Finite Group Databasebeta

← C3×#70482 #11794052

Subgroups — C3×#70482 #11794052

Order 1152.

717 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#204C211yesmaximal, characteristic
2C2×C32×C4⋊C8C211yesmaximal, characteristic, complemented
3C2×C3×#821C211yesmaximal, characteristic
4C2×C3×#816C211yesmaximal, characteristic, complemented
5C3×#4939C211yesmaximal, characteristic
6C3×#4929C211yesmaximal, characteristic, complemented
7C3×#4551C211yesmaximal, characteristic, complemented
8C3×#2055—31nomaximal
9#70482C311yesmaximal, characteristic, direct product factor
10C22×C3×D12C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C22×C32×C8C2211yescharacteristic
14C2×C32×C42C2211yescharacteristic
15C2×C3×(C2×D3)⋊C4—21no—
16C2×C3×(C2×D3)⋊C4—21no—
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×#204—22no—
20C2×C3×#204—22no—
21C2×C3×#204—22no—
22C32×C4⋊C8—22no—
23C3×C3⋊#95—21no—
24C3×C3⋊#95—21no—
25C3×#821—22no—
26C3×#816—22no—
27C22×C3×SD16—31no—
28C22×#204C2×C311yescharacteristic
29C2×C3×C4⋊C8—21no—
30C2×C3×C4⋊C8D311yescharacteristic, complemented
31C2×C3×C4⋊C8C2×C311yescharacteristic, complemented
32C2×C3×#103—31no—
33C2×C3×#102—31no—
34C3×#391—31no—
35C3×#390—31no—
36C2×#821C2×C311yescharacteristic
37C2×#816C2×C311yescharacteristic, complemented
38#4939C2×C311yescharacteristic
39#4929C2×C311yescharacteristic, complemented
40C3×#340—31no—
41#4551C2×C311yescharacteristic, complemented
42C23×C3×D3—21no—
43C22×C32×C4D411yescharacteristic
44C22×C32×C4D411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C22×C3×Dic3—21no—
47C22×C3×Dic3—21no—
48C22×C3×Dic3—21no—
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×C8—21no—
64C2×C32×C8—21no—
65C2×C32×C8—21no—
66C2×C32×C8D412yes—
67C32×C42—21no—
68C32×C42—21no—
69C3×(C2×D3)⋊C4—42no—
70C3×(C2×D3)⋊C4—42no—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3—21no—
73C3×C4⋊Dic3—21no—
74C3×C4⋊Dic3—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—21no—
86C22×C3×C8C2×D311yescharacteristic
87C22×C3×C8C2×D311yescharacteristic
88C22×C3×C8C22×C311yescharacteristic
89C22×C3×C8C22×C311yescharacteristic
90C2×C3×C4⋊C4—31no—
91C2×C3×C4⋊C4—31no—
92C2×C3×C22⋊C4—61no—
93C2×C3×C22⋊C4—61no—
94C2×C3×C42—21no—
95C2×C3×C42C2×D311yescharacteristic
96C2×C3×C42C22×C311yescharacteristic
97C2×(C2×D3)⋊C4—21no—
98C2×(C2×D3)⋊C4—21no—
99C2×C4⋊Dic3C22×C311yescharacteristic
100C2×C4⋊Dic3C22×C311yescharacteristic
101C2×#204—22no—
102C2×#204—22no—
103C2×#204—22no—
104C3×C4⋊C8—24no—
105C3×C4⋊C8—22no—
106C3×C4⋊C8—22no—
107C3×#103—62no—
108C3×#102—62no—
109C3×#95—61no—
110C3×#95—61no—
111C3⋊#95—21no—
112C3⋊#95—21no—
113#821—22no—
114#816—22no—
115C23×C32C2×D411yescharacteristic
116C22×C3×D3—22no—
117C22×C3×D3—41no—
118C22×C3×D3—41no—
119C22×C3×D3—41no—
120C22×C3×D3—41no—
121C22×C3×D3—41no—
122C22×C3×D3—41no—
123C2×C32×C4—21no—
124C2×C32×C4—21no—
125C2×C32×C4—21no—
126C2×C32×C4—21no—
127C2×C32×C4—21no—
128C2×C32×C4SD1612yescomplemented
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4#4111yescharacteristic
133C2×C32×C4#4111yescharacteristic
134C2×C32×C4#4111yescharacteristic
135C2×C3×Dic3—22no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3—41no—
138C2×C3×Dic3—41no—
139C2×C3×Dic3—41no—
140C2×C3×Dic3—41no—
141C2×C3×Dic3—41no—
142C2×C3×Dic3—41no—
143C2×C3×Dic3—41no—
144C3×D12—22no—
145C3×D12—22no—
146C3×D12—41no—
147C3×D12—41no—
148C3×Dic6—22no—
149C3×Dic6—22no—
150C3×Dic6—41no—
151C3×Dic6—41no—
152C32×C8—22no—
153C32×C8—41no—
154C22×SD16—31no—
155C2×C4⋊C8C3×D311yescharacteristic, complemented
156C2×#103—31no—
157C2×#102—31no—
158#391—31no—
159#390—31no—
160#340—31no—
161C24×C3—61no—
162C23×D3—21no—
163C2×C3×Q8—32no—
164C2×C3×Q8—61no—
165C2×C3×Q8—61no—
166C2×C3×Q8—61no—
167C2×C3×Q8—61no—
168C2×C3×Q8—61no—
169C2×C3×D4—32no—
170C2×C3×D4—61no—
171C2×C3×D4—61no—
172C2×C3×D4—61no—
173C2×C3×D4—61no—
174C2×C3×D4—61no—
175C22×C3×C4—21no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—61no—
179C22×C3×C4—61no—
180C22×C3×C4—61no—
181C22×C3×C4D1211yescharacteristic
182C22×C3×C4D1211yescharacteristic
183C22×C3×C4C3×D411yescharacteristic
184C22×C3×C4C3×D411yescharacteristic
185C22×C3×C4C22×D311yescharacteristic
186C22×C3×C4C23×C311yescharacteristic
187C22×Dic3—21no—
188C22×Dic3—21no—
189C22×Dic3—21no—
190C2×D12—21no—
191C2×D12—21no—
192C2×D12—21no—
193C2×D12—21no—
194C2×D12—21no—
195C2×D12C3×D412yes—
196C2×Dic6—21no—
197C2×Dic6—21no—
198C2×Dic6—21no—
199C2×Dic6—21no—
200C2×Dic6—21no—
201C2×Dic6C3×D412yes—
202C3×SD16—68no—
203C2×C3×C8—21no—
204C2×C3×C8—21no—
205C2×C3×C8—21no—
206C2×C3×C8—21no—
207C2×C3×C8—22no—
208C2×C3×C8—21no—
209C2×C3×C8—21no—
210C2×C3×C8—21no—
211C2×C3×C8—21no—
212C2×C3×C8—21no—
213C2×C3×C8—21no—
214C2×C3×C8—22no—
215C2×C3×C8—41no—
216C2×C3×C8—41no—
217C2×C3×C8—41no—
218C2×C3×C8—41no—
219C2×C3×C8#6712yes—
220C2×C3×C8C3×D412yes—
221C3×C4⋊C4—61no—
222C3×C4⋊C4—61no—
223C3×C4⋊C4—61no—
224C3×C4⋊C4—61no—
225C3×C22⋊C4—122no—
226C3×C22⋊C4—122no—
227C3×C42—22no—
228C3×C42—22no—
229C3×C42—21no—
230C3×C42—21no—
231C3×C42—21no—
232C3×C42—21no—
233(C2×D3)⋊C4—42no—
234(C2×D3)⋊C4—42no—
235C4⋊Dic3—21no—
236C4⋊Dic3—21no—
237C4⋊Dic3—21no—
238C4⋊Dic3—21no—
239#204—28no—
240C22×C32#12111yescharacteristic
241C22×C32#12111yescharacteristic
242C22×C32#12111yescharacteristic
243C22×C32C2×SD1611yescharacteristic
244C22×C32#13511yescharacteristic
245C22×C32AGL(1,ℤ/8)11yescharacteristic
246C22×C32#13711yescharacteristic
247C2×C3×D3—42no—
248C2×C3×D3—42no—
249C2×C3×D3—42no—
250C2×C3×D3—81no—
251C2×C3×D3—81no—
252C2×C3×D3—81no—
253C2×C3×D3—81no—
254C32×C4—22no—
255C32×C4—41no—
256C32×C4#12011yescharacteristic
257C32×C4#12311yescharacteristic
258C32×C4#12311yescharacteristic
259C32×C4#12411yescharacteristic
260C3×Dic3—42no—
261C3×Dic3—81no—
262C3×Dic3—81no—
263C22×Q8—31no—
264C22×D4—31no—
265C2×SD16—62no—
266C2×SD16—62no—
267C2×SD16—62no—
268C22×C8C2×C3×D311yescharacteristic
269C22×C8C2×C3×D311yescharacteristic
270C2×C4⋊C4—31no—
271C2×C4⋊C4—31no—
272C2×C22⋊C4—61no—
273C2×C22⋊C4—61no—
274C2×C42C2×C3×D311yescharacteristic
275C4⋊C8—22no—
276#103—62no—
277#102—62no—
278#95—61no—
279#95—61no—
280C23×C3—21no—
281C23×C3—62no—
282C23×C3—121no—
283C23×C3—121no—
284C23×C3—121no—
285C23×C3—121no—
286C23×C3—121no—
287C23×C3—121no—
288C23×C3C2×D1211yescharacteristic
289C23×C3C2×C3×D411yescharacteristic
290C22×D3—22no—
291C22×D3—41no—
292C22×D3—41no—
293C22×D3—41no—
294C22×D3—41no—
295C22×D3—41no—
296C22×D3—41no—
297C3×Q8—62no—
298C3×Q8—62no—
299C3×Q8—121no—
300C3×Q8—121no—
301C3×D4—62no—
302C3×D4—62no—
303C3×D4—121no—
304C3×D4—121no—
305C2×C3×C4—22no—
306C2×C3×C4—22no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—22no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—22no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—41no—
326C2×C3×C4—41no—
327C2×C3×C4—62no—
328C2×C3×C4—121no—
329C2×C3×C4—121no—
330C2×C3×C4—121no—
331C2×C3×C4—121no—
332C2×C3×C4—121no—
333C2×C3×C4—121no—
334C2×C3×C4—121no—
335C2×C3×C4—121no—
336C2×C3×C4#20412yescomplemented
337C2×C3×C4C3×SD1612yescomplemented
338C2×C3×C4#23511yescharacteristic
339C2×C3×C4D3×D411yescharacteristic
340C2×C3×C4D3×D411yescharacteristic
341C2×C3×C4#23911yescharacteristic
342C2×C3×C4#23911yescharacteristic
343C2×C3×C4C2×#6711yescharacteristic
344C2×C3×C4C2×C3×D411yescharacteristic
345C2×C3×C4C2×C3×D411yescharacteristic
346C2×C3×C4C2×C3×D411yescharacteristic
347C2×C3×C4C3×#4111yescharacteristic
348C2×C3×C4C3×#4111yescharacteristic
349C2×C3×C4C3×#4111yescharacteristic
350C2×Dic3—22no—
351C2×Dic3—41no—
352C2×Dic3—41no—
353C2×Dic3—41no—
354C2×Dic3—41no—
355C2×Dic3—41no—
356C2×Dic3—41no—
357C2×Dic3—41no—
358C2×Dic3—41no—
359D12—22no—
360D12—22no—
361D12—41no—
362D12—41no—
363Dic6—22no—
364Dic6—22no—
365Dic6—41no—
366Dic6—41no—
367C3×C8—22no—
368C3×C8—22no—
369C3×C8—42no—
370C3×C8—42no—
371C3×C8—41no—
372C3×C8—41no—
373C2×C32#39411yescharacteristic
374C2×C32#46011yescharacteristic
375C2×C32#46111yescharacteristic
376C2×C32#46311yescharacteristic
377C2×C32#46411yescharacteristic
378C2×C32#46511yescharacteristic
379C2×C32#46811yescharacteristic
380C3×D3—82no—
381C24—61no—
382C2×Q8—32no—
383C2×Q8—61no—
384C2×Q8—61no—
385C2×Q8—61no—
386C2×Q8—61no—
387C2×Q8—61no—
388C2×D4—32no—
389C2×D4—61no—
390C2×D4—61no—
391C2×D4—61no—
392C2×D4—61no—
393C2×D4—61no—
394C22×C4—61no—
395C22×C4—61no—
396C22×C4—61no—
397C22×C4C3×D1211yescharacteristic
398C22×C4C3×D1211yescharacteristic
399C22×C4C22×C3×D311yescharacteristic
400SD16—68no—
401C2×C8—21no—
402C2×C8—21no—
403C2×C8—21no—
404C2×C8—21no—
405C2×C8—21no—
406C2×C8C3×#6712yes—
407C4⋊C4—61no—
408C4⋊C4—61no—
409C4⋊C4—61no—
410C4⋊C4—61no—
411C22⋊C4—122no—
412C22⋊C4—122no—
413C42—21no—
414C42—21no—
415C22×C3—21no—
416C22×C3—21no—
417C22×C3—21no—
418C22×C3—21no—
419C22×C3—21no—
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—122no—
423C22×C3—122no—
424C22×C3—122no—
425C22×C3—241no—
426C22×C3—241no—
427C22×C3—241no—
428C22×C3—241no—
429C22×C3#89511yescharacteristic
430C22×C3#89511yescharacteristic
431C22×C3C2×#20411yescharacteristic
432C22×C3#90411yescharacteristic
433C22×C3#90811yescharacteristic
434C22×C3#90911yescharacteristic
435C22×C3#93011yescharacteristic
436C22×C3C3×#12111yescharacteristic
437C22×C3C3×#12111yescharacteristic
438C22×C3C3×#12111yescharacteristic
439C22×C3C2×C3×SD1611yescharacteristic
440C22×C3C3×#13511yescharacteristic
441C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
442C22×C3C3×#13711yescharacteristic
443C2×D3—42no—
444C2×D3—42no—
445C2×D3—42no—
446C2×D3—81no—
447C2×D3—81no—
448C2×D3—81no—
449C2×D3—81no—
450C3×C4—24no—
451C3×C4—22no—
452C3×C4—22no—
453C3×C4—21no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—42no—
458C3×C4—41no—
459C3×C4—41no—
460C3×C4—122no—
461C3×C4—241no—
462C3×C4—241no—
463C3×C4#89411yescharacteristic
464C3×C4#89411yescharacteristic
465C3×C4#93711yescharacteristic
466C3×C4#94711yescharacteristic
467C3×C4C3×#12011yescharacteristic
468C3×C4C3×#12311yescharacteristic
469C3×C4C3×#12311yescharacteristic
470C3×C4C3×#12411yescharacteristic
471Dic3—42no—
472Dic3—81no—
473Dic3—81no—
474C32#205511yescharacteristic, complemented, Sylow
475C23—62no—
476C23—121no—
477C23—121no—
478C23—121no—
479C23—121no—
480C23—121no—
481C23—121no—
482C23C2×C3×D1211yescharacteristic
483Q8—62no—
484Q8—62no—
485Q8—121no—
486Q8—121no—
487D4—62no—
488D4—62no—
489D4—121no—
490D4—121no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—62no—
497C2×C4—121no—
498C2×C4—121no—
499C2×C4—121no—
500C2×C4—121no—
501C2×C4—121no—
502C2×C4—121no—
503C2×C4—121no—
504C2×C4—121no—
505C2×C4C3×#20412yescomplemented
506C2×C4C3×#23511yescharacteristic
507C2×C4C3×D3×D411yescharacteristic
508C2×C4C3×D3×D411yescharacteristic
509C2×C4C3×#23911yescharacteristic
510C2×C4C3×#23911yescharacteristic
511C2×C4C2×C3×#6711yescharacteristic
512C8—22no—
513C8—41no—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—21no—
521C2×C3—242no—
522C2×C3#484111yescharacteristic
523C2×C3#484411yescharacteristic
524C2×C3#484511yescharacteristic
525C2×C3#484811yescharacteristic
526C2×C3#499111yescharacteristic
527C2×C3#511411yescharacteristic
528C2×C3#513411yescharacteristic
529C2×C3C3×#39411yescharacteristic
530C2×C3C3×#46011yescharacteristic
531C2×C3C3×#46111yescharacteristic
532C2×C3C3×#46311yescharacteristic
533C2×C3C3×#46411yescharacteristic
534C2×C3C3×#46511yescharacteristic
535C2×C3C3×#46811yescharacteristic
536D3—82no—
537C22—122no—
538C22—122no—
539C22—122no—
540C22—241no—
541C22—241no—
542C22—241no—
543C22—241no—
544C22C3×#89511yescharacteristic
545C22C3×#89511yescharacteristic
546C22C2×C3×#20411yescharacteristic
547C22C3×#90411yescharacteristic
548C22C3×#90811yescharacteristic
549C22C3×#90911yescharacteristic
550C22C3×#93011yescharacteristic
551C4—22no—
552C4—41no—
553C4—122no—
554C4—241no—
555C4—241no—
556C4C3×#89411yescharacteristic
557C4C3×#89411yescharacteristic
558C4C3×#93711yescharacteristic
559C4C3×#94711yescharacteristic
560C3—21no—
561C3#7048211yescharacteristic, direct product factor
562C3C3×#205511yescharacteristic, complemented
563C2—242no—
564C2C3×#484111yescharacteristic
565C2C3×#484411yescharacteristic
566C2C3×#484511yescharacteristic
567C2C3×#484811yescharacteristic
568C2C3×#499111yescharacteristic
569C2C3×#511411yescharacteristic
570C2C3×#513411yescharacteristic
subgroupG/H
centerC23×C3C2×D12
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC2×C32×C4⋊C8C2
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC2×C3×C4⋊C8D3
hypocenterC3C3×#2055
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C42 ◁ C2×C3×C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×C32×C4⋊C8C2semidirect
4. C2×C3×#816C2semidirect
6. C3×#4929C2semidirect
7. C3×#4551C2semidirect
9. #70482C3direct (N × H)
30. C2×C3×C4⋊C8D3semidirect
31. C2×C3×C4⋊C8C2×C3semidirect
37. C2×#816C2×C3semidirect
39. #4929C2×C3semidirect
41. #4551C2×C3semidirect
128. C2×C32×C4SD16semidirect
155. C2×C4⋊C8C3×D3semidirect
336. C2×C3×C4#204semidirect
337. C2×C3×C4C3×SD16semidirect
474. C32#2055semidirect
505. C2×C4C3×#204semidirect
561. C3#70482direct (N × H)
562. 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×C32×C4⋊C82
C2×C3×#8212
C2×C3×#8162
C3×#49392
C3×#49292
C3×#45512
C3×#20553
#704823