic3—22no—
668C3×Dic3—32no—
669C3×Dic3—32no—
670C3×Dic3—32no—
671C3×Dic3—32no—
672C3×Dic3—41no—
673C3×Dic3—41no—
674C3×Dic3—41no—
675C3×Dic3—62no—
676C3×Dic3—62no—
677C3×Dic3—61no—
678C3×Dic3—61no—
679C3×Dic3—61no—
680C3×Dic3—61no—
681C3×Dic3—61no—
682C3×Dic3—61no—
683C3×Dic3—121no—
684C3×Dic3—121no—
685C3×Dic3—121no—
686C3×Dic3C2×C4×D312yes—
687C3×Dic3C2×C4×D312yes—
688C23×C4—271no—
689#117—91no—
690#117—271no—
691#117—271no—
692#117—271no—
693#117—271no—
694#117—271no—
695#117—271no—
696#117—271no—
697C2×C4⋊C4—271no—
698C2×C4⋊C4—271no—
699C2×C22⋊C4—91no—
700C2×C22⋊C4—271no—
701C2×C42—91no—
702C2×C42—271no—
703C33C2×#11711yescharacteristic, complemented, Sylow
704C23×C3—31no—
705C23×C3—31no—
706C23×C3—31no—
707C23×C3—31no—
708C23×C3—61no—
709C23×C3—61no—
710C23×C3—94no—
711C23×C3—91no—
712C23×C3—182no—
713C23×C3—182no—
714C22×D3—31no—
715C22×D3—31no—
716C22×D3—34no—
717C22×D3—34no—
718C22×D3—61no—
719C22×D3—62no—
720C22×D3—62no—
721C22×D3—62no—
722C22×D3—62no—
723C22×D3C2×D3211yescharacteristic
724C22×D3C2×D3211yescharacteristic
725C2×C3×C4—21no—
726C2×C3×C4—21no—
727C2×C3×C4—21no—
728C2×C3×C4—31no—
729C2×C3×C4—31no—
730C2×C3×C4—31no—
731C2×C3×C4—31no—
732C2×C3×C4—31no—
733C2×C3×C4—31no—
734C2×C3×C4—31no—
735C2×C3×C4—31no—
736C2×C3×C4—41no—
737C2×C3×C4—61no—
738C2×C3×C4—61no—
739C2×C3×C4—61no—
740C2×C3×C4—61no—
741C2×C3×C4—62no—
742C2×C3×C4—62no—
743C2×C3×C4—94no—
744C2×C3×C4—94no—
745C2×C3×C4—91no—
746C2×C3×C4—91no—
747C2×C3×C4—91no—
748C2×C3×C4—91no—
749C2×C3×C4—91no—
750C2×C3×C4—122no—
751C2×C3×C4—182no—
752C2×C3×C4—182no—
753C2×C3×C4C2×D3211yescharacteristic
754C2×C3×C4C2×D3211yescharacteristic
755C2×C3×C4C2×D3211yescharacteristic
756C2×Dic3—31no—
757C2×Dic3—31no—
758C2×Dic3—31no—
759C2×Dic3—31no—
760C2×Dic3—34no—
761C2×Dic3—34no—
762C2×Dic3—31no—
763C2×Dic3—31no—
764C2×Dic3—31no—
765C2×Dic3—31no—
766C2×Dic3—31no—
767C2×Dic3—31no—
768C2×Dic3—61no—
769C2×Dic3—61no—
770C2×Dic3—61no—
771C2×Dic3—61no—
772C2×Dic3—61no—
773C2×Dic3—62no—
774C2×Dic3—62no—
775C2×Dic3—94no—
776C2×Dic3—94no—
777C2×Dic3—94no—
778C2×Dic3—94no—
779C2×Dic3—94no—
780C2×Dic3—91no—
781C2×Dic3—91no—
782C2×Dic3—91no—
783C2×Dic3—94no—
784C2×Dic3—91no—
785C2×Dic3—91no—
786C2×Dic3—91no—
787C2×Dic3—184no—
788C2×Dic3—184no—
789C2×Dic3—181no—
790C2×Dic3—181no—
791C2×Dic3—181no—
792C2×Dic3—181no—
793C2×Dic3—181no—
794C2×Dic3—181no—
795C2×Dic3—182no—
796C2×Dic3—182no—
797C2×Dic3—361no—
798C2×Dic3—361no—
799C2×Dic3—362no—
800C2×Dic3C2×D3211yescharacteristic
801C2×Dic3C2×D3211yescharacteristic
802C2×Dic3C2×D3211yescharacteristic
803C2×Dic3C2×D3211yescharacteristic
804C4×D3—22no—
805C4×D3—34no—
806C4×D3—34no—
807C4×D3—62no—
808C4×D3—62no—
809C4×D3—94no—
810C4×D3—94no—
811C4×D3—94no—
812C4×D3—94no—
813C4×D3—94no—
814C4×D3—94no—
815C4×D3—184no—
816C4×D3—182no—
817C2×C32—21no—
818C2×C32—21no—
819C2×C32—21no—
820C2×C32—21no—
821C2×C32—21no—
822C2×C32—21no—
823C2×C32—21no—
824C2×C32—21no—
825C2×C32—21no—
826C2×C32—34no—
827C2×C32—41no—
828C2×C32—41no—
829C2×C32—41no—
830C2×C32—62no—
831C2×C32C22×C4×D311yescharacteristic
832C2×C32C22×C4×D311yescharacteristic
833C2×C32C22×C4×D311yescharacteristic
834C2×C32C2×#23511yescharacteristic
835C2×C32C2×#23511yescharacteristic
836C2×C32C2×#23711yescharacteristic
837C2×C32C2×#23711yescharacteristic
838C2×C32D3×#4111yescharacteristic
839C2×C32D3×#4111yescharacteristic
840C3⋊D3—22no—
841C3×D3—22no—
842C3×D3—22no—
843C3×D3—24no—
844C3×D3—42no—
845C3×D3—62no—
846C3×D3—62no—
847C3×D3—122no—
848C3×D3#87214yescomplemented
849C3×D3#87714yescomplemented
850C24—91no—
851C22×C4—31no—
852C22×C4—91no—
853C22×C4—91no—
854C22×C4—91no—
855C22×C4—91no—
856C22×C4—271no—
857C22×C4—271no—
858C22×C4—278no—
859C22×C4—271no—
860C22×C4—271no—
861C22×C4—271no—
862C4⋊C4—91no—
863C4⋊C4—91no—
864C4⋊C4—271no—
865C4⋊C4—271no—
866C4⋊C4—271no—
867C4⋊C4—271no—
868C4⋊C4—271no—
869C4⋊C4—271no—
870C22⋊C4—31no—
871C22⋊C4—91no—
872C22⋊C4—91no—
873C22⋊C4—91no—
874C22⋊C4—91no—
875C22⋊C4—271no—
876C22⋊C4—271no—
877C22⋊C4—271no—
878C42—31no—
879C42—91no—
880C42—91no—
881C42—91no—
882C42—91no—
883C42—271no—
884C42—271no—
885C42—271no—
886C22×C3—21no—
887C22×C3—21no—
888C22×C3—21no—
889C22×C3—32no—
890C22×C3—32no—
891C22×C3—32no—
892C22×C3—32no—
893C22×C3—32no—
894C22×C3—32no—
895C22×C3—32no—
896C22×C3—32no—
897C22×C3—41no—
898C22×C3—62no—
899C22×C3—62no—
900C22×C3—62no—
901C22×C3—62no—
902C22×C3—61no—
903C22×C3—61no—
904C22×C3—61no—
905C22×C3—61no—
906C22×C3—92no—
907C22×C3—121no—
908C22×C3—121no—
909C22×C3—188no—
910C22×C3—181no—
911C22×C3—181no—
912C22×C3C22×D3211yescharacteristic
913C22×C3C22×D3211yescharacteristic
914C22×C3C22×D3211yescharacteristic
915C2×D3—21no—
916C2×D3—21no—
917C2×D3—32no—
918C2×D3—32no—
919C2×D3—62no—
920C2×D3—68no—
921C2×D3—61no—
922C2×D3—61no—
923C2×D3—61no—
924C2×D3—61no—
925C2×D3—68no—
926C2×D3—121no—
927C2×D3—121no—
928C2×D3#379512yes—
929C2×D3C4×D3212yes—
930C2×D3C4×D3212yes—
931C2×D3#380412yes—
932C3×C4—21no—
933C3×C4—21no—
934C3×C4—21no—
935C3×C4—32no—
936C3×C4—32no—
937C3×C4—41no—
938C3×C4—41no—
939C3×C4—41no—
940C3×C4—62no—
941C3×C4—61no—
942C3×C4—61no—
943C3×C4—61no—
944C3×C4—61no—
945C3×C4—61no—
946C3×C4—61no—
947C3×C4—81no—
948C3×C4—92no—
949C3×C4—92no—
950C3×C4—121no—
951C3×C4—121no—
952C3×C4—121no—
953C3×C4—181no—
954C3×C4—181no—
955C3×C4—181no—
956Dic3—21no—
957Dic3—21no—
958Dic3—21no—
959Dic3—32no—
960Dic3—32no—
961Dic3—32no—
962Dic3—32no—
963Dic3—62no—
964Dic3—62no—
965Dic3—61no—
966Dic3—61no—
967Dic3—61no—
968Dic3—61no—
969Dic3—61no—
970Dic3—61no—
971Dic3—92no—
972Dic3—92no—
973Dic3—92no—
974Dic3—121no—
975Dic3—121no—
976Dic3—121no—
977Dic3—182no—
978Dic3—182no—
979Dic3—182no—
980Dic3—181no—
981Dic3—181no—
982Dic3—181no—
983Dic3—362no—
984Dic3—361no—
985Dic3—361no—
986Dic3—361no—
987Dic3—721no—
988Dic3C4×D3212yes—
989C32—21no—
990C32—21no—
991C32—21no—
992C32—41no—
993C32C2×#87211yescharacteristic, complemented
994C32C2×#87711yescharacteristic, complemented
995C32D3×#11711yescharacteristic, complemented
996C23—31no—
997C23—31no—
998C23—94no—
999C23—91no—
1000C23—182no—
1001C23—182no—
1002C2×C4—31no—
1003C2×C4—31no—
1004C2×C4—31no—
1005C2×C4—31no—
1006C2×C4—62no—
1007C2×C4—94no—
1008C2×C4—94no—
1009C2×C4—91no—
1010C2×C4—91no—
1011C2×C4—91no—
1012C2×C4—91no—
1013C2×C4—91no—
1014C2×C4—182no—
1015C2×C4—182no—
1016C2×C4—274no—
1017C2×C4—274no—
1018C2×C4—274no—
1019C2×C4—274no—
1020C2×C4—271no—
1021C2×C4—271no—
1022C2×C4—542no—
1023C2×C4D3311yescharacteristic
1024C2×C3—21no—
1025C2×C3—21no—
1026C2×C3—21no—
1027C2×C3—21no—
1028C2×C3—21no—
1029C2×C3—21no—
1030C2×C3—21no—
1031C2×C3—21no—
1032C2×C3—21no—
1033C2×C3—34no—
1034C2×C3—34no—
1035C2×C3—41no—
1036C2×C3—41no—
1037C2×C3—41no—
1038C2×C3—64no—
1039C2×C3—62no—
1040C2×C3—62no—
1041C2×C3—122no—
1042C2×C3—182no—
1043C2×C3C2×#379511yescharacteristic
1044C2×C3C2×C4×D3211yescharacteristic
1045C2×C3C2×C4×D3211yescharacteristic
1046C2×C3C2×C4×D3211yescharacteristic
1047C2×C3D3×#23511yescharacteristic
1048C2×C3D3×#23511yescharacteristic
1049C2×C3D3×#23711yescharacteristic
1050C2×C3D3×#23711yescharacteristic
1051C2×C3C2×#380411yescharacteristic
1052D3—22no—
1053D3—62no—
1054D3—62no—
1055D3—122no—
1056D3#6387714yesdirect product factor
1057C22—32no—
1058C22—32no—
1059C22—32no—
1060C22—32no—
1061C22—61no—
1062C22—61no—
1063C22—92no—
1064C22—188no—
1065C22—181no—
1066C22—181no—
1067C22C2×D3311yescharacteristic
1068C4—21no—
1069C4—32no—
1070C4—61no—
1071C4—61no—
1072C4—61no—
1073C4—92no—
1074C4—92no—
1075C4—181no—
1076C4—181no—
1077C4—181no—
1078C4—272no—
1079C4—541no—
1080C3—21no—
1081C3—21no—
1082C3—21no—
1083C3—41no—
1084C3D3×#87211yescharacteristic, complemented
1085C3D3×#87711yescharacteristic, complemented
1086C3C2×#6387711yescharacteristic, complemented
1087C2—34no—
1088C2—62no—
1089C2—182no—
1090C2D3×#379511yescharacteristic
1091C2C4×D3311yescharacteristic
1092C2D3×#380411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutatorC2×C33C23×C4
FittingC2×C33×C4C23
socle, cosocleC22×C33C24
prime radicalC22×C3×D32C22
hypercenterC2×C4D33
hypocenterC33C2×#117
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. #11723683C2semidirect
3. #11723464C2semidirect
4. #11723459C2semidirect
5. D3×#3750C2semidirect
7. C3×#63877C2semidirect
8. C3×C4×D3×Dic3C2semidirect
9. #11722922C2semidirect
10. #11722919C2semidirect
11. #11722916C2semidirect
12. #11722913C2semidirect
13. D3×#3724C2semidirect
15. D3×Dic32C2semidirect
30. D32×Dic3C4semidirect
31. #88857C22semidirect
33. C3×#3750C22semidirect
34. C3×C4×C3⋊Dic3C22semidirect
36. C32×C4×Dic3C22semidirect
37. #88815C22semidirect
39. #88813C22semidirect
40. #88807C22semidirect
41. #88806C22semidirect
42. #88806C22semidirect
43. #88806C22semidirect
46. Dic3×C3⋊Dic3C22semidirect
47. Dic3×C3⋊Dic3C22semidirect
48. C3×#3724C22semidirect
52. C3×Dic32C22semidirect
53. C3×Dic32C22semidirect
54. C3×Dic32C22semidirect
90. #63877D3direct (N × H)
98. C4×D3×Dic3D3semidirect
122. #6294C2×C4semidirect
123. Dic3×C3⋊D3C2×C4semidirect
126. D3×C3⋊Dic3C2×C4semidirect
130. C3×D3×Dic3C2×C4semidirect
191. #3750C2×D3semidirect
194. C4×C3⋊Dic3C2×D3semidirect
222. C3×C4×Dic3C2×D3semidirect
223. C3×C4×Dic3C2×D3semidirect
234. #3724C2×D3semidirect
261. Dic32C2×D3semidirect
262. Dic32C2×D3semidirect
263. Dic32C2×D3semidirect
447. D3×Dic3C4×D3semidirect
454. C32×D3#117semidirect
584. C4×Dic3D32semidirect
703. C33C2×#117semidirect
848. C3×D3#872semidirect
849. C3×D3#877semidirect
993. C32C2×#872semidirect
994. C32C2×#877semidirect
995. C32D3×#117semidirect
1056. D3#63877direct (N × H)
1084. C3D3×#872semidirect
1085. C3D3×#877semidirect
1086. C3C2×#63877semidirect

Maximal subgroups

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

subgroupindex
C2×D32×Dic32
#117236832
#117234642
#117234592
D3×#37502
C3×D3×(C2×D3)⋊C42
C3×#638772
C3×C4×D3×Dic32
#117229222
#117229192
#117229162
#117229132
D3×#37242
D3×(C2×D3)⋊Dic32
D3×Dic322
C2×#638773
D3×#8773
D3×#8723