Finite Group Databasebeta

← C3×#79570 #11895717

Subgroups — C3×#79570 #11895717

Order 1152.

859 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5553C211yesmaximal, characteristic, complemented
2C3×#5543C211yesmaximal, characteristic, complemented
3C32×C4×D8C211yesmaximal, characteristic, complemented
4C3×#5150C212yesmaximal, complemented
5C3×#5015C211yesmaximal, characteristic, complemented
6C3×#5008C211yesmaximal, characteristic, complemented
7C3×#4891C212yesmaximal, complemented
8C3×#4785C212yesmaximal, complemented
9C3×#4764C212yesmaximal, complemented
10C3×#4694C211yesmaximal, characteristic, complemented
11C3×#4679C211yesmaximal, characteristic, complemented
12C3×#3366—31nomaximal
13#79570C311yesmaximal, characteristic, direct product factor
14C2×C3×#235—21no—
15C2×C32×D8C2211yescharacteristic
16C32×C4×D4C2211yescharacteristic
17C32×C4×D4C2211yescharacteristic
18C3×#940C2212yes—
19C3×D4×Dic3C2212yes—
20C2×C3×#213C2212yes—
21C3×#930—21no—
22C2×C3×C4⋊Dic3—21no—
23C3×#924—21no—
24C3×#893C2212yes—
25C3×#890C2212yes—
26C3×#884—22no—
27C3×#878—22no—
28C3×#874C2211yescharacteristic
29C3×#869C2211yescharacteristic
30C3×C4×Dic6C2211yescharacteristic
31C32×#107C2211yescharacteristic
32C32×#102C2211yescharacteristic
33C32×#102C2211yescharacteristic
34C32×C4×C8C2211yescharacteristic
35C3×#832C2212yes—
36C3×#821C2212yes—
37C3×#821C2212yes—
38C3×#815C2212yes—
39C3×Dic3⋊C8C2212yes—
40C3×#809C2212yes—
41C3×#808C2212yes—
42C3×C4⋊(C3⋊C8)C2211yescharacteristic
43C3×#554—31no—
44C3×#550—31no—
45#5553C2×C311yescharacteristic, complemented
46#5543C2×C311yescharacteristic, complemented
47C3×#490—32no—
48C3×#486—31no—
49C3×#478—32no—
50C3×#476—31no—
51C3×#459—32no—
52C3×#459—31no—
53C3×#446—31no—
54C3×#442—32no—
55C3×C4×D8—21no—
56C3×C4×D8D311yescharacteristic, complemented
57C3×C4×D8C2×C311yescharacteristic, complemented
58#5150C2×C312yescomplemented
59#5015C2×C311yescharacteristic, complemented
60#5008C2×C311yescharacteristic, complemented
61#4891C2×C312yescomplemented
62#4785C2×C312yescomplemented
63#4764C2×C312yescomplemented
64#4694C2×C311yescharacteristic, complemented
65#4679C2×C311yescharacteristic, complemented
66C2×C32×D4C2311yescharacteristic
67C2×C32×D4C2311yescharacteristic
68C22×C32×C4—21no—
69C22×C32×C4—21no—
70C2×C3×#67—22no—
71C2×C3×#67—22no—
72C22×C3×Dic3—22no—
73C3×#235—44no—
74C2×C3×D12—21no—
75C2×C3×D12—21no—
76C2×C3×D12C2312yes—
77C2×C3×C4×D3—22no—
78C2×C3×Dic6—21no—
79C2×C3×Dic6D411yescharacteristic
80C32×D8—22no—
81C2×C32×C8C2311yescharacteristic
82C2×C32×C8C2311yescharacteristic
83C32×C4⋊C4C2311yescharacteristic
84C32×C4⋊C4C2311yescharacteristic
85C32×C22⋊C4—21no—
86C32×C22⋊C4—21no—
87C32×C42C2311yescharacteristic
88C3×#217—22no—
89C3×#213—24no—
90C3×(C2×D3)⋊C4—22no—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3—22no—
93C3×C4⋊Dic3D411yescharacteristic
94C3×C4⋊Dic3C2312yes—
95C3×Dic3⋊C4—22no—
96C3×Dic3⋊C4D412yes—
97C3×C4×Dic3C2312yes—
98C2×C3×C3⋊C8C2312yes—
99#3366—31noSylow
100C2×C3×#41—61no—
101C2×#235—21no—
102C2×C3×D8—21no—
103C2×C3×D8—32no—
104C2×C3×D8C2×D311yescharacteristic
105C2×C3×D8C22×C311yescharacteristic
106C3×C4⋊Q8—31no—
107C3×#127—32no—
108C3×#127—31no—
109C3×#125—32no—
110C3×C22⋊Q8—62no—
111C3×C22⋊Q8—61no—
112C3×#121—62no—
113C3×#121—61no—
114C3×C4×Q8—31no—
115C3×C4×D4—21no—
116C3×C4×D4—21no—
117C3×C4×D4—32no—
118C3×C4×D4—32no—
119C3×C4×D4C2×D311yescharacteristic
120C3×C4×D4C2×D311yescharacteristic
121C3×C4×D4C22×C311yescharacteristic
122C3×C4×D4C22×C311yescharacteristic
123C2×C3×C4⋊C4—61no—
124#940C22×C312yes—
125D4×Dic3C22×C312yes—
126C2×#213C22×C312yes—
127#930—21no—
128C2×C4⋊Dic3—21no—
129#924—21no—
130#893C22×C312yes—
131#890C22×C312yes—
132#884—22no—
133#878—22no—
134#874C22×C311yescharacteristic
135#869C22×C311yescharacteristic
136C4×Dic6C22×C311yescharacteristic
137C3×#107—21no—
138C3×#107C2×D311yescharacteristic
139C3×#107C22×C311yescharacteristic
140C3×#106—32no—
141C3×C4⋊C8—32no—
142C3×C4⋊C8—31no—
143C3×#102—21no—
144C3×#102—21no—
145C3×#102—32no—
146C3×#102—32no—
147C3×#102—32no—
148C3×#102—32no—
149C3×#102C2×D311yescharacteristic
150C3×#102C2×D311yescharacteristic
151C3×#102C22×C311yescharacteristic
152C3×#102C22×C311yescharacteristic
153C3×#97—32no—
154C3×C4×C8—21no—
155C3×C4×C8C2×D311yescharacteristic
156C3×C4×C8C22×C311yescharacteristic
157#832C22×C312yes—
158#821C22×C312yes—
159#821C22×C312yes—
160#815C22×C312yes—
161Dic3⋊C8C22×C312yes—
162#809C22×C312yes—
163#808C22×C312yes—
164C4⋊(C3⋊C8)C22×C311yescharacteristic
165C23×C32—21no—
166C23×C32—21no—
167C22×C3×D3—22no—
168C32×D4—21no—
169C32×D4—21no—
170C32×D4—21no—
171C32×D4#4112yescomplemented
172C2×C32×C4—21no—
173C2×C32×C4—21no—
174C2×C32×C4—42no—
175C2×C32×C4—42no—
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4C2×D411yescharacteristic
178C2×C32×C4C2411yescharacteristic
179C3×#67—44no—
180C3×#67—82no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—82no—
183C2×C3×Dic3C2×D412yes—
184C2×C3×Dic3C2×D412yes—
185C3×D12—22no—
186C3×D12—22no—
187C3×D12—42no—
188C3×D12—81no—
189C3×C4×D3—44no—
190C3×Dic6—22no—
191C3×Dic6—81no—
192C32×C8—21no—
193C32×C8—21no—
194C3×C3⋊C8—22no—
195#554—31no—
196#550—31no—
197#490—32no—
198#486—31no—
199#478—32no—
200#476—31no—
201#459—32no—
202#459—31no—
203#446—31no—
204#442—32no—
205C4×D8C3×D311yescharacteristic, complemented
206C3×#41—124no—
207C2×C3×Q8—31no—
208C2×C3×Q8—61no—
209C2×C3×D4—21no—
210C2×C3×D4—21no—
211C2×C3×D4—32no—
212C2×C3×D4—62no—
213C2×C3×D4—62no—
214C2×C3×D4—61no—
215C2×C3×D4—61no—
216C2×C3×D4C22×D311yescharacteristic
217C2×C3×D4C22×D311yescharacteristic
218C2×C3×D4C23×C311yescharacteristic
219C2×C3×D4C23×C311yescharacteristic
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—41no—
225C22×C3×C4—41no—
226C22×C3×C4—62no—
227C22×C3×C4—62no—
228C2×#67—22no—
229C2×#67—22no—
230C22×Dic3—22no—
231#235—44no—
232C2×D12—21no—
233C2×D12—21no—
234C2×D12C23×C312yes—
235C2×C4×D3—22no—
236C2×Dic6—21no—
237C2×Dic6C3×D411yescharacteristic
238C3×D8—24no—
239C3×D8—22no—
240C3×D8—22no—
241C3×D8—64no—
242C2×C3×C8—21no—
243C2×C3×C8—21no—
244C2×C3×C8—32no—
245C2×C3×C8C22×D311yescharacteristic
246C2×C3×C8C22×D311yescharacteristic
247C2×C3×C8C23×C311yescharacteristic
248C2×C3×C8C23×C311yescharacteristic
249C3×C4⋊C4—21no—
250C3×C4⋊C4—21no—
251C3×C4⋊C4—32no—
252C3×C4⋊C4—31no—
253C3×C4⋊C4—32no—
254C3×C4⋊C4—62no—
255C3×C4⋊C4—62no—
256C3×C4⋊C4—61no—
257C3×C4⋊C4C22×D311yescharacteristic
258C3×C4⋊C4C22×D311yescharacteristic
259C3×C4⋊C4C23×C311yescharacteristic
260C3×C4⋊C4C23×C311yescharacteristic
261C3×C22⋊C4—21no—
262C3×C22⋊C4—21no—
263C3×C22⋊C4—21no—
264C3×C22⋊C4—21no—
265C3×C22⋊C4—41no—
266C3×C22⋊C4—41no—
267C3×C22⋊C4—62no—
268C3×C22⋊C4—62no—
269C3×C42—21no—
270C3×C42—32no—
271C3×C42C22×D311yescharacteristic
272C3×C42C23×C311yescharacteristic
273#217—22no—
274#213—24no—
275(C2×D3)⋊C4—22no—
276C4⋊Dic3—21no—
277C4⋊Dic3—22no—
278C4⋊Dic3C3×D411yescharacteristic
279C4⋊Dic3C23×C312yes—
280Dic3⋊C4—22no—
281Dic3⋊C4C3×D412yes—
282C4×Dic3C23×C312yes—
283C2×C3⋊C8C23×C312yes—
284C22×C32—22no—
285C22×C32—41no—
286C22×C32—41no—
287C22×C32—41no—
288C22×C32—41no—
289C22×C32—41no—
290C22×C32C22×D411yescharacteristic
291C2×C3×D3—42no—
292C2×C3×D3—42no—
293C2×C3×D3—42no—
294C32×C4—21no—
295C32×C4—41no—
296C32×C4—41no—
297C32×C4AGL(1,ℤ/8)12yes—
298C32×C4C2×#4111yescharacteristic
299C32×C42−1+411yescharacteristic
300C3×Dic3—22no—
301C3×Dic3—22no—
302C3×Dic3—42no—
303C2×#41—61no—
304C2×D8—32no—
305C2×D8C2×C3×D311yescharacteristic
306C4⋊Q8—31no—
307#127—32no—
308#127—31no—
309#125—32no—
310C22⋊Q8—62no—
311C22⋊Q8—61no—
312#121—62no—
313#121—61no—
314C4×Q8—31no—
315C4×D4—32no—
316C4×D4—32no—
317C4×D4C2×C3×D311yescharacteristic
318C4×D4C2×C3×D311yescharacteristic
319C2×C4⋊C4—61no—
320#107C2×C3×D311yescharacteristic
321#106—32no—
322C4⋊C8—32no—
323C4⋊C8—31no—
324#102—32no—
325#102—32no—
326#102—32no—
327#102—32no—
328#102C2×C3×D311yescharacteristic
329#102C2×C3×D311yescharacteristic
330#97—32no—
331C4×C8C2×C3×D311yescharacteristic
332C23×C3—21no—
333C23×C3—21no—
334C23×C3—21no—
335C23×C3—21no—
336C23×C3—41no—
337C23×C3—41no—
338C23×C3—62no—
339C22×D3—22no—
340C3×Q8—62no—
341C3×Q8—241no—
342C3×D4—22no—
343C3×D4—21no—
344C3×D4—21no—
345C3×D4—21no—
346C3×D4—21no—
347C3×D4—21no—
348C3×D4—21no—
349C3×D4—22no—
350C3×D4—41no—
351C3×D4—41no—
352C3×D4—62no—
353C3×D4—62no—
354C3×D4—124no—
355C3×D4—122no—
356C3×D4—241no—
357C3×D4—242no—
358C3×D4#23512yescomplemented
359C3×D4C3×#4112yescomplemented
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—32no—
368C2×C3×C4—32no—
369C2×C3×C4—41no—
370C2×C3×C4—41no—
371C2×C3×C4—42no—
372C2×C3×C4—42no—
373C2×C3×C4—42no—
374C2×C3×C4—42no—
375C2×C3×C4—62no—
376C2×C3×C4—82no—
377C2×C3×C4—82no—
378C2×C3×C4—124no—
379C2×C3×C4—242no—
380C2×C3×C4D3×D411yescharacteristic
381C2×C3×C4D3×D411yescharacteristic
382C2×C3×C4C2×C3×D411yescharacteristic
383C2×C3×C4C2×C3×D411yescharacteristic
384C2×C3×C4C23×D311yescharacteristic
385C2×C3×C4C24×C311yescharacteristic
386#67—44no—
387#67—82no—
388C2×Dic3—22no—
389C2×Dic3—82no—
390C2×Dic3C2×C3×D412yes—
391C2×Dic3C2×C3×D412yes—
392D12—22no—
393D12—22no—
394D12—42no—
395D12—81no—
396C4×D3—44no—
397Dic6—22no—
398Dic6—81no—
399C3×C8—22no—
400C3×C8—21no—
401C3×C8—21no—
402C3×C8—21no—
403C3×C8—21no—
404C3×C8—41no—
405C3×C8—62no—
406C3⋊C8—22no—
407C2×C32—42no—
408C2×C32—81no—
409C2×C32#54811yescharacteristic
410C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
411C2×C32#57611yescharacteristic
412C3×D3—82no—
413#41—124no—
414C2×Q8—31no—
415C2×Q8—61no—
416C2×D4—32no—
417C2×D4—62no—
418C2×D4—62no—
419C2×D4—61no—
420C2×D4—61no—
421C2×D4C22×C3×D311yescharacteristic
422C2×D4C22×C3×D311yescharacteristic
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—62no—
426C22×C4—62no—
427D8—22no—
428D8—64no—
429C2×C8—32no—
430C2×C8C22×C3×D311yescharacteristic
431C2×C8C22×C3×D311yescharacteristic
432C4⋊C4—31no—
433C4⋊C4—32no—
434C4⋊C4—32no—
435C4⋊C4—62no—
436C4⋊C4—62no—
437C4⋊C4—61no—
438C4⋊C4C22×C3×D311yescharacteristic
439C4⋊C4C22×C3×D311yescharacteristic
440C22⋊C4—21no—
441C22⋊C4—21no—
442C22⋊C4—62no—
443C22⋊C4—62no—
444C42—32no—
445C42C22×C3×D311yescharacteristic
446C22×C3—22no—
447C22×C3—22no—
448C22×C3—21no—
449C22×C3—42no—
450C22×C3—42no—
451C22×C3—41no—
452C22×C3—41no—
453C22×C3—41no—
454C22×C3—41no—
455C22×C3—41no—
456C22×C3—41no—
457C22×C3—41no—
458C22×C3—41no—
459C22×C3—41no—
460C22×C3—41no—
461C22×C3—81no—
462C22×C3—81no—
463C22×C3—81no—
464C22×C3—81no—
465C22×C3—122no—
466C22×C3—122no—
467C22×C3—122no—
468C22×C3C2×D3×D411yescharacteristic
469C22×C3C22×C3×D411yescharacteristic
470C2×D3—42no—
471C2×D3—42no—
472C2×D3—42no—
473C3×C4—21no—
474C3×C4—21no—
475C3×C4—22no—
476C3×C4—21no—
477C3×C4—21no—
478C3×C4—41no—
479C3×C4—41no—
480C3×C4—41no—
481C3×C4—41no—
482C3×C4—41no—
483C3×C4—62no—
484C3×C4—62no—
485C3×C4—81no—
486C3×C4—81no—
487C3×C4—122no—
488C3×C4#91112yes—
489C3×C4C3×AGL(1,ℤ/8)12yes—
490C3×C4C2×#23511yescharacteristic
491C3×C4#101011yescharacteristic
492C3×C4C2×C3×#4111yescharacteristic
493C3×C4C3×2−1+411yescharacteristic
494Dic3—22no—
495Dic3—22no—
496Dic3—42no—
497C32#336611yescharacteristic, complemented, Sylow
498C23—21no—
499C23—21no—
500C23—62no—
501Q8—62no—
502Q8—241no—
503D4—21no—
504D4—21no—
505D4—21no—
506D4—62no—
507D4—62no—
508D4—124no—
509D4—122no—
510D4—241no—
511D4—242no—
512D4C3×#23512yescomplemented
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—32no—
516C2×C4—32no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—62no—
520C2×C4—124no—
521C2×C4—242no—
522C2×C4C3×D3×D411yescharacteristic
523C2×C4C3×D3×D411yescharacteristic
524C2×C4C23×C3×D311yescharacteristic
525C8—21no—
526C8—21no—
527C8—62no—
528C2×C3—21no—
529C2×C3—21no—
530C2×C3—21no—
531C2×C3—42no—
532C2×C3—42no—
533C2×C3—82no—
534C2×C3—82no—
535C2×C3—81no—
536C2×C3—81no—
537C2×C3—242no—
538C2×C3#555211yescharacteristic
539C2×C3C2×#91111yescharacteristic
540C2×C3#576911yescharacteristic
541C2×C3C3×#54811yescharacteristic
542C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
543C2×C3C3×#57611yescharacteristic
544D3—82no—
545C22—22no—
546C22—41no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—122no—
552C22—122no—
553C22—122no—
554C22C2×C3×D3×D411yescharacteristic
555C4—21no—
556C4—41no—
557C4—41no—
558C4—62no—
559C4—62no—
560C4—122no—
561C4C3×#91112yes—
562C4C2×C3×#23511yescharacteristic
563C4C3×#101011yescharacteristic
564C3—21no—
565C3#7957011yescharacteristic, direct product factor
566C3C3×#336611yescharacteristic, complemented
567C2—42no—
568C2—81no—
569C2—242no—
570C2C3×#555211yescharacteristic
571C2C2×C3×#91111yescharacteristic
572C2C3×#576911yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×C4×D8C2
socleC22×C32C22×D4
hypercenterC3×C4×D8D3
hypocenterC3C3×#3366
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×C4×D8

Complements

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

NH ≅ G/Ntype
1. C3×#5553C2semidirect
2. C3×#5543C2semidirect
3. C32×C4×D8C2semidirect
4. C3×#5150C2semidirect
5. C3×#5015C2semidirect
6. C3×#5008C2semidirect
7. C3×#4891C2semidirect
8. C3×#4785C2semidirect
9. C3×#4764C2semidirect
10. C3×#4694C2semidirect
11. C3×#4679C2semidirect
13. #79570C3direct (N × H)
45. #5553C2×C3semidirect
46. #5543C2×C3semidirect
56. C3×C4×D8D3semidirect
57. C3×C4×D8C2×C3semidirect
58. #5150C2×C3semidirect
59. #5015C2×C3semidirect
60. #5008C2×C3semidirect
61. #4891C2×C3semidirect
62. #4785C2×C3semidirect
63. #4764C2×C3semidirect
64. #4694C2×C3semidirect
65. #4679C2×C3semidirect
171. C32×D4#41semidirect
205. C4×D8C3×D3semidirect
358. C3×D4#235semidirect
359. C3×D4C3×#41semidirect
497. C32#3366semidirect
512. D4C3×#235semidirect
565. C3#79570direct (N × H)
566. C3C3×#3366semidirect

Maximal subgroups

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

subgroupindex
C3×#55532
C3×#55432
C32×C4×D82
C3×#51502
C3×#50152
C3×#50082
C3×#48912
C3×#47852
C3×#47642
C3×#46942
C3×#46792
C3×#33663
#795703