Finite Group Databasebeta

← C3×#71568 #11773434

Subgroups — C3×#71568 #11773434

Order 1152.

1425 conjugacy classes of subgroups.

The subgroup lattice has 603 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×C4⋊C4C211yesmaximal, characteristic
2C22×C3×Dic3⋊C4C212yesmaximal
3C2×C3×C3⋊#95C211yesmaximal, characteristic
4C2×C3×C3⋊#95C212yesmaximal
5C2×C3×C3⋊#95C211yesmaximal, characteristic
6C3×#1444—31nomaximal
7#71568C311yesmaximal, characteristic, direct product factor
8C23×C32×C4C2212yes—
9C23×C32×C4C2211yescharacteristic
10C23×C3×Dic3C2211yescharacteristic
11C23×C3×Dic3C2211yescharacteristic
12C23×C3×Dic3C2212yes—
13C2×C32×C4⋊C4—24no—
14C2×C32×C4⋊C4—22no—
15C2×C3×Dic3⋊C4—24no—
16C2×C3×Dic3⋊C4—24no—
17C2×C3×Dic3⋊C4—24no—
18C3×C3⋊#95—22no—
19C3×C3⋊#95—24no—
20C3×C3⋊#95C414yescomplemented
21C22×C3×C4⋊C4—21no—
22C22×C3×C4⋊C4—32no—
23C22×C3×C4⋊C4D311yescharacteristic
24C22×C3×C4⋊C4C2×C311yescharacteristic
25C22×Dic3⋊C4C2×C312yes—
26C2×C3×#95—31no—
27C2×C3×#95—32no—
28C2×C3×#95—31no—
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—22no—
36C22×C32×C4—22no—
37C22×C32×C4—22no—
38C22×C32×C4—22no—
39C22×C32×C4—22no—
40C22×C32×C4—22no—
41C22×C32×C4C2×C412yes—
42C22×C32×C4D414yes—
43C22×C32×C4D412yes—
44C22×C32×C4Q812yes—
45C22×C3×Dic3—22no—
46C22×C3×Dic3—22no—
47C22×C3×Dic3—22no—
48C22×C3×Dic3—22no—
49C22×C3×Dic3—22no—
50C22×C3×Dic3—22no—
51C22×C3×Dic3—21no—
52C22×C3×Dic3—22no—
53C22×C3×Dic3—21no—
54C22×C3×Dic3—21no—
55C22×C3×Dic3—22no—
56C22×C3×Dic3—21no—
57C22×C3×Dic3C2×C414yes—
58C22×C3×Dic3D412yes—
59C22×C3×Dic3D414yes—
60C22×C3×Dic3Q812yes—
61C22×C3×Dic3Q814yes—
62C32×C4⋊C4—28no—
63C3×Dic3⋊C4—216no—
64#1444—31noSylow
65C23×C3×C4—21no—
66C23×C3×C4—22no—
67C23×C3×C4—32no—
68C23×C3×C4—31no—
69C23×C3×C4—31no—
70C23×C3×C4C2×D312yes—
71C23×C3×C4C2×D311yescharacteristic
72C23×C3×C4C22×C312yes—
73C23×C3×C4C22×C311yescharacteristic
74C23×Dic3C22×C311yescharacteristic
75C23×Dic3C22×C311yescharacteristic
76C23×Dic3C22×C312yes—
77C2×C3×C4⋊C4—28no—
78C2×C3×C4⋊C4—24no—
79C2×C3×C4⋊C4—24no—
80C2×C3×C4⋊C4—22no—
81C2×C3×C4⋊C4—24no—
82C2×C3×C4⋊C4—22no—
83C2×C3×C4⋊C4—64no—
84C2×C3×C4⋊C4—64no—
85C2×C3×C4⋊C4—64no—
86C2×Dic3⋊C4—24no—
87C2×Dic3⋊C4—24no—
88C2×Dic3⋊C4—24no—
89C3×#95—34no—
90C3×#95—64no—
91C3×#95—62no—
92C3⋊#95—22no—
93C3⋊#95—24no—
94C3⋊#95C3×C414yescomplemented
95C23×C32C22×C411yescharacteristic
96C23×C32C2×D412yes—
97C23×C32C2×D411yescharacteristic
98C23×C32C2×D411yescharacteristic
99C23×C32C2×D412yes—
100C23×C32C2×Q811yescharacteristic
101C23×C32C2×Q812yes—
102C23×C32C2×Q811yescharacteristic
103C23×C32#4112yes—
104C23×C32#4111yescharacteristic
105C23×C32#4111yescharacteristic
106C2×C32×C4—24no—
107C2×C32×C4—22no—
108C2×C32×C4—24no—
109C2×C32×C4—22no—
110C2×C32×C4—24no—
111C2×C32×C4—24no—
112C2×C32×C4—24no—
113C2×C32×C4—42no—
114C2×C32×C4—42no—
115C2×C32×C4—42no—
116C2×C32×C4—42no—
117C2×C32×C4C4⋊C414yescomplemented
118C2×C3×Dic3—24no—
119C2×C3×Dic3—24no—
120C2×C3×Dic3—24no—
121C2×C3×Dic3—24no—
122C2×C3×Dic3—24no—
123C2×C3×Dic3—24no—
124C2×C3×Dic3—24no—
125C2×C3×Dic3—22no—
126C2×C3×Dic3—24no—
127C2×C3×Dic3—22no—
128C2×C3×Dic3—41no—
129C2×C3×Dic3—42no—
130C2×C3×Dic3—42no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3C4⋊C418yescomplemented
135C22×C4⋊C4—32no—
136C22×C4⋊C4C3×D311yescharacteristic
137C2×#95—31no—
138C2×#95—32no—
139C2×#95—31no—
140C24×C3—21no—
141C24×C3C22×D311yescharacteristic
142C24×C3C23×C311yescharacteristic
143C22×C3×C4—24no—
144C22×C3×C4—24no—
145C22×C3×C4—22no—
146C22×C3×C4—22no—
147C22×C3×C4—22no—
148C22×C3×C4—22no—
149C22×C3×C4—24no—
150C22×C3×C4—24no—
151C22×C3×C4—22no—
152C22×C3×C4—22no—
153C22×C3×C4—22no—
154C22×C3×C4—22no—
155C22×C3×C4—22no—
156C22×C3×C4—22no—
157C22×C3×C4—22no—
158C22×C3×C4—22no—
159C22×C3×C4—22no—
160C22×C3×C4—22no—
161C22×C3×C4—22no—
162C22×C3×C4—22no—
163C22×C3×C4—22no—
164C22×C3×C4—22no—
165C22×C3×C4—22no—
166C22×C3×C4—24no—
167C22×C3×C4—34no—
168C22×C3×C4—34no—
169C22×C3×C4—34no—
170C22×C3×C4—32no—
171C22×C3×C4—32no—
172C22×C3×C4—42no—
173C22×C3×C4—42no—
174C22×C3×C4—42no—
175C22×C3×C4—42no—
176C22×C3×C4—62no—
177C22×C3×C4—62no—
178C22×C3×C4—62no—
179C22×C3×C4—62no—
180C22×C3×C4—62no—
181C22×C3×C4—62no—
182C22×C3×C4—62no—
183C22×C3×C4—61no—
184C22×C3×C4—61no—
185C22×C3×C4—61no—
186C22×C3×C4—61no—
187C22×C3×C4—62no—
188C22×C3×C4Dic612yes—
189C22×C3×C4C4×D312yes—
190C22×C3×C4#6714yes—
191C22×C3×C4#6712yes—
192C22×C3×C4C2×C3×C412yes—
193C22×C3×C4C3×D414yes—
194C22×C3×C4C3×D412yes—
195C22×C3×C4C3×Q812yes—
196C22×Dic3—22no—
197C22×Dic3—22no—
198C22×Dic3—22no—
199C22×Dic3—22no—
200C22×Dic3—22no—
201C22×Dic3—21no—
202C22×Dic3—21no—
203C22×Dic3—22no—
204C22×Dic3—22no—
205C22×Dic3—22no—
206C22×Dic3—21no—
207C22×Dic3—21no—
208C22×Dic3C2×C3×C414yes—
209C22×Dic3C3×D412yes—
210C22×Dic3C3×D414yes—
211C22×Dic3C3×Q812yes—
212C22×Dic3C3×Q814yes—
213C3×C4⋊C4—216no—
214C3×C4⋊C4—28no—
215C3×C4⋊C4—28no—
216C3×C4⋊C4—616no—
217Dic3⋊C4—216no—
218C22×C32C2×C4⋊C412yes—
219C22×C32C2×C4⋊C411yescharacteristic
220C22×C32C4×D411yescharacteristic
221C22×C32C4×D412yes—
222C22×C32C4×Q811yescharacteristic
223C22×C32#12012yes—
224C22×C32#12011yescharacteristic
225C22×C32#12111yescharacteristic
226C22×C32#12112yes—
227C22×C32C22⋊Q812yes—
228C22×C32C22⋊Q812yes—
229C22×C32C22⋊Q812yes—
230C22×C32C22⋊Q812yes—
231C22×C32C22⋊Q811yescharacteristic
232C22×C32#12312yes—
233C22×C32#12311yescharacteristic
234C22×C32#12512yes—
235C22×C32#12511yescharacteristic
236C22×C32#12711yescharacteristic
237C22×C32C4⋊Q812yes—
238C22×C32C4⋊Q811yescharacteristic
239C22×C32C4⋊Q811yescharacteristic
240C22×C32C4⋊Q812yes—
241C32×C4—24no—
242C32×C4—44no—
243C3×Dic3—28no—
244C3×Dic3—42no—
245C3×Dic3—42no—
246C23×C4—32no—
247C23×C4—31no—
248C23×C4—31no—
249C23×C4C2×C3×D312yes—
250C23×C4C2×C3×D311yescharacteristic
251C2×C4⋊C4—24no—
252C2×C4⋊C4—22no—
253C2×C4⋊C4—64no—
254C2×C4⋊C4—64no—
255C2×C4⋊C4—64no—
256#95—34no—
257#95—64no—
258#95—62no—
259C23×C3—21no—
260C23×C3—21no—
261C23×C3—22no—
262C23×C3—22no—
263C23×C3—21no—
264C23×C3—21no—
265C23×C3—21no—
266C23×C3—22no—
267C23×C3—21no—
268C23×C3—21no—
269C23×C3—22no—
270C23×C3C2×Dic611yescharacteristic
271C23×C3C2×C4×D311yescharacteristic
272C23×C3#23512yes—
273C23×C3D3×D412yes—
274C23×C3D3×D411yescharacteristic
275C23×C3#23711yescharacteristic
276C23×C3D3×Q811yescharacteristic
277C23×C3D3×Q812yes—
278C23×C3#23911yescharacteristic
279C23×C3C2×#6711yescharacteristic
280C23×C3C2×#6712yes—
281C23×C3C22×C3×C411yescharacteristic
282C23×C3C2×C3×D412yes—
283C23×C3C2×C3×D411yescharacteristic
284C23×C3C2×C3×D411yescharacteristic
285C23×C3C2×C3×D412yes—
286C23×C3C2×C3×Q811yescharacteristic
287C23×C3C2×C3×Q812yes—
288C23×C3C2×C3×Q811yescharacteristic
289C23×C3C3×#4112yes—
290C23×C3C3×#4111yescharacteristic
291C23×C3C3×#4111yescharacteristic
292C2×C3×C4—24no—
293C2×C3×C4—28no—
294C2×C3×C4—28no—
295C2×C3×C4—24no—
296C2×C3×C4—24no—
297C2×C3×C4—24no—
298C2×C3×C4—22no—
299C2×C3×C4—22no—
300C2×C3×C4—24no—
301C2×C3×C4—22no—
302C2×C3×C4—24no—
303C2×C3×C4—22no—
304C2×C3×C4—28no—
305C2×C3×C4—24no—
306C2×C3×C4—24no—
307C2×C3×C4—24no—
308C2×C3×C4—24no—
309C2×C3×C4—24no—
310C2×C3×C4—24no—
311C2×C3×C4—24no—
312C2×C3×C4—38no—
313C2×C3×C4—44no—
314C2×C3×C4—44no—
315C2×C3×C4—44no—
316C2×C3×C4—44no—
317C2×C3×C4—44no—
318C2×C3×C4—44no—
319C2×C3×C4—42no—
320C2×C3×C4—42no—
321C2×C3×C4—42no—
322C2×C3×C4—42no—
323C2×C3×C4—42no—
324C2×C3×C4—42no—
325C2×C3×C4—42no—
326C2×C3×C4—42no—
327C2×C3×C4—64no—
328C2×C3×C4—64no—
329C2×C3×C4—64no—
330C2×C3×C4—64no—
331C2×C3×C4—64no—
332C2×C3×C4—64no—
333C2×C3×C4—64no—
334C2×C3×C4—64no—
335C2×C3×C4—62no—
336C2×C3×C4—62no—
337C2×C3×C4—122no—
338C2×C3×C4—121no—
339C2×C3×C4—122no—
340C2×C3×C4—121no—
341C2×C3×C4—121no—
342C2×C3×C4—121no—
343C2×C3×C4Dic3⋊C414yescomplemented
344C2×C3×C4C3×C4⋊C414yescomplemented
345C2×Dic3—24no—
346C2×Dic3—24no—
347C2×Dic3—24no—
348C2×Dic3—24no—
349C2×Dic3—24no—
350C2×Dic3—24no—
351C2×Dic3—24no—
352C2×Dic3—22no—
353C2×Dic3—24no—
354C2×Dic3—22no—
355C2×Dic3—41no—
356C2×Dic3—42no—
357C2×Dic3—42no—
358C2×Dic3—41no—
359C2×Dic3—41no—
360C2×Dic3—41no—
361C2×Dic3C3×C4⋊C418yescomplemented
362C2×C32#38411yescharacteristic
363C2×C32#38511yescharacteristic
364C2×C32#38512yes—
365C2×C32#38911yescharacteristic
366C2×C32#38912yes—
367C2×C32#39211yescharacteristic
368C2×C32#39511yescharacteristic
369C2×C32#39512yes—
370C2×C32#39812yes—
371C2×C32#39811yescharacteristic
372C2×C32#39911yescharacteristic
373C24C22×C3×D311yescharacteristic
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—34no—
383C22×C4—34no—
384C22×C4—34no—
385C22×C4—32no—
386C22×C4—32no—
387C22×C4—62no—
388C22×C4—62no—
389C22×C4—62no—
390C22×C4—62no—
391C22×C4—62no—
392C22×C4—62no—
393C22×C4—62no—
394C22×C4—61no—
395C22×C4—61no—
396C22×C4—61no—
397C22×C4—61no—
398C22×C4—62no—
399C22×C4C3×Dic612yes—
400C22×C4C3×C4×D312yes—
401C22×C4C3×#6714yes—
402C22×C4C3×#6712yes—
403C4⋊C4—28no—
404C4⋊C4—616no—
405C22×C3—21no—
406C22×C3—21no—
407C22×C3—22no—
408C22×C3—22no—
409C22×C3—21no—
410C22×C3—22no—
411C22×C3—21no—
412C22×C3—22no—
413C22×C3—22no—
414C22×C3—22no—
415C22×C3—21no—
416C22×C3—22no—
417C22×C3—22no—
418C22×C3—21no—
419C22×C3—22no—
420C22×C3—21no—
421C22×C3—22no—
422C22×C3—21no—
423C22×C3—21no—
424C22×C3—22no—
425C22×C3—21no—
426C22×C3—22no—
427C22×C3—21no—
428C22×C3#88711yescharacteristic
429C22×C3#88811yescharacteristic
430C22×C3#88812yes—
431C22×C3#88912yes—
432C22×C3#89011yescharacteristic
433C22×C3D3×C4⋊C412yes—
434C22×C3#89311yescharacteristic
435C22×C3#89412yes—
436C22×C3#89612yes—
437C22×C3#89612yes—
438C22×C3C2×Dic3⋊C411yescharacteristic
439C22×C3#92412yes—
440C22×C3C4×#6712yes—
441C22×C3#92911yescharacteristic
442C22×C3#93712yes—
443C22×C3#93811yescharacteristic
444C22×C3#93912yes—
445C22×C3#94011yescharacteristic
446C22×C3#94411yescharacteristic
447C22×C3#94412yes—
448C22×C3#94611yescharacteristic
449C22×C3#94612yes—
450C22×C3#95311yescharacteristic
451C22×C3C2×C3×C4⋊C412yes—
452C22×C3C2×C3×C4⋊C411yescharacteristic
453C22×C3C3×C4×D411yescharacteristic
454C22×C3C3×C4×D412yes—
455C22×C3C3×C4×Q811yescharacteristic
456C22×C3C3×#12012yes—
457C22×C3C3×#12011yescharacteristic
458C22×C3C3×#12111yescharacteristic
459C22×C3C3×#12112yes—
460C22×C3C3×C22⋊Q812yes—
461C22×C3C3×C22⋊Q812yes—
462C22×C3C3×C22⋊Q812yes—
463C22×C3C3×C22⋊Q812yes—
464C22×C3C3×C22⋊Q811yescharacteristic
465C22×C3C3×#12312yes—
466C22×C3C3×#12311yescharacteristic
467C22×C3C3×#12512yes—
468C22×C3C3×#12511yescharacteristic
469C22×C3C3×#12711yescharacteristic
470C22×C3C3×C4⋊Q812yes—
471C22×C3C3×C4⋊Q811yescharacteristic
472C22×C3C3×C4⋊Q811yescharacteristic
473C22×C3C3×C4⋊Q812yes—
474C3×C4—28no—
475C3×C4—24no—
476C3×C4—24no—
477C3×C4—48no—
478C3×C4—44no—
479C3×C4—44no—
480C3×C4—68no—
481C3×C4—122no—
482C3×C4—122no—
483Dic3—28no—
484Dic3—42no—
485Dic3—42no—
486C32#144411yescharacteristic, complemented, Sylow
487C23C2×C3×Dic611yescharacteristic
488C23C2×C3×C4×D311yescharacteristic
489C23C3×#23512yes—
490C23C3×D3×D412yes—
491C23C3×D3×D411yescharacteristic
492C23C3×#23711yescharacteristic
493C23C3×D3×Q811yescharacteristic
494C23C3×D3×Q812yes—
495C23C3×#23911yescharacteristic
496C23C2×C3×#6711yescharacteristic
497C23C2×C3×#6712yes—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—38no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—64no—
511C2×C4—64no—
512C2×C4—64no—
513C2×C4—64no—
514C2×C4—64no—
515C2×C4—64no—
516C2×C4—64no—
517C2×C4—64no—
518C2×C4—62no—
519C2×C4—62no—
520C2×C4—122no—
521C2×C4—121no—
522C2×C4—122no—
523C2×C4—121no—
524C2×C4—121no—
525C2×C4—121no—
526C2×C4C3×Dic3⋊C414yescomplemented
527C2×C3—21no—
528C2×C3—21no—
529C2×C3—21no—
530C2×C3—21no—
531C2×C3—21no—
532C2×C3—22no—
533C2×C3—22no—
534C2×C3—22no—
535C2×C3—21no—
536C2×C3—22no—
537C2×C3—21no—
538C2×C3#497211yescharacteristic
539C2×C3#497511yescharacteristic
540C2×C3#497612yes—
541C2×C3#497912yes—
542C2×C3#498212yes—
543C2×C3#498311yescharacteristic
544C2×C3#498912yes—
545C2×C3#499311yescharacteristic
546C2×C3#521011yescharacteristic
547C2×C3#522311yescharacteristic
548C2×C3#523011yescharacteristic
549C2×C3C3×#38411yescharacteristic
550C2×C3C3×#38511yescharacteristic
551C2×C3C3×#38512yes—
552C2×C3C3×#38911yescharacteristic
553C2×C3C3×#38912yes—
554C2×C3C3×#39211yescharacteristic
555C2×C3C3×#39511yescharacteristic
556C2×C3C3×#39512yes—
557C2×C3C3×#39812yes—
558C2×C3C3×#39811yescharacteristic
559C2×C3C3×#39911yescharacteristic
560C22C3×#88711yescharacteristic
561C22C3×#88811yescharacteristic
562C22C3×#88812yes—
563C22C3×#88912yes—
564C22C3×#89011yescharacteristic
565C22C3×D3×C4⋊C412yes—
566C22C3×#89311yescharacteristic
567C22C3×#89412yes—
568C22C3×#89612yes—
569C22C3×#89612yes—
570C22C2×C3×Dic3⋊C411yescharacteristic
571C22C3×#92412yes—
572C22C3×C4×#6712yes—
573C22C3×#92911yescharacteristic
574C22C3×#93712yes—
575C22C3×#93811yescharacteristic
576C22C3×#93912yes—
577C22C3×#94011yescharacteristic
578C22C3×#94411yescharacteristic
579C22C3×#94412yes—
580C22C3×#94611yescharacteristic
581C22C3×#94612yes—
582C22C3×#95311yescharacteristic
583C4—24no—
584C4—44no—
585C4—68no—
586C4—122no—
587C4—122no—
588C3—21no—
589C3#7156811yescharacteristic, direct product factor
590C3C3×#144411yescharacteristic, complemented
591C2C3×#497211yescharacteristic
592C2C3×#497511yescharacteristic
593C2C3×#497612yes—
594C2C3×#497912yes—
595C2C3×#498212yes—
596C2C3×#498311yescharacteristic
597C2C3×#498912yes—
598C2C3×#499311yescharacteristic
599C2C3×#521011yescharacteristic
600C2C3×#522311yescharacteristic
601C2C3×#523011yescharacteristic
subgroupG/H
centerC24×C3C22×D3
commutatorC23×C3C22×C3×C4
FrattiniC24C22×C3×D3
FittingC22×C32×C4⋊C4C2
socle, prime radicalC24×C32C23
cosocleC24×C3C23×C3
hypercenterC22×C3×C4⋊C4D3
hypocenterC3C3×#1444
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24×C3 ◁ C22×C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
7. #71568C3direct (N × H)
20. C3×C3⋊#95C4semidirect
94. C3⋊#95C3×C4semidirect
117. C2×C32×C4C4⋊C4semidirect
134. C2×C3×Dic3C4⋊C4semidirect
343. C2×C3×C4Dic3⋊C4semidirect
344. C2×C3×C4C3×C4⋊C4semidirect
361. C2×Dic3C3×C4⋊C4semidirect
486. C32#1444semidirect
526. C2×C4C3×Dic3⋊C4semidirect
589. C3#71568direct (N × H)
590. C3C3×#1444semidirect

Maximal subgroups

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

subgroupindex
C22×C32×C4⋊C42
C22×C3×Dic3⋊C42
C2×C3×C3⋊#952
C3×#14443
#715683