Finite Group Databasebeta

← C3×#69405 #11773233

Subgroups — C3×#69405 #11773233

Order 1152.

1389 conjugacy classes of subgroups.

The subgroup lattice has 571 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×Dic3⋊C4C211yesmaximal, characteristic
2C22×C3×C4×Dic3C211yesmaximal, characteristic
3C2×C32×#95C211yesmaximal, characteristic
4C2×C3×C3⋊#95C212yesmaximal
5C2×C3×C3⋊#95C212yesmaximal
6C3×#1436—31nomaximal
7#69405C311yesmaximal, characteristic, direct product factor
8C23×C32×C4C2212yes—
9C23×C32×C4C2211yescharacteristic
10C23×C3×Dic3C2211yescharacteristic
11C23×C3×Dic3C2211yescharacteristic
12C23×C3×Dic3C2212yes—
13C2×C3×Dic3⋊C4—22no—
14C2×C3×Dic3⋊C4—22no—
15C2×C3×Dic3⋊C4C414yescomplemented
16C2×C3×C4×Dic3—22no—
17C2×C3×C4×Dic3—24no—
18C32×#95—22no—
19C3×C3⋊#95—24no—
20C3×C3⋊#95C418yescomplemented
21C22×C3×C4⋊C4—31no—
22C22×C3×C42—31no—
23C22×Dic3⋊C4C2×C311yescharacteristic
24C22×C4×Dic3C2×C311yescharacteristic
25C2×C3×#95—21no—
26C2×C3×#95—32no—
27C2×C3×#95—32no—
28C2×C3×#95D311yescharacteristic
29C2×C3×#95C2×C311yescharacteristic
30C2×C3⋊#95C2×C312yes—
31C2×C3⋊#95C2×C312yes—
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×C414yes—
42C22×C32×C4C2×C412yes—
43C22×C32×C4D412yes—
44C22×C32×C4D412yes—
45C22×C3×Dic3—22no—
46C22×C3×Dic3—22no—
47C22×C3×Dic3—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3—22no—
50C22×C3×Dic3—22no—
51C22×C3×Dic3—22no—
52C22×C3×Dic3—21no—
53C22×C3×Dic3—21no—
54C22×C3×Dic3—22no—
55C22×C3×Dic3—22no—
56C22×C3×Dic3C2×C412yes—
57C22×C3×Dic3C2×C412yes—
58C22×C3×Dic3C2×C414yes—
59C22×C3×Dic3C2×C414yes—
60C22×C3×Dic3D414yes—
61C22×C3×Dic3Q814yes—
62C3×Dic3⋊C4—28no—
63C3×C4×Dic3—28no—
64#1436—31noSylow
65C23×C3×C4—22no—
66C23×C3×C4—21no—
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—34no—
78C2×C3×C4⋊C4—62no—
79C2×C3×C4⋊C4—62no—
80C2×C3×C42—64no—
81C2×C3×C42—62no—
82C2×Dic3⋊C4—22no—
83C2×Dic3⋊C4—22no—
84C2×Dic3⋊C4C3×C414yescomplemented
85C2×C4×Dic3—22no—
86C2×C4×Dic3—24no—
87C3×#95—24no—
88C3×#95—22no—
89C3×#95—22no—
90C3×#95—38no—
91C3×#95—64no—
92C3⋊#95—24no—
93C3⋊#95C3×C418yescomplemented
94C23×C32C22×C411yescharacteristic
95C23×C32C22×C412yes—
96C23×C32C2×D411yescharacteristic
97C23×C32C2×D412yes—
98C23×C32C2×D411yescharacteristic
99C23×C32C2×Q812yes—
100C23×C32#4112yes—
101C23×C32#4112yes—
102C23×C32#4112yes—
103C2×C32×C4—24no—
104C2×C32×C4—24no—
105C2×C32×C4—22no—
106C2×C32×C4—24no—
107C2×C32×C4—22no—
108C2×C32×C4—24no—
109C2×C32×C4—24no—
110C2×C32×C4—42no—
111C2×C32×C4—42no—
112C2×C32×C4—42no—
113C2×C32×C4—42no—
114C2×C32×C4C22⋊C414yes—
115C2×C3×Dic3—22no—
116C2×C3×Dic3—22no—
117C2×C3×Dic3—24no—
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—41no—
128C2×C3×Dic3—42no—
129C2×C3×Dic3—41no—
130C2×C3×Dic3C4214yescomplemented
131C2×C3×Dic3C4⋊C418yescomplemented
132C22×C4⋊C4—31no—
133C22×C42—31no—
134C2×#95—32no—
135C2×#95—32no—
136C2×#95C3×D311yescharacteristic
137C24×C3—21no—
138C24×C3C22×D311yescharacteristic
139C24×C3C23×C311yescharacteristic
140C22×C3×C4—22no—
141C22×C3×C4—22no—
142C22×C3×C4—22no—
143C22×C3×C4—22no—
144C22×C3×C4—24no—
145C22×C3×C4—24no—
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—24no—
159C22×C3×C4—22no—
160C22×C3×C4—22no—
161C22×C3×C4—22no—
162C22×C3×C4—34no—
163C22×C3×C4—34no—
164C22×C3×C4—32no—
165C22×C3×C4—34no—
166C22×C3×C4—34no—
167C22×C3×C4—32no—
168C22×C3×C4—42no—
169C22×C3×C4—42no—
170C22×C3×C4—42no—
171C22×C3×C4—42no—
172C22×C3×C4—42no—
173C22×C3×C4—42no—
174C22×C3×C4—62no—
175C22×C3×C4—61no—
176C22×C3×C4—62no—
177C22×C3×C4—62no—
178C22×C3×C4—62no—
179C22×C3×C4—62no—
180C22×C3×C4—61no—
181C22×C3×C4—61no—
182C22×C3×C4—62no—
183C22×C3×C4—62no—
184C22×C3×C4—61no—
185C22×C3×C4C4×D314yes—
186C22×C3×C4C4×D312yes—
187C22×C3×C4D1212yes—
188C22×C3×C4#6712yes—
189C22×C3×C4C2×C3×C414yes—
190C22×C3×C4C2×C3×C412yes—
191C22×C3×C4C3×D412yes—
192C22×C3×C4C3×D412yes—
193C22×Dic3—22no—
194C22×Dic3—22no—
195C22×Dic3—21no—
196C22×Dic3—21no—
197C22×Dic3—22no—
198C22×Dic3—22no—
199C22×Dic3—22no—
200C22×Dic3—22no—
201C22×Dic3—21no—
202C22×Dic3—21no—
203C22×Dic3—22no—
204C22×Dic3C2×C3×C412yes—
205C22×Dic3C2×C3×C414yes—
206C22×Dic3C2×C3×C412yes—
207C22×Dic3C2×C3×C414yes—
208C22×Dic3C3×D414yes—
209C22×Dic3C3×Q814yes—
210C3×C4⋊C4—68no—
211C3×C42—68no—
212Dic3⋊C4—28no—
213C4×Dic3—28no—
214C22×C32C2×C4211yescharacteristic
215C22×C32C2×C22⋊C411yescharacteristic
216C22×C32C2×C4⋊C412yes—
217C22×C32#11711yescharacteristic
218C22×C32#11712yes—
219C22×C32C4×D412yes—
220C22×C32C4×D412yes—
221C22×C32C4×D412yes—
222C22×C32C4×D412yes—
223C22×C32C4×Q812yes—
224C22×C32C4×Q812yes—
225C22×C32#12011yescharacteristic
226C22×C32#12112yes—
227C22×C32C22⋊Q812yes—
228C22×C32C22⋊Q812yes—
229C22×C32#12312yes—
230C22×C32#12311yescharacteristic
231C22×C32#12411yescharacteristic
232C22×C32#12512yes—
233C22×C32#12612yes—
234C22×C32C4⋊Q811yescharacteristic
235C32×C4—24no—
236C32×C4—44no—
237C3×Dic3—24no—
238C3×Dic3—28no—
239C3×Dic3—42no—
240C23×C4—31no—
241C23×C4—32no—
242C23×C4—31no—
243C23×C4C2×C3×D312yes—
244C23×C4C2×C3×D311yescharacteristic
245C2×C4⋊C4—34no—
246C2×C4⋊C4—62no—
247C2×C4⋊C4—62no—
248C2×C42—64no—
249C2×C42—62no—
250#95—22no—
251#95—38no—
252#95—64no—
253C23×C3—22no—
254C23×C3—21no—
255C23×C3—21no—
256C23×C3—22no—
257C23×C3—22no—
258C23×C3—22no—
259C23×C3—22no—
260C23×C3—22no—
261C23×C3—21no—
262C23×C3C2×C4×D311yescharacteristic
263C23×C3C2×C4×D312yes—
264C23×C3C2×D1211yescharacteristic
265C23×C3#23512yes—
266C23×C3D3×D412yes—
267C23×C3#23712yes—
268C23×C3#23712yes—
269C23×C3D3×Q812yes—
270C23×C3C2×#6711yescharacteristic
271C23×C3C22×C3×C411yescharacteristic
272C23×C3C22×C3×C412yes—
273C23×C3C2×C3×D411yescharacteristic
274C23×C3C2×C3×D412yes—
275C23×C3C2×C3×D411yescharacteristic
276C23×C3C2×C3×Q812yes—
277C23×C3C3×#4112yes—
278C23×C3C3×#4112yes—
279C23×C3C3×#4112yes—
280C2×C3×C4—24no—
281C2×C3×C4—22no—
282C2×C3×C4—22no—
283C2×C3×C4—24no—
284C2×C3×C4—24no—
285C2×C3×C4—22no—
286C2×C3×C4—24no—
287C2×C3×C4—22no—
288C2×C3×C4—28no—
289C2×C3×C4—24no—
290C2×C3×C4—24no—
291C2×C3×C4—24no—
292C2×C3×C4—24no—
293C2×C3×C4—24no—
294C2×C3×C4—24no—
295C2×C3×C4—24no—
296C2×C3×C4—34no—
297C2×C3×C4—38no—
298C2×C3×C4—44no—
299C2×C3×C4—42no—
300C2×C3×C4—42no—
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—44no—
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—42no—
316C2×C3×C4—62no—
317C2×C3×C4—64no—
318C2×C3×C4—64no—
319C2×C3×C4—64no—
320C2×C3×C4—64no—
321C2×C3×C4—64no—
322C2×C3×C4—64no—
323C2×C3×C4—64no—
324C2×C3×C4—62no—
325C2×C3×C4—64no—
326C2×C3×C4—64no—
327C2×C3×C4—62no—
328C2×C3×C4—121no—
329C2×C3×C4—121no—
330C2×C3×C4—122no—
331C2×C3×C4(C2×D3)⋊C414yes—
332C2×C3×C4C3×C22⋊C414yes—
333C2×Dic3—22no—
334C2×Dic3—22no—
335C2×Dic3—24no—
336C2×Dic3—24no—
337C2×Dic3—24no—
338C2×Dic3—24no—
339C2×Dic3—24no—
340C2×Dic3—24no—
341C2×Dic3—24no—
342C2×Dic3—24no—
343C2×Dic3—22no—
344C2×Dic3—24no—
345C2×Dic3—41no—
346C2×Dic3—42no—
347C2×Dic3—41no—
348C2×Dic3C3×C4214yescomplemented
349C2×Dic3C3×C4⋊C418yescomplemented
350C2×C32C4×C22⋊C411yescharacteristic
351C2×C32C4×C4⋊C412yes—
352C2×C32#38512yes—
353C2×C32#38611yescharacteristic
354C2×C32#38712yes—
355C2×C32#38712yes—
356C2×C32#38812yes—
357C2×C32#38912yes—
358C2×C32#39111yescharacteristic
359C24C22×C3×D311yescharacteristic
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—34no—
369C22×C4—34no—
370C22×C4—32no—
371C22×C4—34no—
372C22×C4—34no—
373C22×C4—32no—
374C22×C4—62no—
375C22×C4—61no—
376C22×C4—62no—
377C22×C4—62no—
378C22×C4—62no—
379C22×C4—62no—
380C22×C4—61no—
381C22×C4—61no—
382C22×C4—62no—
383C22×C4—62no—
384C22×C4—61no—
385C22×C4C3×C4×D314yes—
386C22×C4C3×C4×D312yes—
387C22×C4C3×D1212yes—
388C22×C4C3×#6712yes—
389C4⋊C4—68no—
390C42—68no—
391C22×C3—22no—
392C22×C3—22no—
393C22×C3—22no—
394C22×C3—22no—
395C22×C3—21no—
396C22×C3—22no—
397C22×C3—21no—
398C22×C3—22no—
399C22×C3—22no—
400C22×C3—22no—
401C22×C3—22no—
402C22×C3—22no—
403C22×C3—22no—
404C22×C3—21no—
405C22×C3—22no—
406C22×C3—21no—
407C22×C3—22no—
408C22×C3—21no—
409C22×C3—21no—
410C22×C3—21no—
411C22×C3—22no—
412C22×C3C42×D311yescharacteristic
413C22×C3#87211yescharacteristic
414C22×C3C4×D1212yes—
415C22×C3#87712yes—
416C22×C3#87912yes—
417C22×C3#67⋊C412yes—
418C22×C3#67⋊C412yes—
419C22×C3#88211yescharacteristic
420C22×C3#88312yes—
421C22×C3#88611yescharacteristic
422C22×C3#88712yes—
423C22×C3#88712yes—
424C22×C3#88912yes—
425C22×C3D3×C4⋊C412yes—
426C22×C3#89612yes—
427C22×C3#89712yes—
428C22×C3C2×(C2×D3)⋊C411yescharacteristic
429C22×C3C4×#6712yes—
430C22×C3#93611yescharacteristic
431C22×C3#93912yes—
432C22×C3#94411yescharacteristic
433C22×C3C2×C3×C4211yescharacteristic
434C22×C3C2×C3×C22⋊C411yescharacteristic
435C22×C3C2×C3×C4⋊C412yes—
436C22×C3C3×#11712yes—
437C22×C3C3×#11711yescharacteristic
438C22×C3C3×C4×D412yes—
439C22×C3C3×C4×D412yes—
440C22×C3C3×C4×D412yes—
441C22×C3C3×C4×D412yes—
442C22×C3C3×C4×Q812yes—
443C22×C3C3×C4×Q812yes—
444C22×C3C3×#12011yescharacteristic
445C22×C3C3×#12112yes—
446C22×C3C3×C22⋊Q812yes—
447C22×C3C3×C22⋊Q812yes—
448C22×C3C3×#12312yes—
449C22×C3C3×#12311yescharacteristic
450C22×C3C3×#12411yescharacteristic
451C22×C3C3×#12512yes—
452C22×C3C3×#12612yes—
453C22×C3C3×C4⋊Q811yescharacteristic
454C3×C4—24no—
455C3×C4—24no—
456C3×C4—44no—
457C3×C4—48no—
458C3×C4—44no—
459C3×C4—44no—
460C3×C4—68no—
461C3×C4—64no—
462C3×C4—122no—
463Dic3—24no—
464Dic3—28no—
465Dic3—42no—
466C32#143611yescharacteristic, complemented, Sylow
467C23C2×C3×C4×D312yes—
468C23C2×C3×C4×D311yescharacteristic
469C23C2×C3×D1211yescharacteristic
470C23C3×#23512yes—
471C23C3×D3×D412yes—
472C23C3×#23712yes—
473C23C3×#23712yes—
474C23C3×D3×Q812yes—
475C23C2×C3×#6711yescharacteristic
476C2×C4—24no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—38no—
484C2×C4—34no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—64no—
490C2×C4—64no—
491C2×C4—64no—
492C2×C4—64no—
493C2×C4—64no—
494C2×C4—62no—
495C2×C4—64no—
496C2×C4—62no—
497C2×C4—64no—
498C2×C4—64no—
499C2×C4—64no—
500C2×C4—62no—
501C2×C4—121no—
502C2×C4—121no—
503C2×C4—122no—
504C2×C4C3×(C2×D3)⋊C414yes—
505C2×C3—22no—
506C2×C3—22no—
507C2×C3—22no—
508C2×C3—22no—
509C2×C3—21no—
510C2×C3—22no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—22no—
514C2×C3#464912yes—
515C2×C3#465212yes—
516C2×C3#465312yes—
517C2×C3#466812yes—
518C2×C3C4×(C2×D3)⋊C411yescharacteristic
519C2×C3#494512yes—
520C2×C3#495811yescharacteristic
521C2×C3#497311yescharacteristic
522C2×C3#497612yes—
523C2×C3C3×C4×C22⋊C411yescharacteristic
524C2×C3C3×C4×C4⋊C412yes—
525C2×C3C3×#38512yes—
526C2×C3C3×#38611yescharacteristic
527C2×C3C3×#38712yes—
528C2×C3C3×#38712yes—
529C2×C3C3×#38812yes—
530C2×C3C3×#38912yes—
531C2×C3C3×#39111yescharacteristic
532C22C3×C42×D311yescharacteristic
533C22C3×#87211yescharacteristic
534C22C3×C4×D1212yes—
535C22C3×#87712yes—
536C22C3×#87912yes—
537C22C3×#67⋊C412yes—
538C22C3×#67⋊C412yes—
539C22C3×#88211yescharacteristic
540C22C3×#88312yes—
541C22C3×#88611yescharacteristic
542C22C3×#88712yes—
543C22C3×#88712yes—
544C22C3×#88912yes—
545C22C3×D3×C4⋊C412yes—
546C22C3×#89612yes—
547C22C3×#89712yes—
548C22C2×C3×(C2×D3)⋊C411yescharacteristic
549C22C3×C4×#6712yes—
550C22C3×#93611yescharacteristic
551C22C3×#93912yes—
552C22C3×#94411yescharacteristic
553C4—24no—
554C4—44no—
555C4—68no—
556C4—64no—
557C4—122no—
558C3—21no—
559C3#6940511yescharacteristic, direct product factor
560C3C3×#143611yescharacteristic, complemented
561C2C3×#464912yes—
562C2C3×#465212yes—
563C2C3×#465312yes—
564C2C3×#466812yes—
565C2C3×C4×(C2×D3)⋊C411yescharacteristic
566C2C3×#494512yes—
567C2C3×#495811yescharacteristic
568C2C3×#497311yescharacteristic
569C2C3×#497612yes—
subgroupG/H
centerC24×C3C22×D3
commutatorC22×C3C2×C3×C42
FrattiniC24C22×C3×D3
FittingC2×C32×#95C2
socle, prime radicalC24×C32C23
cosocleC24×C3C23×C3
hypercenterC2×C3×#95D3
hypocenterC3C3×#1436
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C24×C3 ◁ C2×C3×#95

Complements

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

NH ≅ G/Ntype
7. #69405C3direct (N × H)
15. C2×C3×Dic3⋊C4C4semidirect
20. C3×C3⋊#95C4semidirect
84. C2×Dic3⋊C4C3×C4semidirect
93. C3⋊#95C3×C4semidirect
130. C2×C3×Dic3C42semidirect
131. C2×C3×Dic3C4⋊C4semidirect
348. C2×Dic3C3×C42semidirect
349. C2×Dic3C3×C4⋊C4semidirect
466. C32#1436semidirect
559. C3#69405direct (N × H)
560. C3C3×#1436semidirect

Maximal subgroups

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

subgroupindex
C22×C3×Dic3⋊C42
C22×C3×C4×Dic32
C2×C32×#952
C2×C3×C3⋊#952
C3×#14363
#694053