Finite Group Databasebeta

← C3×D3×#809 #13157608

Subgroups — C3×D3×#809 #13157608

Order 1728.

1026 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×D12C211yesmaximal, characteristic
2C32×D3×C4⋊C4C211yesmaximal, characteristic, complemented
3C2×C3×D3×C3⋊C8C211yesmaximal, characteristic, complemented
4C3×#63636C211yesmaximal, characteristic, complemented
5C32×#809C211yesmaximal, characteristic, complemented
6C3×#63564C211yesmaximal, characteristic, complemented
7C3×#63562C211yesmaximal, characteristic, complemented
8C2×C3×#809—31nomaximal
9C3×D3×#102—31nomaximal
10D3×#809C311yesmaximal, characteristic, direct product factor
11C22×C3×D32—21no—
12C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
13C2×C32×D12C2211yescharacteristic
14C2×C32×C4×D3—21no—
15C2×C32×C4×D3C2211yescharacteristic
16C2×C3×#626—21no—
17C3×D3×D12—22no—
18C3×D3×D12C414yescomplemented
19C33×C4⋊C4C2211yescharacteristic, complemented
20C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
21C32×C4⋊Dic3C2211yescharacteristic, complemented
22C32×Dic3⋊C4—21no—
23C2×C32×C3⋊C8C2211yescharacteristic, complemented
24C3×D3×C3⋊C8—22no—
25C2×C3×D3×D4—31no—
26C22×C3×D12—31no—
27C2×D3×D12C2×C311yescharacteristic
28C2×C32×C4⋊C4—31no—
29C22×C3×C3⋊C8—31no—
30C2×C3×D3×C8—31no—
31C3×D3×C4⋊C4—21no—
32C3×D3×C4⋊C4D311yescharacteristic, complemented
33C3×D3×C4⋊C4C2×C311yescharacteristic, complemented
34C2×D3×C3⋊C8C2×C311yescharacteristic, complemented
35C32×#102—31no—
36#63636C2×C311yescharacteristic, complemented
37C3×#832—31no—
38C3×#821—31no—
39C3×#809—21no—
40C3×#809—31no—
41C3×#809—31no—
42C3×#809—31no—
43C3×#809—31no—
44C3×#809—61no—
45C3×#809D311yescharacteristic, direct product factor
46C3×#809C2×C311yescharacteristic, complemented
47#63564C2×C311yescharacteristic, complemented
48#63562C2×C311yescharacteristic, complemented
49C22×C3×C3⋊D3—21no—
50C22×C32×D3—21no—
51C22×C32×D3D411yescharacteristic
52C2×C3×D32—24no—
53C2×C3×D32—42no—
54C2×C3×D32—42no—
55C2×C33×C4—21no—
56C2×C33×C4C2311yescharacteristic
57C3×C4⋊(C3⋊D3)—21no—
58C3×C4⋊(C3⋊D3)C2×C412yescomplemented
59C2×C32×Dic3—21no—
60C2×C32×Dic3D411yescharacteristic
61C32×D12—21no—
62C32×D12C2×C412yescomplemented
63C32×C4×D3—42no—
64C32×C4×D3C2×C412yes—
65C32×C4×D3D412yes—
66C3×#626—24no—
67C3×C3⋊(C3⋊C8)—21no—
68C32×C3⋊C8—21no—
69C2×C3×#102—91no—
70C2×#809—31no—
71D3×#102—31no—
72C23×C3×D3—61no—
73C23×C3×D3—61no—
74C22×D32—21no—
75C2×C32×D4—31no—
76C22×C32×C4—31no—
77C22×C32×C4—61no—
78C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
79C2×C3×#67—61no—
80C3×D3×D4—34no—
81C3×D3×D4—62no—
82C2×C3×D12—21no—
83C2×C3×D12—31no—
84C2×C3×D12—31no—
85C2×C3×D12—34no—
86C2×C3×D12—62no—
87C2×C3×D12—61no—
88C2×C3×D12—61no—
89C2×C3×D12C2×D311yescharacteristic
90C2×C3×D12C22×C311yescharacteristic
91C2×C3×C4×D3—21no—
92C2×C3×C4×D3—22no—
93C2×C3×C4×D3—21no—
94C2×C3×C4×D3—21no—
95C2×C3×C4×D3C2×D311yescharacteristic
96C2×C3×C4×D3C22×C311yescharacteristic
97C2×#626—21no—
98D3×D12—22no—
99D3×D12C3×C414yescomplemented
100C2×C32×C8—31no—
101C32×C4⋊C4—21no—
102C32×C4⋊C4—21no—
103C32×C4⋊C4—21no—
104C32×C4⋊C4—31no—
105C32×C4⋊C4—41no—
106C32×C4⋊C4—61no—
107C32×C4⋊C4C2×D311yescharacteristic, complemented
108C32×C4⋊C4C2×D311yescharacteristic, complemented
109C32×C4⋊C4C22×C311yescharacteristic, complemented
110C2×C3⋊(C3⋊C8)C22×C311yescharacteristic, complemented
111C3×C4⋊Dic3—21no—
112C3×C4⋊Dic3C2×D311yescharacteristic, complemented
113C3×C4⋊Dic3C22×C311yescharacteristic, complemented
114C3×Dic3⋊C4—22no—
115C3×Dic3⋊C4—21no—
116C3×Dic3⋊C4—21no—
117C2×C3×C3⋊C8—21no—
118C2×C3×C3⋊C8—31no—
119C2×C3×C3⋊C8—31no—
120C2×C3×C3⋊C8—62no—
121C2×C3×C3⋊C8—61no—
122C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
123C2×C3×C3⋊C8C22×C311yescharacteristic, complemented
124C3×D3×C8—62no—
125D3×C3⋊C8—22no—
126C22×C33C2×D411yescharacteristic
127C2×C3×C3⋊D3—22no—
128C2×C3×C3⋊D3—41no—
129C2×C3×C3⋊D3—41no—
130C2×C32×D3—22no—
131C2×C32×D3—41no—
132C2×C32×D3—41no—
133C2×C32×D3C22⋊C412yes—
134C2×C32×D3D812yes—
135C2×C32×D3SD1612yes—
136C3×D32—48no—
137C33×C4—41no—
138C33×C4C22×C411yescharacteristic
139C33×C4C2×D411yescharacteristic
140C32×Dic3—41no—
141C32×Dic3C22⋊C412yes—
142C22×C3×D4—91no—
143C2×D3×D4—31no—
144C22×D12—31no—
145C22×C3×C8—91no—
146C2×C3×C4⋊C4—31no—
147C2×C3×C4⋊C4—31no—
148C2×C3×C4⋊C4—61no—
149C22×C3⋊C8—31no—
150C2×D3×C8—31no—
151D3×C4⋊C4C3×D311yescharacteristic, complemented
152C3×#102—31no—
153C3×#102—31no—
154C3×#102—61no—
155C3×#102—91no—
156C3×#102—91no—
157C3×#102—91no—
158#832—31no—
159#821—31no—
160#809—31no—
161#809—31no—
162#809—31no—
163#809—31no—
164#809—61no—
165#809C3×D311yescharacteristic, direct product factor
166C23×C32—31no—
167C23×C32—61no—
168C22×C3⋊D3—21no—
169C22×C3×D3—21no—
170C22×C3×D3—21no—
171C22×C3×D3—21no—
172C22×C3×D3—41no—
173C22×C3×D3—64no—
174C22×C3×D3—61no—
175C22×C3×D3—61no—
176C22×C3×D3—64no—
177C22×C3×D3—121no—
178C22×C3×D3—122no—
179C22×C3×D3—122no—
180C22×C3×D3—122no—
181C22×C3×D3—122no—
182C22×C3×D3#6711yescharacteristic
183C22×C3×D3C3×D411yescharacteristic
184C2×D32—24no—
185C2×D32—42no—
186C2×D32—42no—
187C32×D4—32no—
188C32×D4—61no—
189C2×C32×C4—21no—
190C2×C32×C4—22no—
191C2×C32×C4—21no—
192C2×C32×C4—21no—
193C2×C32×C4—21no—
194C2×C32×C4—21no—
195C2×C32×C4—21no—
196C2×C32×C4—31no—
197C2×C32×C4—32no—
198C2×C32×C4—32no—
199C2×C32×C4—41no—
200C2×C32×C4—41no—
201C2×C32×C4—41no—
202C2×C32×C4—42no—
203C2×C32×C4—61no—
204C2×C32×C4—122no—
205C2×C32×C4C22×D311yescharacteristic
206C2×C32×C4C22×D311yescharacteristic
207C2×C32×C4C23×C311yescharacteristic
208C4⋊(C3⋊D3)—21no—
209C4⋊(C3⋊D3)C2×C3×C412yescomplemented
210C3×#67—64no—
211C2×C3×Dic3—22no—
212C2×C3×Dic3—21no—
213C2×C3×Dic3—21no—
214C2×C3×Dic3—21no—
215C2×C3×Dic3#6711yescharacteristic
216C2×C3×Dic3C3×D411yescharacteristic
217C3×D12—21no—
218C3×D12—21no—
219C3×D12—22no—
220C3×D12—32no—
221C3×D12—32no—
222C3×D12—41no—
223C3×D12—62no—
224C3×D12—64no—
225C3×D12—61no—
226C3×D12—61no—
227C3×D12—121no—
228C3×D12C4×D312yescomplemented
229C3×D12C2×C3×C412yescomplemented
230C3×C4×D3—22no—
231C3×C4×D3—22no—
232C3×C4×D3—44no—
233C3×C4×D3—42no—
234C3×C4×D3—42no—
235C3×C4×D3C4×D312yes—
236C3×C4×D3D1212yes—
237C3×C4×D3C2×C3×C412yes—
238C3×C4×D3C3×D412yes—
239#626—24no—
240C32×C8—61no—
241C3⋊(C3⋊C8)—21no—
242C3×C3⋊C8—21no—
243C3×C3⋊C8—21no—
244C3×C3⋊C8—41no—
245C3×C3⋊C8—61no—
246C3×C3⋊C8—61no—
247C3×C3⋊C8—121no—
248C2×#102—91noSylow
249C2×C33C2×C22⋊C411yescharacteristic
250C2×C33C2×D811yescharacteristic
251C2×C33C2×SD1611yescharacteristic
252C3×C3⋊D3—42no—
253C32×D3—42no—
254C32×D3#10214yescomplemented
255C24×C3—181no—
256C23×D3—61no—
257C23×D3—61no—
258C2×C3×D4—31no—
259C2×C3×D4—31no—
260C2×C3×D4—61no—
261C2×C3×D4—94no—
262C2×C3×D4—91no—
263C2×C3×D4—182no—
264C2×C3×D4—181no—
265C22×C3×C4—31no—
266C22×C3×C4—31no—
267C22×C3×C4—61no—
268C22×C3×C4—61no—
269C22×C3×C4—61no—
270C22×C3×C4—62no—
271C2×#67—61no—
272D3×D4—34no—
273D3×D4—62no—
274C2×D12—31no—
275C2×D12—31no—
276C2×D12—34no—
277C2×D12—61no—
278C2×D12—62no—
279C2×D12—61no—
280C2×D12C2×C3×D311yescharacteristic
281C2×C4×D3—21no—
282C2×C4×D3C2×C3×D311yescharacteristic
283C2×C3×C8—31no—
284C2×C3×C8—31no—
285C2×C3×C8—61no—
286C2×C3×C8—91no—
287C2×C3×C8—182no—
288C3×C4⋊C4—21no—
289C3×C4⋊C4—21no—
290C3×C4⋊C4—21no—
291C3×C4⋊C4—31no—
292C3×C4⋊C4—31no—
293C3×C4⋊C4—41no—
294C3×C4⋊C4—61no—
295C3×C4⋊C4—61no—
296C3×C4⋊C4—61no—
297C3×C4⋊C4—62no—
298C3×C4⋊C4D3211yescharacteristic, complemented
299C3×C4⋊C4C2×C3×D311yescharacteristic, complemented
300C3×C4⋊C4C2×C3×D311yescharacteristic, complemented
301C4⋊Dic3C2×C3×D311yescharacteristic, complemented
302Dic3⋊C4—21no—
303C2×C3⋊C8—31no—
304C2×C3⋊C8—31no—
305C2×C3⋊C8—61no—
306C2×C3⋊C8—62no—
307C2×C3⋊C8C2×C3×D311yescharacteristic, complemented
308D3×C8—62no—
309C22×C32—21no—
310C22×C32—21no—
311C22×C32—21no—
312C22×C32—32no—
313C22×C32—32no—
314C22×C32—32no—
315C22×C32—41no—
316C22×C32—62no—
317C22×C32—121no—
318C22×C32—121no—
319C22×C32D3×D411yescharacteristic
320C22×C32C2×#6711yescharacteristic
321C22×C32C2×C3×D411yescharacteristic
322C2×C3⋊D3—22no—
323C2×C3⋊D3—41no—
324C2×C3⋊D3—41no—
325C2×C3×D3—22no—
326C2×C3×D3—22no—
327C2×C3×D3—22no—
328C2×C3×D3—22no—
329C2×C3×D3—22no—
330C2×C3×D3—42no—
331C2×C3×D3—41no—
332C2×C3×D3—41no—
333C2×C3×D3—41no—
334C2×C3×D3—41no—
335C2×C3×D3—62no—
336C2×C3×D3—62no—
337C2×C3×D3—81no—
338C2×C3×D3—81no—
339C2×C3×D3—122no—
340C2×C3×D3—128no—
341C2×C3×D3—121no—
342C2×C3×D3—121no—
343C2×C3×D3—121no—
344C2×C3×D3—121no—
345C2×C3×D3—128no—
346C2×C3×D3—241no—
347C2×C3×D3—241no—
348C2×C3×D3(C2×D3)⋊C412yes—
349C2×C3×D3#21312yes—
350C2×C3×D3#21512yes—
351C2×C3×D3C3×C22⋊C412yes—
352C2×C3×D3C3×D812yes—
353C2×C3×D3C3×SD1612yes—
354D32—48no—
355C32×C4—21no—
356C32×C4—21no—
357C32×C4—21no—
358C32×C4—21no—
359C32×C4—21no—
360C32×C4—21no—
361C32×C4—32no—
362C32×C4—41no—
363C32×C4—41no—
364C32×C4—41no—
365C32×C4—42no—
366C32×C4—41no—
367C32×C4—41no—
368C32×C4—81no—
369C32×C4—81no—
370C32×C4—82no—
371C32×C4—121no—
372C32×C4C2×C4×D311yescharacteristic
373C32×C4C2×C4×D311yescharacteristic
374C32×C4C2×D1211yescharacteristic
375C32×C4D3×D411yescharacteristic
376C32×C4C22×C3×C411yescharacteristic
377C32×C4C2×C3×D411yescharacteristic
378C3×Dic3—22no—
379C3×Dic3—42no—
380C3×Dic3—41no—
381C3×Dic3—41no—
382C3×Dic3(C2×D3)⋊C412yes—
383C3×Dic3C3×C22⋊C412yes—
384C22×D4—91no—
385C22×C8—91no—
386C2×C4⋊C4—31no—
387#102—31no—
388#102—91no—
389#102—91no—
390#102—91no—
391C33C2×#10211yescharacteristic, complemented, Sylow
392C23×C3—31no—
393C23×C3—31no—
394C23×C3—61no—
395C23×C3—61no—
396C23×C3—61no—
397C23×C3—121no—
398C23×C3—184no—
399C23×C3—181no—
400C23×C3—362no—
401C23×C3—362no—
402C22×D3—21no—
403C22×D3—64no—
404C22×D3—61no—
405C22×D3—61no—
406C22×D3—64no—
407C22×D3—121no—
408C22×D3—122no—
409C22×D3—122no—
410C22×D3—122no—
411C22×D3—122no—
412C22×D3C3×#6711yescharacteristic
413C3×D4—32no—
414C3×D4—32no—
415C3×D4—62no—
416C3×D4—61no—
417C3×D4—61no—
418C3×D4—92no—
419C3×D4—121no—
420C3×D4—184no—
421C3×D4—181no—
422C2×C3×C4—22no—
423C2×C3×C4—21no—
424C2×C3×C4—21no—
425C2×C3×C4—21no—
426C2×C3×C4—21no—
427C2×C3×C4—21no—
428C2×C3×C4—21no—
429C2×C3×C4—31no—
430C2×C3×C4—31no—
431C2×C3×C4—32no—
432C2×C3×C4—32no—
433C2×C3×C4—32no—
434C2×C3×C4—32no—
435C2×C3×C4—41no—
436C2×C3×C4—41no—
437C2×C3×C4—42no—
438C2×C3×C4—41no—
439C2×C3×C4—62no—
440C2×C3×C4—62no—
441C2×C3×C4—61no—
442C2×C3×C4—62no—
443C2×C3×C4—61no—
444C2×C3×C4—61no—
445C2×C3×C4—122no—
446C2×C3×C4—122no—
447C2×C3×C4—124no—
448C2×C3×C4C2×D3211yescharacteristic
449C2×C3×C4C22×C3×D311yescharacteristic
450C2×C3×C4C22×C3×D311yescharacteristic
451#67—64no—
452C2×Dic3—21no—
453C2×Dic3C3×#6711yescharacteristic
454D12—21no—
455D12—32no—
456D12—32no—
457D12—62no—
458D12—64no—
459D12—61no—
460D12—61no—
461D12—121no—
462D12C3×C4×D312yescomplemented
463C4×D3—42no—
464C4×D3C3×C4×D312yes—
465C4×D3C3×D1212yes—
466C3×C8—61no—
467C3×C8—61no—
468C3×C8—121no—
469C3×C8—181no—
470C3⋊C8—21no—
471C3⋊C8—61no—
472C3⋊C8—61no—
473C3⋊C8—121no—
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—34no—
484C2×C32—41no—
485C2×C32—41no—
486C2×C32—41no—
487C2×C32—122no—
488C2×C32D3×C22⋊C411yescharacteristic
489C2×C32D3×D811yescharacteristic
490C2×C32D3×SD1611yescharacteristic
491C2×C32C2×(C2×D3)⋊C411yescharacteristic
492C2×C32C2×#21311yescharacteristic
493C2×C32C2×#21511yescharacteristic
494C2×C32C2×C3×C22⋊C411yescharacteristic
495C2×C32C2×C3×D811yescharacteristic
496C2×C32C2×C3×SD1611yescharacteristic
497C3⋊D3—42no—
498C3×D3—24no—
499C3×D3—42no—
500C3×D3—42no—
501C3×D3—82no—
502C3×D3—122no—
503C3×D3—122no—
504C3×D3—242no—
505C3×D3#80914yesdirect product factor
506C3×D3C3×#10214yescomplemented
507C24—181no—
508C2×D4—31no—
509C2×D4—94no—
510C2×D4—91no—
511C2×D4—182no—
512C2×D4—181no—
513C22×C4—31no—
514C22×C4—61no—
515C2×C8—31no—
516C2×C8—91no—
517C2×C8—182no—
518C4⋊C4—31no—
519C4⋊C4—61no—
520C4⋊C4C3×D3211yescharacteristic, complemented
521C22×C3—21no—
522C22×C3—21no—
523C22×C3—21no—
524C22×C3—32no—
525C22×C3—32no—
526C22×C3—32no—
527C22×C3—32no—
528C22×C3—32no—
529C22×C3—32no—
530C22×C3—41no—
531C22×C3—62no—
532C22×C3—62no—
533C22×C3—62no—
534C22×C3—62no—
535C22×C3—62no—
536C22×C3—122no—
537C22×C3—121no—
538C22×C3—121no—
539C22×C3—121no—
540C22×C3—121no—
541C22×C3—182no—
542C22×C3—241no—
543C22×C3—241no—
544C22×C3—368no—
545C22×C3—361no—
546C22×C3—361no—
547C22×C3D3×#6711yescharacteristic
548C22×C3C3×D3×D411yescharacteristic
549C22×C3C2×C3×#6711yescharacteristic
550C2×D3—22no—
551C2×D3—41no—
552C2×D3—41no—
553C2×D3—62no—
554C2×D3—62no—
555C2×D3—122no—
556C2×D3—128no—
557C2×D3—121no—
558C2×D3—121no—
559C2×D3—121no—
560C2×D3—121no—
561C2×D3—128no—
562C2×D3—241no—
563C2×D3—241no—
564C2×D3C3×(C2×D3)⋊C412yes—
565C2×D3C3×#21312yes—
566C2×D3C3×#21512yes—
567C3×C4—21no—
568C3×C4—21no—
569C3×C4—21no—
570C3×C4—21no—
571C3×C4—21no—
572C3×C4—21no—
573C3×C4—32no—
574C3×C4—32no—
575C3×C4—42no—
576C3×C4—41no—
577C3×C4—41no—
578C3×C4—41no—
579C3×C4—41no—
580C3×C4—41no—
581C3×C4—62no—
582C3×C4—81no—
583C3×C4—81no—
584C3×C4—82no—
585C3×C4—122no—
586C3×C4—121no—
587C3×C4—121no—
588C3×C4C4×D3211yescharacteristic
589C3×C4D3×D1211yescharacteristic
590C3×C4C2×C3×C4×D311yescharacteristic
591C3×C4C2×C3×C4×D311yescharacteristic
592C3×C4C2×C3×D1211yescharacteristic
593C3×C4C3×D3×D411yescharacteristic
594Dic3—41no—
595Dic3C3×(C2×D3)⋊C412yes—
596C32—21no—
597C32—21no—
598C32—21no—
599C32—41no—
600C32D3×#10211yescharacteristic, complemented
601C32C2×#80911yescharacteristic, complemented
602C32C2×C3×#10211yescharacteristic, complemented
603C23—31no—
604C23—61no—
605C23—184no—
606C23—181no—
607C23—362no—
608C23—362no—
609D4—32no—
610D4—61no—
611D4—92no—
612D4—184no—
613D4—181no—
614C2×C4—21no—
615C2×C4—31no—
616C2×C4—32no—
617C2×C4—32no—
618C2×C4—61no—
619C2×C4—122no—
620C2×C4C2×C3×D3211yescharacteristic
621C8—61no—
622C8—181no—
623C2×C3—21no—
624C2×C3—21no—
625C2×C3—21no—
626C2×C3—21no—
627C2×C3—21no—
628C2×C3—21no—
629C2×C3—21no—
630C2×C3—21no—
631C2×C3—21no—
632C2×C3—34no—
633C2×C3—34no—
634C2×C3—41no—
635C2×C3—41no—
636C2×C3—41no—
637C2×C3—64no—
638C2×C3—122no—
639C2×C3—122no—
640C2×C3—242no—
641C2×C3—362no—
642C2×C3D3×(C2×D3)⋊C411yescharacteristic
643C2×C3D3×#21311yescharacteristic
644C2×C3D3×#21511yescharacteristic
645C2×C3C3×D3×C22⋊C411yescharacteristic
646C2×C3C3×D3×D811yescharacteristic
647C2×C3C3×D3×SD1611yescharacteristic
648C2×C3C2×C3×(C2×D3)⋊C411yescharacteristic
649C2×C3C2×C3×#21311yescharacteristic
650C2×C3C2×C3×#21511yescharacteristic
651D3—42no—
652D3—122no—
653D3—122no—
654D3—242no—
655D3C3×#80914yesdirect product factor
656C22—32no—
657C22—32no—
658C22—32no—
659C22—62no—
660C22—121no—
661C22—121no—
662C22—182no—
663C22—368no—
664C22—361no—
665C22—361no—
666C22C3×D3×#6711yescharacteristic
667C4—32no—
668C4—41no—
669C4—121no—
670C4C3×C4×D3211yescharacteristic
671C4C3×D3×D1211yescharacteristic
672C3—21no—
673C3—21no—
674C3—21no—
675C3—41no—
676C3D3×#80911yescharacteristic, direct product factor
677C3C3×D3×#10211yescharacteristic, complemented
678C3C2×C3×#80911yescharacteristic, complemented
679C2—34no—
680C2—122no—
681C2—362no—
682C2C3×D3×(C2×D3)⋊C411yescharacteristic
683C2C3×D3×#21311yescharacteristic
684C2C3×D3×#21511yescharacteristic
subgroupG/H
centerC22×C3D3×#67
commutatorC32×C4C22×C3×C4
FrattiniC2×C4C2×C3×D32
FittingC33×C4⋊C4C22
socleC22×C33C2×D4
prime radicalC2×C3×D3×D12C2
cosocleC2×C32×C4C23×C3
hypercenterC3×C4⋊C4D32
hypocenterC32C2×C3×#102
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C32×D3×C4⋊C4C2semidirect
3. C2×C3×D3×C3⋊C8C2semidirect
4. C3×#63636C2semidirect
5. C32×#809C2semidirect
6. C3×#63564C2semidirect
7. C3×#63562C2semidirect
10. D3×#809C3direct (N × H)
18. C3×D3×D12C4semidirect
19. C33×C4⋊C4C22semidirect
20. C2×C3×C3⋊(C3⋊C8)C22semidirect
21. C32×C4⋊Dic3C22semidirect
23. C2×C32×C3⋊C8C22semidirect
32. C3×D3×C4⋊C4D3semidirect
33. C3×D3×C4⋊C4C2×C3semidirect
34. C2×D3×C3⋊C8C2×C3semidirect
36. #63636C2×C3semidirect
45. C3×#809D3direct (N × H)
46. C3×#809C2×C3semidirect
47. #63564C2×C3semidirect
48. #63562C2×C3semidirect
58. C3×C4⋊(C3⋊D3)C2×C4semidirect
62. C32×D12C2×C4semidirect
99. D3×D12C3×C4semidirect
107. C32×C4⋊C4C2×D3semidirect
108. C32×C4⋊C4C2×D3semidirect
109. C32×C4⋊C4C22×C3semidirect
110. C2×C3⋊(C3⋊C8)C22×C3semidirect
112. C3×C4⋊Dic3C2×D3semidirect
113. C3×C4⋊Dic3C22×C3semidirect
122. C2×C3×C3⋊C8C2×D3semidirect
123. C2×C3×C3⋊C8C22×C3semidirect
151. D3×C4⋊C4C3×D3semidirect
165. #809C3×D3direct (N × H)
209. C4⋊(C3⋊D3)C2×C3×C4semidirect
228. C3×D12C4×D3semidirect
229. C3×D12C2×C3×C4semidirect
254. C32×D3#102semidirect
298. C3×C4⋊C4D32semidirect
299. C3×C4⋊C4C2×C3×D3semidirect
300. C3×C4⋊C4C2×C3×D3semidirect
301. C4⋊Dic3C2×C3×D3semidirect
307. C2×C3⋊C8C2×C3×D3semidirect
391. C33C2×#102semidirect
462. D12C3×C4×D3semidirect
505. C3×D3#809direct (N × H)
506. C3×D3C3×#102semidirect
520. C4⋊C4C3×D32semidirect
600. C32D3×#102semidirect
601. C32C2×#809semidirect
602. C32C2×C3×#102semidirect
655. D3C3×#809direct (N × H)
676. C3D3×#809direct (N × H)
677. C3C3×D3×#102semidirect
678. C3C2×C3×#809semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×D122
C32×D3×C4⋊C42
C2×C3×D3×C3⋊C82
C3×#636362
C32×#8092
C3×#635642
C3×#635622
C2×C3×#8093
C3×D3×#1023
D3×#8093