Finite Group Databasebeta

← C3×#71567 #11773393

Subgroups — C3×#71567 #11773393

Order 1152.

1249 conjugacy classes of subgroups.

The subgroup lattice has 591 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×C4⋊C4C211yesmaximal, characteristic
2C2×C3×C3⋊#95C212yesmaximal
3C2×C3×C3⋊#95C212yesmaximal
4C2×C3×C3⋊#95C211yesmaximal, characteristic
5C2×C3×C3⋊#95C211yesmaximal, characteristic
6C3×#1442—31nomaximal
7#71567C311yesmaximal, characteristic, direct product factor
8C23×C32×C4C2212yes—
9C23×C32×C4C2211yescharacteristic
10C23×C3×Dic3C2212yes—
11C23×C3×Dic3C2211yescharacteristic
12C23×C3×Dic3C2211yescharacteristic
13C2×C32×C4⋊C4—24no—
14C2×C32×C4⋊C4—22no—
15C3×C3⋊#95—24no—
16C3×C3⋊#95—22no—
17C3×C3⋊#95—24no—
18C3×C3⋊#95C414yescomplemented
19C22×C3×C4⋊C4—21no—
20C22×C3×C4⋊C4D311yescharacteristic
21C22×C3×C4⋊C4C2×C311yescharacteristic
22C2×C3×#95—31no—
23C2×C3×#95—32no—
24C2×C3×#95—32no—
25C2×C3×#95—31no—
26C2×C3⋊#95C2×C312yes—
27C2×C3⋊#95C2×C311yescharacteristic
28C2×C3⋊#95C2×C312yes—
29C2×C3⋊#95C2×C311yescharacteristic
30C24×C32C2311yescharacteristic
31C22×C32×C4—22no—
32C22×C32×C4—22no—
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×C4C2×C412yes—
40C22×C32×C4D414yes—
41C22×C32×C4D412yes—
42C22×C32×C4Q812yes—
43C22×C3×Dic3—22no—
44C22×C3×Dic3—22no—
45C22×C3×Dic3—21no—
46C22×C3×Dic3—21no—
47C22×C3×Dic3—22no—
48C22×C3×Dic3—22no—
49C22×C3×Dic3—22no—
50C22×C3×Dic3—22no—
51C22×C3×Dic3—22no—
52C22×C3×Dic3—21no—
53C22×C3×Dic3—22no—
54C22×C3×Dic3—21no—
55C22×C3×Dic3—22no—
56C22×C3×Dic3—22no—
57C22×C3×Dic3C2×C414yes—
58C22×C3×Dic3D412yes—
59C22×C3×Dic3Q812yes—
60C32×C4⋊C4—28no—
61#1442—31noSylow
62C23×C3×C4—21no—
63C23×C3×C4—22no—
64C23×C3×C4—32no—
65C23×C3×C4—31no—
66C23×C3×C4—31no—
67C23×C3×C4C2×D312yes—
68C23×C3×C4C2×D311yescharacteristic
69C23×C3×C4C22×C312yes—
70C23×C3×C4C22×C311yescharacteristic
71C23×Dic3C22×C312yes—
72C23×Dic3C22×C311yescharacteristic
73C23×Dic3C22×C311yescharacteristic
74C2×C3×C4⋊C4—28no—
75C2×C3×C4⋊C4—24no—
76C2×C3×C4⋊C4—24no—
77C2×C3×C4⋊C4—22no—
78C2×C3×C4⋊C4—24no—
79C2×C3×C4⋊C4—22no—
80C3×#95—34no—
81C3×#95—64no—
82C3×#95—64no—
83C3×#95—62no—
84C3⋊#95—24no—
85C3⋊#95—22no—
86C3⋊#95—24no—
87C3⋊#95C3×C414yescomplemented
88C23×C32C22×C411yescharacteristic
89C23×C32C2×D411yescharacteristic
90C23×C32C2×D411yescharacteristic
91C23×C32C2×D412yes—
92C23×C32C2×Q811yescharacteristic
93C23×C32C2×Q811yescharacteristic
94C23×C32#4112yes—
95C23×C32#4112yes—
96C23×C32#4111yescharacteristic
97C23×C32#4112yes—
98C23×C32#4111yescharacteristic
99C2×C32×C4—24no—
100C2×C32×C4—22no—
101C2×C32×C4—24no—
102C2×C32×C4—22no—
103C2×C32×C4—24no—
104C2×C32×C4—24no—
105C2×C32×C4—24no—
106C2×C32×C4—42no—
107C2×C32×C4—42no—
108C2×C32×C4—42no—
109C2×C32×C4—42no—
110C2×C32×C4C4⋊C414yes—
111C2×C3×Dic3—24no—
112C2×C3×Dic3—24no—
113C2×C3×Dic3—24no—
114C2×C3×Dic3—22no—
115C2×C3×Dic3—24no—
116C2×C3×Dic3—22no—
117C2×C3×Dic3—24no—
118C2×C3×Dic3—41no—
119C2×C3×Dic3—42no—
120C2×C3×Dic3—42no—
121C2×C3×Dic3—41no—
122C2×C3×Dic3—42no—
123C2×C3×Dic3—41no—
124C2×C3×Dic3—42no—
125C2×C3×Dic3—41no—
126C2×C3×Dic3—42no—
127C2×C3×Dic3—42no—
128C22×C4⋊C4C3×D311yescharacteristic
129C2×#95—31no—
130C2×#95—32no—
131C2×#95—32no—
132C2×#95—31no—
133C24×C3—21no—
134C24×C3C22×D311yescharacteristic
135C24×C3C23×C311yescharacteristic
136C22×C3×C4—24no—
137C22×C3×C4—24no—
138C22×C3×C4—22no—
139C22×C3×C4—22no—
140C22×C3×C4—22no—
141C22×C3×C4—22no—
142C22×C3×C4—24no—
143C22×C3×C4—24no—
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—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—24no—
160C22×C3×C4—34no—
161C22×C3×C4—32no—
162C22×C3×C4—32no—
163C22×C3×C4—42no—
164C22×C3×C4—42no—
165C22×C3×C4—42no—
166C22×C3×C4—42no—
167C22×C3×C4—62no—
168C22×C3×C4—62no—
169C22×C3×C4—62no—
170C22×C3×C4—62no—
171C22×C3×C4—61no—
172C22×C3×C4—62no—
173C22×C3×C4—62no—
174C22×C3×C4—62no—
175C22×C3×C4—62no—
176C22×C3×C4—61no—
177C22×C3×C4—62no—
178C22×C3×C4—61no—
179C22×C3×C4—61no—
180C22×C3×C4—62no—
181C22×C3×C4Dic612yes—
182C22×C3×C4C4×D312yes—
183C22×C3×C4#6714yes—
184C22×C3×C4#6712yes—
185C22×C3×C4C2×C3×C412yes—
186C22×C3×C4C3×D414yes—
187C22×C3×C4C3×D412yes—
188C22×C3×C4C3×Q812yes—
189C22×Dic3—22no—
190C22×Dic3—22no—
191C22×Dic3—21no—
192C22×Dic3—21no—
193C22×Dic3—22no—
194C22×Dic3—22no—
195C22×Dic3—22no—
196C22×Dic3—22no—
197C22×Dic3—21no—
198C22×Dic3—22no—
199C22×Dic3—22no—
200C22×Dic3—22no—
201C22×Dic3—21no—
202C22×Dic3—22no—
203C22×Dic3C2×C3×C414yes—
204C22×Dic3C3×D412yes—
205C22×Dic3C3×Q812yes—
206C3×C4⋊C4—216no—
207C3×C4⋊C4—28no—
208C3×C4⋊C4—28no—
209C22×C32C2×C4⋊C411yescharacteristic
210C22×C32#11712yes—
211C22×C32C4×D411yescharacteristic
212C22×C32C4×D412yes—
213C22×C32C4×Q811yescharacteristic
214C22×C32#12011yescharacteristic
215C22×C32#12111yescharacteristic
216C22×C32#12112yes—
217C22×C32C22⋊Q812yes—
218C22×C32C22⋊Q812yes—
219C22×C32C22⋊Q811yescharacteristic
220C22×C32#12312yes—
221C22×C32#12311yescharacteristic
222C22×C32#12312yes—
223C22×C32#12411yescharacteristic
224C22×C32#12411yescharacteristic
225C22×C32#12412yes—
226C22×C32#12512yes—
227C22×C32#12512yes—
228C22×C32#12511yescharacteristic
229C22×C32#12612yes—
230C22×C32#12612yes—
231C22×C32C4⋊Q811yescharacteristic
232C32×C4—24no—
233C32×C4—44no—
234C3×Dic3—44no—
235C3×Dic3—42no—
236C3×Dic3—42no—
237C23×C4—32no—
238C23×C4—31no—
239C23×C4—31no—
240C23×C4C2×C3×D312yes—
241C23×C4C2×C3×D311yescharacteristic
242C2×C4⋊C4—24no—
243C2×C4⋊C4—22no—
244#95—34no—
245#95—64no—
246#95—64no—
247#95—62no—
248C23×C3—21no—
249C23×C3—21no—
250C23×C3—22no—
251C23×C3—21no—
252C23×C3—21no—
253C23×C3—22no—
254C23×C3—21no—
255C23×C3—22no—
256C23×C3—21no—
257C23×C3—21no—
258C23×C3—22no—
259C23×C3C2×Dic611yescharacteristic
260C23×C3C2×C4×D311yescharacteristic
261C23×C3#23512yes—
262C23×C3D3×D411yescharacteristic
263C23×C3#23711yescharacteristic
264C23×C3#23712yes—
265C23×C3D3×Q811yescharacteristic
266C23×C3#23912yes—
267C23×C3#23911yescharacteristic
268C23×C3C2×#6711yescharacteristic
269C23×C3C2×#6712yes—
270C23×C3C22×C3×C411yescharacteristic
271C23×C3C2×C3×D411yescharacteristic
272C23×C3C2×C3×D411yescharacteristic
273C23×C3C2×C3×D412yes—
274C23×C3C2×C3×Q811yescharacteristic
275C23×C3C2×C3×Q811yescharacteristic
276C23×C3C3×#4112yes—
277C23×C3C3×#4112yes—
278C23×C3C3×#4111yescharacteristic
279C23×C3C3×#4112yes—
280C23×C3C3×#4111yescharacteristic
281C2×C3×C4—24no—
282C2×C3×C4—28no—
283C2×C3×C4—28no—
284C2×C3×C4—24no—
285C2×C3×C4—24no—
286C2×C3×C4—24no—
287C2×C3×C4—22no—
288C2×C3×C4—22no—
289C2×C3×C4—24no—
290C2×C3×C4—22no—
291C2×C3×C4—24no—
292C2×C3×C4—22no—
293C2×C3×C4—28no—
294C2×C3×C4—24no—
295C2×C3×C4—24no—
296C2×C3×C4—24no—
297C2×C3×C4—24no—
298C2×C3×C4—24no—
299C2×C3×C4—24no—
300C2×C3×C4—24no—
301C2×C3×C4—44no—
302C2×C3×C4—44no—
303C2×C3×C4—44no—
304C2×C3×C4—44no—
305C2×C3×C4—44no—
306C2×C3×C4—44no—
307C2×C3×C4—42no—
308C2×C3×C4—42no—
309C2×C3×C4—42no—
310C2×C3×C4—42no—
311C2×C3×C4—42no—
312C2×C3×C4—42no—
313C2×C3×C4—42no—
314C2×C3×C4—42no—
315C2×C3×C4—64no—
316C2×C3×C4—64no—
317C2×C3×C4—64no—
318C2×C3×C4—64no—
319C2×C3×C4—62no—
320C2×C3×C4—62no—
321C2×C3×C4—64no—
322C2×C3×C4—122no—
323C2×C3×C4—122no—
324C2×C3×C4—122no—
325C2×C3×C4—121no—
326C2×C3×C4—122no—
327C2×C3×C4—121no—
328C2×C3×C4—122no—
329C2×C3×C4—122no—
330C2×C3×C4—121no—
331C2×C3×C4—121no—
332C2×C3×C4Dic3⋊C414yes—
333C2×C3×C4C3×C4⋊C414yes—
334C2×Dic3—24no—
335C2×Dic3—24no—
336C2×Dic3—24no—
337C2×Dic3—22no—
338C2×Dic3—24no—
339C2×Dic3—22no—
340C2×Dic3—24no—
341C2×Dic3—41no—
342C2×Dic3—42no—
343C2×Dic3—42no—
344C2×Dic3—41no—
345C2×Dic3—42no—
346C2×Dic3—41no—
347C2×Dic3—42no—
348C2×Dic3—41no—
349C2×Dic3—42no—
350C2×Dic3—42no—
351C2×C32#38211yescharacteristic
352C2×C32#38511yescharacteristic
353C2×C32#38712yes—
354C2×C32#38812yes—
355C2×C32#38911yescharacteristic
356C2×C32#39311yescharacteristic
357C2×C32#39411yescharacteristic
358C2×C32#39711yescharacteristic
359C2×C32#39812yes—
360C2×C32#40011yescharacteristic
361C2×C32#40012yes—
362C24C22×C3×D311yescharacteristic
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—34no—
372C22×C4—32no—
373C22×C4—32no—
374C22×C4—62no—
375C22×C4—62no—
376C22×C4—62no—
377C22×C4—62no—
378C22×C4—61no—
379C22×C4—62no—
380C22×C4—62no—
381C22×C4—62no—
382C22×C4—62no—
383C22×C4—61no—
384C22×C4—62no—
385C22×C4—61no—
386C22×C4—61no—
387C22×C4—62no—
388C22×C4C3×Dic612yes—
389C22×C4C3×C4×D312yes—
390C22×C4C3×#6714yes—
391C22×C4C3×#6712yes—
392C4⋊C4—28no—
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—22no—
396C22×C3—21no—
397C22×C3—22no—
398C22×C3—22no—
399C22×C3—21no—
400C22×C3—22no—
401C22×C3—22no—
402C22×C3—22no—
403C22×C3—21no—
404C22×C3—22no—
405C22×C3—22no—
406C22×C3—21no—
407C22×C3—22no—
408C22×C3—21no—
409C22×C3—21no—
410C22×C3—22no—
411C22×C3—21no—
412C22×C3—22no—
413C22×C3—21no—
414C22×C3—22no—
415C22×C3—21no—
416C22×C3#88711yescharacteristic
417C22×C3#88811yescharacteristic
418C22×C3#88912yes—
419C22×C3#89011yescharacteristic
420C22×C3#89012yes—
421C22×C3#89212yes—
422C22×C3#89311yescharacteristic
423C22×C3#89412yes—
424C22×C3#89812yes—
425C22×C3#89812yes—
426C22×C3C2×Dic3⋊C411yescharacteristic
427C22×C3#92412yes—
428C22×C3C4×#6712yes—
429C22×C3#92911yescharacteristic
430C22×C3#93512yes—
431C22×C3#93611yescharacteristic
432C22×C3#93811yescharacteristic
433C22×C3#93912yes—
434C22×C3#94611yescharacteristic
435C22×C3#94612yes—
436C22×C3#94711yescharacteristic
437C22×C3#94712yes—
438C22×C3#95311yescharacteristic
439C22×C3C2×C3×C4⋊C411yescharacteristic
440C22×C3C3×#11712yes—
441C22×C3C3×C4×D411yescharacteristic
442C22×C3C3×C4×D412yes—
443C22×C3C3×C4×Q811yescharacteristic
444C22×C3C3×#12011yescharacteristic
445C22×C3C3×#12111yescharacteristic
446C22×C3C3×#12112yes—
447C22×C3C3×C22⋊Q812yes—
448C22×C3C3×C22⋊Q812yes—
449C22×C3C3×C22⋊Q811yescharacteristic
450C22×C3C3×#12312yes—
451C22×C3C3×#12311yescharacteristic
452C22×C3C3×#12312yes—
453C22×C3C3×#12411yescharacteristic
454C22×C3C3×#12411yescharacteristic
455C22×C3C3×#12412yes—
456C22×C3C3×#12512yes—
457C22×C3C3×#12512yes—
458C22×C3C3×#12511yescharacteristic
459C22×C3C3×#12612yes—
460C22×C3C3×#12612yes—
461C22×C3C3×C4⋊Q811yescharacteristic
462C3×C4—28no—
463C3×C4—24no—
464C3×C4—24no—
465C3×C4—48no—
466C3×C4—44no—
467C3×C4—44no—
468C3×C4—122no—
469C3×C4—124no—
470C3×C4—122no—
471Dic3—44no—
472Dic3—42no—
473Dic3—42no—
474C32#144211yescharacteristic, complemented, Sylow
475C23C2×C3×Dic611yescharacteristic
476C23C2×C3×C4×D311yescharacteristic
477C23C3×#23512yes—
478C23C3×D3×D411yescharacteristic
479C23C3×#23711yescharacteristic
480C23C3×#23712yes—
481C23C3×D3×Q811yescharacteristic
482C23C3×#23912yes—
483C23C3×#23911yescharacteristic
484C23C2×C3×#6711yescharacteristic
485C23C2×C3×#6712yes—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—64no—
498C2×C4—64no—
499C2×C4—64no—
500C2×C4—64no—
501C2×C4—62no—
502C2×C4—62no—
503C2×C4—64no—
504C2×C4—122no—
505C2×C4—122no—
506C2×C4—122no—
507C2×C4—121no—
508C2×C4—122no—
509C2×C4—121no—
510C2×C4—122no—
511C2×C4—122no—
512C2×C4—121no—
513C2×C4—121no—
514C2×C4C3×Dic3⋊C414yes—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—22no—
521C2×C3—22no—
522C2×C3—21no—
523C2×C3—22no—
524C2×C3—22no—
525C2×C3—21no—
526C2×C3#497211yescharacteristic
527C2×C3#497711yescharacteristic
528C2×C3#497812yes—
529C2×C3#498212yes—
530C2×C3#498511yescharacteristic
531C2×C3#498612yes—
532C2×C3#499012yes—
533C2×C3#499211yescharacteristic
534C2×C3#521011yescharacteristic
535C2×C3#522211yescharacteristic
536C2×C3#523111yescharacteristic
537C2×C3C3×#38211yescharacteristic
538C2×C3C3×#38511yescharacteristic
539C2×C3C3×#38712yes—
540C2×C3C3×#38812yes—
541C2×C3C3×#38911yescharacteristic
542C2×C3C3×#39311yescharacteristic
543C2×C3C3×#39411yescharacteristic
544C2×C3C3×#39711yescharacteristic
545C2×C3C3×#39812yes—
546C2×C3C3×#40011yescharacteristic
547C2×C3C3×#40012yes—
548C22C3×#88711yescharacteristic
549C22C3×#88811yescharacteristic
550C22C3×#88912yes—
551C22C3×#89011yescharacteristic
552C22C3×#89012yes—
553C22C3×#89212yes—
554C22C3×#89311yescharacteristic
555C22C3×#89412yes—
556C22C3×#89812yes—
557C22C3×#89812yes—
558C22C2×C3×Dic3⋊C411yescharacteristic
559C22C3×#92412yes—
560C22C3×C4×#6712yes—
561C22C3×#92911yescharacteristic
562C22C3×#93512yes—
563C22C3×#93611yescharacteristic
564C22C3×#93811yescharacteristic
565C22C3×#93912yes—
566C22C3×#94611yescharacteristic
567C22C3×#94612yes—
568C22C3×#94711yescharacteristic
569C22C3×#94712yes—
570C22C3×#95311yescharacteristic
571C4—24no—
572C4—44no—
573C4—122no—
574C4—124no—
575C4—122no—
576C3—21no—
577C3#7156711yescharacteristic, direct product factor
578C3C3×#144211yescharacteristic, complemented
579C2C3×#497211yescharacteristic
580C2C3×#497711yescharacteristic
581C2C3×#497812yes—
582C2C3×#498212yes—
583C2C3×#498511yescharacteristic
584C2C3×#498612yes—
585C2C3×#499012yes—
586C2C3×#499211yescharacteristic
587C2C3×#521011yescharacteristic
588C2C3×#522211yescharacteristic
589C2C3×#523111yescharacteristic
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×#1442
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. #71567C3direct (N × H)
18. C3×C3⋊#95C4semidirect
87. C3⋊#95C3×C4semidirect
474. C32#1442semidirect
577. C3#71567direct (N × H)
578. C3C3×#1442semidirect

Maximal subgroups

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

subgroupindex
C22×C32×C4⋊C42
C2×C3×C3⋊#952
C3×#14423
#715673