Finite Group Databasebeta

← C3×#69420 #11773437

Subgroups — C3×#69420 #11773437

Order 1152.

1381 conjugacy classes of subgroups.

The subgroup lattice has 609 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4⋊Dic3C211yesmaximal, characteristic
2C22×C3×Dic3⋊C4C212yesmaximal
3C2×C32×#95C211yesmaximal, characteristic
4C2×C3×C3⋊#95C212yesmaximal
5C2×C3×C3⋊#95C211yesmaximal, characteristic
6C3×#1444—31nomaximal
7#69420C311yesmaximal, characteristic, direct product factor
8C23×C32×C4C2211yescharacteristic
9C23×C32×C4C2211yescharacteristic
10C23×C32×C4C2211yescharacteristic
11C23×C3×Dic3C2212yes—
12C23×C3×Dic3C2212yes—
13C2×C3×C4⋊Dic3—22no—
14C2×C3×C4⋊Dic3—24no—
15C2×C3×Dic3⋊C4—24no—
16C2×C3×Dic3⋊C4—24no—
17C2×C3×Dic3⋊C4—24no—
18C32×#95—22no—
19C3×C3⋊#95—24no—
20C3×C3⋊#95C414yescomplemented
21C22×C3×C4⋊C4—32no—
22C22×C3×C4⋊C4—31no—
23C22×C4⋊Dic3C2×C311yescharacteristic
24C22×Dic3⋊C4C2×C312yes—
25C2×C3×#95—21no—
26C2×C3×#95—31no—
27C2×C3×#95—32no—
28C2×C3×#95D311yescharacteristic
29C2×C3×#95C2×C311yescharacteristic
30C2×C3⋊#95C2×C312yes—
31C2×C3⋊#95C2×C311yescharacteristic
32C24×C32C2311yescharacteristic
33C22×C32×C4—22no—
34C22×C32×C4—22no—
35C22×C32×C4—21no—
36C22×C32×C4—21no—
37C22×C32×C4—22no—
38C22×C32×C4—22no—
39C22×C32×C4—22no—
40C22×C32×C4—21no—
41C22×C32×C4—21no—
42C22×C32×C4—22no—
43C22×C32×C4C2×C412yes—
44C22×C32×C4D412yes—
45C22×C32×C4D412yes—
46C22×C32×C4Q812yes—
47C22×C32×C4Q812yes—
48C22×C3×Dic3—22no—
49C22×C3×Dic3—22no—
50C22×C3×Dic3—22no—
51C22×C3×Dic3—22no—
52C22×C3×Dic3—22no—
53C22×C3×Dic3—22no—
54C22×C3×Dic3—22no—
55C22×C3×Dic3—22no—
56C22×C3×Dic3—22no—
57C22×C3×Dic3—22no—
58C22×C3×Dic3C2×C414yes—
59C22×C3×Dic3D414yes—
60C22×C3×Dic3D414yes—
61C22×C3×Dic3Q814yes—
62C3×C4⋊Dic3—28no—
63C3×Dic3⋊C4—216no—
64#1444—31noSylow
65C23×C3×C4—21no—
66C23×C3×C4—21no—
67C23×C3×C4—21no—
68C23×C3×C4—32no—
69C23×C3×C4—32no—
70C23×C3×C4C2×D311yescharacteristic
71C23×C3×C4C2×D311yescharacteristic
72C23×C3×C4C2×D311yescharacteristic
73C23×C3×C4C22×C311yescharacteristic
74C23×C3×C4C22×C311yescharacteristic
75C23×C3×C4C22×C311yescharacteristic
76C23×Dic3C22×C312yes—
77C23×Dic3C22×C312yes—
78C2×C3×C4⋊C4—64no—
79C2×C3×C4⋊C4—64no—
80C2×C3×C4⋊C4—64no—
81C2×C3×C4⋊C4—64no—
82C2×C3×C4⋊C4—62no—
83C2×C4⋊Dic3—22no—
84C2×C4⋊Dic3—24no—
85C2×Dic3⋊C4—24no—
86C2×Dic3⋊C4—24no—
87C2×Dic3⋊C4—24no—
88C3×#95—24no—
89C3×#95—22no—
90C3×#95—22no—
91C3×#95—34no—
92C3×#95—64no—
93C3⋊#95—24no—
94C3⋊#95C3×C414yescomplemented
95C23×C32C22×C411yescharacteristic
96C23×C32C2×D411yescharacteristic
97C23×C32C2×D412yes—
98C23×C32C2×D412yes—
99C23×C32C2×D411yescharacteristic
100C23×C32C2×Q811yescharacteristic
101C23×C32C2×Q811yescharacteristic
102C23×C32C2×Q812yes—
103C23×C32#4111yescharacteristic
104C23×C32#4111yescharacteristic
105C23×C32#4112yes—
106C2×C32×C4—22no—
107C2×C32×C4—22no—
108C2×C32×C4—24no—
109C2×C32×C4—22no—
110C2×C32×C4—24no—
111C2×C32×C4—22no—
112C2×C32×C4—24no—
113C2×C32×C4—24no—
114C2×C32×C4—41no—
115C2×C32×C4—42no—
116C2×C32×C4—42no—
117C2×C32×C4—41no—
118C2×C32×C4—41no—
119C2×C32×C4—41no—
120C2×C32×C4C4⋊C414yescomplemented
121C2×C3×Dic3—24no—
122C2×C3×Dic3—24no—
123C2×C3×Dic3—24no—
124C2×C3×Dic3—24no—
125C2×C3×Dic3—24no—
126C2×C3×Dic3—24no—
127C2×C3×Dic3—24no—
128C2×C3×Dic3—24no—
129C2×C3×Dic3—24no—
130C2×C3×Dic3—42no—
131C2×C3×Dic3—42no—
132C2×C3×Dic3—42no—
133C2×C3×Dic3—42no—
134C2×C3×Dic3C4⋊C418yescomplemented
135C22×C4⋊C4—32no—
136C22×C4⋊C4—31no—
137C2×#95—31no—
138C2×#95—32no—
139C2×#95C3×D311yescharacteristic
140C24×C3—21no—
141C24×C3C22×D311yescharacteristic
142C24×C3C23×C311yescharacteristic
143C22×C3×C4—22no—
144C22×C3×C4—22no—
145C22×C3×C4—22no—
146C22×C3×C4—22no—
147C22×C3×C4—22no—
148C22×C3×C4—22no—
149C22×C3×C4—22no—
150C22×C3×C4—22no—
151C22×C3×C4—21no—
152C22×C3×C4—21no—
153C22×C3×C4—22no—
154C22×C3×C4—22no—
155C22×C3×C4—22no—
156C22×C3×C4—22no—
157C22×C3×C4—21no—
158C22×C3×C4—21no—
159C22×C3×C4—22no—
160C22×C3×C4—21no—
161C22×C3×C4—21no—
162C22×C3×C4—22no—
163C22×C3×C4—22no—
164C22×C3×C4—21no—
165C22×C3×C4—21no—
166C22×C3×C4—22no—
167C22×C3×C4—22no—
168C22×C3×C4—22no—
169C22×C3×C4—22no—
170C22×C3×C4—22no—
171C22×C3×C4—22no—
172C22×C3×C4—34no—
173C22×C3×C4—34no—
174C22×C3×C4—34no—
175C22×C3×C4—34no—
176C22×C3×C4—42no—
177C22×C3×C4—42no—
178C22×C3×C4—42no—
179C22×C3×C4—42no—
180C22×C3×C4—42no—
181C22×C3×C4—42no—
182C22×C3×C4—62no—
183C22×C3×C4—62no—
184C22×C3×C4—62no—
185C22×C3×C4—62no—
186C22×C3×C4—62no—
187C22×C3×C4—62no—
188C22×C3×C4—62no—
189C22×C3×C4—62no—
190C22×C3×C4—62no—
191C22×C3×C4—62no—
192C22×C3×C4Dic612yes—
193C22×C3×C4Dic612yes—
194C22×C3×C4C4×D312yes—
195C22×C3×C4D1212yes—
196C22×C3×C4#6712yes—
197C22×C3×C4C2×C3×C412yes—
198C22×C3×C4C3×D412yes—
199C22×C3×C4C3×D412yes—
200C22×C3×C4C3×Q812yes—
201C22×C3×C4C3×Q812yes—
202C22×Dic3—22no—
203C22×Dic3—22no—
204C22×Dic3—22no—
205C22×Dic3—22no—
206C22×Dic3—22no—
207C22×Dic3—22no—
208C22×Dic3—22no—
209C22×Dic3—22no—
210C22×Dic3—22no—
211C22×Dic3—22no—
212C22×Dic3C2×C3×C414yes—
213C22×Dic3C3×D414yes—
214C22×Dic3C3×D414yes—
215C22×Dic3C3×Q814yes—
216C3×C4⋊C4—616no—
217C3×C4⋊C4—68no—
218C4⋊Dic3—28no—
219Dic3⋊C4—216no—
220C22×C32C2×C4⋊C412yes—
221C22×C32C2×C4⋊C411yescharacteristic
222C22×C32C4×D411yescharacteristic
223C22×C32C4×D412yes—
224C22×C32C4×Q811yescharacteristic
225C22×C32#12012yes—
226C22×C32#12011yescharacteristic
227C22×C32#12112yes—
228C22×C32#12111yescharacteristic
229C22×C32C22⋊Q812yes—
230C22×C32C22⋊Q812yes—
231C22×C32C22⋊Q812yes—
232C22×C32C22⋊Q812yes—
233C22×C32C22⋊Q811yescharacteristic
234C22×C32#12312yes—
235C22×C32#12311yescharacteristic
236C22×C32#12511yescharacteristic
237C22×C32#12512yes—
238C22×C32#12711yescharacteristic
239C22×C32C4⋊Q811yescharacteristic
240C22×C32C4⋊Q812yes—
241C22×C32C4⋊Q812yes—
242C22×C32C4⋊Q811yescharacteristic
243C32×C4—24no—
244C32×C4—42no—
245C32×C4—42no—
246C3×Dic3—28no—
247C3×Dic3—44no—
248C23×C4—32no—
249C23×C4—32no—
250C23×C4C2×C3×D311yescharacteristic
251C23×C4C2×C3×D311yescharacteristic
252C23×C4C2×C3×D311yescharacteristic
253C2×C4⋊C4—64no—
254C2×C4⋊C4—64no—
255C2×C4⋊C4—64no—
256C2×C4⋊C4—64no—
257C2×C4⋊C4—62no—
258#95—22no—
259#95—34no—
260#95—64no—
261C23×C3—21no—
262C23×C3—21no—
263C23×C3—21no—
264C23×C3—21no—
265C23×C3—21no—
266C23×C3—21no—
267C23×C3—22no—
268C23×C3—22no—
269C23×C3—22no—
270C23×C3—22no—
271C23×C3—21no—
272C23×C3C2×Dic611yescharacteristic
273C23×C3C2×Dic611yescharacteristic
274C23×C3C2×C4×D311yescharacteristic
275C23×C3C2×D1211yescharacteristic
276C23×C3#23511yescharacteristic
277C23×C3#23511yescharacteristic
278C23×C3D3×D412yes—
279C23×C3D3×D412yes—
280C23×C3#23712yes—
281C23×C3D3×Q812yes—
282C23×C3C2×#6711yescharacteristic
283C23×C3C22×C3×C411yescharacteristic
284C23×C3C2×C3×D411yescharacteristic
285C23×C3C2×C3×D412yes—
286C23×C3C2×C3×D412yes—
287C23×C3C2×C3×D411yescharacteristic
288C23×C3C2×C3×Q811yescharacteristic
289C23×C3C2×C3×Q811yescharacteristic
290C23×C3C2×C3×Q812yes—
291C23×C3C3×#4111yescharacteristic
292C23×C3C3×#4111yescharacteristic
293C23×C3C3×#4112yes—
294C2×C3×C4—24no—
295C2×C3×C4—24no—
296C2×C3×C4—22no—
297C2×C3×C4—22no—
298C2×C3×C4—24no—
299C2×C3×C4—22no—
300C2×C3×C4—24no—
301C2×C3×C4—22no—
302C2×C3×C4—24no—
303C2×C3×C4—24no—
304C2×C3×C4—24no—
305C2×C3×C4—24no—
306C2×C3×C4—22no—
307C2×C3×C4—22no—
308C2×C3×C4—24no—
309C2×C3×C4—22no—
310C2×C3×C4—24no—
311C2×C3×C4—22no—
312C2×C3×C4—24no—
313C2×C3×C4—38no—
314C2×C3×C4—44no—
315C2×C3×C4—44no—
316C2×C3×C4—42no—
317C2×C3×C4—42no—
318C2×C3×C4—44no—
319C2×C3×C4—44no—
320C2×C3×C4—44no—
321C2×C3×C4—44no—
322C2×C3×C4—42no—
323C2×C3×C4—42no—
324C2×C3×C4—42no—
325C2×C3×C4—42no—
326C2×C3×C4—42no—
327C2×C3×C4—42no—
328C2×C3×C4—41no—
329C2×C3×C4—41no—
330C2×C3×C4—41no—
331C2×C3×C4—41no—
332C2×C3×C4—41no—
333C2×C3×C4—42no—
334C2×C3×C4—42no—
335C2×C3×C4—41no—
336C2×C3×C4—41no—
337C2×C3×C4—41no—
338C2×C3×C4—64no—
339C2×C3×C4—64no—
340C2×C3×C4—64no—
341C2×C3×C4—64no—
342C2×C3×C4—64no—
343C2×C3×C4—64no—
344C2×C3×C4—64no—
345C2×C3×C4—64no—
346C2×C3×C4—64no—
347C2×C3×C4—122no—
348C2×C3×C4—122no—
349C2×C3×C4—122no—
350C2×C3×C4—122no—
351C2×C3×C4Dic3⋊C414yescomplemented
352C2×C3×C4C3×C4⋊C414yescomplemented
353C2×Dic3—24no—
354C2×Dic3—24no—
355C2×Dic3—24no—
356C2×Dic3—24no—
357C2×Dic3—24no—
358C2×Dic3—24no—
359C2×Dic3—24no—
360C2×Dic3—24no—
361C2×Dic3—24no—
362C2×Dic3—42no—
363C2×Dic3—42no—
364C2×Dic3—42no—
365C2×Dic3—42no—
366C2×Dic3C3×C4⋊C418yescomplemented
367C2×C32#38411yescharacteristic
368C2×C32#38512yes—
369C2×C32#38511yescharacteristic
370C2×C32#38912yes—
371C2×C32#38911yescharacteristic
372C2×C32#39211yescharacteristic
373C2×C32#39512yes—
374C2×C32#39511yescharacteristic
375C2×C32#39812yes—
376C2×C32#39811yescharacteristic
377C2×C32#39911yescharacteristic
378C24C22×C3×D311yescharacteristic
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—34no—
390C22×C4—34no—
391C22×C4—34no—
392C22×C4—34no—
393C22×C4—62no—
394C22×C4—62no—
395C22×C4—62no—
396C22×C4—62no—
397C22×C4—62no—
398C22×C4—62no—
399C22×C4—62no—
400C22×C4—62no—
401C22×C4—62no—
402C22×C4—62no—
403C22×C4C3×Dic612yes—
404C22×C4C3×Dic612yes—
405C22×C4C3×C4×D312yes—
406C22×C4C3×D1212yes—
407C22×C4C3×#6712yes—
408C4⋊C4—616no—
409C4⋊C4—68no—
410C22×C3—22no—
411C22×C3—22no—
412C22×C3—22no—
413C22×C3—22no—
414C22×C3—22no—
415C22×C3—22no—
416C22×C3—22no—
417C22×C3—22no—
418C22×C3—22no—
419C22×C3—22no—
420C22×C3—22no—
421C22×C3—22no—
422C22×C3—21no—
423C22×C3—21no—
424C22×C3—21no—
425C22×C3—21no—
426C22×C3—21no—
427C22×C3—21no—
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3C4×Dic611yescharacteristic
434C22×C3#86911yescharacteristic
435C22×C3#87011yescharacteristic
436C22×C3C4×D1211yescharacteristic
437C22×C3#87812yes—
438C22×C3#87812yes—
439C22×C3#67⋊C412yes—
440C22×C3#88212yes—
441C22×C3#88312yes—
442C22×C3#88412yes—
443C22×C3#88812yes—
444C22×C3#88812yes—
445C22×C3#88912yes—
446C22×C3D3×C4⋊C412yes—
447C22×C3#89612yes—
448C22×C3#89712yes—
449C22×C3C2×Dic3⋊C411yescharacteristic
450C22×C3#92411yescharacteristic
451C22×C3#93011yescharacteristic
452C22×C3#93511yescharacteristic
453C22×C3#93711yescharacteristic
454C22×C3#94011yescharacteristic
455C22×C3#94411yescharacteristic
456C22×C3C2×C3×C4⋊C412yes—
457C22×C3C2×C3×C4⋊C411yescharacteristic
458C22×C3C3×C4×D412yes—
459C22×C3C3×C4×D411yescharacteristic
460C22×C3C3×C4×Q811yescharacteristic
461C22×C3C3×#12012yes—
462C22×C3C3×#12011yescharacteristic
463C22×C3C3×#12112yes—
464C22×C3C3×#12111yescharacteristic
465C22×C3C3×C22⋊Q812yes—
466C22×C3C3×C22⋊Q812yes—
467C22×C3C3×C22⋊Q812yes—
468C22×C3C3×C22⋊Q812yes—
469C22×C3C3×C22⋊Q811yescharacteristic
470C22×C3C3×#12312yes—
471C22×C3C3×#12311yescharacteristic
472C22×C3C3×#12512yes—
473C22×C3C3×#12511yescharacteristic
474C22×C3C3×#12711yescharacteristic
475C22×C3C3×C4⋊Q812yes—
476C22×C3C3×C4⋊Q812yes—
477C22×C3C3×C4⋊Q811yescharacteristic
478C22×C3C3×C4⋊Q811yescharacteristic
479C3×C4—24no—
480C3×C4—24no—
481C3×C4—44no—
482C3×C4—44no—
483C3×C4—44no—
484C3×C4—42no—
485C3×C4—42no—
486C3×C4—42no—
487C3×C4—42no—
488C3×C4—68no—
489C3×C4—124no—
490Dic3—28no—
491Dic3—44no—
492C32#144411yescharacteristic, complemented, Sylow
493C23C2×C3×Dic611yescharacteristic
494C23C2×C3×Dic611yescharacteristic
495C23C2×C3×C4×D311yescharacteristic
496C23C2×C3×D1211yescharacteristic
497C23C3×#23511yescharacteristic
498C23C3×#23511yescharacteristic
499C23C3×D3×D412yes—
500C23C3×D3×D412yes—
501C23C3×#23712yes—
502C23C3×D3×Q812yes—
503C23C2×C3×#6711yescharacteristic
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—38no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—64no—
520C2×C4—64no—
521C2×C4—64no—
522C2×C4—64no—
523C2×C4—64no—
524C2×C4—64no—
525C2×C4—64no—
526C2×C4—64no—
527C2×C4—64no—
528C2×C4—122no—
529C2×C4—122no—
530C2×C4—122no—
531C2×C4—122no—
532C2×C4C3×Dic3⋊C414yescomplemented
533C2×C3—22no—
534C2×C3—22no—
535C2×C3—22no—
536C2×C3—22no—
537C2×C3—21no—
538C2×C3—21no—
539C2×C3—21no—
540C2×C3—21no—
541C2×C3—21no—
542C2×C3—21no—
543C2×C3—21no—
544C2×C3#464712yes—
545C2×C3#465612yes—
546C2×C3#465712yes—
547C2×C3#466812yes—
548C2×C3#492811yescharacteristic
549C2×C3#494611yescharacteristic
550C2×C3#494911yescharacteristic
551C2×C3#496011yescharacteristic
552C2×C3#497511yescharacteristic
553C2×C3#497911yescharacteristic
554C2×C3#498111yescharacteristic
555C2×C3C3×#38411yescharacteristic
556C2×C3C3×#38512yes—
557C2×C3C3×#38511yescharacteristic
558C2×C3C3×#38912yes—
559C2×C3C3×#38911yescharacteristic
560C2×C3C3×#39211yescharacteristic
561C2×C3C3×#39512yes—
562C2×C3C3×#39511yescharacteristic
563C2×C3C3×#39812yes—
564C2×C3C3×#39811yescharacteristic
565C2×C3C3×#39911yescharacteristic
566C22C3×C4×Dic611yescharacteristic
567C22C3×#86911yescharacteristic
568C22C3×#87011yescharacteristic
569C22C3×C4×D1211yescharacteristic
570C22C3×#87812yes—
571C22C3×#87812yes—
572C22C3×#67⋊C412yes—
573C22C3×#88212yes—
574C22C3×#88312yes—
575C22C3×#88412yes—
576C22C3×#88812yes—
577C22C3×#88812yes—
578C22C3×#88912yes—
579C22C3×D3×C4⋊C412yes—
580C22C3×#89612yes—
581C22C3×#89712yes—
582C22C2×C3×Dic3⋊C411yescharacteristic
583C22C3×#92411yescharacteristic
584C22C3×#93011yescharacteristic
585C22C3×#93511yescharacteristic
586C22C3×#93711yescharacteristic
587C22C3×#94011yescharacteristic
588C22C3×#94411yescharacteristic
589C4—24no—
590C4—42no—
591C4—42no—
592C4—68no—
593C4—124no—
594C3—21no—
595C3#6942011yescharacteristic, direct product factor
596C3C3×#144411yescharacteristic, complemented
597C2C3×#464712yes—
598C2C3×#465612yes—
599C2C3×#465712yes—
600C2C3×#466812yes—
601C2C3×#492811yescharacteristic
602C2C3×#494611yescharacteristic
603C2C3×#494911yescharacteristic
604C2C3×#496011yescharacteristic
605C2C3×#497511yescharacteristic
606C2C3×#497911yescharacteristic
607C2C3×#498111yescharacteristic
subgroupG/H
centerC24×C3C22×D3
commutatorC23×C3C22×C3×C4
FrattiniC24C22×C3×D3
FittingC2×C32×#95C2
socle, prime radicalC24×C32C23
cosocleC24×C3C23×C3
hypercenterC2×C3×#95D3
hypocenterC3C3×#1444
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24×C3 ◁ C2×C3×#95

Complements

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

NH ≅ G/Ntype
7. #69420C3direct (N × H)
20. C3×C3⋊#95C4semidirect
94. C3⋊#95C3×C4semidirect
120. C2×C32×C4C4⋊C4semidirect
134. C2×C3×Dic3C4⋊C4semidirect
351. C2×C3×C4Dic3⋊C4semidirect
352. C2×C3×C4C3×C4⋊C4semidirect
366. C2×Dic3C3×C4⋊C4semidirect
492. C32#1444semidirect
532. C2×C4C3×Dic3⋊C4semidirect
595. C3#69420direct (N × H)
596. C3C3×#1444semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C4⋊Dic32
C22×C3×Dic3⋊C42
C2×C32×#952
C2×C3×C3⋊#952
C3×#14443
#694203