Finite Group Databasebeta

← C3×#68863 #11794055

Subgroups — C3×#68863 #11794055

Order 1152.

705 conjugacy classes of subgroups.

The subgroup lattice has 569 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#204C211yesmaximal, characteristic
2C2×C3×Dic3⋊C8C211yesmaximal, characteristic, complemented
3C3×#4988C211yesmaximal, characteristic
4C3×#4973C211yesmaximal, characteristic, complemented
5C2×C3×#810C211yesmaximal, characteristic, complemented
6C2×C3×#809C211yesmaximal, characteristic
7C32×#340C211yesmaximal, characteristic, complemented
8C3×#2055—31nomaximal
9#68863C311yesmaximal, characteristic, direct product factor
10C22×C3×D12C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×C32×C4⋊C4C2211yescharacteristic
15C2×C3×(C2×D3)⋊C4—21no—
16C2×C3×(C2×D3)⋊C4—21no—
17C2×C3×C4×Dic3C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C2×C3×#204—22no—
20C2×C3×#204—22no—
21C2×C3×#204—22no—
22C3×C3⋊#95—21no—
23C3×C3⋊#95—21no—
24C3×Dic3⋊C8—22no—
25C3×#810—22no—
26C3×#809—22no—
27C22×C3×SD16—31no—
28C22×#204C2×C311yescharacteristic
29C2×C3×C4⋊C8—31no—
30C2×C3×#103—31no—
31C2×C3×#102—31no—
32C3×#391—31no—
33C3×#390—31no—
34C2×Dic3⋊C8C2×C311yescharacteristic, complemented
35#4988C2×C311yescharacteristic
36#4973C2×C311yescharacteristic, complemented
37C2×#810C2×C311yescharacteristic, complemented
38C2×#809C2×C311yescharacteristic
39C3×#340—21no—
40C3×#340D311yescharacteristic, complemented
41C3×#340C2×C311yescharacteristic, complemented
42C23×C3×D3—21no—
43C22×C32×C4—21no—
44C22×C32×C4—21no—
45C22×C32×C4C2311yescharacteristic
46C22×C3×Dic3—21no—
47C22×C3×Dic3D411yescharacteristic
48C22×C3×Dic3D411yescharacteristic
49C2×C3×D12—21no—
50C2×C3×D12—21no—
51C2×C3×D12—21no—
52C2×C3×D12—21no—
53C2×C3×D12—21no—
54C2×C3×D12D412yes—
55C2×C3×Dic6—21no—
56C2×C3×Dic6—21no—
57C2×C3×Dic6—21no—
58C2×C3×Dic6—21no—
59C2×C3×Dic6—21no—
60C2×C3×Dic6D412yes—
61C2×C32×C8—21no—
62C2×C32×C8—21no—
63C2×C32×C8D412yes—
64C32×C4⋊C4—21no—
65C32×C4⋊C4—21no—
66C32×C4⋊C4—21no—
67C32×C4⋊C4—21no—
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—
75C3×#204—28no—
76#2055—31noSylow
77C22×C3×Q8—31no—
78C22×C3×D4—31no—
79C22×D12C22×C311yescharacteristic
80C22×Dic6C22×C311yescharacteristic
81C2×C3×SD16—62no—
82C2×C3×SD16—62no—
83C2×C3×SD16—62no—
84C22×C3×C8—21no—
85C22×C3×C8—31no—
86C22×C3×C8C2×D311yescharacteristic
87C22×C3×C8C22×C311yescharacteristic
88C2×C3×C4⋊C4—21no—
89C2×C3×C4⋊C4—21no—
90C2×C3×C4⋊C4C2×D311yescharacteristic
91C2×C3×C4⋊C4C2×D311yescharacteristic
92C2×C3×C4⋊C4C22×C311yescharacteristic
93C2×C3×C4⋊C4C22×C311yescharacteristic
94C2×C3×C22⋊C4—61no—
95C2×C3×C22⋊C4—61no—
96C2×C3×C42—31no—
97C2×(C2×D3)⋊C4—21no—
98C2×(C2×D3)⋊C4—21no—
99C2×C4×Dic3C22×C311yescharacteristic
100C22×C3⋊C8C22×C311yescharacteristic
101C2×#204—22no—
102C2×#204—22no—
103C2×#204—22no—
104C3×C4⋊C8—62no—
105C3×#103—62no—
106C3×#102—62no—
107C3×#95—61no—
108C3×#95—61no—
109C3⋊#95—21no—
110C3⋊#95—21no—
111Dic3⋊C8—22no—
112#810—22no—
113#809—22no—
114C23×C32C2×D411yescharacteristic
115C22×C3×D3—22no—
116C22×C3×D3—41no—
117C22×C3×D3—41no—
118C22×C3×D3—41no—
119C22×C3×D3—41no—
120C22×C3×D3—41no—
121C22×C3×D3—41no—
122C2×C32×C4—41no—
123C2×C32×C4—41no—
124C2×C32×C4—41no—
125C2×C32×C4—41no—
126C2×C32×C4—41no—
127C2×C32×C4—41no—
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4#4111yescharacteristic
132C2×C32×C4#4111yescharacteristic
133C2×C32×C4#4111yescharacteristic
134C2×C3×Dic3—21no—
135C2×C3×Dic3—21no—
136C2×C3×Dic3—21no—
137C2×C3×Dic3—22no—
138C2×C3×Dic3—21no—
139C2×C3×Dic3—21no—
140C2×C3×Dic3—41no—
141C2×C3×Dic3—41no—
142C2×C3×Dic3SD1612yescomplemented
143C3×D12—22no—
144C3×D12—22no—
145C3×D12—41no—
146C3×D12—41no—
147C3×Dic6—22no—
148C3×Dic6—22no—
149C3×Dic6—41no—
150C3×Dic6—41no—
151C32×C8—22no—
152C3×C3⋊C8—41no—
153C22×SD16—31no—
154C2×C4⋊C8—31no—
155C2×#103—31no—
156C2×#102—31no—
157#391—31no—
158#390—31no—
159#340C3×D311yescharacteristic, complemented
160C24×C3—61no—
161C23×D3—21no—
162C2×C3×Q8—32no—
163C2×C3×Q8—61no—
164C2×C3×Q8—61no—
165C2×C3×Q8—61no—
166C2×C3×Q8—61no—
167C2×C3×Q8—61no—
168C2×C3×D4—32no—
169C2×C3×D4—61no—
170C2×C3×D4—61no—
171C2×C3×D4—61no—
172C2×C3×D4—61no—
173C2×C3×D4—61no—
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4—31no—
180C22×C3×C4—31no—
181C22×C3×C4—41no—
182C22×C3×C4—41no—
183C22×C3×C4—61no—
184C22×C3×C4C22×D311yescharacteristic
185C22×C3×C4C23×C311yescharacteristic
186C22×Dic3—21no—
187C22×Dic3C3×D411yescharacteristic
188C22×Dic3C3×D411yescharacteristic
189C2×D12—21no—
190C2×D12—21no—
191C2×D12—21no—
192C2×D12—21no—
193C2×D12—21no—
194C2×D12C3×D412yes—
195C2×Dic6—21no—
196C2×Dic6—21no—
197C2×Dic6—21no—
198C2×Dic6—21no—
199C2×Dic6—21no—
200C2×Dic6C3×D412yes—
201C3×SD16—68no—
202C2×C3×C8—21no—
203C2×C3×C8—21no—
204C2×C3×C8—21no—
205C2×C3×C8—21no—
206C2×C3×C8—22no—
207C2×C3×C8—41no—
208C2×C3×C8—41no—
209C2×C3×C8—61no—
210C2×C3×C8—61no—
211C2×C3×C8—61no—
212C2×C3×C8D1212yes—
213C2×C3×C8C3×D412yes—
214C3×C4⋊C4—22no—
215C3×C4⋊C4—22no—
216C3×C4⋊C4—21no—
217C3×C4⋊C4—21no—
218C3×C4⋊C4—21no—
219C3×C4⋊C4—21no—
220C3×C4⋊C4—21no—
221C3×C4⋊C4—21no—
222C3×C4⋊C4—21no—
223C3×C4⋊C4—21no—
224C3×C4⋊C4—41no—
225C3×C4⋊C4—41no—
226C3×C22⋊C4—122no—
227C3×C22⋊C4—122no—
228C3×C42—61no—
229C3×C42—61no—
230(C2×D3)⋊C4—42no—
231(C2×D3)⋊C4—42no—
232C4×Dic3—21no—
233C4×Dic3—21no—
234C2×C3⋊C8—21no—
235C2×C3⋊C8—21no—
236C2×C3⋊C8—21no—
237#204—28no—
238C22×C32#12111yescharacteristic
239C22×C32#12111yescharacteristic
240C22×C32#12111yescharacteristic
241C22×C32C2×SD1611yescharacteristic
242C22×C32#13511yescharacteristic
243C22×C32AGL(1,ℤ/8)11yescharacteristic
244C22×C32#13711yescharacteristic
245C2×C3×D3—42no—
246C2×C3×D3—42no—
247C2×C3×D3—42no—
248C2×C3×D3—81no—
249C2×C3×D3—81no—
250C2×C3×D3—81no—
251C2×C3×D3—81no—
252C32×C4—81no—
253C32×C4—81no—
254C32×C4#12011yescharacteristic
255C32×C4#12311yescharacteristic
256C32×C4#12311yescharacteristic
257C32×C4#12411yescharacteristic
258C3×Dic3—22no—
259C3×Dic3—42no—
260C3×Dic3—41no—
261C22×Q8—31no—
262C22×D4—31no—
263C2×SD16—62no—
264C2×SD16—62no—
265C2×SD16—62no—
266C22×C8—31no—
267C22×C8C2×C3×D311yescharacteristic
268C2×C4⋊C4C2×C3×D311yescharacteristic
269C2×C4⋊C4C2×C3×D311yescharacteristic
270C2×C22⋊C4—61no—
271C2×C22⋊C4—61no—
272C2×C42—31no—
273C4⋊C8—62no—
274#103—62no—
275#102—62no—
276#95—61no—
277#95—61no—
278C23×C3—21no—
279C23×C3—62no—
280C23×C3—121no—
281C23×C3—121no—
282C23×C3—121no—
283C23×C3—121no—
284C23×C3—121no—
285C23×C3—121no—
286C23×C3D3×D411yescharacteristic
287C23×C3C2×C3×D411yescharacteristic
288C22×D3—22no—
289C22×D3—41no—
290C22×D3—41no—
291C22×D3—41no—
292C22×D3—41no—
293C22×D3—41no—
294C22×D3—41no—
295C3×Q8—62no—
296C3×Q8—62no—
297C3×Q8—121no—
298C3×Q8—121no—
299C3×D4—62no—
300C3×D4—62no—
301C3×D4—121no—
302C3×D4—121no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—32no—
310C2×C3×C4—42no—
311C2×C3×C4—42no—
312C2×C3×C4—41no—
313C2×C3×C4—41no—
314C2×C3×C4—41no—
315C2×C3×C4—41no—
316C2×C3×C4—41no—
317C2×C3×C4—41no—
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—61no—
325C2×C3×C4—61no—
326C2×C3×C4—62no—
327C2×C3×C4—61no—
328C2×C3×C4—61no—
329C2×C3×C4—61no—
330C2×C3×C4—81no—
331C2×C3×C4—81no—
332C2×C3×C4—81no—
333C2×C3×C4—81no—
334C2×C3×C4—121no—
335C2×C3×C4—121no—
336C2×C3×C4C2×D1211yescharacteristic
337C2×C3×C4#23511yescharacteristic
338C2×C3×C4#23511yescharacteristic
339C2×C3×C4D3×D411yescharacteristic
340C2×C3×C4D3×D411yescharacteristic
341C2×C3×C4#23911yescharacteristic
342C2×C3×C4C2×C3×D411yescharacteristic
343C2×C3×C4C2×C3×D411yescharacteristic
344C2×C3×C4C2×C3×D411yescharacteristic
345C2×C3×C4C3×#4111yescharacteristic
346C2×C3×C4C3×#4111yescharacteristic
347C2×C3×C4C3×#4111yescharacteristic
348C2×Dic3—21no—
349C2×Dic3—21no—
350C2×Dic3—21no—
351C2×Dic3—22no—
352C2×Dic3—21no—
353C2×Dic3—21no—
354C2×Dic3—41no—
355C2×Dic3—41no—
356C2×Dic3C3×SD1612yescomplemented
357D12—22no—
358D12—22no—
359D12—41no—
360D12—41no—
361Dic6—22no—
362Dic6—22no—
363Dic6—41no—
364Dic6—41no—
365C3×C8—22no—
366C3×C8—22no—
367C3×C8—42no—
368C3×C8—121no—
369C3⋊C8—41no—
370C2×C32#39411yescharacteristic
371C2×C32#46011yescharacteristic
372C2×C32#46111yescharacteristic
373C2×C32#46311yescharacteristic
374C2×C32#46411yescharacteristic
375C2×C32#46511yescharacteristic
376C2×C32#46811yescharacteristic
377C3×D3—82no—
378C24—61no—
379C2×Q8—32no—
380C2×Q8—61no—
381C2×Q8—61no—
382C2×Q8—61no—
383C2×Q8—61no—
384C2×Q8—61no—
385C2×D4—32no—
386C2×D4—61no—
387C2×D4—61no—
388C2×D4—61no—
389C2×D4—61no—
390C2×D4—61no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—31no—
394C22×C4—31no—
395C22×C4—61no—
396C22×C4C22×C3×D311yescharacteristic
397SD16—68no—
398C2×C8—21no—
399C2×C8—21no—
400C2×C8—61no—
401C2×C8—61no—
402C2×C8—61no—
403C2×C8C3×D1212yes—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C22⋊C4—122no—
409C22⋊C4—122no—
410C42—61no—
411C42—61no—
412C22×C3—21no—
413C22×C3—21no—
414C22×C3—21no—
415C22×C3—21no—
416C22×C3—21no—
417C22×C3—21no—
418C22×C3—21no—
419C22×C3—122no—
420C22×C3—122no—
421C22×C3—122no—
422C22×C3—241no—
423C22×C3—241no—
424C22×C3—241no—
425C22×C3—241no—
426C22×C3#88411yescharacteristic
427C22×C3#88411yescharacteristic
428C22×C3#89511yescharacteristic
429C22×C3#91111yescharacteristic
430C22×C3D3×SD1611yescharacteristic
431C22×C3#91611yescharacteristic
432C22×C3#91811yescharacteristic
433C22×C3C3×#12111yescharacteristic
434C22×C3C3×#12111yescharacteristic
435C22×C3C3×#12111yescharacteristic
436C22×C3C2×C3×SD1611yescharacteristic
437C22×C3C3×#13511yescharacteristic
438C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
439C22×C3C3×#13711yescharacteristic
440C2×D3—42no—
441C2×D3—42no—
442C2×D3—42no—
443C2×D3—81no—
444C2×D3—81no—
445C2×D3—81no—
446C2×D3—81no—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—21no—
450C3×C4—21no—
451C3×C4—62no—
452C3×C4—82no—
453C3×C4—82no—
454C3×C4—81no—
455C3×C4—81no—
456C3×C4—81no—
457C3×C4—81no—
458C3×C4—121no—
459C3×C4—122no—
460C3×C4#87511yescharacteristic
461C3×C4#88211yescharacteristic
462C3×C4#89411yescharacteristic
463C3×C4#89411yescharacteristic
464C3×C4C3×#12011yescharacteristic
465C3×C4C3×#12311yescharacteristic
466C3×C4C3×#12311yescharacteristic
467C3×C4C3×#12411yescharacteristic
468Dic3—22no—
469Dic3—42no—
470Dic3—41no—
471C32#205511yescharacteristic, complemented, Sylow
472C23—62no—
473C23—121no—
474C23—121no—
475C23—121no—
476C23—121no—
477C23—121no—
478C23—121no—
479C23C3×D3×D411yescharacteristic
480Q8—62no—
481Q8—62no—
482Q8—121no—
483Q8—121no—
484D4—62no—
485D4—62no—
486D4—121no—
487D4—121no—
488C2×C4—32no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—61no—
496C2×C4—61no—
497C2×C4—62no—
498C2×C4—61no—
499C2×C4—61no—
500C2×C4—61no—
501C2×C4—121no—
502C2×C4—121no—
503C2×C4C2×C3×D1211yescharacteristic
504C2×C4C3×#23511yescharacteristic
505C2×C4C3×#23511yescharacteristic
506C2×C4C3×D3×D411yescharacteristic
507C2×C4C3×D3×D411yescharacteristic
508C2×C4C3×#23911yescharacteristic
509C8—22no—
510C8—121no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—242no—
519C2×C3#467211yescharacteristic
520C2×C3#476211yescharacteristic
521C2×C3#478711yescharacteristic
522C2×C3#479811yescharacteristic
523C2×C3#481811yescharacteristic
524C2×C3#486411yescharacteristic
525C2×C3#488611yescharacteristic
526C2×C3C3×#39411yescharacteristic
527C2×C3C3×#46011yescharacteristic
528C2×C3C3×#46111yescharacteristic
529C2×C3C3×#46311yescharacteristic
530C2×C3C3×#46411yescharacteristic
531C2×C3C3×#46511yescharacteristic
532C2×C3C3×#46811yescharacteristic
533D3—82no—
534C22—122no—
535C22—122no—
536C22—122no—
537C22—241no—
538C22—241no—
539C22—241no—
540C22—241no—
541C22C3×#88411yescharacteristic
542C22C3×#88411yescharacteristic
543C22C3×#89511yescharacteristic
544C22C3×#91111yescharacteristic
545C22C3×D3×SD1611yescharacteristic
546C22C3×#91611yescharacteristic
547C22C3×#91811yescharacteristic
548C4—62no—
549C4—81no—
550C4—81no—
551C4—122no—
552C4—121no—
553C4C3×#87511yescharacteristic
554C4C3×#88211yescharacteristic
555C4C3×#89411yescharacteristic
556C4C3×#89411yescharacteristic
557C3—21no—
558C3#6886311yescharacteristic, direct product factor
559C3C3×#205511yescharacteristic, complemented
560C2—242no—
561C2C3×#467211yescharacteristic
562C2C3×#476211yescharacteristic
563C2C3×#478711yescharacteristic
564C2C3×#479811yescharacteristic
565C2C3×#481811yescharacteristic
566C2C3×#486411yescharacteristic
567C2C3×#488611yescharacteristic
subgroupG/H
centerC23×C3D3×D4
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#340C2
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC3×#340D3
hypocenterC3C3×#2055
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C3×#340

Complements

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

NH ≅ G/Ntype
2. C2×C3×Dic3⋊C8C2semidirect
4. C3×#4973C2semidirect
5. C2×C3×#810C2semidirect
7. C32×#340C2semidirect
9. #68863C3direct (N × H)
34. C2×Dic3⋊C8C2×C3semidirect
36. #4973C2×C3semidirect
37. C2×#810C2×C3semidirect
40. C3×#340D3semidirect
41. C3×#340C2×C3semidirect
142. C2×C3×Dic3SD16semidirect
159. #340C3×D3semidirect
356. C2×Dic3C3×SD16semidirect
471. C32#2055semidirect
558. C3#68863direct (N × H)
559. C3C3×#2055semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2042
C2×C3×Dic3⋊C82
C3×#49882
C3×#49732
C2×C3×#8102
C2×C3×#8092
C32×#3402
C3×#20553
#688633