Finite Group Databasebeta

← C3×#79055 #11865851

Subgroups — C3×#79055 #11865851

Order 1152.

1159 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#908C212yesmaximal, complemented
2C3×#5477C211yesmaximal, characteristic, complemented
3C2×C3×C4×D12C211yesmaximal, characteristic, complemented
4C32×#423C211yesmaximal, characteristic, complemented
5C3×#5133C212yesmaximal, complemented
6C3×#4844C214yesmaximal, complemented
7C3×#4843C212yesmaximal, complemented
8C3×#4841C212yesmaximal, complemented
9C3×#3036—31nomaximal
10#79055C311yesmaximal, characteristic, direct product factor
11C2×C3×#235C2212yes—
12C22×C3×D12C2211yescharacteristic
13C22×C3×C4×D3—21no—
14C2×C32×M16C2212yes—
15C2×C32×C42C2211yescharacteristic
16C3×#930—21no—
17C3×#930—21no—
18C2×C3×(C2×D3)⋊C4—21no—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C3×#908—28no—
21C2×C3×D24C2214yes—
22C2×C3×#204C2214yes—
23C3×#875C2212yescomplemented
24C3×#874C2211yescharacteristic, complemented
25C3×C4×D12—21no—
26C3×C4×D12—21no—
27C3×C4×D12—21no—
28C3×C4×D12—21no—
29C3×C4×D12C2212yes—
30C3×C4×D12C2212yes—
31C3×#869C2211yescharacteristic, complemented
32C32×C4⋊C8C2212yescomplemented
33C32×C4⋊C8C2212yescomplemented
34C3×#821C2214yescomplemented
35C3×#816C2214yescomplemented
36C2×C3×AGL(1,ℤ/8)—32no—
37C3×#532—31no—
38C2×C3×C4×D4—31no—
39C2×#908C2×C312yescomplemented
40#5477C2×C311yescharacteristic, complemented
41C2×C4×D12C2×C311yescharacteristic, complemented
42C3×#463—34no—
43C3×#461—32no—
44C3×#459—32no—
45C3×#423—21no—
46C3×#423D311yescharacteristic, complemented
47C3×#423C2×C311yescharacteristic, complemented
48C3×#417—32no—
49#5133C2×C312yescomplemented
50#4844C2×C314yescomplemented
51#4843C2×C312yescomplemented
52#4841C2×C312yescomplemented
53C23×C3×D3—21no—
54C22×C32×C4D411yescharacteristic
55C22×C32×C4D411yescharacteristic
56C22×C32×C4C2311yescharacteristic
57C2×C3×#67—22no—
58C22×C3×Dic3—21no—
59C3×#235—24no—
60C3×#235—24no—
61C2×C3×D12—21no—
62C2×C3×D12—22no—
63C2×C3×D12—21no—
64C2×C3×D12—21no—
65C2×C3×D12D414yescomplemented
66C2×C3×D12C2312yes—
67C2×C3×D12C2312yes—
68C2×C3×C4×D3—22no—
69C2×C3×C4×D3—22no—
70C2×C3×C4×D3—22no—
71C2×C3×C4×D3—44no—
72C2×C3×Dic6C2312yes—
73C32×M16—24no—
74C2×C32×C8C2314yes—
75C32×C42D411yescharacteristic
76C32×C42D411yescharacteristic
77C32×C42C2311yescharacteristic
78C32×C42C2311yescharacteristic
79C3×(C2×D3)⋊C4—22no—
80C3×(C2×D3)⋊C4—22no—
81C3×(C2×D3)⋊C4—22no—
82C3×(C2×D3)⋊C4—22no—
83C3×C4⋊Dic3—21no—
84C3×C4⋊Dic3—21no—
85C3×C4⋊Dic3—21no—
86C3×C4⋊Dic3C2312yes—
87C3×D24—28no—
88C3×#204—28no—
89#3036—31noSylow
90C2×C3×#41—32no—
91C22×C3×D4—31no—
92C23×C3×C4—61no—
93C2×#235C22×C312yes—
94C22×D12C22×C311yescharacteristic
95C22×C4×D3—21no—
96C3×AGL(1,ℤ/8)—68no—
97C2×C3×SD16—34no—
98C2×C3×D8—34no—
99C2×C3×M16—22no—
100C2×C3×M16C2×D312yes—
101C2×C3×M16C22×C312yes—
102C3×C4⋊Q8—31no—
103C3×#127—31no—
104C3×#124—32no—
105C3×#121—61no—
106C3×#121—61no—
107C3×C4×D4—32no—
108C3×C4×D4—32no—
109C3×C4×D4—61no—
110C3×C4×D4—61no—
111C3×C4×D4—61no—
112C3×C4×D4—61no—
113C2×C3×C4⋊C4—31no—
114C2×C3×C22⋊C4—61no—
115C2×C3×C42—21no—
116C2×C3×C42C2×D311yescharacteristic
117C2×C3×C42C22×C311yescharacteristic
118#930—21no—
119#930—21no—
120C2×(C2×D3)⋊C4—21no—
121C2×C4⋊Dic3C22×C311yescharacteristic
122#908—28no—
123C2×D24C22×C314yes—
124C2×#204C22×C314yes—
125#875C22×C312yescomplemented
126#874C22×C311yescharacteristic, complemented
127C4×D12—21no—
128C4×D12—21no—
129C4×D12—21no—
130C4×D12—21no—
131C4×D12C22×C312yes—
132C4×D12C22×C312yes—
133#869C22×C311yescharacteristic, complemented
134C3×C4⋊C8—22no—
135C3×C4⋊C8—22no—
136C3×C4⋊C8C2×D312yescomplemented
137C3×C4⋊C8C2×D312yescomplemented
138C3×C4⋊C8C22×C312yescomplemented
139C3×C4⋊C8C22×C312yescomplemented
140C3×#103—34no—
141C3×#102—34no—
142#821C22×C314yescomplemented
143#816C22×C314yescomplemented
144C23×C32C2×D411yescharacteristic
145C22×C3×D3—24no—
146C22×C3×D3—22no—
147C22×C3×D3—22no—
148C22×C3×D3—42no—
149C22×C3×D3—42no—
150C2×C32×C4—22no—
151C2×C32×C4—41no—
152C2×C32×C4C2×D411yescharacteristic
153C2×C32×C4C2×D411yescharacteristic
154C2×C32×C4C2×D411yescharacteristic
155C2×C32×C4C2×D411yescharacteristic
156C2×C32×C4C2×D411yescharacteristic
157C2×C32×C4C2×D412yes—
158C2×C32×C4#4112yes—
159C2×C32×C4C2411yescharacteristic
160C3×#67—44no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—22no—
163C2×C3×Dic3—42no—
164C3×D12—24no—
165C3×D12—22no—
166C3×D12—22no—
167C3×D12—22no—
168C3×D12—42no—
169C3×D12—42no—
170C3×D12C2×D414yes—
171C3×C4×D3—44no—
172C3×C4×D3—44no—
173C3×C4×D3—44no—
174C3×Dic6—22no—
175C3×Dic6—22no—
176C32×C8—24no—
177C2×AGL(1,ℤ/8)—32no—
178#532—31no—
179C2×C4×D4—31no—
180#463—34no—
181#461—32no—
182#459—32no—
183#423C3×D311yescharacteristic, complemented
184#417—32no—
185C24×C3—61no—
186C23×D3—21no—
187C3×#41—64no—
188C3×#41—64no—
189C2×C3×Q8—32no—
190C2×C3×D4—34no—
191C2×C3×D4—32no—
192C2×C3×D4—32no—
193C2×C3×D4—62no—
194C2×C3×D4—61no—
195C2×C3×D4—61no—
196C2×C3×D4—61no—
197C2×C3×D4—62no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—61no—
202C22×C3×C4—62no—
203C22×C3×C4—62no—
204C22×C3×C4—62no—
205C22×C3×C4—124no—
206C22×C3×C4D1211yescharacteristic
207C22×C3×C4D1211yescharacteristic
208C22×C3×C4C3×D411yescharacteristic
209C22×C3×C4C3×D411yescharacteristic
210C22×C3×C4C22×D311yescharacteristic
211C22×C3×C4C23×C311yescharacteristic
212C2×#67—22no—
213C22×Dic3—21no—
214#235—24no—
215#235—24no—
216C2×D12—21no—
217C2×D12—22no—
218C2×D12—21no—
219C2×D12—21no—
220C2×D12C3×D414yescomplemented
221C2×D12C23×C312yes—
222C2×D12C23×C312yes—
223C2×C4×D3—22no—
224C2×C4×D3—22no—
225C2×C4×D3—22no—
226C2×C4×D3—44no—
227C2×Dic6C23×C312yes—
228C3×SD16—68no—
229C3×D8—68no—
230C3×M16—24no—
231C3×M16—24no—
232C3×M16—44no—
233C2×C3×C8—24no—
234C2×C3×C8C22×D314yes—
235C2×C3×C8C23×C314yes—
236C3×C4⋊C4—32no—
237C3×C4⋊C4—61no—
238C3×C4⋊C4—61no—
239C3×C4⋊C4—61no—
240C3×C22⋊C4—62no—
241C3×C22⋊C4—62no—
242C3×C22⋊C4—62no—
243C3×C22⋊C4—62no—
244C3×C42—21no—
245C3×C42—21no—
246C3×C42—21no—
247C3×C42—21no—
248C3×C42D1211yescharacteristic
249C3×C42D1211yescharacteristic
250C3×C42C3×D411yescharacteristic
251C3×C42C3×D411yescharacteristic
252C3×C42C22×D311yescharacteristic
253C3×C42C22×D311yescharacteristic
254C3×C42C23×C311yescharacteristic
255C3×C42C23×C311yescharacteristic
256(C2×D3)⋊C4—22no—
257(C2×D3)⋊C4—22no—
258(C2×D3)⋊C4—22no—
259(C2×D3)⋊C4—22no—
260C4⋊Dic3—21no—
261C4⋊Dic3—21no—
262C4⋊Dic3—21no—
263C4⋊Dic3C23×C312yes—
264D24—28no—
265#204—28no—
266C22×C32—21no—
267C22×C32—21no—
268C22×C32#12112yes—
269C22×C32C22×D411yescharacteristic
270C2×C3×D3—24no—
271C2×C3×D3—48no—
272C2×C3×D3—42no—
273C2×C3×D3—42no—
274C2×C3×D3—42no—
275C2×C3×D3—42no—
276C2×C3×D3—42no—
277C32×C4—21no—
278C32×C4—21no—
279C32×C4—21no—
280C32×C4#12112yes—
281C32×C4AGL(1,ℤ/8)12yescomplemented
282C32×C4C22×D411yescharacteristic
283C32×C4C2×#4111yescharacteristic
284C3×Dic3—42no—
285C3×Dic3—42no—
286C2×#41—32no—
287C22×D4—31no—
288C23×C4—61no—
289AGL(1,ℤ/8)—68no—
290C2×SD16—34no—
291C2×D8—34no—
292C2×M16C2×C3×D312yes—
293C4⋊Q8—31no—
294#127—31no—
295#124—32no—
296#121—61no—
297#121—61no—
298C4×D4—32no—
299C4×D4—32no—
300C4×D4—61no—
301C4×D4—61no—
302C4×D4—61no—
303C4×D4—61no—
304C2×C4⋊C4—31no—
305C2×C22⋊C4—61no—
306C2×C42C2×C3×D311yescharacteristic
307C4⋊C8C2×C3×D312yescomplemented
308C4⋊C8C2×C3×D312yescomplemented
309#103—34no—
310#102—34no—
311C23×C3—21no—
312C23×C3—64no—
313C23×C3—62no—
314C23×C3—62no—
315C23×C3—122no—
316C23×C3—122no—
317C23×C3C2×D1211yescharacteristic
318C23×C3C2×C3×D411yescharacteristic
319C22×D3—24no—
320C22×D3—22no—
321C22×D3—22no—
322C22×D3—42no—
323C22×D3—42no—
324C3×Q8—62no—
325C3×Q8—62no—
326C3×D4—34no—
327C3×D4—64no—
328C3×D4—62no—
329C3×D4—62no—
330C3×D4—62no—
331C3×D4—122no—
332C3×D4—124no—
333C3×D4—122no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—22no—
343C2×C3×C4—22no—
344C2×C3×C4—42no—
345C2×C3×C4—41no—
346C2×C3×C4—41no—
347C2×C3×C4—42no—
348C2×C3×C4—62no—
349C2×C3×C4—62no—
350C2×C3×C4—124no—
351C2×C3×C4—122no—
352C2×C3×C4—124no—
353C2×C3×C4—124no—
354C2×C3×C4C2×D1211yescharacteristic
355C2×C3×C4C2×D1211yescharacteristic
356C2×C3×C4C2×D1211yescharacteristic
357C2×C3×C4C2×D1211yescharacteristic
358C2×C3×C4C2×D1211yescharacteristic
359C2×C3×C4D3×D412yes—
360C2×C3×C4#23912yes—
361C2×C3×C4C2×C3×D411yescharacteristic
362C2×C3×C4C2×C3×D411yescharacteristic
363C2×C3×C4C2×C3×D411yescharacteristic
364C2×C3×C4C2×C3×D411yescharacteristic
365C2×C3×C4C2×C3×D411yescharacteristic
366C2×C3×C4C2×C3×D412yes—
367C2×C3×C4C3×#4112yes—
368C2×C3×C4C23×D311yescharacteristic
369C2×C3×C4C24×C311yescharacteristic
370#67—44no—
371C2×Dic3—22no—
372C2×Dic3—22no—
373C2×Dic3—42no—
374D12—24no—
375D12—22no—
376D12—22no—
377D12—22no—
378D12—42no—
379D12—42no—
380D12C2×C3×D414yes—
381C4×D3—44no—
382C4×D3—44no—
383C4×D3—44no—
384Dic6—22no—
385Dic6—22no—
386C3×C8—24no—
387C3×C8—24no—
388C3×C8—44no—
389C2×C32—22no—
390C2×C32C2×#12111yescharacteristic
391C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
392C2×C32#57511yescharacteristic
393C3×D3—44no—
394C3×D3—82no—
395C24—61no—
396#41—64no—
397#41—64no—
398C2×Q8—32no—
399C2×D4—32no—
400C2×D4—32no—
401C2×D4—34no—
402C2×D4—62no—
403C2×D4—61no—
404C2×D4—61no—
405C2×D4—61no—
406C2×D4—62no—
407C22×C4—61no—
408C22×C4—62no—
409C22×C4—62no—
410C22×C4—62no—
411C22×C4—124no—
412C22×C4C3×D1211yescharacteristic
413C22×C4C3×D1211yescharacteristic
414C22×C4C22×C3×D311yescharacteristic
415SD16—68no—
416D8—68no—
417M16—24no—
418C2×C8C22×C3×D314yes—
419C4⋊C4—32no—
420C4⋊C4—61no—
421C4⋊C4—61no—
422C4⋊C4—61no—
423C22⋊C4—62no—
424C22⋊C4—62no—
425C22⋊C4—62no—
426C22⋊C4—62no—
427C42C3×D1211yescharacteristic
428C42C3×D1211yescharacteristic
429C42C22×C3×D311yescharacteristic
430C42C22×C3×D311yescharacteristic
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—22no—
436C22×C3—21no—
437C22×C3—41no—
438C22×C3—41no—
439C22×C3—64no—
440C22×C3—128no—
441C22×C3—122no—
442C22×C3—122no—
443C22×C3—122no—
444C22×C3—122no—
445C22×C3—122no—
446C22×C3#89512yes—
447C22×C3C3×#12112yes—
448C22×C3C22×D1211yescharacteristic
449C22×C3C22×C3×D411yescharacteristic
450C2×D3—24no—
451C2×D3—48no—
452C2×D3—42no—
453C2×D3—42no—
454C2×D3—42no—
455C2×D3—42no—
456C2×D3—42no—
457C3×C4—22no—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—21no—
461C3×C4—21no—
462C3×C4—21no—
463C3×C4—21no—
464C3×C4—22no—
465C3×C4—22no—
466C3×C4—21no—
467C3×C4—21no—
468C3×C4—41no—
469C3×C4—41no—
470C3×C4—122no—
471C3×C4—122no—
472C3×C4#89512yes—
473C3×C4#90812yescomplemented
474C3×C4C3×#12112yes—
475C3×C4C3×AGL(1,ℤ/8)12yescomplemented
476C3×C4C2×D3×D411yescharacteristic
477C3×C4C2×#23911yescharacteristic
478C3×C4C22×C3×D411yescharacteristic
479C3×C4C2×C3×#4111yescharacteristic
480Dic3—42no—
481Dic3—42no—
482C32#303611yescharacteristic, complemented, Sylow
483C23—64no—
484C23—62no—
485C23—62no—
486C23—122no—
487C23—122no—
488C23C2×C3×D1211yescharacteristic
489Q8—62no—
490Q8—62no—
491D4—34no—
492D4—64no—
493D4—62no—
494D4—62no—
495D4—62no—
496D4—122no—
497D4—124no—
498D4—122no—
499C2×C4—22no—
500C2×C4—41no—
501C2×C4—62no—
502C2×C4—62no—
503C2×C4—124no—
504C2×C4—122no—
505C2×C4—124no—
506C2×C4—124no—
507C2×C4C2×C3×D1211yescharacteristic
508C2×C4C2×C3×D1211yescharacteristic
509C2×C4C2×C3×D1211yescharacteristic
510C2×C4C2×C3×D1211yescharacteristic
511C2×C4C2×C3×D1211yescharacteristic
512C2×C4C3×D3×D412yes—
513C2×C4C3×#23912yes—
514C2×C4C23×C3×D311yescharacteristic
515C8—24no—
516C2×C3—22no—
517C2×C3—22no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—21no—
521C2×C3—42no—
522C2×C3—124no—
523C2×C3—242no—
524C2×C3C2×#89511yescharacteristic
525C2×C3C2×#90811yescharacteristic
526C2×C3#574811yescharacteristic
527C2×C3C2×C3×#12111yescharacteristic
528C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
529C2×C3C3×#57511yescharacteristic
530D3—44no—
531D3—82no—
532C22—21no—
533C22—21no—
534C22—64no—
535C22—128no—
536C22—122no—
537C22—122no—
538C22—122no—
539C22—122no—
540C22—122no—
541C22C3×#89512yes—
542C22C22×C3×D1211yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—122no—
547C4—122no—
548C4C3×#89512yes—
549C4C3×#90812yescomplemented
550C4C2×C3×D3×D411yescharacteristic
551C4C2×C3×#23911yescharacteristic
552C3—21no—
553C3#7905511yescharacteristic, direct product factor
554C3C3×#303611yescharacteristic, complemented
555C2—22no—
556C2—124no—
557C2—242no—
558C2C2×C3×#89511yescharacteristic
559C2C2×C3×#90811yescharacteristic
560C2C3×#574811yescharacteristic
subgroupG/H
centerC22×C3C22×D12
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#423C2
socleC22×C32C22×D4
hypercenterC3×#423D3
hypocenterC3C3×#3036
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ C3×#423

Complements

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

NH ≅ G/Ntype
1. C2×C3×#908C2semidirect
2. C3×#5477C2semidirect
3. C2×C3×C4×D12C2semidirect
4. C32×#423C2semidirect
5. C3×#5133C2semidirect
6. C3×#4844C2semidirect
7. C3×#4843C2semidirect
8. C3×#4841C2semidirect
10. #79055C3direct (N × H)
23. C3×#875C22semidirect
24. C3×#874C22semidirect
31. C3×#869C22semidirect
32. C32×C4⋊C8C22semidirect
33. C32×C4⋊C8C22semidirect
34. C3×#821C22semidirect
35. C3×#816C22semidirect
39. C2×#908C2×C3semidirect
40. #5477C2×C3semidirect
41. C2×C4×D12C2×C3semidirect
46. C3×#423D3semidirect
47. C3×#423C2×C3semidirect
49. #5133C2×C3semidirect
50. #4844C2×C3semidirect
51. #4843C2×C3semidirect
52. #4841C2×C3semidirect
65. C2×C3×D12D4semidirect
125. #875C22×C3semidirect
126. #874C22×C3semidirect
133. #869C22×C3semidirect
136. C3×C4⋊C8C2×D3semidirect
137. C3×C4⋊C8C2×D3semidirect
138. C3×C4⋊C8C22×C3semidirect
139. C3×C4⋊C8C22×C3semidirect
142. #821C22×C3semidirect
143. #816C22×C3semidirect
183. #423C3×D3semidirect
220. C2×D12C3×D4semidirect
281. C32×C4AGL(1,ℤ/8)semidirect
307. C4⋊C8C2×C3×D3semidirect
308. C4⋊C8C2×C3×D3semidirect
473. C3×C4#908semidirect
475. C3×C4C3×AGL(1,ℤ/8)semidirect
482. C32#3036semidirect
549. C4C3×#908semidirect
553. C3#79055direct (N × H)
554. C3C3×#3036semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9082
C3×#54772
C2×C3×C4×D122
C32×#4232
C3×#51332
C3×#48442
C3×#48432
C3×#48412
C3×#30363
#790553