Finite Group Databasebeta

← C3×#69412 #11773387

Subgroups — C3×#69412 #11773387

Order 1152.

1205 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⋊#95C212yesmaximal
4C2×C3×C3⋊#95C212yesmaximal
5C2×C3×C3⋊#95C211yesmaximal, characteristic
6C3×#1442—31nomaximal
7#69412C311yesmaximal, characteristic, direct product factor
8C23×C32×C4C2212yes—
9C23×C32×C4C2211yescharacteristic
10C23×C3×Dic3C2212yes—
11C23×C3×Dic3C2211yescharacteristic
12C23×C3×Dic3C2211yescharacteristic
13C2×C3×C4⋊Dic3—22no—
14C2×C3×C4⋊Dic3—24no—
15C32×#95C414yescomplemented
16C3×C3⋊#95—22no—
17C3×C3⋊#95—24no—
18C3×C3⋊#95—24no—
19C22×C3×C4⋊C4—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—22no—
45C22×C3×Dic3—22no—
46C22×C3×Dic3—21no—
47C22×C3×Dic3—21no—
48C22×C3×Dic3—22no—
49C22×C3×Dic3—22no—
50C22×C3×Dic3—21no—
51C22×C3×Dic3—22no—
52C22×C3×Dic3—21no—
53C22×C3×Dic3—22no—
54C22×C3×Dic3—22no—
55C22×C3×Dic3—22no—
56C22×C3×Dic3—22no—
57C22×C3×Dic3D414yes—
58C22×C3×Dic3D412yes—
59C22×C3×Dic3Q812yes—
60C3×C4⋊Dic3—28no—
61#1442—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×C311yescharacteristic
72C23×Dic3C22×C312yes—
73C23×Dic3C22×C311yescharacteristic
74C2×C3×C4⋊C4—64no—
75C2×C3×C4⋊C4—62no—
76C2×C4⋊Dic3—22no—
77C2×C4⋊Dic3—24no—
78C3×#95—24no—
79C3×#95—64no—
80C3×#95—64no—
81C3×#95—62no—
82C3×#95Dic314yescomplemented
83C3×#95C3×C414yescomplemented
84C3⋊#95—22no—
85C3⋊#95—24no—
86C3⋊#95—24no—
87C23×C32C22×C411yescharacteristic
88C23×C32C2×D411yescharacteristic
89C23×C32C2×D412yes—
90C23×C32C2×D411yescharacteristic
91C23×C32C2×Q811yescharacteristic
92C23×C32C2×Q811yescharacteristic
93C23×C32#4112yes—
94C23×C32#4112yes—
95C23×C32#4112yes—
96C23×C32#4111yescharacteristic
97C23×C32#4111yescharacteristic
98C2×C32×C4—24no—
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—42no—
106C2×C32×C4—42no—
107C2×C32×C4—42no—
108C2×C32×C4—42no—
109C2×C32×C4C4⋊C414yes—
110C2×C3×Dic3—24no—
111C2×C3×Dic3—24no—
112C2×C3×Dic3—22no—
113C2×C3×Dic3—24no—
114C2×C3×Dic3—22no—
115C2×C3×Dic3—24no—
116C2×C3×Dic3—24no—
117C2×C3×Dic3—41no—
118C2×C3×Dic3—42no—
119C2×C3×Dic3—42no—
120C2×C3×Dic3—41no—
121C2×C3×Dic3—42no—
122C2×C3×Dic3—41no—
123C2×C3×Dic3—42no—
124C2×C3×Dic3—41no—
125C2×C3×Dic3—42no—
126C2×C3×Dic3—42no—
127C22×C4⋊C4—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—22no—
155C22×C3×C4—24no—
156C22×C3×C4—22no—
157C22×C3×C4—32no—
158C22×C3×C4—34no—
159C22×C3×C4—32no—
160C22×C3×C4—42no—
161C22×C3×C4—42no—
162C22×C3×C4—42no—
163C22×C3×C4—42no—
164C22×C3×C4—42no—
165C22×C3×C4—42no—
166C22×C3×C4—61no—
167C22×C3×C4—61no—
168C22×C3×C4—62no—
169C22×C3×C4—62no—
170C22×C3×C4—62no—
171C22×C3×C4—62no—
172C22×C3×C4—62no—
173C22×C3×C4—62no—
174C22×C3×C4—62no—
175C22×C3×C4—62no—
176C22×C3×C4—62no—
177C22×C3×C4—61no—
178C22×C3×C4—62no—
179C22×C3×C4—61no—
180C22×C3×C4Dic612yes—
181C22×C3×C4D1212yes—
182C22×C3×C4C2×Dic314yes—
183C22×C3×C4C2×Dic312yes—
184C22×C3×C4C2×C3×C414yes—
185C22×C3×C4C2×C3×C412yes—
186C22×C3×C4C3×D412yes—
187C22×C3×C4C3×Q812yes—
188C22×Dic3—21no—
189C22×Dic3—21no—
190C22×Dic3—22no—
191C22×Dic3—22no—
192C22×Dic3—22no—
193C22×Dic3—22no—
194C22×Dic3—22no—
195C22×Dic3—22no—
196C22×Dic3—22no—
197C22×Dic3—22no—
198C22×Dic3—21no—
199C22×Dic3—22no—
200C22×Dic3—21no—
201C22×Dic3—22no—
202C22×Dic3C3×D412yes—
203C22×Dic3C3×D414yes—
204C22×Dic3C3×Q812yes—
205C3×C4⋊C4—68no—
206C4⋊Dic3—28no—
207C22×C32C2×C4⋊C411yescharacteristic
208C22×C32#11712yes—
209C22×C32C4×D412yes—
210C22×C32C4×D411yescharacteristic
211C22×C32C4×Q811yescharacteristic
212C22×C32#12011yescharacteristic
213C22×C32#12112yes—
214C22×C32#12111yescharacteristic
215C22×C32C22⋊Q812yes—
216C22×C32C22⋊Q812yes—
217C22×C32C22⋊Q811yescharacteristic
218C22×C32#12312yes—
219C22×C32#12311yescharacteristic
220C22×C32#12312yes—
221C22×C32#12411yescharacteristic
222C22×C32#12411yescharacteristic
223C22×C32#12412yes—
224C22×C32#12512yes—
225C22×C32#12512yes—
226C22×C32#12511yescharacteristic
227C22×C32#12612yes—
228C22×C32#12612yes—
229C22×C32C4⋊Q811yescharacteristic
230C32×C4—24no—
231C32×C4—44no—
232C3×Dic3—42no—
233C3×Dic3—44no—
234C3×Dic3—42no—
235C23×C4—32no—
236C23×C4—31no—
237C23×C4—31no—
238C23×C4C2×C3×D312yes—
239C23×C4C2×C3×D311yescharacteristic
240C2×C4⋊C4—64no—
241C2×C4⋊C4—62no—
242#95—64no—
243#95—64no—
244#95—62no—
245#95C3×Dic314yescomplemented
246C23×C3—21no—
247C23×C3—21no—
248C23×C3—22no—
249C23×C3—22no—
250C23×C3—22no—
251C23×C3—21no—
252C23×C3—22no—
253C23×C3—21no—
254C23×C3—21no—
255C23×C3—21no—
256C23×C3—21no—
257C23×C3C2×Dic611yescharacteristic
258C23×C3C2×D1211yescharacteristic
259C23×C3#23512yes—
260C23×C3#23512yes—
261C23×C3D3×D412yes—
262C23×C3D3×D411yescharacteristic
263C23×C3#23712yes—
264C23×C3#23711yescharacteristic
265C23×C3D3×Q811yescharacteristic
266C23×C3#23911yescharacteristic
267C23×C3C22×Dic311yescharacteristic
268C23×C3C22×C3×C411yescharacteristic
269C23×C3C2×C3×D411yescharacteristic
270C23×C3C2×C3×D412yes—
271C23×C3C2×C3×D411yescharacteristic
272C23×C3C2×C3×Q811yescharacteristic
273C23×C3C2×C3×Q811yescharacteristic
274C23×C3C3×#4112yes—
275C23×C3C3×#4112yes—
276C23×C3C3×#4112yes—
277C23×C3C3×#4111yescharacteristic
278C23×C3C3×#4111yescharacteristic
279C2×C3×C4—24no—
280C2×C3×C4—22no—
281C2×C3×C4—22no—
282C2×C3×C4—24no—
283C2×C3×C4—24no—
284C2×C3×C4—22no—
285C2×C3×C4—24no—
286C2×C3×C4—22no—
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—44no—
296C2×C3×C4—42no—
297C2×C3×C4—42no—
298C2×C3×C4—44no—
299C2×C3×C4—44no—
300C2×C3×C4—44no—
301C2×C3×C4—44no—
302C2×C3×C4—44no—
303C2×C3×C4—44no—
304C2×C3×C4—44no—
305C2×C3×C4—42no—
306C2×C3×C4—42no—
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—64no—
314C2×C3×C4—64no—
315C2×C3×C4—64no—
316C2×C3×C4—64no—
317C2×C3×C4—62no—
318C2×C3×C4—64no—
319C2×C3×C4—62no—
320C2×C3×C4—122no—
321C2×C3×C4—121no—
322C2×C3×C4—121no—
323C2×C3×C4—121no—
324C2×C3×C4—122no—
325C2×C3×C4—122no—
326C2×C3×C4—121no—
327C2×C3×C4—122no—
328C2×C3×C4—122no—
329C2×C3×C4—122no—
330C2×C3×C4C4⋊Dic314yes—
331C2×C3×C4C3×C4⋊C414yes—
332C2×Dic3—24no—
333C2×Dic3—24no—
334C2×Dic3—22no—
335C2×Dic3—24no—
336C2×Dic3—22no—
337C2×Dic3—24no—
338C2×Dic3—24no—
339C2×Dic3—41no—
340C2×Dic3—42no—
341C2×Dic3—42no—
342C2×Dic3—41no—
343C2×Dic3—42no—
344C2×Dic3—42no—
345C2×Dic3—41no—
346C2×Dic3—42no—
347C2×Dic3—41no—
348C2×Dic3—42no—
349C2×C32#38211yescharacteristic
350C2×C32#38511yescharacteristic
351C2×C32#38712yes—
352C2×C32#38812yes—
353C2×C32#38911yescharacteristic
354C2×C32#39311yescharacteristic
355C2×C32#39411yescharacteristic
356C2×C32#39711yescharacteristic
357C2×C32#39812yes—
358C2×C32#40011yescharacteristic
359C2×C32#40012yes—
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—32no—
370C22×C4—34no—
371C22×C4—32no—
372C22×C4—61no—
373C22×C4—61no—
374C22×C4—62no—
375C22×C4—62no—
376C22×C4—62no—
377C22×C4—62no—
378C22×C4—62no—
379C22×C4—62no—
380C22×C4—62no—
381C22×C4—62no—
382C22×C4—62no—
383C22×C4—61no—
384C22×C4—62no—
385C22×C4—61no—
386C22×C4C3×Dic612yes—
387C22×C4C3×D1212yes—
388C22×C4C2×C3×Dic314yes—
389C22×C4C2×C3×Dic312yes—
390C4⋊C4—68no—
391C22×C3—22no—
392C22×C3—22no—
393C22×C3—21no—
394C22×C3—22no—
395C22×C3—22no—
396C22×C3—22no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—22no—
400C22×C3—21no—
401C22×C3—22no—
402C22×C3—21no—
403C22×C3—22no—
404C22×C3—21no—
405C22×C3—22no—
406C22×C3—21no—
407C22×C3—22no—
408C22×C3—22no—
409C22×C3—21no—
410C22×C3—21no—
411C22×C3—22no—
412C22×C3—21no—
413C22×C3—21no—
414C22×C3#87012yes—
415C22×C3#87511yescharacteristic
416C22×C3#87511yescharacteristic
417C22×C3#87812yes—
418C22×C3#87912yes—
419C22×C3#88211yescharacteristic
420C22×C3#88312yes—
421C22×C3#88412yes—
422C22×C3#88512yes—
423C22×C3#88611yescharacteristic
424C22×C3#88811yescharacteristic
425C22×C3#88912yes—
426C22×C3#89011yescharacteristic
427C22×C3#89412yes—
428C22×C3#89511yescharacteristic
429C22×C3#89612yes—
430C22×C3#89711yescharacteristic
431C22×C3#89812yes—
432C22×C3C2×C4⋊Dic311yescharacteristic
433C22×C3#92612yes—
434C22×C3D4×Dic312yes—
435C22×C3D4×Dic311yescharacteristic
436C22×C3Q8×Dic311yescharacteristic
437C22×C3C2×C3×C4⋊C411yescharacteristic
438C22×C3C3×#11712yes—
439C22×C3C3×C4×D412yes—
440C22×C3C3×C4×D411yescharacteristic
441C22×C3C3×C4×Q811yescharacteristic
442C22×C3C3×#12011yescharacteristic
443C22×C3C3×#12112yes—
444C22×C3C3×#12111yescharacteristic
445C22×C3C3×C22⋊Q812yes—
446C22×C3C3×C22⋊Q812yes—
447C22×C3C3×C22⋊Q811yescharacteristic
448C22×C3C3×#12312yes—
449C22×C3C3×#12311yescharacteristic
450C22×C3C3×#12312yes—
451C22×C3C3×#12412yes—
452C22×C3C3×#12411yescharacteristic
453C22×C3C3×#12411yescharacteristic
454C22×C3C3×#12512yes—
455C22×C3C3×#12511yescharacteristic
456C22×C3C3×#12512yes—
457C22×C3C3×#12612yes—
458C22×C3C3×#12612yes—
459C22×C3C3×C4⋊Q811yescharacteristic
460C3×C4—24no—
461C3×C4—24no—
462C3×C4—44no—
463C3×C4—48no—
464C3×C4—44no—
465C3×C4—44no—
466C3×C4—124no—
467C3×C4—122no—
468C3×C4—122no—
469Dic3—42no—
470Dic3—44no—
471Dic3—42no—
472C32#144211yescharacteristic, complemented, Sylow
473C23C2×C3×Dic611yescharacteristic
474C23C2×C3×D1211yescharacteristic
475C23C3×#23512yes—
476C23C3×#23512yes—
477C23C3×D3×D412yes—
478C23C3×D3×D411yescharacteristic
479C23C3×#23712yes—
480C23C3×#23711yescharacteristic
481C23C3×D3×Q811yescharacteristic
482C23C3×#23911yescharacteristic
483C23C22×C3×Dic311yescharacteristic
484C2×C4—24no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—64no—
496C2×C4—64no—
497C2×C4—64no—
498C2×C4—64no—
499C2×C4—62no—
500C2×C4—64no—
501C2×C4—62no—
502C2×C4—121no—
503C2×C4—122no—
504C2×C4—122no—
505C2×C4—121no—
506C2×C4—122no—
507C2×C4—122no—
508C2×C4—122no—
509C2×C4—122no—
510C2×C4—121no—
511C2×C4—121no—
512C2×C4C3×C4⋊Dic314yes—
513C2×C3—22no—
514C2×C3—21no—
515C2×C3—22no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—21no—
521C2×C3—22no—
522C2×C3—22no—
523C2×C3—21no—
524C2×C3#465712yes—
525C2×C3#465911yescharacteristic
526C2×C3#466012yes—
527C2×C3#467211yescharacteristic
528C2×C3#467311yescharacteristic
529C2×C3#467411yescharacteristic
530C2×C3#493611yescharacteristic
531C2×C3#495011yescharacteristic
532C2×C3#495112yes—
533C2×C3#498012yes—
534C2×C3#498411yescharacteristic
535C2×C3C3×#38211yescharacteristic
536C2×C3C3×#38511yescharacteristic
537C2×C3C3×#38712yes—
538C2×C3C3×#38812yes—
539C2×C3C3×#38911yescharacteristic
540C2×C3C3×#39311yescharacteristic
541C2×C3C3×#39411yescharacteristic
542C2×C3C3×#39711yescharacteristic
543C2×C3C3×#39812yes—
544C2×C3C3×#40011yescharacteristic
545C2×C3C3×#40012yes—
546C22C3×#87012yes—
547C22C3×#87511yescharacteristic
548C22C3×#87511yescharacteristic
549C22C3×#87812yes—
550C22C3×#87912yes—
551C22C3×#88211yescharacteristic
552C22C3×#88312yes—
553C22C3×#88412yes—
554C22C3×#88512yes—
555C22C3×#88611yescharacteristic
556C22C3×#88811yescharacteristic
557C22C3×#88912yes—
558C22C3×#89011yescharacteristic
559C22C3×#89412yes—
560C22C3×#89511yescharacteristic
561C22C3×#89612yes—
562C22C3×#89711yescharacteristic
563C22C3×#89812yes—
564C22C2×C3×C4⋊Dic311yescharacteristic
565C22C3×#92612yes—
566C22C3×D4×Dic312yes—
567C22C3×D4×Dic311yescharacteristic
568C22C3×Q8×Dic311yescharacteristic
569C4—24no—
570C4—44no—
571C4—124no—
572C4—122no—
573C4—122no—
574C3—21no—
575C3#6941211yescharacteristic, direct product factor
576C3C3×#144211yescharacteristic, complemented
577C2C3×#465712yes—
578C2C3×#465911yescharacteristic
579C2C3×#466012yes—
580C2C3×#467211yescharacteristic
581C2C3×#467311yescharacteristic
582C2C3×#467411yescharacteristic
583C2C3×#493611yescharacteristic
584C2C3×#495011yescharacteristic
585C2C3×#495112yes—
586C2C3×#498012yes—
587C2C3×#498411yescharacteristic
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×#1442
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. #69412C3direct (N × H)
15. C32×#95C4semidirect
82. C3×#95Dic3semidirect
83. C3×#95C3×C4semidirect
245. #95C3×Dic3semidirect
472. C32#1442semidirect
575. C3#69412direct (N × H)
576. C3C3×#1442semidirect

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×#14423
#694123