Finite Group Databasebeta

← #13155403

Subgroups — #13155403

Order 1728.

1150 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×C4⋊(C3⋊D3)C211yesmaximal, characteristic
2C3×#63841C211yesmaximal, characteristic, complemented
3C2×C3×#3711C211yesmaximal, characteristic, complemented
4#11722075C211yesmaximal, characteristic, complemented
5#11722036C211yesmaximal, characteristic, complemented
6#11722035C211yesmaximal, characteristic, complemented
7C3×#63564C211yesmaximal, characteristic, complemented
8#10591096—31nomaximal
9#10590939—31nomaximal
10#10590592—31nomaximal
11C22×D3×C3⋊D3—21no—
12C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
13C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
14C2×C32×C4×D3C2211yescharacteristic
15C2×#6292—21no—
16D3×C4⋊(C3⋊D3)—22no—
17D3×C4⋊(C3⋊D3)C414yescomplemented
18C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
19C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
20C32×C4⋊Dic3C2211yescharacteristic, complemented
21C2×C32×C3⋊C8C2211yescharacteristic, complemented
22C3×(C2×D3)⋊Dic3—21no—
23C3×Dic32—21no—
24C3×#3711—22no—
25C22×C4⋊(C3⋊D3)—31no—
26C2×D3×D12—31no—
27C2×D3×D12—31no—
28C2×D3×D12—61no—
29C3×#926—31no—
30C2×C3×#208—31no—
31C2×C3×ΓL(1,𝔽25)—31no—
32C3×#892—31no—
33#63841D311yescharacteristic, complemented
34C2×#3711D311yescharacteristic, complemented
35#63648—31no—
36#63636—31no—
37C3×#821—31no—
38C3×#809—31no—
39#63564—31no—
40#63564—31no—
41#63564—31no—
42#63564—31no—
43#63564—31no—
44#63564—61no—
45#63564—61no—
46#63564D311yescharacteristic, complemented
47#63563—31no—
48#63562—31no—
49C22×C3⋊(C3⋊D3)—21no—
50C22×C3×C3⋊D3—21no—
51C22×C32×D3D411yescharacteristic
52C2×D3×C3⋊D3—24no—
53C2×D3×C3⋊D3—42no—
54C2×D3×C3⋊D3—42no—
55C2×C33×C4C2311yescharacteristic
56C4⋊(C3⋊(C3⋊D3))—21no—
57C4⋊(C3⋊(C3⋊D3))C2×C412yes—
58C2×C3×C3⋊Dic3—21no—
59C3×C4⋊(C3⋊D3)—21no—
60C3×C4⋊(C3⋊D3)C2×C412yes—
61C2×C32×Dic3—21no—
62C2×C32×Dic3D411yescharacteristic
63C32×C4×D3C2×C412yes—
64C32×C4×D3D412yes—
65#6292—24no—
66C3×C3⋊(C3⋊C8)—21no—
67C32×C3⋊C8—21no—
68#5131—91no—
69#5001—91no—
70#4770—91no—
71C23×C3⋊D3—61no—
72C22×D32—62no—
73C22×D32—61no—
74C22×D32—61no—
75C22×C32×C4—31no—
76C2×C4⋊(C3⋊D3)—31no—
77C2×C4⋊(C3⋊D3)—31no—
78C2×C4⋊(C3⋊D3)—31no—
79C2×C4⋊(C3⋊D3)—34no—
80C2×C4⋊(C3⋊D3)—62no—
81C2×C4⋊(C3⋊D3)—61no—
82C2×C4⋊(C3⋊D3)—61no—
83C2×C4⋊(C3⋊D3)—61no—
84C2×C4⋊(C3⋊D3)—61no—
85C2×C4⋊(C3⋊D3)—121no—
86C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
87C2×C3×D12—31no—
88C2×C3×D12—31no—
89C2×C3×D12—61no—
90C2×C3×C4×D3—21no—
91C2×C3×C4×D3C2×D311yescharacteristic
92C2×C3×C4×D3C2×D311yescharacteristic
93C2×#626—62no—
94C2×#626—61no—
95C2×#626—61no—
96D3×D12—34no—
97D3×D12—34no—
98D3×D12—64no—
99D3×D12—64no—
100D3×D12—62no—
101D3×D12—62no—
102C2×C32×C8—31no—
103C32×C4⋊C4—31no—
104C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
105C2×C3⋊(C3⋊C8)C2×D311yescharacteristic, complemented
106C3×#217—61no—
107C3×(C2×D3)⋊C4—61no—
108C3×C4⋊Dic3—21no—
109C3×C4⋊Dic3—31no—
110C3×C4⋊Dic3—31no—
111C3×C4⋊Dic3—61no—
112C3×C4⋊Dic3C2×D311yescharacteristic, complemented
113C3×C4⋊Dic3C2×D311yescharacteristic, complemented
114C3×C4×Dic3—61no—
115C3×C4×Dic3—61no—
116C3×#208—62no—
117C2×C3×C3⋊C8—21no—
118C2×C3×C3⋊C8—31no—
119C2×C3×C3⋊C8—31no—
120C2×C3×C3⋊C8—61no—
121C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
122C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
123C3×ΓL(1,𝔽25)—62no—
124(C2×D3)⋊Dic3—21no—
125Dic32—21no—
126#3711—22no—
127C22×C33C2×D411yescharacteristic
128C2×C3⋊(C3⋊D3)—22no—
129C2×C3⋊(C3⋊D3)—41no—
130C2×C3⋊(C3⋊D3)—41no—
131C2×C3×C3⋊D3—22no—
132C2×C3×C3⋊D3—41no—
133C2×C3×C3⋊D3—41no—
134C2×C32×D3—21no—
135C2×C32×D3—21no—
136C2×C32×D3C22⋊C412yes—
137D3×C3⋊D3—48no—
138C33×C4C22×C411yescharacteristic
139C33×C4C2×D411yescharacteristic
140C3×C3⋊Dic3—41no—
141C32×Dic3—41no—
142C32×Dic3C22⋊C412yes—
143C2×D3×D4—91no—
144C22×D12—91no—
145C22×D12—91no—
146C22×D12—181no—
147C2×C3×M16—91no—
148C3×#117—91no—
149#926—31no—
150C2×#208—31no—
151C2×ΓL(1,𝔽25)—31no—
152#892—31no—
153C3×#102—91no—
154#832—91no—
155#821—31no—
156#821—91no—
157#821—91no—
158#821—91no—
159#821—91no—
160#821—181no—
161#809—31no—
162#809—91no—
163#809—91no—
164#809—91no—
165#809—91no—
166#809—181no—
167C23×C32—31no—
168C22×C3⋊D3—21no—
169C22×C3⋊D3—64no—
170C22×C3⋊D3—61no—
171C22×C3⋊D3—62no—
172C22×C3⋊D3—61no—
173C22×C3⋊D3—61no—
174C22×C3⋊D3—121no—
175C22×C3⋊D3—121no—
176C22×C3⋊D3—122no—
177C22×C3⋊D3—122no—
178C22×C3⋊D3—122no—
179C22×C3×D3—21no—
180C22×C3×D3—62no—
181C22×C3×D3—61no—
182C22×C3×D3—61no—
183C22×C3×D3D1211yescharacteristic
184C22×C3×D3#6711yescharacteristic
185C2×D32—68no—
186C2×D32—64no—
187C2×D32—64no—
188C2×D32—124no—
189C2×D32—124no—
190C2×D32—122no—
191C2×D32—122no—
192C2×D32—122no—
193C2×D32—122no—
194C2×C32×C4—21no—
195C2×C32×C4—21no—
196C2×C32×C4—21no—
197C2×C32×C4—31no—
198C2×C32×C4—32no—
199C2×C32×C4—32no—
200C2×C32×C4—41no—
201C2×C32×C4—61no—
202C2×C32×C4C22×D311yescharacteristic
203C2×C32×C4C22×D311yescharacteristic
204C2×C32×C4C22×D311yescharacteristic
205C2×C3⋊Dic3—21no—
206C4⋊(C3⋊D3)—21no—
207C4⋊(C3⋊D3)—32no—
208C4⋊(C3⋊D3)—32no—
209C4⋊(C3⋊D3)—32no—
210C4⋊(C3⋊D3)—62no—
211C4⋊(C3⋊D3)—62no—
212C4⋊(C3⋊D3)—62no—
213C4⋊(C3⋊D3)—64no—
214C4⋊(C3⋊D3)—61no—
215C4⋊(C3⋊D3)—62no—
216C4⋊(C3⋊D3)—61no—
217C4⋊(C3⋊D3)—61no—
218C4⋊(C3⋊D3)—122no—
219C4⋊(C3⋊D3)—121no—
220C4⋊(C3⋊D3)—121no—
221C4⋊(C3⋊D3)—122no—
222C4⋊(C3⋊D3)C4×D312yes—
223C2×C3×Dic3—21no—
224C2×C3×Dic3—21no—
225C2×C3×Dic3—21no—
226C2×C3×Dic3—41no—
227C2×C3×Dic3—61no—
228C2×C3×Dic3—61no—
229C2×C3×Dic3—121no—
230C2×C3×Dic3D1211yescharacteristic
231C2×C3×Dic3#6711yescharacteristic
232C3×D12—32no—
233C3×D12—32no—
234C3×D12—62no—
235C3×D12—62no—
236C3×D12—61no—
237C3×D12—61no—
238C3×C4×D3—22no—
239C3×C4×D3—22no—
240C3×C4×D3C4×D312yes—
241C3×C4×D3C4×D312yes—
242C3×C4×D3D1212yes—
243C3×C4×D3#6712yes—
244#626—68no—
245#626—64no—
246#626—64no—
247C32×C8—61no—
248C3⋊(C3⋊C8)—21no—
249C3×C3⋊C8—21no—
250C3×C3⋊C8—21no—
251C3×C3⋊C8—41no—
252C3×C3⋊C8—61no—
253C3×C3⋊C8—61no—
254C3×C3⋊C8—121no—
255#418—271noSylow
256C2×C33C2×C22⋊C411yescharacteristic
257C2×C33AGL(1,ℤ/8)11yescharacteristic
258C2×C33AGL(1,ℤ/8)11yescharacteristic
259C3⋊(C3⋊D3)—42no—
260C3×C3⋊D3—42no—
261C32×D3—22no—
262C23×D3—181no—
263C23×D3—181no—
264C23×D3—182no—
265C23×D3—181no—
266C2×C3×D4—91no—
267C22×C3×C4—31no—
268C22×C3×C4—31no—
269C22×C3×C4—61no—
270C2×#67—181no—
271D3×D4—94no—
272D3×D4—182no—
273C2×D12—31no—
274C2×D12—31no—
275C2×D12—61no—
276C2×D12—94no—
277C2×D12—94no—
278C2×D12—91no—
279C2×D12—91no—
280C2×D12—91no—
281C2×D12—184no—
282C2×D12—181no—
283C2×D12—181no—
284C2×D12—181no—
285C2×D12—182no—
286C2×D12—182no—
287C2×D12—184no—
288C2×D12—181no—
289C2×D12—181no—
290C2×D12—182no—
291C2×D12—361no—
292C2×C4×D3D3211yescharacteristic
293C3×M16—182no—
294C2×C3×C8—31no—
295C2×C3×C8—31no—
296C2×C3×C8—61no—
297C2×C3×C8—91no—
298C3×C4⋊C4—31no—
299C3×C4⋊C4—31no—
300C3×C4⋊C4—61no—
301C3×C4⋊C4—91no—
302C3×C22⋊C4—181no—
303C3×C42—181no—
304#217—61no—
305(C2×D3)⋊C4—61no—
306C4⋊Dic3—31no—
307C4⋊Dic3—31no—
308C4⋊Dic3—61no—
309C4⋊Dic3D3211yescharacteristic, complemented
310C4×Dic3—61no—
311C4×Dic3—61no—
312#208—62no—
313C2×C3⋊C8—31no—
314C2×C3⋊C8—31no—
315C2×C3⋊C8—61no—
316C2×C3⋊C8D3211yescharacteristic, complemented
317ΓL(1,𝔽25)—62no—
318C22×C32—21no—
319C22×C32—21no—
320C22×C32—21no—
321C22×C32—32no—
322C22×C32—41no—
323C22×C32—61no—
324C22×C32—61no—
325C22×C32C2×D1211yescharacteristic
326C22×C32D3×D411yescharacteristic
327C22×C32C2×#6711yescharacteristic
328C2×C3⋊D3—22no—
329C2×C3⋊D3—41no—
330C2×C3⋊D3—41no—
331C2×C3⋊D3—62no—
332C2×C3⋊D3—64no—
333C2×C3⋊D3—62no—
334C2×C3⋊D3—62no—
335C2×C3⋊D3—122no—
336C2×C3⋊D3—122no—
337C2×C3⋊D3—124no—
338C2×C3⋊D3—128no—
339C2×C3⋊D3—121no—
340C2×C3⋊D3—121no—
341C2×C3⋊D3—122no—
342C2×C3⋊D3—122no—
343C2×C3⋊D3—121no—
344C2×C3⋊D3—121no—
345C2×C3⋊D3—121no—
346C2×C3⋊D3—121no—
347C2×C3⋊D3—241no—
348C2×C3⋊D3—241no—
349C2×C3⋊D3—241no—
350C2×C3⋊D3—241no—
351C2×C3⋊D3—242no—
352C2×C3⋊D3—242no—
353C2×C3×D3—22no—
354C2×C3×D3—22no—
355C2×C3×D3—21no—
356C2×C3×D3—21no—
357C2×C3×D3—21no—
358C2×C3×D3—21no—
359C2×C3×D3—22no—
360C2×C3×D3—64no—
361C2×C3×D3—62no—
362C2×C3×D3—62no—
363C2×C3×D3—122no—
364C2×C3×D3—122no—
365C2×C3×D3—121no—
366C2×C3×D3—121no—
367C2×C3×D3—121no—
368C2×C3×D3—121no—
369C2×C3×D3(C2×D3)⋊C412yes—
370C2×C3×D3(C2×D3)⋊C412yes—
371D32—1216no—
372D32—128no—
373D32—128no—
374C32×C4—21no—
375C32×C4—21no—
376C32×C4—21no—
377C32×C4—21no—
378C32×C4—21no—
379C32×C4—21no—
380C32×C4—32no—
381C32×C4—41no—
382C32×C4—41no—
383C32×C4—121no—
384C32×C4C2×C4×D311yescharacteristic
385C32×C4C2×C4×D311yescharacteristic
386C32×C4C2×C4×D311yescharacteristic
387C32×C4C2×D1211yescharacteristic
388C32×C4D3×D411yescharacteristic
389C32×C4C2×#6711yescharacteristic
390C3⋊Dic3—41no—
391C3×Dic3—22no—
392C3×Dic3—41no—
393C3×Dic3—41no—
394C3×Dic3—81no—
395C3×Dic3—121no—
396C3×Dic3—121no—
397C3×Dic3—241no—
398C3×Dic3(C2×D3)⋊C412yes—
399C3×Dic3(C2×D3)⋊C412yes—
400C22×D4—271no—
401C2×M16—91no—
402#117—91no—
403#102—91no—
404#102—271no—
405#102—271no—
406#102—271no—
407C33#41811yescharacteristic, complemented, Sylow
408C23×C3—31no—
409C23×C3—31no—
410C23×C3—61no—
411C23×C3—181no—
412C22×D3—62no—
413C22×D3—61no—
414C22×D3—61no—
415C22×D3—184no—
416C22×D3—184no—
417C22×D3—188no—
418C22×D3—182no—
419C22×D3—181no—
420C22×D3—181no—
421C22×D3—181no—
422C22×D3—184no—
423C22×D3—361no—
424C22×D3—361no—
425C22×D3—362no—
426C22×D3—362no—
427C22×D3—362no—
428C22×D3—364no—
429C22×D3—364no—
430C22×D3—362no—
431C22×D3—362no—
432C22×D3—362no—
433C22×D3—362no—
434C22×D3#62611yescharacteristic
435C3×D4—92no—
436C3×D4—181no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—31no—
441C2×C3×C4—31no—
442C2×C3×C4—32no—
443C2×C3×C4—32no—
444C2×C3×C4—32no—
445C2×C3×C4—32no—
446C2×C3×C4—41no—
447C2×C3×C4—62no—
448C2×C3×C4—62no—
449C2×C3×C4—61no—
450C2×C3×C4—61no—
451C2×C3×C4—61no—
452C2×C3×C4—121no—
453C2×C3×C4—181no—
454C2×C3×C4C2×D3211yescharacteristic
455C2×C3×C4C2×D3211yescharacteristic
456C2×C3×C4C2×D3211yescharacteristic
457#67—184no—
458C2×Dic3—21no—
459C2×Dic3—61no—
460C2×Dic3—61no—
461C2×Dic3—121no—
462C2×Dic3#62611yescharacteristic
463D12—32no—
464D12—32no—
465D12—62no—
466D12—62no—
467D12—61no—
468D12—61no—
469D12—92no—
470D12—92no—
471D12—92no—
472D12—182no—
473D12—182no—
474D12—182no—
475D12—182no—
476D12—184no—
477D12—184no—
478D12—188no—
479D12—181no—
480D12—181no—
481D12—181no—
482D12—362no—
483D12—361no—
484D12—361no—
485D12—362no—
486C4×D3#62412yes—
487C4×D3#62612yes—
488C3×C8—61no—
489C3×C8—61no—
490C3×C8—121no—
491C3×C8—181no—
492C3⋊C8—21no—
493C3⋊C8—61no—
494C3⋊C8—61no—
495C3⋊C8—121no—
496C2×C32—21no—
497C2×C32—21no—
498C2×C32—21no—
499C2×C32—21no—
500C2×C32—21no—
501C2×C32—21no—
502C2×C32—21no—
503C2×C32—21no—
504C2×C32—21no—
505C2×C32—41no—
506C2×C32—41no—
507C2×C32—41no—
508C2×C32—62no—
509C2×C32D3×C22⋊C411yescharacteristic
510C2×C32#90811yescharacteristic
511C2×C32#90811yescharacteristic
512C2×C32#91111yescharacteristic
513C2×C32#91411yescharacteristic
514C2×C32C2×(C2×D3)⋊C411yescharacteristic
515C2×C32C2×(C2×D3)⋊C411yescharacteristic
516C2×C32#94911yescharacteristic
517C2×C32#94911yescharacteristic
518C3⋊D3—42no—
519C3⋊D3—122no—
520C3⋊D3—124no—
521C3⋊D3—122no—
522C3⋊D3—122no—
523C3⋊D3—242no—
524C3⋊D3—242no—
525C3⋊D3—244no—
526C3×D3—24no—
527C3×D3—22no—
528C3×D3—22no—
529C3×D3—124no—
530C3×D3—122no—
531C3×D3—122no—
532C24—541no—
533C2×D4—91no—
534C2×D4—274no—
535C2×D4—271no—
536C2×D4—542no—
537C2×D4—541no—
538C22×C4—31no—
539M16—182no—
540C2×C8—31no—
541C2×C8—91no—
542C4⋊C4—31no—
543C4⋊C4—91no—
544C22⋊C4—181no—
545C42—181no—
546C22×C3—21no—
547C22×C3—21no—
548C22×C3—21no—
549C22×C3—32no—
550C22×C3—32no—
551C22×C3—41no—
552C22×C3—62no—
553C22×C3—62no—
554C22×C3—62no—
555C22×C3—61no—
556C22×C3—61no—
557C22×C3—61no—
558C22×C3—61no—
559C22×C3—182no—
560C22×C3—361no—
561C22×C3—361no—
562C22×C3D3×D1211yescharacteristic
563C22×C3C2×#62611yescharacteristic
564C22×C3D3×#6711yescharacteristic
565C2×D3—21no—
566C2×D3—21no—
567C2×D3—64no—
568C2×D3—62no—
569C2×D3—62no—
570C2×D3—122no—
571C2×D3—122no—
572C2×D3—121no—
573C2×D3—121no—
574C2×D3—121no—
575C2×D3—121no—
576C2×D3—184no—
577C2×D3—182no—
578C2×D3—182no—
579C2×D3—182no—
580C2×D3—362no—
581C2×D3—362no—
582C2×D3—364no—
583C2×D3—368no—
584C2×D3—3616no—
585C2×D3—368no—
586C2×D3—368no—
587C2×D3—362no—
588C2×D3—362no—
589C2×D3—361no—
590C2×D3—361no—
591C2×D3—361no—
592C2×D3—361no—
593C2×D3—361no—
594C2×D3—361no—
595C2×D3—721no—
596C2×D3—721no—
597C2×D3—721no—
598C2×D3—721no—
599C2×D3—722no—
600C2×D3—722no—
601C2×D3#372212yes—
602C3×C4—21no—
603C3×C4—21no—
604C3×C4—21no—
605C3×C4—21no—
606C3×C4—21no—
607C3×C4—21no—
608C3×C4—32no—
609C3×C4—32no—
610C3×C4—41no—
611C3×C4—41no—
612C3×C4—62no—
613C3×C4—121no—
614C3×C4—121no—
615C3×C4—241no—
616C3×C4—361no—
617C3×C4C4×D3211yescharacteristic
618C3×C4C4×D3211yescharacteristic
619C3×C4D3×D1211yescharacteristic
620C3×C4C2×#62411yescharacteristic
621C3×C4C2×#62611yescharacteristic
622C3×C4D3×#6711yescharacteristic
623Dic3—41no—
624Dic3—121no—
625Dic3—121no—
626Dic3—241no—
627Dic3#372212yes—
628C32—21no—
629C32—21no—
630C32—21no—
631C32—41no—
632C32#477011yescharacteristic, complemented
633C32#500111yescharacteristic, complemented
634C32#513111yescharacteristic, complemented
635C23—31no—
636C23—181no—
637C23—544no—
638C23—541no—
639C23—1082no—
640C23—1082no—
641D4—92no—
642D4—181no—
643D4—272no—
644D4—544no—
645D4—541no—
646C2×C4—31no—
647C2×C4—32no—
648C2×C4—32no—
649C2×C4—61no—
650C2×C4—181no—
651C2×C4D3311yescharacteristic
652C8—61no—
653C8—181no—
654C2×C3—21no—
655C2×C3—21no—
656C2×C3—21no—
657C2×C3—21no—
658C2×C3—21no—
659C2×C3—21no—
660C2×C3—21no—
661C2×C3—21no—
662C2×C3—21no—
663C2×C3—41no—
664C2×C3—41no—
665C2×C3—41no—
666C2×C3—64no—
667C2×C3—62no—
668C2×C3—62no—
669C2×C3—362no—
670C2×C3#6379411yescharacteristic
671C2×C3#6379511yescharacteristic
672C2×C3#6382511yescharacteristic
673C2×C3#6382511yescharacteristic
674C2×C3D3×(C2×D3)⋊C411yescharacteristic
675C2×C3D3×(C2×D3)⋊C411yescharacteristic
676C2×C3#6392511yescharacteristic
677C2×C3#6393911yescharacteristic
678C2×C3C2×#372211yescharacteristic
679D3—22no—
680D3—124no—
681D3—122no—
682D3—122no—
683D3—364no—
684D3—362no—
685D3—362no—
686D3—362no—
687D3—722no—
688D3—722no—
689D3—724no—
690C22—32no—
691C22—61no—
692C22—61no—
693C22—182no—
694C22—361no—
695C22—361no—
696C22—542no—
697C22—1088no—
698C22—1081no—
699C22—1081no—
700C22D3×#62611yescharacteristic
701C4—32no—
702C4—121no—
703C4—361no—
704C4D3×#62411yescharacteristic
705C4D3×#62611yescharacteristic
706C3—21no—
707C3—21no—
708C3—21no—
709C3—41no—
710C3#1059059211yescharacteristic, complemented
711C3#1059093911yescharacteristic, complemented
712C3#1059109611yescharacteristic, complemented
713C2—62no—
714C2—362no—
715C2—1082no—
716C2#1172287011yescharacteristic
717C2#1172287111yescharacteristic
718C2D3×#372211yescharacteristic
subgroupG/H
centerC22D3×#626
commutatorC33×C4C22×C4
Frattini, hypercenterC2×C4D33
Fitting, cosocleC2×C33×C4C23
socleC22×C33C2×D4
prime radicalC2×D3×C4⋊(C3⋊D3)C2
hypocenterC33#418
LCSG ▷ C33×C4 ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C3×#63841C2semidirect
3. C2×C3×#3711C2semidirect
4. #11722075C2semidirect
5. #11722036C2semidirect
6. #11722035C2semidirect
7. C3×#63564C2semidirect
17. D3×C4⋊(C3⋊D3)C4semidirect
18. C3×C4⋊(C3⋊Dic3)C22semidirect
19. C2×C3×C3⋊(C3⋊C8)C22semidirect
20. C32×C4⋊Dic3C22semidirect
21. C2×C32×C3⋊C8C22semidirect
33. #63841D3semidirect
34. C2×#3711D3semidirect
46. #63564D3semidirect
104. C4⋊(C3⋊Dic3)C2×D3semidirect
105. C2×C3⋊(C3⋊C8)C2×D3semidirect
112. C3×C4⋊Dic3C2×D3semidirect
113. C3×C4⋊Dic3C2×D3semidirect
121. C2×C3×C3⋊C8C2×D3semidirect
122. C2×C3×C3⋊C8C2×D3semidirect
309. C4⋊Dic3D32semidirect
316. C2×C3⋊C8D32semidirect
407. C33#418semidirect
632. C32#4770semidirect
633. C32#5001semidirect
634. C32#5131semidirect
710. C3#10590592semidirect
711. C3#10590939semidirect
712. C3#10591096semidirect

Maximal subgroups

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

subgroupindex
C2×D3×C4⋊(C3⋊D3)2
C3×#638412
C2×C3×#37112
#117220752
#117220362
#117220352
C3×#635642
#105910963
#105909393
#105905923