Finite Group Databasebeta

← C3×#69410 #11773358

Subgroups — C3×#69410 #11773358

Order 1152.

1293 conjugacy classes of subgroups.

The subgroup lattice has 617 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4⋊Dic3C211yesmaximal, characteristic
2C22×C3×Dic3⋊C4C211yesmaximal, characteristic
3C2×C32×#95C211yesmaximal, characteristic
4C2×C3×C3⋊#95C212yesmaximal
5C2×C3×C3⋊#95C212yesmaximal
6C3×#1441—31nomaximal
7#69410C311yesmaximal, characteristic, direct product factor
8C23×C32×C4C2212yes—
9C23×C32×C4C2211yescharacteristic
10C23×C3×Dic3C2211yescharacteristic
11C23×C3×Dic3C2212yes—
12C23×C3×Dic3C2211yescharacteristic
13C2×C3×C4⋊Dic3—22no—
14C2×C3×C4⋊Dic3—24no—
15C2×C3×Dic3⋊C4—22no—
16C2×C3×Dic3⋊C4—22no—
17C2×C3×Dic3⋊C4C414yescomplemented
18C32×#95—22no—
19C3×C3⋊#95—24no—
20C3×C3⋊#95—24no—
21C22×C3×C4⋊C4—31no—
22C22×C3×C4⋊C4—31no—
23C22×C4⋊Dic3C2×C311yescharacteristic
24C22×Dic3⋊C4C2×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×C412yes—
42C22×C32×C4D412yes—
43C22×C32×C4D412yes—
44C22×C32×C4Q814yes—
45C22×C3×Dic3—21no—
46C22×C3×Dic3—21no—
47C22×C3×Dic3—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3—21no—
50C22×C3×Dic3—21no—
51C22×C3×Dic3—22no—
52C22×C3×Dic3—22no—
53C22×C3×Dic3—22no—
54C22×C3×Dic3—22no—
55C22×C3×Dic3—22no—
56C22×C3×Dic3—22no—
57C22×C3×Dic3—22no—
58C22×C3×Dic3—22no—
59C22×C3×Dic3C2×C412yes—
60C22×C3×Dic3C2×C412yes—
61C22×C3×Dic3D414yes—
62C22×C3×Dic3D412yes—
63C22×C3×Dic3Q812yes—
64C3×C4⋊Dic3—28no—
65C3×Dic3⋊C4—28no—
66#1441—31noSylow
67C23×C3×C4—22no—
68C23×C3×C4—21no—
69C23×C3×C4—31no—
70C23×C3×C4—31no—
71C23×C3×C4—32no—
72C23×C3×C4C2×D312yes—
73C23×C3×C4C2×D311yescharacteristic
74C23×C3×C4C22×C312yes—
75C23×C3×C4C22×C311yescharacteristic
76C23×Dic3C22×C311yescharacteristic
77C23×Dic3C22×C312yes—
78C23×Dic3C22×C311yescharacteristic
79C2×C3×C4⋊C4—34no—
80C2×C3×C4⋊C4—64no—
81C2×C3×C4⋊C4—62no—
82C2×C3×C4⋊C4—62no—
83C2×C3×C4⋊C4—62no—
84C2×C4⋊Dic3—22no—
85C2×C4⋊Dic3—24no—
86C2×Dic3⋊C4—22no—
87C2×Dic3⋊C4—22no—
88C2×Dic3⋊C4C3×C414yescomplemented
89C3×#95—24no—
90C3×#95—22no—
91C3×#95—22no—
92C3×#95—64no—
93C3×#95—64no—
94C3⋊#95—24no—
95C3⋊#95—24no—
96C23×C32C22×C411yescharacteristic
97C23×C32C2×D411yescharacteristic
98C23×C32C2×D411yescharacteristic
99C23×C32C2×D412yes—
100C23×C32C2×D411yescharacteristic
101C23×C32C2×Q812yes—
102C23×C32C2×Q811yescharacteristic
103C23×C32#4112yes—
104C23×C32#4111yescharacteristic
105C23×C32#4112yes—
106C23×C32#4111yescharacteristic
107C2×C32×C4—24no—
108C2×C32×C4—24no—
109C2×C32×C4—22no—
110C2×C32×C4—24no—
111C2×C32×C4—22no—
112C2×C32×C4—24no—
113C2×C32×C4—24no—
114C2×C32×C4—42no—
115C2×C32×C4—42no—
116C2×C32×C4—42no—
117C2×C32×C4—42no—
118C2×C32×C4C22⋊C414yes—
119C2×C3×Dic3—22no—
120C2×C3×Dic3—22no—
121C2×C3×Dic3—22no—
122C2×C3×Dic3—22no—
123C2×C3×Dic3—22no—
124C2×C3×Dic3—22no—
125C2×C3×Dic3—22no—
126C2×C3×Dic3—24no—
127C2×C3×Dic3—24no—
128C2×C3×Dic3—24no—
129C2×C3×Dic3—24no—
130C2×C3×Dic3—41no—
131C2×C3×Dic3—42no—
132C2×C3×Dic3—42no—
133C2×C3×Dic3—42no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—42no—
136C2×C3×Dic3—42no—
137C2×C3×Dic3C4⋊C414yescomplemented
138C22×C4⋊C4—31no—
139C22×C4⋊C4—31no—
140C2×#95—32no—
141C2×#95—32no—
142C2×#95C3×D311yescharacteristic
143C24×C3—21no—
144C24×C3C22×D311yescharacteristic
145C24×C3C23×C311yescharacteristic
146C22×C3×C4—22no—
147C22×C3×C4—22no—
148C22×C3×C4—22no—
149C22×C3×C4—22no—
150C22×C3×C4—24no—
151C22×C3×C4—24no—
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—24no—
165C22×C3×C4—22no—
166C22×C3×C4—22no—
167C22×C3×C4—22no—
168C22×C3×C4—32no—
169C22×C3×C4—32no—
170C22×C3×C4—32no—
171C22×C3×C4—32no—
172C22×C3×C4—34no—
173C22×C3×C4—42no—
174C22×C3×C4—42no—
175C22×C3×C4—42no—
176C22×C3×C4—42no—
177C22×C3×C4—42no—
178C22×C3×C4—42no—
179C22×C3×C4—61no—
180C22×C3×C4—61no—
181C22×C3×C4—61no—
182C22×C3×C4—61no—
183C22×C3×C4—62no—
184C22×C3×C4—61no—
185C22×C3×C4—62no—
186C22×C3×C4—62no—
187C22×C3×C4—62no—
188C22×C3×C4—62no—
189C22×C3×C4—62no—
190C22×C3×C4—62no—
191C22×C3×C4—62no—
192C22×C3×C4—61no—
193C22×C3×C4Dic614yes—
194C22×C3×C4C4×D312yes—
195C22×C3×C4D1212yes—
196C22×C3×C4#6712yes—
197C22×C3×C4C2×C3×C412yes—
198C22×C3×C4C3×D412yes—
199C22×C3×C4C3×D412yes—
200C22×C3×C4C3×Q814yes—
201C22×Dic3—21no—
202C22×Dic3—21no—
203C22×Dic3—21no—
204C22×Dic3—21no—
205C22×Dic3—22no—
206C22×Dic3—22no—
207C22×Dic3—21no—
208C22×Dic3—21no—
209C22×Dic3—22no—
210C22×Dic3—22no—
211C22×Dic3—22no—
212C22×Dic3—22no—
213C22×Dic3—22no—
214C22×Dic3—22no—
215C22×Dic3C2×C3×C412yes—
216C22×Dic3C2×C3×C412yes—
217C22×Dic3C3×D414yes—
218C22×Dic3C3×D412yes—
219C22×Dic3C3×Q812yes—
220C3×C4⋊C4—68no—
221C3×C4⋊C4—68no—
222C4⋊Dic3—28no—
223Dic3⋊C4—28no—
224C22×C32C2×C22⋊C411yescharacteristic
225C22×C32C2×C4⋊C411yescharacteristic
226C22×C32#11711yescharacteristic
227C22×C32C4×D412yes—
228C22×C32C4×Q812yes—
229C22×C32#12011yescharacteristic
230C22×C32#12112yes—
231C22×C32#12111yescharacteristic
232C22×C32#12111yescharacteristic
233C22×C32#12112yes—
234C22×C32C22⋊Q812yes—
235C22×C32C22⋊Q812yes—
236C22×C32C22⋊Q811yescharacteristic
237C22×C32C22⋊Q812yes—
238C22×C32C22⋊Q811yescharacteristic
239C22×C32#12311yescharacteristic
240C22×C32#12312yes—
241C22×C32#12411yescharacteristic
242C22×C32#12512yes—
243C22×C32#12512yes—
244C22×C32#12612yes—
245C22×C32C4⋊Q811yescharacteristic
246C22×C32C4⋊Q812yes—
247C32×C4—24no—
248C32×C4—44no—
249C3×Dic3—24no—
250C3×Dic3—42no—
251C3×Dic3—44no—
252C23×C4—31no—
253C23×C4—31no—
254C23×C4—32no—
255C23×C4C2×C3×D312yes—
256C23×C4C2×C3×D311yescharacteristic
257C2×C4⋊C4—34no—
258C2×C4⋊C4—64no—
259C2×C4⋊C4—62no—
260C2×C4⋊C4—62no—
261C2×C4⋊C4—62no—
262#95—22no—
263#95—64no—
264#95—64no—
265C23×C3—22no—
266C23×C3—21no—
267C23×C3—21no—
268C23×C3—22no—
269C23×C3—21no—
270C23×C3—22no—
271C23×C3—21no—
272C23×C3—22no—
273C23×C3—21no—
274C23×C3—21no—
275C23×C3—21no—
276C23×C3C2×Dic612yes—
277C23×C3C2×C4×D311yescharacteristic
278C23×C3C2×D1211yescharacteristic
279C23×C3#23512yes—
280C23×C3D3×D411yescharacteristic
281C23×C3D3×D412yes—
282C23×C3#23711yescharacteristic
283C23×C3#23712yes—
284C23×C3D3×Q811yescharacteristic
285C23×C3#23911yescharacteristic
286C23×C3C2×#6711yescharacteristic
287C23×C3C22×C3×C411yescharacteristic
288C23×C3C2×C3×D411yescharacteristic
289C23×C3C2×C3×D411yescharacteristic
290C23×C3C2×C3×D412yes—
291C23×C3C2×C3×D411yescharacteristic
292C23×C3C2×C3×Q812yes—
293C23×C3C2×C3×Q811yescharacteristic
294C23×C3C3×#4112yes—
295C23×C3C3×#4111yescharacteristic
296C23×C3C3×#4112yes—
297C23×C3C3×#4111yescharacteristic
298C2×C3×C4—24no—
299C2×C3×C4—22no—
300C2×C3×C4—22no—
301C2×C3×C4—24no—
302C2×C3×C4—24no—
303C2×C3×C4—22no—
304C2×C3×C4—24no—
305C2×C3×C4—22no—
306C2×C3×C4—28no—
307C2×C3×C4—24no—
308C2×C3×C4—24no—
309C2×C3×C4—24no—
310C2×C3×C4—24no—
311C2×C3×C4—24no—
312C2×C3×C4—24no—
313C2×C3×C4—24no—
314C2×C3×C4—34no—
315C2×C3×C4—44no—
316C2×C3×C4—42no—
317C2×C3×C4—42no—
318C2×C3×C4—44no—
319C2×C3×C4—44no—
320C2×C3×C4—44no—
321C2×C3×C4—44no—
322C2×C3×C4—44no—
323C2×C3×C4—44no—
324C2×C3×C4—44no—
325C2×C3×C4—42no—
326C2×C3×C4—42no—
327C2×C3×C4—42no—
328C2×C3×C4—42no—
329C2×C3×C4—42no—
330C2×C3×C4—42no—
331C2×C3×C4—42no—
332C2×C3×C4—42no—
333C2×C3×C4—62no—
334C2×C3×C4—62no—
335C2×C3×C4—62no—
336C2×C3×C4—62no—
337C2×C3×C4—62no—
338C2×C3×C4—62no—
339C2×C3×C4—64no—
340C2×C3×C4—64no—
341C2×C3×C4—64no—
342C2×C3×C4—64no—
343C2×C3×C4—62no—
344C2×C3×C4—122no—
345C2×C3×C4—121no—
346C2×C3×C4—122no—
347C2×C3×C4—121no—
348C2×C3×C4—122no—
349C2×C3×C4—122no—
350C2×C3×C4—122no—
351C2×C3×C4(C2×D3)⋊C414yes—
352C2×C3×C4C3×C22⋊C414yes—
353C2×Dic3—22no—
354C2×Dic3—22no—
355C2×Dic3—22no—
356C2×Dic3—22no—
357C2×Dic3—22no—
358C2×Dic3—22no—
359C2×Dic3—22no—
360C2×Dic3—24no—
361C2×Dic3—24no—
362C2×Dic3—24no—
363C2×Dic3—24no—
364C2×Dic3—41no—
365C2×Dic3—42no—
366C2×Dic3—42no—
367C2×Dic3—42no—
368C2×Dic3—41no—
369C2×Dic3—42no—
370C2×Dic3—42no—
371C2×Dic3C3×C4⋊C414yescomplemented
372C2×C32#38011yescharacteristic
373C2×C32#38611yescharacteristic
374C2×C32#38712yes—
375C2×C32#38912yes—
376C2×C32#39111yescharacteristic
377C2×C32#39411yescharacteristic
378C2×C32#39511yescharacteristic
379C2×C32#39612yes—
380C2×C32#39811yescharacteristic
381C2×C32#39812yes—
382C2×C32#40011yescharacteristic
383C24C22×C3×D311yescharacteristic
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—32no—
393C22×C4—32no—
394C22×C4—32no—
395C22×C4—32no—
396C22×C4—34no—
397C22×C4—61no—
398C22×C4—61no—
399C22×C4—61no—
400C22×C4—61no—
401C22×C4—62no—
402C22×C4—61no—
403C22×C4—62no—
404C22×C4—62no—
405C22×C4—62no—
406C22×C4—62no—
407C22×C4—62no—
408C22×C4—62no—
409C22×C4—62no—
410C22×C4—61no—
411C22×C4C3×Dic614yes—
412C22×C4C3×C4×D312yes—
413C22×C4C3×D1212yes—
414C22×C4C3×#6712yes—
415C4⋊C4—68no—
416C4⋊C4—68no—
417C22×C3—22no—
418C22×C3—22no—
419C22×C3—22no—
420C22×C3—22no—
421C22×C3—21no—
422C22×C3—22no—
423C22×C3—21no—
424C22×C3—22no—
425C22×C3—22no—
426C22×C3—22no—
427C22×C3—21no—
428C22×C3—21no—
429C22×C3—22no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—22no—
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—22no—
436C22×C3—21no—
437C22×C3—22no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3C4×Dic612yes—
441C22×C3#86911yescharacteristic
442C22×C3#87511yescharacteristic
443C22×C3#87812yes—
444C22×C3#87812yes—
445C22×C3#87912yes—
446C22×C3#67⋊C412yes—
447C22×C3#88211yescharacteristic
448C22×C3#88412yes—
449C22×C3#88611yescharacteristic
450C22×C3#88812yes—
451C22×C3#88912yes—
452C22×C3#89012yes—
453C22×C3D3×C4⋊C411yescharacteristic
454C22×C3#89211yescharacteristic
455C22×C3#89412yes—
456C22×C3#89511yescharacteristic
457C22×C3#89711yescharacteristic
458C22×C3#92412yes—
459C22×C3C2×(C2×D3)⋊C411yescharacteristic
460C22×C3#93811yescharacteristic
461C22×C3#93912yes—
462C22×C3#94611yescharacteristic
463C22×C3C2×C3×C22⋊C411yescharacteristic
464C22×C3C2×C3×C4⋊C411yescharacteristic
465C22×C3C3×#11711yescharacteristic
466C22×C3C3×C4×D412yes—
467C22×C3C3×C4×Q812yes—
468C22×C3C3×#12011yescharacteristic
469C22×C3C3×#12112yes—
470C22×C3C3×#12111yescharacteristic
471C22×C3C3×#12111yescharacteristic
472C22×C3C3×#12112yes—
473C22×C3C3×C22⋊Q812yes—
474C22×C3C3×C22⋊Q812yes—
475C22×C3C3×C22⋊Q811yescharacteristic
476C22×C3C3×C22⋊Q812yes—
477C22×C3C3×C22⋊Q811yescharacteristic
478C22×C3C3×#12311yescharacteristic
479C22×C3C3×#12312yes—
480C22×C3C3×#12411yescharacteristic
481C22×C3C3×#12512yes—
482C22×C3C3×#12512yes—
483C22×C3C3×#12612yes—
484C22×C3C3×C4⋊Q812yes—
485C22×C3C3×C4⋊Q811yescharacteristic
486C3×C4—24no—
487C3×C4—24no—
488C3×C4—44no—
489C3×C4—48no—
490C3×C4—44no—
491C3×C4—44no—
492C3×C4—64no—
493C3×C4—124no—
494C3×C4—122no—
495Dic3—24no—
496Dic3—42no—
497Dic3—44no—
498C32#144111yescharacteristic, complemented, Sylow
499C23C2×C3×Dic612yes—
500C23C2×C3×C4×D311yescharacteristic
501C23C2×C3×D1211yescharacteristic
502C23C3×#23512yes—
503C23C3×D3×D411yescharacteristic
504C23C3×D3×D412yes—
505C23C3×#23711yescharacteristic
506C23C3×#23712yes—
507C23C3×D3×Q811yescharacteristic
508C23C3×#23911yescharacteristic
509C23C2×C3×#6711yescharacteristic
510C2×C4—24no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—34no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—62no—
523C2×C4—62no—
524C2×C4—62no—
525C2×C4—62no—
526C2×C4—62no—
527C2×C4—62no—
528C2×C4—64no—
529C2×C4—64no—
530C2×C4—64no—
531C2×C4—64no—
532C2×C4—62no—
533C2×C4—121no—
534C2×C4—122no—
535C2×C4—121no—
536C2×C4—122no—
537C2×C4—122no—
538C2×C4—122no—
539C2×C4—122no—
540C2×C4C3×(C2×D3)⋊C414yes—
541C2×C3—22no—
542C2×C3—22no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—22no—
549C2×C3—21no—
550C2×C3—22no—
551C2×C3—21no—
552C2×C3#464712yes—
553C2×C3#465512yes—
554C2×C3#465611yescharacteristic
555C2×C3#465911yescharacteristic
556C2×C3#466111yescharacteristic
557C2×C3#467211yescharacteristic
558C2×C3#492911yescharacteristic
559C2×C3#494812yes—
560C2×C3#495811yescharacteristic
561C2×C3#498212yes—
562C2×C3#498711yescharacteristic
563C2×C3C3×#38011yescharacteristic
564C2×C3C3×#38611yescharacteristic
565C2×C3C3×#38712yes—
566C2×C3C3×#38912yes—
567C2×C3C3×#39111yescharacteristic
568C2×C3C3×#39411yescharacteristic
569C2×C3C3×#39511yescharacteristic
570C2×C3C3×#39612yes—
571C2×C3C3×#39811yescharacteristic
572C2×C3C3×#39812yes—
573C2×C3C3×#40011yescharacteristic
574C22C3×C4×Dic612yes—
575C22C3×#86911yescharacteristic
576C22C3×#87511yescharacteristic
577C22C3×#87812yes—
578C22C3×#87812yes—
579C22C3×#87912yes—
580C22C3×#67⋊C412yes—
581C22C3×#88211yescharacteristic
582C22C3×#88412yes—
583C22C3×#88611yescharacteristic
584C22C3×#88812yes—
585C22C3×#88912yes—
586C22C3×#89012yes—
587C22C3×D3×C4⋊C411yescharacteristic
588C22C3×#89211yescharacteristic
589C22C3×#89412yes—
590C22C3×#89511yescharacteristic
591C22C3×#89711yescharacteristic
592C22C3×#92412yes—
593C22C2×C3×(C2×D3)⋊C411yescharacteristic
594C22C3×#93811yescharacteristic
595C22C3×#93912yes—
596C22C3×#94611yescharacteristic
597C4—24no—
598C4—44no—
599C4—64no—
600C4—124no—
601C4—122no—
602C3—21no—
603C3#6941011yescharacteristic, direct product factor
604C3C3×#144111yescharacteristic, complemented
605C2C3×#464712yes—
606C2C3×#465512yes—
607C2C3×#465611yescharacteristic
608C2C3×#465911yescharacteristic
609C2C3×#466111yescharacteristic
610C2C3×#467211yescharacteristic
611C2C3×#492911yescharacteristic
612C2C3×#494812yes—
613C2C3×#495811yescharacteristic
614C2C3×#498212yes—
615C2C3×#498711yescharacteristic
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×#1441
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. #69410C3direct (N × H)
17. C2×C3×Dic3⋊C4C4semidirect
88. C2×Dic3⋊C4C3×C4semidirect
137. C2×C3×Dic3C4⋊C4semidirect
371. C2×Dic3C3×C4⋊C4semidirect
498. C32#1441semidirect
603. C3#69410direct (N × H)
604. C3C3×#1441semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C4⋊Dic32
C22×C3×Dic3⋊C42
C2×C32×#952
C2×C3×C3⋊#952
C3×#14413
#694103