Finite Group Databasebeta

← C3×#70230 #11791473

Subgroups — C3×#70230 #11791473

Order 1152.

769 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#947C211yesmaximal, characteristic
2C2×C32×#103C211yesmaximal, characteristic, complemented
3C2×C3×#835C211yesmaximal, characteristic, complemented
4C2×C3×#821C211yesmaximal, characteristic
5C2×C3×Dic3⋊C8C211yesmaximal, characteristic, complemented
6C3×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
7C2×C3×#809C211yesmaximal, characteristic
8C3×#1983—31nomaximal
9#70230C311yesmaximal, characteristic, direct product factor
10C22×C32×Q8C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C3×#947—22no—
15C3×#947C414yescomplemented
16C2×C3×(C2×D3)⋊C4—21no—
17C2×C3×(C2×D3)⋊C4—21no—
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4×Dic3—21no—
20C2×C3×C4×Dic3C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C32×#103—22no—
23C3×#835—22no—
24C3×C3⋊#95—21no—
25C3×#821—22no—
26C3×Dic3⋊C8—22no—
27C3×#809—22no—
28C2×C3×#124—31no—
29C2×#947C2×C311yescharacteristic
30C2×C3×C4⋊C8—31no—
31C2×C3×#103—21no—
32C2×C3×#103—31no—
33C2×C3×#103D311yescharacteristic, complemented
34C2×C3×#103C2×C311yescharacteristic, complemented
35C2×C3×#102—31no—
36C2×C3×#102—31no—
37C3×C4×C4⋊C4—31no—
38C2×#835C2×C311yescharacteristic, complemented
39C2×#821C2×C311yescharacteristic
40C2×Dic3⋊C8C2×C311yescharacteristic, complemented
41Dic3×C4⋊C4C2×C311yescharacteristic, complemented
42C2×#809C2×C311yescharacteristic
43C23×C3×D3—21no—
44C2×C32×Q8—21no—
45C2×C32×Q8—21no—
46C2×C32×Q8—21no—
47C2×C32×Q8—21no—
48C2×C32×Q8—21no—
49C2×C32×Q8C2×C412yes—
50C22×C32×C4—21no—
51C22×C32×C4—21no—
52C22×C32×C4C2311yescharacteristic
53C22×C3×Dic3—21no—
54C22×C3×Dic3D411yescharacteristic
55C22×C3×Dic3D411yescharacteristic
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12—21no—
59C2×C3×D12—21no—
60C2×C3×D12—21no—
61C2×C3×D12C2×C412yes—
62C2×C32×C8—21no—
63C2×C32×C8—21no—
64C2×C32×C8—21no—
65C32×C4⋊C4—21no—
66C32×C4⋊C4D412yes—
67C3×(C2×D3)⋊C4—24no—
68C3×(C2×D3)⋊C4—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—21no—
79C22×C3×Q8C2×D311yescharacteristic
80C22×C3×Q8C22×C311yescharacteristic
81C22×C3×D4—31no—
82C22×D12C22×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—
97#947—22no—
98#947C3×C414yescomplemented
99C2×(C2×D3)⋊C4—21no—
100C2×(C2×D3)⋊C4—21no—
101C2×C4⋊Dic3C22×C311yescharacteristic
102C2×C4×Dic3—21no—
103C2×C4×Dic3C22×C311yescharacteristic
104C22×C3⋊C8C22×C311yescharacteristic
105C3×C4⋊C8—62no—
106C3×#103—24no—
107C3×#103—22no—
108C3×#103—22no—
109C3×#103—62no—
110C3×#102—62no—
111C3×#102—62no—
112C3×#95—61no—
113#835—22no—
114C3⋊#95—21no—
115#821—22no—
116Dic3⋊C8—22no—
117#809—22no—
118C23×C32C2×D411yescharacteristic
119C22×C3×D3—22no—
120C22×C3×D3—41no—
121C22×C3×D3—41no—
122C22×C3×D3—41no—
123C22×C3×D3—41no—
124C22×C3×D3—41no—
125C22×C3×D3—41no—
126C32×Q8—22no—
127C32×Q8—22no—
128C32×Q8—41no—
129C32×Q8—41no—
130C2×C32×C4—22no—
131C2×C32×C4—22no—
132C2×C32×C4—41no—
133C2×C32×C4—41no—
134C2×C32×C4—41no—
135C2×C32×C4—41no—
136C2×C32×C4C22×C411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4#4111yescharacteristic
141C2×C32×C4#4111yescharacteristic
142C2×C3×Dic3—21no—
143C2×C3×Dic3—21no—
144C2×C3×Dic3—21no—
145C2×C3×Dic3—21no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—41no—
148C2×C3×Dic3—41no—
149C2×C3×Dic3C22⋊C412yes—
150C2×C3×Dic3C22⋊C412yes—
151C3×D12—22no—
152C3×D12—22no—
153C3×D12—41no—
154C3×D12—41no—
155C32×C8—41no—
156C3×C3⋊C8—41no—
157C2×#124—31no—
158C2×C4⋊C8—31no—
159C2×#103—31no—
160C2×#103C3×D311yescharacteristic, complemented
161C2×#102—31no—
162C2×#102—31no—
163C4×C4⋊C4—31no—
164C24×C3—61no—
165C23×D3—21no—
166C2×C3×Q8—21no—
167C2×C3×Q8—21no—
168C2×C3×Q8—22no—
169C2×C3×Q8—22no—
170C2×C3×Q8—21no—
171C2×C3×Q8—21no—
172C2×C3×Q8—21no—
173C2×C3×Q8—21no—
174C2×C3×Q8—21no—
175C2×C3×Q8—21no—
176C2×C3×Q8—21no—
177C2×C3×Q8—21no—
178C2×C3×Q8—22no—
179C2×C3×Q8—41no—
180C2×C3×Q8—41no—
181C2×C3×Q8—41no—
182C2×C3×Q8C4×D312yes—
183C2×C3×Q8C2×C3×C412yes—
184C2×C3×D4—32no—
185C2×C3×D4—61no—
186C2×C3×D4—61no—
187C2×C3×D4—61no—
188C2×C3×D4—61no—
189C2×C3×D4—61no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—31no—
196C22×C3×C4—31no—
197C22×C3×C4—41no—
198C22×C3×C4—41no—
199C22×C3×C4—61no—
200C22×C3×C4C22×D311yescharacteristic
201C22×C3×C4C23×C311yescharacteristic
202C22×Dic3—21no—
203C22×Dic3C3×D411yescharacteristic
204C22×Dic3C3×D411yescharacteristic
205C2×D12—21no—
206C2×D12—21no—
207C2×D12—21no—
208C2×D12—21no—
209C2×D12—21no—
210C2×D12C2×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(C2×D3)⋊C4—24no—
237(C2×D3)⋊C4—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×C32C2×C22⋊C411yescharacteristic
247C22×C32#12111yescharacteristic
248C22×C32#12111yescharacteristic
249C22×C32#13511yescharacteristic
250C22×C32#13511yescharacteristic
251C22×C32AGL(1,ℤ/8)11yescharacteristic
252C22×C32#13711yescharacteristic
253C2×C3×D3—42no—
254C2×C3×D3—42no—
255C2×C3×D3—42no—
256C2×C3×D3—81no—
257C2×C3×D3—81no—
258C2×C3×D3—81no—
259C2×C3×D3—81no—
260C32×C4—42no—
261C32×C4—42no—
262C32×C4C4×D411yescharacteristic
263C32×C4C4×D411yescharacteristic
264C32×C4#12411yescharacteristic
265C32×C4#12711yescharacteristic
266C3×Dic3—22no—
267C3×Dic3—22no—
268C3×Dic3—42no—
269C22×Q8C2×C3×D311yescharacteristic
270C22×D4—31no—
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—22no—
283#103—62no—
284#102—62no—
285#102—62no—
286#95—61no—
287C23×C3—21no—
288C23×C3—62no—
289C23×C3—121no—
290C23×C3—121no—
291C23×C3—121no—
292C23×C3—121no—
293C23×C3—121no—
294C23×C3—121no—
295C23×C3D3×D411yescharacteristic
296C23×C3C2×C3×D411yescharacteristic
297C22×D3—22no—
298C22×D3—41no—
299C22×D3—41no—
300C22×D3—41no—
301C22×D3—41no—
302C22×D3—41no—
303C22×D3—41no—
304C3×Q8—24no—
305C3×Q8—22no—
306C3×Q8—22no—
307C3×Q8—22no—
308C3×Q8—22no—
309C3×Q8—42no—
310C3×Q8—42no—
311C3×Q8—42no—
312C3×Q8—41no—
313C3×Q8—41no—
314C3×Q8—41no—
315C3×Q8—41no—
316C3×D4—62no—
317C3×D4—62no—
318C3×D4—121no—
319C3×D4—121no—
320C2×C3×C4—22no—
321C2×C3×C4—22no—
322C2×C3×C4—22no—
323C2×C3×C4—22no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—32no—
331C2×C3×C4—32no—
332C2×C3×C4—42no—
333C2×C3×C4—42no—
334C2×C3×C4—42no—
335C2×C3×C4—42no—
336C2×C3×C4—41no—
337C2×C3×C4—41no—
338C2×C3×C4—41no—
339C2×C3×C4—41no—
340C2×C3×C4—41no—
341C2×C3×C4—41no—
342C2×C3×C4—41no—
343C2×C3×C4—41no—
344C2×C3×C4—61no—
345C2×C3×C4—61no—
346C2×C3×C4—61no—
347C2×C3×C4—61no—
348C2×C3×C4—62no—
349C2×C3×C4—81no—
350C2×C3×C4—81no—
351C2×C3×C4—121no—
352C2×C3×C4—121no—
353C2×C3×C4C2×C4×D311yescharacteristic
354C2×C3×C4#23511yescharacteristic
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4#23711yescharacteristic
358C2×C3×C4C2×#6711yescharacteristic
359C2×C3×C4C22×C3×C411yescharacteristic
360C2×C3×C4C2×C3×D411yescharacteristic
361C2×C3×C4C2×C3×D411yescharacteristic
362C2×C3×C4C2×C3×D411yescharacteristic
363C2×C3×C4C3×#4111yescharacteristic
364C2×C3×C4C3×#4111yescharacteristic
365C2×Dic3—21no—
366C2×Dic3—21no—
367C2×Dic3—21no—
368C2×Dic3—21no—
369C2×Dic3—22no—
370C2×Dic3—41no—
371C2×Dic3—41no—
372C2×Dic3C3×C22⋊C412yes—
373C2×Dic3C3×C22⋊C412yes—
374D12—22no—
375D12—22no—
376D12—41no—
377D12—41no—
378C3×C8—42no—
379C3×C8—41no—
380C3×C8—41no—
381C3×C8—121no—
382C3⋊C8—41no—
383C2×C32#39011yescharacteristic
384C2×C32#41611yescharacteristic
385C2×C32#41711yescharacteristic
386C2×C32#46311yescharacteristic
387C2×C32#46311yescharacteristic
388C2×C32#46411yescharacteristic
389C2×C32#46411yescharacteristic
390C3×D3—82no—
391C24—61no—
392C2×Q8—21no—
393C2×Q8—21no—
394C2×Q8—21no—
395C2×Q8—21no—
396C2×Q8—21no—
397C2×Q8C3×C4×D312yes—
398C2×D4—32no—
399C2×D4—61no—
400C2×D4—61no—
401C2×D4—61no—
402C2×D4—61no—
403C2×D4—61no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—31no—
407C22×C4—31no—
408C22×C4—61no—
409C22×C4C22×C3×D311yescharacteristic
410C2×C8—21no—
411C2×C8—21no—
412C2×C8—21no—
413C2×C8—61no—
414C2×C8—61no—
415C2×C8—61no—
416C4⋊C4—21no—
417C4⋊C4—32no—
418C4⋊C4—61no—
419C4⋊C4C3×#6712yes—
420C22⋊C4—64no—
421C22⋊C4—64no—
422C42—32no—
423C42—32no—
424C42—122no—
425C22×C3—21no—
426C22×C3—21no—
427C22×C3—21no—
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—122no—
433C22×C3—122no—
434C22×C3—122no—
435C22×C3—241no—
436C22×C3—241no—
437C22×C3—241no—
438C22×C3—241no—
439C22×C3D3×C22⋊C411yescharacteristic
440C22×C3#88411yescharacteristic
441C22×C3#91411yescharacteristic
442C22×C3#91611yescharacteristic
443C22×C3#91811yescharacteristic
444C22×C3#91911yescharacteristic
445C22×C3#93911yescharacteristic
446C22×C3C2×C3×C22⋊C411yescharacteristic
447C22×C3C3×#12111yescharacteristic
448C22×C3C3×#12111yescharacteristic
449C22×C3C3×#13511yescharacteristic
450C22×C3C3×#13511yescharacteristic
451C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
452C22×C3C3×#13711yescharacteristic
453C2×D3—42no—
454C2×D3—42no—
455C2×D3—42no—
456C2×D3—81no—
457C2×D3—81no—
458C2×D3—81no—
459C2×D3—81no—
460C3×C4—21no—
461C3×C4—21no—
462C3×C4—21no—
463C3×C4—21no—
464C3×C4—44no—
465C3×C4—42no—
466C3×C4—42no—
467C3×C4—42no—
468C3×C4—42no—
469C3×C4—62no—
470C3×C4—62no—
471C3×C4—82no—
472C3×C4—122no—
473C3×C4#67⋊C411yescharacteristic
474C3×C4#88511yescharacteristic
475C3×C4C4×#6711yescharacteristic
476C3×C4#94011yescharacteristic
477C3×C4C3×C4×D411yescharacteristic
478C3×C4C3×C4×D411yescharacteristic
479C3×C4C3×#12411yescharacteristic
480C3×C4C3×#12711yescharacteristic
481Dic3—22no—
482Dic3—22no—
483Dic3—42no—
484C32#198311yescharacteristic, complemented, Sylow
485C23—62no—
486C23—121no—
487C23—121no—
488C23—121no—
489C23—121no—
490C23—121no—
491C23—121no—
492C23C3×D3×D411yescharacteristic
493Q8—22no—
494Q8—22no—
495Q8—41no—
496Q8—41no—
497D4—62no—
498D4—62no—
499D4—121no—
500D4—121no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—32no—
504C2×C4—32no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—61no—
510C2×C4—61no—
511C2×C4—61no—
512C2×C4—61no—
513C2×C4—62no—
514C2×C4—121no—
515C2×C4—121no—
516C2×C4C2×C3×C4×D311yescharacteristic
517C2×C4C3×#23511yescharacteristic
518C2×C4C3×D3×D411yescharacteristic
519C2×C4C3×D3×D411yescharacteristic
520C2×C4C3×#23711yescharacteristic
521C2×C4C2×C3×#6711yescharacteristic
522C8—41no—
523C8—121no—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3—21no—
530C2×C3—21no—
531C2×C3—242no—
532C2×C3#479811yescharacteristic
533C2×C3#480311yescharacteristic
534C2×C3#480411yescharacteristic
535C2×C3#481911yescharacteristic
536C2×C3#495711yescharacteristic
537C2×C3#516511yescharacteristic
538C2×C3#518511yescharacteristic
539C2×C3C3×#39011yescharacteristic
540C2×C3C3×#41611yescharacteristic
541C2×C3C3×#41711yescharacteristic
542C2×C3C3×#46311yescharacteristic
543C2×C3C3×#46311yescharacteristic
544C2×C3C3×#46411yescharacteristic
545C2×C3C3×#46411yescharacteristic
546D3—82no—
547C22—122no—
548C22—122no—
549C22—122no—
550C22—241no—
551C22—241no—
552C22—241no—
553C22—241no—
554C22C3×D3×C22⋊C411yescharacteristic
555C22C3×#88411yescharacteristic
556C22C3×#91411yescharacteristic
557C22C3×#91611yescharacteristic
558C22C3×#91811yescharacteristic
559C22C3×#91911yescharacteristic
560C22C3×#93911yescharacteristic
561C4—42no—
562C4—42no—
563C4—62no—
564C4—62no—
565C4—122no—
566C4C3×#67⋊C411yescharacteristic
567C4C3×#88511yescharacteristic
568C4C3×C4×#6711yescharacteristic
569C4C3×#94011yescharacteristic
570C3—21no—
571C3#7023011yescharacteristic, direct product factor
572C3C3×#198311yescharacteristic, complemented
573C2—242no—
574C2C3×#479811yescharacteristic
575C2C3×#480311yescharacteristic
576C2C3×#480411yescharacteristic
577C2C3×#481911yescharacteristic
578C2C3×#495711yescharacteristic
579C2C3×#516511yescharacteristic
580C2C3×#518511yescharacteristic
subgroupG/H
centerC23×C3D3×D4
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#103C2
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×#103D3
hypocenterC3C3×#1983
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C2×C3×#103

Complements

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

NH ≅ G/Ntype
2. C2×C32×#103C2semidirect
3. C2×C3×#835C2semidirect
5. C2×C3×Dic3⋊C8C2semidirect
6. C3×Dic3×C4⋊C4C2semidirect
9. #70230C3direct (N × H)
15. C3×#947C4semidirect
33. C2×C3×#103D3semidirect
34. C2×C3×#103C2×C3semidirect
38. C2×#835C2×C3semidirect
40. C2×Dic3⋊C8C2×C3semidirect
41. Dic3×C4⋊C4C2×C3semidirect
98. #947C3×C4semidirect
160. C2×#103C3×D3semidirect
484. C32#1983semidirect
571. C3#70230direct (N × H)
572. C3C3×#1983semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9472
C2×C32×#1032
C2×C3×#8352
C2×C3×#8212
C2×C3×Dic3⋊C82
C3×Dic3×C4⋊C42
C2×C3×#8092
C3×#19833
#702303