Finite Group Databasebeta

← C3×#76314 #11811946

Subgroups — C3×#76314 #11811946

Order 1152.

2825 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×D4C211yesmaximal, characteristic, complemented
2C2×C3×#940C211yesmaximal, characteristic, complemented
3C2×C3×#895C211yesmaximal, characteristic, complemented
4C2×C3×#882C214yesmaximal, complemented
5C2×C3×#874C211yesmaximal, characteristic, complemented
6C32×#390C211yesmaximal, characteristic, complemented
7C3×#4988C211yesmaximal, characteristic, complemented
8C3×#4960C214yesmaximal, complemented
9C3×C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10C3×#2433—31nomaximal
11#76314C311yesmaximal, characteristic, direct product factor
12C24×C3×D3C2212yes—
13C22×C32×D4C2211yescharacteristic
14C22×C3×#67C2212yes—
15C22×C3×#67C2214yescomplemented
16C2×C3×D3×D4—24no—
17C2×C3×D3×D4—24no—
18C2×C3×D3×D4—24no—
19C22×C3×D12C2212yes—
20C22×C3×D12C2211yescharacteristic
21C22×C3×D12C2211yescharacteristic, complemented
22C22×C3×D12C2214yescomplemented
23C22×C3×C4×D3C2211yescharacteristic
24C2×C32×C4⋊C4C2211yescharacteristic, complemented
25C2×C32×C22⋊C4C2214yescomplemented
26C2×C32×C42C2211yescharacteristic, complemented
27C3×#940—24no—
28C2×C3×(C2×D3)⋊C4C2212yes—
29C2×C3×(C2×D3)⋊C4C2214yescomplemented
30C2×C3×(C2×D3)⋊C4C2212yescomplemented
31C2×C3×C4×Dic3C2211yescharacteristic, complemented
32C3×#895—24no—
33C3×#882—216no—
34C3×#874—24no—
35C3×C3⋊#95C2212yescomplemented
36C23×C3×D4—31no—
37C22×D3×D4C2×C311yescharacteristic, complemented
38C2×C3×#127—31no—
39C2×C3×#127—31no—
40C2×C3×#121—31no—
41C2×C3×#120—34no—
42C2×#940C2×C311yescharacteristic, complemented
43C2×#895C2×C311yescharacteristic, complemented
44C2×#882C2×C314yescomplemented
45C2×#874C2×C311yescharacteristic, complemented
46C3×#392—34no—
47C3×#390—21no—
48C3×#390—31no—
49C3×#390D311yescharacteristic, complemented
50C3×#390C2×C311yescharacteristic, complemented
51C3×C4×C22⋊C4—31no—
52#4988C2×C311yescharacteristic, complemented
53#4960C2×C314yescomplemented
54C4×(C2×D3)⋊C4C2×C311yescharacteristic, complemented
55C24×C32C2312yes—
56C23×C3×D3—24no—
57C23×C3×D3—24no—
58C23×C3×D3—24no—
59C23×C3×D3—28no—
60C23×C3×D3—44no—
61C23×C3×D3C2312yes—
62C23×C3×D3C2312yes—
63C23×C3×D3C2311yescharacteristic
64C2×C32×D4—22no—
65C2×C32×D4—22no—
66C2×C32×D4D414yescomplemented
67C22×C32×C4C2312yes—
68C22×C32×C4C2312yes—
69C22×C32×C4C2311yescharacteristic
70C2×C3×#67—24no—
71C2×C3×#67—24no—
72C2×C3×#67—28no—
73C2×C3×#67—24no—
74C2×C3×#67—28no—
75C2×C3×#67—44no—
76C22×C3×Dic3C2311yescharacteristic
77C22×C3×Dic3C2312yes—
78C3×D3×D4—232no—
79C2×C3×D12—22no—
80C2×C3×D12—22no—
81C2×C3×D12—28no—
82C2×C3×D12—24no—
83C2×C3×D12—28no—
84C2×C3×D12—22no—
85C2×C3×D12—22no—
86C2×C3×D12—22no—
87C2×C3×D12—28no—
88C2×C3×D12—44no—
89C2×C3×D12D414yescomplemented
90C2×C3×C4×D3—22no—
91C2×C3×C4×D3—22no—
92C2×C3×C4×D3D414yescomplemented
93C32×C4⋊C4—22no—
94C32×C22⋊C4—28no—
95C32×C42—22no—
96C3×(C2×D3)⋊C4—24no—
97C3×(C2×D3)⋊C4—28no—
98C3×(C2×D3)⋊C4D418yescomplemented
99C3×C4×Dic3—22no—
100#2433—31noSylow
101C25×C3—32no—
102C24×D3C22×C312yes—
103C22×C3×D4—21no—
104C22×C3×D4—32no—
105C22×C3×D4—34no—
106C22×C3×D4—31no—
107C22×C3×D4—32no—
108C22×C3×D4—31no—
109C22×C3×D4—34no—
110C22×C3×D4—64no—
111C22×C3×D4—64no—
112C22×C3×D4—64no—
113C22×C3×D4C2×D311yescharacteristic
114C22×C3×D4C22×C311yescharacteristic
115C23×C3×C4—31no—
116C22×#67C22×C312yes—
117C22×#67C22×C314yescomplemented
118C2×D3×D4—24no—
119C2×D3×D4—24no—
120C2×D3×D4—24no—
121C22×D12C22×C312yes—
122C22×D12C22×C311yescharacteristic
123C22×D12C22×C311yescharacteristic, complemented
124C22×D12C22×C314yescomplemented
125C22×C4×D3C22×C311yescharacteristic
126C3×#127—64no—
127C3×#127—64no—
128C3×#121—64no—
129C3×#120—616no—
130C2×C3×C4⋊C4—21no—
131C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
132C2×C3×C4⋊C4C22×C311yescharacteristic, complemented
133C2×C3×C22⋊C4—24no—
134C2×C3×C22⋊C4—32no—
135C2×C3×C22⋊C4—34no—
136C2×C3×C22⋊C4—32no—
137C2×C3×C22⋊C4C2×D314yescomplemented
138C2×C3×C22⋊C4C22×C314yescomplemented
139C2×C3×C42—21no—
140C2×C3×C42—31no—
141C2×C3×C42C2×D311yescharacteristic, complemented
142C2×C3×C42C22×C311yescharacteristic, complemented
143#940—24no—
144C2×(C2×D3)⋊C4C22×C312yes—
145C2×(C2×D3)⋊C4C22×C312yescomplemented
146C2×(C2×D3)⋊C4C22×C314yescomplemented
147C2×C4×Dic3C22×C311yescharacteristic, complemented
148#895—24no—
149#882—216no—
150#874—24no—
151C3×#95—32no—
152C3⋊#95C22×C312yescomplemented
153C23×C32—24no—
154C23×C32—22no—
155C23×C32—22no—
156C23×C32—24no—
157C23×C32C2×D414yes—
158C23×C32C2411yescharacteristic
159C22×C3×D3—21no—
160C22×C3×D3—21no—
161C22×C3×D3—22no—
162C22×C3×D3—216no—
163C22×C3×D3—24no—
164C22×C3×D3—22no—
165C22×C3×D3—22no—
166C22×C3×D3—24no—
167C22×C3×D3—22no—
168C22×C3×D3—22no—
169C22×C3×D3—24no—
170C22×C3×D3—22no—
171C22×C3×D3—24no—
172C22×C3×D3—416no—
173C22×C3×D3—416no—
174C22×C3×D3—48no—
175C22×C3×D3—48no—
176C22×C3×D3C2×D414yes—
177C22×C3×D3C2×D414yes—
178C22×C3×D3C2×D412yes—
179C32×D4—28no—
180C2×C32×C4—22no—
181C2×C32×C4—22no—
182C2×C32×C4—24no—
183C2×C32×C4—22no—
184C2×C32×C4C2×D412yes—
185C2×C32×C4C2×D412yes—
186C2×C32×C4C2×D412yes—
187C2×C32×C4C2×D414yescomplemented
188C3×#67—216no—
189C3×#67—416no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—21no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3C2×D412yes—
195C2×C3×Dic3C2×D414yescomplemented
196C3×D12—28no—
197C3×D12—416no—
198C3×D12—48no—
199C3×D12—44no—
200C3×C4×D3—28no—
201C23×D4—31no—
202C2×#127—31no—
203C2×#127—31no—
204C2×#121—31no—
205C2×#120—34no—
206#392—34no—
207#390—31no—
208#390C3×D311yescharacteristic, complemented
209C4×C22⋊C4—31no—
210C24×C3—22no—
211C24×C3—31no—
212C24×C3—32no—
213C24×C3—32no—
214C24×C3—64no—
215C24×C3—64no—
216C24×C3—68no—
217C24×C3—64no—
218C24×C3—124no—
219C24×C3C22×D312yes—
220C24×C3C23×C312yes—
221C23×D3—24no—
222C23×D3—24no—
223C23×D3—24no—
224C23×D3—28no—
225C23×D3—44no—
226C23×D3C23×C312yes—
227C23×D3C23×C312yes—
228C23×D3C23×C311yescharacteristic
229C2×C3×D4—22no—
230C2×C3×D4—22no—
231C2×C3×D4—22no—
232C2×C3×D4—22no—
233C2×C3×D4—24no—
234C2×C3×D4—34no—
235C2×C3×D4—42no—
236C2×C3×D4—42no—
237C2×C3×D4—68no—
238C2×C3×D4—64no—
239C2×C3×D4—68no—
240C2×C3×D4—64no—
241C2×C3×D4—68no—
242C2×C3×D4—632no—
243C2×C3×D4—64no—
244C2×C3×D4—64no—
245C2×C3×D4—68no—
246C2×C3×D4—62no—
247C2×C3×D4—62no—
248C2×C3×D4—62no—
249C2×C3×D4—62no—
250C2×C3×D4—62no—
251C2×C3×D4—68no—
252C2×C3×D4—124no—
253C2×C3×D4—124no—
254C2×C3×D4D1214yescomplemented
255C2×C3×D4C3×D414yescomplemented
256C22×C3×C4—21no—
257C22×C3×C4—22no—
258C22×C3×C4—22no—
259C22×C3×C4—31no—
260C22×C3×C4—32no—
261C22×C3×C4—34no—
262C22×C3×C4—62no—
263C22×C3×C4—62no—
264C22×C3×C4C22×D312yes—
265C22×C3×C4C22×D312yes—
266C22×C3×C4C22×D311yescharacteristic
267C22×C3×C4C23×C312yes—
268C22×C3×C4C23×C312yes—
269C22×C3×C4C23×C311yescharacteristic
270C2×#67—24no—
271C2×#67—24no—
272C2×#67—28no—
273C2×#67—24no—
274C2×#67—28no—
275C2×#67—44no—
276C22×Dic3C23×C311yescharacteristic
277C22×Dic3C23×C312yes—
278D3×D4—232no—
279C2×D12—22no—
280C2×D12—22no—
281C2×D12—28no—
282C2×D12—28no—
283C2×D12—24no—
284C2×D12—22no—
285C2×D12—22no—
286C2×D12—22no—
287C2×D12—28no—
288C2×D12—44no—
289C2×D12C3×D414yescomplemented
290C2×C4×D3—22no—
291C2×C4×D3—22no—
292C2×C4×D3C3×D414yescomplemented
293C3×C4⋊C4—22no—
294C3×C4⋊C4—22no—
295C3×C4⋊C4—42no—
296C3×C22⋊C4—28no—
297C3×C22⋊C4—28no—
298C3×C22⋊C4—38no—
299C3×C22⋊C4—48no—
300C3×C22⋊C4—68no—
301C3×C22⋊C4—64no—
302C3×C42—22no—
303C3×C42—22no—
304C3×C42—42no—
305C3×C42—62no—
306(C2×D3)⋊C4—24no—
307(C2×D3)⋊C4—28no—
308(C2×D3)⋊C4C3×D418yescomplemented
309C4×Dic3—22no—
310C22×C32—24no—
311C22×C32—28no—
312C22×C32—42no—
313C22×C32—42no—
314C22×C32—44no—
315C22×C32C22×D411yescharacteristic
316C22×C32C22×D411yescharacteristic
317C22×C32C22×D411yescharacteristic
318C22×C32C22×D412yes—
319C22×C32H(5,𝔽2)12yes—
320C2×C3×D3—22no—
321C2×C3×D3—22no—
322C2×C3×D3—24no—
323C2×C3×D3—24no—
324C2×C3×D3—24no—
325C2×C3×D3—28no—
326C2×C3×D3—432no—
327C2×C3×D3—42no—
328C2×C3×D3—42no—
329C2×C3×D3—44no—
330C2×C3×D3—42no—
331C2×C3×D3—42no—
332C2×C3×D3—42no—
333C2×C3×D3—44no—
334C2×C3×D3—44no—
335C2×C3×D3#12714yescomplemented
336C32×C4—24no—
337C32×C4—42no—
338C32×C4#12014yescomplemented
339C3×Dic3—22no—
340C3×Dic3—24no—
341C25—32no—
342C22×D4—32no—
343C22×D4—34no—
344C22×D4—31no—
345C22×D4—32no—
346C22×D4—31no—
347C22×D4—34no—
348C22×D4—64no—
349C22×D4—64no—
350C22×D4—64no—
351C22×D4C2×C3×D311yescharacteristic
352C23×C4—31no—
353#127—64no—
354#127—64no—
355#121—64no—
356#120—616no—
357C2×C4⋊C4C2×C3×D311yescharacteristic, complemented
358C2×C22⋊C4—32no—
359C2×C22⋊C4—34no—
360C2×C22⋊C4—32no—
361C2×C22⋊C4C2×C3×D314yescomplemented
362C2×C42—31no—
363C2×C42C2×C3×D311yescharacteristic, complemented
364#95—32no—
365C23×C3—24no—
366C23×C3—22no—
367C23×C3—22no—
368C23×C3—24no—
369C23×C3—24no—
370C23×C3—22no—
371C23×C3—22no—
372C23×C3—24no—
373C23×C3—21no—
374C23×C3—24no—
375C23×C3—34no—
376C23×C3—32no—
377C23×C3—34no—
378C23×C3—44no—
379C23×C3—42no—
380C23×C3—42no—
381C23×C3—44no—
382C23×C3—616no—
383C23×C3—61no—
384C23×C3—61no—
385C23×C3—62no—
386C23×C3—62no—
387C23×C3—64no—
388C23×C3—62no—
389C23×C3—64no—
390C23×C3—62no—
391C23×C3—62no—
392C23×C3—64no—
393C23×C3—62no—
394C23×C3—64no—
395C23×C3—1216no—
396C23×C3—128no—
397C23×C3—1216no—
398C23×C3—128no—
399C23×C3C2×D1214yes—
400C23×C3C2×C3×D414yes—
401C23×C3C23×D311yescharacteristic
402C23×C3C24×C311yescharacteristic
403C22×D3—21no—
404C22×D3—21no—
405C22×D3—22no—
406C22×D3—216no—
407C22×D3—24no—
408C22×D3—22no—
409C22×D3—22no—
410C22×D3—24no—
411C22×D3—22no—
412C22×D3—22no—
413C22×D3—24no—
414C22×D3—22no—
415C22×D3—24no—
416C22×D3—416no—
417C22×D3—416no—
418C22×D3—48no—
419C22×D3—48no—
420C22×D3C2×C3×D414yes—
421C22×D3C2×C3×D414yes—
422C22×D3C2×C3×D412yes—
423C3×D4—28no—
424C3×D4—28no—
425C3×D4—48no—
426C3×D4—616no—
427C3×D4—68no—
428C3×D4—1216no—
429C3×D4—128no—
430C3×D4—1216no—
431C3×D4—124no—
432C2×C3×C4—22no—
433C2×C3×C4—22no—
434C2×C3×C4—22no—
435C2×C3×C4—22no—
436C2×C3×C4—24no—
437C2×C3×C4—22no—
438C2×C3×C4—24no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—22no—
442C2×C3×C4—22no—
443C2×C3×C4—24no—
444C2×C3×C4—32no—
445C2×C3×C4—34no—
446C2×C3×C4—42no—
447C2×C3×C4—42no—
448C2×C3×C4—44no—
449C2×C3×C4—42no—
450C2×C3×C4—62no—
451C2×C3×C4—61no—
452C2×C3×C4—61no—
453C2×C3×C4—62no—
454C2×C3×C4—68no—
455C2×C3×C4C2×D1212yes—
456C2×C3×C4D3×D412yes—
457C2×C3×C4D3×D412yes—
458C2×C3×C4D3×D414yescomplemented
459C2×C3×C4C2×C3×D412yes—
460C2×C3×C4C2×C3×D412yes—
461C2×C3×C4C2×C3×D412yes—
462C2×C3×C4C2×C3×D414yescomplemented
463#67—216no—
464#67—416no—
465C2×Dic3—22no—
466C2×Dic3—21no—
467C2×Dic3—21no—
468C2×Dic3—22no—
469C2×Dic3C2×C3×D412yes—
470C2×Dic3C2×C3×D414yescomplemented
471D12—28no—
472D12—416no—
473D12—48no—
474D12—44no—
475C4×D3—28no—
476C2×C32—44no—
477C2×C32C2×#12011yescharacteristic
478C2×C32C2×#12711yescharacteristic
479C2×C32#53511yescharacteristic
480C2×C32D4212yes—
481C2×C32D4212yes—
482C3×D3—24no—
483C3×D3—44no—
484C3×D3—82no—
485C24—31no—
486C24—32no—
487C24—32no—
488C24—64no—
489C24—64no—
490C24—68no—
491C24—64no—
492C24—124no—
493C24C22×C3×D312yes—
494C2×D4—22no—
495C2×D4—22no—
496C2×D4—34no—
497C2×D4—68no—
498C2×D4—64no—
499C2×D4—68no—
500C2×D4—64no—
501C2×D4—68no—
502C2×D4—632no—
503C2×D4—64no—
504C2×D4—64no—
505C2×D4—68no—
506C2×D4—62no—
507C2×D4—62no—
508C2×D4—62no—
509C2×D4—62no—
510C2×D4—62no—
511C2×D4—68no—
512C2×D4—124no—
513C2×D4—124no—
514C2×D4C3×D1214yescomplemented
515C22×C4—31no—
516C22×C4—32no—
517C22×C4—34no—
518C22×C4—62no—
519C22×C4—62no—
520C22×C4C22×C3×D312yes—
521C22×C4C22×C3×D312yes—
522C22×C4C22×C3×D311yescharacteristic
523C4⋊C4—22no—
524C22⋊C4—28no—
525C22⋊C4—38no—
526C22⋊C4—68no—
527C22⋊C4—64no—
528C42—22no—
529C42—62no—
530C22×C3—24no—
531C22×C3—28no—
532C22×C3—24no—
533C22×C3—28no—
534C22×C3—21no—
535C22×C3—21no—
536C22×C3—21no—
537C22×C3—22no—
538C22×C3—22no—
539C22×C3—34no—
540C22×C3—44no—
541C22×C3—48no—
542C22×C3—42no—
543C22×C3—42no—
544C22×C3—42no—
545C22×C3—44no—
546C22×C3—42no—
547C22×C3—44no—
548C22×C3—62no—
549C22×C3—62no—
550C22×C3—64no—
551C22×C3—64no—
552C22×C3—64no—
553C22×C3—68no—
554C22×C3—84no—
555C22×C3—82no—
556C22×C3—82no—
557C22×C3—1232no—
558C22×C3—122no—
559C22×C3—122no—
560C22×C3—124no—
561C22×C3—122no—
562C22×C3—122no—
563C22×C3—122no—
564C22×C3—124no—
565C22×C3—124no—
566C22×C3C22×D1211yescharacteristic
567C22×C3C2×D3×D411yescharacteristic
568C22×C3C2×D3×D412yes—
569C22×C3C2×D3×D411yescharacteristic
570C22×C3#100912yes—
571C22×C3C22×C3×D411yescharacteristic
572C22×C3C22×C3×D411yescharacteristic
573C22×C3C22×C3×D411yescharacteristic
574C22×C3C22×C3×D412yes—
575C22×C3C3×H(5,𝔽2)12yes—
576C2×D3—22no—
577C2×D3—22no—
578C2×D3—24no—
579C2×D3—24no—
580C2×D3—24no—
581C2×D3—28no—
582C2×D3—432no—
583C2×D3—42no—
584C2×D3—42no—
585C2×D3—44no—
586C2×D3—42no—
587C2×D3—42no—
588C2×D3—42no—
589C2×D3—44no—
590C2×D3—44no—
591C2×D3C3×#12714yescomplemented
592C3×C4—24no—
593C3×C4—24no—
594C3×C4—24no—
595C3×C4—44no—
596C3×C4—42no—
597C3×C4—42no—
598C3×C4—62no—
599C3×C4—64no—
600C3×C4—82no—
601C3×C4#88214yescomplemented
602C3×C4C3×#12014yescomplemented
603Dic3—22no—
604Dic3—24no—
605C32#243311yescharacteristic, complemented, Sylow
606C23—24no—
607C23—22no—
608C23—22no—
609C23—24no—
610C23—34no—
611C23—32no—
612C23—34no—
613C23—616no—
614C23—61no—
615C23—61no—
616C23—62no—
617C23—62no—
618C23—64no—
619C23—62no—
620C23—64no—
621C23—62no—
622C23—62no—
623C23—62no—
624C23—64no—
625C23—64no—
626C23—1216no—
627C23—128no—
628C23—1216no—
629C23—128no—
630C23C2×C3×D1214yes—
631C23C23×C3×D311yescharacteristic
632D4—28no—
633D4—616no—
634D4—68no—
635D4—1216no—
636D4—128no—
637D4—1216no—
638D4—124no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—24no—
642C2×C4—22no—
643C2×C4—34no—
644C2×C4—32no—
645C2×C4—62no—
646C2×C4—61no—
647C2×C4—61no—
648C2×C4—62no—
649C2×C4—68no—
650C2×C4C2×C3×D1212yes—
651C2×C4C3×D3×D412yes—
652C2×C4C3×D3×D412yes—
653C2×C4C3×D3×D414yescomplemented
654C2×C3—21no—
655C2×C3—22no—
656C2×C3—22no—
657C2×C3—21no—
658C2×C3—21no—
659C2×C3—44no—
660C2×C3—44no—
661C2×C3—64no—
662C2×C3—84no—
663C2×C3—124no—
664C2×C3—242no—
665C2×C3C2×#88211yescharacteristic
666C2×C3D4×D1212yes—
667C2×C3#560912yes—
668C2×C3#567411yescharacteristic
669C2×C3D3×#12711yescharacteristic
670C2×C3C2×C3×#12011yescharacteristic
671C2×C3C2×C3×#12711yescharacteristic
672C2×C3C3×#53511yescharacteristic
673C2×C3C3×D4212yes—
674C2×C3C3×D4212yes—
675D3—24no—
676D3—44no—
677D3—82no—
678C22—24no—
679C22—28no—
680C22—34no—
681C22—44no—
682C22—42no—
683C22—42no—
684C22—62no—
685C22—64no—
686C22—64no—
687C22—62no—
688C22—64no—
689C22—68no—
690C22—1232no—
691C22—124no—
692C22—122no—
693C22—122no—
694C22—122no—
695C22—124no—
696C22—124no—
697C22—122no—
698C22—122no—
699C22C22×C3×D1211yescharacteristic
700C22C2×C3×D3×D411yescharacteristic
701C22C2×C3×D3×D411yescharacteristic
702C22C2×C3×D3×D412yes—
703C22C3×#100912yes—
704C4—24no—
705C4—42no—
706C4—62no—
707C4—64no—
708C4C3×#88214yescomplemented
709C3—21no—
710C3#7631411yescharacteristic, direct product factor
711C3C3×#243311yescharacteristic, complemented
712C2—44no—
713C2—64no—
714C2—124no—
715C2—242no—
716C2C2×C3×#88211yescharacteristic
717C2C3×D4×D1212yes—
718C2C3×#560912yes—
719C2C3×#567411yescharacteristic
720C2C3×D3×#12711yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×#390C2
socleC23×C32C24
hypercenterC3×#390D3
hypocenterC3C3×#2433
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#390

Complements

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

NH ≅ G/Ntype
1. C22×C3×D3×D4C2semidirect
2. C2×C3×#940C2semidirect
3. C2×C3×#895C2semidirect
4. C2×C3×#882C2semidirect
5. C2×C3×#874C2semidirect
6. C32×#390C2semidirect
7. C3×#4988C2semidirect
8. C3×#4960C2semidirect
9. C3×C4×(C2×D3)⋊C4C2semidirect
11. #76314C3direct (N × H)
15. C22×C3×#67C22semidirect
21. C22×C3×D12C22semidirect
22. C22×C3×D12C22semidirect
24. C2×C32×C4⋊C4C22semidirect
25. C2×C32×C22⋊C4C22semidirect
26. C2×C32×C42C22semidirect
29. C2×C3×(C2×D3)⋊C4C22semidirect
30. C2×C3×(C2×D3)⋊C4C22semidirect
31. C2×C3×C4×Dic3C22semidirect
35. C3×C3⋊#95C22semidirect
37. C22×D3×D4C2×C3semidirect
42. C2×#940C2×C3semidirect
43. C2×#895C2×C3semidirect
44. C2×#882C2×C3semidirect
45. C2×#874C2×C3semidirect
49. C3×#390D3semidirect
50. C3×#390C2×C3semidirect
52. #4988C2×C3semidirect
53. #4960C2×C3semidirect
54. C4×(C2×D3)⋊C4C2×C3semidirect
66. C2×C32×D4D4semidirect
89. C2×C3×D12D4semidirect
92. C2×C3×C4×D3D4semidirect
98. C3×(C2×D3)⋊C4D4semidirect
117. C22×#67C22×C3semidirect
123. C22×D12C22×C3semidirect
124. C22×D12C22×C3semidirect
131. C2×C3×C4⋊C4C2×D3semidirect
132. C2×C3×C4⋊C4C22×C3semidirect
137. C2×C3×C22⋊C4C2×D3semidirect
138. C2×C3×C22⋊C4C22×C3semidirect
141. C2×C3×C42C2×D3semidirect
142. C2×C3×C42C22×C3semidirect
145. C2×(C2×D3)⋊C4C22×C3semidirect
146. C2×(C2×D3)⋊C4C22×C3semidirect
147. C2×C4×Dic3C22×C3semidirect
152. C3⋊#95C22×C3semidirect
187. C2×C32×C4C2×D4semidirect
195. C2×C3×Dic3C2×D4semidirect
208. #390C3×D3semidirect
254. C2×C3×D4D12semidirect
255. C2×C3×D4C3×D4semidirect
289. C2×D12C3×D4semidirect
292. C2×C4×D3C3×D4semidirect
308. (C2×D3)⋊C4C3×D4semidirect
335. C2×C3×D3#127semidirect
338. C32×C4#120semidirect
357. C2×C4⋊C4C2×C3×D3semidirect
361. C2×C22⋊C4C2×C3×D3semidirect
363. C2×C42C2×C3×D3semidirect
458. C2×C3×C4D3×D4semidirect
462. C2×C3×C4C2×C3×D4semidirect
470. C2×Dic3C2×C3×D4semidirect
514. C2×D4C3×D12semidirect
591. C2×D3C3×#127semidirect
601. C3×C4#882semidirect
602. C3×C4C3×#120semidirect
605. C32#2433semidirect
653. C2×C4C3×D3×D4semidirect
708. C4C3×#882semidirect
710. C3#76314direct (N × H)
711. C3C3×#2433semidirect

Maximal subgroups

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

subgroupindex
C22×C3×D3×D42
C2×C3×#9402
C2×C3×#8952
C2×C3×#8822
C2×C3×#8742
C32×#3902
C3×#49882
C3×#49602
C3×C4×(C2×D3)⋊C42
C3×#24333
#763143