Finite Group Databasebeta

← C3×#69523 #11793155

Subgroups — C3×#69523 #11793155

Order 1152.

853 conjugacy classes of subgroups.

The subgroup lattice has 655 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#930C211yesmaximal, characteristic
2C32×#380C211yesmaximal, characteristic, complemented
3C2×C3×#830C211yesmaximal, characteristic, complemented
4C2×C3×#809C211yesmaximal, characteristic, complemented
5C2×C3×#809C211yesmaximal, characteristic, complemented
6C2×C3×#807C211yesmaximal, characteristic, complemented
7C3×#4529C211yesmaximal, characteristic, complemented
8C3×#2033—31nomaximal
9#69523C311yesmaximal, characteristic, direct product factor
10C23×C32×C4C2211yescharacteristic
11C22×C3×#67—21no—
12C22×C3×D12C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×C32×C4⋊C4C2211yescharacteristic
15C2×C32×C22⋊C4—21no—
16C3×#930—22no—
17C3×#930—22no—
18C2×C3×(C2×D3)⋊C4—21no—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C32×#95—21no—
23C3×#830—22no—
24C3×#809—22no—
25C3×#809—22no—
26C3×#807—22no—
27C2×C3×#121—31no—
28C2×#930C2×C311yescharacteristic
29C2×C3×#107—31no—
30C2×C3×#102—31no—
31C2×C3×#102—31no—
32C2×C3×C22⋊C8—31no—
33C3×#380—21no—
34C3×#380D311yescharacteristic, complemented
35C3×#380C2×C311yescharacteristic, complemented
36C2×#830C2×C311yescharacteristic, complemented
37C2×#809C2×C311yescharacteristic, complemented
38C2×#809C2×C311yescharacteristic, complemented
39C2×#807C2×C311yescharacteristic, complemented
40C3×#340—31no—
41#4529C2×C311yescharacteristic, complemented
42C24×C32D411yescharacteristic
43C23×C3×D3—21no—
44C22×C32×C4—21no—
45C22×C32×C4—21no—
46C22×C32×C4—21no—
47C22×C32×C4—21no—
48C22×C32×C4—21no—
49C22×C32×C4—21no—
50C22×C32×C4—21no—
51C22×C32×C4—21no—
52C22×C32×C4D411yescharacteristic
53C22×C32×C4C2311yescharacteristic
54C2×C3×#67—24no—
55C2×C3×#67—42no—
56C2×C3×#67—42no—
57C22×C3×Dic3—21no—
58C2×C3×D12—21no—
59C2×C3×D12—21no—
60C2×C3×D12—21no—
61C2×C3×D12—21no—
62C2×C3×D12—21no—
63C2×C3×D12D412yes—
64C32×C4⋊C4—21no—
65C32×C4⋊C4—21no—
66C32×C4⋊C4—21no—
67C32×C4⋊C4—21no—
68C32×C22⋊C4—42no—
69C3×(C2×D3)⋊C4—24no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3D412yes—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8D412yescomplemented
78#2033—31noSylow
79C22×C3×D4—31no—
80C22×C3×D4—61no—
81C23×C3×C4—21no—
82C23×C3×C4C2×D311yescharacteristic
83C23×C3×C4C22×C311yescharacteristic
84C22×#67—21no—
85C22×D12C22×C311yescharacteristic
86C22×C3×C8—31no—
87C22×C3×C8—31no—
88C3×#121—62no—
89C3×#121—62no—
90C2×C3×C4⋊C4—21no—
91C2×C3×C4⋊C4—21no—
92C2×C3×C4⋊C4—31no—
93C2×C3×C4⋊C4C2×D311yescharacteristic
94C2×C3×C4⋊C4C2×D311yescharacteristic
95C2×C3×C4⋊C4C22×C311yescharacteristic
96C2×C3×C4⋊C4C22×C311yescharacteristic
97C2×C3×C22⋊C4—22no—
98C2×C3×C22⋊C4—21no—
99C2×C3×C22⋊C4—21no—
100C2×C3×C22⋊C4—61no—
101#930—22no—
102#930—22no—
103C2×(C2×D3)⋊C4—21no—
104C2×C4⋊Dic3C22×C311yescharacteristic
105C22×C3⋊C8C22×C311yescharacteristic
106C22×C3⋊C8C22×C311yescharacteristic
107C3×#107—62no—
108C3×#102—62no—
109C3×#102—62no—
110C3×C22⋊C8—62no—
111C3×#95—22no—
112C3×#95—21no—
113C3×#95—21no—
114#830—22no—
115#809—22no—
116#809—22no—
117#807—22no—
118C23×C32—21no—
119C23×C32—21no—
120C23×C32—21no—
121C23×C32—21no—
122C23×C32—21no—
123C23×C32—21no—
124C23×C32D812yes—
125C23×C32C2×D411yescharacteristic
126C22×C3×D3—22no—
127C22×C3×D3—41no—
128C22×C3×D3—41no—
129C22×C3×D3—41no—
130C22×C3×D3—41no—
131C22×C3×D3—41no—
132C22×C3×D3—41no—
133C2×C32×C4—21no—
134C2×C32×C4—21no—
135C2×C32×C4—21no—
136C2×C32×C4—41no—
137C2×C32×C4—41no—
138C2×C32×C4—41no—
139C2×C32×C4—41no—
140C2×C32×C4—41no—
141C2×C32×C4—41no—
142C2×C32×C4—41no—
143C2×C32×C4—41no—
144C2×C32×C4—41no—
145C2×C32×C4—41no—
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4#4111yescharacteristic
150C2×C32×C4#4111yescharacteristic
151C2×C32×C4#4111yescharacteristic
152C3×#67—48no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—41no—
155C2×C3×Dic3—41no—
156C3×D12—22no—
157C3×D12—22no—
158C3×D12—41no—
159C3×D12—41no—
160C3×C3⋊C8—22no—
161C3×C3⋊C8—41no—
162C2×#121—31no—
163C2×#107—31no—
164C2×#102—31no—
165C2×#102—31no—
166C2×C22⋊C8—31no—
167#380C3×D311yescharacteristic, complemented
168#340—31no—
169C24×C3—21no—
170C24×C3—61no—
171C24×C3#6711yescharacteristic
172C24×C3C3×D411yescharacteristic
173C23×D3—21no—
174C2×C3×D4—32no—
175C2×C3×D4—64no—
176C2×C3×D4—61no—
177C2×C3×D4—61no—
178C2×C3×D4—61no—
179C2×C3×D4—61no—
180C2×C3×D4—61no—
181C2×C3×D4—122no—
182C2×C3×D4—122no—
183C22×C3×C4—22no—
184C22×C3×C4—22no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—22no—
198C22×C3×C4—22no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—41no—
206C22×C3×C4—41no—
207C22×C3×C4—41no—
208C22×C3×C4—41no—
209C22×C3×C4—61no—
210C22×C3×C4#6711yescharacteristic
211C22×C3×C4C3×D411yescharacteristic
212C22×C3×C4C22×D311yescharacteristic
213C22×C3×C4C23×C311yescharacteristic
214C2×#67—24no—
215C2×#67—42no—
216C2×#67—42no—
217C22×Dic3—21no—
218C2×D12—21no—
219C2×D12—21no—
220C2×D12—21no—
221C2×D12—21no—
222C2×D12—21no—
223C2×D12C3×D412yes—
224C2×C3×C8—32no—
225C2×C3×C8—61no—
226C2×C3×C8—61no—
227C2×C3×C8—61no—
228C2×C3×C8—61no—
229C2×C3×C8—61no—
230C3×C4⋊C4—21no—
231C3×C4⋊C4—21no—
232C3×C4⋊C4—21no—
233C3×C4⋊C4—21no—
234C3×C4⋊C4—21no—
235C3×C4⋊C4—21no—
236C3×C4⋊C4—21no—
237C3×C4⋊C4—21no—
238C3×C4⋊C4—32no—
239C3×C4⋊C4—41no—
240C3×C4⋊C4—41no—
241C3×C4⋊C4—41no—
242C3×C4⋊C4—41no—
243C3×C4⋊C4—61no—
244C3×C22⋊C4—44no—
245C3×C22⋊C4—42no—
246C3×C22⋊C4—42no—
247C3×C22⋊C4—64no—
248(C2×D3)⋊C4—24no—
249C4⋊Dic3—21no—
250C4⋊Dic3C3×D412yes—
251C2×C3⋊C8—21no—
252C2×C3⋊C8—21no—
253C2×C3⋊C8—21no—
254C2×C3⋊C8—21no—
255C2×C3⋊C8—21no—
256C2×C3⋊C8C3×D412yescomplemented
257C22×C32—22no—
258C22×C32—22no—
259C22×C32—22no—
260C22×C32—41no—
261C22×C32—41no—
262C22×C32—41no—
263C22×C32—41no—
264C22×C32#12011yescharacteristic
265C22×C32#12111yescharacteristic
266C22×C32#12311yescharacteristic
267C22×C32C2×D811yescharacteristic
268C22×C32#13511yescharacteristic
269C22×C32AGL(1,ℤ/8)11yescharacteristic
270C22×C32#13711yescharacteristic
271C2×C3×D3—42no—
272C2×C3×D3—42no—
273C2×C3×D3—42no—
274C2×C3×D3—81no—
275C2×C3×D3—81no—
276C2×C3×D3—81no—
277C2×C3×D3—81no—
278C32×C4—41no—
279C32×C4—81no—
280C32×C4—81no—
281C32×C4#12111yescharacteristic
282C32×C4#12111yescharacteristic
283C32×C4#12311yescharacteristic
284C32×C4#12411yescharacteristic
285C3×Dic3—42no—
286C22×D4—31no—
287C22×D4—61no—
288C23×C4C2×C3×D311yescharacteristic
289C22×C8—31no—
290C22×C8—31no—
291#121—62no—
292#121—62no—
293C2×C4⋊C4—31no—
294C2×C4⋊C4C2×C3×D311yescharacteristic
295C2×C4⋊C4C2×C3×D311yescharacteristic
296C2×C22⋊C4—21no—
297C2×C22⋊C4—61no—
298#107—62no—
299#102—62no—
300#102—62no—
301C22⋊C8—62no—
302#95—21no—
303C23×C3—22no—
304C23×C3—22no—
305C23×C3—21no—
306C23×C3—21no—
307C23×C3—21no—
308C23×C3—21no—
309C23×C3—21no—
310C23×C3—21no—
311C23×C3—21no—
312C23×C3—21no—
313C23×C3—21no—
314C23×C3—21no—
315C23×C3—21no—
316C23×C3—21no—
317C23×C3—22no—
318C23×C3—21no—
319C23×C3—41no—
320C23×C3—41no—
321C23×C3—41no—
322C23×C3—41no—
323C23×C3—62no—
324C23×C3—121no—
325C23×C3—121no—
326C23×C3—121no—
327C23×C3—121no—
328C23×C3—121no—
329C23×C3—121no—
330C23×C3#21312yes—
331C23×C3C3×D812yes—
332C23×C3C2×#6711yescharacteristic
333C23×C3C2×C3×D411yescharacteristic
334C22×D3—22no—
335C22×D3—41no—
336C22×D3—41no—
337C22×D3—41no—
338C22×D3—41no—
339C22×D3—41no—
340C22×D3—41no—
341C3×D4—62no—
342C3×D4—62no—
343C3×D4—128no—
344C3×D4—121no—
345C3×D4—121no—
346C2×C3×C4—22no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—41no—
360C2×C3×C4—41no—
361C2×C3×C4—42no—
362C2×C3×C4—42no—
363C2×C3×C4—42no—
364C2×C3×C4—42no—
365C2×C3×C4—41no—
366C2×C3×C4—41no—
367C2×C3×C4—41no—
368C2×C3×C4—41no—
369C2×C3×C4—41no—
370C2×C3×C4—41no—
371C2×C3×C4—41no—
372C2×C3×C4—41no—
373C2×C3×C4—42no—
374C2×C3×C4—42no—
375C2×C3×C4—42no—
376C2×C3×C4—42no—
377C2×C3×C4—42no—
378C2×C3×C4—42no—
379C2×C3×C4—41no—
380C2×C3×C4—41no—
381C2×C3×C4—41no—
382C2×C3×C4—41no—
383C2×C3×C4—41no—
384C2×C3×C4—41no—
385C2×C3×C4—41no—
386C2×C3×C4—41no—
387C2×C3×C4—41no—
388C2×C3×C4—41no—
389C2×C3×C4—41no—
390C2×C3×C4—41no—
391C2×C3×C4—62no—
392C2×C3×C4—121no—
393C2×C3×C4—121no—
394C2×C3×C4#23511yescharacteristic
395C2×C3×C4#23511yescharacteristic
396C2×C3×C4D3×D411yescharacteristic
397C2×C3×C4D3×D411yescharacteristic
398C2×C3×C4D3×D411yescharacteristic
399C2×C3×C4#23711yescharacteristic
400C2×C3×C4C2×C3×D411yescharacteristic
401C2×C3×C4C2×C3×D411yescharacteristic
402C2×C3×C4C2×C3×D411yescharacteristic
403C2×C3×C4C3×#4111yescharacteristic
404C2×C3×C4C3×#4111yescharacteristic
405C2×C3×C4C3×#4111yescharacteristic
406#67—48no—
407C2×Dic3—22no—
408C2×Dic3—41no—
409C2×Dic3—41no—
410D12—22no—
411D12—22no—
412D12—41no—
413D12—41no—
414C3×C8—62no—
415C3×C8—121no—
416C3⋊C8—22no—
417C3⋊C8—41no—
418C2×C32—42no—
419C2×C32#39411yescharacteristic
420C2×C32#44711yescharacteristic
421C2×C32#45211yescharacteristic
422C2×C32#46611yescharacteristic
423C2×C32#46811yescharacteristic
424C2×C32#48011yescharacteristic
425C2×C32#48211yescharacteristic
426C3×D3—82no—
427C24—61no—
428C24C3×#6711yescharacteristic
429C2×D4—32no—
430C2×D4—64no—
431C2×D4—61no—
432C2×D4—61no—
433C2×D4—61no—
434C2×D4—61no—
435C2×D4—61no—
436C2×D4—122no—
437C2×D4—122no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—61no—
447C22×C4C3×#6711yescharacteristic
448C22×C4C22×C3×D311yescharacteristic
449C2×C8—32no—
450C2×C8—61no—
451C2×C8—61no—
452C2×C8—61no—
453C2×C8—61no—
454C2×C8—61no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—32no—
460C4⋊C4—61no—
461C22⋊C4—42no—
462C22⋊C4—64no—
463C22×C3—24no—
464C22×C3—22no—
465C22×C3—22no—
466C22×C3—22no—
467C22×C3—22no—
468C22×C3—22no—
469C22×C3—22no—
470C22×C3—21no—
471C22×C3—21no—
472C22×C3—21no—
473C22×C3—21no—
474C22×C3—21no—
475C22×C3—21no—
476C22×C3—21no—
477C22×C3—42no—
478C22×C3—42no—
479C22×C3—42no—
480C22×C3—42no—
481C22×C3—42no—
482C22×C3—42no—
483C22×C3—41no—
484C22×C3—41no—
485C22×C3—41no—
486C22×C3—41no—
487C22×C3—41no—
488C22×C3—41no—
489C22×C3—41no—
490C22×C3—41no—
491C22×C3—122no—
492C22×C3—122no—
493C22×C3—122no—
494C22×C3—241no—
495C22×C3—241no—
496C22×C3—241no—
497C22×C3—241no—
498C22×C3#92911yescharacteristic
499C22×C3C2×#21311yescharacteristic
500C22×C3#93711yescharacteristic
501C22×C3#93911yescharacteristic
502C22×C3#94211yescharacteristic
503C22×C3#94911yescharacteristic
504C22×C3#95011yescharacteristic
505C22×C3C3×#12011yescharacteristic
506C22×C3C3×#12111yescharacteristic
507C22×C3C3×#12311yescharacteristic
508C22×C3C2×C3×D811yescharacteristic
509C22×C3C3×#13511yescharacteristic
510C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
511C22×C3C3×#13711yescharacteristic
512C2×D3—42no—
513C2×D3—42no—
514C2×D3—42no—
515C2×D3—81no—
516C2×D3—81no—
517C2×D3—81no—
518C2×D3—81no—
519C3×C4—21no—
520C3×C4—21no—
521C3×C4—21no—
522C3×C4—21no—
523C3×C4—42no—
524C3×C4—41no—
525C3×C4—41no—
526C3×C4—82no—
527C3×C4—82no—
528C3×C4—81no—
529C3×C4—81no—
530C3×C4—81no—
531C3×C4—81no—
532C3×C4—122no—
533C3×C4#88311yescharacteristic
534C3×C4#88411yescharacteristic
535C3×C4#88411yescharacteristic
536C3×C4#88511yescharacteristic
537C3×C4C3×#12111yescharacteristic
538C3×C4C3×#12111yescharacteristic
539C3×C4C3×#12311yescharacteristic
540C3×C4C3×#12411yescharacteristic
541Dic3—42no—
542C32#203311yescharacteristic, complemented, Sylow
543C23—21no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—62no—
550C23—121no—
551C23—121no—
552C23—121no—
553C23—121no—
554C23—121no—
555C23—121no—
556C23C3×#21312yes—
557C23C2×C3×#6711yescharacteristic
558D4—62no—
559D4—62no—
560D4—128no—
561D4—121no—
562D4—121no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—62no—
577C2×C4—121no—
578C2×C4—121no—
579C2×C4C3×#23511yescharacteristic
580C2×C4C3×#23511yescharacteristic
581C2×C4C3×D3×D411yescharacteristic
582C2×C4C3×D3×D411yescharacteristic
583C2×C4C3×D3×D411yescharacteristic
584C2×C4C3×#23711yescharacteristic
585C8—62no—
586C8—121no—
587C2×C3—21no—
588C2×C3—21no—
589C2×C3—21no—
590C2×C3—21no—
591C2×C3—21no—
592C2×C3—21no—
593C2×C3—21no—
594C2×C3—44no—
595C2×C3—42no—
596C2×C3—42no—
597C2×C3—242no—
598C2×C3#495911yescharacteristic
599C2×C3#496711yescharacteristic
600C2×C3#500311yescharacteristic
601C2×C3#503611yescharacteristic
602C2×C3#503811yescharacteristic
603C2×C3#504711yescharacteristic
604C2×C3#504911yescharacteristic
605C2×C3C3×#39411yescharacteristic
606C2×C3C3×#44711yescharacteristic
607C2×C3C3×#45211yescharacteristic
608C2×C3C3×#46611yescharacteristic
609C2×C3C3×#46811yescharacteristic
610C2×C3C3×#48011yescharacteristic
611C2×C3C3×#48211yescharacteristic
612D3—82no—
613C22—22no—
614C22—22no—
615C22—22no—
616C22—41no—
617C22—41no—
618C22—41no—
619C22—41no—
620C22—122no—
621C22—122no—
622C22—122no—
623C22—241no—
624C22—241no—
625C22—241no—
626C22—241no—
627C22C3×#92911yescharacteristic
628C22C2×C3×#21311yescharacteristic
629C22C3×#93711yescharacteristic
630C22C3×#93911yescharacteristic
631C22C3×#94211yescharacteristic
632C22C3×#94911yescharacteristic
633C22C3×#95011yescharacteristic
634C4—41no—
635C4—81no—
636C4—81no—
637C4—122no—
638C4C3×#88311yescharacteristic
639C4C3×#88411yescharacteristic
640C4C3×#88411yescharacteristic
641C4C3×#88511yescharacteristic
642C3—21no—
643C3#6952311yescharacteristic, direct product factor
644C3C3×#203311yescharacteristic, complemented
645C2—42no—
646C2—242no—
647C2C3×#495911yescharacteristic
648C2C3×#496711yescharacteristic
649C2C3×#500311yescharacteristic
650C2C3×#503611yescharacteristic
651C2C3×#503811yescharacteristic
652C2C3×#504711yescharacteristic
653C2C3×#504911yescharacteristic
subgroupG/H
centerC23×C3C2×#67
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#380C2
socleC23×C32C2×D4
prime radicalC2×C3×#930C2
hypercenterC3×#380D3
hypocenterC3C3×#2033
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C23×C3×C4 ◁ C3×#380

Complements

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

NH ≅ G/Ntype
2. C32×#380C2semidirect
3. C2×C3×#830C2semidirect
4. C2×C3×#809C2semidirect
5. C2×C3×#809C2semidirect
6. C2×C3×#807C2semidirect
7. C3×#4529C2semidirect
9. #69523C3direct (N × H)
34. C3×#380D3semidirect
35. C3×#380C2×C3semidirect
36. C2×#830C2×C3semidirect
37. C2×#809C2×C3semidirect
38. C2×#809C2×C3semidirect
39. C2×#807C2×C3semidirect
41. #4529C2×C3semidirect
77. C2×C3×C3⋊C8D4semidirect
167. #380C3×D3semidirect
256. C2×C3⋊C8C3×D4semidirect
542. C32#2033semidirect
643. C3#69523direct (N × H)
644. C3C3×#2033semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9302
C32×#3802
C2×C3×#8302
C2×C3×#8092
C2×C3×#8072
C3×#45292
C3×#20333
#695233