Finite Group Databasebeta

← C3×#70162 #11791479

Subgroups — C3×#70162 #11791479

Order 1152.

789 conjugacy classes of subgroups.

The subgroup lattice has 593 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#936C211yesmaximal, characteristic
2C2×C32×#102C211yesmaximal, characteristic
3C2×C3×#832C211yesmaximal, characteristic
4C2×C3×#816C211yesmaximal, characteristic, complemented
5C2×C3×Dic3⋊C8C211yesmaximal, characteristic, complemented
6C3×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
7C2×C3×#810C211yesmaximal, characteristic, complemented
8C3×#1983—31nomaximal
9#70162C311yesmaximal, characteristic, direct product factor
10C22×C32×D4C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×C3×#217—21no—
15C2×C3×#217—21no—
16C3×#936—22no—
17C3×#936C414yescomplemented
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4×Dic3—21no—
20C2×C3×C4×Dic3C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C32×#102—22no—
23C3×#832—22no—
24C3×C3⋊#95—21no—
25C3×#816—22no—
26C3×Dic3⋊C8—22no—
27C3×#810—22no—
28C2×C3×#124—31no—
29C2×#936C2×C311yescharacteristic
30C2×C3×C4⋊C8—31no—
31C2×C3×#103—31no—
32C2×C3×#103—31no—
33C2×C3×#102—21no—
34C2×C3×#102—31no—
35C2×C3×#102D311yescharacteristic
36C2×C3×#102C2×C311yescharacteristic
37C3×C4×C4⋊C4—31no—
38C2×#832C2×C311yescharacteristic
39C2×#816C2×C311yescharacteristic, complemented
40C2×Dic3⋊C8C2×C311yescharacteristic, complemented
41Dic3×C4⋊C4C2×C311yescharacteristic, complemented
42C2×#810C2×C311yescharacteristic, complemented
43C24×C32—21no—
44C2×C32×D4—21no—
45C2×C32×D4—21no—
46C2×C32×D4—21no—
47C2×C32×D4—21no—
48C2×C32×D4—21no—
49C2×C32×D4C2×C412yes—
50C22×C32×C4—21no—
51C22×C32×C4C2311yescharacteristic
52C22×C3×Dic3—21no—
53C22×C3×Dic3—21no—
54C22×C3×Dic3D411yescharacteristic
55C22×C3×Dic3D411yescharacteristic
56C2×C3×Dic6—21no—
57C2×C3×Dic6—21no—
58C2×C3×Dic6—21no—
59C2×C3×Dic6—21no—
60C2×C3×Dic6—21no—
61C2×C3×Dic6C2×C412yes—
62C2×C32×C8—21no—
63C2×C32×C8—21no—
64C2×C32×C8—21no—
65C32×C4⋊C4—21no—
66C32×C4⋊C4D412yes—
67C3×#217—24no—
68C3×#217—24no—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3D412yes—
71C3×C4×Dic3—42no—
72C3×C4×Dic3C2×C412yes—
73C3×C4×Dic3D412yes—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8—21no—
77#1983—31noSylow
78C22×C3×Q8—31no—
79C22×C3×D4—21no—
80C22×C3×D4C2×D311yescharacteristic
81C22×C3×D4C22×C311yescharacteristic
82C22×Dic6C22×C311yescharacteristic
83C22×C3×C8—21no—
84C22×C3×C8—31no—
85C22×C3×C8C2×D311yescharacteristic
86C22×C3×C8C22×C311yescharacteristic
87C3×#124—34no—
88C3×#124—62no—
89C2×C3×C4⋊C4—21no—
90C2×C3×C4⋊C4—31no—
91C2×C3×C4⋊C4C2×D311yescharacteristic
92C2×C3×C4⋊C4C22×C311yescharacteristic
93C2×C3×C22⋊C4—61no—
94C2×C3×C22⋊C4—61no—
95C2×C3×C42—31no—
96C2×C3×C42—61no—
97C2×#217—21no—
98C2×#217—21no—
99#936—22no—
100#936C3×C414yescomplemented
101C2×C4⋊Dic3C22×C311yescharacteristic
102C2×C4×Dic3—21no—
103C2×C4×Dic3C22×C311yescharacteristic
104C22×C3⋊C8C22×C311yescharacteristic
105C3×C4⋊C8—62no—
106C3×#103—62no—
107C3×#103—62no—
108C3×#102—24no—
109C3×#102—22no—
110C3×#102—22no—
111C3×#102—62no—
112C3×#95—61no—
113#832—22no—
114C3⋊#95—21no—
115#816—22no—
116Dic3⋊C8—22no—
117#810—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
126C32×D4—22no—
127C32×D4—22no—
128C32×D4—41no—
129C32×D4—41no—
130C2×C32×C4—22no—
131C2×C32×C4—41no—
132C2×C32×C4—41no—
133C2×C32×C4C22×C411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4#4111yescharacteristic
138C2×C32×C4#4111yescharacteristic
139C2×C3×Dic3—21no—
140C2×C3×Dic3—21no—
141C2×C3×Dic3—21no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—41no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3—41no—
148C2×C3×Dic3—41no—
149C2×C3×Dic3C22⋊C412yes—
150C2×C3×Dic3C22⋊C412yes—
151C3×Dic6—22no—
152C3×Dic6—22no—
153C3×Dic6—41no—
154C3×Dic6—41no—
155C32×C8—41no—
156C3×C3⋊C8—41no—
157C2×#124—31no—
158C2×C4⋊C8—31no—
159C2×#103—31no—
160C2×#103—31no—
161C2×#102—31no—
162C2×#102C3×D311yescharacteristic
163C4×C4⋊C4—31no—
164C24×C3—21no—
165C24×C3—21no—
166C24×C3—41no—
167C2×C3×Q8—32no—
168C2×C3×Q8—61no—
169C2×C3×Q8—61no—
170C2×C3×Q8—61no—
171C2×C3×Q8—61no—
172C2×C3×Q8—61no—
173C2×C3×D4—22no—
174C2×C3×D4—22no—
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—21no—
185C2×C3×D4—22no—
186C2×C3×D4—41no—
187C2×C3×D4—41no—
188C2×C3×D4—41no—
189C2×C3×D4C4×D312yes—
190C2×C3×D4C2×C3×C412yes—
191C22×C3×C4—21no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—31no—
195C22×C3×C4—31no—
196C22×C3×C4—41no—
197C22×C3×C4—61no—
198C22×C3×C4—61no—
199C22×C3×C4C22×D311yescharacteristic
200C22×C3×C4C23×C311yescharacteristic
201C22×Dic3—21no—
202C22×Dic3—21no—
203C22×Dic3C3×D411yescharacteristic
204C22×Dic3C3×D411yescharacteristic
205C2×Dic6—21no—
206C2×Dic6—21no—
207C2×Dic6—21no—
208C2×Dic6—21no—
209C2×Dic6—21no—
210C2×Dic6C2×C3×C412yes—
211C2×C3×C8—22no—
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—41no—
219C2×C3×C8—41no—
220C2×C3×C8—61no—
221C2×C3×C8—61no—
222C2×C3×C8—61no—
223C3×C4⋊C4—21no—
224C3×C4⋊C4—21no—
225C3×C4⋊C4—22no—
226C3×C4⋊C4—32no—
227C3×C4⋊C4—41no—
228C3×C4⋊C4—61no—
229C3×C4⋊C4#6712yes—
230C3×C4⋊C4C3×D412yes—
231C3×C22⋊C4—64no—
232C3×C22⋊C4—64no—
233C3×C42—32no—
234C3×C42—32no—
235C3×C42—122no—
236#217—24no—
237#217—24no—
238C4⋊Dic3—21no—
239C4⋊Dic3C3×D412yes—
240C4×Dic3—42no—
241C4×Dic3C2×C3×C412yes—
242C4×Dic3C3×D412yes—
243C2×C3⋊C8—21no—
244C2×C3⋊C8—21no—
245C2×C3⋊C8—21no—
246C22×C32—42no—
247C22×C32—42no—
248C22×C32—42no—
249C22×C32—81no—
250C22×C32—81no—
251C22×C32—81no—
252C22×C32—81no—
253C22×C32C2×C22⋊C411yescharacteristic
254C22×C32#12111yescharacteristic
255C22×C32#12111yescharacteristic
256C22×C32#13511yescharacteristic
257C22×C32#13511yescharacteristic
258C22×C32AGL(1,ℤ/8)11yescharacteristic
259C22×C32#13711yescharacteristic
260C32×C4—42no—
261C32×C4C4×D411yescharacteristic
262C32×C4C4×D411yescharacteristic
263C32×C4#12411yescharacteristic
264C32×C4#12711yescharacteristic
265C3×Dic3—22no—
266C3×Dic3—22no—
267C3×Dic3—42no—
268C3×Dic3—42no—
269C22×Q8—31no—
270C22×D4C2×C3×D311yescharacteristic
271C22×C8—31no—
272C22×C8C2×C3×D311yescharacteristic
273#124—34no—
274#124—62no—
275C2×C4⋊C4—31no—
276C2×C4⋊C4C2×C3×D311yescharacteristic
277C2×C22⋊C4—61no—
278C2×C22⋊C4—61no—
279C2×C42—31no—
280C2×C42—61no—
281C4⋊C8—62no—
282#103—62no—
283#103—62no—
284#102—22no—
285#102—62no—
286#95—61no—
287C23×C3—22no—
288C23×C3—22no—
289C23×C3—21no—
290C23×C3—42no—
291C23×C3—42no—
292C23×C3—42no—
293C23×C3—41no—
294C23×C3—41no—
295C23×C3—41no—
296C23×C3—41no—
297C23×C3—41no—
298C23×C3—41no—
299C23×C3—41no—
300C23×C3—41no—
301C23×C3—41no—
302C23×C3—41no—
303C23×C3—41no—
304C23×C3—41no—
305C23×C3—81no—
306C23×C3—81no—
307C23×C3—81no—
308C23×C3—81no—
309C23×C3D3×D411yescharacteristic
310C23×C3C2×C3×D411yescharacteristic
311C3×Q8—62no—
312C3×Q8—62no—
313C3×Q8—121no—
314C3×Q8—121no—
315C3×D4—24no—
316C3×D4—22no—
317C3×D4—22no—
318C3×D4—22no—
319C3×D4—22no—
320C3×D4—42no—
321C3×D4—42no—
322C3×D4—42no—
323C3×D4—41no—
324C3×D4—41no—
325C3×D4—41no—
326C3×D4—41no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—32no—
336C2×C3×C4—32no—
337C2×C3×C4—42no—
338C2×C3×C4—41no—
339C2×C3×C4—41no—
340C2×C3×C4—41no—
341C2×C3×C4—41no—
342C2×C3×C4—61no—
343C2×C3×C4—61no—
344C2×C3×C4—61no—
345C2×C3×C4—61no—
346C2×C3×C4—62no—
347C2×C3×C4—62no—
348C2×C3×C4—81no—
349C2×C3×C4—81no—
350C2×C3×C4—121no—
351C2×C3×C4—121no—
352C2×C3×C4—121no—
353C2×C3×C4—121no—
354C2×C3×C4C2×C4×D311yescharacteristic
355C2×C3×C4#23511yescharacteristic
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4#23711yescharacteristic
359C2×C3×C4C2×#6711yescharacteristic
360C2×C3×C4C22×C3×C411yescharacteristic
361C2×C3×C4C2×C3×D411yescharacteristic
362C2×C3×C4C2×C3×D411yescharacteristic
363C2×C3×C4C2×C3×D411yescharacteristic
364C2×C3×C4C3×#4111yescharacteristic
365C2×C3×C4C3×#4111yescharacteristic
366C2×Dic3—21no—
367C2×Dic3—21no—
368C2×Dic3—21no—
369C2×Dic3—21no—
370C2×Dic3—22no—
371C2×Dic3—22no—
372C2×Dic3—41no—
373C2×Dic3—41no—
374C2×Dic3—41no—
375C2×Dic3—41no—
376C2×Dic3C3×C22⋊C412yes—
377C2×Dic3C3×C22⋊C412yes—
378Dic6—22no—
379Dic6—22no—
380Dic6—41no—
381Dic6—41no—
382C3×C8—42no—
383C3×C8—41no—
384C3×C8—41no—
385C3×C8—121no—
386C3⋊C8—41no—
387C2×C32—82no—
388C2×C32#39011yescharacteristic
389C2×C32#41611yescharacteristic
390C2×C32#41711yescharacteristic
391C2×C32#46311yescharacteristic
392C2×C32#46311yescharacteristic
393C2×C32#46411yescharacteristic
394C2×C32#46411yescharacteristic
395C24—21no—
396C2×Q8—32no—
397C2×Q8—61no—
398C2×Q8—61no—
399C2×Q8—61no—
400C2×Q8—61no—
401C2×Q8—61no—
402C2×D4—21no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4C3×C4×D312yes—
408C22×C4—21no—
409C22×C4—31no—
410C22×C4—31no—
411C22×C4—61no—
412C22×C4—61no—
413C22×C4C22×C3×D311yescharacteristic
414C2×C8—21no—
415C2×C8—21no—
416C2×C8—21no—
417C2×C8—61no—
418C2×C8—61no—
419C2×C8—61no—
420C4⋊C4—21no—
421C4⋊C4—32no—
422C4⋊C4—61no—
423C4⋊C4C3×#6712yes—
424C22⋊C4—64no—
425C22⋊C4—64no—
426C42—32no—
427C42—32no—
428C42—122no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—21no—
436C22×C3—44no—
437C22×C3—42no—
438C22×C3—42no—
439C22×C3—42no—
440C22×C3—42no—
441C22×C3—42no—
442C22×C3—42no—
443C22×C3—82no—
444C22×C3—82no—
445C22×C3—82no—
446C22×C3—82no—
447C22×C3—82no—
448C22×C3—82no—
449C22×C3—81no—
450C22×C3—81no—
451C22×C3—81no—
452C22×C3—81no—
453C22×C3—81no—
454C22×C3—81no—
455C22×C3—81no—
456C22×C3—81no—
457C22×C3D3×C22⋊C411yescharacteristic
458C22×C3#88411yescharacteristic
459C22×C3#91111yescharacteristic
460C22×C3#91211yescharacteristic
461C22×C3#91511yescharacteristic
462C22×C3#91611yescharacteristic
463C22×C3#93911yescharacteristic
464C22×C3C2×C3×C22⋊C411yescharacteristic
465C22×C3C3×#12111yescharacteristic
466C22×C3C3×#12111yescharacteristic
467C22×C3C3×#13511yescharacteristic
468C22×C3C3×#13511yescharacteristic
469C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
470C22×C3C3×#13711yescharacteristic
471C3×C4—21no—
472C3×C4—21no—
473C3×C4—21no—
474C3×C4—21no—
475C3×C4—42no—
476C3×C4—42no—
477C3×C4—62no—
478C3×C4—62no—
479C3×C4—82no—
480C3×C4—122no—
481C3×C4—122no—
482C3×C4#67⋊C411yescharacteristic
483C3×C4#88511yescharacteristic
484C3×C4C4×#6711yescharacteristic
485C3×C4#94011yescharacteristic
486C3×C4C3×C4×D411yescharacteristic
487C3×C4C3×C4×D411yescharacteristic
488C3×C4C3×#12411yescharacteristic
489C3×C4C3×#12711yescharacteristic
490Dic3—22no—
491Dic3—22no—
492Dic3—42no—
493Dic3—42no—
494C32#198311yescharacteristic, complemented, Sylow
495C23—22no—
496C23—41no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23C3×D3×D411yescharacteristic
503Q8—62no—
504Q8—62no—
505Q8—121no—
506Q8—121no—
507D4—22no—
508D4—22no—
509D4—41no—
510D4—41no—
511C2×C4—22no—
512C2×C4—32no—
513C2×C4—32no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—61no—
517C2×C4—61no—
518C2×C4—61no—
519C2×C4—61no—
520C2×C4—62no—
521C2×C4—62no—
522C2×C4—121no—
523C2×C4—121no—
524C2×C4—121no—
525C2×C4—121no—
526C2×C4C2×C3×C4×D311yescharacteristic
527C2×C4C3×#23511yescharacteristic
528C2×C4C3×D3×D411yescharacteristic
529C2×C4C3×D3×D411yescharacteristic
530C2×C4C3×#23711yescharacteristic
531C2×C4C2×C3×#6711yescharacteristic
532C8—41no—
533C8—121no—
534C2×C3—21no—
535C2×C3—21no—
536C2×C3—21no—
537C2×C3—21no—
538C2×C3—21no—
539C2×C3—21no—
540C2×C3—21no—
541C2×C3—84no—
542C2×C3—82no—
543C2×C3—82no—
544C2×C3#476711yescharacteristic
545C2×C3#477111yescharacteristic
546C2×C3#477211yescharacteristic
547C2×C3#478711yescharacteristic
548C2×C3#495711yescharacteristic
549C2×C3#515311yescharacteristic
550C2×C3#516611yescharacteristic
551C2×C3C3×#39011yescharacteristic
552C2×C3C3×#41611yescharacteristic
553C2×C3C3×#41711yescharacteristic
554C2×C3C3×#46311yescharacteristic
555C2×C3C3×#46311yescharacteristic
556C2×C3C3×#46411yescharacteristic
557C2×C3C3×#46411yescharacteristic
558C22—42no—
559C22—42no—
560C22—42no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22C3×D3×C22⋊C411yescharacteristic
566C22C3×#88411yescharacteristic
567C22C3×#91111yescharacteristic
568C22C3×#91211yescharacteristic
569C22C3×#91511yescharacteristic
570C22C3×#91611yescharacteristic
571C22C3×#93911yescharacteristic
572C4—42no—
573C4—62no—
574C4—62no—
575C4—122no—
576C4—122no—
577C4C3×#67⋊C411yescharacteristic
578C4C3×#88511yescharacteristic
579C4C3×C4×#6711yescharacteristic
580C4C3×#94011yescharacteristic
581C3—21no—
582C3#7016211yescharacteristic, direct product factor
583C3C3×#198311yescharacteristic, complemented
584C2—82no—
585C2C3×#476711yescharacteristic
586C2C3×#477111yescharacteristic
587C2C3×#477211yescharacteristic
588C2C3×#478711yescharacteristic
589C2C3×#495711yescharacteristic
590C2C3×#515311yescharacteristic
591C2C3×#516611yescharacteristic
subgroupG/H
centerC23×C3D3×D4
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#102C2
socleC23×C32C2×D4
prime radicalC22×C32×D4C22
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×#102D3
hypocenterC3C3×#1983
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C2×C3×#102

Complements

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

NH ≅ G/Ntype
4. C2×C3×#816C2semidirect
5. C2×C3×Dic3⋊C8C2semidirect
6. C3×Dic3×C4⋊C4C2semidirect
7. C2×C3×#810C2semidirect
9. #70162C3direct (N × H)
17. C3×#936C4semidirect
39. C2×#816C2×C3semidirect
40. C2×Dic3⋊C8C2×C3semidirect
41. Dic3×C4⋊C4C2×C3semidirect
42. C2×#810C2×C3semidirect
100. #936C3×C4semidirect
494. C32#1983semidirect
582. C3#70162direct (N × H)
583. C3C3×#1983semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9362
C2×C32×#1022
C2×C3×#8322
C2×C3×#8162
C2×C3×Dic3⋊C82
C3×Dic3×C4⋊C42
C2×C3×#8102
C3×#19833
#701623