Finite Group Databasebeta

← #13167872

Subgroups — #13167872

Order 1728.

1542 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3795C211yesmaximal, characteristic
2#11723668C211yesmaximal, characteristic, complemented
3#11723499C211yesmaximal, characteristic, complemented
4C4×D3×C3⋊Dic3C211yesmaximal, characteristic, complemented
5#11723410C211yesmaximal, characteristic, complemented
6C3×#63898C211yesmaximal, characteristic, complemented
7C3×#63841C211yesmaximal, characteristic, complemented
8#11722925C212yesmaximal, complemented
9#11722924C212yesmaximal, complemented
10#11722913C212yesmaximal, complemented
11D3×Dic32C212yesmaximal, complemented
12Dic3×#237—31nomaximal
13#10594958—31nomaximal
14#10594358—31nomaximal
15C2×C3×#634C2211yescharacteristic
16C2×C32×D12C2211yescharacteristic
17C2×C32×C4×D3C2211yescharacteristic
18C2×D3×C3⋊Dic3C2212yes—
19C2×D3×C3⋊Dic3C2211yescharacteristic
20C2×D3×C3⋊Dic3C2211yescharacteristic
21C2×C3×#625C2212yes—
22C2×C3×D3×Dic3C2212yes—
23C2×C3×D3×Dic3C2212yes—
24C3×#3795C418yescomplemented
25C4×C3⋊(C3⋊Dic3)C2211yescharacteristic
26C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
27C3×C4×C3⋊Dic3C2211yescharacteristic
28C32×C4⋊Dic3C2211yescharacteristic
29#88815C2212yes—
30#88813C2212yes—
31#88807C2212yes—
32(C2×D3)⋊(C3⋊Dic3)C2212yes—
33Dic3×C3⋊Dic3C2211yescharacteristic
34Dic3×C3⋊Dic3C2212yes—
35Dic3×C3⋊Dic3C2211yescharacteristic
36C3×(C2×D3)⋊Dic3C2212yes—
37C3×(C2×D3)⋊Dic3C2212yes—
38C3×Dic32C2212yes—
39C2×C3×#237—31no—
40C2×C3×#235—31no—
41C2×#3795D311yescharacteristic
42D4×C3⋊Dic3—31no—
43C2×C4×C3⋊Dic3—31no—
44#64096—31no—
45C3×D4×Dic3—31no—
46C3×#926—31no—
47C3×#893—31no—
48C3×#892—31no—
49#67⋊Dic3—32no—
50#67⋊Dic3—32no—
51#67⋊Dic3—32no—
52Dic3×#67—32no—
53#63955—32no—
54C2×Dic32—32no—
55#63902—32no—
56#63898—31no—
57#63898—31no—
58#63898—61no—
59#63898D311yescharacteristic, complemented
60#63879—32no—
61#63877—32no—
62C4×D3×Dic3—31no—
63C4×D3×Dic3—31no—
64C4×D3×Dic3—32no—
65C4×D3×Dic3—32no—
66C4×D3×Dic3—61no—
67#63855—32no—
68#63844—31no—
69#63843—31no—
70#63843—31no—
71#63843—31no—
72#63843—61no—
73Dic3×Dic6—31no—
74#63841D311yescharacteristic, complemented
75C22×C32×D3C2312yes—
76C22×C32×D3C2311yescharacteristic
77C2×C33×C4C2311yescharacteristic
78C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
79C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
80C2×C3×C3⋊Dic3C2311yescharacteristic
81C2×C3×C3⋊Dic3C2312yes—
82C2×C3×C3⋊Dic3C2312yes—
83C2×C3×C3⋊Dic3C2311yescharacteristic
84C3×#634C2×C414yescomplemented
85C2×C32×Dic3C2312yes—
86C2×C32×Dic3C2311yescharacteristic
87C32×D12C2×C414yescomplemented
88C32×C4×D3C2×C414yescomplemented
89D3×C3⋊Dic3—22no—
90D3×C3⋊Dic3—24no—
91D3×C3⋊Dic3—22no—
92C3×#625C2×C418yescomplemented
93C3×D3×Dic3—24no—
94C3×D3×Dic3C2×C418yescomplemented
95Dic3×#41—91no—
96C4×#237—91no—
97#5522—91no—
98C2×C32×D4—31no—
99C22×C32×C4—31no—
100C22×C3⋊Dic3—31no—
101C22×C3⋊Dic3—31no—
102C22×C3⋊Dic3—32no—
103C2×#634C2×D311yescharacteristic
104C2×C3×#67—32no—
105C2×C3×#67—32no—
106C22×C3×Dic3—32no—
107C22×C3×Dic3—32no—
108C3×#237—38no—
109C3×#235—38no—
110C2×C3×D12—21no—
111C2×C3×D12C2×D311yescharacteristic
112C2×C3×D12C2×D311yescharacteristic
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3—32no—
115C2×C3×C4×D3—32no—
116C2×C3×C4×D3C2×D311yescharacteristic
117C2×C3×C4×D3C2×D311yescharacteristic
118C2×C3×Dic6—31no—
119C2×C3×Dic6—31no—
120C2×C3×Dic6—61no—
121C2×#625C2×D312yes—
122C2×D3×Dic3—31no—
123C2×D3×Dic3—32no—
124C2×D3×Dic3—32no—
125C2×D3×Dic3—31no—
126C2×D3×Dic3—31no—
127C2×D3×Dic3—31no—
128C2×D3×Dic3—61no—
129C2×D3×Dic3—61no—
130C2×D3×Dic3—62no—
131C2×D3×Dic3C2×D312yes—
132C2×D3×Dic3C2×D312yes—
133#3795Dic318yescomplemented
134C32×C4⋊C4—31no—
135#3757—32no—
136C4⋊(C3⋊Dic3)C2×D311yescharacteristic
137#3750—32no—
138C4×C3⋊Dic3—31no—
139C4×C3⋊Dic3—31no—
140C4×C3⋊Dic3—31no—
141C4×C3⋊Dic3—32no—
142C4×C3⋊Dic3—31no—
143C4×C3⋊Dic3—31no—
144C4×C3⋊Dic3—61no—
145C4×C3⋊Dic3—61no—
146C4×C3⋊Dic3—61no—
147C4×C3⋊Dic3—121no—
148C4×C3⋊Dic3C2×D311yescharacteristic
149C3×#217—32no—
150C3×#217—32no—
151C3×(C2×D3)⋊C4—32no—
152C3×(C2×D3)⋊C4—32no—
153C3×C4⋊Dic3—21no—
154C3×C4⋊Dic3—31no—
155C3×C4⋊Dic3—31no—
156C3×C4⋊Dic3—61no—
157C3×C4⋊Dic3C2×D311yescharacteristic
158C3×C4⋊Dic3C2×D311yescharacteristic
159C3×C4×Dic3—31no—
160C3×C4×Dic3—31no—
161C3×C4×Dic3—32no—
162C3×C4×Dic3—32no—
163C3×C4×Dic3—61no—
164#3724—32no—
165Dic3⋊Dic3—32no—
166Dic3⋊Dic3—32no—
167Dic3⋊Dic3—32no—
168Dic3⋊Dic3—32no—
169Dic3⋊Dic3—62no—
170(C2×D3)⋊Dic3—32no—
171(C2×D3)⋊Dic3—32no—
172(C2×D3)⋊Dic3—62no—
173(C2×D3)⋊Dic3C2×D312yes—
174(C2×D3)⋊Dic3C2×D312yes—
175Dic32—32no—
176Dic32—32no—
177Dic32—32no—
178Dic32—32no—
179Dic32—32no—
180Dic32—31no—
181Dic32—31no—
182Dic32—31no—
183Dic32—31no—
184Dic32—62no—
185Dic32—61no—
186Dic32—61no—
187Dic32C2×D312yes—
188C22×C33C2411yescharacteristic
189C2×C32×D3—21no—
190C2×C32×D3—21no—
191C2×C32×D3—22no—
192C2×C32×D3—22no—
193C2×C32×D3C22×C414yes—
194C2×C32×D3C22×C412yes—
195C33×C4C22×C412yes—
196C3⋊(C3⋊Dic3)—21no—
197C3⋊(C3⋊Dic3)#4112yescomplemented
198C3×C3⋊Dic3—21no—
199C3×C3⋊Dic3—22no—
200C3×C3⋊Dic3C22×C414yes—
201C3×C3⋊Dic3#4112yescomplemented
202C32×Dic3—22no—
203C32×Dic3C22×C412yes—
204C2×C3×#41—91no—
205C2×#237—31no—
206C2×#235—31no—
207C3×C4×D4—91no—
208C3×#117—91no—
209Q8×Dic3—91no—
210Q8×Dic3—91no—
211D4×Dic3—31no—
212D4×Dic3—91no—
213D4×Dic3—91no—
214D4×Dic3—92no—
215D4×Dic3—92no—
216D4×Dic3—181no—
217C4×#67—92no—
218#926—31no—
219#926—92no—
220C2×C4×Dic3—92no—
221C2×C4×Dic3—92no—
222C2×C4×Dic3—91no—
223C2×C4×Dic3—91no—
224C2×C4×Dic3—181no—
225#893—31no—
226#893—91no—
227#892—31no—
228#887—91no—
229#887—91no—
230#887—91no—
231#887—181no—
232#67⋊C4—92no—
233#67⋊C4—92no—
234#67⋊C4—92no—
235#877—92no—
236#872—92no—
237C42×D3—92no—
238C42×D3—91no—
239C4×Dic6—91no—
240C23×C32—31no—
241C23×C32—32no—
242C22×C3×D3—21no—
243C22×C3×D3—22no—
244C22×C3×D3C22×D312yes—
245C22×C3×D3C22×D311yescharacteristic
246C22×C3×D3C22×D312yes—
247C22×C3×D3C22×D311yescharacteristic
248C32×D4—34no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—31no—
253C2×C32×C4—34no—
254C2×C32×C4—32no—
255C2×C32×C4—41no—
256C2×C32×C4C22×D311yescharacteristic
257C2×C32×C4C22×D311yescharacteristic
258C2×C32×C4C22×D311yescharacteristic
259C2×C3⋊Dic3—31no—
260C2×C3⋊Dic3—31no—
261C2×C3⋊Dic3—31no—
262C2×C3⋊Dic3—31no—
263C2×C3⋊Dic3—31no—
264C2×C3⋊Dic3—31no—
265C2×C3⋊Dic3—61no—
266C2×C3⋊Dic3—61no—
267C2×C3⋊Dic3—61no—
268C2×C3⋊Dic3—61no—
269C2×C3⋊Dic3—61no—
270C2×C3⋊Dic3—61no—
271C2×C3⋊Dic3—62no—
272C2×C3⋊Dic3—62no—
273C2×C3⋊Dic3—64no—
274C2×C3⋊Dic3—121no—
275C2×C3⋊Dic3—121no—
276C2×C3⋊Dic3C22×D312yes—
277C2×C3⋊Dic3C22×D311yescharacteristic
278C2×C3⋊Dic3C22×D311yescharacteristic
279C2×C3⋊Dic3C22×D312yes—
280#634C2×Dic314yescomplemented
281C3×#67—38no—
282C3×#67—38no—
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—38no—
290C2×C3×Dic3—32no—
291C2×C3×Dic3—32no—
292C2×C3×Dic3—31no—
293C2×C3×Dic3—31no—
294C2×C3×Dic3—62no—
295C2×C3×Dic3—61no—
296C2×C3×Dic3—61no—
297C2×C3×Dic3—62no—
298C2×C3×Dic3—64no—
299C2×C3×Dic3C22×D312yes—
300C2×C3×Dic3C22×D312yes—
301C2×C3×Dic3C22×D311yescharacteristic
302C2×C3×Dic3C22×D311yescharacteristic
303C3×D12—24no—
304C3×D12C4×D314yescomplemented
305C3×D12C2×Dic314yescomplemented
306C3×C4×D3—24no—
307C3×C4×D3—38no—
308C3×C4×D3—64no—
309C3×C4×D3C4×D314yescomplemented
310C3×C4×D3C2×Dic314yescomplemented
311C3×Dic6—34no—
312C3×Dic6—34no—
313C3×Dic6—64no—
314#625C2×Dic318yescomplemented
315D3×Dic3—24no—
316D3×Dic3—62no—
317D3×Dic3—62no—
318D3×Dic3—62no—
319D3×Dic3—62no—
320D3×Dic3—64no—
321D3×Dic3—64no—
322D3×Dic3—64no—
323D3×Dic3—64no—
324D3×Dic3—124no—
325D3×Dic3C2×Dic318yescomplemented
326C4×#41—271noSylow
327C2×C33C23×C411yescharacteristic
328C2×C33C2×#4111yescharacteristic
329C2×C33C2×#4111yescharacteristic
330C32×D3—22no—
331C32×D3—24no—
332C3×#41—98no—
333C2×C3×Q8—91no—
334C2×C3×D4—31no—
335C2×C3×D4—31no—
336C2×C3×D4—61no—
337C2×C3×D4—92no—
338C22×C3×C4—31no—
339C22×C3×C4—31no—
340C22×C3×C4—61no—
341C22×C3×C4—92no—
342C22×C3×C4—92no—
343C2×#67—32no—
344C2×#67—32no—
345C22×Dic3—32no—
346C22×Dic3—32no—
347C22×Dic3—91no—
348C22×Dic3—91no—
349C22×Dic3—92no—
350C22×Dic3—91no—
351C22×Dic3—92no—
352C22×Dic3—91no—
353C22×Dic3—181no—
354C22×Dic3—181no—
355C22×Dic3—182no—
356#237—38no—
357#235—38no—
358C2×D12D3211yescharacteristic
359C2×C4×D3—32no—
360C2×C4×D3—32no—
361C2×C4×D3—91no—
362C2×C4×D3—92no—
363C2×C4×D3—91no—
364C2×C4×D3D3211yescharacteristic
365C2×Dic6—31no—
366C2×Dic6—31no—
367C2×Dic6—61no—
368C3×C4⋊C4—31no—
369C3×C4⋊C4—31no—
370C3×C4⋊C4—61no—
371C3×C4⋊C4—91no—
372C3×C22⋊C4—92no—
373C3×C22⋊C4—92no—
374C3×C42—92no—
375C3×C42—91no—
376#217—32no—
377#217—32no—
378#217—92no—
379#217—92no—
380#217—182no—
381(C2×D3)⋊C4—32no—
382(C2×D3)⋊C4—32no—
383(C2×D3)⋊C4—92no—
384C4⋊Dic3—31no—
385C4⋊Dic3—31no—
386C4⋊Dic3—61no—
387C4⋊Dic3—92no—
388C4⋊Dic3—92no—
389C4⋊Dic3D3211yescharacteristic
390Dic3⋊C4—92no—
391Dic3⋊C4—92no—
392Dic3⋊C4—92no—
393Dic3⋊C4—92no—
394Dic3⋊C4—182no—
395C4×Dic3—31no—
396C4×Dic3—31no—
397C4×Dic3—32no—
398C4×Dic3—32no—
399C4×Dic3—61no—
400C4×Dic3—92no—
401C4×Dic3—92no—
402C4×Dic3—92no—
403C4×Dic3—91no—
404C4×Dic3—92no—
405C4×Dic3—91no—
406C4×Dic3—92no—
407C4×Dic3—91no—
408C4×Dic3—91no—
409C4×Dic3—91no—
410C4×Dic3—91no—
411C4×Dic3—91no—
412C4×Dic3—91no—
413C4×Dic3—91no—
414C4×Dic3—92no—
415C4×Dic3—182no—
416C4×Dic3—181no—
417C4×Dic3—181no—
418C4×Dic3—181no—
419C4×Dic3—181no—
420C4×Dic3—181no—
421C4×Dic3—361no—
422C22×C32—21no—
423C22×C32—21no—
424C22×C32—21no—
425C22×C32—34no—
426C22×C32—32no—
427C22×C32—41no—
428C22×C32—61no—
429C22×C32—61no—
430C22×C32—62no—
431C22×C32—62no—
432C22×C32C23×D311yescharacteristic
433C22×C32C23×D311yescharacteristic
434C22×C32C23×D311yescharacteristic
435C2×C3×D3—22no—
436C2×C3×D3—22no—
437C2×C3×D3—22no—
438C2×C3×D3—21no—
439C2×C3×D3—21no—
440C2×C3×D3—21no—
441C2×C3×D3—21no—
442C2×C3×D3—22no—
443C2×C3×D3—22no—
444C2×C3×D3—22no—
445C2×C3×D3—22no—
446C2×C3×D3—24no—
447C2×C3×D3—42no—
448C2×C3×D3—42no—
449C2×C3×D3C2×C4×D314yes—
450C2×C3×D3C2×C4×D312yes—
451C2×C3×D3C22×Dic314yes—
452C2×C3×D3C22×Dic312yes—
453C32×C4—22no—
454C32×C4—22no—
455C32×C4—22no—
456C32×C4—32no—
457C32×C4—42no—
458C32×C4—62no—
459C32×C4C2×C4×D312yes—
460C32×C4C2×C4×D312yes—
461C32×C4C22×Dic312yes—
462C3⋊Dic3—21no—
463C3⋊Dic3—22no—
464C3⋊Dic3—32no—
465C3⋊Dic3—32no—
466C3⋊Dic3—32no—
467C3⋊Dic3—62no—
468C3⋊Dic3—62no—
469C3⋊Dic3—62no—
470C3⋊Dic3—61no—
471C3⋊Dic3—62no—
472C3⋊Dic3—61no—
473C3⋊Dic3—61no—
474C3⋊Dic3—122no—
475C3⋊Dic3—121no—
476C3⋊Dic3—121no—
477C3⋊Dic3—122no—
478C3⋊Dic3#23712yescomplemented
479C3⋊Dic3C22×Dic314yes—
480C3×Dic3—22no—
481C3×Dic3—22no—
482C3×Dic3—22no—
483C3×Dic3—34no—
484C3×Dic3—34no—
485C3×Dic3—32no—
486C3×Dic3—32no—
487C3×Dic3—42no—
488C3×Dic3—64no—
489C3×Dic3—62no—
490C3×Dic3—62no—
491C3×Dic3—62no—
492C3×Dic3—61no—
493C3×Dic3—61no—
494C3×Dic3—62no—
495C3×Dic3—122no—
496C3×Dic3C2×C4×D312yes—
497C3×Dic3C22×Dic312yes—
498C2×#41—91no—
499C4×Q8—271no—
500C4×Q8—271no—
501C4×D4—91no—
502C4×D4—272no—
503C4×D4—272no—
504C4×D4—271no—
505#117—91no—
506#117—272no—
507C2×C42—271no—
508C2×C42—272no—
509C33C4×#4111yescharacteristic, complemented, Sylow
510C23×C3—31no—
511C23×C3—32no—
512C23×C3—32no—
513C23×C3—31no—
514C23×C3—61no—
515C23×C3—62no—
516C22×D3C2×D3211yescharacteristic
517C22×D3C2×D3212yes—
518C3×Q8—94no—
519C3×D4—34no—
520C3×D4—34no—
521C3×D4—64no—
522C3×D4—98no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—31no—
527C2×C3×C4—31no—
528C2×C3×C4—34no—
529C2×C3×C4—34no—
530C2×C3×C4—32no—
531C2×C3×C4—32no—
532C2×C3×C4—41no—
533C2×C3×C4—64no—
534C2×C3×C4—61no—
535C2×C3×C4—62no—
536C2×C3×C4—98no—
537C2×C3×C4—91no—
538C2×C3×C4—92no—
539C2×C3×C4—91no—
540C2×C3×C4—92no—
541C2×C3×C4—184no—
542C2×C3×C4C2×D3211yescharacteristic
543C2×C3×C4C2×D3211yescharacteristic
544C2×C3×C4C2×D3211yescharacteristic
545#67—38no—
546#67—38no—
547C2×Dic3—31no—
548C2×Dic3—31no—
549C2×Dic3—32no—
550C2×Dic3—32no—
551C2×Dic3—38no—
552C2×Dic3—31no—
553C2×Dic3—32no—
554C2×Dic3—32no—
555C2×Dic3—31no—
556C2×Dic3—61no—
557C2×Dic3—61no—
558C2×Dic3—62no—
559C2×Dic3—62no—
560C2×Dic3—64no—
561C2×Dic3—91no—
562C2×Dic3—91no—
563C2×Dic3—91no—
564C2×Dic3—91no—
565C2×Dic3—91no—
566C2×Dic3—91no—
567C2×Dic3—181no—
568C2×Dic3—181no—
569C2×Dic3—181no—
570C2×Dic3—181no—
571C2×Dic3—181no—
572C2×Dic3—181no—
573C2×Dic3—182no—
574C2×Dic3—182no—
575C2×Dic3—182no—
576C2×Dic3—182no—
577C2×Dic3—184no—
578C2×Dic3—184no—
579C2×Dic3—184no—
580C2×Dic3—184no—
581C2×Dic3—361no—
582C2×Dic3—361no—
583C2×Dic3—364no—
584C2×Dic3C2×D3212yes—
585C2×Dic3C2×D3211yescharacteristic
586D12D3×Dic314yescomplemented
587C4×D3—38no—
588C4×D3—64no—
589C4×D3—182no—
590C4×D3—184no—
591C4×D3—182no—
592C4×D3D3×Dic314yescomplemented
593Dic6—34no—
594Dic6—34no—
595Dic6—64no—
596C2×C32—21no—
597C2×C32—21no—
598C2×C32—21no—
599C2×C32—21no—
600C2×C32—21no—
601C2×C32—21no—
602C2×C32—21no—
603C2×C32—21no—
604C2×C32—21no—
605C2×C32—41no—
606C2×C32—41no—
607C2×C32—41no—
608C2×C32—62no—
609C2×C32—64no—
610C2×C32C22×C4×D311yescharacteristic
611C2×C32C22×C4×D311yescharacteristic
612C2×C32C2×#23711yescharacteristic
613C2×C32D3×#4111yescharacteristic
614C2×C32D3×#4111yescharacteristic
615C2×C32D3×#4111yescharacteristic
616C2×C32D3×#4111yescharacteristic
617C2×C32D3×#4111yescharacteristic
618C2×C32C23×Dic311yescharacteristic
619C3×D3—24no—
620C3×D3—22no—
621C3×D3—24no—
622C3×D3—24no—
623C3×D3—22no—
624C3×D3—44no—
625#41—98no—
626C2×Q8—91no—
627C2×D4—31no—
628C2×D4—92no—
629C22×C4—31no—
630C22×C4—92no—
631C22×C4—92no—
632C22×C4—271no—
633C22×C4—271no—
634C22×C4—272no—
635C4⋊C4—31no—
636C4⋊C4—91no—
637C4⋊C4—272no—
638C4⋊C4—272no—
639C22⋊C4—92no—
640C22⋊C4—92no—
641C22⋊C4—272no—
642C42—92no—
643C42—91no—
644C42—271no—
645C42—271no—
646C42—272no—
647C42—272no—
648C42—271no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—32no—
653C22×C3—34no—
654C22×C3—34no—
655C22×C3—32no—
656C22×C3—41no—
657C22×C3—62no—
658C22×C3—64no—
659C22×C3—62no—
660C22×C3—62no—
661C22×C3—62no—
662C22×C3—62no—
663C22×C3—62no—
664C22×C3—61no—
665C22×C3—61no—
666C22×C3—61no—
667C22×C3—61no—
668C22×C3—62no—
669C22×C3—122no—
670C22×C3—122no—
671C22×C3C22×D3211yescharacteristic
672C22×C3C22×D3211yescharacteristic
673C22×C3C22×D3211yescharacteristic
674C2×D3—21no—
675C2×D3—21no—
676C2×D3—22no—
677C2×D3—22no—
678C2×D3C2×D3×Dic314yes—
679C2×D3C2×D3×Dic312yes—
680C3×C4—22no—
681C3×C4—22no—
682C3×C4—22no—
683C3×C4—32no—
684C3×C4—32no—
685C3×C4—42no—
686C3×C4—62no—
687C3×C4—62no—
688C3×C4—62no—
689C3×C4—94no—
690C3×C4—92no—
691C3×C4—122no—
692C3×C4—181no—
693C3×C4—182no—
694C3×C4C4×D3212yes—
695C3×C4C2×D3×Dic312yes—
696C3×C4C2×D3×Dic312yes—
697Dic3—22no—
698Dic3—32no—
699Dic3—32no—
700Dic3—34no—
701Dic3—34no—
702Dic3—64no—
703Dic3—62no—
704Dic3—62no—
705Dic3—62no—
706Dic3—61no—
707Dic3—61no—
708Dic3—62no—
709Dic3—92no—
710Dic3—92no—
711Dic3—92no—
712Dic3—122no—
713Dic3—182no—
714Dic3—182no—
715Dic3—182no—
716Dic3—182no—
717Dic3—181no—
718Dic3—181no—
719Dic3—181no—
720Dic3—362no—
721Dic3—361no—
722Dic3—361no—
723Dic3—362no—
724Dic3C2×D3×Dic312yes—
725C32—21no—
726C32—21no—
727C32—21no—
728C32—41no—
729C32#552211yescharacteristic, complemented
730C32C4×#23711yescharacteristic, complemented
731C32Dic3×#4111yescharacteristic, complemented
732C23—31no—
733C23—32no—
734Q8—94no—
735D4—34no—
736D4—98no—
737C2×C4—31no—
738C2×C4—34no—
739C2×C4—32no—
740C2×C4—98no—
741C2×C4—91no—
742C2×C4—92no—
743C2×C4—91no—
744C2×C4—92no—
745C2×C4—184no—
746C2×C4—271no—
747C2×C4—271no—
748C2×C4—542no—
749C2×C4—542no—
750C2×C4—544no—
751C2×C4D3311yescharacteristic
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—21no—
755C2×C3—21no—
756C2×C3—21no—
757C2×C3—21no—
758C2×C3—21no—
759C2×C3—21no—
760C2×C3—21no—
761C2×C3—41no—
762C2×C3—41no—
763C2×C3—41no—
764C2×C3—64no—
765C2×C3—62no—
766C2×C3—64no—
767C2×C3—62no—
768C2×C3—64no—
769C2×C3—124no—
770C2×C3C2×C4×D3211yescharacteristic
771C2×C3#6430611yescharacteristic
772C2×C3#6430611yescharacteristic
773C2×C3D3×#23711yescharacteristic
774C2×C3D3×#23711yescharacteristic
775C2×C3#6431211yescharacteristic
776C2×C3#6431911yescharacteristic
777C2×C3C22×D3×Dic311yescharacteristic
778C2×C3C22×D3×Dic311yescharacteristic
779D3—24no—
780D3—22no—
781C22—32no—
782C22—34no—
783C22—62no—
784C22—61no—
785C22—61no—
786C22—62no—
787C22C2×D3311yescharacteristic
788C4—32no—
789C4—62no—
790C4—92no—
791C4—94no—
792C4—181no—
793C4—182no—
794C4—272no—
795C4—541no—
796C4D32×Dic312yes—
797C3—21no—
798C3—21no—
799C3—21no—
800C3—41no—
801C3#1059435811yescharacteristic, complemented
802C3#1059495811yescharacteristic, complemented
803C3Dic3×#23711yescharacteristic, complemented
804C2—62no—
805C2—64no—
806C2#1172437311yescharacteristic
807C2#1172437611yescharacteristic
808C2C2×D32×Dic311yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutatorC2×C33C23×C4
FittingC2×C33×C4C23
socle, cosocleC22×C33C24
prime radicalC2×C3×#3795C2
hypercenterC2×C4D33
hypocenterC33C4×#41
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. #11723668C2semidirect
3. #11723499C2semidirect
4. C4×D3×C3⋊Dic3C2semidirect
5. #11723410C2semidirect
6. C3×#63898C2semidirect
7. C3×#63841C2semidirect
8. #11722925C2semidirect
9. #11722924C2semidirect
10. #11722913C2semidirect
11. D3×Dic32C2semidirect
24. C3×#3795C4semidirect
59. #63898D3semidirect
74. #63841D3semidirect
84. C3×#634C2×C4semidirect
87. C32×D12C2×C4semidirect
88. C32×C4×D3C2×C4semidirect
92. C3×#625C2×C4semidirect
94. C3×D3×Dic3C2×C4semidirect
133. #3795Dic3semidirect
197. C3⋊(C3⋊Dic3)#41semidirect
201. C3×C3⋊Dic3#41semidirect
280. #634C2×Dic3semidirect
304. C3×D12C4×D3semidirect
305. C3×D12C2×Dic3semidirect
309. C3×C4×D3C4×D3semidirect
310. C3×C4×D3C2×Dic3semidirect
314. #625C2×Dic3semidirect
325. D3×Dic3C2×Dic3semidirect
478. C3⋊Dic3#237semidirect
509. C33C4×#41semidirect
586. D12D3×Dic3semidirect
592. C4×D3D3×Dic3semidirect
729. C32#5522semidirect
730. C32C4×#237semidirect
731. C32Dic3×#41semidirect
801. C3#10594358semidirect
802. C3#10594958semidirect
803. C3Dic3×#237semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#37952
#117236682
#117234992
C4×D3×C3⋊Dic32
#117234102
C3×#638982
C3×#638412
#117229252
#117229242
#117229132
D3×Dic322
Dic3×#2373
#105949583
#105943583