Finite Group Databasebeta

← C3×#69403 #11773179

Subgroups — C3×#69403 #11773179

Order 1152.

1301 conjugacy classes of subgroups.

The subgroup lattice has 589 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4×Dic3C211yesmaximal, characteristic
2C2×C32×#95C211yesmaximal, characteristic
3C2×C3×C3⋊#95C211yesmaximal, characteristic
4C2×C3×C3⋊#95C212yesmaximal
5C2×C3×C3⋊#95C212yesmaximal
6C3×#1434—31nomaximal
7#69403C311yesmaximal, characteristic, direct product factor
8C23×C32×C4C2212yes—
9C23×C32×C4C2211yescharacteristic
10C23×C3×Dic3C2212yes—
11C23×C3×Dic3C2211yescharacteristic
12C23×C3×Dic3C2211yescharacteristic
13C2×C3×C4×Dic3—24no—
14C2×C3×C4×Dic3C414yescomplemented
15C32×#95—22no—
16C3×C3⋊#95—22no—
17C3×C3⋊#95—24no—
18C3×C3⋊#95C418yescomplemented
19C22×C3×C42—31no—
20C22×C4×Dic3C2×C311yescharacteristic
21C2×C3×#95—21no—
22C2×C3×#95—32no—
23C2×C3×#95—32no—
24C2×C3×#95—31no—
25C2×C3×#95D311yescharacteristic
26C2×C3×#95C2×C311yescharacteristic
27C2×C3⋊#95C2×C311yescharacteristic
28C2×C3⋊#95C2×C312yes—
29C2×C3⋊#95C2×C312yes—
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×C414yes—
40C22×C32×C4C2×C412yes—
41C22×C32×C4D412yes—
42C22×C32×C4Q812yes—
43C22×C3×Dic3—22no—
44C22×C3×Dic3—21no—
45C22×C3×Dic3—21no—
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—22no—
53C22×C3×Dic3—22no—
54C22×C3×Dic3—22no—
55C22×C3×Dic3C2×C414yes—
56C22×C3×Dic3C2×C412yes—
57C22×C3×Dic3C2×C414yes—
58C22×C3×Dic3C2×C412yes—
59C22×C3×Dic3D414yes—
60C3×C4×Dic3—28no—
61#1434—31noSylow
62C23×C3×C4—22no—
63C23×C3×C4—21no—
64C23×C3×C4—31no—
65C23×C3×C4—31no—
66C23×C3×C4—32no—
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×C42—34no—
75C2×C3×C42—64no—
76C2×C4×Dic3—24no—
77C2×C4×Dic3C3×C414yescomplemented
78C3×#95—24no—
79C3×#95—22no—
80C3×#95—22no—
81C3×#95—38no—
82C3×#95—64no—
83C3×#95—62no—
84C3⋊#95—22no—
85C3⋊#95—24no—
86C3⋊#95C3×C418yescomplemented
87C23×C32C22×C411yescharacteristic
88C23×C32C22×C412yes—
89C23×C32C2×D412yes—
90C23×C32C2×D411yescharacteristic
91C23×C32C2×Q811yescharacteristic
92C23×C32#4112yes—
93C23×C32#4112yes—
94C23×C32#4111yescharacteristic
95C23×C32#4111yescharacteristic
96C23×C32#4111yescharacteristic
97C23×C32#4111yescharacteristic
98C2×C32×C4—24no—
99C2×C32×C4—22no—
100C2×C32×C4—22no—
101C2×C32×C4—24no—
102C2×C32×C4—24no—
103C2×C32×C4—24no—
104C2×C32×C4—24no—
105C2×C32×C4—42no—
106C2×C32×C4—42no—
107C2×C32×C4—42no—
108C2×C32×C4—42no—
109C2×C32×C4C4⋊C414yes—
110C2×C3×Dic3—22no—
111C2×C3×Dic3—22no—
112C2×C3×Dic3—22no—
113C2×C3×Dic3—22no—
114C2×C3×Dic3—24no—
115C2×C3×Dic3—24no—
116C2×C3×Dic3—24no—
117C2×C3×Dic3—24no—
118C2×C3×Dic3—24no—
119C2×C3×Dic3—24no—
120C2×C3×Dic3—24no—
121C2×C3×Dic3—42no—
122C2×C3×Dic3—42no—
123C2×C3×Dic3—42no—
124C2×C3×Dic3—42no—
125C2×C3×Dic3C4214yes—
126C2×C3×Dic3C22⋊C414yes—
127C22×C42—31no—
128C2×#95—32no—
129C2×#95—32no—
130C2×#95—31no—
131C2×#95C3×D311yescharacteristic
132C24×C3—21no—
133C24×C3C22×D311yescharacteristic
134C24×C3C23×C311yescharacteristic
135C22×C3×C4—22no—
136C22×C3×C4—22no—
137C22×C3×C4—22no—
138C22×C3×C4—22no—
139C22×C3×C4—24no—
140C22×C3×C4—24no—
141C22×C3×C4—22no—
142C22×C3×C4—22no—
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—22no—
152C22×C3×C4—22no—
153C22×C3×C4—22no—
154C22×C3×C4—24no—
155C22×C3×C4—22no—
156C22×C3×C4—22no—
157C22×C3×C4—34no—
158C22×C3×C4—32no—
159C22×C3×C4—32no—
160C22×C3×C4—34no—
161C22×C3×C4—34no—
162C22×C3×C4—42no—
163C22×C3×C4—42no—
164C22×C3×C4—42no—
165C22×C3×C4—42no—
166C22×C3×C4—42no—
167C22×C3×C4—42no—
168C22×C3×C4—62no—
169C22×C3×C4—62no—
170C22×C3×C4—61no—
171C22×C3×C4—61no—
172C22×C3×C4—61no—
173C22×C3×C4—61no—
174C22×C3×C4—62no—
175C22×C3×C4—62no—
176C22×C3×C4—62no—
177C22×C3×C4—62no—
178C22×C3×C4—62no—
179C22×C3×C4—62no—
180C22×C3×C4Dic612yes—
181C22×C3×C4C4×D314yes—
182C22×C3×C4C4×D312yes—
183C22×C3×C4#6712yes—
184C22×C3×C4C2×C3×C414yes—
185C22×C3×C4C2×C3×C412yes—
186C22×C3×C4C3×D412yes—
187C22×C3×C4C3×Q812yes—
188C22×Dic3—22no—
189C22×Dic3—22no—
190C22×Dic3—21no—
191C22×Dic3—21no—
192C22×Dic3—21no—
193C22×Dic3—21no—
194C22×Dic3—22no—
195C22×Dic3—22no—
196C22×Dic3—22no—
197C22×Dic3—22no—
198C22×Dic3—22no—
199C22×Dic3—22no—
200C22×Dic3C2×C3×C414yes—
201C22×Dic3C2×C3×C414yes—
202C22×Dic3C2×C3×C412yes—
203C22×Dic3C2×C3×C412yes—
204C22×Dic3C3×D414yes—
205C3×C42—68no—
206C4×Dic3—28no—
207C22×C32C2×C4211yescharacteristic
208C22×C32C2×C22⋊C411yescharacteristic
209C22×C32C2×C4⋊C411yescharacteristic
210C22×C32#11711yescharacteristic
211C22×C32#11711yescharacteristic
212C22×C32#11712yes—
213C22×C32#11711yescharacteristic
214C22×C32#11712yes—
215C22×C32#11711yescharacteristic
216C22×C32C4×D412yes—
217C22×C32C4×D412yes—
218C22×C32C4×D412yes—
219C22×C32C4×Q812yes—
220C22×C32#12112yes—
221C22×C32C22⋊Q812yes—
222C22×C32#12312yes—
223C22×C32#12312yes—
224C22×C32#12411yescharacteristic
225C22×C32#12411yescharacteristic
226C22×C32#12511yescharacteristic
227C22×C32#12511yescharacteristic
228C22×C32#12612yes—
229C22×C32#12612yes—
230C32×C4—24no—
231C32×C4—44no—
232C3×Dic3—24no—
233C3×Dic3—24no—
234C3×Dic3—44no—
235C23×C4—31no—
236C23×C4—31no—
237C23×C4—32no—
238C23×C4C2×C3×D312yes—
239C23×C4C2×C3×D311yescharacteristic
240C2×C42—34no—
241C2×C42—64no—
242#95—22no—
243#95—38no—
244#95—64no—
245#95—62no—
246C23×C3—21no—
247C23×C3—21no—
248C23×C3—22no—
249C23×C3—22no—
250C23×C3—22no—
251C23×C3—22no—
252C23×C3—21no—
253C23×C3—21no—
254C23×C3—21no—
255C23×C3—21no—
256C23×C3—21no—
257C23×C3C2×Dic611yescharacteristic
258C23×C3C2×C4×D312yes—
259C23×C3C2×C4×D311yescharacteristic
260C23×C3#23512yes—
261C23×C3D3×D412yes—
262C23×C3#23712yes—
263C23×C3#23711yescharacteristic
264C23×C3#23711yescharacteristic
265C23×C3#23911yescharacteristic
266C23×C3#23911yescharacteristic
267C23×C3C2×#6711yescharacteristic
268C23×C3C22×C3×C411yescharacteristic
269C23×C3C22×C3×C412yes—
270C23×C3C2×C3×D412yes—
271C23×C3C2×C3×D411yescharacteristic
272C23×C3C2×C3×Q811yescharacteristic
273C23×C3C3×#4112yes—
274C23×C3C3×#4112yes—
275C23×C3C3×#4111yescharacteristic
276C23×C3C3×#4111yescharacteristic
277C23×C3C3×#4111yescharacteristic
278C23×C3C3×#4111yescharacteristic
279C2×C3×C4—22no—
280C2×C3×C4—24no—
281C2×C3×C4—22no—
282C2×C3×C4—24no—
283C2×C3×C4—22no—
284C2×C3×C4—22no—
285C2×C3×C4—24no—
286C2×C3×C4—24no—
287C2×C3×C4—28no—
288C2×C3×C4—24no—
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—34no—
296C2×C3×C4—34no—
297C2×C3×C4—42no—
298C2×C3×C4—44no—
299C2×C3×C4—42no—
300C2×C3×C4—44no—
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—62no—
316C2×C3×C4—62no—
317C2×C3×C4—64no—
318C2×C3×C4—64no—
319C2×C3×C4—62no—
320C2×C3×C4—62no—
321C2×C3×C4—64no—
322C2×C3×C4—64no—
323C2×C3×C4—64no—
324C2×C3×C4—64no—
325C2×C3×C4—64no—
326C2×C3×C4—122no—
327C2×C3×C4—122no—
328C2×C3×C4—122no—
329C2×C3×C4—122no—
330C2×C3×C4Dic3⋊C414yes—
331C2×C3×C4C3×C4⋊C414yes—
332C2×Dic3—22no—
333C2×Dic3—22no—
334C2×Dic3—22no—
335C2×Dic3—22no—
336C2×Dic3—24no—
337C2×Dic3—24no—
338C2×Dic3—24no—
339C2×Dic3—24no—
340C2×Dic3—24no—
341C2×Dic3—24no—
342C2×Dic3—24no—
343C2×Dic3—42no—
344C2×Dic3—42no—
345C2×Dic3—42no—
346C2×Dic3—42no—
347C2×Dic3C3×C4214yes—
348C2×Dic3C3×C22⋊C414yes—
349C2×C32#37611yescharacteristic
350C2×C32C4×C22⋊C411yescharacteristic
351C2×C32C4×C4⋊C411yescharacteristic
352C2×C32#38011yescharacteristic
353C2×C32#38111yescharacteristic
354C2×C32#38211yescharacteristic
355C2×C32#38311yescharacteristic
356C2×C32#38712yes—
357C2×C32#38712yes—
358C2×C32#38812yes—
359C2×C32#38812yes—
360C24C22×C3×D311yescharacteristic
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—34no—
370C22×C4—32no—
371C22×C4—32no—
372C22×C4—34no—
373C22×C4—34no—
374C22×C4—62no—
375C22×C4—62no—
376C22×C4—61no—
377C22×C4—61no—
378C22×C4—61no—
379C22×C4—61no—
380C22×C4—62no—
381C22×C4—62no—
382C22×C4—62no—
383C22×C4—62no—
384C22×C4—62no—
385C22×C4—62no—
386C22×C4C3×Dic612yes—
387C22×C4C3×C4×D314yes—
388C22×C4C3×C4×D312yes—
389C22×C4C3×#6712yes—
390C42—68no—
391C22×C3—21no—
392C22×C3—22no—
393C22×C3—22no—
394C22×C3—22no—
395C22×C3—21no—
396C22×C3—22no—
397C22×C3—22no—
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—22no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—22no—
404C22×C3—22no—
405C22×C3—22no—
406C22×C3—21no—
407C22×C3—22no—
408C22×C3—21no—
409C22×C3—22no—
410C22×C3—21no—
411C22×C3—22no—
412C22×C3—21no—
413C22×C3—21no—
414C22×C3C4×Dic612yes—
415C22×C3C42×D311yescharacteristic
416C22×C3#87211yescharacteristic
417C22×C3#87711yescharacteristic
418C22×C3#87712yes—
419C22×C3#87812yes—
420C22×C3#87912yes—
421C22×C3D3×C22⋊C411yescharacteristic
422C22×C3#67⋊C412yes—
423C22×C3#88312yes—
424C22×C3#89011yescharacteristic
425C22×C3#89011yescharacteristic
426C22×C3#89212yes—
427C22×C3#89211yescharacteristic
428C22×C3#89211yescharacteristic
429C22×C3#89312yes—
430C22×C3#89412yes—
431C22×C3#89812yes—
432C22×C3C2×Dic3⋊C411yescharacteristic
433C22×C3C4×#6712yes—
434C22×C3#93611yescharacteristic
435C22×C3#93912yes—
436C22×C3#94711yescharacteristic
437C22×C3C2×C3×C4211yescharacteristic
438C22×C3C2×C3×C22⋊C411yescharacteristic
439C22×C3C2×C3×C4⋊C411yescharacteristic
440C22×C3C3×#11711yescharacteristic
441C22×C3C3×#11712yes—
442C22×C3C3×#11711yescharacteristic
443C22×C3C3×#11712yes—
444C22×C3C3×#11711yescharacteristic
445C22×C3C3×#11711yescharacteristic
446C22×C3C3×C4×D412yes—
447C22×C3C3×C4×D412yes—
448C22×C3C3×C4×D412yes—
449C22×C3C3×C4×Q812yes—
450C22×C3C3×#12112yes—
451C22×C3C3×C22⋊Q812yes—
452C22×C3C3×#12312yes—
453C22×C3C3×#12312yes—
454C22×C3C3×#12411yescharacteristic
455C22×C3C3×#12411yescharacteristic
456C22×C3C3×#12511yescharacteristic
457C22×C3C3×#12511yescharacteristic
458C22×C3C3×#12612yes—
459C22×C3C3×#12612yes—
460C3×C4—24no—
461C3×C4—24no—
462C3×C4—44no—
463C3×C4—48no—
464C3×C4—44no—
465C3×C4—44no—
466C3×C4—64no—
467C3×C4—64no—
468C3×C4—124no—
469Dic3—24no—
470Dic3—24no—
471Dic3—44no—
472C32#143411yescharacteristic, complemented, Sylow
473C23C2×C3×Dic611yescharacteristic
474C23C2×C3×C4×D311yescharacteristic
475C23C2×C3×C4×D312yes—
476C23C3×#23512yes—
477C23C3×D3×D412yes—
478C23C3×#23712yes—
479C23C3×#23711yescharacteristic
480C23C3×#23711yescharacteristic
481C23C3×#23911yescharacteristic
482C23C3×#23911yescharacteristic
483C23C2×C3×#6711yescharacteristic
484C2×C4—22no—
485C2×C4—24no—
486C2×C4—22no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—34no—
492C2×C4—34no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—62no—
498C2×C4—64no—
499C2×C4—64no—
500C2×C4—62no—
501C2×C4—62no—
502C2×C4—64no—
503C2×C4—64no—
504C2×C4—62no—
505C2×C4—64no—
506C2×C4—64no—
507C2×C4—64no—
508C2×C4—122no—
509C2×C4—122no—
510C2×C4—122no—
511C2×C4—122no—
512C2×C4C3×Dic3⋊C414yes—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3—22no—
516C2×C3—22no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—21no—
521C2×C3—22no—
522C2×C3—21no—
523C2×C3—22no—
524C2×C3#464811yescharacteristic
525C2×C3#465111yescharacteristic
526C2×C3#465412yes—
527C2×C3#465512yes—
528C2×C3#466411yescharacteristic
529C2×C3#466611yescharacteristic
530C2×C3C4×Dic3⋊C411yescharacteristic
531C2×C3#494211yescharacteristic
532C2×C3#494512yes—
533C2×C3#497711yescharacteristic
534C2×C3#499012yes—
535C2×C3C3×#37611yescharacteristic
536C2×C3C3×C4×C22⋊C411yescharacteristic
537C2×C3C3×C4×C4⋊C411yescharacteristic
538C2×C3C3×#38011yescharacteristic
539C2×C3C3×#38111yescharacteristic
540C2×C3C3×#38211yescharacteristic
541C2×C3C3×#38311yescharacteristic
542C2×C3C3×#38712yes—
543C2×C3C3×#38712yes—
544C2×C3C3×#38812yes—
545C2×C3C3×#38812yes—
546C22C3×C4×Dic612yes—
547C22C3×C42×D311yescharacteristic
548C22C3×#87211yescharacteristic
549C22C3×#87711yescharacteristic
550C22C3×#87712yes—
551C22C3×#87812yes—
552C22C3×#87912yes—
553C22C3×D3×C22⋊C411yescharacteristic
554C22C3×#67⋊C412yes—
555C22C3×#88312yes—
556C22C3×#89011yescharacteristic
557C22C3×#89011yescharacteristic
558C22C3×#89212yes—
559C22C3×#89211yescharacteristic
560C22C3×#89211yescharacteristic
561C22C3×#89312yes—
562C22C3×#89412yes—
563C22C3×#89812yes—
564C22C2×C3×Dic3⋊C411yescharacteristic
565C22C3×C4×#6712yes—
566C22C3×#93611yescharacteristic
567C22C3×#93912yes—
568C22C3×#94711yescharacteristic
569C4—24no—
570C4—44no—
571C4—64no—
572C4—64no—
573C4—124no—
574C3—21no—
575C3#6940311yescharacteristic, direct product factor
576C3C3×#143411yescharacteristic, complemented
577C2C3×#464811yescharacteristic
578C2C3×#465111yescharacteristic
579C2C3×#465412yes—
580C2C3×#465512yes—
581C2C3×#466411yescharacteristic
582C2C3×#466611yescharacteristic
583C2C3×C4×Dic3⋊C411yescharacteristic
584C2C3×#494211yescharacteristic
585C2C3×#494512yes—
586C2C3×#497711yescharacteristic
587C2C3×#499012yes—
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×#1434
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. #69403C3direct (N × H)
14. C2×C3×C4×Dic3C4semidirect
18. C3×C3⋊#95C4semidirect
77. C2×C4×Dic3C3×C4semidirect
86. C3⋊#95C3×C4semidirect
472. C32#1434semidirect
575. C3#69403direct (N × H)
576. C3C3×#1434semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C4×Dic32
C2×C32×#952
C2×C3×C3⋊#952
C3×#14343
#694033