Finite Group Databasebeta

← C3×#73660 #11807149

Subgroups — C3×#73660 #11807149

Order 1152.

1025 conjugacy classes of subgroups.

The subgroup lattice has 543 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#890C211yesmaximal, characteristic
2C32×C4×C4⋊C4C211yesmaximal, characteristic
3C3×#4984C211yesmaximal, characteristic
4C3×Dic3×C4⋊C4C211yesmaximal, characteristic
5C3×Dic3×C4⋊C4C211yesmaximal, characteristic
6C3×C4×Dic3⋊C4C212yesmaximal
7C3×C4×Dic3⋊C4C211yesmaximal, characteristic
8C3×#4928C211yesmaximal, characteristic
9C3×#4928C212yesmaximal
10C3×#4655C212yesmaximal
11C3×#4654C212yesmaximal
12C3×#2370—31nomaximal
13#73660C311yesmaximal, characteristic, direct product factor
14C2×C32×C4⋊C4C2211yescharacteristic
15C2×C32×C4⋊C4C2211yescharacteristic
16C2×C32×C42C2211yescharacteristic
17C2×C32×C42C2212yes—
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4⋊Dic3C2212yes—
20C2×C3×C4⋊Dic3C2212yes—
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×Dic3⋊C4C2211yescharacteristic
23C2×C3×Dic3⋊C4C2211yescharacteristic
24C2×C3×Dic3⋊C4C2212yes—
25C2×C3×Dic3⋊C4C2212yes—
26C2×C3×C4×Dic3C2212yes—
27C2×C3×C4×Dic3C2211yescharacteristic
28C2×C3×C4×Dic3C2212yes—
29C2×C3×C4×Dic3C2211yescharacteristic
30C3×#890C418yescomplemented
31C32×#95C2212yes—
32C3×C3⋊#95C2212yes—
33C3×C3⋊#95C2212yes—
34C3×C3⋊#95C2212yes—
35C3×C3⋊#95C2211yescharacteristic
36C3×C3⋊#95C2212yes—
37C3×C3⋊#95C2211yescharacteristic
38C2×C3×#125—31no—
39C2×#890C2×C311yescharacteristic
40C3×#389—31no—
41C3×#389—32no—
42C3×#389—31no—
43C3×#387—32no—
44C3×#387—32no—
45C3×C4×C4⋊C4—21no—
46C3×C4×C4⋊C4—31no—
47C3×C4×C4⋊C4—31no—
48C3×C4×C4⋊C4—31no—
49C3×C4×C4⋊C4—32no—
50C3×C4×C4⋊C4D311yescharacteristic
51C3×C4×C4⋊C4C2×C311yescharacteristic
52#4984C2×C311yescharacteristic
53Dic3×C4⋊C4C2×C311yescharacteristic
54Dic3×C4⋊C4C2×C311yescharacteristic
55C4×Dic3⋊C4C2×C312yes—
56C4×Dic3⋊C4C2×C311yescharacteristic
57#4928C2×C311yescharacteristic
58#4928C2×C312yes—
59#4655C2×C312yes—
60#4654C2×C312yes—
61C22×C32×C4C2311yescharacteristic
62C22×C32×C4C2312yes—
63C22×C32×C4C2312yes—
64C22×C32×C4C2311yescharacteristic
65C22×C32×C4C2311yescharacteristic
66C22×C3×Dic3C2311yescharacteristic
67C22×C3×Dic3C2312yes—
68C22×C3×Dic3C2311yescharacteristic
69C22×C3×Dic3C2312yes—
70C22×C3×Dic3C2311yescharacteristic
71C22×C3×Dic3C2311yescharacteristic
72C32×C4⋊C4C2×C414yes—
73C32×C4⋊C4Q814yes—
74C32×C42—22no—
75C32×C42—42no—
76C3×C4⋊Dic3—22no—
77C3×C4⋊Dic3—42no—
78C3×C4⋊Dic3C2×C418yes—
79C3×C4⋊Dic3C2×C414yes—
80C3×Dic3⋊C4—24no—
81C3×Dic3⋊C4—22no—
82C3×Dic3⋊C4—22no—
83C3×Dic3⋊C4C2×C418yes—
84C3×C4×Dic3—22no—
85C3×C4×Dic3—24no—
86C3×C4×Dic3—42no—
87C3×C4×Dic3C2×C414yes—
88#2370—31noSylow
89C3×#125—38no—
90C2×C3×C4⋊C4—21no—
91C2×C3×C4⋊C4—21no—
92C2×C3×C4⋊C4—32no—
93C2×C3×C4⋊C4—31no—
94C2×C3×C4⋊C4—32no—
95C2×C3×C4⋊C4—31no—
96C2×C3×C4⋊C4—31no—
97C2×C3×C4⋊C4—32no—
98C2×C3×C4⋊C4—31no—
99C2×C3×C4⋊C4—32no—
100C2×C3×C4⋊C4C2×D311yescharacteristic
101C2×C3×C4⋊C4C2×D311yescharacteristic
102C2×C3×C4⋊C4C22×C311yescharacteristic
103C2×C3×C4⋊C4C22×C311yescharacteristic
104C2×C3×C42—21no—
105C2×C3×C42—22no—
106C2×C3×C42—31no—
107C2×C3×C42—32no—
108C2×C3×C42—31no—
109C2×C3×C42—32no—
110C2×C3×C42C2×D311yescharacteristic
111C2×C3×C42C2×D312yes—
112C2×C3×C42C22×C311yescharacteristic
113C2×C3×C42C22×C312yes—
114C2×C4⋊Dic3C22×C311yescharacteristic
115C2×C4⋊Dic3C22×C312yes—
116C2×C4⋊Dic3C22×C312yes—
117C2×C4⋊Dic3C22×C311yescharacteristic
118C2×Dic3⋊C4C22×C311yescharacteristic
119C2×Dic3⋊C4C22×C311yescharacteristic
120C2×Dic3⋊C4C22×C312yes—
121C2×Dic3⋊C4C22×C312yes—
122C2×C4×Dic3C22×C312yes—
123C2×C4×Dic3C22×C311yescharacteristic
124C2×C4×Dic3C22×C312yes—
125C2×C4×Dic3C22×C311yescharacteristic
126#890C3×C418yescomplemented
127C3×#95—22no—
128C3×#95—31no—
129C3×#95—31no—
130C3×#95—32no—
131C3×#95—32no—
132C3×#95—32no—
133C3×#95—32no—
134C3×#95C2×D312yes—
135C3×#95C22×C312yes—
136C3⋊#95C22×C312yes—
137C3⋊#95C22×C312yes—
138C3⋊#95C22×C312yes—
139C3⋊#95C22×C311yescharacteristic
140C3⋊#95C22×C312yes—
141C3⋊#95C22×C311yescharacteristic
142C23×C32C2411yescharacteristic
143C2×C32×C4—21no—
144C2×C32×C4—21no—
145C2×C32×C4—21no—
146C2×C32×C4—22no—
147C2×C32×C4—22no—
148C2×C32×C4—22no—
149C2×C32×C4—22no—
150C2×C32×C4—21no—
151C2×C32×C4—21no—
152C2×C32×C4C22×C414yes—
153C2×C32×C4C22×C412yes—
154C2×C32×C4C2×Q814yes—
155C2×C32×C4C2×Q812yes—
156C2×C32×C4#4112yes—
157C2×C32×C4#4112yes—
158C2×C3×Dic3—21no—
159C2×C3×Dic3—22no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—21no—
162C2×C3×Dic3—21no—
163C2×C3×Dic3—21no—
164C2×C3×Dic3—21no—
165C2×C3×Dic3—21no—
166C2×C3×Dic3—21no—
167C2×C3×Dic3—21no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—21no—
172C2×C3×Dic3C22×C412yes—
173C2×C3×Dic3C22×C412yes—
174C2×C3×Dic3C22×C414yes—
175C2×C3×Dic3#4112yes—
176C2×#125—31no—
177#389—31no—
178#389—32no—
179#389—31no—
180#387—32no—
181#387—32no—
182C4×C4⋊C4—31no—
183C4×C4⋊C4—31no—
184C4×C4⋊C4—31no—
185C4×C4⋊C4—32no—
186C4×C4⋊C4C3×D311yescharacteristic
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—22no—
191C22×C3×C4—22no—
192C22×C3×C4—31no—
193C22×C3×C4—31no—
194C22×C3×C4—31no—
195C22×C3×C4—32no—
196C22×C3×C4—31no—
197C22×C3×C4—32no—
198C22×C3×C4C22×D311yescharacteristic
199C22×C3×C4C22×D312yes—
200C22×C3×C4C22×D312yes—
201C22×C3×C4C22×D311yescharacteristic
202C22×C3×C4C22×D311yescharacteristic
203C22×C3×C4C23×C311yescharacteristic
204C22×C3×C4C23×C312yes—
205C22×C3×C4C23×C312yes—
206C22×C3×C4C23×C311yescharacteristic
207C22×C3×C4C23×C311yescharacteristic
208C22×Dic3C23×C311yescharacteristic
209C22×Dic3C23×C312yes—
210C22×Dic3C23×C311yescharacteristic
211C22×Dic3C23×C312yes—
212C22×Dic3C23×C311yescharacteristic
213C22×Dic3C23×C311yescharacteristic
214C3×C4⋊C4—24no—
215C3×C4⋊C4—24no—
216C3×C4⋊C4—38no—
217C3×C4⋊C4—38no—
218C3×C4⋊C4—34no—
219C3×C4⋊C4—62no—
220C3×C4⋊C4—62no—
221C3×C4⋊C4—62no—
222C3×C4⋊C4—64no—
223C3×C4⋊C4—122no—
224C3×C4⋊C4Dic614yes—
225C3×C4⋊C4C4×D314yes—
226C3×C4⋊C4C2×C3×C414yes—
227C3×C4⋊C4C3×Q814yes—
228C3×C42—24no—
229C3×C42—22no—
230C3×C42—22no—
231C3×C42—34no—
232C3×C42—42no—
233C3×C42—42no—
234C3×C42—44no—
235C3×C42—64no—
236C3×C42—62no—
237C3×C42—122no—
238C4⋊Dic3—22no—
239C4⋊Dic3—42no—
240C4⋊Dic3C2×C3×C418yes—
241C4⋊Dic3C2×C3×C414yes—
242Dic3⋊C4—24no—
243Dic3⋊C4—22no—
244Dic3⋊C4—22no—
245Dic3⋊C4C2×C3×C418yes—
246C4×Dic3—22no—
247C4×Dic3—24no—
248C4×Dic3—42no—
249C4×Dic3C2×C3×C414yes—
250C22×C32C23×C411yescharacteristic
251C22×C32C22×Q811yescharacteristic
252C22×C32C2×#4111yescharacteristic
253C22×C32C2×#4111yescharacteristic
254C22×C32C2×#4111yescharacteristic
255C22×C32H(5,𝔽2)11yescharacteristic
256C22×C322−1+411yescharacteristic
257C32×C4—22no—
258C32×C4—24no—
259C32×C4—24no—
260C32×C4—41no—
261C32×C4C4×Q814yes—
262C3×Dic3—24no—
263C3×Dic3—22no—
264C3×Dic3—22no—
265C3×Dic3—22no—
266C3×Dic3—41no—
267C3×Dic3—42no—
268#125—38no—
269C2×C4⋊C4—32no—
270C2×C4⋊C4—31no—
271C2×C4⋊C4—32no—
272C2×C4⋊C4—31no—
273C2×C4⋊C4—31no—
274C2×C4⋊C4—32no—
275C2×C4⋊C4—31no—
276C2×C4⋊C4—32no—
277C2×C4⋊C4C2×C3×D311yescharacteristic
278C2×C4⋊C4C2×C3×D311yescharacteristic
279C2×C42—31no—
280C2×C42—32no—
281C2×C42—31no—
282C2×C42—32no—
283C2×C42C2×C3×D311yescharacteristic
284C2×C42C2×C3×D312yes—
285#95—31no—
286#95—31no—
287#95—32no—
288#95—32no—
289#95—32no—
290#95—32no—
291#95C2×C3×D312yes—
292C23×C3—21no—
293C23×C3C23×D311yescharacteristic
294C23×C3C24×C311yescharacteristic
295C2×C3×C4—22no—
296C2×C3×C4—22no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—22no—
300C2×C3×C4—22no—
301C2×C3×C4—22no—
302C2×C3×C4—22no—
303C2×C3×C4—22no—
304C2×C3×C4—21no—
305C2×C3×C4—22no—
306C2×C3×C4—22no—
307C2×C3×C4—21no—
308C2×C3×C4—22no—
309C2×C3×C4—22no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—22no—
317C2×C3×C4—24no—
318C2×C3×C4—22no—
319C2×C3×C4—24no—
320C2×C3×C4—22no—
321C2×C3×C4—22no—
322C2×C3×C4—32no—
323C2×C3×C4—32no—
324C2×C3×C4—34no—
325C2×C3×C4—32no—
326C2×C3×C4—42no—
327C2×C3×C4—42no—
328C2×C3×C4—42no—
329C2×C3×C4—42no—
330C2×C3×C4—41no—
331C2×C3×C4—41no—
332C2×C3×C4—61no—
333C2×C3×C4—61no—
334C2×C3×C4—61no—
335C2×C3×C4—62no—
336C2×C3×C4—62no—
337C2×C3×C4—61no—
338C2×C3×C4—61no—
339C2×C3×C4—61no—
340C2×C3×C4—61no—
341C2×C3×C4—62no—
342C2×C3×C4—62no—
343C2×C3×C4—61no—
344C2×C3×C4—61no—
345C2×C3×C4—62no—
346C2×C3×C4C2×Dic614yes—
347C2×C3×C4C2×Dic612yes—
348C2×C3×C4C2×C4×D314yes—
349C2×C3×C4C2×C4×D312yes—
350C2×C3×C4#23512yes—
351C2×C3×C4#23912yes—
352C2×C3×C4C22×C3×C414yes—
353C2×C3×C4C22×C3×C412yes—
354C2×C3×C4C2×C3×Q814yes—
355C2×C3×C4C2×C3×Q812yes—
356C2×C3×C4C3×#4112yes—
357C2×C3×C4C3×#4112yes—
358C2×Dic3—21no—
359C2×Dic3—22no—
360C2×Dic3—22no—
361C2×Dic3—21no—
362C2×Dic3—21no—
363C2×Dic3—21no—
364C2×Dic3—21no—
365C2×Dic3—21no—
366C2×Dic3—21no—
367C2×Dic3—21no—
368C2×Dic3—22no—
369C2×Dic3—22no—
370C2×Dic3—22no—
371C2×Dic3—21no—
372C2×Dic3C22×C3×C412yes—
373C2×Dic3C22×C3×C412yes—
374C2×Dic3C22×C3×C414yes—
375C2×Dic3C3×#4112yes—
376C2×C32C2×C4×Q811yescharacteristic
377C2×C32C4×#4111yescharacteristic
378C2×C32#52011yescharacteristic
379C2×C32#55211yescharacteristic
380C2×C32#55311yescharacteristic
381C2×C32#55411yescharacteristic
382C2×C32#55711yescharacteristic
383C22×C4—31no—
384C22×C4—31no—
385C22×C4—31no—
386C22×C4—32no—
387C22×C4—31no—
388C22×C4—32no—
389C22×C4C22×C3×D311yescharacteristic
390C22×C4C22×C3×D312yes—
391C22×C4C22×C3×D312yes—
392C22×C4C22×C3×D311yescharacteristic
393C22×C4C22×C3×D311yescharacteristic
394C4⋊C4—38no—
395C4⋊C4—38no—
396C4⋊C4—34no—
397C4⋊C4—62no—
398C4⋊C4—62no—
399C4⋊C4—62no—
400C4⋊C4—64no—
401C4⋊C4—122no—
402C4⋊C4C3×Dic614yes—
403C4⋊C4C3×C4×D314yes—
404C42—22no—
405C42—34no—
406C42—42no—
407C42—64no—
408C42—62no—
409C42—122no—
410C22×C3—21no—
411C22×C3—21no—
412C22×C3—21no—
413C22×C3—21no—
414C22×C3—21no—
415C22×C3—21no—
416C22×C3—21no—
417C22×C3C22×Dic611yescharacteristic
418C22×C3C22×C4×D311yescharacteristic
419C22×C3C2×#23511yescharacteristic
420C22×C3#100411yescharacteristic
421C22×C3C2×#23911yescharacteristic
422C22×C3D3×#4111yescharacteristic
423C22×C3#101011yescharacteristic
424C22×C3C23×C3×C411yescharacteristic
425C22×C3C22×C3×Q811yescharacteristic
426C22×C3C2×C3×#4111yescharacteristic
427C22×C3C2×C3×#4111yescharacteristic
428C22×C3C2×C3×#4111yescharacteristic
429C22×C3C3×H(5,𝔽2)11yescharacteristic
430C22×C3C3×2−1+411yescharacteristic
431C3×C4—24no—
432C3×C4—22no—
433C3×C4—24no—
434C3×C4—24no—
435C3×C4—24no—
436C3×C4—22no—
437C3×C4—24no—
438C3×C4—24no—
439C3×C4—44no—
440C3×C4—44no—
441C3×C4—42no—
442C3×C4—41no—
443C3×C4—41no—
444C3×C4—62no—
445C3×C4—62no—
446C3×C4—62no—
447C3×C4—64no—
448C3×C4—121no—
449C3×C4—122no—
450C3×C4C4×Dic614yes—
451C3×C4C3×C4×Q814yes—
452Dic3—24no—
453Dic3—22no—
454Dic3—22no—
455Dic3—22no—
456Dic3—41no—
457Dic3—42no—
458C32#237011yescharacteristic, complemented, Sylow
459C23C23×C3×D311yescharacteristic
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—32no—
470C2×C4—32no—
471C2×C4—34no—
472C2×C4—32no—
473C2×C4—61no—
474C2×C4—61no—
475C2×C4—61no—
476C2×C4—62no—
477C2×C4—62no—
478C2×C4—61no—
479C2×C4—61no—
480C2×C4—61no—
481C2×C4—61no—
482C2×C4—62no—
483C2×C4—62no—
484C2×C4—61no—
485C2×C4—61no—
486C2×C4—62no—
487C2×C4C2×C3×Dic614yes—
488C2×C4C2×C3×Dic612yes—
489C2×C4C2×C3×C4×D314yes—
490C2×C4C2×C3×C4×D312yes—
491C2×C4C3×#23512yes—
492C2×C4C3×#23912yes—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3C2×C4×Dic611yescharacteristic
501C2×C3#551411yescharacteristic
502C2×C3#552911yescharacteristic
503C2×C3#553911yescharacteristic
504C2×C3#554611yescharacteristic
505C2×C3#557011yescharacteristic
506C2×C3C4×#23911yescharacteristic
507C2×C3C2×C3×C4×Q811yescharacteristic
508C2×C3C3×C4×#4111yescharacteristic
509C2×C3C3×#52011yescharacteristic
510C2×C3C3×#55211yescharacteristic
511C2×C3C3×#55311yescharacteristic
512C2×C3C3×#55411yescharacteristic
513C2×C3C3×#55711yescharacteristic
514C22C22×C3×Dic611yescharacteristic
515C22C22×C3×C4×D311yescharacteristic
516C22C2×C3×#23511yescharacteristic
517C22C3×#100411yescharacteristic
518C22C2×C3×#23911yescharacteristic
519C22C3×D3×#4111yescharacteristic
520C22C3×#101011yescharacteristic
521C4—22no—
522C4—24no—
523C4—24no—
524C4—41no—
525C4—62no—
526C4—62no—
527C4—62no—
528C4—64no—
529C4—121no—
530C4—122no—
531C4C3×C4×Dic614yes—
532C3—21no—
533C3#7366011yescharacteristic, direct product factor
534C3C3×#237011yescharacteristic, complemented
535C2C2×C3×C4×Dic611yescharacteristic
536C2C3×#551411yescharacteristic
537C2C3×#552911yescharacteristic
538C2C3×#553911yescharacteristic
539C2C3×#554611yescharacteristic
540C2C3×#557011yescharacteristic
541C2C3×C4×#23911yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×C4×C4⋊C4C2
socle, prime radicalC23×C32C24
cosocleC23×C3C24×C3
hypercenterC3×C4×C4⋊C4D3
hypocenterC3C3×#2370
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
13. #73660C3direct (N × H)
30. C3×#890C4semidirect
126. #890C3×C4semidirect
458. C32#2370semidirect
533. C3#73660direct (N × H)
534. C3C3×#2370semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8902
C32×C4×C4⋊C42
C3×#49842
C3×Dic3×C4⋊C42
C3×C4×Dic3⋊C42
C3×#49282
C3×#46552
C3×#46542
C3×#23703
#736603