Finite Group Databasebeta

← C3×#78130 #11808655

Subgroups — C3×#78130 #11808655

Order 1152.

1123 conjugacy classes of subgroups.

The subgroup lattice has 559 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#892C211yesmaximal, characteristic
2C2×C3×#887C211yesmaximal, characteristic, complemented
3C32×#400C211yesmaximal, characteristic, complemented
4C3×#4993C211yesmaximal, characteristic
5C3×#4979C211yesmaximal, characteristic, complemented
6C3×#4676C212yesmaximal
7C3×#4673C211yesmaximal, characteristic
8C3×#4666C212yesmaximal
9C3×#4657C212yesmaximal, complemented
10C3×#4649C212yesmaximal, complemented
11C3×#4649C211yesmaximal, characteristic, complemented
12C3×#2396—31nomaximal
13#78130C311yesmaximal, characteristic, direct product factor
14C22×C3×C4×D3C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×C32×C4⋊C4C2211yescharacteristic
18C2×C3×(C2×D3)⋊C4C2211yescharacteristic
19C2×C3×(C2×D3)⋊C4C2211yescharacteristic
20C2×C3×(C2×D3)⋊C4C2212yes—
21C2×C3×(C2×D3)⋊C4C2212yes—
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×Dic3⋊C4C2212yes—
24C2×C3×Dic3⋊C4C2212yes—
25C2×C3×Dic3⋊C4C2212yes—
26C2×C3×Dic3⋊C4C2212yes—
27C2×C3×C4×Dic3C2211yescharacteristic
28C2×C3×C4×Dic3C2212yes—
29C2×C3×C4×Dic3C2212yes—
30C2×C3×C4×Dic3C2211yescharacteristic
31C3×#892—24no—
32C3×#887—24no—
33C32×#95C2211yescharacteristic
34C32×#95C2212yes—
35C32×#95C2212yes—
36C3×C3⋊#95C2212yes—
37C3×C3⋊#95C2211yescharacteristic
38C3×C3⋊#95C2212yes—
39C2×C3×C4×Q8—31no—
40C2×C3×#117—31no—
41C2×#892C2×C311yescharacteristic
42C2×#887C2×C311yescharacteristic, complemented
43C3×#400—21no—
44C3×#400D311yescharacteristic, complemented
45C3×#400C2×C311yescharacteristic, complemented
46C3×#399—31no—
47C3×#398—32no—
48C3×#396—32no—
49C3×#395—31no—
50C3×#393—31no—
51C3×C4×C4⋊C4—32no—
52C3×C4×C4⋊C4—31no—
53C3×C4×C22⋊C4—32no—
54#4993C2×C311yescharacteristic
55#4979C2×C311yescharacteristic, complemented
56#4676C2×C312yes—
57#4673C2×C311yescharacteristic
58#4666C2×C312yes—
59#4657C2×C312yescomplemented
60#4649C2×C312yescomplemented
61#4649C2×C311yescharacteristic, complemented
62C23×C3×D3C2311yescharacteristic
63C22×C32×C4C2312yes—
64C22×C32×C4C2311yescharacteristic
65C22×C32×C4C2312yes—
66C22×C32×C4C2311yescharacteristic
67C22×C32×C4C2311yescharacteristic
68C22×C3×Dic3C2311yescharacteristic
69C22×C3×Dic3C2311yescharacteristic
70C22×C3×Dic3C2312yes—
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2311yescharacteristic
73C2×C3×C4×D3—22no—
74C2×C3×C4×D3—22no—
75C2×C3×C4×D3Q814yescomplemented
76C2×C3×Dic6—22no—
77C2×C3×Dic6—24no—
78C32×C4⋊C4—22no—
79C32×C4⋊C4—22no—
80C3×(C2×D3)⋊C4—22no—
81C3×(C2×D3)⋊C4—22no—
82C3×(C2×D3)⋊C4—24no—
83C3×(C2×D3)⋊C4—24no—
84C3×C4⋊Dic3—22no—
85C3×Dic3⋊C4—24no—
86C3×Dic3⋊C4—24no—
87C3×Dic3⋊C4—24no—
88C3×Dic3⋊C4—24no—
89C3×C4×Dic3—24no—
90C3×C4×Dic3—22no—
91C3×C4×Dic3—24no—
92C3×C4×Dic3D414yes—
93#2396—31noSylow
94C22×C3×Q8—31no—
95C23×C3×C4—31no—
96C22×C4×D3C22×C311yescharacteristic
97C22×Dic6C22×C311yescharacteristic
98C3×C4×Q8—64no—
99C3×#117—64no—
100C2×C3×C4⋊C4—21no—
101C2×C3×C4⋊C4—21no—
102C2×C3×C4⋊C4—32no—
103C2×C3×C4⋊C4—32no—
104C2×C3×C4⋊C4—32no—
105C2×C3×C4⋊C4—32no—
106C2×C3×C4⋊C4—31no—
107C2×C3×C4⋊C4C2×D311yescharacteristic
108C2×C3×C4⋊C4C2×D311yescharacteristic
109C2×C3×C4⋊C4C22×C311yescharacteristic
110C2×C3×C4⋊C4C22×C311yescharacteristic
111C2×C3×C22⋊C4—32no—
112C2×C3×C22⋊C4—32no—
113C2×C3×C22⋊C4—31no—
114C2×C3×C22⋊C4—31no—
115C2×C3×C42—31no—
116C2×C3×C42—32no—
117C2×C3×C42—32no—
118C2×C3×C42—31no—
119C2×(C2×D3)⋊C4C22×C312yes—
120C2×(C2×D3)⋊C4C22×C312yes—
121C2×(C2×D3)⋊C4C22×C311yescharacteristic
122C2×(C2×D3)⋊C4C22×C311yescharacteristic
123C2×C4⋊Dic3C22×C311yescharacteristic
124C2×Dic3⋊C4C22×C312yes—
125C2×Dic3⋊C4C22×C312yes—
126C2×Dic3⋊C4C22×C312yes—
127C2×Dic3⋊C4C22×C312yes—
128C2×C4×Dic3C22×C312yes—
129C2×C4×Dic3C22×C311yescharacteristic
130C2×C4×Dic3C22×C312yes—
131C2×C4×Dic3C22×C311yescharacteristic
132#892—24no—
133#887—24no—
134C3×#95—22no—
135C3×#95—21no—
136C3×#95—22no—
137C3×#95—32no—
138C3×#95—32no—
139C3×#95—31no—
140C3×#95C2×D312yes—
141C3×#95C2×D311yescharacteristic
142C3×#95C2×D312yes—
143C3×#95C22×C311yescharacteristic
144C3×#95C22×C312yes—
145C3×#95C22×C312yes—
146C3⋊#95C22×C312yes—
147C3⋊#95C22×C311yescharacteristic
148C3⋊#95C22×C312yes—
149C23×C32C2411yescharacteristic
150C22×C3×D3—21no—
151C22×C3×D3—22no—
152C22×C3×D3—22no—
153C22×C3×D3—21no—
154C22×C3×D3C2×Q812yes—
155C2×C32×C4—21no—
156C2×C32×C4—22no—
157C2×C32×C4—21no—
158C2×C32×C4—22no—
159C2×C32×C4—21no—
160C2×C32×C4—22no—
161C2×C32×C4—22no—
162C2×C32×C4—22no—
163C2×C32×C4—22no—
164C2×C32×C4—22no—
165C2×C32×C4—22no—
166C2×C32×C4C2×D412yes—
167C2×C32×C4C2×Q812yes—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3C2×D412yes—
176C2×C3×Dic3C2×D412yes—
177C2×C3×Dic3C2×Q812yes—
178C2×C3×Dic3#4114yes—
179C2×C3×Dic3#4114yes—
180C2×C3×Dic3#4112yes—
181C3×C4×D3—28no—
182C3×Dic6—28no—
183C2×C4×Q8—31no—
184C2×#117—31no—
185#400C3×D311yescharacteristic, complemented
186#399—31no—
187#398—32no—
188#396—32no—
189#395—31no—
190#393—31no—
191C4×C4⋊C4—32no—
192C4×C4⋊C4—31no—
193C4×C22⋊C4—32no—
194C24×C3—31no—
195C23×D3C23×C311yescharacteristic
196C2×C3×Q8—64no—
197C2×C3×Q8—62no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—22no—
201C22×C3×C4—21no—
202C22×C3×C4—22no—
203C22×C3×C4—31no—
204C22×C3×C4—32no—
205C22×C3×C4—32no—
206C22×C3×C4—31no—
207C22×C3×C4—34no—
208C22×C3×C4—31no—
209C22×C3×C4—62no—
210C22×C3×C4—62no—
211C22×C3×C4C22×D312yes—
212C22×C3×C4C22×D311yescharacteristic
213C22×C3×C4C22×D312yes—
214C22×C3×C4C22×D311yescharacteristic
215C22×C3×C4C22×D311yescharacteristic
216C22×C3×C4C23×C312yes—
217C22×C3×C4C23×C312yes—
218C22×C3×C4C23×C311yescharacteristic
219C22×C3×C4C23×C311yescharacteristic
220C22×C3×C4C23×C311yescharacteristic
221C22×Dic3C23×C311yescharacteristic
222C22×Dic3C23×C311yescharacteristic
223C22×Dic3C23×C312yes—
224C22×Dic3C23×C312yes—
225C22×Dic3C23×C311yescharacteristic
226C2×C4×D3—22no—
227C2×C4×D3—22no—
228C2×C4×D3C3×Q814yescomplemented
229C2×Dic6—22no—
230C2×Dic6—24no—
231C3×C4⋊C4—22no—
232C3×C4⋊C4—22no—
233C3×C4⋊C4—22no—
234C3×C4⋊C4—22no—
235C3×C4⋊C4—42no—
236C3×C4⋊C4—42no—
237C3×C4⋊C4—64no—
238C3×C4⋊C4—64no—
239C3×C4⋊C4—64no—
240C3×C4⋊C4—64no—
241C3×C4⋊C4—62no—
242C3×C22⋊C4—64no—
243C3×C22⋊C4—64no—
244C3×C22⋊C4—62no—
245C3×C22⋊C4—62no—
246C3×C42—34no—
247C3×C42—64no—
248C3×C42—62no—
249C3×C42—64no—
250(C2×D3)⋊C4—22no—
251(C2×D3)⋊C4—22no—
252(C2×D3)⋊C4—24no—
253(C2×D3)⋊C4—24no—
254C4⋊Dic3—22no—
255Dic3⋊C4—24no—
256Dic3⋊C4—24no—
257Dic3⋊C4—24no—
258Dic3⋊C4—24no—
259C4×Dic3—24no—
260C4×Dic3—22no—
261C4×Dic3—24no—
262C4×Dic3C3×D414yes—
263C22×C32C22×D411yescharacteristic
264C22×C32C22×Q811yescharacteristic
265C22×C32C2×#4111yescharacteristic
266C22×C32C2×#4112yes—
267C22×C32C2×#4112yes—
268C2×C3×D3—22no—
269C2×C3×D3—24no—
270C2×C3×D3—41no—
271C2×C3×D3—42no—
272C2×C3×D3—41no—
273C32×C4—22no—
274C32×C4—22no—
275C32×C4—41no—
276C32×C4—42no—
277C32×C4—42no—
278C3×Dic3—24no—
279C3×Dic3—24no—
280C3×Dic3—22no—
281C3×Dic3—41no—
282C3×Dic3C22⋊Q814yes—
283C22×Q8—31no—
284C23×C4—31no—
285C4×Q8—64no—
286#117—64no—
287C2×C4⋊C4—31no—
288C2×C4⋊C4—32no—
289C2×C4⋊C4—32no—
290C2×C4⋊C4—32no—
291C2×C4⋊C4—32no—
292C2×C4⋊C4C2×C3×D311yescharacteristic
293C2×C4⋊C4C2×C3×D311yescharacteristic
294C2×C22⋊C4—31no—
295C2×C22⋊C4—31no—
296C2×C22⋊C4—32no—
297C2×C22⋊C4—32no—
298C2×C42—31no—
299C2×C42—31no—
300C2×C42—32no—
301C2×C42—32no—
302#95—32no—
303#95—32no—
304#95—31no—
305#95C2×C3×D312yes—
306#95C2×C3×D311yescharacteristic
307#95C2×C3×D312yes—
308C23×C3—21no—
309C23×C3—32no—
310C23×C3—61no—
311C23×C3—62no—
312C23×C3—62no—
313C23×C3—61no—
314C23×C3C23×D311yescharacteristic
315C23×C3C24×C311yescharacteristic
316C22×D3—21no—
317C22×D3—22no—
318C22×D3—22no—
319C22×D3—21no—
320C22×D3C2×C3×Q812yes—
321C3×Q8—68no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—22no—
325C2×C3×C4—21no—
326C2×C3×C4—22no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—22no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—22no—
337C2×C3×C4—21no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4—22no—
341C2×C3×C4—22no—
342C2×C3×C4—22no—
343C2×C3×C4—22no—
344C2×C3×C4—22no—
345C2×C3×C4—22no—
346C2×C3×C4—32no—
347C2×C3×C4—32no—
348C2×C3×C4—32no—
349C2×C3×C4—32no—
350C2×C3×C4—34no—
351C2×C3×C4—34no—
352C2×C3×C4—41no—
353C2×C3×C4—41no—
354C2×C3×C4—42no—
355C2×C3×C4—41no—
356C2×C3×C4—42no—
357C2×C3×C4—42no—
358C2×C3×C4—42no—
359C2×C3×C4—42no—
360C2×C3×C4—42no—
361C2×C3×C4—42no—
362C2×C3×C4—42no—
363C2×C3×C4—68no—
364C2×C3×C4—62no—
365C2×C3×C4—62no—
366C2×C3×C4—62no—
367C2×C3×C4—62no—
368C2×C3×C4—62no—
369C2×C3×C4—61no—
370C2×C3×C4—62no—
371C2×C3×C4D3×D412yes—
372C2×C3×C4D3×Q812yes—
373C2×C3×C4C2×C3×D412yes—
374C2×C3×C4C2×C3×Q812yes—
375C2×Dic3—22no—
376C2×Dic3—22no—
377C2×Dic3—22no—
378C2×Dic3—22no—
379C2×Dic3—22no—
380C2×Dic3—21no—
381C2×Dic3—22no—
382C2×Dic3C2×C3×D412yes—
383C2×Dic3C2×C3×D412yes—
384C2×Dic3C2×C3×Q812yes—
385C2×Dic3C3×#4114yes—
386C2×Dic3C3×#4114yes—
387C2×Dic3C3×#4112yes—
388C4×D3—28no—
389Dic6—28no—
390C2×C32C2×C22⋊Q811yescharacteristic
391C2×C32#52511yescharacteristic
392C2×C32#52912yes—
393C2×C32#53211yescharacteristic
394C2×C32#53312yes—
395C3×D3—42no—
396C24—31no—
397C2×Q8—64no—
398C2×Q8—62no—
399C22×C4—31no—
400C22×C4—32no—
401C22×C4—32no—
402C22×C4—31no—
403C22×C4—34no—
404C22×C4—31no—
405C22×C4—62no—
406C22×C4—62no—
407C22×C4C22×C3×D312yes—
408C22×C4C22×C3×D311yescharacteristic
409C22×C4C22×C3×D312yes—
410C22×C4C22×C3×D311yescharacteristic
411C22×C4C22×C3×D311yescharacteristic
412C4⋊C4—22no—
413C4⋊C4—22no—
414C4⋊C4—62no—
415C4⋊C4—64no—
416C4⋊C4—64no—
417C4⋊C4—64no—
418C4⋊C4—64no—
419C22⋊C4—62no—
420C22⋊C4—64no—
421C22⋊C4—64no—
422C22⋊C4—62no—
423C42—34no—
424C42—62no—
425C42—64no—
426C42—64no—
427C22×C3—21no—
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—22no—
431C22×C3—22no—
432C22×C3—64no—
433C22×C3—62no—
434C22×C3—121no—
435C22×C3—121no—
436C22×C3—122no—
437C22×C3C2×D3×D411yescharacteristic
438C22×C3C2×D3×Q811yescharacteristic
439C22×C3D3×#4112yes—
440C22×C3D3×#4112yes—
441C22×C3D3×#4111yescharacteristic
442C22×C3C22×C3×D411yescharacteristic
443C22×C3C22×C3×Q811yescharacteristic
444C22×C3C2×C3×#4111yescharacteristic
445C22×C3C2×C3×#4112yes—
446C22×C3C2×C3×#4112yes—
447C2×D3—22no—
448C2×D3—24no—
449C2×D3—41no—
450C2×D3—42no—
451C2×D3—41no—
452C3×C4—22no—
453C3×C4—22no—
454C3×C4—22no—
455C3×C4—22no—
456C3×C4—34no—
457C3×C4—42no—
458C3×C4—42no—
459C3×C4—41no—
460C3×C4—42no—
461C3×C4—42no—
462C3×C4—41no—
463C3×C4—42no—
464C3×C4—42no—
465C3×C4—64no—
466C3×C4—62no—
467C3×C4—64no—
468C3×C4—81no—
469C3×C4—82no—
470C3×C4—82no—
471C3×C4—121no—
472Dic3—24no—
473Dic3—24no—
474Dic3—22no—
475Dic3—41no—
476Dic3C3×C22⋊Q814yes—
477C32#239611yescharacteristic, complemented, Sylow
478C23—32no—
479C23—61no—
480C23—62no—
481C23—62no—
482C23—61no—
483C23C23×C3×D311yescharacteristic
484Q8—68no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—22no—
488C2×C4—21no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—32no—
497C2×C4—32no—
498C2×C4—32no—
499C2×C4—32no—
500C2×C4—34no—
501C2×C4—34no—
502C2×C4—68no—
503C2×C4—62no—
504C2×C4—62no—
505C2×C4—62no—
506C2×C4—62no—
507C2×C4—62no—
508C2×C4—61no—
509C2×C4—62no—
510C2×C4C3×D3×D412yes—
511C2×C4C3×D3×Q812yes—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3—22no—
516C2×C3—22no—
517C2×C3—122no—
518C2×C3D3×C22⋊Q811yescharacteristic
519C2×C3#565611yescharacteristic
520C2×C3#566811yescharacteristic
521C2×C3#568812yes—
522C2×C3#570612yes—
523C2×C3C2×C3×C22⋊Q811yescharacteristic
524C2×C3C3×#52511yescharacteristic
525C2×C3C3×#52912yes—
526C2×C3C3×#53211yescharacteristic
527C2×C3C3×#53312yes—
528D3—42no—
529C22—62no—
530C22—64no—
531C22—121no—
532C22—121no—
533C22—122no—
534C22C2×C3×D3×D411yescharacteristic
535C22C2×C3×D3×Q811yescharacteristic
536C22C3×D3×#4111yescharacteristic
537C22C3×D3×#4112yes—
538C22C3×D3×#4112yes—
539C4—22no—
540C4—22no—
541C4—34no—
542C4—41no—
543C4—42no—
544C4—42no—
545C4—64no—
546C4—62no—
547C4—64no—
548C4—121no—
549C3—21no—
550C3#7813011yescharacteristic, direct product factor
551C3C3×#239611yescharacteristic, complemented
552C2—122no—
553C2C3×D3×C22⋊Q811yescharacteristic
554C2C3×#565611yescharacteristic
555C2C3×#566811yescharacteristic
556C2C3×#568812yes—
557C2C3×#570612yes—
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×#400C2
socleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC3×#400D3
hypocenterC3C3×#2396
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#400

Complements

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

NH ≅ G/Ntype
2. C2×C3×#887C2semidirect
3. C32×#400C2semidirect
5. C3×#4979C2semidirect
9. C3×#4657C2semidirect
10. C3×#4649C2semidirect
11. C3×#4649C2semidirect
13. #78130C3direct (N × H)
42. C2×#887C2×C3semidirect
44. C3×#400D3semidirect
45. C3×#400C2×C3semidirect
55. #4979C2×C3semidirect
59. #4657C2×C3semidirect
60. #4649C2×C3semidirect
61. #4649C2×C3semidirect
75. C2×C3×C4×D3Q8semidirect
185. #400C3×D3semidirect
228. C2×C4×D3C3×Q8semidirect
477. C32#2396semidirect
550. C3#78130direct (N × H)
551. C3C3×#2396semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8922
C2×C3×#8872
C32×#4002
C3×#49932
C3×#49792
C3×#46762
C3×#46732
C3×#46662
C3×#46572
C3×#46492
C3×#23963
#781303