Finite Group Databasebeta

← D3×#63898 #13170771

Subgroups — D3×#63898 #13170771

Order 1728.

2030 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×D12C211yesmaximal, characteristic
2C2×D32×Dic3C212yesmaximal, complemented
3#11723691C211yesmaximal, characteristic, complemented
4#11723501C211yesmaximal, characteristic, complemented
5#11723499C211yesmaximal, characteristic, complemented
6C4×D3×C3⋊Dic3C211yesmaximal, characteristic, complemented
7C3×#63898C211yesmaximal, characteristic, complemented
8C3×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
9#11722929C212yesmaximal, complemented
10#11722927C212yesmaximal, complemented
11D3×(C2×D3)⋊Dic3C212yesmaximal, complemented
12D3×D4×Dic3—31nomaximal
13C2×#63898—31nomaximal
14D3×#893—31nomaximal
15C22×C3×D32C2212yes—
16C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
17C2×C32×D12C2211yescharacteristic
18C2×C32×C4×D3C2211yescharacteristic
19C2×#6294C2212yescomplemented
20C2×Dic3×C3⋊D3C2212yescomplemented
21C2×D3×C3⋊Dic3C2211yescharacteristic
22C2×D3×C3⋊Dic3C2211yescharacteristic
23C2×D3×C3⋊Dic3C2212yescomplemented
24C2×C3×#626C2212yes—
25C2×C3×D3×Dic3C2212yes—
26C2×C3×D3×Dic3C2212yescomplemented
27C3×D3×D12C418yescomplemented
28D32×Dic3—28no—
29C4×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
30C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
31C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
32C32×C4⋊Dic3C2211yescharacteristic, complemented
33#88814C2212yescomplemented
34#88803C2212yescomplemented
35(C2×D3)⋊(C3⋊Dic3)C2212yescomplemented
36Dic3×C3⋊Dic3C2211yescharacteristic, complemented
37Dic3×C3⋊Dic3C2211yescharacteristic, complemented
38C3×Dic3⋊Dic3C2212yescomplemented
39C3×(C2×D3)⋊Dic3C2212yescomplemented
40C2×C3×D3×D4—31no—
41C22×C3×D12—31no—
42C22×D3×Dic3—32no—
43C22×D3×Dic3—32no—
44C2×D3×D12D311yescharacteristic
45C2×C4×D32—32no—
46D4×C3⋊Dic3—31no—
47C2×C4×C3⋊Dic3—31no—
48#64102—31no—
49C3×D4×Dic3—31no—
50C2×C3×C4⋊Dic3—31no—
51C3×#893—31no—
52C3×D3×C4⋊C4—31no—
53#67⋊Dic3—32no—
54Dic3×#67—32no—
55D3×#217—32no—
56C2×(C2×D3)⋊Dic3—32no—
57D3×(C2×D3)⋊C4—32no—
58#63904—32no—
59#63898—31no—
60#63898—31no—
61#63898—32no—
62#63898—31no—
63#63898—31no—
64#63898—31no—
65#63898—32no—
66#63898—61no—
67#63898—61no—
68#63898D311yescharacteristic, direct product factor
69#63894—31no—
70Dic3×D12—31no—
71D3×C4⋊Dic3D311yescharacteristic, complemented
72#63881—32no—
73C4×D3×Dic3—31no—
74C4×D3×Dic3—31no—
75C4×D3×Dic3—61no—
76C22×C3×C3⋊D3C2312yes—
77C22×C32×D3C2312yes—
78C22×C32×D3C2311yescharacteristic
79C2×C3×D32—24no—
80C2×C3×D32—24no—
81C2×C3×D32C2×C418yescomplemented
82C2×C33×C4C2311yescharacteristic
83C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
84C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
85C2×C3×C3⋊Dic3C2311yescharacteristic
86C2×C3×C3⋊Dic3C2312yes—
87C2×C3×C3⋊Dic3C2311yescharacteristic
88C3×C4⋊(C3⋊D3)C2×C414yescomplemented
89C2×C32×Dic3C2312yes—
90C2×C32×Dic3C2311yescharacteristic
91C32×D12C2×C414yescomplemented
92C32×C4×D3C2×C414yescomplemented
93#6294—24no—
94Dic3×C3⋊D3—24no—
95D3×C3⋊Dic3—22no—
96D3×C3⋊Dic3—24no—
97D3×C3⋊Dic3D414yescomplemented
98C3×#626C2×C418yescomplemented
99C3×D3×Dic3—24no—
100C3×D3×Dic3—24no—
101C2×D4×Dic3—91no—
102C4×D3×D4—91no—
103C2×#893—91no—
104C23×C3×D3—32no—
105C23×C3×D3—32no—
106C22×D32C2×D312yes—
107C2×C32×D4—31no—
108C22×C32×C4—31no—
109C22×C3⋊Dic3—31no—
110C22×C3⋊Dic3—32no—
111C22×C3⋊Dic3—31no—
112C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
113C2×C4×C3⋊D3—32no—
114C2×C3×#67—32no—
115C22×C3×Dic3—32no—
116C22×C3×Dic3—32no—
117C3×D3×D4—38no—
118C2×C3×D12—21no—
119C2×C3×D12—32no—
120C2×C3×D12—31no—
121C2×C3×D12—31no—
122C2×C3×D12—38no—
123C2×C3×D12—61no—
124C2×C3×D12C2×D311yescharacteristic
125C2×C3×D12C2×D311yescharacteristic
126C2×C3×C4×D3—21no—
127C2×C3×C4×D3—32no—
128C2×C3×C4×D3—32no—
129C2×C3×C4×D3C2×D311yescharacteristic
130C2×C3×C4×D3C2×D311yescharacteristic
131C2×#626C2×D312yes—
132C2×#624—32no—
133C2×D3×Dic3—31no—
134C2×D3×Dic3—31no—
135C2×D3×Dic3—32no—
136C2×D3×Dic3—32no—
137C2×D3×Dic3—31no—
138C2×D3×Dic3—31no—
139C2×D3×Dic3—32no—
140C2×D3×Dic3—32no—
141C2×D3×Dic3—32no—
142C2×D3×Dic3—32no—
143C2×D3×Dic3—68no—
144C2×D3×Dic3—68no—
145C2×D3×Dic3—61no—
146C2×D3×Dic3—61no—
147C2×D3×Dic3—62no—
148C2×D3×Dic3—62no—
149C2×D3×Dic3C2×D312yes—
150C2×D3×Dic3C2×D312yescomplemented
151D3×D12Dic318yescomplemented
152C4×D32—68no—
153C32×C4⋊C4—31no—
154#3757—32no—
155#3752—32no—
156C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
157C4×C3⋊Dic3—31no—
158C4×C3⋊Dic3—31no—
159C4×C3⋊Dic3—31no—
160C4×C3⋊Dic3—31no—
161C4×C3⋊Dic3—31no—
162C4×C3⋊Dic3—61no—
163C4×C3⋊Dic3—61no—
164C4×C3⋊Dic3—61no—
165C4×C3⋊Dic3—121no—
166C4×C3⋊Dic3C2×D311yescharacteristic, complemented
167C3×#217—32no—
168C3×(C2×D3)⋊C4—32no—
169C3×C4⋊Dic3—21no—
170C3×C4⋊Dic3—31no—
171C3×C4⋊Dic3—31no—
172C3×C4⋊Dic3—32no—
173C3×C4⋊Dic3—61no—
174C3×C4⋊Dic3C2×D311yescharacteristic, complemented
175C3×C4⋊Dic3C2×D311yescharacteristic, complemented
176C3×Dic3⋊C4—32no—
177C3×C4×Dic3—31no—
178C3×C4×Dic3—31no—
179C3×C4×Dic3—61no—
180Dic3⋊Dic3C2×D312yescomplemented
181#3722—32no—
182(C2×D3)⋊Dic3—32no—
183(C2×D3)⋊Dic3—32no—
184(C2×D3)⋊Dic3—32no—
185(C2×D3)⋊Dic3—32no—
186(C2×D3)⋊Dic3—32no—
187(C2×D3)⋊Dic3—32no—
188(C2×D3)⋊Dic3—62no—
189(C2×D3)⋊Dic3—62no—
190(C2×D3)⋊Dic3C2×D312yescomplemented
191Dic32—31no—
192Dic32—31no—
193Dic32—31no—
194Dic32—31no—
195Dic32—61no—
196Dic32—61no—
197C22×C33C2411yescharacteristic
198C2×C3×C3⋊D3—22no—
199C2×C3×C3⋊D3—22no—
200C2×C3×C3⋊D3C22×C414yescomplemented
201C2×C32×D3—22no—
202C2×C32×D3—22no—
203C2×C32×D3C22×C412yes—
204C2×C32×D3C22×C414yescomplemented
205C2×C32×D3C2×D412yes—
206C2×C32×D3#4112yes—
207C3×D32—216no—
208C33×C4C22×C412yescomplemented
209C3⋊(C3⋊Dic3)—21no—
210C3⋊(C3⋊Dic3)C2×D412yescomplemented
211C3×C3⋊Dic3—22no—
212C3×C3⋊Dic3—21no—
213C3×C3⋊Dic3C2×D412yescomplemented
214C32×Dic3—22no—
215C32×Dic3C22×C412yescomplemented
216C22×C3×D4—91no—
217C23×Dic3—92no—
218C2×D3×D4—31no—
219C22×D12—31no—
220C22×C4×D3—92no—
221C22×C4×D3—92no—
222C3×C4×D4—91no—
223C2×C3×C4⋊C4—91no—
224C2×#217—92no—
225D4×Dic3—31no—
226D4×Dic3—91no—
227D4×Dic3—92no—
228D4×Dic3—92no—
229D4×Dic3—91no—
230D4×Dic3—91no—
231D4×Dic3—91no—
232D4×Dic3—181no—
233C4×#67—92no—
234C2×(C2×D3)⋊C4—92no—
235C2×C4⋊Dic3—31no—
236C2×C4×Dic3—91no—
237C2×C4×Dic3—91no—
238C2×C4×Dic3—181no—
239#893—31no—
240#893—91no—
241#893—92no—
242#893—91no—
243#893—91no—
244#893—92no—
245#893—91no—
246#893—181no—
247D3×C4⋊C4—31no—
248#67⋊C4—92no—
249D3×C22⋊C4—92no—
250C4×D12—91no—
251C42×D3—91no—
252C23×C32—31no—
253C23×C32—32no—
254C22×C3⋊D3C22×D312yes—
255C22×C3×D3—21no—
256C22×C3×D3—22no—
257C22×C3×D3—32no—
258C22×C3×D3—32no—
259C22×C3×D3—38no—
260C22×C3×D3—38no—
261C22×C3×D3—62no—
262C22×C3×D3—64no—
263C22×C3×D3—64no—
264C22×C3×D3—64no—
265C22×C3×D3—64no—
266C22×C3×D3C22×D312yes—
267C22×C3×D3C22×D312yes—
268C22×C3×D3C22×D311yescharacteristic
269C22×C3×D3C22×D311yescharacteristic
270C2×D32—24no—
271C2×D32—24no—
272C2×D32C2×Dic318yescomplemented
273C32×D4—34no—
274C2×C32×C4—21no—
275C2×C32×C4—21no—
276C2×C32×C4—21no—
277C2×C32×C4—31no—
278C2×C32×C4—34no—
279C2×C32×C4—32no—
280C2×C32×C4—41no—
281C2×C32×C4C22×D311yescharacteristic
282C2×C32×C4C22×D311yescharacteristic
283C2×C32×C4C22×D311yescharacteristic
284C2×C3⋊Dic3—31no—
285C2×C3⋊Dic3—31no—
286C2×C3⋊Dic3—31no—
287C2×C3⋊Dic3—34no—
288C2×C3⋊Dic3—31no—
289C2×C3⋊Dic3—31no—
290C2×C3⋊Dic3—31no—
291C2×C3⋊Dic3—61no—
292C2×C3⋊Dic3—61no—
293C2×C3⋊Dic3—61no—
294C2×C3⋊Dic3—61no—
295C2×C3⋊Dic3—61no—
296C2×C3⋊Dic3—61no—
297C2×C3⋊Dic3—62no—
298C2×C3⋊Dic3—64no—
299C2×C3⋊Dic3—121no—
300C2×C3⋊Dic3—121no—
301C2×C3⋊Dic3C22×D311yescharacteristic
302C2×C3⋊Dic3C22×D312yes—
303C2×C3⋊Dic3C22×D311yescharacteristic
304C4⋊(C3⋊D3)C2×Dic314yescomplemented
305C4×C3⋊D3—64no—
306C3×#67—38no—
307C2×C3×Dic3—21no—
308C2×C3×Dic3—22no—
309C2×C3×Dic3—31no—
310C2×C3×Dic3—31no—
311C2×C3×Dic3—31no—
312C2×C3×Dic3—31no—
313C2×C3×Dic3—32no—
314C2×C3×Dic3—32no—
315C2×C3×Dic3—61no—
316C2×C3×Dic3—61no—
317C2×C3×Dic3—62no—
318C2×C3×Dic3—64no—
319C2×C3×Dic3—64no—
320C2×C3×Dic3C22×D312yes—
321C2×C3×Dic3C22×D312yes—
322C2×C3×Dic3C22×D311yescharacteristic
323C2×C3×Dic3C22×D311yescharacteristic
324C3×D12—24no—
325C3×D12—38no—
326C3×D12—34no—
327C3×D12—34no—
328C3×D12—64no—
329C3×D12C4×D314yescomplemented
330C3×D12C2×Dic314yescomplemented
331C3×C4×D3—24no—
332C3×C4×D3—64no—
333C3×C4×D3—64no—
334C3×C4×D3C4×D314yescomplemented
335C3×C4×D3C2×Dic314yescomplemented
336#626C2×Dic318yescomplemented
337#624—64no—
338D3×Dic3—24no—
339D3×Dic3—24no—
340D3×Dic3—34no—
341D3×Dic3—34no—
342D3×Dic3—64no—
343D3×Dic3—64no—
344D3×Dic3—64no—
345D3×Dic3—64no—
346D3×Dic3—64no—
347D3×Dic3—64no—
348D3×Dic3—64no—
349D3×Dic3—62no—
350D3×Dic3—62no—
351D3×Dic3—64no—
352D3×Dic3—124no—
353D3×Dic3—124no—
354C2×C4×D4—271noSylow
355C2×C33C23×C411yescharacteristic
356C2×C33C22×D411yescharacteristic
357C2×C33C2×#4111yescharacteristic
358C3×C3⋊D3—24no—
359C32×D3—24no—
360C32×D3C4×D414yescomplemented
361C24×C3—92no—
362C23×D3—32no—
363C23×D3—32no—
364C2×C3×D4—31no—
365C2×C3×D4—31no—
366C2×C3×D4—61no—
367C2×C3×D4—98no—
368C2×C3×D4—92no—
369C2×C3×D4—91no—
370C22×C3×C4—31no—
371C22×C3×C4—31no—
372C22×C3×C4—61no—
373C22×C3×C4—92no—
374C22×C3×C4—92no—
375C2×#67—32no—
376C22×Dic3—32no—
377C22×Dic3—32no—
378C22×Dic3—92no—
379C22×Dic3—91no—
380C22×Dic3—91no—
381C22×Dic3—92no—
382C22×Dic3—91no—
383C22×Dic3—91no—
384C22×Dic3—92no—
385C22×Dic3—92no—
386C22×Dic3—181no—
387C22×Dic3—181no—
388C22×Dic3—182no—
389C22×Dic3—188no—
390D3×D4—38no—
391C2×D12—32no—
392C2×D12—31no—
393C2×D12—31no—
394C2×D12—38no—
395C2×D12—61no—
396C2×D12D3211yescharacteristic
397C2×C4×D3—32no—
398C2×C4×D3—32no—
399C2×C4×D3—91no—
400C2×C4×D3—92no—
401C2×C4×D3—92no—
402C2×C4×D3—92no—
403C2×C4×D3—92no—
404C2×C4×D3—91no—
405C2×C4×D3—92no—
406C2×C4×D3—182no—
407C2×C4×D3—188no—
408C2×C4×D3—188no—
409C2×C4×D3D3211yescharacteristic
410C3×C4⋊C4—31no—
411C3×C4⋊C4—31no—
412C3×C4⋊C4—61no—
413C3×C4⋊C4—92no—
414C3×C4⋊C4—91no—
415C3×C22⋊C4—92no—
416C3×C42—91no—
417#217—32no—
418#217—92no—
419#217—92no—
420#217—92no—
421#217—92no—
422#217—182no—
423(C2×D3)⋊C4—32no—
424(C2×D3)⋊C4—92no—
425(C2×D3)⋊C4—92no—
426(C2×D3)⋊C4—92no—
427(C2×D3)⋊C4—92no—
428(C2×D3)⋊C4—92no—
429(C2×D3)⋊C4—182no—
430C4⋊Dic3—31no—
431C4⋊Dic3—31no—
432C4⋊Dic3—32no—
433C4⋊Dic3—61no—
434C4⋊Dic3D3211yescharacteristic, complemented
435Dic3⋊C4—32no—
436C4×Dic3—31no—
437C4×Dic3—31no—
438C4×Dic3—61no—
439C4×Dic3—91no—
440C4×Dic3—91no—
441C4×Dic3—91no—
442C4×Dic3—91no—
443C4×Dic3—91no—
444C4×Dic3—91no—
445C4×Dic3—91no—
446C4×Dic3—91no—
447C4×Dic3—91no—
448C4×Dic3—181no—
449C4×Dic3—181no—
450C4×Dic3—181no—
451C4×Dic3—181no—
452C4×Dic3—181no—
453C4×Dic3—361no—
454C22×C32—21no—
455C22×C32—21no—
456C22×C32—21no—
457C22×C32—32no—
458C22×C32—32no—
459C22×C32—32no—
460C22×C32—34no—
461C22×C32—41no—
462C22×C32—62no—
463C22×C32—62no—
464C22×C32C23×D311yescharacteristic
465C22×C32C23×D311yescharacteristic
466C22×C32C23×D311yescharacteristic
467C2×C3⋊D3—22no—
468C2×C3⋊D3—22no—
469C2×C3⋊D3C22×Dic314yescomplemented
470C2×C3×D3—22no—
471C2×C3×D3—22no—
472C2×C3×D3—22no—
473C2×C3×D3—22no—
474C2×C3×D3—22no—
475C2×C3×D3—22no—
476C2×C3×D3—22no—
477C2×C3×D3—24no—
478C2×C3×D3—34no—
479C2×C3×D3—34no—
480C2×C3×D3—42no—
481C2×C3×D3—42no—
482C2×C3×D3—64no—
483C2×C3×D3—616no—
484C2×C3×D3—62no—
485C2×C3×D3—62no—
486C2×C3×D3—62no—
487C2×C3×D3—62no—
488C2×C3×D3—616no—
489C2×C3×D3—122no—
490C2×C3×D3—122no—
491C2×C3×D3C2×C4×D312yes—
492C2×C3×D3C2×C4×D314yescomplemented
493C2×C3×D3D3×D412yes—
494C2×C3×D3D3×D412yes—
495C2×C3×D3#23712yes—
496C2×C3×D3#23912yes—
497C2×C3×D3C22×Dic312yes—
498C2×C3×D3C22×Dic314yescomplemented
499D32—216no—
500C32×C4—22no—
501C32×C4—22no—
502C32×C4—22no—
503C32×C4—32no—
504C32×C4—42no—
505C32×C4—62no—
506C32×C4C2×C4×D312yescomplemented
507C32×C4C2×C4×D312yescomplemented
508C32×C4C22×Dic312yescomplemented
509C3⋊Dic3—21no—
510C3⋊Dic3—22no—
511C3⋊Dic3—32no—
512C3⋊Dic3—32no—
513C3⋊Dic3—32no—
514C3⋊Dic3—62no—
515C3⋊Dic3—62no—
516C3⋊Dic3—62no—
517C3⋊Dic3—61no—
518C3⋊Dic3—62no—
519C3⋊Dic3—61no—
520C3⋊Dic3—61no—
521C3⋊Dic3—122no—
522C3⋊Dic3—121no—
523C3⋊Dic3—121no—
524C3⋊Dic3—122no—
525C3⋊Dic3D3×D412yescomplemented
526C3×Dic3—22no—
527C3×Dic3—22no—
528C3×Dic3—22no—
529C3×Dic3—32no—
530C3×Dic3—32no—
531C3×Dic3—42no—
532C3×Dic3—62no—
533C3×Dic3—62no—
534C3×Dic3—62no—
535C3×Dic3—62no—
536C3×Dic3—61no—
537C3×Dic3—61no—
538C3×Dic3—122no—
539C3×Dic3C2×C4×D312yescomplemented
540C3×Dic3C22×Dic312yescomplemented
541C22×D4—91no—
542C23×C4—272no—
543C4×D4—91no—
544C4×D4—271no—
545C4×D4—272no—
546C4×D4—271no—
547C4×D4—272no—
548C4×D4—271no—
549C2×C4⋊C4—91no—
550C2×C22⋊C4—272no—
551C2×C42—271no—
552C33C2×C4×D411yescharacteristic, complemented, Sylow
553C23×C3—31no—
554C23×C3—31no—
555C23×C3—32no—
556C23×C3—32no—
557C23×C3—61no—
558C23×C3—62no—
559C23×C3—98no—
560C23×C3—92no—
561C23×C3—184no—
562C23×C3—184no—
563C22×D3—32no—
564C22×D3—32no—
565C22×D3—38no—
566C22×D3—38no—
567C22×D3—62no—
568C22×D3—64no—
569C22×D3—64no—
570C22×D3—64no—
571C22×D3—64no—
572C22×D3C2×D3212yes—
573C22×D3C2×D3211yescharacteristic
574C3×D4—34no—
575C3×D4—34no—
576C3×D4—64no—
577C3×D4—98no—
578C3×D4—94no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—31no—
583C2×C3×C4—31no—
584C2×C3×C4—34no—
585C2×C3×C4—34no—
586C2×C3×C4—32no—
587C2×C3×C4—32no—
588C2×C3×C4—41no—
589C2×C3×C4—64no—
590C2×C3×C4—61no—
591C2×C3×C4—62no—
592C2×C3×C4—91no—
593C2×C3×C4—91no—
594C2×C3×C4—92no—
595C2×C3×C4—184no—
596C2×C3×C4—184no—
597C2×C3×C4C2×D3211yescharacteristic
598C2×C3×C4C2×D3211yescharacteristic
599C2×C3×C4C2×D3211yescharacteristic
600#67—38no—
601C2×Dic3—31no—
602C2×Dic3—31no—
603C2×Dic3—31no—
604C2×Dic3—31no—
605C2×Dic3—32no—
606C2×Dic3—32no—
607C2×Dic3—61no—
608C2×Dic3—61no—
609C2×Dic3—62no—
610C2×Dic3—64no—
611C2×Dic3—64no—
612C2×Dic3—94no—
613C2×Dic3—94no—
614C2×Dic3—91no—
615C2×Dic3—91no—
616C2×Dic3—91no—
617C2×Dic3—91no—
618C2×Dic3—91no—
619C2×Dic3—91no—
620C2×Dic3—184no—
621C2×Dic3—181no—
622C2×Dic3—181no—
623C2×Dic3—181no—
624C2×Dic3—181no—
625C2×Dic3—181no—
626C2×Dic3—181no—
627C2×Dic3—184no—
628C2×Dic3—184no—
629C2×Dic3—184no—
630C2×Dic3—184no—
631C2×Dic3—182no—
632C2×Dic3—182no—
633C2×Dic3—184no—
634C2×Dic3—361no—
635C2×Dic3—361no—
636C2×Dic3—364no—
637C2×Dic3C2×D3212yes—
638C2×Dic3C2×D3211yescharacteristic
639D12—38no—
640D12—34no—
641D12—34no—
642D12—64no—
643D12D3×Dic314yescomplemented
644C4×D3—64no—
645C4×D3—64no—
646C4×D3—94no—
647C4×D3—184no—
648C4×D3—184no—
649C4×D3—184no—
650C4×D3—184no—
651C4×D3—184no—
652C4×D3—182no—
653C4×D3—364no—
654C4×D3D3×Dic314yescomplemented
655C2×C32—21no—
656C2×C32—21no—
657C2×C32—21no—
658C2×C32—21no—
659C2×C32—21no—
660C2×C32—21no—
661C2×C32—21no—
662C2×C32—21no—
663C2×C32—21no—
664C2×C32—34no—
665C2×C32—41no—
666C2×C32—41no—
667C2×C32—41no—
668C2×C32—64no—
669C2×C32C22×C4×D311yescharacteristic
670C2×C32C22×C4×D311yescharacteristic
671C2×C32C2×D3×D411yescharacteristic
672C2×C32C2×D3×D411yescharacteristic
673C2×C32C2×D3×D411yescharacteristic
674C2×C32C2×#23711yescharacteristic
675C2×C32C2×#23911yescharacteristic
676C2×C32D3×#4111yescharacteristic
677C2×C32C23×Dic311yescharacteristic
678C3⋊D3—24no—
679C3×D3—24no—
680C3×D3—24no—
681C3×D3—24no—
682C3×D3—44no—
683C3×D3—64no—
684C3×D3—64no—
685C3×D3—124no—
686C3×D3#89314yescomplemented
687C3×D3D4×Dic314yescomplemented
688C24—92no—
689C2×D4—31no—
690C2×D4—98no—
691C2×D4—92no—
692C2×D4—91no—
693C22×C4—31no—
694C22×C4—92no—
695C22×C4—92no—
696C22×C4—272no—
697C22×C4—272no—
698C22×C4—271no—
699C22×C4—271no—
700C22×C4—272no—
701C22×C4—548no—
702C4⋊C4—31no—
703C4⋊C4—92no—
704C4⋊C4—91no—
705C22⋊C4—92no—
706C22⋊C4—272no—
707C22⋊C4—272no—
708C22⋊C4—272no—
709C42—91no—
710C42—271no—
711C42—271no—
712C42—271no—
713C22×C3—21no—
714C22×C3—21no—
715C22×C3—21no—
716C22×C3—32no—
717C22×C3—32no—
718C22×C3—32no—
719C22×C3—32no—
720C22×C3—32no—
721C22×C3—32no—
722C22×C3—34no—
723C22×C3—34no—
724C22×C3—41no—
725C22×C3—62no—
726C22×C3—62no—
727C22×C3—62no—
728C22×C3—64no—
729C22×C3—62no—
730C22×C3—62no—
731C22×C3—62no—
732C22×C3—62no—
733C22×C3—94no—
734C22×C3—122no—
735C22×C3—122no—
736C22×C3—1816no—
737C22×C3—182no—
738C22×C3—182no—
739C22×C3C22×D3211yescharacteristic
740C22×C3C22×D3211yescharacteristic
741C22×C3C22×D3211yescharacteristic
742C2×D3—22no—
743C2×D3—22no—
744C2×D3—34no—
745C2×D3—34no—
746C2×D3—64no—
747C2×D3—616no—
748C2×D3—62no—
749C2×D3—62no—
750C2×D3—62no—
751C2×D3—62no—
752C2×D3—616no—
753C2×D3—122no—
754C2×D3—122no—
755C2×D3#379612yes—
756C2×D3#380212yes—
757C2×D3C2×D3×Dic312yes—
758C2×D3C2×D3×Dic314yescomplemented
759C3×C4—22no—
760C3×C4—22no—
761C3×C4—22no—
762C3×C4—32no—
763C3×C4—32no—
764C3×C4—42no—
765C3×C4—62no—
766C3×C4—62no—
767C3×C4—62no—
768C3×C4—92no—
769C3×C4—122no—
770C3×C4—181no—
771C3×C4—182no—
772C3×C4C4×D3212yescomplemented
773C3×C4C2×D3×Dic312yescomplemented
774C3×C4C2×D3×Dic312yescomplemented
775Dic3—22no—
776Dic3—32no—
777Dic3—32no—
778Dic3—62no—
779Dic3—62no—
780Dic3—62no—
781Dic3—62no—
782Dic3—61no—
783Dic3—61no—
784Dic3—92no—
785Dic3—92no—
786Dic3—92no—
787Dic3—122no—
788Dic3—182no—
789Dic3—182no—
790Dic3—182no—
791Dic3—182no—
792Dic3—181no—
793Dic3—181no—
794Dic3—181no—
795Dic3—362no—
796Dic3—361no—
797Dic3—361no—
798Dic3—362no—
799Dic3C2×D3×Dic312yescomplemented
800C32—21no—
801C32—21no—
802C32—21no—
803C32—41no—
804C32C2×#89311yescharacteristic, complemented
805C32C4×D3×D411yescharacteristic, complemented
806C32C2×D4×Dic311yescharacteristic, complemented
807C23—31no—
808C23—32no—
809C23—98no—
810C23—92no—
811C23—184no—
812C23—184no—
813D4—34no—
814D4—98no—
815D4—94no—
816C2×C4—31no—
817C2×C4—34no—
818C2×C4—32no—
819C2×C4—91no—
820C2×C4—91no—
821C2×C4—92no—
822C2×C4—184no—
823C2×C4—184no—
824C2×C4—274no—
825C2×C4—271no—
826C2×C4—271no—
827C2×C4—544no—
828C2×C4—544no—
829C2×C4—544no—
830C2×C4—542no—
831C2×C4D3311yescharacteristic
832C2×C3—21no—
833C2×C3—21no—
834C2×C3—21no—
835C2×C3—21no—
836C2×C3—21no—
837C2×C3—21no—
838C2×C3—21no—
839C2×C3—21no—
840C2×C3—21no—
841C2×C3—34no—
842C2×C3—34no—
843C2×C3—41no—
844C2×C3—41no—
845C2×C3—41no—
846C2×C3—64no—
847C2×C3—64no—
848C2×C3—64no—
849C2×C3—124no—
850C2×C3—184no—
851C2×C3C2×#379611yescharacteristic
852C2×C3C2×C4×D3211yescharacteristic
853C2×C3C2×#380211yescharacteristic
854C2×C3D32×D411yescharacteristic
855C2×C3D32×D411yescharacteristic
856C2×C3D3×#23711yescharacteristic
857C2×C3D3×#23911yescharacteristic
858C2×C3C22×D3×Dic311yescharacteristic
859C2×C3C22×D3×Dic311yescharacteristic
860D3—24no—
861D3—64no—
862D3—64no—
863D3—124no—
864D3#6389814yesdirect product factor
865C22—32no—
866C22—32no—
867C22—32no—
868C22—34no—
869C22—62no—
870C22—62no—
871C22—94no—
872C22—1816no—
873C22—182no—
874C22—182no—
875C22C2×D3311yescharacteristic
876C4—32no—
877C4—62no—
878C4—92no—
879C4—181no—
880C4—182no—
881C4—272no—
882C4—541no—
883C4D32×Dic312yescomplemented
884C3—21no—
885C3—21no—
886C3—21no—
887C3—41no—
888C3D3×#89311yescharacteristic, complemented
889C3C2×#6389811yescharacteristic, complemented
890C3D3×D4×Dic311yescharacteristic, complemented
891C2—34no—
892C2—64no—
893C2—184no—
894C2D3×#379611yescharacteristic
895C2D3×#380211yescharacteristic
896C2C2×D32×Dic311yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutatorC2×C33C23×C4
FittingC2×C33×C4C23
socle, cosocleC22×C33C24
prime radicalC2×C3×D3×D12C2
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×D32×Dic3C2semidirect
3. #11723691C2semidirect
4. #11723501C2semidirect
5. #11723499C2semidirect
6. C4×D3×C3⋊Dic3C2semidirect
7. C3×#63898C2semidirect
8. C3×D3×C4⋊Dic3C2semidirect
9. #11722929C2semidirect
10. #11722927C2semidirect
11. D3×(C2×D3)⋊Dic3C2semidirect
19. C2×#6294C22semidirect
20. C2×Dic3×C3⋊D3C22semidirect
23. C2×D3×C3⋊Dic3C22semidirect
26. C2×C3×D3×Dic3C22semidirect
27. C3×D3×D12C4semidirect
29. C4×C3⋊(C3⋊Dic3)C22semidirect
30. C3×C4⋊(C3⋊Dic3)C22semidirect
31. C3×C4×C3⋊Dic3C22semidirect
32. C32×C4⋊Dic3C22semidirect
33. #88814C22semidirect
34. #88803C22semidirect
35. (C2×D3)⋊(C3⋊Dic3)C22semidirect
36. Dic3×C3⋊Dic3C22semidirect
37. Dic3×C3⋊Dic3C22semidirect
38. C3×Dic3⋊Dic3C22semidirect
39. C3×(C2×D3)⋊Dic3C22semidirect
68. #63898D3direct (N × H)
71. D3×C4⋊Dic3D3semidirect
81. C2×C3×D32C2×C4semidirect
88. C3×C4⋊(C3⋊D3)C2×C4semidirect
91. C32×D12C2×C4semidirect
92. C32×C4×D3C2×C4semidirect
97. D3×C3⋊Dic3D4semidirect
98. C3×#626C2×C4semidirect
150. C2×D3×Dic3C2×D3semidirect
151. D3×D12Dic3semidirect
156. C4⋊(C3⋊Dic3)C2×D3semidirect
166. C4×C3⋊Dic3C2×D3semidirect
174. C3×C4⋊Dic3C2×D3semidirect
175. C3×C4⋊Dic3C2×D3semidirect
180. Dic3⋊Dic3C2×D3semidirect
190. (C2×D3)⋊Dic3C2×D3semidirect
200. C2×C3×C3⋊D3C22×C4semidirect
204. C2×C32×D3C22×C4semidirect
208. C33×C4C22×C4semidirect
210. C3⋊(C3⋊Dic3)C2×D4semidirect
213. C3×C3⋊Dic3C2×D4semidirect
215. C32×Dic3C22×C4semidirect
272. C2×D32C2×Dic3semidirect
304. C4⋊(C3⋊D3)C2×Dic3semidirect
329. C3×D12C4×D3semidirect
330. C3×D12C2×Dic3semidirect
334. C3×C4×D3C4×D3semidirect
335. C3×C4×D3C2×Dic3semidirect
336. #626C2×Dic3semidirect
360. C32×D3C4×D4semidirect
434. C4⋊Dic3D32semidirect
469. C2×C3⋊D3C22×Dic3semidirect
492. C2×C3×D3C2×C4×D3semidirect
498. C2×C3×D3C22×Dic3semidirect
506. C32×C4C2×C4×D3semidirect
507. C32×C4C2×C4×D3semidirect
508. C32×C4C22×Dic3semidirect
525. C3⋊Dic3D3×D4semidirect
539. C3×Dic3C2×C4×D3semidirect
540. C3×Dic3C22×Dic3semidirect
552. C33C2×C4×D4semidirect
643. D12D3×Dic3semidirect
654. C4×D3D3×Dic3semidirect
686. C3×D3#893semidirect
687. C3×D3D4×Dic3semidirect
758. C2×D3C2×D3×Dic3semidirect
772. C3×C4C4×D32semidirect
773. C3×C4C2×D3×Dic3semidirect
774. C3×C4C2×D3×Dic3semidirect
799. Dic3C2×D3×Dic3semidirect
804. C32C2×#893semidirect
805. C32C4×D3×D4semidirect
806. C32C2×D4×Dic3semidirect
864. D3#63898direct (N × H)
883. C4D32×Dic3semidirect
888. C3D3×#893semidirect
889. C3C2×#63898semidirect
890. C3D3×D4×Dic3semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×D122
C2×D32×Dic32
#117236912
#117235012
#117234992
C4×D3×C3⋊Dic32
C3×#638982
C3×D3×C4⋊Dic32
#117229292
#117229272
D3×(C2×D3)⋊Dic32
D3×D4×Dic33
C2×#638983
D3×#8933