Finite Group Databasebeta

← C3×#69644 #11789804

Subgroups — C3×#69644 #11789804

Order 1152.

713 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#390C211yesmaximal, characteristic
2C2×C3×#832C211yesmaximal, characteristic
3C2×C3×#832C211yesmaximal, characteristic
4C3×#4928C211yesmaximal, characteristic, complemented
5C2×C3×C4×C3⋊C8C211yesmaximal, characteristic, complemented
6C3×#4529C211yesmaximal, characteristic, complemented
7C3×#4529C211yesmaximal, characteristic, complemented
8C3×#1934—31nomaximal
9#69644C311yesmaximal, characteristic, direct product factor
10C22×C32×D4C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×C32×C22⋊C4—21no—
13C2×C32×C22⋊C4—21no—
14C2×C32×C42C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×Dic3⋊C4—21no—
18C22×C3×C3⋊C8C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C3×#832—22no—
21C3×#832C414yescomplemented
22C3×C3⋊#95—21no—
23C3×C4×C3⋊C8—22no—
24C2×C3×#102—31no—
25C2×C3×#102—31no—
26C2×C3×C4×C8—31no—
27C3×#390—21no—
28C3×#390D311yescharacteristic
29C3×#390C2×C311yescharacteristic
30C3×#389—31no—
31C2×#832C2×C311yescharacteristic
32C2×#832C2×C311yescharacteristic
33#4928C2×C311yescharacteristic, complemented
34C2×C4×C3⋊C8C2×C311yescharacteristic, complemented
35C3×#340—31no—
36C3×#340—31no—
37#4529C2×C311yescharacteristic, complemented
38#4529C2×C311yescharacteristic, complemented
39C24×C32—21no—
40C2×C32×D4—21no—
41C2×C32×D4—21no—
42C2×C32×D4—21no—
43C2×C32×D4—21no—
44C2×C32×D4—21no—
45C2×C32×D4C2×C412yes—
46C22×C32×C4—21no—
47C22×C32×C4D411yescharacteristic
48C22×C32×C4D411yescharacteristic
49C22×C32×C4C2311yescharacteristic
50C22×C3×Dic3—21no—
51C22×C3×Dic3—21no—
52C32×C4⋊C4—21no—
53C32×C4⋊C4—21no—
54C32×C22⋊C4—42no—
55C32×C22⋊C4—42no—
56C32×C42—21no—
57C32×C42—21no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3C2×C412yes—
62C3×Dic3⋊C4—42no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8C2×C412yes—
68C2×C3×C3⋊C8D412yes—
69#1934—31noSylow
70C22×C3×D4—21no—
71C22×C3×D4C2×D311yescharacteristic
72C22×C3×D4C22×C311yescharacteristic
73C22×C3×C8—31no—
74C22×C3×C8—31no—
75C2×C3×C4⋊C4—21no—
76C2×C3×C4⋊C4—31no—
77C2×C3×C4⋊C4—31no—
78C2×C3×C4⋊C4—61no—
79C2×C3×C4⋊C4C2×D311yescharacteristic
80C2×C3×C4⋊C4C22×C311yescharacteristic
81C2×C3×C22⋊C4—22no—
82C2×C3×C22⋊C4—22no—
83C2×C3×C22⋊C4—21no—
84C2×C3×C22⋊C4—21no—
85C2×C3×C22⋊C4—21no—
86C2×C3×C22⋊C4—21no—
87C2×C3×C42—21no—
88C2×C3×C42C2×D311yescharacteristic
89C2×C3×C42C22×C311yescharacteristic
90C2×C4⋊Dic3C22×C311yescharacteristic
91C2×C4⋊Dic3C22×C311yescharacteristic
92C2×Dic3⋊C4—21no—
93C22×C3⋊C8C22×C311yescharacteristic
94C22×C3⋊C8C22×C311yescharacteristic
95C3×#102—34no—
96C3×#102—62no—
97C3×C4×C8—62no—
98C3×#95—61no—
99#832—22no—
100#832C3×C414yescomplemented
101C3⋊#95—21no—
102C4×C3⋊C8—22no—
103C23×C32—22no—
104C23×C32—41no—
105C23×C32—41no—
106C23×C32—41no—
107C23×C32—41no—
108C23×C32—41no—
109C23×C32—41no—
110C23×C32C2×D411yescharacteristic
111C32×D4—22no—
112C32×D4—22no—
113C32×D4—41no—
114C32×D4—41no—
115C2×C32×C4—21no—
116C2×C32×C4—21no—
117C2×C32×C4—21no—
118C2×C32×C4—21no—
119C2×C32×C4—41no—
120C2×C32×C4—41no—
121C2×C32×C4—41no—
122C2×C32×C4D812yes—
123C2×C32×C4SD1612yes—
124C2×C32×C4C22×C411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4#4111yescharacteristic
127C2×C32×C4#4111yescharacteristic
128C2×C32×C4#4111yescharacteristic
129C2×C32×C4#4111yescharacteristic
130C2×C3×Dic3—22no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—41no—
136C3×C3⋊C8—22no—
137C3×C3⋊C8—22no—
138C2×#102—31no—
139C2×#102—31no—
140C2×C4×C8—31no—
141#390C3×D311yescharacteristic
142#389—31no—
143#340—31no—
144#340—31no—
145C24×C3—22no—
146C24×C3—21no—
147C24×C3—21no—
148C2×C3×D4—22no—
149C2×C3×D4—21no—
150C2×C3×D4—21no—
151C2×C3×D4—21no—
152C2×C3×D4—21no—
153C2×C3×D4—21no—
154C2×C3×D4—21no—
155C2×C3×D4—21no—
156C2×C3×D4—21no—
157C2×C3×D4—21no—
158C2×C3×D4—21no—
159C2×C3×D4—22no—
160C2×C3×D4—41no—
161C2×C3×D4—41no—
162C2×C3×D4—41no—
163C2×C3×D4—41no—
164C2×C3×D4C4×D312yes—
165C2×C3×D4C2×C3×C412yes—
166C22×C3×C4—22no—
167C22×C3×C4—21no—
168C22×C3×C4—21no—
169C22×C3×C4—21no—
170C22×C3×C4—21no—
171C22×C3×C4—21no—
172C22×C3×C4—61no—
173C22×C3×C4—61no—
174C22×C3×C4#6711yescharacteristic
175C22×C3×C4#6711yescharacteristic
176C22×C3×C4C3×D411yescharacteristic
177C22×C3×C4C3×D411yescharacteristic
178C22×C3×C4C22×D311yescharacteristic
179C22×C3×C4C23×C311yescharacteristic
180C22×Dic3—21no—
181C22×Dic3—21no—
182C2×C3×C8—32no—
183C2×C3×C8—32no—
184C2×C3×C8—61no—
185C2×C3×C8—61no—
186C2×C3×C8—61no—
187C2×C3×C8—61no—
188C3×C4⋊C4—21no—
189C3×C4⋊C4—21no—
190C3×C4⋊C4—21no—
191C3×C4⋊C4—21no—
192C3×C4⋊C4—32no—
193C3×C4⋊C4—41no—
194C3×C4⋊C4—41no—
195C3×C4⋊C4—61no—
196C3×C4⋊C4—61no—
197C3×C4⋊C4—61no—
198C3×C4⋊C4—122no—
199C3×C22⋊C4—44no—
200C3×C22⋊C4—44no—
201C3×C22⋊C4—42no—
202C3×C22⋊C4—42no—
203C3×C22⋊C4—42no—
204C3×C22⋊C4—42no—
205C3×C42—21no—
206C3×C42—21no—
207C3×C42—21no—
208C3×C42—21no—
209C3×C42—41no—
210C3×C42—41no—
211C4⋊Dic3—21no—
212C4⋊Dic3—21no—
213C4⋊Dic3—21no—
214C4⋊Dic3C2×C3×C412yes—
215Dic3⋊C4—42no—
216C2×C3⋊C8—21no—
217C2×C3⋊C8—21no—
218C2×C3⋊C8—21no—
219C2×C3⋊C8—21no—
220C2×C3⋊C8C2×C3×C412yes—
221C2×C3⋊C8C3×D412yes—
222C22×C32—42no—
223C22×C32—42no—
224C22×C32—42no—
225C22×C32—81no—
226C22×C32—81no—
227C22×C32—81no—
228C22×C32—81no—
229C22×C32C4×D411yescharacteristic
230C22×C32#12111yescharacteristic
231C22×C32#12411yescharacteristic
232C22×C32C2×D811yescharacteristic
233C22×C32C2×SD1611yescharacteristic
234C22×C32#13511yescharacteristic
235C22×C32#13511yescharacteristic
236C32×C4—22no—
237C32×C4—22no—
238C32×C4—81no—
239C32×C4#11711yescharacteristic
240C32×C4C4×D411yescharacteristic
241C32×C4#12311yescharacteristic
242C32×C4#12611yescharacteristic
243C3×Dic3—42no—
244C3×Dic3—81no—
245C22×D4C2×C3×D311yescharacteristic
246C22×C8—31no—
247C22×C8—31no—
248C2×C4⋊C4—31no—
249C2×C4⋊C4—31no—
250C2×C4⋊C4—61no—
251C2×C4⋊C4C2×C3×D311yescharacteristic
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C42C2×C3×D311yescharacteristic
255#102—34no—
256#102—62no—
257C4×C8—62no—
258#95—61no—
259C23×C3—24no—
260C23×C3—22no—
261C23×C3—22no—
262C23×C3—21no—
263C23×C3—42no—
264C23×C3—42no—
265C23×C3—42no—
266C23×C3—42no—
267C23×C3—42no—
268C23×C3—42no—
269C23×C3—41no—
270C23×C3—41no—
271C23×C3—41no—
272C23×C3—41no—
273C23×C3—41no—
274C23×C3—41no—
275C23×C3—41no—
276C23×C3—41no—
277C23×C3—41no—
278C23×C3—41no—
279C23×C3—41no—
280C23×C3—41no—
281C23×C3C2×#6711yescharacteristic
282C23×C3C2×C3×D411yescharacteristic
283C3×D4—22no—
284C3×D4—22no—
285C3×D4—22no—
286C3×D4—22no—
287C3×D4—42no—
288C3×D4—42no—
289C3×D4—42no—
290C3×D4—42no—
291C3×D4—41no—
292C3×D4—41no—
293C3×D4—41no—
294C3×D4—41no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—22no—
304C2×C3×C4—22no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—41no—
312C2×C3×C4—41no—
313C2×C3×C4—41no—
314C2×C3×C4—41no—
315C2×C3×C4—42no—
316C2×C3×C4—42no—
317C2×C3×C4—42no—
318C2×C3×C4—41no—
319C2×C3×C4—41no—
320C2×C3×C4—41no—
321C2×C3×C4—41no—
322C2×C3×C4—41no—
323C2×C3×C4—41no—
324C2×C3×C4—62no—
325C2×C3×C4—121no—
326C2×C3×C4—121no—
327C2×C3×C4—121no—
328C2×C3×C4—121no—
329C2×C3×C4—121no—
330C2×C3×C4#21312yes—
331C2×C3×C4#21412yes—
332C2×C3×C4C3×D812yes—
333C2×C3×C4C3×SD1612yes—
334C2×C3×C4C2×C4×D311yescharacteristic
335C2×C3×C4#23511yescharacteristic
336C2×C3×C4D3×D411yescharacteristic
337C2×C3×C4#23711yescharacteristic
338C2×C3×C4#23711yescharacteristic
339C2×C3×C4#23711yescharacteristic
340C2×C3×C4C22×C3×C411yescharacteristic
341C2×C3×C4C2×C3×D411yescharacteristic
342C2×C3×C4C3×#4111yescharacteristic
343C2×C3×C4C3×#4111yescharacteristic
344C2×C3×C4C3×#4111yescharacteristic
345C2×C3×C4C3×#4111yescharacteristic
346C2×Dic3—22no—
347C2×Dic3—41no—
348C2×Dic3—41no—
349C2×Dic3—41no—
350C2×Dic3—41no—
351C2×Dic3—41no—
352C3×C8—62no—
353C3×C8—62no—
354C3⋊C8—22no—
355C3⋊C8—22no—
356C2×C32—82no—
357C2×C32#38811yescharacteristic
358C2×C32C4×D811yescharacteristic
359C2×C32C4×SD1611yescharacteristic
360C2×C32#46511yescharacteristic
361C2×C32#46611yescharacteristic
362C2×C32#48611yescharacteristic
363C2×C32#48811yescharacteristic
364C24—21no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4—21no—
369C2×D4—21no—
370C2×D4C3×C4×D312yes—
371C22×C4—21no—
372C22×C4—61no—
373C22×C4—61no—
374C22×C4C3×#6711yescharacteristic
375C22×C4C3×#6711yescharacteristic
376C22×C4C22×C3×D311yescharacteristic
377C2×C8—32no—
378C2×C8—32no—
379C2×C8—61no—
380C2×C8—61no—
381C2×C8—61no—
382C2×C8—61no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—32no—
386C4⋊C4—61no—
387C4⋊C4—61no—
388C4⋊C4—61no—
389C4⋊C4—122no—
390C22⋊C4—42no—
391C22⋊C4—42no—
392C42—21no—
393C42—21no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—44no—
402C22×C3—44no—
403C22×C3—44no—
404C22×C3—42no—
405C22×C3—42no—
406C22×C3—42no—
407C22×C3—42no—
408C22×C3—42no—
409C22×C3—42no—
410C22×C3—82no—
411C22×C3—82no—
412C22×C3—82no—
413C22×C3—82no—
414C22×C3—81no—
415C22×C3—81no—
416C22×C3—81no—
417C22×C3—81no—
418C22×C3—81no—
419C22×C3—81no—
420C22×C3—81no—
421C22×C3—81no—
422C22×C3C4×#6711yescharacteristic
423C22×C3C2×#21311yescharacteristic
424C22×C3C2×#21411yescharacteristic
425C22×C3#93611yescharacteristic
426C22×C3#93911yescharacteristic
427C22×C3#95011yescharacteristic
428C22×C3#95011yescharacteristic
429C22×C3C3×C4×D411yescharacteristic
430C22×C3C3×#12111yescharacteristic
431C22×C3C3×#12411yescharacteristic
432C22×C3C2×C3×D811yescharacteristic
433C22×C3C2×C3×SD1611yescharacteristic
434C22×C3C3×#13511yescharacteristic
435C22×C3C3×#13511yescharacteristic
436C3×C4—22no—
437C3×C4—22no—
438C3×C4—22no—
439C3×C4—22no—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—42no—
445C3×C4—42no—
446C3×C4—82no—
447C3×C4—81no—
448C3×C4—81no—
449C3×C4—122no—
450C3×C4—241no—
451C3×C4#87711yescharacteristic
452C3×C4#87911yescharacteristic
453C3×C4#67⋊C411yescharacteristic
454C3×C4#88311yescharacteristic
455C3×C4C3×#11711yescharacteristic
456C3×C4C3×C4×D411yescharacteristic
457C3×C4C3×#12311yescharacteristic
458C3×C4C3×#12611yescharacteristic
459Dic3—42no—
460Dic3—81no—
461C32#193411yescharacteristic, complemented, Sylow
462C23—22no—
463C23—41no—
464C23—41no—
465C23—41no—
466C23—41no—
467C23—41no—
468C23—41no—
469C23C2×C3×#6711yescharacteristic
470D4—22no—
471D4—22no—
472D4—41no—
473D4—41no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—62no—
482C2×C4—121no—
483C2×C4—121no—
484C2×C4—121no—
485C2×C4—121no—
486C2×C4—121no—
487C2×C4C3×#21312yes—
488C2×C4C3×#21412yes—
489C2×C4C2×C3×C4×D311yescharacteristic
490C2×C4C3×#23511yescharacteristic
491C2×C4C3×D3×D411yescharacteristic
492C2×C4C3×#23711yescharacteristic
493C2×C4C3×#23711yescharacteristic
494C2×C4C3×#23711yescharacteristic
495C8—62no—
496C8—62no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—84no—
505C2×C3—82no—
506C2×C3—82no—
507C2×C3#494511yescharacteristic
508C2×C3C4×#21311yescharacteristic
509C2×C3C4×#21411yescharacteristic
510C2×C3#503811yescharacteristic
511C2×C3#504111yescharacteristic
512C2×C3#505611yescharacteristic
513C2×C3#507011yescharacteristic
514C2×C3C3×#38811yescharacteristic
515C2×C3C3×C4×D811yescharacteristic
516C2×C3C3×C4×SD1611yescharacteristic
517C2×C3C3×#46511yescharacteristic
518C2×C3C3×#46611yescharacteristic
519C2×C3C3×#48611yescharacteristic
520C2×C3C3×#48811yescharacteristic
521C22—42no—
522C22—42no—
523C22—42no—
524C22—81no—
525C22—81no—
526C22—81no—
527C22—81no—
528C22C3×C4×#6711yescharacteristic
529C22C2×C3×#21311yescharacteristic
530C22C2×C3×#21411yescharacteristic
531C22C3×#93611yescharacteristic
532C22C3×#93911yescharacteristic
533C22C3×#95011yescharacteristic
534C22C3×#95011yescharacteristic
535C4—22no—
536C4—22no—
537C4—81no—
538C4—122no—
539C4—241no—
540C4C3×#87711yescharacteristic
541C4C3×#87911yescharacteristic
542C4C3×#67⋊C411yescharacteristic
543C4C3×#88311yescharacteristic
544C3—21no—
545C3#6964411yescharacteristic, direct product factor
546C3C3×#193411yescharacteristic, complemented
547C2—82no—
548C2C3×#494511yescharacteristic
549C2C3×C4×#21311yescharacteristic
550C2C3×C4×#21411yescharacteristic
551C2C3×#503811yescharacteristic
552C2C3×#504111yescharacteristic
553C2C3×#505611yescharacteristic
554C2C3×#507011yescharacteristic
subgroupG/H
centerC23×C3C2×#67
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#390C2
socleC23×C32C2×D4
prime radicalC22×C32×D4C22
cosocleC22×C3×C4C23×C3
hypercenterC3×#390D3
hypocenterC3C3×#1934
LCSG ▷ C2×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
4. C3×#4928C2semidirect
5. C2×C3×C4×C3⋊C8C2semidirect
6. C3×#4529C2semidirect
7. C3×#4529C2semidirect
9. #69644C3direct (N × H)
21. C3×#832C4semidirect
33. #4928C2×C3semidirect
34. C2×C4×C3⋊C8C2×C3semidirect
37. #4529C2×C3semidirect
38. #4529C2×C3semidirect
100. #832C3×C4semidirect
461. C32#1934semidirect
545. C3#69644direct (N × H)
546. C3C3×#1934semidirect

Maximal subgroups

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

subgroupindex
C32×#3902
C2×C3×#8322
C3×#49282
C2×C3×C4×C3⋊C82
C3×#45292
C3×#19343
#696443