Finite Group Databasebeta

← C3×#29445 #10648052

Subgroups — C3×#29445 #10648052

Order 768.

788 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2860C211yesmaximal, characteristic, complemented
2C3×#2293C211yesmaximal, characteristic, complemented
3C3×#2088C211yesmaximal, characteristic, complemented
4C3×#2067C211yesmaximal, characteristic, complemented
5C3×#2065C211yesmaximal, characteristic, complemented
6C3×#2054C211yesmaximal, characteristic
7C3×#1972C211yesmaximal, characteristic
8C3×#1944C211yesmaximal, characteristic, complemented
9C3×#1936C211yesmaximal, characteristic, complemented
10C3×#1936C211yesmaximal, characteristic, complemented
11C3×#1925C211yesmaximal, characteristic, complemented
12C3×#1920C211yesmaximal, characteristic, complemented
13C3×#1879C211yesmaximal, characteristic
14C3×#1864C211yesmaximal, characteristic, complemented
15C3×#1767C211yesmaximal, characteristic, complemented
16#29445C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×D8C2211yescharacteristic
18C2×C3×#126—21no—
19C2×C3×C4×D4C2211yescharacteristic
20C2×C3×#117—21no—
21C2×C3×#107C2211yescharacteristic
22C2×C3×#106C2211yescharacteristic
23C2×C3×#106C2211yescharacteristic
24C2×C3×C4⋊C8C2211yescharacteristic
25C2×C3×C4⋊C8C2211yescharacteristic
26C2×C3×#102C2211yescharacteristic
27C2×C3×#102C2211yescharacteristic
28C2×C3×#102C2211yescharacteristic
29C2×C3×#102C2211yescharacteristic
30C2×C3×#102C2211yescharacteristic
31C2×C3×#102C2211yescharacteristic
32C2×C3×#97C2211yescharacteristic
33C2×C3×#97C2211yescharacteristic
34C3×#390C2211yescharacteristic
35C3×#390C2211yescharacteristic
36C3×#390C2211yescharacteristic
37C3×#390C2211yescharacteristic
38C3×#390C2211yescharacteristic
39C3×#389C2211yescharacteristic
40C3×#389C2211yescharacteristic
41C3×#389C2211yescharacteristic
42C3×#389C2211yescharacteristic
43C3×#389C2211yescharacteristic
44C3×#388—21no—
45C3×#388—21no—
46C3×#388—21no—
47C3×#388—21no—
48C3×#388—21no—
49C3×C4×C4⋊C4C2211yescharacteristic
50C3×C4×C22⋊C4—21no—
51C3×C43C2211yescharacteristic
52C3×#340C2211yescharacteristic
53C3×#340C2211yescharacteristic
54C3×#340C2211yescharacteristic
55C3×#340C2211yescharacteristic
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#336C2211yescharacteristic
59C3×#336C2211yescharacteristic
60#2860C2×C311yescharacteristic, complemented
61#2293C2×C311yescharacteristic, complemented
62#2088C2×C311yescharacteristic, complemented
63#2067C2×C311yescharacteristic, complemented
64#2065C2×C311yescharacteristic, complemented
65#2054C2×C311yescharacteristic
66#1972C2×C311yescharacteristic
67#1944C2×C311yescharacteristic, complemented
68#1936C2×C311yescharacteristic, complemented
69#1936C2×C311yescharacteristic, complemented
70#1925C2×C311yescharacteristic, complemented
71#1920C2×C311yescharacteristic, complemented
72#1879C2×C311yescharacteristic
73#1864C2×C311yescharacteristic, complemented
74#1767C2×C311yescharacteristic, complemented
75C22×C3×D4C2311yescharacteristic
76C22×C3×D4C2311yescharacteristic
77C23×C3×C4—21no—
78C2×C3×D8—22no—
79C2×C3×D8—22no—
80C2×C3×D8—41no—
81C22×C3×C8C2311yescharacteristic
82C22×C3×C8C2311yescharacteristic
83C22×C3×C8C2311yescharacteristic
84C22×C3×C8C2311yescharacteristic
85C3×#126—44no—
86C3×C4×D4—22no—
87C3×C4×D4—22no—
88C3×#117—44no—
89C2×C3×C4⋊C4—21no—
90C2×C3×C4⋊C4—21no—
91C2×C3×C4⋊C4—21no—
92C2×C3×C4⋊C4—21no—
93C2×C3×C4⋊C4—21no—
94C2×C3×C4⋊C4C2311yescharacteristic
95C2×C3×C4⋊C4C2311yescharacteristic
96C2×C3×C4⋊C4C2311yescharacteristic
97C2×C3×C4⋊C4C2311yescharacteristic
98C2×C3×C4⋊C4C2311yescharacteristic
99C2×C3×C4⋊C4C2311yescharacteristic
100C2×C3×C22⋊C4—21no—
101C2×C3×C22⋊C4—21no—
102C2×C3×C22⋊C4—21no—
103C2×C3×C22⋊C4—21no—
104C2×C3×C22⋊C4—21no—
105C2×C3×C22⋊C4—21no—
106C2×C3×C22⋊C4—21no—
107C2×C3×C22⋊C4—21no—
108C2×C3×C22⋊C4—21no—
109C2×C3×C22⋊C4—21no—
110C2×C3×C22⋊C4—21no—
111C2×C3×C42—21no—
112C2×C3×C42D411yescharacteristic
113C2×C3×C42D411yescharacteristic
114C2×C3×C42D411yescharacteristic
115C2×C3×C42D411yescharacteristic
116C2×C3×C42C2311yescharacteristic
117C2×C3×C42C2311yescharacteristic
118C2×C3×C42C2311yescharacteristic
119C3×#107—41no—
120C3×#106—22no—
121C3×#106—22no—
122C3×C4⋊C8—22no—
123C3×C4⋊C8—22no—
124C3×#102—22no—
125C3×#102—22no—
126C3×#102—22no—
127C3×#102—22no—
128C3×#102—41no—
129C3×#102—41no—
130C3×#97—41no—
131C3×#97—41no—
132C3×#95—21no—
133C3×#95—21no—
134C3×#95—21no—
135C3×#95—21no—
136C3×#95—21no—
137C3×#95—21no—
138C22×D8C22×C311yescharacteristic
139C2×#126—21no—
140C2×C4×D4C22×C311yescharacteristic
141C2×#117—21no—
142C2×#107C22×C311yescharacteristic
143C2×#106C22×C311yescharacteristic
144C2×#106C22×C311yescharacteristic
145C2×C4⋊C8C22×C311yescharacteristic
146C2×C4⋊C8C22×C311yescharacteristic
147C2×#102C22×C311yescharacteristic
148C2×#102C22×C311yescharacteristic
149C2×#102C22×C311yescharacteristic
150C2×#102C22×C311yescharacteristic
151C2×#102C22×C311yescharacteristic
152C2×#102C22×C311yescharacteristic
153C2×#97C22×C311yescharacteristic
154C2×#97C22×C311yescharacteristic
155#390C22×C311yescharacteristic
156#390C22×C311yescharacteristic
157#390C22×C311yescharacteristic
158#390C22×C311yescharacteristic
159#390C22×C311yescharacteristic
160#389C22×C311yescharacteristic
161#389C22×C311yescharacteristic
162#389C22×C311yescharacteristic
163#389C22×C311yescharacteristic
164#389C22×C311yescharacteristic
165#388—21no—
166#388—21no—
167#388—21no—
168#388—21no—
169#388—21no—
170C4×C4⋊C4C22×C311yescharacteristic
171C4×C22⋊C4—21no—
172C43C22×C311yescharacteristic
173#340C22×C311yescharacteristic
174#340C22×C311yescharacteristic
175#340C22×C311yescharacteristic
176#340C22×C311yescharacteristic
177#340C22×C311yescharacteristic
178#340C22×C311yescharacteristic
179#336C22×C311yescharacteristic
180#336C22×C311yescharacteristic
181C24×C3—21no—
182C24×C3—21no—
183C2×C3×D4—21no—
184C2×C3×D4—21no—
185C2×C3×D4—21no—
186C2×C3×D4—21no—
187C2×C3×D4—21no—
188C2×C3×D4—21no—
189C2×C3×D4—21no—
190C2×C3×D4—21no—
191C2×C3×D4—21no—
192C2×C3×D4—21no—
193C2×C3×D4—21no—
194C2×C3×D4#4112yes—
195C22×C3×C4—24no—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—42no—
203C22×C3×C4—42no—
204C22×C3×C4C2×D411yescharacteristic
205C22×C3×C4C2×D411yescharacteristic
206C22×C3×C4C2×D411yescharacteristic
207C22×C3×C4C2×D411yescharacteristic
208C22×C3×C4C2×D411yescharacteristic
209C22×C3×C4C2×D411yescharacteristic
210C22×C3×C4C2411yescharacteristic
211C3×D8—44no—
212C2×C3×C8—21no—
213C2×C3×C8—21no—
214C2×C3×C8—21no—
215C2×C3×C8—21no—
216C2×C3×C8—21no—
217C2×C3×C8—21no—
218C2×C3×C8—21no—
219C2×C3×C8—21no—
220C2×C3×C8—21no—
221C2×C3×C8—21no—
222C2×C3×C8#4112yes—
223C2×C3×C8#4112yes—
224C3×C4⋊C4—21no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4—21no—
229C3×C4⋊C4—21no—
230C3×C4⋊C4—21no—
231C3×C4⋊C4—21no—
232C3×C4⋊C4—21no—
233C3×C4⋊C4—21no—
234C3×C4⋊C4—21no—
235C3×C4⋊C4—42no—
236C3×C4⋊C4—42no—
237C3×C4⋊C4—42no—
238C3×C4⋊C4—42no—
239C3×C4⋊C4—42no—
240C3×C4⋊C4#4112yes—
241C3×C22⋊C4—24no—
242C3×C22⋊C4—42no—
243C3×C22⋊C4—42no—
244C3×C22⋊C4—42no—
245C3×C22⋊C4—42no—
246C3×C22⋊C4—42no—
247C3×C22⋊C4—42no—
248C3×C22⋊C4—42no—
249C3×C22⋊C4—42no—
250C3×C22⋊C4—42no—
251C3×C22⋊C4—42no—
252C3×C42—22no—
253C3×C42—22no—
254C3×C42—21no—
255C3×C42—21no—
256C3×C42—21no—
257C3×C42—21no—
258C3×C42—21no—
259C3×C42—21no—
260C3×C42—41no—
261C3×C42—41no—
262C3×C42—42no—
263C22×D4C23×C311yescharacteristic
264C22×D4C23×C311yescharacteristic
265C23×C4—21no—
266C2×D8—22no—
267C2×D8—22no—
268C2×D8—41no—
269C22×C8C23×C311yescharacteristic
270C22×C8C23×C311yescharacteristic
271C22×C8C23×C311yescharacteristic
272C22×C8C23×C311yescharacteristic
273#126—44no—
274C4×D4—22no—
275C4×D4—22no—
276#117—44no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4C23×C311yescharacteristic
283C2×C4⋊C4C23×C311yescharacteristic
284C2×C4⋊C4C23×C311yescharacteristic
285C2×C4⋊C4C23×C311yescharacteristic
286C2×C4⋊C4C23×C311yescharacteristic
287C2×C4⋊C4C23×C311yescharacteristic
288C2×C22⋊C4—21no—
289C2×C22⋊C4—21no—
290C2×C22⋊C4—21no—
291C2×C22⋊C4—21no—
292C2×C22⋊C4—21no—
293C2×C22⋊C4—21no—
294C2×C22⋊C4—21no—
295C2×C22⋊C4—21no—
296C2×C22⋊C4—21no—
297C2×C22⋊C4—21no—
298C2×C22⋊C4—21no—
299C2×C42—21no—
300C2×C42C3×D411yescharacteristic
301C2×C42C3×D411yescharacteristic
302C2×C42C3×D411yescharacteristic
303C2×C42C3×D411yescharacteristic
304C2×C42C23×C311yescharacteristic
305C2×C42C23×C311yescharacteristic
306C2×C42C23×C311yescharacteristic
307#107—41no—
308#106—22no—
309#106—22no—
310C4⋊C8—22no—
311C4⋊C8—22no—
312#102—22no—
313#102—22no—
314#102—22no—
315#102—22no—
316#102—41no—
317#102—41no—
318#97—41no—
319#97—41no—
320#95—21no—
321#95—21no—
322#95—21no—
323#95—21no—
324#95—21no—
325#95—21no—
326C23×C3—22no—
327C23×C3—41no—
328C23×C3—41no—
329C23×C3—41no—
330C23×C3—41no—
331C23×C3—41no—
332C23×C3—41no—
333C23×C3—41no—
334C23×C3—41no—
335C23×C3—41no—
336C23×C3—41no—
337C23×C3—41no—
338C23×C3—41no—
339C23×C3—41no—
340C23×C3C22×D411yescharacteristic
341C3×D4—22no—
342C3×D4—22no—
343C3×D4—41no—
344C3×D4—41no—
345C3×D4—41no—
346C3×D4—41no—
347C3×D4—41no—
348C3×D4—41no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—22no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—48no—
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—41no—
374C2×C3×C4—41no—
375C2×C3×C4—41no—
376C2×C3×C4—41no—
377C2×C3×C4—41no—
378C2×C3×C4—41no—
379C2×C3×C4—41no—
380C2×C3×C4—41no—
381C2×C3×C4—41no—
382C2×C3×C4—41no—
383C2×C3×C4—41no—
384C2×C3×C4AGL(1,ℤ/8)12yes—
385C2×C3×C4AGL(1,ℤ/8)12yes—
386C2×C3×C4C2×#4111yescharacteristic
387C2×C3×C4C2×#4111yescharacteristic
388C2×C3×C4C2×#4111yescharacteristic
389C2×C3×C4C2×#4111yescharacteristic
390C2×C3×C4H(5,𝔽2)11yescharacteristic
391C2×C3×C42−1+411yescharacteristic
392C3×C8—22no—
393C3×C8—22no—
394C3×C8—41no—
395C3×C8—41no—
396C24—21no—
397C24—21no—
398C2×D4—21no—
399C2×D4—21no—
400C2×D4—21no—
401C2×D4—21no—
402C2×D4—21no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4C3×#4112yes—
410C22×C4—24no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—42no—
418C22×C4—42no—
419C22×C4C2×C3×D411yescharacteristic
420C22×C4C2×C3×D411yescharacteristic
421C22×C4C2×C3×D411yescharacteristic
422C22×C4C2×C3×D411yescharacteristic
423C22×C4C2×C3×D411yescharacteristic
424C22×C4C2×C3×D411yescharacteristic
425C22×C4C24×C311yescharacteristic
426D8—44no—
427C2×C8—21no—
428C2×C8—21no—
429C2×C8—21no—
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8C3×#4112yes—
438C2×C8C3×#4112yes—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—42no—
451C4⋊C4—42no—
452C4⋊C4—42no—
453C4⋊C4—42no—
454C4⋊C4—42no—
455C4⋊C4C3×#4112yes—
456C22⋊C4—24no—
457C22⋊C4—42no—
458C22⋊C4—42no—
459C22⋊C4—42no—
460C22⋊C4—42no—
461C22⋊C4—42no—
462C22⋊C4—42no—
463C22⋊C4—42no—
464C22⋊C4—42no—
465C22⋊C4—42no—
466C22⋊C4—42no—
467C42—22no—
468C42—22no—
469C42—21no—
470C42—21no—
471C42—21no—
472C42—21no—
473C42—21no—
474C42—21no—
475C42—41no—
476C42—41no—
477C42—42no—
478C22×C3—42no—
479C22×C3—42no—
480C22×C3—42no—
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—81no—
490C22×C3—81no—
491C22×C3—81no—
492C22×C3#52511yescharacteristic
493C22×C3#53211yescharacteristic
494C22×C3#53711yescharacteristic
495C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
496C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
497C22×C3#57511yescharacteristic
498C22×C3#57511yescharacteristic
499C3×C4—22no—
500C3×C4—22no—
501C3×C4—42no—
502C3×C4—41no—
503C3×C4—41no—
504C3×C4—41no—
505C3×C4—41no—
506C3×C4—81no—
507C3×C4—81no—
508C3×C4—81no—
509C3×C4—81no—
510C3×C4—81no—
511C3×C4#55111yescharacteristic
512C3×C4#55211yescharacteristic
513C3×C4#55311yescharacteristic
514C3×C4#55611yescharacteristic
515C23—22no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23—41no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23—41no—
526C23—41no—
527C23—41no—
528C23—41no—
529C23C22×C3×D411yescharacteristic
530D4—22no—
531D4—22no—
532D4—41no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—41no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—22no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—48no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4C3×AGL(1,ℤ/8)12yes—
574C2×C4C3×AGL(1,ℤ/8)12yes—
575C2×C4C2×C3×#4111yescharacteristic
576C2×C4C2×C3×#4111yescharacteristic
577C2×C4C2×C3×#4111yescharacteristic
578C2×C4C2×C3×#4111yescharacteristic
579C2×C4C3×H(5,𝔽2)11yescharacteristic
580C2×C4C3×2−1+411yescharacteristic
581C8—22no—
582C8—22no—
583C8—41no—
584C8—41no—
585C2×C3—82no—
586C2×C3—161no—
587C2×C3#260111yescharacteristic
588C2×C3#311411yescharacteristic
589C2×C3#311511yescharacteristic
590C2×C3#317111yescharacteristic
591C2×C3#318011yescharacteristic
592C2×C3#325311yescharacteristic
593C2×C3#325611yescharacteristic
594C22—42no—
595C22—42no—
596C22—42no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22—81no—
601C22—81no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22—81no—
608C22C3×#52511yescharacteristic
609C22C3×#53211yescharacteristic
610C22C3×#53711yescharacteristic
611C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
612C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
613C22C3×#57511yescharacteristic
614C22C3×#57511yescharacteristic
615C4—22no—
616C4—22no—
617C4—41no—
618C4—41no—
619C4—41no—
620C4—42no—
621C4—41no—
622C4—81no—
623C4—81no—
624C4—81no—
625C4—81no—
626C4—81no—
627C4C3×#55111yescharacteristic
628C4C3×#55211yescharacteristic
629C4C3×#55311yescharacteristic
630C4C3×#55611yescharacteristic
631C3#2944511yescharacteristic, direct product factor, Sylow
632C2—82no—
633C2—161no—
634C2C3×#260111yescharacteristic
635C2C3×#311411yescharacteristic
636C2C3×#311511yescharacteristic
637C2C3×#317111yescharacteristic
638C2C3×#318011yescharacteristic
639C2C3×#325311yescharacteristic
640C2C3×#325611yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC22×C3×D8C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C3×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×#2860C2semidirect
2. C3×#2293C2semidirect
3. C3×#2088C2semidirect
4. C3×#2067C2semidirect
5. C3×#2065C2semidirect
8. C3×#1944C2semidirect
9. C3×#1936C2semidirect
10. C3×#1936C2semidirect
11. C3×#1925C2semidirect
12. C3×#1920C2semidirect
14. C3×#1864C2semidirect
15. C3×#1767C2semidirect
16. #29445C3direct (N × H)
60. #2860C2×C3semidirect
61. #2293C2×C3semidirect
62. #2088C2×C3semidirect
63. #2067C2×C3semidirect
64. #2065C2×C3semidirect
67. #1944C2×C3semidirect
68. #1936C2×C3semidirect
69. #1936C2×C3semidirect
70. #1925C2×C3semidirect
71. #1920C2×C3semidirect
73. #1864C2×C3semidirect
74. #1767C2×C3semidirect
631. C3#29445direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#28602
C3×#22932
C3×#20882
C3×#20672
C3×#20652
C3×#20542
C3×#19722
C3×#19442
C3×#19362
C3×#19252
C3×#19202
C3×#18792
C3×#18642
C3×#17672
#294453