Finite Group Databasebeta

← #13156738

Subgroups — #13156738

Order 1728.

834 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×Dic32C211yesmaximal, characteristic
2#11722082C211yesmaximal, characteristic
3#11722061C211yesmaximal, characteristic
4#11722061C211yesmaximal, characteristic
5#11722061C211yesmaximal, characteristic
6C3×#63579C211yesmaximal, characteristic
7C3×#63579C211yesmaximal, characteristic
8#10591248—31nomaximal
9#10591223—31nomaximal
10#10591223—31nomaximal
11C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
12C22×C3×C3⋊Dic3C2211yescharacteristic
13C22×C3×C3⋊Dic3C2211yescharacteristic
14C22×C3×C3⋊Dic3C2211yescharacteristic
15C22×C32×Dic3C2211yescharacteristic
16C22×C32×Dic3C2211yescharacteristic
17C22×C32×Dic3C2211yescharacteristic
18C3×Dic32C414yescomplemented
19C2×C3×C4×Dic3—31no—
20C2×C3×C4×Dic3—31no—
21C2×Dic32D311yescharacteristic
22#63658—31no—
23#63658—31no—
24#63658—31no—
25C3×C3⋊#95—31no—
26C3×C3⋊#95—31no—
27C3×C3⋊#95—31no—
28C3×C3⋊#95—31no—
29#63579—31no—
30#63579—31no—
31#63579—31no—
32#63579—31no—
33#63579—31no—
34#63579—31no—
35#63579—31no—
36#63579—31no—
37#63579—31no—
38#63579—61no—
39#63579—61no—
40#63579—61no—
41#63579D311yescharacteristic
42#63579D311yescharacteristic
43C23×C33C2311yescharacteristic
44C2×C3⋊(C3⋊Dic3)—21no—
45C2×C3⋊(C3⋊Dic3)—21no—
46C2×C3⋊(C3⋊Dic3)—21no—
47C2×C3×C3⋊Dic3—21no—
48C2×C3×C3⋊Dic3—21no—
49C2×C3×C3⋊Dic3—21no—
50C2×C3×C3⋊Dic3—21no—
51C2×C3×C3⋊Dic3—21no—
52C2×C3×C3⋊Dic3—21no—
53C2×C3×C3⋊Dic3—21no—
54C2×C3×C3⋊Dic3—21no—
55C2×C3×C3⋊Dic3C2×C412yes—
56C2×C32×Dic3—21no—
57C2×C32×Dic3—21no—
58C2×C32×Dic3—21no—
59C2×C32×Dic3—21no—
60C2×C32×Dic3—21no—
61C2×C32×Dic3—21no—
62C2×C32×Dic3—21no—
63C2×C32×Dic3C2×C412yes—
64C2×C32×Dic3C2×C412yes—
65#4937—91no—
66#4651—91no—
67#4651—91no—
68C22×C32×C4—31no—
69C22×C32×C4—31no—
70C22×C32×C4—31no—
71C22×C3⋊Dic3—31no—
72C22×C3⋊Dic3—31no—
73C22×C3⋊Dic3—31no—
74C22×C3⋊Dic3—61no—
75C22×C3⋊Dic3—61no—
76C22×C3⋊Dic3—61no—
77C22×C3⋊Dic3—121no—
78C22×C3⋊Dic3C2×D311yescharacteristic
79C22×C3⋊Dic3C2×D311yescharacteristic
80C22×C3⋊Dic3C2×D311yescharacteristic
81C22×C3×Dic3—21no—
82C22×C3×Dic3—21no—
83C22×C3×Dic3—21no—
84C22×C3×Dic3—31no—
85C22×C3×Dic3—31no—
86C22×C3×Dic3—31no—
87C22×C3×Dic3—31no—
88C22×C3×Dic3—31no—
89C22×C3×Dic3—31no—
90C22×C3×Dic3—61no—
91C22×C3×Dic3—61no—
92C22×C3×Dic3—61no—
93C22×C3×Dic3C2×D311yescharacteristic
94C22×C3×Dic3C2×D311yescharacteristic
95C22×C3×Dic3C2×D311yescharacteristic
96C22×C3×Dic3C2×D311yescharacteristic
97C22×C3×Dic3C2×D311yescharacteristic
98C22×C3×Dic3C2×D311yescharacteristic
99C3×C4×Dic3—34no—
100C3×C4×Dic3—34no—
101Dic32Dic314yescomplemented
102C22×C33C22×C411yescharacteristic
103C22×C33#4111yescharacteristic
104C22×C33#4111yescharacteristic
105C22×C33#4111yescharacteristic
106C22×C33#4111yescharacteristic
107C22×C33#4111yescharacteristic
108C22×C33#4111yescharacteristic
109C3⋊(C3⋊Dic3)—41no—
110C3×C3⋊Dic3—22no—
111C3×C3⋊Dic3—41no—
112C3×C3⋊Dic3—41no—
113C32×Dic3—22no—
114C32×Dic3—22no—
115C32×Dic3—41no—
116C2×C3×C42—91no—
117C2×C4×Dic3—31no—
118C2×C4×Dic3—31no—
119C3×#95—91no—
120C3×#95—91no—
121C3⋊#95—31no—
122C3⋊#95—31no—
123C3⋊#95—31no—
124C3⋊#95—31no—
125C3⋊#95—91no—
126C3⋊#95—91no—
127C3⋊#95—91no—
128C3⋊#95—91no—
129C3⋊#95—91no—
130C3⋊#95—91no—
131C3⋊#95—91no—
132C3⋊#95—91no—
133C3⋊#95—91no—
134C3⋊#95—91no—
135C3⋊#95—91no—
136C3⋊#95—91no—
137C3⋊#95—181no—
138C3⋊#95—181no—
139C3⋊#95—181no—
140C23×C32—21no—
141C23×C32—21no—
142C23×C32—21no—
143C23×C32—41no—
144C23×C32C22×D311yescharacteristic
145C23×C32C22×D311yescharacteristic
146C23×C32C22×D311yescharacteristic
147C2×C32×C4—32no—
148C2×C32×C4—32no—
149C2×C32×C4—61no—
150C2×C32×C4—61no—
151C2×C32×C4—61no—
152C2×C32×C4—61no—
153C2×C32×C4—61no—
154C2×C32×C4—61no—
155C2×C32×C4—61no—
156C2×C3⋊Dic3—21no—
157C2×C3⋊Dic3—21no—
158C2×C3⋊Dic3—21no—
159C2×C3⋊Dic3—21no—
160C2×C3⋊Dic3—21no—
161C2×C3⋊Dic3—21no—
162C2×C3⋊Dic3—21no—
163C2×C3⋊Dic3—21no—
164C2×C3⋊Dic3—61no—
165C2×C3⋊Dic3—61no—
166C2×C3⋊Dic3—61no—
167C2×C3⋊Dic3—62no—
168C2×C3⋊Dic3—62no—
169C2×C3⋊Dic3—62no—
170C2×C3⋊Dic3—61no—
171C2×C3⋊Dic3—61no—
172C2×C3⋊Dic3—61no—
173C2×C3⋊Dic3—61no—
174C2×C3⋊Dic3—61no—
175C2×C3⋊Dic3—61no—
176C2×C3⋊Dic3—121no—
177C2×C3⋊Dic3—121no—
178C2×C3⋊Dic3—121no—
179C2×C3⋊Dic3—121no—
180C2×C3⋊Dic3—121no—
181C2×C3⋊Dic3—121no—
182C2×C3⋊Dic3—122no—
183C2×C3⋊Dic3—122no—
184C2×C3⋊Dic3—122no—
185C2×C3⋊Dic3C2×Dic312yes—
186C2×C3×Dic3—21no—
187C2×C3×Dic3—21no—
188C2×C3×Dic3—21no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—21no—
193C2×C3×Dic3—21no—
194C2×C3×Dic3—22no—
195C2×C3×Dic3—21no—
196C2×C3×Dic3—21no—
197C2×C3×Dic3—21no—
198C2×C3×Dic3—21no—
199C2×C3×Dic3—21no—
200C2×C3×Dic3—21no—
201C2×C3×Dic3—22no—
202C2×C3×Dic3—22no—
203C2×C3×Dic3—32no—
204C2×C3×Dic3—32no—
205C2×C3×Dic3—41no—
206C2×C3×Dic3—41no—
207C2×C3×Dic3—41no—
208C2×C3×Dic3—41no—
209C2×C3×Dic3—41no—
210C2×C3×Dic3—41no—
211C2×C3×Dic3—62no—
212C2×C3×Dic3—61no—
213C2×C3×Dic3—61no—
214C2×C3×Dic3—61no—
215C2×C3×Dic3—61no—
216C2×C3×Dic3—62no—
217C2×C3×Dic3—62no—
218C2×C3×Dic3—61no—
219C2×C3×Dic3—61no—
220C2×C3×Dic3—61no—
221C2×C3×Dic3—61no—
222C2×C3×Dic3—61no—
223C2×C3×Dic3—61no—
224C2×C3×Dic3—61no—
225C2×C3×Dic3—61no—
226C2×C3×Dic3—61no—
227C2×C3×Dic3—61no—
228C2×C3×Dic3—61no—
229C2×C3×Dic3—61no—
230C2×C3×Dic3—121no—
231C2×C3×Dic3—121no—
232C2×C3×Dic3—121no—
233C2×C3×Dic3—121no—
234C2×C3×Dic3—121no—
235C2×C3×Dic3—121no—
236C2×C3×Dic3C4×D312yes—
237C2×C3×Dic3C4×D312yes—
238C2×C3×Dic3C2×Dic312yes—
239C2×C3×Dic3C2×Dic312yes—
240#383—271noSylow
241C2×C33#11711yescharacteristic
242C2×C33#11711yescharacteristic
243C2×C33#11711yescharacteristic
244C2×C33#12611yescharacteristic
245C2×C33#12611yescharacteristic
246C2×C33#12611yescharacteristic
247C2×C33#12611yescharacteristic
248C22×C3×C4—31no—
249C22×C3×C4—31no—
250C22×C3×C4—31no—
251C22×C3×C4—31no—
252C22×C3×C4—31no—
253C22×C3×C4—31no—
254C22×C3×C4—61no—
255C22×C3×C4—61no—
256C22×C3×C4—61no—
257C22×C3×C4—91no—
258C22×C3×C4—91no—
259C22×C3×C4—91no—
260C22×Dic3—31no—
261C22×Dic3—31no—
262C22×Dic3—31no—
263C22×Dic3—31no—
264C22×Dic3—31no—
265C22×Dic3—31no—
266C22×Dic3—61no—
267C22×Dic3—61no—
268C22×Dic3—61no—
269C22×Dic3—91no—
270C22×Dic3—91no—
271C22×Dic3—91no—
272C22×Dic3—181no—
273C22×Dic3—181no—
274C22×Dic3—181no—
275C22×Dic3—361no—
276C22×Dic3D3211yescharacteristic
277C22×Dic3D3211yescharacteristic
278C22×Dic3D3211yescharacteristic
279C3×C42—94no—
280C4×Dic3—34no—
281C4×Dic3—34no—
282C22×C32—21no—
283C22×C32—21no—
284C22×C32—21no—
285C22×C32—21no—
286C22×C32—21no—
287C22×C32—21no—
288C22×C32—21no—
289C22×C32—21no—
290C22×C32—21no—
291C22×C32—21no—
292C22×C32—21no—
293C22×C32—21no—
294C22×C32—21no—
295C22×C32—21no—
296C22×C32—21no—
297C22×C32—21no—
298C22×C32—21no—
299C22×C32—21no—
300C22×C32—21no—
301C22×C32—21no—
302C22×C32—21no—
303C22×C32—41no—
304C22×C32—41no—
305C22×C32—41no—
306C22×C32—41no—
307C22×C32—41no—
308C22×C32—41no—
309C22×C32—41no—
310C22×C32C2×C4×D311yescharacteristic
311C22×C32C2×C4×D311yescharacteristic
312C22×C32#23511yescharacteristic
313C22×C32#23511yescharacteristic
314C22×C32#23511yescharacteristic
315C22×C32#23511yescharacteristic
316C22×C32#23511yescharacteristic
317C22×C32#23511yescharacteristic
318C22×C32#23511yescharacteristic
319C22×C32#23511yescharacteristic
320C22×C32#23511yescharacteristic
321C22×C32#23511yescharacteristic
322C22×C32#23711yescharacteristic
323C22×C32#23711yescharacteristic
324C22×C32#23711yescharacteristic
325C22×C32#23711yescharacteristic
326C22×C32#23711yescharacteristic
327C22×C32#23711yescharacteristic
328C22×C32#23911yescharacteristic
329C22×C32#23911yescharacteristic
330C22×C32C22×Dic311yescharacteristic
331C32×C4—62no—
332C32×C4—62no—
333C32×C4—121no—
334C3⋊Dic3—22no—
335C3⋊Dic3—41no—
336C3⋊Dic3—41no—
337C3⋊Dic3—122no—
338C3⋊Dic3—122no—
339C3⋊Dic3—122no—
340C3⋊Dic3—124no—
341C3⋊Dic3—121no—
342C3⋊Dic3—121no—
343C3⋊Dic3—121no—
344C3×Dic3—22no—
345C3×Dic3—22no—
346C3×Dic3—22no—
347C3×Dic3—22no—
348C3×Dic3—42no—
349C3×Dic3—42no—
350C3×Dic3—42no—
351C3×Dic3—41no—
352C3×Dic3—41no—
353C3×Dic3—62no—
354C3×Dic3—62no—
355C3×Dic3—122no—
356C3×Dic3—122no—
357C3×Dic3—122no—
358C3×Dic3—121no—
359C3×Dic3—121no—
360C3×Dic3—121no—
361C3×Dic3—121no—
362C2×C42—91no—
363#95—91no—
364#95—91no—
365#95—271no—
366#95—271no—
367#95—271no—
368#95—271no—
369C33#38311yescharacteristic, complemented, Sylow
370C23×C3—21no—
371C23×C3—21no—
372C23×C3—21no—
373C23×C3—41no—
374C23×C3C2×D3211yescharacteristic
375C23×C3C2×D3211yescharacteristic
376C23×C3C2×D3211yescharacteristic
377C2×C3×C4—32no—
378C2×C3×C4—32no—
379C2×C3×C4—32no—
380C2×C3×C4—32no—
381C2×C3×C4—62no—
382C2×C3×C4—62no—
383C2×C3×C4—61no—
384C2×C3×C4—61no—
385C2×C3×C4—61no—
386C2×C3×C4—61no—
387C2×C3×C4—61no—
388C2×C3×C4—61no—
389C2×C3×C4—61no—
390C2×C3×C4—61no—
391C2×C3×C4—62no—
392C2×C3×C4—61no—
393C2×C3×C4—61no—
394C2×C3×C4—61no—
395C2×C3×C4—61no—
396C2×C3×C4—61no—
397C2×C3×C4—61no—
398C2×C3×C4—92no—
399C2×C3×C4—121no—
400C2×C3×C4—121no—
401C2×C3×C4—121no—
402C2×C3×C4—121no—
403C2×C3×C4—121no—
404C2×C3×C4—121no—
405C2×C3×C4—181no—
406C2×C3×C4—181no—
407C2×C3×C4—181no—
408C2×C3×C4—181no—
409C2×C3×C4—181no—
410C2×C3×C4—181no—
411C2×C3×C4—181no—
412C2×C3×C4—181no—
413C2×Dic3—21no—
414C2×Dic3—21no—
415C2×Dic3—21no—
416C2×Dic3—21no—
417C2×Dic3—21no—
418C2×Dic3—21no—
419C2×Dic3—21no—
420C2×Dic3—32no—
421C2×Dic3—32no—
422C2×Dic3—62no—
423C2×Dic3—61no—
424C2×Dic3—61no—
425C2×Dic3—61no—
426C2×Dic3—61no—
427C2×Dic3—62no—
428C2×Dic3—62no—
429C2×Dic3—61no—
430C2×Dic3—61no—
431C2×Dic3—61no—
432C2×Dic3—61no—
433C2×Dic3—61no—
434C2×Dic3—61no—
435C2×Dic3—61no—
436C2×Dic3—61no—
437C2×Dic3—61no—
438C2×Dic3—61no—
439C2×Dic3—61no—
440C2×Dic3—61no—
441C2×Dic3—121no—
442C2×Dic3—121no—
443C2×Dic3—121no—
444C2×Dic3—121no—
445C2×Dic3—121no—
446C2×Dic3—121no—
447C2×Dic3—182no—
448C2×Dic3—182no—
449C2×Dic3—182no—
450C2×Dic3—181no—
451C2×Dic3—181no—
452C2×Dic3—181no—
453C2×Dic3—181no—
454C2×Dic3—181no—
455C2×Dic3—181no—
456C2×Dic3—181no—
457C2×Dic3—181no—
458C2×Dic3—181no—
459C2×Dic3—361no—
460C2×Dic3—361no—
461C2×Dic3—361no—
462C2×Dic3—361no—
463C2×Dic3—361no—
464C2×Dic3—361no—
465C2×Dic3—362no—
466C2×Dic3—362no—
467C2×Dic3—362no—
468C2×Dic3D3×Dic312yes—
469C2×Dic3D3×Dic312yes—
470C2×C32—21no—
471C2×C32—21no—
472C2×C32—21no—
473C2×C32—21no—
474C2×C32—21no—
475C2×C32—21no—
476C2×C32—21no—
477C2×C32—21no—
478C2×C32—21no—
479C2×C32—21no—
480C2×C32—21no—
481C2×C32—21no—
482C2×C32—21no—
483C2×C32—21no—
484C2×C32—21no—
485C2×C32—21no—
486C2×C32—21no—
487C2×C32—21no—
488C2×C32—21no—
489C2×C32—21no—
490C2×C32—21no—
491C2×C32—41no—
492C2×C32—41no—
493C2×C32—41no—
494C2×C32—41no—
495C2×C32—41no—
496C2×C32—41no—
497C2×C32—41no—
498C2×C32#87211yescharacteristic
499C2×C32#87211yescharacteristic
500C2×C32#87611yescharacteristic
501C2×C32#87611yescharacteristic
502C2×C32#87611yescharacteristic
503C2×C32#87611yescharacteristic
504C2×C32#87711yescharacteristic
505C2×C32#87711yescharacteristic
506C2×C32#87911yescharacteristic
507C2×C32#87911yescharacteristic
508C2×C32#87911yescharacteristic
509C2×C32#87911yescharacteristic
510C2×C32#89211yescharacteristic
511C2×C32#89211yescharacteristic
512C2×C32#89811yescharacteristic
513C2×C32#89811yescharacteristic
514C2×C32#89811yescharacteristic
515C2×C32#89811yescharacteristic
516C2×C32#92611yescharacteristic
517C2×C32#92611yescharacteristic
518C2×C32#92611yescharacteristic
519C22×C4—31no—
520C22×C4—31no—
521C22×C4—31no—
522C22×C4—91no—
523C22×C4—91no—
524C22×C4—91no—
525C22×C4—271no—
526C42—94no—
527C22×C3—21no—
528C22×C3—21no—
529C22×C3—21no—
530C22×C3—21no—
531C22×C3—21no—
532C22×C3—21no—
533C22×C3—21no—
534C22×C3—21no—
535C22×C3—21no—
536C22×C3—21no—
537C22×C3—21no—
538C22×C3—21no—
539C22×C3—21no—
540C22×C3—21no—
541C22×C3—21no—
542C22×C3—21no—
543C22×C3—21no—
544C22×C3—21no—
545C22×C3—21no—
546C22×C3—21no—
547C22×C3—21no—
548C22×C3—41no—
549C22×C3—41no—
550C22×C3—41no—
551C22×C3—41no—
552C22×C3—41no—
553C22×C3—41no—
554C22×C3—41no—
555C22×C3#379511yescharacteristic
556C22×C3#379511yescharacteristic
557C22×C3#379511yescharacteristic
558C22×C3#379611yescharacteristic
559C22×C3#379811yescharacteristic
560C22×C3#379811yescharacteristic
561C22×C3#379811yescharacteristic
562C22×C3#379811yescharacteristic
563C22×C3#379911yescharacteristic
564C22×C3#379911yescharacteristic
565C22×C3#379911yescharacteristic
566C22×C3C4×D3211yescharacteristic
567C22×C3C2×D3×Dic311yescharacteristic
568C22×C3C2×D3×Dic311yescharacteristic
569C22×C3#380411yescharacteristic
570C22×C3#380411yescharacteristic
571C22×C3#380411yescharacteristic
572C22×C3#380411yescharacteristic
573C22×C3#380411yescharacteristic
574C22×C3#380411yescharacteristic
575C22×C3#380511yescharacteristic
576C3×C4—62no—
577C3×C4—62no—
578C3×C4—62no—
579C3×C4—62no—
580C3×C4—122no—
581C3×C4—122no—
582C3×C4—122no—
583C3×C4—121no—
584C3×C4—121no—
585C3×C4—182no—
586C3×C4—361no—
587C3×C4—361no—
588Dic3—22no—
589Dic3—22no—
590Dic3—41no—
591Dic3—62no—
592Dic3—62no—
593Dic3—122no—
594Dic3—122no—
595Dic3—122no—
596Dic3—121no—
597Dic3—121no—
598Dic3—121no—
599Dic3—121no—
600Dic3—362no—
601Dic3—362no—
602Dic3—362no—
603Dic3—364no—
604Dic3—361no—
605Dic3—361no—
606Dic3—361no—
607C32—21no—
608C32—21no—
609C32—21no—
610C32—41no—
611C32#465111yescharacteristic, complemented
612C32#465111yescharacteristic, complemented
613C32#493711yescharacteristic, complemented
614C23D3311yescharacteristic
615C2×C4—32no—
616C2×C4—32no—
617C2×C4—61no—
618C2×C4—61no—
619C2×C4—61no—
620C2×C4—61no—
621C2×C4—61no—
622C2×C4—61no—
623C2×C4—61no—
624C2×C4—92no—
625C2×C4—181no—
626C2×C4—181no—
627C2×C4—181no—
628C2×C4—181no—
629C2×C4—181no—
630C2×C4—181no—
631C2×C4—181no—
632C2×C4—181no—
633C2×C4—541no—
634C2×C4—541no—
635C2×C4—541no—
636C2×C3—21no—
637C2×C3—21no—
638C2×C3—21no—
639C2×C3—21no—
640C2×C3—21no—
641C2×C3—21no—
642C2×C3—21no—
643C2×C3—21no—
644C2×C3—21no—
645C2×C3—21no—
646C2×C3—21no—
647C2×C3—21no—
648C2×C3—21no—
649C2×C3—21no—
650C2×C3—21no—
651C2×C3—21no—
652C2×C3—21no—
653C2×C3—21no—
654C2×C3—21no—
655C2×C3—21no—
656C2×C3—21no—
657C2×C3—41no—
658C2×C3—41no—
659C2×C3—41no—
660C2×C3—41no—
661C2×C3—41no—
662C2×C3—41no—
663C2×C3—41no—
664C2×C3#6383611yescharacteristic
665C2×C3#6384111yescharacteristic
666C2×C3#6384111yescharacteristic
667C2×C3#6384811yescharacteristic
668C2×C3#6385511yescharacteristic
669C2×C3#6385511yescharacteristic
670C2×C3#6385811yescharacteristic
671C2×C3#6385911yescharacteristic
672C2×C3#6385911yescharacteristic
673C2×C3#6385911yescharacteristic
674C2×C3#6385911yescharacteristic
675C2×C3#6386111yescharacteristic
676C2×C3#6386811yescharacteristic
677C2×C3#6386811yescharacteristic
678C2×C3#6386811yescharacteristic
679C2×C3#6386811yescharacteristic
680C2×C3#6387711yescharacteristic
681C2×C3#6387811yescharacteristic
682C2×C3#6395511yescharacteristic
683C2×C3#6395511yescharacteristic
684C2×C3#6395611yescharacteristic
685C22D32×Dic311yescharacteristic
686C22#8895911yescharacteristic
687C22#8896011yescharacteristic
688C22#8896011yescharacteristic
689C22#8896111yescharacteristic
690C22#8896211yescharacteristic
691C22#8896511yescharacteristic
692C4—62no—
693C4—62no—
694C4—121no—
695C4—182no—
696C4—361no—
697C4—361no—
698C4—1081no—
699C3—21no—
700C3—21no—
701C3—21no—
702C3—41no—
703C3#1059122311yescharacteristic, complemented
704C3#1059122311yescharacteristic, complemented
705C3#1059124811yescharacteristic, complemented
706C2#1172291311yescharacteristic
707C2#1172291411yescharacteristic
708C2#1172291511yescharacteristic
709C2#1172302011yescharacteristic
710C2#1172302111yescharacteristic
711C2#1172302311yescharacteristic
712C2#1172302411yescharacteristic
subgroupG/H
center, Frattini, hypercenterC23D33
commutatorC22×C33C22×C4
Fitting, socle, prime radical, cosocleC23×C33C23
hypocenterC33#383
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C23

Complements

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

NH ≅ G/Ntype
18. C3×Dic32C4semidirect
101. Dic32Dic3semidirect
369. C33#383semidirect
611. C32#4651semidirect
612. C32#4651semidirect
613. C32#4937semidirect
703. C3#10591223semidirect
704. C3#10591223semidirect
705. C3#10591248semidirect

Maximal subgroups

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

subgroupindex
C2×C3×Dic322
#117220822
#117220612
C3×#635792
#105912483
#105912233