Finite Group Databasebeta

← C3×#77170 #11808649

Subgroups — C3×#77170 #11808649

Order 1152.

1147 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×Q8×Dic3C211yesmaximal, characteristic, complemented
2C2×C3×#892C211yesmaximal, characteristic
3C32×#395C211yesmaximal, characteristic, complemented
4C3×#5231C211yesmaximal, characteristic
5C3×#4994C212yesmaximal
6C3×#4986C211yesmaximal, characteristic, complemented
7C3×Dic3×C4⋊C4C212yesmaximal, complemented
8C3×#4677C211yesmaximal, characteristic
9C3×#4666C212yesmaximal
10C3×#4661C212yesmaximal, complemented
11C3×#4649C211yesmaximal, characteristic, complemented
12C3×#2396—31nomaximal
13#77170C311yesmaximal, characteristic, direct product factor
14C22×C32×Q8C2211yescharacteristic
15C22×C3×C4×D3C2211yescharacteristic
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×C32×C4⋊C4C2212yes—
18C3×Q8×Dic3—24no—
19C2×C3×(C2×D3)⋊C4C2211yescharacteristic
20C2×C3×(C2×D3)⋊C4C2211yescharacteristic
21C2×C3×(C2×D3)⋊C4C2212yes—
22C2×C3×(C2×D3)⋊C4C2212yes—
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×C4⋊Dic3C2212yes—
25C2×C3×C4⋊Dic3C2212yes—
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×Dic3⋊C4C2212yes—
28C2×C3×C4×Dic3C2212yes—
29C2×C3×C4×Dic3C2211yescharacteristic
30C2×C3×C4×Dic3C2212yes—
31C2×C3×C4×Dic3C2211yescharacteristic
32C3×#892—24no—
33C32×#95C2211yescharacteristic
34C32×#95C2212yes—
35C3×C3⋊#95C2211yescharacteristic
36C3×C3⋊#95C2212yes—
37C3×C3⋊#95C2212yes—
38C3×C3⋊#95C2212yes—
39C2×C3×C4×Q8—31no—
40C2×C3×#117—31no—
41C2×Q8×Dic3C2×C311yescharacteristic, complemented
42C2×#892C2×C311yescharacteristic
43C3×#400—31no—
44C3×#399—31no—
45C3×#398—32no—
46C3×#396—32no—
47C3×#395—21no—
48C3×#395D311yescharacteristic, complemented
49C3×#395C2×C311yescharacteristic, complemented
50C3×#393—31no—
51C3×C4×C4⋊C4—32no—
52C3×C4×C4⋊C4—31no—
53C3×C4×C22⋊C4—32no—
54#5231C2×C311yescharacteristic
55#4994C2×C312yes—
56#4986C2×C311yescharacteristic, complemented
57Dic3×C4⋊C4C2×C312yescomplemented
58#4677C2×C311yescharacteristic
59#4666C2×C312yes—
60#4661C2×C312yescomplemented
61#4649C2×C311yescharacteristic, complemented
62C23×C3×D3C2311yescharacteristic
63C2×C32×Q8—22no—
64C2×C32×Q8—24no—
65C22×C32×C4C2311yescharacteristic
66C22×C32×C4C2311yescharacteristic
67C22×C32×C4C2311yescharacteristic
68C22×C32×C4C2312yes—
69C22×C32×C4C2312yes—
70C22×C3×Dic3C2312yes—
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2311yescharacteristic
73C22×C3×Dic3C2311yescharacteristic
74C22×C3×Dic3C2311yescharacteristic
75C2×C3×C4×D3—22no—
76C2×C3×C4×D3—22no—
77C2×C3×C4×D3Q814yescomplemented
78C32×C4⋊C4—22no—
79C32×C4⋊C4—24no—
80C3×(C2×D3)⋊C4—22no—
81C3×(C2×D3)⋊C4—24no—
82C3×(C2×D3)⋊C4—24no—
83C3×(C2×D3)⋊C4—22no—
84C3×C4⋊Dic3—22no—
85C3×C4⋊Dic3—24no—
86C3×C4⋊Dic3—22no—
87C3×C4⋊Dic3—24no—
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—21no—
95C22×C3×Q8C2×D311yescharacteristic
96C22×C3×Q8C22×C311yescharacteristic
97C23×C3×C4—31no—
98C22×C4×D3C22×C311yescharacteristic
99C3×C4×Q8—64no—
100C3×#117—64no—
101C2×C3×C4⋊C4—21no—
102C2×C3×C4⋊C4—22no—
103C2×C3×C4⋊C4—32no—
104C2×C3×C4⋊C4—32no—
105C2×C3×C4⋊C4—32no—
106C2×C3×C4⋊C4—31no—
107C2×C3×C4⋊C4—31no—
108C2×C3×C4⋊C4C2×D312yes—
109C2×C3×C4⋊C4C2×D311yescharacteristic
110C2×C3×C4⋊C4C22×C312yes—
111C2×C3×C4⋊C4C22×C311yescharacteristic
112C2×C3×C22⋊C4—32no—
113C2×C3×C22⋊C4—32no—
114C2×C3×C22⋊C4—31no—
115C2×C3×C22⋊C4—31no—
116C2×C3×C42—31no—
117C2×C3×C42—32no—
118C2×C3×C42—32no—
119C2×C3×C42—31no—
120Q8×Dic3—24no—
121C2×(C2×D3)⋊C4C22×C312yes—
122C2×(C2×D3)⋊C4C22×C312yes—
123C2×(C2×D3)⋊C4C22×C311yescharacteristic
124C2×(C2×D3)⋊C4C22×C311yescharacteristic
125C2×C4⋊Dic3C22×C311yescharacteristic
126C2×C4⋊Dic3C22×C312yes—
127C2×C4⋊Dic3C22×C312yes—
128C2×C4⋊Dic3C22×C311yescharacteristic
129C2×Dic3⋊C4C22×C312yes—
130C2×C4×Dic3C22×C312yes—
131C2×C4×Dic3C22×C312yes—
132C2×C4×Dic3C22×C311yescharacteristic
133C2×C4×Dic3C22×C311yescharacteristic
134#892—24no—
135C3×#95—22no—
136C3×#95—21no—
137C3×#95—32no—
138C3×#95—32no—
139C3×#95—31no—
140C3×#95—32no—
141C3×#95C2×D312yes—
142C3×#95C2×D311yescharacteristic
143C3×#95C22×C311yescharacteristic
144C3×#95C22×C312yes—
145C3⋊#95C22×C311yescharacteristic
146C3⋊#95C22×C312yes—
147C3⋊#95C22×C312yes—
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—
155C32×Q8—28no—
156C2×C32×C4—22no—
157C2×C32×C4—21no—
158C2×C32×C4—22no—
159C2×C32×C4—22no—
160C2×C32×C4—21no—
161C2×C32×C4—22no—
162C2×C32×C4—22no—
163C2×C32×C4—21no—
164C2×C32×C4—22no—
165C2×C32×C4C2×D412yes—
166C2×C32×C4C2×Q812yes—
167C2×C32×C4#4114yes—
168C2×C32×C4#4114yes—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—21no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3C2×D412yes—
179C2×C3×Dic3C2×D412yes—
180C2×C3×Dic3C2×Q812yes—
181C2×C3×Dic3#4112yes—
182C3×C4×D3—28no—
183C2×C4×Q8—31no—
184C2×#117—31no—
185#400—31no—
186#399—31no—
187#398—32no—
188#396—32no—
189#395C3×D311yescharacteristic, complemented
190#393—31no—
191C4×C4⋊C4—32no—
192C4×C4⋊C4—31no—
193C4×C22⋊C4—32no—
194C24×C3—31no—
195C23×D3C23×C311yescharacteristic
196C2×C3×Q8—22no—
197C2×C3×Q8—24no—
198C2×C3×Q8—22no—
199C2×C3×Q8—24no—
200C2×C3×Q8—42no—
201C2×C3×Q8—44no—
202C22×C3×C4—21no—
203C22×C3×C4—22no—
204C22×C3×C4—21no—
205C22×C3×C4—22no—
206C22×C3×C4—21no—
207C22×C3×C4—31no—
208C22×C3×C4—31no—
209C22×C3×C4—34no—
210C22×C3×C4—32no—
211C22×C3×C4—31no—
212C22×C3×C4—32no—
213C22×C3×C4—62no—
214C22×C3×C4—62no—
215C22×C3×C4C22×D311yescharacteristic
216C22×C3×C4C22×D311yescharacteristic
217C22×C3×C4C22×D312yes—
218C22×C3×C4C22×D311yescharacteristic
219C22×C3×C4C22×D312yes—
220C22×C3×C4C23×C311yescharacteristic
221C22×C3×C4C23×C311yescharacteristic
222C22×C3×C4C23×C311yescharacteristic
223C22×C3×C4C23×C312yes—
224C22×C3×C4C23×C312yes—
225C22×Dic3C23×C312yes—
226C22×Dic3C23×C312yes—
227C22×Dic3C23×C311yescharacteristic
228C22×Dic3C23×C311yescharacteristic
229C22×Dic3C23×C311yescharacteristic
230C2×C4×D3—22no—
231C2×C4×D3—22no—
232C2×C4×D3C3×Q814yescomplemented
233C3×C4⋊C4—22no—
234C3×C4⋊C4—24no—
235C3×C4⋊C4—22no—
236C3×C4⋊C4—24no—
237C3×C4⋊C4—42no—
238C3×C4⋊C4—44no—
239C3×C4⋊C4—62no—
240C3×C4⋊C4—64no—
241C3×C4⋊C4—62no—
242C3×C4⋊C4—64no—
243C3×C4⋊C4—64no—
244C3×C22⋊C4—62no—
245C3×C22⋊C4—62no—
246C3×C22⋊C4—64no—
247C3×C22⋊C4—64no—
248C3×C42—34no—
249C3×C42—64no—
250C3×C42—62no—
251C3×C42—64no—
252(C2×D3)⋊C4—22no—
253(C2×D3)⋊C4—24no—
254(C2×D3)⋊C4—24no—
255(C2×D3)⋊C4—22no—
256C4⋊Dic3—22no—
257C4⋊Dic3—24no—
258C4⋊Dic3—22no—
259C4⋊Dic3—24no—
260Dic3⋊C4—24no—
261C4×Dic3—22no—
262C4×Dic3—24no—
263C4×Dic3—24no—
264C4×Dic3C3×D414yes—
265C22×C32C22×D411yescharacteristic
266C22×C32C22×Q811yescharacteristic
267C22×C32C2×#4112yes—
268C22×C32C2×#4112yes—
269C22×C32C2×#4111yescharacteristic
270C2×C3×D3—22no—
271C2×C3×D3—24no—
272C2×C3×D3—41no—
273C2×C3×D3—42no—
274C2×C3×D3—41no—
275C32×C4—22no—
276C32×C4—22no—
277C32×C4—24no—
278C32×C4—24no—
279C32×C4—41no—
280C3×Dic3—22no—
281C3×Dic3—42no—
282C3×Dic3—42no—
283C3×Dic3—41no—
284C3×Dic3C22⋊Q814yes—
285C22×Q8C2×C3×D311yescharacteristic
286C23×C4—31no—
287C4×Q8—64no—
288#117—64no—
289C2×C4⋊C4—31no—
290C2×C4⋊C4—32no—
291C2×C4⋊C4—31no—
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—31no—
298C2×C22⋊C4—32no—
299C2×C22⋊C4—32no—
300C2×C42—31no—
301C2×C42—31no—
302C2×C42—32no—
303C2×C42—32no—
304#95—32no—
305#95—32no—
306#95—31no—
307#95—32no—
308#95C2×C3×D312yes—
309#95C2×C3×D311yescharacteristic
310C23×C3—21no—
311C23×C3—32no—
312C23×C3—61no—
313C23×C3—62no—
314C23×C3—62no—
315C23×C3—61no—
316C23×C3C23×D311yescharacteristic
317C23×C3C24×C311yescharacteristic
318C22×D3—21no—
319C22×D3—22no—
320C22×D3—22no—
321C22×D3—21no—
322C22×D3C2×C3×Q812yes—
323C3×Q8—28no—
324C3×Q8—28no—
325C3×Q8—48no—
326C2×C3×C4—22no—
327C2×C3×C4—21no—
328C2×C3×C4—22no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—21no—
333C2×C3×C4—22no—
334C2×C3×C4—21no—
335C2×C3×C4—22no—
336C2×C3×C4—22no—
337C2×C3×C4—21no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4—21no—
341C2×C3×C4—22no—
342C2×C3×C4—21no—
343C2×C3×C4—22no—
344C2×C3×C4—22no—
345C2×C3×C4—24no—
346C2×C3×C4—22no—
347C2×C3×C4—24no—
348C2×C3×C4—32no—
349C2×C3×C4—32no—
350C2×C3×C4—32no—
351C2×C3×C4—32no—
352C2×C3×C4—41no—
353C2×C3×C4—42no—
354C2×C3×C4—42no—
355C2×C3×C4—41no—
356C2×C3×C4—42no—
357C2×C3×C4—42no—
358C2×C3×C4—42no—
359C2×C3×C4—41no—
360C2×C3×C4—42no—
361C2×C3×C4—68no—
362C2×C3×C4—62no—
363C2×C3×C4—61no—
364C2×C3×C4—62no—
365C2×C3×C4—62no—
366C2×C3×C4—62no—
367C2×C3×C4—62no—
368C2×C3×C4—62no—
369C2×C3×C4—62no—
370C2×C3×C4—62no—
371C2×C3×C4D3×D412yes—
372C2×C3×C4#23714yes—
373C2×C3×C4D3×Q812yes—
374C2×C3×C4#23914yes—
375C2×C3×C4C2×C3×D412yes—
376C2×C3×C4C2×C3×Q812yes—
377C2×C3×C4C3×#4114yes—
378C2×C3×C4C3×#4114yes—
379C2×Dic3—22no—
380C2×Dic3—22no—
381C2×Dic3—21no—
382C2×Dic3—22no—
383C2×Dic3—22no—
384C2×Dic3—22no—
385C2×Dic3—22no—
386C2×Dic3—22no—
387C2×Dic3—22no—
388C2×Dic3C2×C3×D412yes—
389C2×Dic3C2×C3×D412yes—
390C2×Dic3C2×C3×Q812yes—
391C2×Dic3C3×#4112yes—
392C4×D3—28no—
393C2×C32C2×C22⋊Q811yescharacteristic
394C2×C32#52511yescharacteristic
395C2×C32#52912yes—
396C2×C32#53211yescharacteristic
397C2×C32#53312yes—
398C3×D3—42no—
399C24—31no—
400C2×Q8—22no—
401C2×Q8—24no—
402C22×C4—31no—
403C22×C4—31no—
404C22×C4—34no—
405C22×C4—32no—
406C22×C4—31no—
407C22×C4—32no—
408C22×C4—62no—
409C22×C4—62no—
410C22×C4C22×C3×D311yescharacteristic
411C22×C4C22×C3×D311yescharacteristic
412C22×C4C22×C3×D312yes—
413C22×C4C22×C3×D311yescharacteristic
414C22×C4C22×C3×D312yes—
415C4⋊C4—22no—
416C4⋊C4—24no—
417C4⋊C4—62no—
418C4⋊C4—64no—
419C4⋊C4—62no—
420C4⋊C4—64no—
421C4⋊C4—64no—
422C22⋊C4—62no—
423C22⋊C4—62no—
424C22⋊C4—64no—
425C22⋊C4—64no—
426C42—34no—
427C42—62no—
428C42—64no—
429C42—64no—
430C22×C3—21no—
431C22×C3—22no—
432C22×C3—21no—
433C22×C3—22no—
434C22×C3—21no—
435C22×C3—64no—
436C22×C3—62no—
437C22×C3—121no—
438C22×C3—121no—
439C22×C3—122no—
440C22×C3C2×D3×D411yescharacteristic
441C22×C3C2×#23712yes—
442C22×C3C2×D3×Q811yescharacteristic
443C22×C3C2×#23912yes—
444C22×C3D3×#4111yescharacteristic
445C22×C3C22×C3×D411yescharacteristic
446C22×C3C22×C3×Q811yescharacteristic
447C22×C3C2×C3×#4112yes—
448C22×C3C2×C3×#4112yes—
449C22×C3C2×C3×#4111yescharacteristic
450C2×D3—22no—
451C2×D3—24no—
452C2×D3—41no—
453C2×D3—42no—
454C2×D3—41no—
455C3×C4—22no—
456C3×C4—24no—
457C3×C4—22no—
458C3×C4—22no—
459C3×C4—24no—
460C3×C4—24no—
461C3×C4—24no—
462C3×C4—22no—
463C3×C4—34no—
464C3×C4—42no—
465C3×C4—44no—
466C3×C4—44no—
467C3×C4—42no—
468C3×C4—41no—
469C3×C4—41no—
470C3×C4—62no—
471C3×C4—81no—
472C3×C4—121no—
473C3×C4—122no—
474C3×C4—122no—
475Dic3—22no—
476Dic3—42no—
477Dic3—42no—
478Dic3—41no—
479Dic3C3×C22⋊Q814yes—
480C32#239611yescharacteristic, complemented, Sylow
481C23—32no—
482C23—61no—
483C23—62no—
484C23—62no—
485C23—61no—
486C23C23×C3×D311yescharacteristic
487Q8—28no—
488C2×C4—22no—
489C2×C4—21no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—22no—
497C2×C4—32no—
498C2×C4—32no—
499C2×C4—32no—
500C2×C4—32no—
501C2×C4—68no—
502C2×C4—62no—
503C2×C4—61no—
504C2×C4—62no—
505C2×C4—62no—
506C2×C4—62no—
507C2×C4—62no—
508C2×C4—62no—
509C2×C4—62no—
510C2×C4—62no—
511C2×C4C3×D3×D412yes—
512C2×C4C3×#23714yes—
513C2×C4C3×D3×Q812yes—
514C2×C4C3×#23914yes—
515C2×C3—21no—
516C2×C3—22no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—22no—
520C2×C3—122no—
521C2×C3#558611yescharacteristic
522C2×C3#562412yes—
523C2×C3D3×C22⋊Q811yescharacteristic
524C2×C3#572511yescharacteristic
525C2×C3#572812yes—
526C2×C3C2×C3×C22⋊Q811yescharacteristic
527C2×C3C3×#52511yescharacteristic
528C2×C3C3×#52912yes—
529C2×C3C3×#53211yescharacteristic
530C2×C3C3×#53312yes—
531D3—42no—
532C22—62no—
533C22—64no—
534C22—121no—
535C22—122no—
536C22—121no—
537C22C2×C3×D3×D411yescharacteristic
538C22C2×C3×#23712yes—
539C22C2×C3×D3×Q811yescharacteristic
540C22C2×C3×#23912yes—
541C22C3×D3×#4111yescharacteristic
542C4—22no—
543C4—24no—
544C4—24no—
545C4—22no—
546C4—34no—
547C4—41no—
548C4—62no—
549C4—122no—
550C4—121no—
551C4—122no—
552C3—21no—
553C3#7717011yescharacteristic, direct product factor
554C3C3×#239611yescharacteristic, complemented
555C2—122no—
556C2C3×#558611yescharacteristic
557C2C3×#562412yes—
558C2C3×D3×C22⋊Q811yescharacteristic
559C2C3×#572511yescharacteristic
560C2C3×#572812yes—
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×#395C2
socleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC3×#395D3
hypocenterC3C3×#2396
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#395

Complements

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

NH ≅ G/Ntype
1. C2×C3×Q8×Dic3C2semidirect
3. C32×#395C2semidirect
6. C3×#4986C2semidirect
7. C3×Dic3×C4⋊C4C2semidirect
10. C3×#4661C2semidirect
11. C3×#4649C2semidirect
13. #77170C3direct (N × H)
41. C2×Q8×Dic3C2×C3semidirect
48. C3×#395D3semidirect
49. C3×#395C2×C3semidirect
56. #4986C2×C3semidirect
57. Dic3×C4⋊C4C2×C3semidirect
60. #4661C2×C3semidirect
61. #4649C2×C3semidirect
77. C2×C3×C4×D3Q8semidirect
189. #395C3×D3semidirect
232. C2×C4×D3C3×Q8semidirect
480. C32#2396semidirect
553. C3#77170direct (N × H)
554. C3C3×#2396semidirect

Maximal subgroups

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

subgroupindex
C2×C3×Q8×Dic32
C2×C3×#8922
C32×#3952
C3×#52312
C3×#49942
C3×#49862
C3×Dic3×C4⋊C42
C3×#46772
C3×#46662
C3×#46612
C3×#46492
C3×#23963
#771703