Finite Group Databasebeta

← C3×#10591067 #13158337

Subgroups — C3×#10591067 #13158337

Order 1728.

754 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3748C211yesmaximal, characteristic, complemented
2C32×C4×#67C211yesmaximal, characteristic
3C2×C3×#3711C211yesmaximal, characteristic, complemented
4C32×#830C211yesmaximal, characteristic, complemented
5C3×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6C3×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
7C3×Dic3×C3⋊C8C211yesmaximal, characteristic, complemented
8C3×#5012—31nomaximal
9C3×#4729—31nomaximal
10#10591067C311yesmaximal, characteristic, direct product factor
11C22×C33×C4C2211yescharacteristic
12C2×C32×#67C411yescharacteristic
13C2×C32×C4×D3C2211yescharacteristic
14C3×#3748—22no—
15C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
16C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
17C32×#217C411yescharacteristic
18C32×(C2×D3)⋊C4C411yescharacteristic
19C32×Dic3⋊C4C411yescharacteristic
20C32×C4×Dic3C2211yescharacteristic
21C2×C32×C3⋊C8C2211yescharacteristic
22C2×C32×C3⋊C8C2211yescharacteristic
23C3×#3711—22no—
24C32×C4×D4—31no—
25C2×#3748C2×C311yescharacteristic, complemented
26C3×C4×#67—21no—
27C3×C4×#67D311yescharacteristic
28C3×C4×#67C2×C311yescharacteristic
29C2×C3×#208—31no—
30C2×C3×#208—31no—
31C2×C3×#208—31no—
32C2×C3×#208—61no—
33C2×C3×ΓL(1,𝔽25)—31no—
34C2×#3711C2×C311yescharacteristic, complemented
35C32×C22⋊C8—31no—
36C3×#830—21no—
37C3×#830—31no—
38C3×#830D311yescharacteristic, complemented
39C3×#830C2×C311yescharacteristic, complemented
40C3×(C2×D3)⋊C8—31no—
41C3×Dic3⋊C8—31no—
42C3×C8×Dic3—31no—
43C3×C4⋊(C3⋊C8)—31no—
44C3×C4×C3⋊C8—31no—
45Dic3⋊(C3⋊C8)C2×C311yescharacteristic, complemented
46(C2×D3)⋊(C3⋊C8)C2×C311yescharacteristic, complemented
47Dic3×C3⋊C8C2×C311yescharacteristic, complemented
48C23×C33C2×C411yescharacteristic
49C22×C32×D3C2×C411yescharacteristic
50C2×C33×C4—21no—
51C2×C33×C4—21no—
52C2×C33×C4C2×C411yescharacteristic
53C2×C33×C4C2311yescharacteristic
54C32×#67—22no—
55C2×C32×Dic3C2×C411yescharacteristic
56C2×C32×Dic3C2×C411yescharacteristic
57C2×C32×Dic3C2×C411yescharacteristic
58C32×C4×D3—21no—
59C32×C4×D3—21no—
60C3×C3⋊(C3⋊C8)—21no—
61C3×C3⋊(C3⋊C8)D412yescomplemented
62C32×C3⋊C8—21no—
63C32×C3⋊C8—21no—
64C3×#436—91no—
65#5012—31no—
66#4729—31no—
67C2×C32×D4—31no—
68C22×C32×C4—21no—
69C22×C32×C4—21no—
70C22×C32×C4—21no—
71C22×C32×C4—31no—
72C22×C32×C4—41no—
73C22×C32×C4C2×D311yescharacteristic
74C22×C32×C4C2×D311yescharacteristic
75C22×C32×C4C22×C311yescharacteristic
76C2×C3×#67—21no—
77C2×C3×#67Dic311yescharacteristic
78C2×C3×#67C3×C411yescharacteristic
79C2×C3×C4×D3—21no—
80C2×C3×C4×D3C2×D311yescharacteristic
81C2×C3×C4×D3C22×C311yescharacteristic
82C2×C32×C8—31no—
83C2×C32×C8—31no—
84C32×C4⋊C4—31no—
85C32×C22⋊C4—31no—
86C32×C22⋊C4—31no—
87C32×C42—31no—
88#3748—22no—
89C2×C3⋊(C3⋊C8)C22×C311yescharacteristic
90C2×C3⋊(C3⋊C8)C22×C311yescharacteristic
91C3×#217—21no—
92C3×#217Dic311yescharacteristic
93C3×#217C3×C411yescharacteristic
94C3×(C2×D3)⋊C4—21no—
95C3×(C2×D3)⋊C4Dic311yescharacteristic
96C3×(C2×D3)⋊C4C3×C411yescharacteristic
97C3×Dic3⋊C4—21no—
98C3×Dic3⋊C4Dic311yescharacteristic
99C3×Dic3⋊C4C3×C411yescharacteristic
100C3×C4×Dic3—21no—
101C3×C4×Dic3C2×D311yescharacteristic
102C3×C4×Dic3C22×C311yescharacteristic
103C3×#208—62no—
104C3×#208—62no—
105C3×#208—62no—
106C3×#208—64no—
107C2×C3×C3⋊C8—21no—
108C2×C3×C3⋊C8—21no—
109C2×C3×C3⋊C8—31no—
110C2×C3×C3⋊C8—31no—
111C2×C3×C3⋊C8—31no—
112C2×C3×C3⋊C8—31no—
113C2×C3×C3⋊C8—61no—
114C2×C3×C3⋊C8—61no—
115C2×C3×C3⋊C8C2×D311yescharacteristic
116C2×C3×C3⋊C8C2×D311yescharacteristic
117C2×C3×C3⋊C8C22×C311yescharacteristic
118C2×C3×C3⋊C8C22×C311yescharacteristic
119C3×ΓL(1,𝔽25)—62no—
120#3711—22no—
121C22×C33—21no—
122C22×C33—21no—
123C22×C33—21no—
124C22×C33C22×C411yescharacteristic
125C2×C32×D3—21no—
126C2×C32×D3—21no—
127C2×C32×D3—21no—
128C33×C4—21no—
129C33×C4C2×D411yescharacteristic
130C33×C4#4111yescharacteristic
131C32×Dic3—21no—
132C32×Dic3—21no—
133C32×Dic3M1612yescomplemented
134C2×C3×M16—91no—
135C2×C3×M16—91no—
136C3×C4×D4—31no—
137C3×C4×D4—31no—
138C3×C4×D4—61no—
139C4×#67C3×D311yescharacteristic
140C2×#208—31no—
141C2×#208—31no—
142C2×#208—31no—
143C2×#208—61no—
144C2×ΓL(1,𝔽25)—31no—
145C3×C4⋊C8—91no—
146C3×C22⋊C8—31no—
147C3×C22⋊C8—31no—
148C3×C22⋊C8—61no—
149C3×C22⋊C8—91no—
150C3×C4×C8—91no—
151#830—31no—
152#830C3×D311yescharacteristic, complemented
153(C2×D3)⋊C8—31no—
154Dic3⋊C8—31no—
155C8×Dic3—31no—
156C4⋊(C3⋊C8)—31no—
157C4×C3⋊C8—31no—
158C23×C32—21no—
159C23×C32—21no—
160C23×C32—21no—
161C23×C32—31no—
162C23×C32—41no—
163C23×C32C4×D311yescharacteristic
164C23×C32C2×Dic311yescharacteristic
165C23×C32C2×C3×C411yescharacteristic
166C22×C3×D3—21no—
167C22×C3×D3C2×Dic311yescharacteristic
168C22×C3×D3C2×C3×C411yescharacteristic
169C32×D4—62no—
170C2×C32×C4—21no—
171C2×C32×C4—21no—
172C2×C32×C4—22no—
173C2×C32×C4—22no—
174C2×C32×C4—21no—
175C2×C32×C4—21no—
176C2×C32×C4—21no—
177C2×C32×C4—21no—
178C2×C32×C4—21no—
179C2×C32×C4—21no—
180C2×C32×C4—21no—
181C2×C32×C4—21no—
182C2×C32×C4—21no—
183C2×C32×C4—21no—
184C2×C32×C4—31no—
185C2×C32×C4—31no—
186C2×C32×C4—31no—
187C2×C32×C4—41no—
188C2×C32×C4—41no—
189C2×C32×C4—41no—
190C2×C32×C4—41no—
191C2×C32×C4—41no—
192C2×C32×C4—41no—
193C2×C32×C4—42no—
194C2×C32×C4—42no—
195C2×C32×C4—61no—
196C2×C32×C4—61no—
197C2×C32×C4C4×D311yescharacteristic
198C2×C32×C4C2×Dic311yescharacteristic
199C2×C32×C4C2×C3×C411yescharacteristic
200C2×C32×C4C22×D311yescharacteristic
201C2×C32×C4C22×D311yescharacteristic
202C2×C32×C4C23×C311yescharacteristic
203C3×#67—24no—
204C3×#67—22no—
205C3×#67—22no—
206C2×C3×Dic3—21no—
207C2×C3×Dic3—21no—
208C2×C3×Dic3—21no—
209C2×C3×Dic3C2×Dic311yescharacteristic
210C2×C3×Dic3C2×Dic311yescharacteristic
211C2×C3×Dic3C2×Dic311yescharacteristic
212C2×C3×Dic3C2×C3×C411yescharacteristic
213C2×C3×Dic3C2×C3×C411yescharacteristic
214C2×C3×Dic3C2×C3×C411yescharacteristic
215C3×C4×D3—21no—
216C3×C4×D3—21no—
217C3×C4×D3—21no—
218C3×C4×D3—21no—
219C3×C4×D3—41no—
220C3×C4×D3—41no—
221C32×C8—61no—
222C32×C8—61no—
223C3⋊(C3⋊C8)—21no—
224C3⋊(C3⋊C8)C3×D412yescomplemented
225C3×C3⋊C8—21no—
226C3×C3⋊C8—21no—
227C3×C3⋊C8—21no—
228C3×C3⋊C8—21no—
229C3×C3⋊C8—32no—
230C3×C3⋊C8—32no—
231C3×C3⋊C8—41no—
232C3×C3⋊C8—41no—
233C3×C3⋊C8—62no—
234C3×C3⋊C8—62no—
235C3×C3⋊C8—61no—
236C3×C3⋊C8—61no—
237#436—91noSylow
238C2×C33—41no—
239C2×C33C4×D411yescharacteristic
240C2×C33C2×M1611yescharacteristic
241C2×C33#13111yescharacteristic
242C32×D3—41no—
243C2×C3×D4—31no—
244C2×C3×D4—31no—
245C2×C3×D4—61no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—31no—
250C22×C3×C4—31no—
251C22×C3×C4—41no—
252C22×C3×C4—61no—
253C22×C3×C4D3211yescharacteristic
254C22×C3×C4C2×C3×D311yescharacteristic
255C22×C3×C4C2×C3×D311yescharacteristic
256C2×#67C3×Dic311yescharacteristic
257C2×C4×D3C2×C3×D311yescharacteristic
258C3×M16—182no—
259C3×M16—182no—
260C2×C3×C8—31no—
261C2×C3×C8—31no—
262C2×C3×C8—31no—
263C2×C3×C8—31no—
264C2×C3×C8—61no—
265C2×C3×C8—61no—
266C2×C3×C8—91no—
267C2×C3×C8—91no—
268C3×C4⋊C4—31no—
269C3×C4⋊C4—31no—
270C3×C4⋊C4—61no—
271C3×C22⋊C4—31no—
272C3×C22⋊C4—31no—
273C3×C22⋊C4—31no—
274C3×C22⋊C4—31no—
275C3×C22⋊C4—61no—
276C3×C22⋊C4—61no—
277C3×C42—31no—
278C3×C42—31no—
279C3×C42—61no—
280#217C3×Dic311yescharacteristic
281(C2×D3)⋊C4C3×Dic311yescharacteristic
282Dic3⋊C4C3×Dic311yescharacteristic
283C4×Dic3C2×C3×D311yescharacteristic
284#208—62no—
285#208—62no—
286#208—62no—
287#208—64no—
288C2×C3⋊C8—31no—
289C2×C3⋊C8—31no—
290C2×C3⋊C8—31no—
291C2×C3⋊C8—31no—
292C2×C3⋊C8—61no—
293C2×C3⋊C8—61no—
294C2×C3⋊C8C2×C3×D311yescharacteristic
295C2×C3⋊C8C2×C3×D311yescharacteristic
296ΓL(1,𝔽25)—62no—
297C22×C32—21no—
298C22×C32—21no—
299C22×C32—21no—
300C22×C32—22no—
301C22×C32—22no—
302C22×C32—22no—
303C22×C32—21no—
304C22×C32—21no—
305C22×C32—21no—
306C22×C32—21no—
307C22×C32—21no—
308C22×C32—21no—
309C22×C32—21no—
310C22×C32—21no—
311C22×C32—21no—
312C22×C32—41no—
313C22×C32—41no—
314C22×C32—41no—
315C22×C32—41no—
316C22×C32—41no—
317C22×C32—41no—
318C22×C32—41no—
319C22×C32—42no—
320C22×C32—42no—
321C22×C32—42no—
322C22×C32—61no—
323C22×C32—61no—
324C22×C32—61no—
325C22×C32C2×C4×D311yescharacteristic
326C22×C32C22×Dic311yescharacteristic
327C22×C32C22×C3×C411yescharacteristic
328C2×C3×D3—22no—
329C2×C3×D3—21no—
330C2×C3×D3—21no—
331C2×C3×D3—21no—
332C2×C3×D3—21no—
333C2×C3×D3—21no—
334C2×C3×D3—21no—
335C2×C3×D3—41no—
336C2×C3×D3—41no—
337C32×C4—21no—
338C32×C4—22no—
339C32×C4—21no—
340C32×C4—21no—
341C32×C4—21no—
342C32×C4—21no—
343C32×C4—21no—
344C32×C4—21no—
345C32×C4—21no—
346C32×C4—21no—
347C32×C4—32no—
348C32×C4—41no—
349C32×C4—41no—
350C32×C4—41no—
351C32×C4—41no—
352C32×C4—42no—
353C32×C4—61no—
354C32×C4—61no—
355C32×C4D3×D411yescharacteristic
356C32×C4D3×D411yescharacteristic
357C32×C4#23711yescharacteristic
358C32×C4#23711yescharacteristic
359C32×C4C2×C3×D411yescharacteristic
360C32×C4C3×#4111yescharacteristic
361C3×Dic3—21no—
362C3×Dic3—21no—
363C3×Dic3—21no—
364C3×Dic3—21no—
365C3×Dic3—22no—
366C3×Dic3—41no—
367C3×Dic3—41no—
368C3×Dic3#20812yescomplemented
369C3×Dic3C3×M1612yescomplemented
370C2×M16—91no—
371C2×M16—91no—
372C4×D4—31no—
373C4⋊C8—91no—
374C22⋊C8—31no—
375C22⋊C8—91no—
376C4×C8—91no—
377C33#43611yescharacteristic, complemented, Sylow
378C23×C3—21no—
379C23×C3—21no—
380C23×C3—21no—
381C23×C3—31no—
382C23×C3—31no—
383C23×C3—41no—
384C23×C3—61no—
385C23×C3D3×Dic311yescharacteristic
386C23×C3C3×C4×D311yescharacteristic
387C23×C3C2×C3×Dic311yescharacteristic
388C22×D3C2×C3×Dic311yescharacteristic
389C3×D4—62no—
390C3×D4—62no—
391C3×D4—64no—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—21no—
397C2×C3×C4—21no—
398C2×C3×C4—21no—
399C2×C3×C4—21no—
400C2×C3×C4—21no—
401C2×C3×C4—21no—
402C2×C3×C4—21no—
403C2×C3×C4—21no—
404C2×C3×C4—21no—
405C2×C3×C4—21no—
406C2×C3×C4—31no—
407C2×C3×C4—31no—
408C2×C3×C4—31no—
409C2×C3×C4—31no—
410C2×C3×C4—31no—
411C2×C3×C4—31no—
412C2×C3×C4—41no—
413C2×C3×C4—41no—
414C2×C3×C4—41no—
415C2×C3×C4—41no—
416C2×C3×C4—42no—
417C2×C3×C4—42no—
418C2×C3×C4—41no—
419C2×C3×C4—41no—
420C2×C3×C4—61no—
421C2×C3×C4—61no—
422C2×C3×C4—61no—
423C2×C3×C4—61no—
424C2×C3×C4—61no—
425C2×C3×C4—61no—
426C2×C3×C4—61no—
427C2×C3×C4—121no—
428C2×C3×C4—121no—
429C2×C3×C4D3×Dic311yescharacteristic
430C2×C3×C4C3×C4×D311yescharacteristic
431C2×C3×C4C2×C3×Dic311yescharacteristic
432C2×C3×C4C2×D3211yescharacteristic
433C2×C3×C4C22×C3×D311yescharacteristic
434C2×C3×C4C22×C3×D311yescharacteristic
435#67—22no—
436C2×Dic3C2×C3×Dic311yescharacteristic
437C2×Dic3C2×C3×Dic311yescharacteristic
438C2×Dic3C2×C3×Dic311yescharacteristic
439C4×D3—21no—
440C4×D3—21no—
441C3×C8—61no—
442C3×C8—61no—
443C3×C8—61no—
444C3×C8—61no—
445C3×C8—92no—
446C3×C8—121no—
447C3×C8—121no—
448C3×C8—181no—
449C3⋊C8—21no—
450C3⋊C8—21no—
451C3⋊C8—32no—
452C3⋊C8—32no—
453C3⋊C8—62no—
454C3⋊C8—62no—
455C3⋊C8—61no—
456C3⋊C8—61no—
457C2×C32—21no—
458C2×C32—21no—
459C2×C32—21no—
460C2×C32—21no—
461C2×C32—21no—
462C2×C32—21no—
463C2×C32—21no—
464C2×C32—21no—
465C2×C32—21no—
466C2×C32—41no—
467C2×C32—41no—
468C2×C32—41no—
469C2×C32—42no—
470C2×C32—42no—
471C2×C32—42no—
472C2×C32—44no—
473C2×C32—41no—
474C2×C32—41no—
475C2×C32—41no—
476C2×C32—121no—
477C2×C32#67⋊C411yescharacteristic
478C2×C32#90111yescharacteristic
479C2×C32D3×M1611yescharacteristic
480C2×C32C2×#20811yescharacteristic
481C2×C32D4×Dic311yescharacteristic
482C2×C32#94811yescharacteristic
483C2×C32C3×C4×D411yescharacteristic
484C2×C32C2×C3×M1611yescharacteristic
485C2×C32C3×#13111yescharacteristic
486C3×D3—42no—
487C3×D3—41no—
488C3×D3—41no—
489C2×D4—31no—
490C22×C4—31no—
491C22×C4C3×D3211yescharacteristic
492M16—182no—
493M16—182no—
494C2×C8—31no—
495C2×C8—31no—
496C2×C8—91no—
497C2×C8—91no—
498C4⋊C4—31no—
499C22⋊C4—31no—
500C22⋊C4—31no—
501C42—31no—
502C22×C3—22no—
503C22×C3—22no—
504C22×C3—22no—
505C22×C3—21no—
506C22×C3—21no—
507C22×C3—21no—
508C22×C3—21no—
509C22×C3—21no—
510C22×C3—21no—
511C22×C3—21no—
512C22×C3—21no—
513C22×C3—21no—
514C22×C3—21no—
515C22×C3—21no—
516C22×C3—21no—
517C22×C3—41no—
518C22×C3—41no—
519C22×C3—41no—
520C22×C3—41no—
521C22×C3—41no—
522C22×C3—41no—
523C22×C3—42no—
524C22×C3—42no—
525C22×C3—42no—
526C22×C3—41no—
527C22×C3—62no—
528C22×C3—61no—
529C22×C3—61no—
530C22×C3—61no—
531C22×C3—61no—
532C22×C3—61no—
533C22×C3—61no—
534C22×C3—121no—
535C22×C3—121no—
536C22×C3C2×D3×Dic311yescharacteristic
537C22×C3C2×C3×C4×D311yescharacteristic
538C22×C3C22×C3×Dic311yescharacteristic
539C2×D3—21no—
540C2×D3—21no—
541C2×D3—21no—
542C3×C4—22no—
543C3×C4—21no—
544C3×C4—21no—
545C3×C4—21no—
546C3×C4—21no—
547C3×C4—21no—
548C3×C4—21no—
549C3×C4—21no—
550C3×C4—21no—
551C3×C4—21no—
552C3×C4—32no—
553C3×C4—32no—
554C3×C4—41no—
555C3×C4—41no—
556C3×C4—42no—
557C3×C4—41no—
558C3×C4—41no—
559C3×C4—62no—
560C3×C4—61no—
561C3×C4—61no—
562C3×C4—61no—
563C3×C4—61no—
564C3×C4—121no—
565C3×C4—121no—
566C3×C4#380511yescharacteristic
567C3×C4#381111yescharacteristic
568C3×C4C3×D3×D411yescharacteristic
569C3×C4C3×D3×D411yescharacteristic
570C3×C4C3×#23711yescharacteristic
571C3×C4C3×#23711yescharacteristic
572Dic3—21no—
573Dic3—21no—
574Dic3C3×#20812yescomplemented
575C32—21no—
576C32—21no—
577C32—21no—
578C32—41no—
579C32#472911yescharacteristic, complemented
580C32#501211yescharacteristic, complemented
581C32C3×#43611yescharacteristic, complemented
582C23—31no—
583C23C3×D3×Dic311yescharacteristic
584D4—62no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—31no—
588C2×C4—31no—
589C2×C4—31no—
590C2×C4—61no—
591C2×C4—61no—
592C2×C4C3×D3×Dic311yescharacteristic
593C2×C4C2×C3×D3211yescharacteristic
594C8—61no—
595C8—61no—
596C8—92no—
597C8—181no—
598C2×C3—21no—
599C2×C3—21no—
600C2×C3—21no—
601C2×C3—21no—
602C2×C3—21no—
603C2×C3—21no—
604C2×C3—21no—
605C2×C3—21no—
606C2×C3—21no—
607C2×C3—42no—
608C2×C3—42no—
609C2×C3—42no—
610C2×C3—44no—
611C2×C3—41no—
612C2×C3—41no—
613C2×C3—41no—
614C2×C3—41no—
615C2×C3—41no—
616C2×C3—41no—
617C2×C3—122no—
618C2×C3—121no—
619C2×C3—121no—
620C2×C3D3×#20811yescharacteristic
621C2×C3#6381411yescharacteristic
622C2×C3#67⋊Dic311yescharacteristic
623C2×C3C3×#67⋊C411yescharacteristic
624C2×C3C3×#90111yescharacteristic
625C2×C3C3×D3×M1611yescharacteristic
626C2×C3C2×C3×#20811yescharacteristic
627C2×C3C3×D4×Dic311yescharacteristic
628C2×C3C3×#94811yescharacteristic
629D3—41no—
630C22—21no—
631C22—21no—
632C22—21no—
633C22—61no—
634C22—61no—
635C22—61no—
636C22C2×C3×D3×Dic311yescharacteristic
637C4—21no—
638C4—32no—
639C4—61no—
640C4—61no—
641C4C3×#380511yescharacteristic
642C4C3×#381111yescharacteristic
643C3—21no—
644C3—21no—
645C3—21no—
646C3—41no—
647C3#1059106711yescharacteristic, direct product factor
648C3C3×#472911yescharacteristic, complemented
649C3C3×#501211yescharacteristic, complemented
650C2—41no—
651C2—121no—
652C2C3×D3×#20811yescharacteristic
653C2C3×#6381411yescharacteristic
654C2C3×#67⋊Dic311yescharacteristic
subgroupG/H
centerC2×C3×C4C2×D32
commutatorC22×C32C22×C3×C4
FrattiniC2×C4C2×C3×D32
FittingC22×C33×C4C22
socleC22×C33C22×C4
prime radicalC2×C32×#67C4
cosocleC2×C32×C4C23×C3
hypercenterC22×C3×C4D32
hypocenterC32C3×#436
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3748C2semidirect
3. C2×C3×#3711C2semidirect
4. C32×#830C2semidirect
5. C3×Dic3⋊(C3⋊C8)C2semidirect
6. C3×(C2×D3)⋊(C3⋊C8)C2semidirect
7. C3×Dic3×C3⋊C8C2semidirect
10. #10591067C3direct (N × H)
25. C2×#3748C2×C3semidirect
34. C2×#3711C2×C3semidirect
38. C3×#830D3semidirect
39. C3×#830C2×C3semidirect
45. Dic3⋊(C3⋊C8)C2×C3semidirect
46. (C2×D3)⋊(C3⋊C8)C2×C3semidirect
47. Dic3×C3⋊C8C2×C3semidirect
61. C3×C3⋊(C3⋊C8)D4semidirect
133. C32×Dic3M16semidirect
152. #830C3×D3semidirect
224. C3⋊(C3⋊C8)C3×D4semidirect
368. C3×Dic3#208semidirect
369. C3×Dic3C3×M16semidirect
377. C33#436semidirect
574. Dic3C3×#208semidirect
579. C32#4729semidirect
580. C32#5012semidirect
581. C32C3×#436semidirect
647. C3#10591067direct (N × H)
648. C3C3×#4729semidirect
649. C3C3×#5012semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#37482
C32×C4×#672
C2×C3×#37112
C32×#8302
C3×Dic3⋊(C3⋊C8)2
C3×(C2×D3)⋊(C3⋊C8)2
C3×Dic3×C3⋊C82
C3×#50123
C3×#47293
#105910673