Finite Group Databasebeta

← C3×#78018 #11808643

Subgroups — C3×#78018 #11808643

Order 1152.

1149 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#887C211yesmaximal, characteristic, complemented
2C2×C3×#877C211yesmaximal, characteristic
3C32×#399C211yesmaximal, characteristic
4C3×#4985C211yesmaximal, characteristic, complemented
5C3×#4983C212yesmaximal, complemented
6C3×Dic3×C4⋊C4C212yesmaximal, complemented
7C3×#4948C212yesmaximal
8C3×#4947C211yesmaximal, characteristic
9C3×Dic3×C22⋊C4C212yesmaximal
10C3×#4656C211yesmaximal, characteristic, complemented
11C3×#4649C211yesmaximal, characteristic, complemented
12C3×#2396—31nomaximal
13#78018C311yesmaximal, characteristic, direct product factor
14C23×C3×Dic3C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×C32×C4⋊C4C2212yes—
18C2×C32×C22⋊C4C2212yes—
19C2×C32×C22⋊C4C2211yescharacteristic
20C2×C3×#217C2212yes—
21C2×C3×#217C2211yescharacteristic
22C2×C3×C4⋊Dic3C2212yes—
23C2×C3×Dic3⋊C4C2212yes—
24C2×C3×Dic3⋊C4C2211yescharacteristic
25C2×C3×Dic3⋊C4C2212yes—
26C2×C3×Dic3⋊C4C2211yescharacteristic
27C2×C3×C4×Dic3C2212yes—
28C2×C3×C4×Dic3C2212yes—
29C2×C3×C4×Dic3C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C3×#887—24no—
32C3×#877—24no—
33C32×#95C2211yescharacteristic
34C3×C3⋊#95C2211yescharacteristic
35C3×C3⋊#95C2212yes—
36C3×C3⋊#95C2212yes—
37C3×C3⋊#95C2212yes—
38C3×C3⋊#95C2212yes—
39C2×C3×C4×Q8—31no—
40C2×C3×#117—31no—
41C2×#887C2×C311yescharacteristic, complemented
42C2×#877C2×C311yescharacteristic
43C3×#400—31no—
44C3×#399—21no—
45C3×#399D311yescharacteristic
46C3×#399C2×C311yescharacteristic
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#4985C2×C311yescharacteristic, complemented
55#4983C2×C312yescomplemented
56Dic3×C4⋊C4C2×C312yescomplemented
57#4948C2×C312yes—
58#4947C2×C311yescharacteristic
59Dic3×C22⋊C4C2×C312yes—
60#4656C2×C311yescharacteristic, complemented
61#4649C2×C311yescharacteristic, complemented
62C24×C32C2311yescharacteristic
63C22×C32×C4C2311yescharacteristic
64C22×C32×C4C2312yes—
65C22×C32×C4C2311yescharacteristic
66C22×C32×C4C2312yes—
67C22×C3×Dic3—22no—
68C22×C3×Dic3—22no—
69C22×C3×Dic3Q814yescomplemented
70C22×C3×Dic3C2311yescharacteristic
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2311yescharacteristic
73C22×C3×Dic3C2311yescharacteristic
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2311yescharacteristic
76C2×C3×Dic6—22no—
77C2×C3×Dic6—24no—
78C32×C4⋊C4—22no—
79C32×C4⋊C4—24no—
80C32×C22⋊C4—22no—
81C32×C22⋊C4—24no—
82C3×#217—22no—
83C3×#217—24no—
84C3×C4⋊Dic3—24no—
85C3×Dic3⋊C4—22no—
86C3×Dic3⋊C4—24no—
87C3×Dic3⋊C4—22no—
88C3×Dic3⋊C4—24no—
89C3×C4×Dic3—22no—
90C3×C4×Dic3—24no—
91C3×C4×Dic3—24no—
92C3×C4×Dic3D414yes—
93#2396—31noSylow
94C22×C3×Q8—31no—
95C23×C3×C4—31no—
96C23×Dic3C22×C311yescharacteristic
97C22×Dic6C22×C311yescharacteristic
98C3×C4×Q8—64no—
99C3×#117—64no—
100C2×C3×C4⋊C4—21no—
101C2×C3×C4⋊C4—22no—
102C2×C3×C4⋊C4—32no—
103C2×C3×C4⋊C4—31no—
104C2×C3×C4⋊C4—32no—
105C2×C3×C4⋊C4—31no—
106C2×C3×C4⋊C4—32no—
107C2×C3×C4⋊C4C2×D312yes—
108C2×C3×C4⋊C4C2×D311yescharacteristic
109C2×C3×C4⋊C4C22×C312yes—
110C2×C3×C4⋊C4C22×C311yescharacteristic
111C2×C3×C22⋊C4—21no—
112C2×C3×C22⋊C4—22no—
113C2×C3×C22⋊C4—32no—
114C2×C3×C22⋊C4—31no—
115C2×C3×C22⋊C4C2×D312yes—
116C2×C3×C22⋊C4C2×D311yescharacteristic
117C2×C3×C22⋊C4C22×C312yes—
118C2×C3×C22⋊C4C22×C311yescharacteristic
119C2×C3×C42—31no—
120C2×C3×C42—32no—
121C2×C3×C42—32no—
122C2×C3×C42—31no—
123C2×#217C22×C312yes—
124C2×#217C22×C311yescharacteristic
125C2×C4⋊Dic3C22×C312yes—
126C2×Dic3⋊C4C22×C312yes—
127C2×Dic3⋊C4C22×C311yescharacteristic
128C2×Dic3⋊C4C22×C312yes—
129C2×Dic3⋊C4C22×C311yescharacteristic
130C2×C4×Dic3C22×C312yes—
131C2×C4×Dic3C22×C312yes—
132C2×C4×Dic3C22×C311yescharacteristic
133C2×C4×Dic3C22×C311yescharacteristic
134#887—24no—
135#877—24no—
136C3×#95—21no—
137C3×#95—32no—
138C3×#95—32no—
139C3×#95—32no—
140C3×#95—31no—
141C3×#95—32no—
142C3×#95C2×D311yescharacteristic
143C3×#95C22×C311yescharacteristic
144C3⋊#95C22×C311yescharacteristic
145C3⋊#95C22×C312yes—
146C3⋊#95C22×C312yes—
147C3⋊#95C22×C312yes—
148C3⋊#95C22×C312yes—
149C23×C32—21no—
150C23×C32—22no—
151C23×C32—22no—
152C23×C32—21no—
153C23×C32C2×Q812yes—
154C23×C32C2411yescharacteristic
155C2×C32×C4—22no—
156C2×C32×C4—22no—
157C2×C32×C4—22no—
158C2×C32×C4—21no—
159C2×C32×C4—22no—
160C2×C32×C4—22no—
161C2×C32×C4—22no—
162C2×C32×C4—22no—
163C2×C32×C4C2×D412yes—
164C2×C32×C4#4114yes—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—21no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—21no—
170C2×C3×Dic3—28no—
171C2×C3×Dic3—21no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3C2×D412yes—
177C2×C3×Dic3C2×D412yes—
178C2×C3×Dic3C2×Q812yes—
179C2×C3×Dic3C2×Q812yes—
180C2×C3×Dic3#4114yes—
181C2×C3×Dic3#4112yes—
182C3×Dic6—28no—
183C2×C4×Q8—31no—
184C2×#117—31no—
185#400—31no—
186#399C3×D311yescharacteristic
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—21no—
195C24×C3C22×D311yescharacteristic
196C24×C3C23×C311yescharacteristic
197C2×C3×Q8—64no—
198C2×C3×Q8—62no—
199C22×C3×C4—21no—
200C22×C3×C4—22no—
201C22×C3×C4—21no—
202C22×C3×C4—22no—
203C22×C3×C4—31no—
204C22×C3×C4—34no—
205C22×C3×C4—31no—
206C22×C3×C4—32no—
207C22×C3×C4—31no—
208C22×C3×C4—32no—
209C22×C3×C4—31no—
210C22×C3×C4—62no—
211C22×C3×C4—62no—
212C22×C3×C4C22×D311yescharacteristic
213C22×C3×C4C22×D312yes—
214C22×C3×C4C22×D311yescharacteristic
215C22×C3×C4C22×D312yes—
216C22×C3×C4C23×C311yescharacteristic
217C22×C3×C4C23×C312yes—
218C22×C3×C4C23×C311yescharacteristic
219C22×C3×C4C23×C312yes—
220C22×Dic3—22no—
221C22×Dic3—22no—
222C22×Dic3C3×Q814yescomplemented
223C22×Dic3C23×C312yes—
224C22×Dic3C23×C311yescharacteristic
225C22×Dic3C23×C311yescharacteristic
226C22×Dic3C23×C311yescharacteristic
227C22×Dic3C23×C312yes—
228C22×Dic3C23×C311yescharacteristic
229C2×Dic6—22no—
230C2×Dic6—24no—
231C3×C4⋊C4—22no—
232C3×C4⋊C4—24no—
233C3×C4⋊C4—22no—
234C3×C4⋊C4—24no—
235C3×C4⋊C4—42no—
236C3×C4⋊C4—44no—
237C3×C4⋊C4—62no—
238C3×C4⋊C4—64no—
239C3×C4⋊C4—64no—
240C3×C4⋊C4—62no—
241C3×C4⋊C4—64no—
242C3×C22⋊C4—22no—
243C3×C22⋊C4—24no—
244C3×C22⋊C4—22no—
245C3×C22⋊C4—24no—
246C3×C22⋊C4—42no—
247C3×C22⋊C4—44no—
248C3×C22⋊C4—64no—
249C3×C22⋊C4—62no—
250C3×C42—34no—
251C3×C42—64no—
252C3×C42—62no—
253C3×C42—64no—
254#217—22no—
255#217—24no—
256C4⋊Dic3—24no—
257Dic3⋊C4—22no—
258Dic3⋊C4—24no—
259Dic3⋊C4—22no—
260Dic3⋊C4—24no—
261C4×Dic3—22no—
262C4×Dic3—24no—
263C4×Dic3—24no—
264C4×Dic3C3×D414yes—
265C22×C32—22no—
266C22×C32—24no—
267C22×C32—41no—
268C22×C32—42no—
269C22×C32—41no—
270C22×C32C22×D411yescharacteristic
271C22×C32C22×Q811yescharacteristic
272C22×C32C2×#4112yes—
273C22×C32C2×#4111yescharacteristic
274C22×C32C2×#4112yes—
275C32×C4—22no—
276C32×C4—24no—
277C32×C4—41no—
278C32×C4—42no—
279C3×Dic3—22no—
280C3×Dic3—24no—
281C3×Dic3—22no—
282C3×Dic3—41no—
283C3×Dic3—42no—
284C3×Dic3C22⋊Q814yes—
285C22×Q8—31no—
286C23×C4—31no—
287C4×Q8—64no—
288#117—64no—
289C2×C4⋊C4—31no—
290C2×C4⋊C4—31no—
291C2×C4⋊C4—32no—
292C2×C4⋊C4—32no—
293C2×C4⋊C4—32no—
294C2×C4⋊C4C2×C3×D311yescharacteristic
295C2×C4⋊C4C2×C3×D312yes—
296C2×C22⋊C4—31no—
297C2×C22⋊C4—32no—
298C2×C22⋊C4C2×C3×D311yescharacteristic
299C2×C22⋊C4C2×C3×D312yes—
300C2×C42—31no—
301C2×C42—31no—
302C2×C42—32no—
303C2×C42—32no—
304#95—32no—
305#95—32no—
306#95—32no—
307#95—31no—
308#95—32no—
309#95C2×C3×D311yescharacteristic
310C23×C3—21no—
311C23×C3—22no—
312C23×C3—22no—
313C23×C3—21no—
314C23×C3—21no—
315C23×C3—22no—
316C23×C3—22no—
317C23×C3—21no—
318C23×C3—21no—
319C23×C3—22no—
320C23×C3—41no—
321C23×C3—42no—
322C23×C3—42no—
323C23×C3—41no—
324C23×C3D3×Q812yes—
325C23×C3C2×C3×Q812yes—
326C23×C3C23×D311yescharacteristic
327C23×C3C24×C311yescharacteristic
328C3×Q8—68no—
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—21no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4—21no—
341C2×C3×C4—22no—
342C2×C3×C4—22no—
343C2×C3×C4—22no—
344C2×C3×C4—22no—
345C2×C3×C4—22no—
346C2×C3×C4—24no—
347C2×C3×C4—32no—
348C2×C3×C4—32no—
349C2×C3×C4—32no—
350C2×C3×C4—32no—
351C2×C3×C4—32no—
352C2×C3×C4—34no—
353C2×C3×C4—42no—
354C2×C3×C4—42no—
355C2×C3×C4—42no—
356C2×C3×C4—41no—
357C2×C3×C4—42no—
358C2×C3×C4—42no—
359C2×C3×C4—42no—
360C2×C3×C4—42no—
361C2×C3×C4—68no—
362C2×C3×C4—62no—
363C2×C3×C4—61no—
364C2×C3×C4—62no—
365C2×C3×C4—61no—
366C2×C3×C4—62no—
367C2×C3×C4—61no—
368C2×C3×C4—62no—
369C2×C3×C4—62no—
370C2×C3×C4—62no—
371C2×C3×C4—62no—
372C2×C3×C4D3×D412yes—
373C2×C3×C4#23714yes—
374C2×C3×C4C2×C3×D412yes—
375C2×C3×C4C3×#4114yes—
376C2×Dic3—22no—
377C2×Dic3—21no—
378C2×Dic3—22no—
379C2×Dic3—22no—
380C2×Dic3—21no—
381C2×Dic3—28no—
382C2×Dic3—21no—
383C2×Dic3—22no—
384C2×Dic3—22no—
385C2×Dic3—22no—
386C2×Dic3—22no—
387C2×Dic3C2×C3×D412yes—
388C2×Dic3C2×C3×D412yes—
389C2×Dic3C2×C3×Q812yes—
390C2×Dic3C2×C3×Q812yes—
391C2×Dic3C3×#4114yes—
392C2×Dic3C3×#4112yes—
393Dic6—28no—
394C2×C32—42no—
395C2×C32C2×C22⋊Q811yescharacteristic
396C2×C32#52511yescharacteristic
397C2×C32#52912yes—
398C2×C32#53211yescharacteristic
399C2×C32#53312yes—
400C24C22×C3×D311yescharacteristic
401C2×Q8—64no—
402C2×Q8—62no—
403C22×C4—31no—
404C22×C4—31no—
405C22×C4—32no—
406C22×C4—31no—
407C22×C4—34no—
408C22×C4—32no—
409C22×C4—31no—
410C22×C4—62no—
411C22×C4—62no—
412C22×C4C22×C3×D311yescharacteristic
413C22×C4C22×C3×D312yes—
414C22×C4C22×C3×D311yescharacteristic
415C22×C4C22×C3×D312yes—
416C4⋊C4—22no—
417C4⋊C4—24no—
418C4⋊C4—62no—
419C4⋊C4—64no—
420C4⋊C4—64no—
421C4⋊C4—62no—
422C4⋊C4—64no—
423C22⋊C4—22no—
424C22⋊C4—24no—
425C22⋊C4—62no—
426C22⋊C4—64no—
427C42—34no—
428C42—62no—
429C42—64no—
430C42—64no—
431C22×C3—22no—
432C22×C3—24no—
433C22×C3—24no—
434C22×C3—22no—
435C22×C3—21no—
436C22×C3—22no—
437C22×C3—21no—
438C22×C3—22no—
439C22×C3—21no—
440C22×C3—44no—
441C22×C3—42no—
442C22×C3—42no—
443C22×C3—41no—
444C22×C3—41no—
445C22×C3—41no—
446C22×C3—42no—
447C22×C3—41no—
448C22×C3—82no—
449C22×C3—81no—
450C22×C3—81no—
451C22×C3C2×D3×D411yescharacteristic
452C22×C3C2×#23712yes—
453C22×C3C2×D3×Q811yescharacteristic
454C22×C3D3×#4111yescharacteristic
455C22×C3D3×#4112yes—
456C22×C3C22×C3×D411yescharacteristic
457C22×C3C22×C3×Q811yescharacteristic
458C22×C3C2×C3×#4112yes—
459C22×C3C2×C3×#4111yescharacteristic
460C22×C3C2×C3×#4112yes—
461C3×C4—24no—
462C3×C4—22no—
463C3×C4—22no—
464C3×C4—24no—
465C3×C4—34no—
466C3×C4—44no—
467C3×C4—42no—
468C3×C4—41no—
469C3×C4—42no—
470C3×C4—41no—
471C3×C4—42no—
472C3×C4—64no—
473C3×C4—62no—
474C3×C4—62no—
475C3×C4—81no—
476C3×C4—82no—
477C3×C4—122no—
478C3×C4—121no—
479Dic3—22no—
480Dic3—24no—
481Dic3—22no—
482Dic3—41no—
483Dic3—42no—
484Dic3C3×C22⋊Q814yes—
485C32#239611yescharacteristic, complemented, Sylow
486C23—21no—
487C23—22no—
488C23—22no—
489C23—21no—
490C23C3×D3×Q812yes—
491C23C23×C3×D311yescharacteristic
492Q8—68no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—21no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—32no—
502C2×C4—32no—
503C2×C4—32no—
504C2×C4—32no—
505C2×C4—32no—
506C2×C4—34no—
507C2×C4—68no—
508C2×C4—62no—
509C2×C4—61no—
510C2×C4—62no—
511C2×C4—61no—
512C2×C4—62no—
513C2×C4—61no—
514C2×C4—62no—
515C2×C4—62no—
516C2×C4—62no—
517C2×C4—62no—
518C2×C4C3×D3×D412yes—
519C2×C4C3×#23714yes—
520C2×C3—22no—
521C2×C3—21no—
522C2×C3—22no—
523C2×C3—21no—
524C2×C3—21no—
525C2×C3—42no—
526C2×C3—42no—
527C2×C3—82no—
528C2×C3#562212yes—
529C2×C3D3×C22⋊Q811yescharacteristic
530C2×C3#564912yes—
531C2×C3#565611yescharacteristic
532C2×C3#571611yescharacteristic
533C2×C3C2×C3×C22⋊Q811yescharacteristic
534C2×C3C3×#52511yescharacteristic
535C2×C3C3×#52912yes—
536C2×C3C3×#53211yescharacteristic
537C2×C3C3×#53312yes—
538C22—24no—
539C22—22no—
540C22—42no—
541C22—41no—
542C22—41no—
543C22C2×C3×D3×D411yescharacteristic
544C22C2×C3×#23712yes—
545C22C2×C3×D3×Q811yescharacteristic
546C22C3×D3×#4112yes—
547C22C3×D3×#4111yescharacteristic
548C4—24no—
549C4—22no—
550C4—34no—
551C4—41no—
552C4—42no—
553C4—62no—
554C4—64no—
555C4—62no—
556C4—122no—
557C4—121no—
558C3—21no—
559C3#7801811yescharacteristic, direct product factor
560C3C3×#239611yescharacteristic, complemented
561C2—42no—
562C2C3×#562212yes—
563C2C3×D3×C22⋊Q811yescharacteristic
564C2C3×#564912yes—
565C2C3×#565611yescharacteristic
566C2C3×#571611yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×#399C2
socleC23×C32C24
prime radicalC24×C32C23
hypercenterC3×#399D3
hypocenterC3C3×#2396
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#399

Complements

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

NH ≅ G/Ntype
1. C2×C3×#887C2semidirect
4. C3×#4985C2semidirect
5. C3×#4983C2semidirect
6. C3×Dic3×C4⋊C4C2semidirect
10. C3×#4656C2semidirect
11. C3×#4649C2semidirect
13. #78018C3direct (N × H)
41. C2×#887C2×C3semidirect
54. #4985C2×C3semidirect
55. #4983C2×C3semidirect
56. Dic3×C4⋊C4C2×C3semidirect
60. #4656C2×C3semidirect
61. #4649C2×C3semidirect
69. C22×C3×Dic3Q8semidirect
222. C22×Dic3C3×Q8semidirect
485. C32#2396semidirect
559. C3#78018direct (N × H)
560. C3C3×#2396semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8872
C2×C3×#8772
C32×#3992
C3×#49852
C3×#49832
C3×Dic3×C4⋊C42
C3×#49482
C3×#49472
C3×Dic3×C22⋊C42
C3×#46562
C3×#46492
C3×#23963
#780183