Finite Group Databasebeta

← C3×#69650 #11794011

Subgroups — C3×#69650 #11794011

Order 1152.

849 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#213C211yesmaximal, characteristic
2C32×#390C211yesmaximal, characteristic, complemented
3C2×C3×#832C211yesmaximal, characteristic, complemented
4C2×C3×#809C211yesmaximal, characteristic, complemented
5C3×#4939C211yesmaximal, characteristic, complemented
6C2×C3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
7C3×#4529C211yesmaximal, characteristic, complemented
8C3×#2054—31nomaximal
9#69650C311yesmaximal, characteristic, direct product factor
10C22×C32×D4C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×C32×C22⋊C4—21no—
14C2×C32×C22⋊C4—21no—
15C2×C32×C42C2211yescharacteristic
16C2×C3×#213—22no—
17C2×C3×#213—22no—
18C2×C3×#213—22no—
19C2×C3×(C2×D3)⋊C4—21no—
20C2×C3×(C2×D3)⋊C4—21no—
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C22×C3×C3⋊C8C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24C3×#832—22no—
25C3×#809—22no—
26C3×C4⋊(C3⋊C8)—22no—
27C22×C3×D8—31no—
28C22×#213C2×C311yescharacteristic
29C2×C3×C4⋊C8—31no—
30C2×C3×#102—31no—
31C2×C3×#102—31no—
32C3×#390—21no—
33C3×#390—31no—
34C3×#390D311yescharacteristic, complemented
35C3×#390C2×C311yescharacteristic, complemented
36C2×#832C2×C311yescharacteristic, complemented
37C2×#809C2×C311yescharacteristic, complemented
38#4939C2×C311yescharacteristic, complemented
39C2×C4⋊(C3⋊C8)C2×C311yescharacteristic, complemented
40C3×#340—31no—
41#4529C2×C311yescharacteristic, complemented
42C24×C32—21no—
43C23×C3×D3—21no—
44C2×C32×D4—21no—
45C2×C32×D4—21no—
46C2×C32×D4—21no—
47C2×C32×D4—21no—
48C2×C32×D4—21no—
49C2×C32×D4D412yes—
50C22×C32×C4—21no—
51C22×C32×C4D411yescharacteristic
52C22×C32×C4D411yescharacteristic
53C22×C32×C4C2311yescharacteristic
54C22×C3×Dic3—21no—
55C2×C3×D12—21no—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12—21no—
59C2×C3×D12—21no—
60C2×C3×D12D412yes—
61C32×C4⋊C4—21no—
62C32×C4⋊C4—21no—
63C32×C22⋊C4—42no—
64C32×C22⋊C4—42no—
65C32×C42—21no—
66C32×C42—21no—
67C3×#213—28no—
68C3×(C2×D3)⋊C4—42no—
69C3×(C2×D3)⋊C4—42no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3—21no—
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⋊C8D412yes—
78#2054—31noSylow
79C22×C3×D4—21no—
80C22×C3×D4—31no—
81C22×C3×D4C2×D311yescharacteristic
82C22×C3×D4C22×C311yescharacteristic
83C22×D12C22×C311yescharacteristic
84C2×C3×D8—62no—
85C2×C3×D8—62no—
86C2×C3×D8—62no—
87C22×C3×C8—31no—
88C22×C3×C8—31no—
89C2×C3×C4⋊C4—21no—
90C2×C3×C4⋊C4—31no—
91C2×C3×C4⋊C4C2×D311yescharacteristic
92C2×C3×C4⋊C4C22×C311yescharacteristic
93C2×C3×C22⋊C4—22no—
94C2×C3×C22⋊C4—22no—
95C2×C3×C22⋊C4—21no—
96C2×C3×C22⋊C4—21no—
97C2×C3×C22⋊C4—21no—
98C2×C3×C22⋊C4—21no—
99C2×C3×C22⋊C4—61no—
100C2×C3×C22⋊C4—61no—
101C2×C3×C42—21no—
102C2×C3×C42C2×D311yescharacteristic
103C2×C3×C42C22×C311yescharacteristic
104C2×#213—22no—
105C2×#213—22no—
106C2×#213—22no—
107C2×(C2×D3)⋊C4—21no—
108C2×(C2×D3)⋊C4—21no—
109C2×C4⋊Dic3C22×C311yescharacteristic
110C22×C3⋊C8C22×C311yescharacteristic
111C22×C3⋊C8C22×C311yescharacteristic
112C3×C4⋊C8—62no—
113C3×#102—62no—
114C3×#102—62no—
115#832—22no—
116#809—22no—
117C4⋊(C3⋊C8)—22no—
118C23×C32—22no—
119C23×C32—41no—
120C23×C32—41no—
121C23×C32—41no—
122C23×C32—41no—
123C23×C32—41no—
124C23×C32—41no—
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—
133C32×D4—22no—
134C32×D4—22no—
135C32×D4—41no—
136C32×D4—41no—
137C2×C32×C4—21no—
138C2×C32×C4—21no—
139C2×C32×C4—21no—
140C2×C32×C4—21no—
141C2×C32×C4—21no—
142C2×C32×C4—41no—
143C2×C32×C4—41no—
144C2×C32×C4—41no—
145C2×C32×C4D812yescomplemented
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4#4111yescharacteristic
150C2×C32×C4#4111yescharacteristic
151C2×C32×C4#4111yescharacteristic
152C2×C3×Dic3—41no—
153C2×C3×Dic3—41no—
154C2×C3×Dic3—41no—
155C3×D12—22no—
156C3×D12—22no—
157C3×D12—41no—
158C3×D12—41no—
159C3×C3⋊C8—22no—
160C3×C3⋊C8—41no—
161C22×D8—31no—
162C2×C4⋊C8—31no—
163C2×#102—31no—
164C2×#102—31no—
165#390—31no—
166#390C3×D311yescharacteristic, complemented
167#340—31no—
168C24×C3—22no—
169C24×C3—21no—
170C24×C3—21no—
171C24×C3—61no—
172C23×D3—21no—
173C2×C3×D4—22no—
174C2×C3×D4—21no—
175C2×C3×D4—21no—
176C2×C3×D4—21no—
177C2×C3×D4—21no—
178C2×C3×D4—21no—
179C2×C3×D4—21no—
180C2×C3×D4—21no—
181C2×C3×D4—21no—
182C2×C3×D4—21no—
183C2×C3×D4—21no—
184C2×C3×D4—22no—
185C2×C3×D4—32no—
186C2×C3×D4—41no—
187C2×C3×D4—41no—
188C2×C3×D4—41no—
189C2×C3×D4—41no—
190C2×C3×D4—61no—
191C2×C3×D4—61no—
192C2×C3×D4—61no—
193C2×C3×D4—61no—
194C2×C3×D4—61no—
195C2×C3×D4D1212yes—
196C2×C3×D4C3×D412yes—
197C22×C3×C4—22no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—61no—
204C22×C3×C4#6711yescharacteristic
205C22×C3×C4#6711yescharacteristic
206C22×C3×C4C3×D411yescharacteristic
207C22×C3×C4C3×D411yescharacteristic
208C22×C3×C4C22×D311yescharacteristic
209C22×C3×C4C23×C311yescharacteristic
210C22×Dic3—21no—
211C2×D12—21no—
212C2×D12—21no—
213C2×D12—21no—
214C2×D12—21no—
215C2×D12—21no—
216C2×D12C3×D412yes—
217C3×D8—68no—
218C2×C3×C8—32no—
219C2×C3×C8—61no—
220C2×C3×C8—61no—
221C2×C3×C8—61no—
222C2×C3×C8—61no—
223C2×C3×C8—61no—
224C3×C4⋊C4—21no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4—41no—
229C3×C4⋊C4—41no—
230C3×C4⋊C4—61no—
231C3×C4⋊C4—61no—
232C3×C22⋊C4—44no—
233C3×C22⋊C4—42no—
234C3×C22⋊C4—42no—
235C3×C22⋊C4—44no—
236C3×C22⋊C4—42no—
237C3×C22⋊C4—42no—
238C3×C22⋊C4—122no—
239C3×C22⋊C4—122no—
240C3×C42—21no—
241C3×C42—21no—
242C3×C42—21no—
243C3×C42—21no—
244C3×C42—41no—
245C3×C42—41no—
246#213—28no—
247(C2×D3)⋊C4—42no—
248(C2×D3)⋊C4—42no—
249C4⋊Dic3—21no—
250C4⋊Dic3—21no—
251C2×C3⋊C8—21no—
252C2×C3⋊C8—21no—
253C2×C3⋊C8—21no—
254C2×C3⋊C8—21no—
255C2×C3⋊C8—21no—
256C2×C3⋊C8C3×D412yes—
257C22×C32—42no—
258C22×C32—42no—
259C22×C32—42no—
260C22×C32—81no—
261C22×C32—81no—
262C22×C32—81no—
263C22×C32—81no—
264C22×C32#12111yescharacteristic
265C22×C32#12111yescharacteristic
266C22×C32#12111yescharacteristic
267C22×C32C2×D811yescharacteristic
268C22×C32#13511yescharacteristic
269C22×C32AGL(1,ℤ/8)11yescharacteristic
270C22×C32AGL(1,ℤ/8)11yescharacteristic
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—22no—
279C32×C4—41no—
280C32×C4—81no—
281C32×C4#12011yescharacteristic
282C32×C4#12311yescharacteristic
283C32×C4#12311yescharacteristic
284C32×C4#12411yescharacteristic
285C3×Dic3—81no—
286C22×D4—31no—
287C22×D4C2×C3×D311yescharacteristic
288C2×D8—62no—
289C2×D8—62no—
290C2×D8—62no—
291C22×C8—31no—
292C22×C8—31no—
293C2×C4⋊C4—31no—
294C2×C4⋊C4C2×C3×D311yescharacteristic
295C2×C22⋊C4—21no—
296C2×C22⋊C4—21no—
297C2×C22⋊C4—61no—
298C2×C22⋊C4—61no—
299C2×C42C2×C3×D311yescharacteristic
300C4⋊C8—62no—
301#102—62no—
302#102—62no—
303C23×C3—24no—
304C23×C3—22no—
305C23×C3—22no—
306C23×C3—21no—
307C23×C3—42no—
308C23×C3—42no—
309C23×C3—42no—
310C23×C3—42no—
311C23×C3—42no—
312C23×C3—42no—
313C23×C3—41no—
314C23×C3—41no—
315C23×C3—41no—
316C23×C3—41no—
317C23×C3—41no—
318C23×C3—41no—
319C23×C3—41no—
320C23×C3—41no—
321C23×C3—41no—
322C23×C3—41no—
323C23×C3—41no—
324C23×C3—41no—
325C23×C3—62no—
326C23×C3—121no—
327C23×C3—121no—
328C23×C3—121no—
329C23×C3—121no—
330C23×C3—121no—
331C23×C3—121no—
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—22no—
342C3×D4—22no—
343C3×D4—22no—
344C3×D4—22no—
345C3×D4—42no—
346C3×D4—42no—
347C3×D4—42no—
348C3×D4—42no—
349C3×D4—41no—
350C3×D4—41no—
351C3×D4—41no—
352C3×D4—41no—
353C3×D4—62no—
354C3×D4—62no—
355C3×D4—121no—
356C3×D4—121no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—22no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—21no—
368C2×C3×C4—22no—
369C2×C3×C4—21no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—41no—
376C2×C3×C4—41no—
377C2×C3×C4—41no—
378C2×C3×C4—41no—
379C2×C3×C4—42no—
380C2×C3×C4—42no—
381C2×C3×C4—42no—
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—121no—
389C2×C3×C4—121no—
390C2×C3×C4—121no—
391C2×C3×C4#21312yescomplemented
392C2×C3×C4C3×D812yescomplemented
393C2×C3×C4C2×D1211yescharacteristic
394C2×C3×C4#23511yescharacteristic
395C2×C3×C4D3×D411yescharacteristic
396C2×C3×C4D3×D411yescharacteristic
397C2×C3×C4#23711yescharacteristic
398C2×C3×C4#23711yescharacteristic
399C2×C3×C4C2×C3×D411yescharacteristic
400C2×C3×C4C2×C3×D411yescharacteristic
401C2×C3×C4C2×C3×D411yescharacteristic
402C2×C3×C4C3×#4111yescharacteristic
403C2×C3×C4C3×#4111yescharacteristic
404C2×C3×C4C3×#4111yescharacteristic
405C2×Dic3—41no—
406C2×Dic3—41no—
407C2×Dic3—41no—
408D12—22no—
409D12—22no—
410D12—41no—
411D12—41no—
412C3×C8—62no—
413C3×C8—121no—
414C3⋊C8—22no—
415C3⋊C8—41no—
416C2×C32—82no—
417C2×C32#39411yescharacteristic
418C2×C32#45911yescharacteristic
419C2×C32#45911yescharacteristic
420C2×C32#46311yescharacteristic
421C2×C32#46311yescharacteristic
422C2×C32#46611yescharacteristic
423C2×C32#46911yescharacteristic
424C3×D3—82no—
425C24—21no—
426C24—61no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—32no—
433C2×D4—61no—
434C2×D4—61no—
435C2×D4—61no—
436C2×D4—61no—
437C2×D4—61no—
438C2×D4C3×D1212yes—
439C22×C4—21no—
440C22×C4—61no—
441C22×C4C3×#6711yescharacteristic
442C22×C4C3×#6711yescharacteristic
443C22×C4C22×C3×D311yescharacteristic
444D8—68no—
445C2×C8—32no—
446C2×C8—61no—
447C2×C8—61no—
448C2×C8—61no—
449C2×C8—61no—
450C2×C8—61no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—61no—
454C4⋊C4—61no—
455C22⋊C4—42no—
456C22⋊C4—42no—
457C22⋊C4—122no—
458C22⋊C4—122no—
459C42—21no—
460C42—21no—
461C22×C3—21no—
462C22×C3—21no—
463C22×C3—21no—
464C22×C3—21no—
465C22×C3—21no—
466C22×C3—21no—
467C22×C3—21no—
468C22×C3—44no—
469C22×C3—44no—
470C22×C3—44no—
471C22×C3—42no—
472C22×C3—42no—
473C22×C3—42no—
474C22×C3—42no—
475C22×C3—42no—
476C22×C3—42no—
477C22×C3—82no—
478C22×C3—82no—
479C22×C3—82no—
480C22×C3—82no—
481C22×C3—81no—
482C22×C3—81no—
483C22×C3—81no—
484C22×C3—81no—
485C22×C3—81no—
486C22×C3—81no—
487C22×C3—81no—
488C22×C3—81no—
489C22×C3—122no—
490C22×C3—122no—
491C22×C3—122no—
492C22×C3—241no—
493C22×C3—241no—
494C22×C3—241no—
495C22×C3—241no—
496C22×C3#93011yescharacteristic
497C22×C3C2×#21311yescharacteristic
498C22×C3#93211yescharacteristic
499C22×C3#93811yescharacteristic
500C22×C3#93911yescharacteristic
501C22×C3#94911yescharacteristic
502C22×C3#95011yescharacteristic
503C22×C3C3×#12111yescharacteristic
504C22×C3C3×#12111yescharacteristic
505C22×C3C3×#12111yescharacteristic
506C22×C3C2×C3×D811yescharacteristic
507C22×C3C3×#13511yescharacteristic
508C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
509C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
510C2×D3—42no—
511C2×D3—42no—
512C2×D3—42no—
513C2×D3—81no—
514C2×D3—81no—
515C2×D3—81no—
516C2×D3—81no—
517C3×C4—22no—
518C3×C4—22no—
519C3×C4—21no—
520C3×C4—21no—
521C3×C4—21no—
522C3×C4—21no—
523C3×C4—42no—
524C3×C4—42no—
525C3×C4—41no—
526C3×C4—41no—
527C3×C4—82no—
528C3×C4—81no—
529C3×C4—81no—
530C3×C4—241no—
531C3×C4#88211yescharacteristic
532C3×C4#88311yescharacteristic
533C3×C4#88511yescharacteristic
534C3×C4#88611yescharacteristic
535C3×C4C3×#12011yescharacteristic
536C3×C4C3×#12311yescharacteristic
537C3×C4C3×#12311yescharacteristic
538C3×C4C3×#12411yescharacteristic
539Dic3—81no—
540C32#205411yescharacteristic, complemented, Sylow
541C23—22no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23—62no—
549C23—121no—
550C23—121no—
551C23—121no—
552C23—121no—
553C23—121no—
554C23—121no—
555C23C2×C3×#6711yescharacteristic
556D4—22no—
557D4—22no—
558D4—41no—
559D4—41no—
560D4—62no—
561D4—62no—
562D4—121no—
563D4—121no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—121no—
573C2×C4—121no—
574C2×C4—121no—
575C2×C4C3×#21312yescomplemented
576C2×C4C2×C3×D1211yescharacteristic
577C2×C4C3×#23511yescharacteristic
578C2×C4C3×D3×D411yescharacteristic
579C2×C4C3×D3×D411yescharacteristic
580C2×C4C3×#23711yescharacteristic
581C2×C4C3×#23711yescharacteristic
582C8—62no—
583C8—121no—
584C2×C3—21no—
585C2×C3—21no—
586C2×C3—21no—
587C2×C3—21no—
588C2×C3—21no—
589C2×C3—21no—
590C2×C3—21no—
591C2×C3—84no—
592C2×C3—82no—
593C2×C3—82no—
594C2×C3—242no—
595C2×C3#496111yescharacteristic
596C2×C3#501511yescharacteristic
597C2×C3#501611yescharacteristic
598C2×C3#503811yescharacteristic
599C2×C3#503911yescharacteristic
600C2×C3#505711yescharacteristic
601C2×C3#507211yescharacteristic
602C2×C3C3×#39411yescharacteristic
603C2×C3C3×#45911yescharacteristic
604C2×C3C3×#45911yescharacteristic
605C2×C3C3×#46311yescharacteristic
606C2×C3C3×#46311yescharacteristic
607C2×C3C3×#46611yescharacteristic
608C2×C3C3×#46911yescharacteristic
609D3—82no—
610C22—42no—
611C22—42no—
612C22—42no—
613C22—81no—
614C22—81no—
615C22—81no—
616C22—81no—
617C22—122no—
618C22—122no—
619C22—122no—
620C22—241no—
621C22—241no—
622C22—241no—
623C22—241no—
624C22C3×#93011yescharacteristic
625C22C2×C3×#21311yescharacteristic
626C22C3×#93211yescharacteristic
627C22C3×#93811yescharacteristic
628C22C3×#93911yescharacteristic
629C22C3×#94911yescharacteristic
630C22C3×#95011yescharacteristic
631C4—22no—
632C4—41no—
633C4—81no—
634C4—241no—
635C4C3×#88211yescharacteristic
636C4C3×#88311yescharacteristic
637C4C3×#88511yescharacteristic
638C4C3×#88611yescharacteristic
639C3—21no—
640C3#6965011yescharacteristic, direct product factor
641C3C3×#205411yescharacteristic, complemented
642C2—82no—
643C2—242no—
644C2C3×#496111yescharacteristic
645C2C3×#501511yescharacteristic
646C2C3×#501611yescharacteristic
647C2C3×#503811yescharacteristic
648C2C3×#503911yescharacteristic
649C2C3×#505711yescharacteristic
650C2C3×#507211yescharacteristic
subgroupG/H
centerC23×C3C2×#67
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#390C2
socleC23×C32C2×D4
prime radicalC22×C3×#213C2
hypercenterC3×#390D3
hypocenterC3C3×#2054
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C42 ◁ C3×#390

Complements

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

NH ≅ G/Ntype
2. C32×#390C2semidirect
3. C2×C3×#832C2semidirect
4. C2×C3×#809C2semidirect
5. C3×#4939C2semidirect
6. C2×C3×C4⋊(C3⋊C8)C2semidirect
7. C3×#4529C2semidirect
9. #69650C3direct (N × H)
34. C3×#390D3semidirect
35. C3×#390C2×C3semidirect
36. C2×#832C2×C3semidirect
37. C2×#809C2×C3semidirect
38. #4939C2×C3semidirect
39. C2×C4⋊(C3⋊C8)C2×C3semidirect
41. #4529C2×C3semidirect
145. C2×C32×C4D8semidirect
166. #390C3×D3semidirect
391. C2×C3×C4#213semidirect
392. C2×C3×C4C3×D8semidirect
540. C32#2054semidirect
575. C2×C4C3×#213semidirect
640. C3#69650direct (N × H)
641. C3C3×#2054semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2132
C32×#3902
C2×C3×#8322
C2×C3×#8092
C3×#49392
C2×C3×C4⋊(C3⋊C8)2
C3×#45292
C3×#20543
#696503