Finite Group Databasebeta

← C3×#82296 #11868652

Subgroups — C3×#82296 #11868652

Order 1152.

1093 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×D4C211yesmaximal, characteristic
2C3×#5470C211yesmaximal, characteristic, complemented
3C3×#5215C212yesmaximal
4C3×#5009C214yesmaximal, complemented
5C3×#5008C212yesmaximal, complemented
6C3×#5007C212yesmaximal, complemented
7C3×#4964C212yesmaximal, complemented
8C3×#4924C211yesmaximal, characteristic, complemented
9C3×#3077—31nomaximal
10#82296C311yesmaximal, characteristic, direct product factor
11C22×C32×D4C2211yescharacteristic
12C23×C32×C4—21no—
13C32×C4×D4—21no—
14C32×C4×D4—21no—
15C32×C4×D4C2212yes—
16C32×C4×D4C2212yes—
17C2×C32×C4⋊C4C2211yescharacteristic
18C2×C32×C22⋊C4—21no—
19C2×C32×C42C2211yescharacteristic
20C3×#926C2212yes—
21C3×#924—21no—
22C3×#924—21no—
23C2×C3×#208C2212yes—
24C3×#870C2212yescomplemented
25C3×#869C2211yescharacteristic, complemented
26C3×#869C2211yescharacteristic, complemented
27C3×C4×Dic6—21no—
28C3×C4×Dic6—21no—
29C3×#832C2214yes—
30C3×#832C2214yes—
31C3×#808C2214yescomplemented
32C3×#807C2214yescomplemented
33C3×C4⋊(C3⋊C8)C2212yescomplemented
34C3×C4⋊(C3⋊C8)C2212yescomplemented
35C3×#533—31no—
36C2×C3×C4×D4—21no—
37C2×C3×C4×D4D311yescharacteristic
38C2×C3×C4×D4C2×C311yescharacteristic
39#5470C2×C311yescharacteristic, complemented
40C3×#478—34no—
41C3×#476—32no—
42C3×#474—32no—
43C3×#428—32no—
44C3×#423—31no—
45C3×#418—32no—
46#5215C2×C312yes—
47#5009C2×C314yescomplemented
48#5008C2×C312yescomplemented
49#5007C2×C312yescomplemented
50#4964C2×C312yescomplemented
51#4924C2×C311yescharacteristic, complemented
52C24×C32—21no—
53C2×C32×D4—21no—
54C2×C32×D4—22no—
55C2×C32×D4Q814yescomplemented
56C2×C32×D4C2312yes—
57C22×C32×C4—21no—
58C22×C32×C4—22no—
59C22×C32×C4—22no—
60C22×C32×C4—44no—
61C22×C32×C4D411yescharacteristic
62C22×C32×C4D411yescharacteristic
63C22×C32×C4C2311yescharacteristic
64C2×C3×Dic6—21no—
65C2×C3×Dic6—21no—
66C32×C4⋊C4—21no—
67C32×C4⋊C4C2312yes—
68C32×C22⋊C4—22no—
69C32×C22⋊C4—22no—
70C32×C42D411yescharacteristic
71C32×C42D411yescharacteristic
72C32×C42C2311yescharacteristic
73C32×C42C2311yescharacteristic
74C3×#217—22no—
75C3×C4⋊Dic3—21no—
76C3×C4⋊Dic3—21no—
77C3×C4⋊Dic3C2312yes—
78C3×C4⋊Dic3C2312yes—
79C3×Dic3⋊C4—22no—
80C3×Dic3⋊C4—22no—
81C3×C4×Dic3—22no—
82C3×#208—24no—
83C2×C3×C3⋊C8C2314yes—
84#3077—31noSylow
85C22×C3×D4—21no—
86C22×C3×D4C2×D311yescharacteristic
87C22×C3×D4C22×C311yescharacteristic
88C23×C3×C4—22no—
89C23×C3×C4—21no—
90C23×C3×C4—21no—
91C2×C3×M16—32no—
92C3×C4⋊Q8—31no—
93C3×C4⋊Q8—31no—
94C3×#125—32no—
95C3×C22⋊Q8—61no—
96C3×C22⋊Q8—61no—
97C3×C4×Q8—61no—
98C3×C4×Q8—61no—
99C3×C4×D4—22no—
100C3×C4×D4—22no—
101C3×C4×D4—21no—
102C3×C4×D4—21no—
103C3×C4×D4—21no—
104C3×C4×D4—21no—
105C3×C4×D4—22no—
106C3×C4×D4—22no—
107C3×C4×D4C2×D312yes—
108C3×C4×D4C2×D312yes—
109C3×C4×D4C22×C312yes—
110C3×C4×D4C22×C312yes—
111C3×#117—32no—
112C2×C3×C4⋊C4—21no—
113C2×C3×C4⋊C4C2×D311yescharacteristic
114C2×C3×C4⋊C4C22×C311yescharacteristic
115C2×C3×C22⋊C4—22no—
116C2×C3×C22⋊C4—21no—
117C2×C3×C22⋊C4—21no—
118C2×C3×C42—21no—
119C2×C3×C42C2×D311yescharacteristic
120C2×C3×C42C22×C311yescharacteristic
121#926C22×C312yes—
122#924—21no—
123#924—21no—
124C2×#208C22×C312yes—
125#870C22×C312yescomplemented
126#869C22×C311yescharacteristic, complemented
127#869C22×C311yescharacteristic, complemented
128C4×Dic6—21no—
129C4×Dic6—21no—
130C3×#107—34no—
131C3×#106—34no—
132C3×C4⋊C8—32no—
133C3×C4⋊C8—32no—
134C3×#102—34no—
135C3×#102—34no—
136#832C22×C314yes—
137#832C22×C314yes—
138#808C22×C314yescomplemented
139#807C22×C314yescomplemented
140C4⋊(C3⋊C8)C22×C312yescomplemented
141C4⋊(C3⋊C8)C22×C312yescomplemented
142C23×C32—24no—
143C23×C32—22no—
144C23×C32—42no—
145C23×C32—42no—
146C23×C32C2×D411yescharacteristic
147C32×D4—24no—
148C32×D4—22no—
149C32×D4C2×Q814yes—
150C2×C32×C4—22no—
151C2×C32×C4—22no—
152C2×C32×C4—41no—
153C2×C32×C4—44no—
154C2×C32×C4—42no—
155C2×C32×C4—44no—
156C2×C32×C4C2×D411yescharacteristic
157C2×C32×C4C2×D411yescharacteristic
158C2×C32×C4C2×D411yescharacteristic
159C2×C32×C4C2×D411yescharacteristic
160C2×C32×C4C2×D411yescharacteristic
161C2×C32×C4C2×Q812yes—
162C2×C32×C4#4112yes—
163C2×C32×C4C2411yescharacteristic
164C2×C3×Dic3—22no—
165C2×C3×Dic3—22no—
166C3×Dic6—42no—
167C3×Dic6—42no—
168C3×C3⋊C8—24no—
169#533—31no—
170C2×C4×D4C3×D311yescharacteristic
171#478—34no—
172#476—32no—
173#474—32no—
174#428—32no—
175#423—31no—
176#418—32no—
177C24×C3—22no—
178C24×C3—21no—
179C24×C3—21no—
180C2×C3×Q8—61no—
181C2×C3×Q8—61no—
182C2×C3×D4—22no—
183C2×C3×D4—24no—
184C2×C3×D4—22no—
185C2×C3×D4—21no—
186C2×C3×D4—21no—
187C2×C3×D4—22no—
188C2×C3×D4—24no—
189C2×C3×D4—22no—
190C2×C3×D4Dic614yescomplemented
191C2×C3×D4C3×Q814yescomplemented
192C2×C3×D4C22×D312yes—
193C2×C3×D4C23×C312yes—
194C22×C3×C4—22no—
195C22×C3×C4—24no—
196C22×C3×C4—24no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—22no—
200C22×C3×C4—22no—
201C22×C3×C4—22no—
202C22×C3×C4—22no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—48no—
207C22×C3×C4—44no—
208C22×C3×C4—44no—
209C22×C3×C4#6711yescharacteristic
210C22×C3×C4#6711yescharacteristic
211C22×C3×C4C3×D411yescharacteristic
212C22×C3×C4C3×D411yescharacteristic
213C22×C3×C4C22×D311yescharacteristic
214C22×C3×C4C23×C311yescharacteristic
215C2×Dic6—21no—
216C2×Dic6—21no—
217C3×M16—64no—
218C2×C3×C8—34no—
219C3×C4⋊C4—22no—
220C3×C4⋊C4—21no—
221C3×C4⋊C4—21no—
222C3×C4⋊C4—22no—
223C3×C4⋊C4—32no—
224C3×C4⋊C4—32no—
225C3×C4⋊C4—62no—
226C3×C4⋊C4—62no—
227C3×C4⋊C4—61no—
228C3×C4⋊C4—61no—
229C3×C4⋊C4C22×D312yes—
230C3×C4⋊C4C23×C312yes—
231C3×C22⋊C4—24no—
232C3×C22⋊C4—24no—
233C3×C22⋊C4—22no—
234C3×C22⋊C4—22no—
235C3×C22⋊C4—22no—
236C3×C22⋊C4—22no—
237C3×C22⋊C4—62no—
238C3×C42—21no—
239C3×C42—21no—
240C3×C42—21no—
241C3×C42—21no—
242C3×C42—62no—
243C3×C42#6711yescharacteristic
244C3×C42#6711yescharacteristic
245C3×C42C3×D411yescharacteristic
246C3×C42C3×D411yescharacteristic
247C3×C42C22×D311yescharacteristic
248C3×C42C22×D311yescharacteristic
249C3×C42C23×C311yescharacteristic
250C3×C42C23×C311yescharacteristic
251#217—22no—
252C4⋊Dic3—21no—
253C4⋊Dic3—21no—
254C4⋊Dic3C23×C312yes—
255C4⋊Dic3C23×C312yes—
256Dic3⋊C4—22no—
257Dic3⋊C4—22no—
258C4×Dic3—22no—
259#208—24no—
260C2×C3⋊C8C23×C314yes—
261C22×C32—21no—
262C22×C32—21no—
263C22×C32—24no—
264C22×C32—48no—
265C22×C32—42no—
266C22×C32—42no—
267C22×C32C22⋊Q812yes—
268C22×C32C22×D411yescharacteristic
269C32×C4—21no—
270C32×C4—21no—
271C32×C4—21no—
272C32×C4—42no—
273C32×C4C22⋊Q812yes—
274C32×C4AGL(1,ℤ/8)12yes—
275C32×C4C22×Q811yescharacteristic
276C32×C4C2×#4111yescharacteristic
277C3×Dic3—42no—
278C3×Dic3—42no—
279C22×D4C2×C3×D311yescharacteristic
280C23×C4—21no—
281C2×M16—32no—
282C4⋊Q8—31no—
283C4⋊Q8—31no—
284#125—32no—
285C22⋊Q8—61no—
286C22⋊Q8—61no—
287C4×Q8—61no—
288C4×Q8—61no—
289C4×D4—21no—
290C4×D4—21no—
291C4×D4C2×C3×D312yes—
292C4×D4C2×C3×D312yes—
293#117—32no—
294C2×C4⋊C4C2×C3×D311yescharacteristic
295C2×C22⋊C4—21no—
296C2×C42C2×C3×D311yescharacteristic
297#107—34no—
298#106—34no—
299C4⋊C8—32no—
300C4⋊C8—32no—
301#102—34no—
302#102—34no—
303C23×C3—24no—
304C23×C3—28no—
305C23×C3—24no—
306C23×C3—24no—
307C23×C3—22no—
308C23×C3—22no—
309C23×C3—21no—
310C23×C3—44no—
311C23×C3—42no—
312C23×C3—42no—
313C23×C3—44no—
314C23×C3—42no—
315C23×C3—42no—
316C23×C3C2×#6711yescharacteristic
317C23×C3C2×C3×D411yescharacteristic
318C3×Q8—122no—
319C3×Q8—122no—
320C3×D4—28no—
321C3×D4—24no—
322C3×D4—24no—
323C3×D4—24no—
324C3×D4—22no—
325C3×D4—22no—
326C3×D4—24no—
327C3×D4C2×Dic614yes—
328C3×D4C2×C3×Q814yes—
329C2×C3×C4—24no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—24no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—21no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—41no—
344C2×C3×C4—41no—
345C2×C3×C4—48no—
346C2×C3×C4—44no—
347C2×C3×C4—44no—
348C2×C3×C4—48no—
349C2×C3×C4—42no—
350C2×C3×C4—44no—
351C2×C3×C4—42no—
352C2×C3×C4—42no—
353C2×C3×C4—44no—
354C2×C3×C4—44no—
355C2×C3×C4—62no—
356C2×C3×C4—62no—
357C2×C3×C4C2×Dic612yes—
358C2×C3×C4#23512yes—
359C2×C3×C4C2×#6711yescharacteristic
360C2×C3×C4C2×#6711yescharacteristic
361C2×C3×C4C2×#6711yescharacteristic
362C2×C3×C4C2×#6711yescharacteristic
363C2×C3×C4C2×#6711yescharacteristic
364C2×C3×C4C2×C3×D411yescharacteristic
365C2×C3×C4C2×C3×D411yescharacteristic
366C2×C3×C4C2×C3×D411yescharacteristic
367C2×C3×C4C2×C3×D411yescharacteristic
368C2×C3×C4C2×C3×D411yescharacteristic
369C2×C3×C4C2×C3×Q812yes—
370C2×C3×C4C3×#4112yes—
371C2×C3×C4C23×D311yescharacteristic
372C2×C3×C4C24×C311yescharacteristic
373C2×Dic3—22no—
374C2×Dic3—22no—
375Dic6—42no—
376Dic6—42no—
377C3×C8—64no—
378C3⋊C8—24no—
379C2×C32—22no—
380C2×C32—44no—
381C2×C32C2×C22⋊Q811yescharacteristic
382C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
383C2×C32#57511yescharacteristic
384C24—21no—
385C2×Q8—61no—
386C2×Q8—61no—
387C2×D4—22no—
388C2×D4—21no—
389C2×D4C3×Dic614yescomplemented
390C2×D4C22×C3×D312yes—
391C22×C4—21no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—44no—
395C22×C4C3×#6711yescharacteristic
396C22×C4C3×#6711yescharacteristic
397C22×C4C22×C3×D311yescharacteristic
398M16—64no—
399C2×C8—34no—
400C4⋊C4—21no—
401C4⋊C4—32no—
402C4⋊C4—32no—
403C4⋊C4—62no—
404C4⋊C4—62no—
405C4⋊C4—61no—
406C4⋊C4—61no—
407C4⋊C4C22×C3×D312yes—
408C22⋊C4—22no—
409C22⋊C4—22no—
410C22⋊C4—62no—
411C42—62no—
412C42C3×#6711yescharacteristic
413C42C3×#6711yescharacteristic
414C42C22×C3×D311yescharacteristic
415C42C22×C3×D311yescharacteristic
416C22×C3—22no—
417C22×C3—22no—
418C22×C3—21no—
419C22×C3—21no—
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—28no—
423C22×C3—24no—
424C22×C3—24no—
425C22×C3—22no—
426C22×C3—21no—
427C22×C3—44no—
428C22×C3—416no—
429C22×C3—48no—
430C22×C3—48no—
431C22×C3—44no—
432C22×C3—42no—
433C22×C3—42no—
434C22×C3—42no—
435C22×C3—42no—
436C22×C3#92412yes—
437C22×C3C3×C22⋊Q812yes—
438C22×C3C22×#6711yescharacteristic
439C22×C3C22×C3×D411yescharacteristic
440C3×C4—22no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—21no—
445C3×C4—21no—
446C3×C4—21no—
447C3×C4—22no—
448C3×C4—22no—
449C3×C4—21no—
450C3×C4—21no—
451C3×C4—41no—
452C3×C4—41no—
453C3×C4—44no—
454C3×C4—42no—
455C3×C4—42no—
456C3×C4—122no—
457C3×C4—122no—
458C3×C4#92412yes—
459C3×C4#93212yes—
460C3×C4C3×C22⋊Q812yes—
461C3×C4C3×AGL(1,ℤ/8)12yes—
462C3×C4C22×Dic611yescharacteristic
463C3×C4C2×#23511yescharacteristic
464C3×C4C22×C3×Q811yescharacteristic
465C3×C4C2×C3×#4111yescharacteristic
466Dic3—42no—
467Dic3—42no—
468C32#307711yescharacteristic, complemented, Sylow
469C23—24no—
470C23—22no—
471C23—42no—
472C23—42no—
473C23C2×C3×#6711yescharacteristic
474Q8—122no—
475Q8—122no—
476D4—24no—
477D4—22no—
478D4C2×C3×Dic614yes—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—41no—
482C2×C4—44no—
483C2×C4—42no—
484C2×C4—44no—
485C2×C4—62no—
486C2×C4—62no—
487C2×C4C2×C3×Dic612yes—
488C2×C4C3×#23512yes—
489C2×C4C2×C3×#6711yescharacteristic
490C2×C4C2×C3×#6711yescharacteristic
491C2×C4C2×C3×#6711yescharacteristic
492C2×C4C2×C3×#6711yescharacteristic
493C2×C4C2×C3×#6711yescharacteristic
494C2×C4C23×C3×D311yescharacteristic
495C8—64no—
496C2×C3—24no—
497C2×C3—22no—
498C2×C3—22no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—48no—
503C2×C3—44no—
504C2×C3—44no—
505C2×C3C2×#92411yescharacteristic
506C2×C3C2×#93211yescharacteristic
507C2×C3#582211yescharacteristic
508C2×C3C2×C3×C22⋊Q811yescharacteristic
509C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
510C2×C3C3×#57511yescharacteristic
511C22—21no—
512C22—21no—
513C22—24no—
514C22—48no—
515C22—42no—
516C22—42no—
517C22C3×#92412yes—
518C22C22×C3×#6711yescharacteristic
519C4—21no—
520C4—21no—
521C4—21no—
522C4—42no—
523C4—122no—
524C4—122no—
525C4C3×#92412yes—
526C4C3×#93212yes—
527C4C22×C3×Dic611yescharacteristic
528C4C2×C3×#23511yescharacteristic
529C3—21no—
530C3#8229611yescharacteristic, direct product factor
531C3C3×#307711yescharacteristic, complemented
532C2—22no—
533C2—44no—
534C2C2×C3×#92411yescharacteristic
535C2C2×C3×#93211yescharacteristic
536C2C3×#582211yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×C4×D4C2
socleC22×C32C22×D4
prime radicalC22×C32×D4C22
hypercenterC2×C3×C4×D4D3
hypocenterC3C3×#3077
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ C2×C3×C4×D4

Complements

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

NH ≅ G/Ntype
2. C3×#5470C2semidirect
4. C3×#5009C2semidirect
5. C3×#5008C2semidirect
6. C3×#5007C2semidirect
7. C3×#4964C2semidirect
8. C3×#4924C2semidirect
10. #82296C3direct (N × H)
24. C3×#870C22semidirect
25. C3×#869C22semidirect
26. C3×#869C22semidirect
31. C3×#808C22semidirect
32. C3×#807C22semidirect
33. C3×C4⋊(C3⋊C8)C22semidirect
34. C3×C4⋊(C3⋊C8)C22semidirect
39. #5470C2×C3semidirect
47. #5009C2×C3semidirect
48. #5008C2×C3semidirect
49. #5007C2×C3semidirect
50. #4964C2×C3semidirect
51. #4924C2×C3semidirect
55. C2×C32×D4Q8semidirect
125. #870C22×C3semidirect
126. #869C22×C3semidirect
127. #869C22×C3semidirect
138. #808C22×C3semidirect
139. #807C22×C3semidirect
140. C4⋊(C3⋊C8)C22×C3semidirect
141. C4⋊(C3⋊C8)C22×C3semidirect
190. C2×C3×D4Dic6semidirect
191. C2×C3×D4C3×Q8semidirect
389. C2×D4C3×Dic6semidirect
468. C32#3077semidirect
530. C3#82296direct (N × H)
531. C3C3×#3077semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×D42
C3×#54702
C3×#52152
C3×#50092
C3×#50082
C3×#50072
C3×#49642
C3×#49242
C3×#30773
#822963