Finite Group Databasebeta

← #13168689

Subgroups — #13168689

Order 1728.

1462 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3798C211yesmaximal, characteristic
2#11723667C211yesmaximal, characteristic, complemented
3C3⋊D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
4D3×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
5#11723424C211yesmaximal, characteristic, complemented
6C3×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
7C3×#63841C211yesmaximal, characteristic, complemented
8#11722940C212yesmaximal, complemented
9#11722929C212yesmaximal, complemented
10Dic3×#626C212yesmaximal, complemented
11#11722924C212yesmaximal, complemented
12#10594992—31nomaximal
13#10594986—31nomaximal
14#10594510—31nomaximal
15C2×C3×C4×C3⋊D3C2211yescharacteristic
16C2×C32×C4×D3C2211yescharacteristic
17C2×C32×C4×D3C2211yescharacteristic
18C2×Dic3×C3⋊D3C2212yes—
19C2×D3×C3⋊Dic3C2212yes—
20C2×C3×#627C2211yescharacteristic
21C2×C3×#626C2211yescharacteristic
22C2×C3×#626C2211yescharacteristic
23C2×C3×#625C2211yescharacteristic
24C2×C3×D3×Dic3C2212yes—
25C3×#3798C418yescomplemented
26C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic
27C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
28C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
29C32×C4⋊Dic3C2211yescharacteristic
30#88814C2212yes—
31#88813C2212yes—
32#88807C2212yes—
33Dic3⋊(C3⋊Dic3)C2212yes—
34(C2×D3)⋊(C3⋊Dic3)C2212yes—
35Dic3×C3⋊Dic3C2212yes—
36C3×Dic3⋊Dic3C2212yes—
37C3×(C2×D3)⋊Dic3C2212yes—
38C3×Dic32C2212yes—
39C2×C3×#235—31no—
40C2×C3×#235—31no—
41C2×#3798D311yescharacteristic
42#64135—31no—
43C2×C4⋊(C3⋊Dic3)—31no—
44C4⋊C4×C3⋊D3—31no—
45C3×#926—31no—
46C2×C3×C4⋊Dic3—31no—
47C3×#892—31no—
48C3×D3×C4⋊C4—31no—
49#67⋊Dic3—32no—
50#67⋊Dic3—32no—
51Dic3×#67—32no—
52Dic3×#67—32no—
53C4×#626—32no—
54#63898—32no—
55Dic3×D12—32no—
56D3×C4⋊Dic3—31no—
57D3×C4⋊Dic3—31no—
58D3×C4⋊Dic3—31no—
59D3×C4⋊Dic3—31no—
60D3×C4⋊Dic3—61no—
61D3×C4⋊Dic3—61no—
62D3×C4⋊Dic3D311yescharacteristic, complemented
63#63881—32no—
64#63879—32no—
65#63849—31no—
66#63843—32no—
67Dic3×Dic6—32no—
68#63841—31no—
69#63841—31no—
70#63841—31no—
71#63841—31no—
72#63841—61no—
73#63841D311yescharacteristic, complemented
74#63837—32no—
75C22×C3×C3⋊D3C2311yescharacteristic
76C22×C32×D3C2311yescharacteristic
77C22×C32×D3C2311yescharacteristic
78C2×C33×C4C2311yescharacteristic
79C2×C3⋊(C3⋊Dic3)C2312yes—
80C2×C3×C3⋊Dic3C2312yes—
81C2×C3×C3⋊Dic3C2312yes—
82C2×C3×C3⋊Dic3C2311yescharacteristic
83C3×C4×C3⋊D3C2×C414yescomplemented
84C2×C32×Dic3C2312yes—
85C2×C32×Dic3C2311yescharacteristic
86C2×C32×Dic3C2311yescharacteristic
87C32×C4×D3C2×C414yescomplemented
88C32×C4×D3C2×C414yescomplemented
89Dic3×C3⋊D3—42no—
90D3×C3⋊Dic3—42no—
91C3×#627C2×C414yescomplemented
92C3×#626C2×C414yescomplemented
93C3×#626C2×C414yescomplemented
94C3×#625C2×C414yescomplemented
95C3×D3×Dic3—42no—
96#5827—91no—
97#5523—91no—
98#5504—91no—
99C22×C32×C4—31no—
100C22×C32×C4—31no—
101C22×C3⋊Dic3—32no—
102C2×C4×C3⋊D3—32no—
103C2×C4×C3⋊D3C2×D311yescharacteristic
104C2×C3×#67—31no—
105C2×C3×#67—31no—
106C2×C3×#67—31no—
107C2×C3×#67—31no—
108C22×C3×Dic3—32no—
109C3×#235—38no—
110C3×#235—38no—
111C2×C3×D12—31no—
112C2×C3×D12—31no—
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3—21no—
115C2×C3×C4×D3—31no—
116C2×C3×C4×D3—31no—
117C2×C3×C4×D3—32no—
118C2×C3×C4×D3—61no—
119C2×C3×C4×D3C2×D311yescharacteristic
120C2×C3×C4×D3C2×D311yescharacteristic
121C2×C3×C4×D3C2×D311yescharacteristic
122C2×C3×C4×D3C2×D311yescharacteristic
123C2×C3×Dic6—31no—
124C2×C3×Dic6—31no—
125C2×#627C2×D311yescharacteristic
126C2×#626C2×D311yescharacteristic
127C2×#626C2×D311yescharacteristic
128C2×#625C2×D311yescharacteristic
129C2×D3×Dic3—32no—
130C2×D3×Dic3—32no—
131C2×D3×Dic3—32no—
132C2×D3×Dic3—32no—
133C2×D3×Dic3—62no—
134C2×D3×Dic3—62no—
135C2×D3×Dic3C2×D312yes—
136#3798Dic318yescomplemented
137C32×C4⋊C4—31no—
138#3757—32no—
139C4⋊(C3⋊Dic3)—31no—
140C4⋊(C3⋊Dic3)—31no—
141C4⋊(C3⋊Dic3)—31no—
142C4⋊(C3⋊Dic3)—32no—
143C4⋊(C3⋊Dic3)—61no—
144C4⋊(C3⋊Dic3)—61no—
145C4⋊(C3⋊Dic3)—61no—
146C4⋊(C3⋊Dic3)—121no—
147C4⋊(C3⋊Dic3)C2×D311yescharacteristic
148C4⋊(C3⋊Dic3)C2×D311yescharacteristic
149#3750—32no—
150C4×C3⋊Dic3—32no—
151C3×#217—32no—
152C3×(C2×D3)⋊C4—32no—
153C3×C4⋊Dic3—21no—
154C3×C4⋊Dic3—31no—
155C3×C4⋊Dic3—31no—
156C3×C4⋊Dic3—31no—
157C3×C4⋊Dic3—31no—
158C3×C4⋊Dic3—32no—
159C3×C4⋊Dic3—61no—
160C3×C4⋊Dic3—61no—
161C3×C4⋊Dic3C2×D311yescharacteristic
162C3×C4⋊Dic3C2×D311yescharacteristic
163C3×Dic3⋊C4—32no—
164C3×C4×Dic3—32no—
165C3×C4×Dic3—32no—
166Dic3⋊Dic3—32no—
167Dic3⋊Dic3—32no—
168Dic3⋊Dic3—32no—
169Dic3⋊Dic3—32no—
170Dic3⋊Dic3—62no—
171Dic3⋊Dic3—62no—
172Dic3⋊Dic3C2×D312yes—
173#3722—32no—
174(C2×D3)⋊Dic3—32no—
175(C2×D3)⋊Dic3—32no—
176(C2×D3)⋊Dic3—32no—
177(C2×D3)⋊Dic3—32no—
178(C2×D3)⋊Dic3—62no—
179(C2×D3)⋊Dic3C2×D312yes—
180Dic32—32no—
181Dic32—32no—
182Dic32—32no—
183Dic32—32no—
184Dic32—32no—
185Dic32—62no—
186Dic32C2×D312yes—
187C22×C33C2411yescharacteristic
188C2×C3×C3⋊D3—21no—
189C2×C3×C3⋊D3—21no—
190C2×C3×C3⋊D3C22×C412yes—
191C2×C32×D3—21no—
192C2×C32×D3—21no—
193C2×C32×D3—21no—
194C2×C32×D3—21no—
195C2×C32×D3C22×C412yes—
196C2×C32×D3C22×C412yes—
197C33×C4C22×C412yes—
198C3⋊(C3⋊Dic3)—22no—
199C3×C3⋊Dic3—22no—
200C3×C3⋊Dic3—22no—
201C3×C3⋊Dic3C22×C412yes—
202C32×Dic3—22no—
203C32×Dic3C22×C412yes—
204C32×Dic3C22×C412yes—
205C2×C3×#41—91no—
206C2×#235—31no—
207C2×#235—31no—
208C3×#117—91no—
209C2×C3×C4⋊C4—91no—
210Q8×Dic3—92no—
211D4×Dic3—92no—
212D4×Dic3—92no—
213D4×Dic3—92no—
214C4×#67—92no—
215C4×#67—92no—
216#926—31no—
217#926—91no—
218#926—91no—
219#926—91no—
220#926—181no—
221C2×C4⋊Dic3—31no—
222C2×C4⋊Dic3—91no—
223C2×C4⋊Dic3—91no—
224C2×C4⋊Dic3—91no—
225C2×C4⋊Dic3—181no—
226#893—92no—
227#892—31no—
228#892—91no—
229#892—91no—
230#892—91no—
231D3×C4⋊C4—31no—
232D3×C4⋊C4—91no—
233D3×C4⋊C4—91no—
234D3×C4⋊C4—91no—
235D3×C4⋊C4—181no—
236#887—92no—
237#67⋊C4—92no—
238#67⋊C4—92no—
239C4×D12—92no—
240C4×Dic6—92no—
241C23×C32—31no—
242C23×C32—31no—
243C22×C3⋊D3C22×D311yescharacteristic
244C22×C3×D3—21no—
245C22×C3×D3—21no—
246C22×C3×D3—31no—
247C22×C3×D3—31no—
248C22×C3×D3—61no—
249C22×C3×D3C22×D311yescharacteristic
250C22×C3×D3C22×D311yescharacteristic
251C22×C3×D3C22×D311yescharacteristic
252C22×C3×D3C22×D311yescharacteristic
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—31no—
257C2×C32×C4—31no—
258C2×C32×C4—34no—
259C2×C32×C4—34no—
260C2×C32×C4—32no—
261C2×C32×C4—41no—
262C2×C32×C4C22×D311yescharacteristic
263C2×C32×C4C22×D311yescharacteristic
264C2×C32×C4C22×D311yescharacteristic
265C2×C3⋊Dic3—32no—
266C2×C3⋊Dic3—32no—
267C2×C3⋊Dic3—32no—
268C2×C3⋊Dic3—62no—
269C2×C3⋊Dic3—62no—
270C2×C3⋊Dic3—62no—
271C2×C3⋊Dic3—122no—
272C2×C3⋊Dic3—122no—
273C2×C3⋊Dic3C22×D312yes—
274C2×C3⋊Dic3C22×D312yes—
275C2×C3⋊Dic3C22×D311yescharacteristic
276C4×C3⋊D3—122no—
277C4×C3⋊D3C2×Dic314yescomplemented
278C3×#67—34no—
279C3×#67—34no—
280C3×#67—34no—
281C3×#67—34no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—22no—
285C2×C3×Dic3—31no—
286C2×C3×Dic3—31no—
287C2×C3×Dic3—32no—
288C2×C3×Dic3—32no—
289C2×C3×Dic3—32no—
290C2×C3×Dic3—32no—
291C2×C3×Dic3—61no—
292C2×C3×Dic3—62no—
293C2×C3×Dic3—62no—
294C2×C3×Dic3—122no—
295C2×C3×Dic3C22×D312yes—
296C2×C3×Dic3C22×D312yes—
297C2×C3×Dic3C22×D311yescharacteristic
298C2×C3×Dic3C22×D311yescharacteristic
299C2×C3×Dic3C22×D311yescharacteristic
300C2×C3×Dic3C22×D311yescharacteristic
301C3×D12—34no—
302C3×D12—34no—
303C3×C4×D3—24no—
304C3×C4×D3—24no—
305C3×C4×D3—34no—
306C3×C4×D3—34no—
307C3×C4×D3—64no—
308C3×C4×D3—122no—
309C3×C4×D3C4×D314yescomplemented
310C3×C4×D3C4×D314yescomplemented
311C3×C4×D3C2×Dic314yescomplemented
312C3×C4×D3C2×Dic314yescomplemented
313C3×Dic6—34no—
314C3×Dic6—34no—
315#627C2×Dic314yescomplemented
316#626C2×Dic314yescomplemented
317#626C2×Dic314yescomplemented
318#625C2×Dic314yescomplemented
319D3×Dic3—42no—
320D3×Dic3—122no—
321D3×Dic3—122no—
322D3×Dic3—124no—
323D3×Dic3—122no—
324D3×Dic3—122no—
325D3×Dic3—124no—
326#520—271noSylow
327C2×C33C23×C411yescharacteristic
328C2×C33H(5,𝔽2)11yescharacteristic
329C2×C332−1+411yescharacteristic
330C3×C3⋊D3—22no—
331C32×D3—22no—
332C32×D3—22no—
333C3×#41—98no—
334C2×C3×Q8—91no—
335C2×C3×D4—91no—
336C2×C3×D4—91no—
337C2×C3×D4—91no—
338C22×C3×C4—31no—
339C22×C3×C4—31no—
340C22×C3×C4—31no—
341C22×C3×C4—31no—
342C22×C3×C4—61no—
343C22×C3×C4—61no—
344C22×C3×C4—92no—
345C22×C3×C4—91no—
346C2×#67—31no—
347C2×#67—31no—
348C2×#67—31no—
349C2×#67—31no—
350C22×Dic3—32no—
351C22×Dic3—92no—
352C22×Dic3—92no—
353C22×Dic3—92no—
354C22×Dic3—182no—
355#235—38no—
356#235—38no—
357C2×D12—31no—
358C2×D12—31no—
359C2×C4×D3—31no—
360C2×C4×D3—31no—
361C2×C4×D3—32no—
362C2×C4×D3—61no—
363C2×C4×D3—92no—
364C2×C4×D3—92no—
365C2×C4×D3—92no—
366C2×C4×D3—182no—
367C2×C4×D3D3211yescharacteristic
368C2×C4×D3D3211yescharacteristic
369C2×Dic6—31no—
370C2×Dic6—31no—
371C3×C4⋊C4—31no—
372C3×C4⋊C4—31no—
373C3×C4⋊C4—61no—
374C3×C4⋊C4—92no—
375C3×C4⋊C4—91no—
376C3×C4⋊C4—91no—
377C3×C22⋊C4—92no—
378C3×C42—92no—
379#217—32no—
380#217—92no—
381#217—92no—
382#217—92no—
383#217—182no—
384(C2×D3)⋊C4—32no—
385(C2×D3)⋊C4—92no—
386(C2×D3)⋊C4—92no—
387(C2×D3)⋊C4—92no—
388C4⋊Dic3—31no—
389C4⋊Dic3—31no—
390C4⋊Dic3—31no—
391C4⋊Dic3—31no—
392C4⋊Dic3—32no—
393C4⋊Dic3—61no—
394C4⋊Dic3—61no—
395C4⋊Dic3—92no—
396C4⋊Dic3—92no—
397C4⋊Dic3—91no—
398C4⋊Dic3—91no—
399C4⋊Dic3—91no—
400C4⋊Dic3—92no—
401C4⋊Dic3—182no—
402C4⋊Dic3—181no—
403C4⋊Dic3—181no—
404C4⋊Dic3—181no—
405C4⋊Dic3—361no—
406C4⋊Dic3D3211yescharacteristic
407Dic3⋊C4—32no—
408Dic3⋊C4—92no—
409Dic3⋊C4—92no—
410Dic3⋊C4—92no—
411Dic3⋊C4—182no—
412C4×Dic3—32no—
413C4×Dic3—32no—
414C4×Dic3—92no—
415C4×Dic3—92no—
416C4×Dic3—92no—
417C4×Dic3—92no—
418C4×Dic3—92no—
419C4×Dic3—92no—
420C4×Dic3—182no—
421C22×C32—21no—
422C22×C32—21no—
423C22×C32—21no—
424C22×C32—32no—
425C22×C32—32no—
426C22×C32—41no—
427C22×C32—61no—
428C22×C32—61no—
429C22×C32—61no—
430C22×C32—61no—
431C22×C32C23×D311yescharacteristic
432C22×C32C23×D311yescharacteristic
433C22×C32C23×D311yescharacteristic
434C2×C3⋊D3—21no—
435C2×C3⋊D3—21no—
436C2×C3⋊D3C22×Dic312yes—
437C2×C3×D3—22no—
438C2×C3×D3—22no—
439C2×C3×D3—21no—
440C2×C3×D3—21no—
441C2×C3×D3—21no—
442C2×C3×D3—21no—
443C2×C3×D3—21no—
444C2×C3×D3—21no—
445C2×C3×D3—21no—
446C2×C3×D3—21no—
447C2×C3×D3—22no—
448C2×C3×D3—22no—
449C2×C3×D3—32no—
450C2×C3×D3—32no—
451C2×C3×D3—41no—
452C2×C3×D3—41no—
453C2×C3×D3—62no—
454C2×C3×D3—62no—
455C2×C3×D3—62no—
456C2×C3×D3—61no—
457C2×C3×D3—61no—
458C2×C3×D3—61no—
459C2×C3×D3—61no—
460C2×C3×D3C2×C4×D312yes—
461C2×C3×D3C2×C4×D312yes—
462C2×C3×D3C22×Dic312yes—
463C2×C3×D3C22×Dic312yes—
464C32×C4—22no—
465C32×C4—22no—
466C32×C4—22no—
467C32×C4—32no—
468C32×C4—32no—
469C32×C4—42no—
470C32×C4—62no—
471C32×C4C2×C4×D312yes—
472C32×C4C2×C4×D312yes—
473C32×C4C22×Dic312yes—
474C3⋊Dic3—22no—
475C3⋊Dic3—22no—
476C3⋊Dic3—62no—
477C3⋊Dic3—62no—
478C3⋊Dic3—62no—
479C3⋊Dic3—122no—
480C3⋊Dic3—122no—
481C3⋊Dic3—122no—
482C3⋊Dic3—242no—
483C3⋊Dic3C22×Dic312yes—
484C3×Dic3—22no—
485C3×Dic3—22no—
486C3×Dic3—22no—
487C3×Dic3—22no—
488C3×Dic3—32no—
489C3×Dic3—32no—
490C3×Dic3—42no—
491C3×Dic3—62no—
492C3×Dic3—62no—
493C3×Dic3—62no—
494C3×Dic3—62no—
495C3×Dic3—62no—
496C3×Dic3—122no—
497C3×Dic3—122no—
498C3×Dic3C2×C4×D312yes—
499C3×Dic3C2×C4×D312yes—
500C3×Dic3C22×Dic312yes—
501C3×Dic3C22×Dic312yes—
502C2×#41—91no—
503C4×Q8—272no—
504C4×D4—272no—
505C4×D4—272no—
506C4×D4—272no—
507#117—91no—
508#117—271no—
509#117—271no—
510C2×C4⋊C4—91no—
511C2×C4⋊C4—271no—
512C2×C4⋊C4—271no—
513C33#52011yescharacteristic, complemented, Sylow
514C23×C3—31no—
515C23×C3—31no—
516C23×C3—31no—
517C23×C3—31no—
518C23×C3—61no—
519C23×C3—61no—
520C23×C3—91no—
521C22×D3—31no—
522C22×D3—31no—
523C22×D3—61no—
524C22×D3C2×D3211yescharacteristic
525C22×D3C2×D3211yescharacteristic
526C3×Q8—94no—
527C3×D4—94no—
528C3×D4—94no—
529C3×D4—94no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—31no—
534C2×C3×C4—31no—
535C2×C3×C4—31no—
536C2×C3×C4—31no—
537C2×C3×C4—34no—
538C2×C3×C4—34no—
539C2×C3×C4—34no—
540C2×C3×C4—34no—
541C2×C3×C4—32no—
542C2×C3×C4—32no—
543C2×C3×C4—41no—
544C2×C3×C4—64no—
545C2×C3×C4—64no—
546C2×C3×C4—61no—
547C2×C3×C4—61no—
548C2×C3×C4—62no—
549C2×C3×C4—91no—
550C2×C3×C4—94no—
551C2×C3×C4—92no—
552C2×C3×C4—92no—
553C2×C3×C4—362no—
554C2×C3×C4C2×D3211yescharacteristic
555C2×C3×C4C2×D3211yescharacteristic
556C2×C3×C4C2×D3211yescharacteristic
557#67—34no—
558#67—34no—
559#67—34no—
560#67—34no—
561C2×Dic3—31no—
562C2×Dic3—31no—
563C2×Dic3—32no—
564C2×Dic3—32no—
565C2×Dic3—32no—
566C2×Dic3—32no—
567C2×Dic3—61no—
568C2×Dic3—62no—
569C2×Dic3—62no—
570C2×Dic3—92no—
571C2×Dic3—92no—
572C2×Dic3—92no—
573C2×Dic3—122no—
574C2×Dic3—182no—
575C2×Dic3—182no—
576C2×Dic3—182no—
577C2×Dic3—362no—
578C2×Dic3—362no—
579C2×Dic3—362no—
580C2×Dic3—362no—
581C2×Dic3—364no—
582C2×Dic3C2×D3212yes—
583C2×Dic3C2×D3211yescharacteristic
584C2×Dic3C2×D3211yescharacteristic
585D12—34no—
586D12—34no—
587C4×D3—34no—
588C4×D3—34no—
589C4×D3—64no—
590C4×D3—122no—
591C4×D3—362no—
592C4×D3—362no—
593C4×D3—362no—
594C4×D3—364no—
595C4×D3D3×Dic314yescomplemented
596C4×D3D3×Dic314yescomplemented
597Dic6—34no—
598Dic6—34no—
599C2×C32—21no—
600C2×C32—21no—
601C2×C32—21no—
602C2×C32—21no—
603C2×C32—21no—
604C2×C32—21no—
605C2×C32—21no—
606C2×C32—21no—
607C2×C32—21no—
608C2×C32—41no—
609C2×C32—41no—
610C2×C32—41no—
611C2×C32—62no—
612C2×C32—62no—
613C2×C32C22×C4×D311yescharacteristic
614C2×C32C22×C4×D311yescharacteristic
615C2×C32#100411yescharacteristic
616C2×C32#100711yescharacteristic
617C2×C32#100911yescharacteristic
618C2×C32#100911yescharacteristic
619C2×C32#101011yescharacteristic
620C2×C32#101011yescharacteristic
621C2×C32C23×Dic311yescharacteristic
622C3⋊D3—22no—
623C3×D3—24no—
624C3×D3—22no—
625C3×D3—22no—
626C3×D3—22no—
627C3×D3—22no—
628C3×D3—42no—
629C3×D3—64no—
630C3×D3—62no—
631C3×D3—62no—
632#41—98no—
633C2×Q8—91no—
634C2×D4—91no—
635C2×D4—91no—
636C2×D4—91no—
637C22×C4—31no—
638C22×C4—31no—
639C22×C4—92no—
640C22×C4—91no—
641C22×C4—272no—
642C22×C4—272no—
643C4⋊C4—31no—
644C4⋊C4—92no—
645C4⋊C4—91no—
646C4⋊C4—91no—
647C4⋊C4—272no—
648C4⋊C4—272no—
649C4⋊C4—271no—
650C22⋊C4—92no—
651C22⋊C4—272no—
652C22⋊C4—272no—
653C42—92no—
654C42—272no—
655C42—272no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—32no—
660C22×C3—32no—
661C22×C3—32no—
662C22×C3—32no—
663C22×C3—41no—
664C22×C3—62no—
665C22×C3—62no—
666C22×C3—62no—
667C22×C3—62no—
668C22×C3—61no—
669C22×C3—61no—
670C22×C3—61no—
671C22×C3—61no—
672C22×C3—61no—
673C22×C3—61no—
674C22×C3—61no—
675C22×C3—61no—
676C22×C3—92no—
677C22×C3—121no—
678C22×C3—121no—
679C22×C3—181no—
680C22×C3—181no—
681C22×C3C22×D3211yescharacteristic
682C22×C3C22×D3211yescharacteristic
683C22×C3C22×D3211yescharacteristic
684C2×D3—21no—
685C2×D3—21no—
686C2×D3—21no—
687C2×D3—21no—
688C2×D3—32no—
689C2×D3—32no—
690C2×D3—62no—
691C2×D3—62no—
692C2×D3—62no—
693C2×D3—61no—
694C2×D3—61no—
695C2×D3—61no—
696C2×D3—61no—
697C2×D3C2×D3×Dic312yes—
698C2×D3C2×D3×Dic312yes—
699C3×C4—22no—
700C3×C4—22no—
701C3×C4—22no—
702C3×C4—32no—
703C3×C4—32no—
704C3×C4—32no—
705C3×C4—32no—
706C3×C4—42no—
707C3×C4—62no—
708C3×C4—62no—
709C3×C4—62no—
710C3×C4—62no—
711C3×C4—92no—
712C3×C4—122no—
713C3×C4—182no—
714C3×C4—182no—
715C3×C4C4×D3212yes—
716C3×C4C2×D3×Dic312yes—
717C3×C4C2×D3×Dic312yes—
718Dic3—22no—
719Dic3—32no—
720Dic3—32no—
721Dic3—62no—
722Dic3—62no—
723Dic3—62no—
724Dic3—62no—
725Dic3—62no—
726Dic3—122no—
727Dic3—122no—
728Dic3—182no—
729Dic3—182no—
730Dic3—182no—
731Dic3—362no—
732Dic3—362no—
733Dic3—362no—
734Dic3—722no—
735Dic3C2×D3×Dic312yes—
736Dic3C2×D3×Dic312yes—
737C32—21no—
738C32—21no—
739C32—21no—
740C32—41no—
741C32#550411yescharacteristic, complemented
742C32#552311yescharacteristic, complemented
743C32#582711yescharacteristic, complemented
744C23—31no—
745C23—31no—
746C23—91no—
747Q8—94no—
748D4—94no—
749D4—94no—
750D4—94no—
751C2×C4—31no—
752C2×C4—31no—
753C2×C4—34no—
754C2×C4—34no—
755C2×C4—32no—
756C2×C4—91no—
757C2×C4—94no—
758C2×C4—92no—
759C2×C4—92no—
760C2×C4—272no—
761C2×C4—362no—
762C2×C4—1082no—
763C2×C4—1082no—
764C2×C4D3311yescharacteristic
765C2×C3—21no—
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—21no—
769C2×C3—21no—
770C2×C3—21no—
771C2×C3—21no—
772C2×C3—21no—
773C2×C3—21no—
774C2×C3—41no—
775C2×C3—41no—
776C2×C3—41no—
777C2×C3—64no—
778C2×C3—62no—
779C2×C3—62no—
780C2×C3—62no—
781C2×C3—62no—
782C2×C3—122no—
783C2×C3—182no—
784C2×C3#6429711yescharacteristic
785C2×C3#6429811yescharacteristic
786C2×C3C2×C4×D3211yescharacteristic
787C2×C3#6430711yescharacteristic
788C2×C3#6430811yescharacteristic
789C2×C3#6431411yescharacteristic
790C2×C3#6431511yescharacteristic
791C2×C3C22×D3×Dic311yescharacteristic
792C2×C3C22×D3×Dic311yescharacteristic
793D3—22no—
794D3—22no—
795D3—64no—
796D3—62no—
797D3—62no—
798C22—32no—
799C22—32no—
800C22—61no—
801C22—61no—
802C22—61no—
803C22—61no—
804C22—92no—
805C22—181no—
806C22—181no—
807C22C2×D3311yescharacteristic
808C4—32no—
809C4—32no—
810C4—62no—
811C4—92no—
812C4—182no—
813C4—182no—
814C4—542no—
815C4D32×Dic312yes—
816C3—21no—
817C3—21no—
818C3—21no—
819C3—41no—
820C3#1059451011yescharacteristic, complemented
821C3#1059498611yescharacteristic, complemented
822C3#1059499211yescharacteristic, complemented
823C2—62no—
824C2—62no—
825C2—182no—
826C2#1172438411yescharacteristic
827C2#1172439611yescharacteristic
828C2C2×D32×Dic311yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutatorC2×C33C23×C4
FittingC2×C33×C4C23
socle, cosocleC22×C33C24
prime radicalC2×C3×#3798C2
hypercenterC2×C4D33
hypocenterC33#520
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. #11723667C2semidirect
3. C3⋊D3×C4⋊Dic3C2semidirect
4. D3×C4⋊(C3⋊Dic3)C2semidirect
5. #11723424C2semidirect
6. C3×D3×C4⋊Dic3C2semidirect
7. C3×#63841C2semidirect
8. #11722940C2semidirect
9. #11722929C2semidirect
10. Dic3×#626C2semidirect
11. #11722924C2semidirect
25. C3×#3798C4semidirect
62. D3×C4⋊Dic3D3semidirect
73. #63841D3semidirect
83. C3×C4×C3⋊D3C2×C4semidirect
87. C32×C4×D3C2×C4semidirect
88. C32×C4×D3C2×C4semidirect
91. C3×#627C2×C4semidirect
92. C3×#626C2×C4semidirect
93. C3×#626C2×C4semidirect
94. C3×#625C2×C4semidirect
136. #3798Dic3semidirect
277. C4×C3⋊D3C2×Dic3semidirect
309. C3×C4×D3C4×D3semidirect
310. C3×C4×D3C4×D3semidirect
311. C3×C4×D3C2×Dic3semidirect
312. C3×C4×D3C2×Dic3semidirect
315. #627C2×Dic3semidirect
316. #626C2×Dic3semidirect
317. #626C2×Dic3semidirect
318. #625C2×Dic3semidirect
513. C33#520semidirect
595. C4×D3D3×Dic3semidirect
596. C4×D3D3×Dic3semidirect
741. C32#5504semidirect
742. C32#5523semidirect
743. C32#5827semidirect
820. C3#10594510semidirect
821. C3#10594986semidirect
822. C3#10594992semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#37982
#117236672
C3⋊D3×C4⋊Dic32
D3×C4⋊(C3⋊Dic3)2
#117234242
C3×D3×C4⋊Dic32
C3×#638412
#117229402
#117229292
Dic3×#6262
#117229242
#105949923
#105949863
#105945103