Finite Group Databasebeta

← C3×#70210 #11792550

Subgroups — C3×#70210 #11792550

Order 1152.

1049 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#940C211yesmaximal, characteristic
2C22×C3×#214C211yesmaximal, characteristic, complemented
3C22×C3×#204C211yesmaximal, characteristic, complemented
4C2×C32×#102C211yesmaximal, characteristic, complemented
5C3×#4973C211yesmaximal, characteristic, complemented
6C2×C3×#809C211yesmaximal, characteristic, complemented
7C3×#4550C211yesmaximal, characteristic, complemented
8C3×#2014—31nomaximal
9#70210C311yesmaximal, characteristic, direct product factor
10C22×C32×D4C2211yescharacteristic
11C22×C3×#67—22no—
12C22×C3×D12C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C22×C32×C8C2211yescharacteristic
15C2×C32×C4⋊C4C2211yescharacteristic
16C3×#940—22no—
17C3×#940—22no—
18C2×C3×#214—22no—
19C2×C3×#214—22no—
20C2×C3×#214—22no—
21C2×C3×C4×Dic3C2211yescharacteristic
22C22×C3×C3⋊C8C2211yescharacteristic
23C2×C3×#204—22no—
24C2×C3×#204—22no—
25C2×C3×#204—22no—
26C32×#102—22no—
27C3×C3⋊#95—22no—
28C3×#809—22no—
29C22×C3×SD16—31no—
30C22×C3×SD16—31no—
31C2×C3×#127—31no—
32C2×#940C2×C311yescharacteristic
33C22×#214C2×C311yescharacteristic, complemented
34C22×#204C2×C311yescharacteristic, complemented
35C2×C3×#102—21no—
36C2×C3×#102—31no—
37C2×C3×#102D311yescharacteristic, complemented
38C2×C3×#102C2×C311yescharacteristic, complemented
39C3×#391—31no—
40#4973C2×C311yescharacteristic, complemented
41C2×#809C2×C311yescharacteristic, complemented
42C3×#336—31no—
43#4550C2×C311yescharacteristic, complemented
44C24×C32—21no—
45C23×C3×D3—21no—
46C2×C32×D4—21no—
47C2×C32×D4—21no—
48C2×C32×D4—21no—
49C2×C32×D4—21no—
50C2×C32×D4—21no—
51C2×C32×D4D412yes—
52C22×C32×C4—21no—
53C22×C32×C4C2311yescharacteristic
54C2×C3×#67—28no—
55C2×C3×#67—44no—
56C2×C3×#67—44no—
57C22×C3×Dic3—21no—
58C22×C3×Dic3D412yes—
59C2×C3×D12—21no—
60C2×C3×D12—21no—
61C2×C3×D12—21no—
62C2×C3×D12—21no—
63C2×C3×D12—21no—
64C2×C3×D12D412yes—
65C2×C3×Dic6—21no—
66C2×C3×Dic6—21no—
67C2×C3×Dic6—21no—
68C2×C3×Dic6—21no—
69C2×C3×Dic6—21no—
70C2×C3×Dic6D412yescomplemented
71C2×C32×C8—21no—
72C2×C32×C8—21no—
73C2×C32×C8D412yescomplemented
74C32×C4⋊C4—21no—
75C32×C4⋊C4—21no—
76C3×#214—28no—
77C3×C4×Dic3—21no—
78C3×C4×Dic3—21no—
79C2×C3×C3⋊C8—21no—
80C2×C3×C3⋊C8—21no—
81C2×C3×C3⋊C8D412yescomplemented
82C3×#204—28no—
83#2014—31noSylow
84C22×C3×Q8—31no—
85C22×C3×D4—21no—
86C22×C3×D4—31no—
87C22×C3×D4—62no—
88C22×C3×D4C2×D311yescharacteristic
89C22×C3×D4C22×C311yescharacteristic
90C22×#67—22no—
91C22×D12C22×C311yescharacteristic
92C22×Dic6C22×C311yescharacteristic
93C2×C3×SD16—62no—
94C2×C3×SD16—62no—
95C2×C3×SD16—62no—
96C2×C3×SD16—62no—
97C2×C3×SD16—62no—
98C2×C3×SD16—62no—
99C22×C3×C8—21no—
100C22×C3×C8—31no—
101C22×C3×C8C2×D311yescharacteristic
102C22×C3×C8C22×C311yescharacteristic
103C3×#127—62no—
104C3×#127—62no—
105C2×C3×C4⋊C4—21no—
106C2×C3×C4⋊C4C2×D311yescharacteristic
107C2×C3×C4⋊C4C22×C311yescharacteristic
108C2×C3×C42—31no—
109#940—22no—
110#940—22no—
111C2×#214—22no—
112C2×#214—22no—
113C2×#214—22no—
114C2×C4×Dic3C22×C311yescharacteristic
115C22×C3⋊C8C22×C311yescharacteristic
116C2×#204—22no—
117C2×#204—22no—
118C2×#204—22no—
119C3×#102—24no—
120C3×#102—22no—
121C3×#102—22no—
122C3×#102—62no—
123C3×#95—62no—
124C3⋊#95—22no—
125#809—22no—
126C23×C32—22no—
127C23×C32—41no—
128C23×C32—41no—
129C23×C32—42no—
130C23×C32—42no—
131C23×C32C2×D411yescharacteristic
132C22×C3×D3—22no—
133C22×C3×D3—41no—
134C22×C3×D3—41no—
135C22×C3×D3—42no—
136C22×C3×D3—42no—
137C32×D4—22no—
138C32×D4—22no—
139C32×D4—41no—
140C32×D4—41no—
141C2×C32×C4—41no—
142C2×C32×C4—42no—
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4#4111yescharacteristic
149C3×#67—416no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—41no—
154C2×C3×Dic3—41no—
155C2×C3×Dic3SD1614yescomplemented
156C3×D12—22no—
157C3×D12—22no—
158C3×D12—41no—
159C3×D12—41no—
160C3×Dic6—22no—
161C3×Dic6—22no—
162C3×Dic6—41no—
163C3×Dic6—41no—
164C32×C8—22no—
165C3×C3⋊C8—22no—
166C22×SD16—31no—
167C22×SD16—31no—
168C2×#127—31no—
169C2×#102—31no—
170C2×#102C3×D311yescharacteristic, complemented
171#391—31no—
172#336—31no—
173C24×C3—21no—
174C24×C3—21no—
175C24×C3—41no—
176C24×C3—61no—
177C23×D3—21no—
178C2×C3×Q8—32no—
179C2×C3×Q8—61no—
180C2×C3×Q8—61no—
181C2×C3×Q8—61no—
182C2×C3×Q8—61no—
183C2×C3×Q8—61no—
184C2×C3×D4—22no—
185C2×C3×D4—22no—
186C2×C3×D4—21no—
187C2×C3×D4—21no—
188C2×C3×D4—21no—
189C2×C3×D4—21no—
190C2×C3×D4—21no—
191C2×C3×D4—21no—
192C2×C3×D4—21no—
193C2×C3×D4—21no—
194C2×C3×D4—21no—
195C2×C3×D4—21no—
196C2×C3×D4—22no—
197C2×C3×D4—32no—
198C2×C3×D4—41no—
199C2×C3×D4—41no—
200C2×C3×D4—41no—
201C2×C3×D4—68no—
202C2×C3×D4—61no—
203C2×C3×D4—61no—
204C2×C3×D4—61no—
205C2×C3×D4—61no—
206C2×C3×D4—61no—
207C2×C3×D4—124no—
208C2×C3×D4—124no—
209C2×C3×D4D1212yes—
210C2×C3×D4C3×D412yes—
211C22×C3×C4—21no—
212C22×C3×C4—21no—
213C22×C3×C4—21no—
214C22×C3×C4—32no—
215C22×C3×C4—41no—
216C22×C3×C4—61no—
217C22×C3×C4C22×D311yescharacteristic
218C22×C3×C4C23×C311yescharacteristic
219C2×#67—28no—
220C2×#67—44no—
221C2×#67—44no—
222C22×Dic3—21no—
223C22×Dic3C3×D412yes—
224C2×D12—21no—
225C2×D12—21no—
226C2×D12—21no—
227C2×D12—21no—
228C2×D12—21no—
229C2×D12C3×D412yes—
230C2×Dic6—21no—
231C2×Dic6—21no—
232C2×Dic6—21no—
233C2×Dic6—21no—
234C2×Dic6—21no—
235C2×Dic6C3×D412yescomplemented
236C3×SD16—68no—
237C3×SD16—68no—
238C2×C3×C8—21no—
239C2×C3×C8—21no—
240C2×C3×C8—21no—
241C2×C3×C8—21no—
242C2×C3×C8—22no—
243C2×C3×C8—32no—
244C2×C3×C8—41no—
245C2×C3×C8—41no—
246C2×C3×C8—61no—
247C2×C3×C8—61no—
248C2×C3×C8#6712yescomplemented
249C2×C3×C8C3×D412yescomplemented
250C3×C4⋊C4—22no—
251C3×C4⋊C4—21no—
252C3×C4⋊C4—21no—
253C3×C4⋊C4—21no—
254C3×C4⋊C4—21no—
255C3×C4⋊C4—41no—
256C3×C42—61no—
257C3×C42—61no—
258#214—28no—
259C4×Dic3—21no—
260C4×Dic3—21no—
261C2×C3⋊C8—21no—
262C2×C3⋊C8—21no—
263C2×C3⋊C8C3×D412yescomplemented
264#204—28no—
265C22×C32—42no—
266C22×C32—44no—
267C22×C32—82no—
268C22×C32—81no—
269C22×C32—81no—
270C22×C32#12011yescharacteristic
271C22×C32#12111yescharacteristic
272C22×C32#12711yescharacteristic
273C22×C32C2×SD1612yes—
274C22×C32AGL(1,ℤ/8)12yes—
275C2×C3×D3—42no—
276C2×C3×D3—44no—
277C2×C3×D3—82no—
278C2×C3×D3—81no—
279C2×C3×D3—81no—
280C32×C4—81no—
281C32×C4#12011yescharacteristic
282C32×C4#12011yescharacteristic
283C32×C4#12111yescharacteristic
284C32×C4#12111yescharacteristic
285C3×Dic3—24no—
286C3×Dic3—42no—
287C22×Q8—31no—
288C22×D4—31no—
289C22×D4—62no—
290C22×D4C2×C3×D311yescharacteristic
291C2×SD16—62no—
292C2×SD16—62no—
293C2×SD16—62no—
294C2×SD16—62no—
295C2×SD16—62no—
296C2×SD16—62no—
297C22×C8—31no—
298C22×C8C2×C3×D311yescharacteristic
299#127—62no—
300#127—62no—
301C2×C4⋊C4C2×C3×D311yescharacteristic
302C2×C42—31no—
303#102—22no—
304#102—62no—
305#95—62no—
306C23×C3—22no—
307C23×C3—22no—
308C23×C3—21no—
309C23×C3—42no—
310C23×C3—42no—
311C23×C3—42no—
312C23×C3—41no—
313C23×C3—42no—
314C23×C3—42no—
315C23×C3—41no—
316C23×C3—41no—
317C23×C3—41no—
318C23×C3—42no—
319C23×C3—42no—
320C23×C3—62no—
321C23×C3—82no—
322C23×C3—82no—
323C23×C3—121no—
324C23×C3—122no—
325C23×C3—122no—
326C23×C3—121no—
327C23×C3D3×D411yescharacteristic
328C23×C3C2×C3×D411yescharacteristic
329C22×D3—22no—
330C22×D3—41no—
331C22×D3—41no—
332C22×D3—42no—
333C22×D3—42no—
334C3×Q8—62no—
335C3×Q8—62no—
336C3×Q8—121no—
337C3×Q8—121no—
338C3×D4—24no—
339C3×D4—22no—
340C3×D4—22no—
341C3×D4—22no—
342C3×D4—22no—
343C3×D4—42no—
344C3×D4—42no—
345C3×D4—42no—
346C3×D4—41no—
347C3×D4—41no—
348C3×D4—41no—
349C3×D4—41no—
350C3×D4—62no—
351C3×D4—62no—
352C3×D4—1216no—
353C3×D4—121no—
354C3×D4—121no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—34no—
362C2×C3×C4—42no—
363C2×C3×C4—42no—
364C2×C3×C4—41no—
365C2×C3×C4—41no—
366C2×C3×C4—42no—
367C2×C3×C4—62no—
368C2×C3×C4—62no—
369C2×C3×C4—62no—
370C2×C3×C4—82no—
371C2×C3×C4—121no—
372C2×C3×C4—121no—
373C2×C3×C4C2×D1211yescharacteristic
374C2×C3×C4#23511yescharacteristic
375C2×C3×C4D3×D411yescharacteristic
376C2×C3×C4D3×D411yescharacteristic
377C2×C3×C4D3×D411yescharacteristic
378C2×C3×C4C2×#6711yescharacteristic
379C2×C3×C4C2×C3×D411yescharacteristic
380C2×C3×C4C2×C3×D411yescharacteristic
381C2×C3×C4C2×C3×D411yescharacteristic
382C2×C3×C4C2×C3×D411yescharacteristic
383C2×C3×C4C2×C3×D411yescharacteristic
384C2×C3×C4C3×#4111yescharacteristic
385#67—416no—
386C2×Dic3—22no—
387C2×Dic3—22no—
388C2×Dic3—22no—
389C2×Dic3—41no—
390C2×Dic3—41no—
391C2×Dic3C3×SD1614yescomplemented
392D12—22no—
393D12—22no—
394D12—41no—
395D12—41no—
396Dic6—22no—
397Dic6—22no—
398Dic6—41no—
399Dic6—41no—
400C3×C8—22no—
401C3×C8—22no—
402C3×C8—42no—
403C3×C8—62no—
404C3⋊C8—22no—
405C2×C32—82no—
406C2×C32#39211yescharacteristic
407C2×C32#45012yes—
408C2×C32#46012yes—
409C2×C32#49211yescharacteristic
410C2×C32#49611yescharacteristic
411C3×D3—82no—
412C24—21no—
413C24—61no—
414C2×Q8—32no—
415C2×Q8—61no—
416C2×Q8—61no—
417C2×Q8—61no—
418C2×Q8—61no—
419C2×Q8—61no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—32no—
426C2×D4—68no—
427C2×D4—61no—
428C2×D4—61no—
429C2×D4—61no—
430C2×D4—61no—
431C2×D4—61no—
432C2×D4—124no—
433C2×D4—124no—
434C2×D4C3×D1212yes—
435C22×C4—21no—
436C22×C4—32no—
437C22×C4—61no—
438C22×C4C22×C3×D311yescharacteristic
439SD16—68no—
440SD16—68no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—32no—
444C2×C8—61no—
445C2×C8—61no—
446C2×C8C3×#6712yescomplemented
447C4⋊C4—21no—
448C4⋊C4—21no—
449C42—61no—
450C42—61no—
451C22×C3—21no—
452C22×C3—21no—
453C22×C3—22no—
454C22×C3—22no—
455C22×C3—21no—
456C22×C3—44no—
457C22×C3—42no—
458C22×C3—42no—
459C22×C3—44no—
460C22×C3—44no—
461C22×C3—84no—
462C22×C3—82no—
463C22×C3—84no—
464C22×C3—82no—
465C22×C3—81no—
466C22×C3—81no—
467C22×C3—82no—
468C22×C3—82no—
469C22×C3—81no—
470C22×C3—81no—
471C22×C3—122no—
472C22×C3—124no—
473C22×C3—241no—
474C22×C3—241no—
475C22×C3—242no—
476C22×C3#88211yescharacteristic
477C22×C3#88411yescharacteristic
478C22×C3#91112yes—
479C22×C3D3×SD1612yes—
480C22×C3#94011yescharacteristic
481C22×C3C3×#12011yescharacteristic
482C22×C3C3×#12111yescharacteristic
483C22×C3C3×#12711yescharacteristic
484C22×C3C2×C3×SD1612yes—
485C22×C3C3×AGL(1,ℤ/8)12yes—
486C2×D3—42no—
487C2×D3—44no—
488C2×D3—82no—
489C2×D3—81no—
490C2×D3—81no—
491C3×C4—21no—
492C3×C4—21no—
493C3×C4—21no—
494C3×C4—21no—
495C3×C4—64no—
496C3×C4—82no—
497C3×C4—81no—
498C3×C4—81no—
499C3×C4—122no—
500C3×C4#88211yescharacteristic
501C3×C4#88411yescharacteristic
502C3×C4#93011yescharacteristic
503C3×C4#93711yescharacteristic
504C3×C4C3×#12011yescharacteristic
505C3×C4C3×#12011yescharacteristic
506C3×C4C3×#12111yescharacteristic
507C3×C4C3×#12111yescharacteristic
508Dic3—24no—
509Dic3—42no—
510C32#201411yescharacteristic, complemented, Sylow
511C23—22no—
512C23—41no—
513C23—42no—
514C23—42no—
515C23—41no—
516C23—62no—
517C23—121no—
518C23—122no—
519C23—122no—
520C23—121no—
521C23C3×D3×D411yescharacteristic
522Q8—62no—
523Q8—62no—
524Q8—121no—
525Q8—121no—
526D4—22no—
527D4—22no—
528D4—41no—
529D4—41no—
530D4—62no—
531D4—62no—
532D4—1216no—
533D4—121no—
534D4—121no—
535C2×C4—34no—
536C2×C4—42no—
537C2×C4—41no—
538C2×C4—62no—
539C2×C4—62no—
540C2×C4—62no—
541C2×C4—121no—
542C2×C4—121no—
543C2×C4C2×C3×D1211yescharacteristic
544C2×C4C3×#23511yescharacteristic
545C2×C4C3×D3×D411yescharacteristic
546C2×C4C3×D3×D411yescharacteristic
547C2×C4C3×D3×D411yescharacteristic
548C2×C4C2×C3×#6711yescharacteristic
549C8—22no—
550C8—62no—
551C2×C3—21no—
552C2×C3—21no—
553C2×C3—22no—
554C2×C3—22no—
555C2×C3—21no—
556C2×C3—84no—
557C2×C3—82no—
558C2×C3—82no—
559C2×C3—242no—
560C2×C3#476212yes—
561C2×C3#477612yes—
562C2×C3#496011yescharacteristic
563C2×C3#515411yescharacteristic
564C2×C3#517511yescharacteristic
565C2×C3C3×#39211yescharacteristic
566C2×C3C3×#45012yes—
567C2×C3C3×#46012yes—
568C2×C3C3×#49211yescharacteristic
569C2×C3C3×#49611yescharacteristic
570D3—82no—
571C22—42no—
572C22—44no—
573C22—81no—
574C22—82no—
575C22—81no—
576C22—122no—
577C22—124no—
578C22—241no—
579C22—242no—
580C22—241no—
581C22C3×#88211yescharacteristic
582C22C3×#88411yescharacteristic
583C22C3×#91112yes—
584C22C3×D3×SD1612yes—
585C22C3×#94011yescharacteristic
586C4—64no—
587C4—81no—
588C4—122no—
589C4C3×#88211yescharacteristic
590C4C3×#88411yescharacteristic
591C4C3×#93011yescharacteristic
592C4C3×#93711yescharacteristic
593C3—21no—
594C3#7021011yescharacteristic, direct product factor
595C3C3×#201411yescharacteristic, complemented
596C2—82no—
597C2—242no—
598C2C3×#476212yes—
599C2C3×#477612yes—
600C2C3×#496011yescharacteristic
601C2C3×#515411yescharacteristic
602C2C3×#517511yescharacteristic
subgroupG/H
centerC23×C3D3×D4
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#102C2
socleC23×C32C2×D4
prime radicalC2×C3×#940C2
hypercenterC2×C3×#102D3
hypocenterC3C3×#2014
LCSG ▷ C22×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
2. C22×C3×#214C2semidirect
3. C22×C3×#204C2semidirect
4. C2×C32×#102C2semidirect
5. C3×#4973C2semidirect
6. C2×C3×#809C2semidirect
7. C3×#4550C2semidirect
9. #70210C3direct (N × H)
33. C22×#214C2×C3semidirect
34. C22×#204C2×C3semidirect
37. C2×C3×#102D3semidirect
38. C2×C3×#102C2×C3semidirect
40. #4973C2×C3semidirect
41. C2×#809C2×C3semidirect
43. #4550C2×C3semidirect
70. C2×C3×Dic6D4semidirect
73. C2×C32×C8D4semidirect
81. C2×C3×C3⋊C8D4semidirect
155. C2×C3×Dic3SD16semidirect
170. C2×#102C3×D3semidirect
235. C2×Dic6C3×D4semidirect
248. C2×C3×C8#67semidirect
249. C2×C3×C8C3×D4semidirect
263. C2×C3⋊C8C3×D4semidirect
391. C2×Dic3C3×SD16semidirect
446. C2×C8C3×#67semidirect
510. C32#2014semidirect
594. C3#70210direct (N × H)
595. C3C3×#2014semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9402
C22×C3×#2142
C22×C3×#2042
C2×C32×#1022
C3×#49732
C2×C3×#8092
C3×#45502
C3×#20143
#702103