Finite Group Databasebeta

← C3×#76295 #11803102

Subgroups — C3×#76295 #11803102

Order 1152.

1209 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×Dic3C211yesmaximal, characteristic
2C32×#390C211yesmaximal, characteristic
3C3×#5221C211yesmaximal, characteristic
4C3×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
5C3×#4972C211yesmaximal, characteristic, complemented
6C3×#4945C212yesmaximal, complemented
7C3×#4944C212yesmaximal, complemented
8C3×#4943C212yesmaximal, complemented
9C3×#4942C212yesmaximal, complemented
10C3×#4932C211yesmaximal, characteristic, complemented
11C3×#4928C211yesmaximal, characteristic, complemented
12C3×#2319—31nomaximal
13#76295C311yesmaximal, characteristic, direct product factor
14C22×C32×D4C2211yescharacteristic
15C23×C3×Dic3C2212yes—
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×C32×C22⋊C4C2212yes—
18C2×C32×C22⋊C4C2212yes—
19C2×C32×C42C2211yescharacteristic
20C2×C3×#217C2212yes—
21C2×C3×#217C2212yes—
22C2×C3×#217C2212yes—
23C3×D4×Dic3C418yescomplemented
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×Dic3⋊C4C2212yes—
27C2×C3×Dic3⋊C4C2212yes—
28C2×C3×C4×Dic3C2211yescharacteristic
29C2×C3×C4×Dic3C2212yes—
30C2×C3×C4×Dic3C2211yescharacteristic
31C3×C3⋊#95C2212yes—
32C3×C3⋊#95C2211yescharacteristic
33C3×C3⋊#95C2211yescharacteristic
34C3×C3⋊#95C2211yescharacteristic
35C3×C3⋊#95C2211yescharacteristic
36C3×C3⋊#95C2212yes—
37C3×C3⋊#95C2212yes—
38C2×C3×C4×D4—31no—
39C2×D4×Dic3C2×C311yescharacteristic
40C3×#390—21no—
41C3×#390—31no—
42C3×#390D311yescharacteristic
43C3×#390C2×C311yescharacteristic
44C3×#389—31no—
45C3×#389—31no—
46C3×#388—32no—
47C3×#388—32no—
48C3×#381—32no—
49C3×#380—32no—
50C3×C4×C4⋊C4—31no—
51C3×#376—31no—
52#5221C2×C311yescharacteristic
53Dic3×C4⋊C4C2×C311yescharacteristic, complemented
54#4972C2×C311yescharacteristic, complemented
55#4945C2×C312yescomplemented
56#4944C2×C312yescomplemented
57#4943C2×C312yescomplemented
58#4942C2×C312yescomplemented
59#4932C2×C311yescharacteristic, complemented
60#4928C2×C311yescharacteristic, complemented
61C24×C32C2312yes—
62C2×C32×D4—22no—
63C2×C32×D4—22no—
64C2×C32×D4C2×C414yes—
65C22×C32×C4C2312yes—
66C22×C32×C4C2311yescharacteristic
67C22×C32×C4C2311yescharacteristic
68C22×C32×C4C2311yescharacteristic
69C22×C3×Dic3—42no—
70C22×C3×Dic3—42no—
71C22×C3×Dic3C2×C418yes—
72C22×C3×Dic3C2311yescharacteristic
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2311yescharacteristic
75C22×C3×Dic3C2311yescharacteristic
76C22×C3×Dic3C2311yescharacteristic
77C22×C3×Dic3C2312yes—
78C32×C4⋊C4—22no—
79C32×C22⋊C4—42no—
80C32×C22⋊C4—42no—
81C32×C42—22no—
82C3×#217—42no—
83C3×#217—42no—
84C3×#217C2×C418yes—
85C3×C4⋊Dic3—22no—
86C3×C4⋊Dic3C2×C414yes—
87C3×Dic3⋊C4—42no—
88C3×Dic3⋊C4—42no—
89C3×C4×Dic3—22no—
90C3×C4×Dic3—42no—
91C3×C4×Dic3C2×C414yes—
92#2319—31noSylow
93C22×C3×D4—21no—
94C22×C3×D4C2×D311yescharacteristic
95C22×C3×D4C22×C311yescharacteristic
96C23×C3×C4—32no—
97C23×Dic3C22×C312yes—
98C3×C4×D4—38no—
99C2×C3×C4⋊C4—21no—
100C2×C3×C4⋊C4—31no—
101C2×C3×C4⋊C4—31no—
102C2×C3×C4⋊C4—32no—
103C2×C3×C4⋊C4—32no—
104C2×C3×C4⋊C4C2×D311yescharacteristic
105C2×C3×C4⋊C4C22×C311yescharacteristic
106C2×C3×C22⋊C4—22no—
107C2×C3×C22⋊C4—22no—
108C2×C3×C22⋊C4—32no—
109C2×C3×C22⋊C4—32no—
110C2×C3×C22⋊C4—32no—
111C2×C3×C22⋊C4C2×D312yes—
112C2×C3×C22⋊C4C2×D312yes—
113C2×C3×C22⋊C4C22×C312yes—
114C2×C3×C22⋊C4C22×C312yes—
115C2×C3×C42—21no—
116C2×C3×C42—31no—
117C2×C3×C42—31no—
118C2×C3×C42—32no—
119C2×C3×C42C2×D311yescharacteristic
120C2×C3×C42C22×C311yescharacteristic
121C2×#217C22×C312yes—
122C2×#217C22×C312yes—
123C2×#217C22×C312yes—
124D4×Dic3C3×C418yescomplemented
125C2×C4⋊Dic3C22×C311yescharacteristic
126C2×C4⋊Dic3C22×C311yescharacteristic
127C2×Dic3⋊C4C22×C312yes—
128C2×Dic3⋊C4C22×C312yes—
129C2×C4×Dic3C22×C311yescharacteristic
130C2×C4×Dic3C22×C312yes—
131C2×C4×Dic3C22×C311yescharacteristic
132C3×#95—31no—
133C3×#95—31no—
134C3×#95—31no—
135C3×#95—31no—
136C3×#95—32no—
137C3×#95—32no—
138C3×#95—32no—
139C3⋊#95C22×C312yes—
140C3⋊#95C22×C311yescharacteristic
141C3⋊#95C22×C311yescharacteristic
142C3⋊#95C22×C311yescharacteristic
143C3⋊#95C22×C311yescharacteristic
144C3⋊#95C22×C312yes—
145C3⋊#95C22×C312yes—
146C23×C32—22no—
147C23×C32—22no—
148C23×C32—22no—
149C23×C32—22no—
150C23×C32—22no—
151C23×C32—22no—
152C23×C32C22×C414yes—
153C23×C32C2411yescharacteristic
154C32×D4—28no—
155C2×C32×C4—21no—
156C2×C32×C4—21no—
157C2×C32×C4—21no—
158C2×C32×C4—21no—
159C2×C32×C4—22no—
160C2×C32×C4—22no—
161C2×C32×C4—21no—
162C2×C32×C4—22no—
163C2×C32×C4—21no—
164C2×C32×C4C22×C412yes—
165C2×C32×C4#4112yes—
166C2×C32×C4#4112yes—
167C2×C3×Dic3—21no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—21no—
171C2×C3×Dic3—21no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—21no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—21no—
180C2×C3×Dic3—21no—
181C2×C3×Dic3—21no—
182C2×C3×Dic3—48no—
183C2×C3×Dic3C22×C412yes—
184C2×C3×Dic3C22×C412yes—
185C2×C3×Dic3C22×C414yes—
186C2×C4×D4—31no—
187#390—31no—
188#390C3×D311yescharacteristic
189#389—31no—
190#389—31no—
191#388—32no—
192#388—32no—
193#381—32no—
194#380—32no—
195C4×C4⋊C4—31no—
196#376—31no—
197C24×C3—22no—
198C24×C3C22×D312yes—
199C24×C3C23×C312yes—
200C2×C3×D4—22no—
201C2×C3×D4—22no—
202C2×C3×D4—22no—
203C2×C3×D4—22no—
204C2×C3×D4—24no—
205C2×C3×D4—42no—
206C2×C3×D4—42no—
207C2×C3×D4C4×D314yes—
208C2×C3×D4C2×C3×C414yes—
209C22×C3×C4—21no—
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4—22no—
213C22×C3×C4—31no—
214C22×C3×C4—31no—
215C22×C3×C4—32no—
216C22×C3×C4—38no—
217C22×C3×C4—31no—
218C22×C3×C4—31no—
219C22×C3×C4—32no—
220C22×C3×C4—122no—
221C22×C3×C4—122no—
222C22×C3×C4C22×D311yescharacteristic
223C22×C3×C4C22×D312yes—
224C22×C3×C4C22×D311yescharacteristic
225C22×C3×C4C22×D311yescharacteristic
226C22×C3×C4C23×C311yescharacteristic
227C22×C3×C4C23×C312yes—
228C22×C3×C4C23×C311yescharacteristic
229C22×C3×C4C23×C311yescharacteristic
230C22×Dic3—42no—
231C22×Dic3—42no—
232C22×Dic3C2×C3×C418yes—
233C22×Dic3C23×C311yescharacteristic
234C22×Dic3C23×C311yescharacteristic
235C22×Dic3C23×C312yes—
236C22×Dic3C23×C311yescharacteristic
237C22×Dic3C23×C311yescharacteristic
238C22×Dic3C23×C312yes—
239C3×C4⋊C4—22no—
240C3×C4⋊C4—22no—
241C3×C4⋊C4—34no—
242C3×C4⋊C4—42no—
243C3×C4⋊C4—62no—
244C3×C4⋊C4—122no—
245C3×C4⋊C4—122no—
246C3×C22⋊C4—38no—
247C3×C22⋊C4—42no—
248C3×C22⋊C4—42no—
249C3×C22⋊C4—42no—
250C3×C22⋊C4—42no—
251C3×C22⋊C4—44no—
252C3×C22⋊C4—44no—
253C3×C22⋊C4—122no—
254C3×C22⋊C4—122no—
255C3×C42—22no—
256C3×C42—22no—
257C3×C42—34no—
258C3×C42—42no—
259C3×C42—62no—
260C3×C42—122no—
261#217—42no—
262#217—42no—
263#217C2×C3×C418yes—
264C4⋊Dic3—22no—
265C4⋊Dic3C2×C3×C414yes—
266Dic3⋊C4—42no—
267Dic3⋊C4—42no—
268C4×Dic3—22no—
269C4×Dic3—42no—
270C4×Dic3C2×C3×C414yes—
271C22×C32—24no—
272C22×C32—24no—
273C22×C32—24no—
274C22×C32—42no—
275C22×C32—42no—
276C22×C32—42no—
277C22×C32—42no—
278C22×C32C23×C411yescharacteristic
279C22×C32C2×#4111yescharacteristic
280C22×C32C2×#4111yescharacteristic
281C22×C32H(5,𝔽2)11yescharacteristic
282C22×C32H(5,𝔽2)11yescharacteristic
283C22×C32H(5,𝔽2)11yescharacteristic
284C22×C322−1+411yescharacteristic
285C32×C4—41no—
286C32×C4—41no—
287C32×C4—42no—
288C32×C4#11714yes—
289C3×Dic3—22no—
290C3×Dic3—24no—
291C3×Dic3—22no—
292C3×Dic3—41no—
293C3×Dic3—42no—
294C3×Dic3—41no—
295C22×D4C2×C3×D311yescharacteristic
296C23×C4—32no—
297C4×D4—38no—
298C2×C4⋊C4—31no—
299C2×C4⋊C4—31no—
300C2×C4⋊C4—32no—
301C2×C4⋊C4—32no—
302C2×C4⋊C4C2×C3×D311yescharacteristic
303C2×C22⋊C4—32no—
304C2×C22⋊C4—32no—
305C2×C22⋊C4—32no—
306C2×C22⋊C4C2×C3×D312yes—
307C2×C22⋊C4C2×C3×D312yes—
308C2×C42—31no—
309C2×C42—31no—
310C2×C42—32no—
311C2×C42C2×C3×D311yescharacteristic
312#95—31no—
313#95—31no—
314#95—31no—
315#95—31no—
316#95—32no—
317#95—32no—
318#95—32no—
319C23×C3—22no—
320C23×C3—22no—
321C23×C3—22no—
322C23×C3—22no—
323C23×C3—22no—
324C23×C3—22no—
325C23×C3—22no—
326C23×C3—22no—
327C23×C3—22no—
328C23×C3—22no—
329C23×C3—22no—
330C23×C3—22no—
331C23×C3—21no—
332C23×C3—24no—
333C23×C3—42no—
334C23×C3—42no—
335C23×C3—42no—
336C23×C3—42no—
337C23×C3—42no—
338C23×C3—42no—
339C23×C3C2×C4×D314yes—
340C23×C3C22×C3×C414yes—
341C23×C3C23×D311yescharacteristic
342C23×C3C24×C311yescharacteristic
343C3×D4—28no—
344C3×D4—28no—
345C3×D4—48no—
346C2×C3×C4—22no—
347C2×C3×C4—22no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—22no—
351C2×C3×C4—22no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—22no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—21no—
362C2×C3×C4—22no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—22no—
367C2×C3×C4—22no—
368C2×C3×C4—22no—
369C2×C3×C4—32no—
370C2×C3×C4—32no—
371C2×C3×C4—34no—
372C2×C3×C4—41no—
373C2×C3×C4—41no—
374C2×C3×C4—41no—
375C2×C3×C4—41no—
376C2×C3×C4—42no—
377C2×C3×C4—42no—
378C2×C3×C4—42no—
379C2×C3×C4—61no—
380C2×C3×C4—62no—
381C2×C3×C4—61no—
382C2×C3×C4—62no—
383C2×C3×C4—61no—
384C2×C3×C4—61no—
385C2×C3×C4—61no—
386C2×C3×C4—61no—
387C2×C3×C4—62no—
388C2×C3×C4—62no—
389C2×C3×C4—61no—
390C2×C3×C4—61no—
391C2×C3×C4—61no—
392C2×C3×C4—62no—
393C2×C3×C4—61no—
394C2×C3×C4—128no—
395C2×C3×C4C2×C4×D312yes—
396C2×C3×C4#23712yes—
397C2×C3×C4#23712yes—
398C2×C3×C4C22×C3×C412yes—
399C2×C3×C4C3×#4112yes—
400C2×C3×C4C3×#4112yes—
401C2×Dic3—21no—
402C2×Dic3—22no—
403C2×Dic3—22no—
404C2×Dic3—21no—
405C2×Dic3—21no—
406C2×Dic3—21no—
407C2×Dic3—21no—
408C2×Dic3—21no—
409C2×Dic3—22no—
410C2×Dic3—22no—
411C2×Dic3—21no—
412C2×Dic3—22no—
413C2×Dic3—21no—
414C2×Dic3—21no—
415C2×Dic3—21no—
416C2×Dic3—48no—
417C2×Dic3C22×C3×C412yes—
418C2×Dic3C22×C3×C412yes—
419C2×Dic3C22×C3×C414yes—
420C2×C32—44no—
421C2×C32C2×#11711yescharacteristic
422C2×C32#51811yescharacteristic
423C2×C32#52011yescharacteristic
424C2×C32#54011yescharacteristic
425C2×C32#54011yescharacteristic
426C2×C32#54211yescharacteristic
427C2×C32#54211yescharacteristic
428C24C22×C3×D312yes—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4C3×C4×D314yes—
432C22×C4—31no—
433C22×C4—31no—
434C22×C4—32no—
435C22×C4—38no—
436C22×C4—31no—
437C22×C4—31no—
438C22×C4—32no—
439C22×C4—122no—
440C22×C4—122no—
441C22×C4C22×C3×D311yescharacteristic
442C22×C4C22×C3×D312yes—
443C22×C4C22×C3×D311yescharacteristic
444C22×C4C22×C3×D311yescharacteristic
445C4⋊C4—22no—
446C4⋊C4—34no—
447C4⋊C4—62no—
448C4⋊C4—122no—
449C4⋊C4—122no—
450C22⋊C4—38no—
451C22⋊C4—42no—
452C22⋊C4—42no—
453C22⋊C4—122no—
454C22⋊C4—122no—
455C42—22no—
456C42—34no—
457C42—62no—
458C42—122no—
459C22×C3—24no—
460C22×C3—24no—
461C22×C3—24no—
462C22×C3—24no—
463C22×C3—24no—
464C22×C3—24no—
465C22×C3—21no—
466C22×C3—21no—
467C22×C3—21no—
468C22×C3—21no—
469C22×C3—21no—
470C22×C3—21no—
471C22×C3—21no—
472C22×C3—44no—
473C22×C3—44no—
474C22×C3—44no—
475C22×C3—42no—
476C22×C3—42no—
477C22×C3—42no—
478C22×C3—42no—
479C22×C3—42no—
480C22×C3—42no—
481C22×C3—42no—
482C22×C3—42no—
483C22×C3—82no—
484C22×C3—82no—
485C22×C3—82no—
486C22×C3—82no—
487C22×C3C22×C4×D311yescharacteristic
488C22×C3C2×#23711yescharacteristic
489C22×C3C2×#23711yescharacteristic
490C22×C3#100411yescharacteristic
491C22×C3#100411yescharacteristic
492C22×C3#100911yescharacteristic
493C22×C3#101011yescharacteristic
494C22×C3C23×C3×C411yescharacteristic
495C22×C3C2×C3×#4111yescharacteristic
496C22×C3C2×C3×#4111yescharacteristic
497C22×C3C3×H(5,𝔽2)11yescharacteristic
498C22×C3C3×H(5,𝔽2)11yescharacteristic
499C22×C3C3×H(5,𝔽2)11yescharacteristic
500C22×C3C3×2−1+411yescharacteristic
501C3×C4—24no—
502C3×C4—42no—
503C3×C4—42no—
504C3×C4—42no—
505C3×C4—41no—
506C3×C4—41no—
507C3×C4—42no—
508C3×C4—41no—
509C3×C4—41no—
510C3×C4—62no—
511C3×C4—64no—
512C3×C4—62no—
513C3×C4—82no—
514C3×C4—121no—
515C3×C4—121no—
516C3×C4—122no—
517C3×C4#87714yes—
518C3×C4C3×#11714yes—
519Dic3—22no—
520Dic3—24no—
521Dic3—22no—
522Dic3—42no—
523Dic3—41no—
524Dic3—41no—
525C32#231911yescharacteristic, complemented, Sylow
526C23—22no—
527C23—22no—
528C23—22no—
529C23—22no—
530C23—22no—
531C23—22no—
532C23C2×C3×C4×D314yes—
533C23C23×C3×D311yescharacteristic
534D4—28no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—22no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—32no—
545C2×C4—32no—
546C2×C4—34no—
547C2×C4—61no—
548C2×C4—62no—
549C2×C4—61no—
550C2×C4—62no—
551C2×C4—61no—
552C2×C4—61no—
553C2×C4—61no—
554C2×C4—61no—
555C2×C4—62no—
556C2×C4—62no—
557C2×C4—61no—
558C2×C4—61no—
559C2×C4—61no—
560C2×C4—62no—
561C2×C4—61no—
562C2×C4—128no—
563C2×C4C2×C3×C4×D312yes—
564C2×C4C3×#23712yes—
565C2×C4C3×#23712yes—
566C2×C3—21no—
567C2×C3—21no—
568C2×C3—21no—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—21no—
572C2×C3—21no—
573C2×C3—44no—
574C2×C3—44no—
575C2×C3—84no—
576C2×C3C2×#87711yescharacteristic
577C2×C3#554511yescharacteristic
578C2×C3#554611yescharacteristic
579C2×C3#560311yescharacteristic
580C2×C3#561911yescharacteristic
581C2×C3#568211yescharacteristic
582C2×C3#571911yescharacteristic
583C2×C3C2×C3×#11711yescharacteristic
584C2×C3C3×#51811yescharacteristic
585C2×C3C3×#52011yescharacteristic
586C2×C3C3×#54011yescharacteristic
587C2×C3C3×#54011yescharacteristic
588C2×C3C3×#54211yescharacteristic
589C2×C3C3×#54211yescharacteristic
590C22—24no—
591C22—24no—
592C22—24no—
593C22—42no—
594C22—42no—
595C22—42no—
596C22—42no—
597C22C22×C3×C4×D311yescharacteristic
598C22C2×C3×#23711yescharacteristic
599C22C2×C3×#23711yescharacteristic
600C22C3×#100411yescharacteristic
601C22C3×#100411yescharacteristic
602C22C3×#100911yescharacteristic
603C22C3×#101011yescharacteristic
604C4—41no—
605C4—41no—
606C4—42no—
607C4—62no—
608C4—64no—
609C4—62no—
610C4—122no—
611C4—121no—
612C4—121no—
613C4C3×#87714yes—
614C3—21no—
615C3#7629511yescharacteristic, direct product factor
616C3C3×#231911yescharacteristic, complemented
617C2—44no—
618C2C2×C3×#87711yescharacteristic
619C2C3×#554511yescharacteristic
620C2C3×#554611yescharacteristic
621C2C3×#560311yescharacteristic
622C2C3×#561911yescharacteristic
623C2C3×#568211yescharacteristic
624C2C3×#571911yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×#390C2
socleC23×C32C24
prime radicalC22×C32×D4C22
cosocleC23×C3C24×C3
hypercenterC3×#390D3
hypocenterC3C3×#2319
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#390

Complements

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

NH ≅ G/Ntype
4. C3×Dic3×C4⋊C4C2semidirect
5. C3×#4972C2semidirect
6. C3×#4945C2semidirect
7. C3×#4944C2semidirect
8. C3×#4943C2semidirect
9. C3×#4942C2semidirect
10. C3×#4932C2semidirect
11. C3×#4928C2semidirect
13. #76295C3direct (N × H)
23. C3×D4×Dic3C4semidirect
53. Dic3×C4⋊C4C2×C3semidirect
54. #4972C2×C3semidirect
55. #4945C2×C3semidirect
56. #4944C2×C3semidirect
57. #4943C2×C3semidirect
58. #4942C2×C3semidirect
59. #4932C2×C3semidirect
60. #4928C2×C3semidirect
124. D4×Dic3C3×C4semidirect
525. C32#2319semidirect
615. C3#76295direct (N × H)
616. C3C3×#2319semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×Dic32
C32×#3902
C3×#52212
C3×Dic3×C4⋊C42
C3×#49722
C3×#49452
C3×#49442
C3×#49432
C3×#49422
C3×#49322
C3×#49282
C3×#23193
#762953