Finite Group Databasebeta

← D3×#63856 #13167994

Subgroups — D3×#63856 #13167994

Order 1728.

1554 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×D32C211yesmaximal, characteristic
2C2×C3×D3×Dic6C211yesmaximal, characteristic, complemented
3#11723674C211yesmaximal, characteristic, complemented
4D3×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
5#11723435C211yesmaximal, characteristic, complemented
6#11723425C211yesmaximal, characteristic, complemented
7C3×#63856C211yesmaximal, characteristic, complemented
8#11722970C212yesmaximal, complemented
9#11722969C212yesmaximal, complemented
10D3×#3724C212yesmaximal, complemented
11D3×(C2×D3)⋊Dic3C212yesmaximal
12D3×#946—31nomaximal
13D3×#924—31nomaximal
14C2×#63856—31nomaximal
15C22×C3×D32C2211yescharacteristic
16C2×C3×C4×C3⋊D3C2211yescharacteristic
17C2×C3×#634C2211yescharacteristic, complemented
18C2×C32×C4×D3C2211yescharacteristic
19C2×C32×C4×D3C2211yescharacteristic
20C2×C32×Dic6C2211yescharacteristic, complemented
21C2×D3×C3⋊Dic3C2212yes—
22C2×C3×#627C2212yescomplemented
23C2×C3×#624C2211yescharacteristic
24C2×C3×D3×Dic3C2212yes—
25C2×C3×D3×Dic3C2211yescharacteristic
26C2×C3×D3×Dic3C2211yescharacteristic
27C3×C4×D32—24no—
28C3×D3×Dic6—24no—
29C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic, complemented
30C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
31#88815C2212yescomplemented
32#88814C2212yes—
33#88806C2212yescomplemented
34#88806C2212yescomplemented
35Dic3⋊(C3⋊Dic3)C2212yescomplemented
36#88803C2212yes—
37(C2×D3)⋊(C3⋊Dic3)C2212yes—
38C3×#3724C2212yescomplemented
39C3×(C2×D3)⋊Dic3C2212yes—
40C2×C3×D3×Q8—31no—
41C22×C3×C4×D3—31no—
42C22×C3×C4×D3—31no—
43C22×C3×Dic6—31no—
44C2×C4×D32D311yescharacteristic
45C2×D3×Dic6D311yescharacteristic, complemented
46#64155—31no—
47C2×C4⋊(C3⋊Dic3)—31no—
48#64133—31no—
49C3×#946—31no—
50C3×#924—31no—
51D3×#217—32no—
52C2×#3724—32no—
53#63964—32no—
54C2×(C2×D3)⋊Dic3—32no—
55D3×(C2×D3)⋊C4—32no—
56D3×C4⋊Dic3—31no—
57D3×C4⋊Dic3—31no—
58D3×C4⋊Dic3—61no—
59#63888—32no—
60#63887—32no—
61D3×Dic3⋊C4—32no—
62D3×Dic3⋊C4—32no—
63#63871—31no—
64#63857—31no—
65#63856—31no—
66#63856—31no—
67#63856—31no—
68#63856—31no—
69#63856—31no—
70#63856—32no—
71#63856—32no—
72#63856—61no—
73#63856—61no—
74#63856D311yescharacteristic, direct product factor
75#63851—32no—
76C22×C3×C3⋊D3C2311yescharacteristic
77C22×C32×D3C2311yescharacteristic
78C22×C32×D3C2311yescharacteristic
79C2×C3×D32—22no—
80C2×C3×D32—22no—
81C2×C3×D32Q814yescomplemented
82C2×C33×C4C2311yescharacteristic
83C2×C3⋊(C3⋊Dic3)C2312yes—
84C2×C3×C3⋊Dic3C2312yes—
85C2×C3×C3⋊Dic3C2311yescharacteristic
86C2×C3×C3⋊Dic3C2312yes—
87C3×C4×C3⋊D3—22no—
88C3×#634—22no—
89C2×C32×Dic3C2311yescharacteristic
90C2×C32×Dic3C2312yes—
91C2×C32×Dic3C2311yescharacteristic
92C32×C4×D3—22no—
93C32×C4×D3D414yes—
94C32×Dic6—22no—
95D3×C3⋊Dic3—24no—
96C3×#627—24no—
97C3×#624—22no—
98C3×D3×Dic3—24no—
99C3×D3×Dic3—22no—
100C3×D3×Dic3—22no—
101C2×#946—91no—
102C2×#924—91no—
103D3×C22⋊Q8—91no—
104C23×C3×D3—31no—
105C23×C3×D3—31no—
106C22×D32C2×D311yescharacteristic
107C2×C32×Q8—31no—
108C22×C32×C4—31no—
109C22×C32×C4—31no—
110C22×C3⋊Dic3—32no—
111C2×C4×C3⋊D3C2×D311yescharacteristic
112C2×#634C2×D311yescharacteristic, complemented
113C22×C3×Dic3—32no—
114C22×C3×Dic3—31no—
115C22×C3×Dic3—31no—
116C3×D3×Q8—64no—
117C2×C3×C4×D3—21no—
118C2×C3×C4×D3—21no—
119C2×C3×C4×D3—31no—
120C2×C3×C4×D3—31no—
121C2×C3×C4×D3—32no—
122C2×C3×C4×D3—31no—
123C2×C3×C4×D3—31no—
124C2×C3×C4×D3—31no—
125C2×C3×C4×D3—31no—
126C2×C3×C4×D3—64no—
127C2×C3×C4×D3—64no—
128C2×C3×C4×D3—61no—
129C2×C3×C4×D3C2×D311yescharacteristic
130C2×C3×C4×D3C2×D311yescharacteristic
131C2×C3×C4×D3C2×D311yescharacteristic
132C2×C3×C4×D3C2×D311yescharacteristic
133C2×C3×Dic6—21no—
134C2×C3×Dic6—31no—
135C2×C3×Dic6—31no—
136C2×C3×Dic6—32no—
137C2×C3×Dic6—32no—
138C2×C3×Dic6—64no—
139C2×C3×Dic6—61no—
140C2×C3×Dic6C2×D311yescharacteristic, complemented
141C2×C3×Dic6C2×D311yescharacteristic, complemented
142C2×#627C2×D312yescomplemented
143C2×#624C2×D311yescharacteristic
144C2×D3×Dic3—32no—
145C2×D3×Dic3—32no—
146C2×D3×Dic3—62no—
147C2×D3×Dic3C2×D312yes—
148C2×D3×Dic3C2×D311yescharacteristic
149C2×D3×Dic3C2×D311yescharacteristic
150C4×D32—24no—
151D3×Dic6—24no—
152#3757—32no—
153#3752—32no—
154C4⋊(C3⋊Dic3)—31no—
155C4⋊(C3⋊Dic3)—31no—
156C4⋊(C3⋊Dic3)—31no—
157C4⋊(C3⋊Dic3)—32no—
158C4⋊(C3⋊Dic3)—61no—
159C4⋊(C3⋊Dic3)—61no—
160C4⋊(C3⋊Dic3)—61no—
161C4⋊(C3⋊Dic3)—121no—
162C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
163#3750—32no—
164#3750—32no—
165C3×#217—32no—
166C3×(C2×D3)⋊C4—32no—
167C3×C4⋊Dic3—31no—
168C3×C4⋊Dic3—31no—
169C3×C4⋊Dic3—61no—
170C3×Dic3⋊C4—32no—
171C3×Dic3⋊C4—32no—
172#3724—32no—
173#3724—32no—
174#3724—32no—
175#3724—32no—
176#3724—32no—
177#3724—62no—
178#3724—62no—
179#3724C2×D312yescomplemented
180Dic3⋊Dic3—32no—
181Dic3⋊Dic3—32no—
182Dic3⋊Dic3—32no—
183Dic3⋊Dic3—32no—
184Dic3⋊Dic3—62no—
185#3722—32no—
186(C2×D3)⋊Dic3—32no—
187(C2×D3)⋊Dic3—32no—
188(C2×D3)⋊Dic3—32no—
189(C2×D3)⋊Dic3—32no—
190(C2×D3)⋊Dic3—32no—
191(C2×D3)⋊Dic3—32no—
192(C2×D3)⋊Dic3—62no—
193(C2×D3)⋊Dic3—62no—
194(C2×D3)⋊Dic3C2×D312yes—
195C22×C33C2411yescharacteristic
196C2×C3×C3⋊D3—21no—
197C2×C3×C3⋊D3—21no—
198C2×C3×C3⋊D3C2×Q812yescomplemented
199C2×C32×D3—21no—
200C2×C32×D3—21no—
201C2×C32×D3C2×D412yes—
202C2×C32×D3C2×Q812yes—
203C2×C32×D3C2×Q812yescomplemented
204C2×C32×D3#4112yes—
205C3×D32—28no—
206C33×C4C2×D412yes—
207C3⋊(C3⋊Dic3)—22no—
208C3×C3⋊Dic3—21no—
209C3×C3⋊Dic3—22no—
210C3×C3⋊Dic3—22no—
211C32×Dic3—21no—
212C32×Dic3—22no—
213C32×Dic3C2×D412yes—
214C22×C3×Q8—91no—
215C23×C3×C4—91no—
216C2×D3×Q8—31no—
217C22×C4×D3—31no—
218C22×C4×D3—31no—
219C22×Dic6—31no—
220C3×C22⋊Q8—91no—
221C2×#217—92no—
222#946—31no—
223#946—92no—
224#946—91no—
225#946—92no—
226#946—91no—
227#946—91no—
228#946—91no—
229#946—181no—
230C2×(C2×D3)⋊C4—92no—
231C2×C4⋊Dic3—91no—
232C2×C4⋊Dic3—91no—
233C2×C4⋊Dic3—181no—
234#924—31no—
235#924—92no—
236#924—91no—
237#924—92no—
238#924—91no—
239#924—91no—
240#924—91no—
241#924—181no—
242C2×Dic3⋊C4—92no—
243C2×Dic3⋊C4—92no—
244#897—91no—
245#896—92no—
246D3×C4⋊C4—92no—
247D3×C4⋊C4—91no—
248D3×C22⋊C4—92no—
249#878—92no—
250C23×C32—31no—
251C23×C32—31no—
252C22×C3⋊D3C22×D311yescharacteristic
253C22×C3×D3—21no—
254C22×C3×D3—21no—
255C22×C3×D3—31no—
256C22×C3×D3—31no—
257C22×C3×D3—34no—
258C22×C3×D3—34no—
259C22×C3×D3—61no—
260C22×C3×D3—62no—
261C22×C3×D3—62no—
262C22×C3×D3—62no—
263C22×C3×D3—62no—
264C22×C3×D3C22×D311yescharacteristic
265C22×C3×D3C22×D311yescharacteristic
266C22×C3×D3C22×D311yescharacteristic
267C22×C3×D3C22×D311yescharacteristic
268C2×D32—22no—
269C2×D32—22no—
270C2×D32Dic614yescomplemented
271C32×Q8—62no—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4—21no—
275C2×C32×C4—31no—
276C2×C32×C4—34no—
277C2×C32×C4—31no—
278C2×C32×C4—32no—
279C2×C32×C4—41no—
280C2×C32×C4—62no—
281C2×C32×C4C22×D311yescharacteristic
282C2×C32×C4C22×D311yescharacteristic
283C2×C32×C4C22×D311yescharacteristic
284C2×C3⋊Dic3—32no—
285C2×C3⋊Dic3—32no—
286C2×C3⋊Dic3—32no—
287C2×C3⋊Dic3—62no—
288C2×C3⋊Dic3—62no—
289C2×C3⋊Dic3—62no—
290C2×C3⋊Dic3—64no—
291C2×C3⋊Dic3—122no—
292C2×C3⋊Dic3C22×D312yes—
293C2×C3⋊Dic3C22×D312yes—
294C2×C3⋊Dic3C22×D311yescharacteristic
295C4×C3⋊D3—22no—
296#634—22no—
297C2×C3×Dic3—21no—
298C2×C3×Dic3—22no—
299C2×C3×Dic3—21no—
300C2×C3×Dic3—32no—
301C2×C3×Dic3—32no—
302C2×C3×Dic3—32no—
303C2×C3×Dic3—32no—
304C2×C3×Dic3—31no—
305C2×C3×Dic3—31no—
306C2×C3×Dic3—62no—
307C2×C3×Dic3—62no—
308C2×C3×Dic3—61no—
309C2×C3×Dic3—64no—
310C2×C3×Dic3—62no—
311C2×C3×Dic3—62no—
312C2×C3×Dic3C22×D312yes—
313C2×C3×Dic3C22×D312yes—
314C2×C3×Dic3C22×D311yescharacteristic
315C2×C3×Dic3C22×D311yescharacteristic
316C2×C3×Dic3C22×D311yescharacteristic
317C2×C3×Dic3C22×D311yescharacteristic
318C3×C4×D3—22no—
319C3×C4×D3—22no—
320C3×C4×D3—24no—
321C3×C4×D3—42no—
322C3×C4×D3—62no—
323C3×C4×D3—62no—
324C3×C4×D3—62no—
325C3×C4×D3—64no—
326C3×C4×D3—62no—
327C3×C4×D3—62no—
328C3×C4×D3—62no—
329C3×C4×D3—122no—
330C3×C4×D3#6714yes—
331C3×C4×D3#6714yes—
332C3×Dic6—22no—
333C3×Dic6—22no—
334C3×Dic6—42no—
335C3×Dic6—64no—
336C3×Dic6—62no—
337C3×Dic6—62no—
338C3×Dic6—64no—
339C3×Dic6—122no—
340#627—24no—
341#624—22no—
342D3×Dic3—24no—
343D3×Dic3—22no—
344D3×Dic3—22no—
345D3×Dic3—64no—
346D3×Dic3—64no—
347D3×Dic3—124no—
348C2×C22⋊Q8—271noSylow
349C2×C33C22×D411yescharacteristic
350C2×C33C22×Q811yescharacteristic
351C2×C33C2×#4111yescharacteristic
352C3×C3⋊D3—22no—
353C32×D3—22no—
354C32×D3C22⋊Q814yescomplemented
355C24×C3—91no—
356C23×D3—31no—
357C23×D3—31no—
358C2×C3×Q8—31no—
359C2×C3×Q8—31no—
360C2×C3×Q8—61no—
361C2×C3×Q8—92no—
362C2×C3×Q8—91no—
363C2×C3×Q8—184no—
364C22×C3×C4—31no—
365C22×C3×C4—31no—
366C22×C3×C4—31no—
367C22×C3×C4—31no—
368C22×C3×C4—61no—
369C22×C3×C4—61no—
370C22×C3×C4—91no—
371C22×C3×C4—91no—
372C22×C3×C4—92no—
373C22×C3×C4—91no—
374C22×C3×C4—91no—
375C22×C3×C4—184no—
376C22×Dic3—31no—
377C22×Dic3—31no—
378C22×Dic3—32no—
379C22×Dic3—92no—
380C22×Dic3—92no—
381C22×Dic3—182no—
382D3×Q8—64no—
383C2×C4×D3—32no—
384C2×C4×D3—31no—
385C2×C4×D3—31no—
386C2×C4×D3—31no—
387C2×C4×D3—31no—
388C2×C4×D3—31no—
389C2×C4×D3—31no—
390C2×C4×D3—61no—
391C2×C4×D3—64no—
392C2×C4×D3—64no—
393C2×C4×D3—92no—
394C2×C4×D3D3211yescharacteristic
395C2×C4×D3D3211yescharacteristic
396C2×Dic6—31no—
397C2×Dic6—31no—
398C2×Dic6—32no—
399C2×Dic6—32no—
400C2×Dic6—61no—
401C2×Dic6—64no—
402C2×Dic6D3211yescharacteristic, complemented
403C3×C4⋊C4—92no—
404C3×C4⋊C4—91no—
405C3×C22⋊C4—92no—
406#217—32no—
407#217—92no—
408#217—92no—
409#217—92no—
410#217—92no—
411#217—182no—
412(C2×D3)⋊C4—32no—
413(C2×D3)⋊C4—92no—
414(C2×D3)⋊C4—92no—
415(C2×D3)⋊C4—92no—
416(C2×D3)⋊C4—92no—
417(C2×D3)⋊C4—92no—
418(C2×D3)⋊C4—182no—
419C4⋊Dic3—31no—
420C4⋊Dic3—31no—
421C4⋊Dic3—61no—
422C4⋊Dic3—92no—
423C4⋊Dic3—92no—
424C4⋊Dic3—92no—
425C4⋊Dic3—91no—
426C4⋊Dic3—91no—
427C4⋊Dic3—91no—
428C4⋊Dic3—182no—
429C4⋊Dic3—181no—
430C4⋊Dic3—181no—
431C4⋊Dic3—181no—
432C4⋊Dic3—361no—
433Dic3⋊C4—32no—
434Dic3⋊C4—32no—
435Dic3⋊C4—92no—
436Dic3⋊C4—92no—
437Dic3⋊C4—92no—
438Dic3⋊C4—92no—
439Dic3⋊C4—92no—
440Dic3⋊C4—92no—
441Dic3⋊C4—92no—
442Dic3⋊C4—92no—
443Dic3⋊C4—92no—
444Dic3⋊C4—182no—
445Dic3⋊C4—182no—
446C22×C32—21no—
447C22×C32—21no—
448C22×C32—21no—
449C22×C32—32no—
450C22×C32—32no—
451C22×C32—32no—
452C22×C32—32no—
453C22×C32—41no—
454C22×C32—61no—
455C22×C32—61no—
456C22×C32C23×D311yescharacteristic
457C22×C32C23×D311yescharacteristic
458C22×C32C23×D311yescharacteristic
459C2×C3⋊D3—21no—
460C2×C3⋊D3—21no—
461C2×C3⋊D3C2×Dic612yescomplemented
462C2×C3×D3—21no—
463C2×C3×D3—21no—
464C2×C3×D3—21no—
465C2×C3×D3—21no—
466C2×C3×D3—22no—
467C2×C3×D3—22no—
468C2×C3×D3—22no—
469C2×C3×D3—22no—
470C2×C3×D3—32no—
471C2×C3×D3—32no—
472C2×C3×D3—41no—
473C2×C3×D3—41no—
474C2×C3×D3—62no—
475C2×C3×D3—68no—
476C2×C3×D3—61no—
477C2×C3×D3—61no—
478C2×C3×D3—61no—
479C2×C3×D3—61no—
480C2×C3×D3—68no—
481C2×C3×D3—121no—
482C2×C3×D3—121no—
483C2×C3×D3C2×Dic612yes—
484C2×C3×D3C2×Dic612yescomplemented
485C2×C3×D3#23512yes—
486C2×C3×D3D3×Q812yes—
487C2×C3×D3D3×Q812yescomplemented
488C2×C3×D3#23912yes—
489C2×C3×D3C2×#6712yes—
490C2×C3×D3C2×#6712yes—
491D32—28no—
492C32×C4—22no—
493C32×C4—22no—
494C32×C4—22no—
495C32×C4—32no—
496C32×C4—42no—
497C32×C4—62no—
498C32×C4—61no—
499C32×C4D3×D412yes—
500C32×C4C2×#6712yes—
501C32×C4C2×#6712yes—
502C3⋊Dic3—22no—
503C3⋊Dic3—21no—
504C3⋊Dic3—22no—
505C3⋊Dic3—62no—
506C3⋊Dic3—62no—
507C3⋊Dic3—62no—
508C3⋊Dic3—122no—
509C3⋊Dic3—122no—
510C3⋊Dic3—122no—
511C3⋊Dic3—242no—
512C3×Dic3—22no—
513C3×Dic3—21no—
514C3×Dic3—21no—
515C3×Dic3—22no—
516C3×Dic3—22no—
517C3×Dic3—42no—
518C3×Dic3—41no—
519C3×Dic3—62no—
520C3×Dic3—62no—
521C3×Dic3—61no—
522C3×Dic3—62no—
523C3×Dic3—62no—
524C3×Dic3—61no—
525C3×Dic3—122no—
526C3×Dic3—122no—
527C3×Dic3—121no—
528C3×Dic3C2×#6712yes—
529C3×Dic3C2×#6712yes—
530C22×Q8—91no—
531C23×C4—91no—
532C22⋊Q8—91no—
533C22⋊Q8—272no—
534C22⋊Q8—272no—
535C22⋊Q8—271no—
536C22⋊Q8—271no—
537C22⋊Q8—271no—
538C2×C4⋊C4—271no—
539C2×C4⋊C4—272no—
540C2×C22⋊C4—272no—
541C33C2×C22⋊Q811yescharacteristic, complemented, Sylow
542C23×C3—31no—
543C23×C3—31no—
544C23×C3—31no—
545C23×C3—31no—
546C23×C3—61no—
547C23×C3—61no—
548C23×C3—94no—
549C23×C3—91no—
550C23×C3—182no—
551C23×C3—182no—
552C22×D3—31no—
553C22×D3—31no—
554C22×D3—34no—
555C22×D3—34no—
556C22×D3—61no—
557C22×D3—62no—
558C22×D3—62no—
559C22×D3—62no—
560C22×D3—62no—
561C22×D3C2×D3211yescharacteristic
562C22×D3C2×D3211yescharacteristic
563C3×Q8—62no—
564C3×Q8—62no—
565C3×Q8—122no—
566C3×Q8—184no—
567C3×Q8—182no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—31no—
572C2×C3×C4—31no—
573C2×C3×C4—34no—
574C2×C3×C4—34no—
575C2×C3×C4—31no—
576C2×C3×C4—32no—
577C2×C3×C4—31no—
578C2×C3×C4—32no—
579C2×C3×C4—41no—
580C2×C3×C4—64no—
581C2×C3×C4—61no—
582C2×C3×C4—61no—
583C2×C3×C4—62no—
584C2×C3×C4—62no—
585C2×C3×C4—62no—
586C2×C3×C4—91no—
587C2×C3×C4—92no—
588C2×C3×C4—92no—
589C2×C3×C4—122no—
590C2×C3×C4—182no—
591C2×C3×C4—182no—
592C2×C3×C4—182no—
593C2×C3×C4—184no—
594C2×C3×C4—182no—
595C2×C3×C4C2×D3211yescharacteristic
596C2×C3×C4C2×D3211yescharacteristic
597C2×C3×C4C2×D3211yescharacteristic
598C2×Dic3—32no—
599C2×Dic3—32no—
600C2×Dic3—31no—
601C2×Dic3—31no—
602C2×Dic3—32no—
603C2×Dic3—32no—
604C2×Dic3—61no—
605C2×Dic3—62no—
606C2×Dic3—62no—
607C2×Dic3—64no—
608C2×Dic3—62no—
609C2×Dic3—62no—
610C2×Dic3—92no—
611C2×Dic3—92no—
612C2×Dic3—92no—
613C2×Dic3—182no—
614C2×Dic3—182no—
615C2×Dic3—182no—
616C2×Dic3—184no—
617C2×Dic3—184no—
618C2×Dic3—362no—
619C2×Dic3—364no—
620C2×Dic3C2×D3211yescharacteristic
621C2×Dic3C2×D3212yes—
622C2×Dic3C2×D3211yescharacteristic
623C4×D3—22no—
624C4×D3—62no—
625C4×D3—62no—
626C4×D3—62no—
627C4×D3—64no—
628C4×D3—62no—
629C4×D3—62no—
630C4×D3—62no—
631C4×D3—122no—
632C4×D3—184no—
633C4×D3#62514yes—
634Dic6—22no—
635Dic6—64no—
636Dic6—62no—
637Dic6—62no—
638Dic6—64no—
639Dic6—122no—
640C2×C32—21no—
641C2×C32—21no—
642C2×C32—21no—
643C2×C32—21no—
644C2×C32—21no—
645C2×C32—21no—
646C2×C32—21no—
647C2×C32—21no—
648C2×C32—21no—
649C2×C32—34no—
650C2×C32—41no—
651C2×C32—41no—
652C2×C32—41no—
653C2×C32—62no—
654C2×C32C22×Dic611yescharacteristic
655C2×C32C2×#23511yescharacteristic
656C2×C32C2×D3×D411yescharacteristic
657C2×C32C2×D3×Q811yescharacteristic
658C2×C32C2×D3×Q811yescharacteristic
659C2×C32C2×#23911yescharacteristic
660C2×C32D3×#4111yescharacteristic
661C2×C32C22×#6711yescharacteristic
662C2×C32C22×#6711yescharacteristic
663C3⋊D3—22no—
664C3×D3—22no—
665C3×D3—22no—
666C3×D3—24no—
667C3×D3—42no—
668C3×D3—62no—
669C3×D3—62no—
670C3×D3—122no—
671C3×D3#92414yescomplemented
672C3×D3#94614yescomplemented
673C24—91no—
674C2×Q8—31no—
675C2×Q8—92no—
676C2×Q8—91no—
677C2×Q8—184no—
678C22×C4—31no—
679C22×C4—31no—
680C22×C4—91no—
681C22×C4—92no—
682C22×C4—91no—
683C22×C4—91no—
684C22×C4—91no—
685C22×C4—184no—
686C22×C4—272no—
687C4⋊C4—92no—
688C4⋊C4—91no—
689C4⋊C4—272no—
690C4⋊C4—272no—
691C4⋊C4—272no—
692C4⋊C4—272no—
693C4⋊C4—271no—
694C22⋊C4—92no—
695C22⋊C4—272no—
696C22⋊C4—272no—
697C22⋊C4—272no—
698C22×C3—21no—
699C22×C3—21no—
700C22×C3—21no—
701C22×C3—32no—
702C22×C3—32no—
703C22×C3—32no—
704C22×C3—32no—
705C22×C3—32no—
706C22×C3—32no—
707C22×C3—32no—
708C22×C3—32no—
709C22×C3—41no—
710C22×C3—62no—
711C22×C3—62no—
712C22×C3—62no—
713C22×C3—62no—
714C22×C3—61no—
715C22×C3—61no—
716C22×C3—61no—
717C22×C3—61no—
718C22×C3—92no—
719C22×C3—121no—
720C22×C3—121no—
721C22×C3—188no—
722C22×C3—181no—
723C22×C3—181no—
724C22×C3C22×D3211yescharacteristic
725C22×C3C22×D3211yescharacteristic
726C22×C3C22×D3211yescharacteristic
727C2×D3—21no—
728C2×D3—21no—
729C2×D3—32no—
730C2×D3—32no—
731C2×D3—62no—
732C2×D3—68no—
733C2×D3—61no—
734C2×D3—61no—
735C2×D3—61no—
736C2×D3—61no—
737C2×D3—68no—
738C2×D3—121no—
739C2×D3—121no—
740C2×D3D3×Dic612yes—
741C2×D3D3×Dic612yescomplemented
742C2×D3#379912yes—
743C2×D3C2×#62512yes—
744C3×C4—22no—
745C3×C4—22no—
746C3×C4—22no—
747C3×C4—32no—
748C3×C4—32no—
749C3×C4—42no—
750C3×C4—62no—
751C3×C4—62no—
752C3×C4—61no—
753C3×C4—61no—
754C3×C4—62no—
755C3×C4—121no—
756C3×C4—122no—
757C3×C4—182no—
758C3×C4—181no—
759C3×C4—182no—
760C3×C4C2×#62512yes—
761C3×C4D3×#6712yes—
762C3×C4D3×#6712yes—
763Dic3—22no—
764Dic3—21no—
765Dic3—62no—
766Dic3—62no—
767Dic3—62no—
768Dic3—61no—
769Dic3—62no—
770Dic3—61no—
771Dic3—122no—
772Dic3—121no—
773Dic3—122no—
774Dic3—182no—
775Dic3—182no—
776Dic3—182no—
777Dic3—362no—
778Dic3—362no—
779Dic3—362no—
780Dic3—722no—
781Dic3C2×#62512yes—
782C32—21no—
783C32—21no—
784C32—21no—
785C32—41no—
786C32D3×C22⋊Q811yescharacteristic, complemented
787C32C2×#92411yescharacteristic, complemented
788C32C2×#94611yescharacteristic, complemented
789C23—31no—
790C23—31no—
791C23—94no—
792C23—91no—
793C23—182no—
794C23—182no—
795Q8—62no—
796Q8—184no—
797Q8—182no—
798C2×C4—31no—
799C2×C4—34no—
800C2×C4—32no—
801C2×C4—31no—
802C2×C4—62no—
803C2×C4—92no—
804C2×C4—92no—
805C2×C4—91no—
806C2×C4—182no—
807C2×C4—182no—
808C2×C4—182no—
809C2×C4—184no—
810C2×C4—182no—
811C2×C4—272no—
812C2×C4—544no—
813C2×C4D3311yescharacteristic
814C2×C3—21no—
815C2×C3—21no—
816C2×C3—21no—
817C2×C3—21no—
818C2×C3—21no—
819C2×C3—21no—
820C2×C3—21no—
821C2×C3—21no—
822C2×C3—21no—
823C2×C3—34no—
824C2×C3—34no—
825C2×C3—41no—
826C2×C3—41no—
827C2×C3—41no—
828C2×C3—64no—
829C2×C3—62no—
830C2×C3—62no—
831C2×C3—122no—
832C2×C3—182no—
833C2×C3C2×D3×Dic611yescharacteristic
834C2×C3C2×D3×Dic611yescharacteristic
835C2×C3C2×#379911yescharacteristic
836C2×C3D3×#23511yescharacteristic
837C2×C3D32×Q811yescharacteristic
838C2×C3D3×#23911yescharacteristic
839C2×C3C22×#62511yescharacteristic
840C2×C3C2×D3×#6711yescharacteristic
841C2×C3C2×D3×#6711yescharacteristic
842D3—22no—
843D3—62no—
844D3—62no—
845D3—122no—
846D3#6385614yesdirect product factor
847C22—32no—
848C22—32no—
849C22—32no—
850C22—32no—
851C22—61no—
852C22—61no—
853C22—92no—
854C22—188no—
855C22—181no—
856C22—181no—
857C22C2×D3311yescharacteristic
858C4—32no—
859C4—61no—
860C4—62no—
861C4—182no—
862C4—181no—
863C4—182no—
864C4—542no—
865C4D3×#62512yes—
866C3—21no—
867C3—21no—
868C3—21no—
869C3—41no—
870C3C2×#6385611yescharacteristic, complemented
871C3D3×#92411yescharacteristic, complemented
872C3D3×#94611yescharacteristic, complemented
873C2—34no—
874C2—62no—
875C2—182no—
876C2D32×Dic611yescharacteristic
877C2D3×#379911yescharacteristic
878C2C2×D3×#62511yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC22×C3×D32C22
hypercenterC2×C4D33
hypocenterC33C2×C22⋊Q8
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×D3×Dic6C2semidirect
3. #11723674C2semidirect
4. D3×C4⋊(C3⋊Dic3)C2semidirect
5. #11723435C2semidirect
6. #11723425C2semidirect
7. C3×#63856C2semidirect
8. #11722970C2semidirect
9. #11722969C2semidirect
10. D3×#3724C2semidirect
17. C2×C3×#634C22semidirect
20. C2×C32×Dic6C22semidirect
22. C2×C3×#627C22semidirect
29. C4⋊(C3⋊(C3⋊Dic3))C22semidirect
30. C3×C4⋊(C3⋊Dic3)C22semidirect
31. #88815C22semidirect
33. #88806C22semidirect
34. #88806C22semidirect
35. Dic3⋊(C3⋊Dic3)C22semidirect
38. C3×#3724C22semidirect
45. C2×D3×Dic6D3semidirect
74. #63856D3direct (N × H)
81. C2×C3×D32Q8semidirect
112. C2×#634C2×D3semidirect
140. C2×C3×Dic6C2×D3semidirect
141. C2×C3×Dic6C2×D3semidirect
142. C2×#627C2×D3semidirect
162. C4⋊(C3⋊Dic3)C2×D3semidirect
179. #3724C2×D3semidirect
198. C2×C3×C3⋊D3C2×Q8semidirect
203. C2×C32×D3C2×Q8semidirect
270. C2×D32Dic6semidirect
354. C32×D3C22⋊Q8semidirect
402. C2×Dic6D32semidirect
461. C2×C3⋊D3C2×Dic6semidirect
484. C2×C3×D3C2×Dic6semidirect
487. C2×C3×D3D3×Q8semidirect
541. C33C2×C22⋊Q8semidirect
671. C3×D3#924semidirect
672. C3×D3#946semidirect
741. C2×D3D3×Dic6semidirect
786. C32D3×C22⋊Q8semidirect
787. C32C2×#924semidirect
788. C32C2×#946semidirect
846. D3#63856direct (N × H)
870. C3C2×#63856semidirect
871. C3D3×#924semidirect
872. C3D3×#946semidirect

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×C3×D3×Dic62
#117236742
D3×C4⋊(C3⋊Dic3)2
#117234352
#117234252
C3×#638562
#117229702
#117229692
D3×#37242
D3×(C2×D3)⋊Dic32
D3×#9463
D3×#9243
C2×#638563