Finite Group Databasebeta

← C3×#76293 #11802523

Subgroups — C3×#76293 #11802523

Order 1152.

1977 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×#940C211yesmaximal, characteristic
2C2×C3×D4×Dic3C211yesmaximal, characteristic, complemented
3C2×C3×#893C211yesmaximal, characteristic, complemented
4C2×C3×#67⋊C4C214yesmaximal, complemented
5C32×#390C211yesmaximal, characteristic, complemented
6C3×#4975C211yesmaximal, characteristic, complemented
7C3×#4957C214yesmaximal, complemented
8C3×#4939C211yesmaximal, characteristic, complemented
9C3×C42×Dic3C211yesmaximal, characteristic, complemented
10C3×C4×#127—31nomaximal
11#76293C311yesmaximal, characteristic, direct product factor
12C22×C32×D4C2211yescharacteristic
13C22×C3×#67C2214yes—
14C23×C3×Dic3C2212yes—
15C22×C3×D12C2211yescharacteristic
16C22×C3×C4×D3C2212yes—
17C2×C32×C4⋊C4C2211yescharacteristic
18C2×C32×C22⋊C4C2214yes—
19C2×C32×C42C2211yescharacteristic
20C2×C3×#217C2212yes—
21C3×#940C418yescomplemented
22C3×D4×Dic3—24no—
23C2×C3×(C2×D3)⋊C4C2212yes—
24C2×C3×(C2×D3)⋊C4C2214yes—
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×Dic3⋊C4C2214yes—
27C2×C3×C4×Dic3C2212yes—
28C2×C3×C4×Dic3C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30C2×C3×C4×Dic3C2212yes—
31C3×#893—24no—
32C3×#67⋊C4—216no—
33C2×C3×#127—31no—
34C2×C3×C4×D4—31no—
35C2×C3×C4×D4—31no—
36C2×C3×C4×D4—34no—
37C2×#940C2×C311yescharacteristic
38C2×D4×Dic3C2×C311yescharacteristic, complemented
39C2×#893C2×C311yescharacteristic, complemented
40C2×#67⋊C4C2×C314yescomplemented
41C3×#390—21no—
42C3×#390—34no—
43C3×#390—31no—
44C3×#390D311yescharacteristic, complemented
45C3×#390C2×C311yescharacteristic, complemented
46C3×#384—31no—
47C3×C43—31no—
48#4975C2×C311yescharacteristic, complemented
49#4957C2×C314yescomplemented
50#4939C2×C311yescharacteristic, complemented
51C42×Dic3C2×C311yescharacteristic, complemented
52C24×C32C2312yes—
53C23×C3×D3C2312yes—
54C2×C32×D4—22no—
55C2×C32×D4—22no—
56C2×C32×D4C2×C414yescomplemented
57C22×C32×C4C2312yes—
58C22×C32×C4C2312yes—
59C22×C32×C4C2311yescharacteristic
60C2×C3×#67—28no—
61C2×C3×#67—28no—
62C2×C3×#67C2×C4116yescomplemented
63C22×C3×Dic3—28no—
64C22×C3×Dic3—24no—
65C22×C3×Dic3C2312yes—
66C22×C3×Dic3C2311yescharacteristic
67C22×C3×Dic3C2312yes—
68C22×C3×Dic3C2311yescharacteristic
69C2×C3×D12—22no—
70C2×C3×D12—22no—
71C2×C3×D12C2×C414yescomplemented
72C2×C3×C4×D3—28no—
73C2×C3×C4×D3—24no—
74C32×C4⋊C4—22no—
75C32×C22⋊C4—28no—
76C32×C42—22no—
77C3×#217—24no—
78C3×(C2×D3)⋊C4—28no—
79C3×(C2×D3)⋊C4—24no—
80C3×C4⋊Dic3—22no—
81C3×Dic3⋊C4—28no—
82C3×C4×Dic3—24no—
83C3×C4×Dic3C2×C414yescomplemented
84C3×C4×Dic3D418yescomplemented
85C3×C4×Dic3D414yescomplemented
86C4×#127—31noSylow
87C22×C3×D4—21no—
88C22×C3×D4—34no—
89C22×C3×D4—31no—
90C22×C3×D4C2×D311yescharacteristic
91C22×C3×D4C22×C311yescharacteristic
92C23×C3×C4—32no—
93C23×C3×C4—32no—
94C22×#67C22×C314yes—
95C23×Dic3C22×C312yes—
96C22×D12C22×C311yescharacteristic
97C22×C4×D3C22×C312yes—
98C3×#127—38no—
99C3×C4×D4—616no—
100C3×C4×D4—64no—
101C3×C4×D4—64no—
102C2×C3×C4⋊C4—21no—
103C2×C3×C4⋊C4—34no—
104C2×C3×C4⋊C4—31no—
105C2×C3×C4⋊C4C2×D311yescharacteristic
106C2×C3×C4⋊C4C22×C311yescharacteristic
107C2×C3×C22⋊C4—24no—
108C2×C3×C22⋊C4—32no—
109C2×C3×C22⋊C4—32no—
110C2×C3×C22⋊C4—34no—
111C2×C3×C22⋊C4C2×D314yes—
112C2×C3×C22⋊C4C22×C314yes—
113C2×C3×C42—21no—
114C2×C3×C42—31no—
115C2×C3×C42—32no—
116C2×C3×C42—31no—
117C2×C3×C42—32no—
118C2×C3×C42C2×D311yescharacteristic
119C2×C3×C42C22×C311yescharacteristic
120C2×#217C22×C312yes—
121#940C3×C418yescomplemented
122D4×Dic3—24no—
123C2×(C2×D3)⋊C4C22×C314yes—
124C2×(C2×D3)⋊C4C22×C312yes—
125C2×C4⋊Dic3C22×C311yescharacteristic
126C2×Dic3⋊C4C22×C314yes—
127C2×C4×Dic3C22×C312yes—
128C2×C4×Dic3C22×C311yescharacteristic
129C2×C4×Dic3C22×C312yes—
130C2×C4×Dic3C22×C311yescharacteristic
131#893—24no—
132#67⋊C4—216no—
133C23×C32—22no—
134C23×C32—24no—
135C23×C32—24no—
136C23×C32—22no—
137C23×C32C22×C414yes—
138C23×C32C2411yescharacteristic
139C22×C3×D3—22no—
140C22×C3×D3—24no—
141C22×C3×D3—22no—
142C22×C3×D3—24no—
143C22×C3×D3C22×C414yes—
144C32×D4—28no—
145C2×C32×C4—22no—
146C2×C32×C4—22no—
147C2×C32×C4—24no—
148C2×C32×C4—22no—
149C2×C32×C4C22×C412yes—
150C2×C32×C4C2×D414yes—
151C2×C32×C4C2×D412yes—
152C2×C32×C4#4112yes—
153C3×#67—232no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3—24no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—48no—
158C2×C3×Dic3C22×C414yes—
159C2×C3×Dic3C2×D412yes—
160C2×C3×Dic3C2×D414yes—
161C2×C3×Dic3C2×D414yes—
162C2×C3×Dic3C2×D412yes—
163C2×C3×Dic3#4114yes—
164C3×D12—28no—
165C3×C4×D3—48no—
166C2×#127—31no—
167C2×C4×D4—31no—
168C2×C4×D4—31no—
169C2×C4×D4—34no—
170#390—34no—
171#390—31no—
172#390C3×D311yescharacteristic, complemented
173#384—31no—
174C43—31no—
175C24×C3—22no—
176C24×C3—32no—
177C24×C3C22×D312yes—
178C24×C3C23×C312yes—
179C23×D3C23×C312yes—
180C2×C3×D4—22no—
181C2×C3×D4—22no—
182C2×C3×D4—22no—
183C2×C3×D4—22no—
184C2×C3×D4—24no—
185C2×C3×D4—316no—
186C2×C3×D4—34no—
187C2×C3×D4—42no—
188C2×C3×D4—42no—
189C2×C3×D4—68no—
190C2×C3×D4—68no—
191C2×C3×D4—62no—
192C2×C3×D4—62no—
193C2×C3×D4C4×D314yescomplemented
194C2×C3×D4C2×C3×C414yescomplemented
195C22×C3×C4—21no—
196C22×C3×C4—22no—
197C22×C3×C4—22no—
198C22×C3×C4—32no—
199C22×C3×C4—31no—
200C22×C3×C4—31no—
201C22×C3×C4—32no—
202C22×C3×C4—68no—
203C22×C3×C4—64no—
204C22×C3×C4—68no—
205C22×C3×C4—64no—
206C22×C3×C4C22×D312yes—
207C22×C3×C4C22×D312yes—
208C22×C3×C4C22×D311yescharacteristic
209C22×C3×C4C23×C312yes—
210C22×C3×C4C23×C312yes—
211C22×C3×C4C23×C311yescharacteristic
212C2×#67—28no—
213C2×#67—28no—
214C2×#67C2×C3×C4116yescomplemented
215C22×Dic3—28no—
216C22×Dic3—24no—
217C22×Dic3C23×C312yes—
218C22×Dic3C23×C311yescharacteristic
219C22×Dic3C23×C312yes—
220C22×Dic3C23×C311yescharacteristic
221C2×D12—22no—
222C2×D12—22no—
223C2×D12C2×C3×C414yescomplemented
224C2×C4×D3—28no—
225C2×C4×D3—24no—
226C3×C4⋊C4—22no—
227C3×C4⋊C4—22no—
228C3×C4⋊C4—42no—
229C3×C4⋊C4—68no—
230C3×C4⋊C4—62no—
231C3×C22⋊C4—28no—
232C3×C22⋊C4—28no—
233C3×C22⋊C4—48no—
234C3×C22⋊C4—64no—
235C3×C22⋊C4—64no—
236C3×C22⋊C4—68no—
237C3×C42—22no—
238C3×C42—22no—
239C3×C42—34no—
240C3×C42—38no—
241C3×C42—34no—
242C3×C42—42no—
243C3×C42—64no—
244#217—24no—
245(C2×D3)⋊C4—28no—
246(C2×D3)⋊C4—24no—
247C4⋊Dic3—22no—
248Dic3⋊C4—28no—
249C4×Dic3—24no—
250C4×Dic3C2×C3×C414yescomplemented
251C4×Dic3C3×D418yescomplemented
252C4×Dic3C3×D414yescomplemented
253C22×C32—28no—
254C22×C32—24no—
255C22×C32—42no—
256C22×C32—42no—
257C22×C32—44no—
258C22×C32C23×C411yescharacteristic
259C22×C32C22×D411yescharacteristic
260C22×C32C22×D412yes—
261C22×C32C2×#4111yescharacteristic
262C22×C32C2×#4112yes—
263C2×C3×D3—24no—
264C2×C3×D3—28no—
265C2×C3×D3—42no—
266C2×C3×D3—42no—
267C2×C3×D3—44no—
268C32×C4—24no—
269C32×C4—42no—
270C32×C4C4×D414yescomplemented
271C3×Dic3—22no—
272C3×Dic3—42no—
273C3×Dic3C4×D418yescomplemented
274C3×Dic3#12714yescomplemented
275C22×D4—34no—
276C22×D4—31no—
277C22×D4C2×C3×D311yescharacteristic
278C23×C4—32no—
279C23×C4—32no—
280#127—38no—
281C4×D4—616no—
282C4×D4—64no—
283C4×D4—64no—
284C2×C4⋊C4—34no—
285C2×C4⋊C4—31no—
286C2×C4⋊C4C2×C3×D311yescharacteristic
287C2×C22⋊C4—32no—
288C2×C22⋊C4—32no—
289C2×C22⋊C4—34no—
290C2×C22⋊C4C2×C3×D314yes—
291C2×C42—32no—
292C2×C42—31no—
293C2×C42—31no—
294C2×C42—32no—
295C2×C42C2×C3×D311yescharacteristic
296C23×C3—24no—
297C23×C3—22no—
298C23×C3—22no—
299C23×C3—24no—
300C23×C3—22no—
301C23×C3—24no—
302C23×C3—24no—
303C23×C3—22no—
304C23×C3—21no—
305C23×C3—24no—
306C23×C3—34no—
307C23×C3—44no—
308C23×C3—42no—
309C23×C3—42no—
310C23×C3—44no—
311C23×C3—62no—
312C23×C3—64no—
313C23×C3—62no—
314C23×C3—64no—
315C23×C3C2×C4×D314yes—
316C23×C3C22×C3×C414yes—
317C23×C3C23×D311yescharacteristic
318C23×C3C24×C311yescharacteristic
319C22×D3—22no—
320C22×D3—24no—
321C22×D3—22no—
322C22×D3—24no—
323C22×D3C22×C3×C414yes—
324C3×D4—28no—
325C3×D4—28no—
326C3×D4—48no—
327C3×D4—632no—
328C3×D4—68no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—22no—
333C2×C3×C4—24no—
334C2×C3×C4—22no—
335C2×C3×C4—24no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—24no—
340C2×C3×C4—22no—
341C2×C3×C4—34no—
342C2×C3×C4—34no—
343C2×C3×C4—32no—
344C2×C3×C4—34no—
345C2×C3×C4—34no—
346C2×C3×C4—32no—
347C2×C3×C4—42no—
348C2×C3×C4—42no—
349C2×C3×C4—44no—
350C2×C3×C4—42no—
351C2×C3×C4—62no—
352C2×C3×C4—62no—
353C2×C3×C4—64no—
354C2×C3×C4—128no—
355C2×C3×C4—128no—
356C2×C3×C4C2×C4×D312yes—
357C2×C3×C4D3×D414yes—
358C2×C3×C4D3×D412yes—
359C2×C3×C4#23712yes—
360C2×C3×C4C22×C3×C412yes—
361C2×C3×C4C2×C3×D414yes—
362C2×C3×C4C2×C3×D412yes—
363C2×C3×C4C3×#4112yes—
364#67—232no—
365C2×Dic3—22no—
366C2×Dic3—24no—
367C2×Dic3—22no—
368C2×Dic3—48no—
369C2×Dic3C22×C3×C414yes—
370C2×Dic3C2×C3×D412yes—
371C2×Dic3C2×C3×D414yes—
372C2×Dic3C2×C3×D414yes—
373C2×Dic3C2×C3×D412yes—
374C2×Dic3C3×#4114yes—
375D12—28no—
376C4×D3—48no—
377C2×C32—44no—
378C2×C32C2×C4×D411yescharacteristic
379C2×C32C2×C4×D412yes—
380C2×C32C2×#12711yescharacteristic
381C2×C32#53211yescharacteristic
382C2×C32#53212yes—
383C3×D3—44no—
384C24—32no—
385C24C22×C3×D312yes—
386C2×D4—22no—
387C2×D4—22no—
388C2×D4—316no—
389C2×D4—34no—
390C2×D4—68no—
391C2×D4—68no—
392C2×D4—62no—
393C2×D4—62no—
394C2×D4C3×C4×D314yescomplemented
395C22×C4—32no—
396C22×C4—31no—
397C22×C4—31no—
398C22×C4—32no—
399C22×C4—68no—
400C22×C4—64no—
401C22×C4—68no—
402C22×C4—64no—
403C22×C4C22×C3×D312yes—
404C22×C4C22×C3×D312yes—
405C22×C4C22×C3×D311yescharacteristic
406C4⋊C4—22no—
407C4⋊C4—68no—
408C4⋊C4—62no—
409C22⋊C4—28no—
410C22⋊C4—64no—
411C22⋊C4—64no—
412C22⋊C4—68no—
413C42—22no—
414C42—34no—
415C42—38no—
416C42—34no—
417C42—64no—
418C22×C3—24no—
419C22×C3—28no—
420C22×C3—28no—
421C22×C3—24no—
422C22×C3—21no—
423C22×C3—22no—
424C22×C3—21no—
425C22×C3—21no—
426C22×C3—22no—
427C22×C3—44no—
428C22×C3—48no—
429C22×C3—42no—
430C22×C3—42no—
431C22×C3—44no—
432C22×C3—42no—
433C22×C3—44no—
434C22×C3—42no—
435C22×C3—64no—
436C22×C3—68no—
437C22×C3—84no—
438C22×C3—82no—
439C22×C3—82no—
440C22×C3—122no—
441C22×C3—122no—
442C22×C3—124no—
443C22×C3C22×C4×D311yescharacteristic
444C22×C3C2×D3×D411yescharacteristic
445C22×C3C2×D3×D412yes—
446C22×C3C2×#23711yescharacteristic
447C22×C3D3×#4112yes—
448C22×C3C23×C3×C411yescharacteristic
449C22×C3C22×C3×D412yes—
450C22×C3C22×C3×D411yescharacteristic
451C22×C3C2×C3×#4111yescharacteristic
452C22×C3C2×C3×#4112yes—
453C2×D3—24no—
454C2×D3—28no—
455C2×D3—42no—
456C2×D3—44no—
457C2×D3—42no—
458C3×C4—24no—
459C3×C4—24no—
460C3×C4—24no—
461C3×C4—34no—
462C3×C4—38no—
463C3×C4—44no—
464C3×C4—42no—
465C3×C4—42no—
466C3×C4—62no—
467C3×C4—82no—
468C3×C4—122no—
469C3×C4#67⋊C414yescomplemented
470C3×C4C3×C4×D414yescomplemented
471Dic3—22no—
472Dic3—42no—
473Dic3C3×C4×D418yescomplemented
474Dic3C3×#12714yescomplemented
475C32C4×#12711yescharacteristic, complemented, Sylow
476C23—24no—
477C23—22no—
478C23—22no—
479C23—24no—
480C23—34no—
481C23—64no—
482C23—62no—
483C23—62no—
484C23—64no—
485C23C2×C3×C4×D314yes—
486C23C23×C3×D311yescharacteristic
487D4—28no—
488D4—632no—
489D4—68no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—24no—
493C2×C4—22no—
494C2×C4—34no—
495C2×C4—34no—
496C2×C4—34no—
497C2×C4—32no—
498C2×C4—34no—
499C2×C4—32no—
500C2×C4—62no—
501C2×C4—64no—
502C2×C4—62no—
503C2×C4—128no—
504C2×C4—128no—
505C2×C4C2×C3×C4×D312yes—
506C2×C4C3×D3×D414yes—
507C2×C4C3×D3×D412yes—
508C2×C4C3×#23712yes—
509C2×C3—22no—
510C2×C3—22no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—44no—
515C2×C3—44no—
516C2×C3—84no—
517C2×C3—124no—
518C2×C3C2×#67⋊C411yescharacteristic
519C2×C3C4×D3×D412yes—
520C2×C3#559612yes—
521C2×C3#566811yescharacteristic
522C2×C3D3×#12711yescharacteristic
523C2×C3C2×C3×C4×D412yes—
524C2×C3C2×C3×C4×D411yescharacteristic
525C2×C3C2×C3×#12711yescharacteristic
526C2×C3C3×#53212yes—
527C2×C3C3×#53211yescharacteristic
528D3—44no—
529C22—28no—
530C22—24no—
531C22—44no—
532C22—42no—
533C22—42no—
534C22—68no—
535C22—64no—
536C22—124no—
537C22—122no—
538C22—122no—
539C22C22×C3×C4×D311yescharacteristic
540C22C2×C3×D3×D412yes—
541C22C2×C3×D3×D411yescharacteristic
542C22C2×C3×#23711yescharacteristic
543C22C3×D3×#4112yes—
544C4—24no—
545C4—38no—
546C4—34no—
547C4—42no—
548C4—62no—
549C4—122no—
550C4C3×#67⋊C414yescomplemented
551C3—21no—
552C3#7629311yescharacteristic, direct product factor
553C3C3×C4×#12711yescharacteristic, complemented
554C2—44no—
555C2—124no—
556C2C2×C3×#67⋊C411yescharacteristic
557C2C3×C4×D3×D412yes—
558C2C3×#559612yes—
559C2C3×#566811yescharacteristic
560C2C3×D3×#12711yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×#390C2
socleC23×C32C24
prime radicalC2×C3×#940C2
cosocleC23×C3C24×C3
hypercenterC3×#390D3
hypocenterC3C3×C4×#127
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#390

Complements

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

NH ≅ G/Ntype
2. C2×C3×D4×Dic3C2semidirect
3. C2×C3×#893C2semidirect
4. C2×C3×#67⋊C4C2semidirect
5. C32×#390C2semidirect
6. C3×#4975C2semidirect
7. C3×#4957C2semidirect
8. C3×#4939C2semidirect
9. C3×C42×Dic3C2semidirect
11. #76293C3direct (N × H)
21. C3×#940C4semidirect
38. C2×D4×Dic3C2×C3semidirect
39. C2×#893C2×C3semidirect
40. C2×#67⋊C4C2×C3semidirect
44. C3×#390D3semidirect
45. C3×#390C2×C3semidirect
48. #4975C2×C3semidirect
49. #4957C2×C3semidirect
50. #4939C2×C3semidirect
51. C42×Dic3C2×C3semidirect
56. C2×C32×D4C2×C4semidirect
62. C2×C3×#67C2×C4semidirect
71. C2×C3×D12C2×C4semidirect
83. C3×C4×Dic3C2×C4semidirect
84. C3×C4×Dic3D4semidirect
85. C3×C4×Dic3D4semidirect
121. #940C3×C4semidirect
172. #390C3×D3semidirect
193. C2×C3×D4C4×D3semidirect
194. C2×C3×D4C2×C3×C4semidirect
214. C2×#67C2×C3×C4semidirect
223. C2×D12C2×C3×C4semidirect
250. C4×Dic3C2×C3×C4semidirect
251. C4×Dic3C3×D4semidirect
252. C4×Dic3C3×D4semidirect
270. C32×C4C4×D4semidirect
273. C3×Dic3C4×D4semidirect
274. C3×Dic3#127semidirect
394. C2×D4C3×C4×D3semidirect
469. C3×C4#67⋊C4semidirect
470. C3×C4C3×C4×D4semidirect
473. Dic3C3×C4×D4semidirect
474. Dic3C3×#127semidirect
475. C32C4×#127semidirect
550. C4C3×#67⋊C4semidirect
552. C3#76293direct (N × H)
553. C3C3×C4×#127semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9402
C2×C3×D4×Dic32
C2×C3×#8932
C2×C3×#67⋊C42
C32×#3902
C3×#49752
C3×#49572
C3×#49392
C3×C42×Dic32
C3×C4×#1273
#762933