Finite Group Databasebeta

← C3×#69498 #11784595

Subgroups — C3×#69498 #11784595

Order 1152.

2013 conjugacy classes of subgroups.

The subgroup lattice has 537 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×#67C211yesmaximal, characteristic
2C32×#379C211yesmaximal, characteristic, complemented
3C3×#5247C211yesmaximal, characteristic, complemented
4C2×C3×#806C214yesmaximal, complemented
5C3×#1781—31nomaximal
6#69498C311yesmaximal, characteristic, direct product factor
7C25×C32C2211yescharacteristic
8C24×C3×D3C411yescharacteristic, complemented
9C22×C3×#67—28no—
10C22×C3×#67—22no—
11C22×C3×#67—22no—
12C22×C3×#67C412yescomplemented
13C22×C3×#67C2212yes—
14C23×C3×Dic3C411yescharacteristic, complemented
15C2×C32×C22⋊C4—22no—
16C2×C32×C22⋊C4C2212yescomplemented
17C2×C3×#217—22no—
18C2×C3×#217C2212yescomplemented
19C3×#806—28no—
20C23×C3×D4—31no—
21C23×#67C2×C311yescharacteristic
22C2×C3×#99—34no—
23C3×#379—21no—
24C3×#379—31no—
25C3×#379D311yescharacteristic, complemented
26C3×#379C2×C311yescharacteristic, complemented
27#5247C2×C311yescharacteristic, complemented
28C2×#806C2×C314yescomplemented
29C24×C32—24no—
30C24×C32—44no—
31C24×C32C2×C411yescharacteristic
32C24×C32C2×C411yescharacteristic
33C24×C32D412yes—
34C24×C32D412yes—
35C24×C32C2311yescharacteristic
36C23×C3×D3—22no—
37C23×C3×D3—24no—
38C23×C3×D3—44no—
39C23×C3×D3C2×C412yes—
40C22×C32×C4—22no—
41C2×C3×#67—216no—
42C2×C3×#67—216no—
43C2×C3×#67—24no—
44C2×C3×#67—22no—
45C2×C3×#67—24no—
46C2×C3×#67—22no—
47C2×C3×#67—24no—
48C2×C3×#67—24no—
49C2×C3×#67D418yes—
50C22×C3×Dic3—22no—
51C22×C3×Dic3—24no—
52C22×C3×Dic3—22no—
53C22×C3×Dic3C2×C412yes—
54C32×C22⋊C4—24no—
55C32×C22⋊C4—44no—
56C3×#217—24no—
57C3×#217—44no—
58#1781—31noSylow
59C25×C3—21no—
60C25×C3—31no—
61C25×C3C2×D311yescharacteristic
62C25×C3C22×C311yescharacteristic
63C24×D3C3×C411yescharacteristic, complemented
64C22×C3×D4—32no—
65C22×C3×D4—32no—
66C22×C3×D4—68no—
67C22×C3×D4—62no—
68C22×C3×D4—62no—
69C23×C3×C4—31no—
70C22×#67—22no—
71C22×#67—22no—
72C22×#67—28no—
73C22×#67C3×C412yescomplemented
74C22×#67C22×C312yes—
75C23×Dic3C3×C411yescharacteristic, complemented
76C2×C3×C22⋊C4—24no—
77C2×C3×C22⋊C4—22no—
78C2×C3×C22⋊C4—22no—
79C2×C3×C22⋊C4—22no—
80C2×C3×C22⋊C4—32no—
81C2×C3×C22⋊C4—62no—
82C2×C3×C22⋊C4C2×D312yescomplemented
83C2×C3×C22⋊C4C22×C312yescomplemented
84C2×#217—22no—
85C2×#217C22×C312yescomplemented
86C3×#99—68no—
87#806—28no—
88C23×C32—24no—
89C23×C32—24no—
90C23×C32—22no—
91C23×C32—24no—
92C23×C32—22no—
93C23×C32—24no—
94C23×C32—24no—
95C23×C32—42no—
96C23×C32—42no—
97C23×C32—42no—
98C23×C32—42no—
99C23×C32—416no—
100C23×C32C22⋊C412yes—
101C23×C32C22⋊C412yes—
102C23×C32C22×C411yescharacteristic
103C23×C32C2×D411yescharacteristic
104C23×C32C2×D414yes—
105C23×C32C2×D411yescharacteristic
106C22×C3×D3—28no—
107C22×C3×D3—22no—
108C22×C3×D3—22no—
109C22×C3×D3—416no—
110C22×C3×D3—44no—
111C22×C3×D3—44no—
112C22×C3×D3—44no—
113C22×C3×D3C22⋊C414yescomplemented
114C2×C32×C4—44no—
115C2×C32×C4—42no—
116C3×#67—216no—
117C3×#67—28no—
118C3×#67—28no—
119C2×C3×Dic3—28no—
120C2×C3×Dic3—22no—
121C2×C3×Dic3—22no—
122C2×C3×Dic3—44no—
123C2×C3×Dic3—42no—
124C2×C3×Dic3C22⋊C414yescomplemented
125C23×D4—31no—
126C2×#99—34no—
127#379—31no—
128#379C3×D311yescharacteristic, complemented
129C24×C3—24no—
130C24×C3—24no—
131C24×C3—21no—
132C24×C3—21no—
133C24×C3—22no—
134C24×C3—22no—
135C24×C3—21no—
136C24×C3—32no—
137C24×C3—44no—
138C24×C3—44no—
139C24×C3—44no—
140C24×C3—48no—
141C24×C3—64no—
142C24×C3—62no—
143C24×C3—124no—
144C24×C3C4×D311yescharacteristic
145C24×C3C4×D311yescharacteristic
146C24×C3D1212yes—
147C24×C3#6712yes—
148C24×C3C2×C3×C411yescharacteristic
149C24×C3C2×C3×C411yescharacteristic
150C24×C3C3×D412yes—
151C24×C3C3×D412yes—
152C24×C3C22×D311yescharacteristic
153C24×C3C23×C311yescharacteristic
154C23×D3—22no—
155C23×D3—24no—
156C23×D3—44no—
157C23×D3C2×C3×C412yes—
158C2×C3×D4—38no—
159C2×C3×D4—64no—
160C2×C3×D4—64no—
161C2×C3×D4—616no—
162C2×C3×D4—616no—
163C2×C3×D4—64no—
164C2×C3×D4—62no—
165C2×C3×D4—64no—
166C2×C3×D4—62no—
167C22×C3×C4—24no—
168C22×C3×C4—22no—
169C22×C3×C4—22no—
170C22×C3×C4—32no—
171C22×C3×C4—64no—
172C22×C3×C4—62no—
173C22×C3×C4—62no—
174C2×#67—216no—
175C2×#67—216no—
176C2×#67—24no—
177C2×#67—22no—
178C2×#67—24no—
179C2×#67—22no—
180C2×#67—24no—
181C2×#67—24no—
182C2×#67C3×D418yes—
183C22×Dic3—22no—
184C22×Dic3—24no—
185C22×Dic3—22no—
186C22×Dic3C2×C3×C412yes—
187C3×C22⋊C4—24no—
188C3×C22⋊C4—24no—
189C3×C22⋊C4—44no—
190C3×C22⋊C4—48no—
191C3×C22⋊C4—44no—
192C3×C22⋊C4—44no—
193C3×C22⋊C4—64no—
194C3×C22⋊C4—124no—
195#217—24no—
196#217—44no—
197C22×C32—22no—
198C22×C32—22no—
199C22×C32—28no—
200C22×C32—22no—
201C22×C32—22no—
202C22×C32—22no—
203C22×C32—22no—
204C22×C32—22no—
205C22×C32—22no—
206C22×C32—44no—
207C22×C32—48no—
208C22×C32—48no—
209C22×C32—44no—
210C22×C32#9914yescomplemented
211C22×C32C2×C22⋊C412yes—
212C22×C32C2×C22⋊C411yescharacteristic
213C22×C32#12012yes—
214C22×C32#12012yes—
215C2×C3×D3—24no—
216C2×C3×D3—416no—
217C2×C3×D3—44no—
218C2×C3×D3—44no—
219C2×C3×D3—44no—
220C32×C4—82no—
221C3×Dic3—24no—
222C3×Dic3—82no—
223C25—31no—
224C25C2×C3×D311yescharacteristic
225C22×D4—32no—
226C22×D4—32no—
227C22×D4—68no—
228C22×D4—62no—
229C22×D4—62no—
230C23×C4—31no—
231C2×C22⋊C4—22no—
232C2×C22⋊C4—32no—
233C2×C22⋊C4—62no—
234C2×C22⋊C4C2×C3×D312yescomplemented
235#99—68no—
236C23×C3—24no—
237C23×C3—24no—
238C23×C3—22no—
239C23×C3—22no—
240C23×C3—28no—
241C23×C3—24no—
242C23×C3—24no—
243C23×C3—24no—
244C23×C3—24no—
245C23×C3—22no—
246C23×C3—24no—
247C23×C3—24no—
248C23×C3—22no—
249C23×C3—24no—
250C23×C3—24no—
251C23×C3—22no—
252C23×C3—22no—
253C23×C3—21no—
254C23×C3—21no—
255C23×C3—24no—
256C23×C3—21no—
257C23×C3—34no—
258C23×C3—42no—
259C23×C3—44no—
260C23×C3—42no—
261C23×C3—44no—
262C23×C3—44no—
263C23×C3—44no—
264C23×C3—42no—
265C23×C3—42no—
266C23×C3—42no—
267C23×C3—42no—
268C23×C3—42no—
269C23×C3—42no—
270C23×C3—42no—
271C23×C3—42no—
272C23×C3—44no—
273C23×C3—44no—
274C23×C3—44no—
275C23×C3—44no—
276C23×C3—416no—
277C23×C3—416no—
278C23×C3—432no—
279C23×C3—68no—
280C23×C3—62no—
281C23×C3—62no—
282C23×C3—124no—
283C23×C3—1216no—
284C23×C3—124no—
285C23×C3—124no—
286C23×C3(C2×D3)⋊C412yes—
287C23×C3(C2×D3)⋊C412yes—
288C23×C3C3×C22⋊C412yes—
289C23×C3C3×C22⋊C412yes—
290C23×C3C2×C4×D311yescharacteristic
291C23×C3C2×D1211yescharacteristic
292C23×C3D3×D414yes—
293C23×C3C2×#6711yescharacteristic
294C23×C3C22×C3×C411yescharacteristic
295C23×C3C2×C3×D411yescharacteristic
296C23×C3C2×C3×D414yes—
297C23×C3C2×C3×D411yescharacteristic
298C22×D3—28no—
299C22×D3—22no—
300C22×D3—22no—
301C22×D3—416no—
302C22×D3—44no—
303C22×D3—44no—
304C22×D3—44no—
305C22×D3C3×C22⋊C414yescomplemented
306C3×D4—616no—
307C3×D4—68no—
308C3×D4—68no—
309C2×C3×C4—34no—
310C2×C3×C4—48no—
311C2×C3×C4—44no—
312C2×C3×C4—44no—
313C2×C3×C4—44no—
314C2×C3×C4—42no—
315C2×C3×C4—42no—
316C2×C3×C4—68no—
317C2×C3×C4—62no—
318C2×C3×C4—62no—
319C2×C3×C4—124no—
320C2×C3×C4—122no—
321#67—216no—
322#67—28no—
323#67—28no—
324C2×Dic3—28no—
325C2×Dic3—22no—
326C2×Dic3—22no—
327C2×Dic3—44no—
328C2×Dic3—42no—
329C2×Dic3C3×C22⋊C414yescomplemented
330C2×C32—22no—
331C2×C32—22no—
332C2×C32—24no—
333C2×C32—22no—
334C2×C32—42no—
335C2×C32#37911yescharacteristic
336C2×C32C2×#9912yes—
337C3×D3—44no—
338C24—24no—
339C24—32no—
340C24—44no—
341C24—64no—
342C24—62no—
343C24—124no—
344C24C3×C4×D311yescharacteristic
345C24C3×C4×D311yescharacteristic
346C24C3×D1212yes—
347C24C3×#6712yes—
348C24C22×C3×D311yescharacteristic
349C2×D4—38no—
350C2×D4—64no—
351C2×D4—64no—
352C2×D4—616no—
353C2×D4—616no—
354C2×D4—64no—
355C2×D4—62no—
356C2×D4—64no—
357C2×D4—62no—
358C22×C4—22no—
359C22×C4—32no—
360C22×C4—64no—
361C22×C4—62no—
362C22×C4—62no—
363C22⋊C4—24no—
364C22⋊C4—44no—
365C22⋊C4—64no—
366C22⋊C4—124no—
367C22×C3—24no—
368C22×C3—28no—
369C22×C3—28no—
370C22×C3—22no—
371C22×C3—22no—
372C22×C3—22no—
373C22×C3—22no—
374C22×C3—22no—
375C22×C3—22no—
376C22×C3—22no—
377C22×C3—22no—
378C22×C3—22no—
379C22×C3—22no—
380C22×C3—24no—
381C22×C3—22no—
382C22×C3—22no—
383C22×C3—22no—
384C22×C3—22no—
385C22×C3—22no—
386C22×C3—22no—
387C22×C3—22no—
388C22×C3—22no—
389C22×C3—21no—
390C22×C3—22no—
391C22×C3—24no—
392C22×C3—42no—
393C22×C3—42no—
394C22×C3—42no—
395C22×C3—42no—
396C22×C3—42no—
397C22×C3—42no—
398C22×C3—48no—
399C22×C3—44no—
400C22×C3—44no—
401C22×C3—48no—
402C22×C3—48no—
403C22×C3—48no—
404C22×C3—48no—
405C22×C3—48no—
406C22×C3—416no—
407C22×C3—44no—
408C22×C3—44no—
409C22×C3—416no—
410C22×C3—48no—
411C22×C3—64no—
412C22×C3—124no—
413C22×C3—1216no—
414C22×C3—124no—
415C22×C3—124no—
416C22×C3#80614yescomplemented
417C22×C3C3×#9914yescomplemented
418C22×C3D3×C22⋊C412yes—
419C22×C3#88212yes—
420C22×C3C2×(C2×D3)⋊C411yescharacteristic
421C22×C3#93712yes—
422C22×C3C2×C3×C22⋊C412yes—
423C22×C3C2×C3×C22⋊C411yescharacteristic
424C22×C3C3×#12012yes—
425C22×C3C3×#12012yes—
426C2×D3—24no—
427C2×D3—416no—
428C2×D3—44no—
429C2×D3—44no—
430C2×D3—44no—
431C3×C4—64no—
432C3×C4—84no—
433C3×C4—82no—
434C3×C4—82no—
435C3×C4—242no—
436Dic3—24no—
437Dic3—82no—
438C32#178111yescharacteristic, complemented, Sylow
439C23—22no—
440C23—24no—
441C23—22no—
442C23—24no—
443C23—24no—
444C23—24no—
445C23—24no—
446C23—34no—
447C23—42no—
448C23—42no—
449C23—42no—
450C23—42no—
451C23—416no—
452C23—68no—
453C23—62no—
454C23—62no—
455C23—124no—
456C23—1216no—
457C23—124no—
458C23—124no—
459C23C3×(C2×D3)⋊C412yes—
460C23C3×(C2×D3)⋊C412yes—
461C23C2×C3×C4×D311yescharacteristic
462C23C2×C3×D1211yescharacteristic
463C23C3×D3×D414yes—
464C23C2×C3×#6711yescharacteristic
465D4—616no—
466D4—68no—
467D4—68no—
468C2×C4—34no—
469C2×C4—44no—
470C2×C4—42no—
471C2×C4—68no—
472C2×C4—62no—
473C2×C4—62no—
474C2×C4—124no—
475C2×C4—122no—
476C2×C3—24no—
477C2×C3—22no—
478C2×C3—22no—
479C2×C3—24no—
480C2×C3—22no—
481C2×C3—22no—
482C2×C3—22no—
483C2×C3—24no—
484C2×C3—22no—
485C2×C3—22no—
486C2×C3—21no—
487C2×C3—42no—
488C2×C3—42no—
489C2×C3—44no—
490C2×C3—44no—
491C2×C3—42no—
492C2×C3—42no—
493C2×C3—124no—
494C2×C3C2×#80612yes—
495C2×C3#495511yescharacteristic
496C2×C3C3×#37911yescharacteristic
497C2×C3C2×C3×#9912yes—
498D3—44no—
499C22—28no—
500C22—22no—
501C22—22no—
502C22—22no—
503C22—22no—
504C22—22no—
505C22—22no—
506C22—22no—
507C22—22no—
508C22—44no—
509C22—48no—
510C22—48no—
511C22—44no—
512C22—64no—
513C22—124no—
514C22—124no—
515C22—1216no—
516C22—124no—
517C22C3×#80614yescomplemented
518C22C3×D3×C22⋊C412yes—
519C22C3×#88212yes—
520C22C2×C3×(C2×D3)⋊C411yescharacteristic
521C22C3×#93712yes—
522C4—64no—
523C4—82no—
524C4—242no—
525C3—21no—
526C3#6949811yescharacteristic, direct product factor
527C3C3×#178111yescharacteristic, complemented
528C2—22no—
529C2—22no—
530C2—22no—
531C2—24no—
532C2—42no—
533C2—124no—
534C2C2×C3×#80612yes—
535C2C3×#495511yescharacteristic
subgroupG/H
centerC22×C3C2×(C2×D3)⋊C4
commutatorC23×C3C22×C3×C4
FrattiniC24C22×C3×D3
FittingC32×#379C2
socleC22×C32C2×C22⋊C4
prime radicalC23×C3×#67C2
cosocleC24×C3C23×C3
hypercenterC3×#379D3
hypocenterC3C3×#1781
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C25×C3 ◁ C3×#379

Complements

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

NH ≅ G/Ntype
2. C32×#379C2semidirect
3. C3×#5247C2semidirect
4. C2×C3×#806C2semidirect
6. #69498C3direct (N × H)
8. C24×C3×D3C4semidirect
12. C22×C3×#67C4semidirect
14. C23×C3×Dic3C4semidirect
16. C2×C32×C22⋊C4C22semidirect
18. C2×C3×#217C22semidirect
25. C3×#379D3semidirect
26. C3×#379C2×C3semidirect
27. #5247C2×C3semidirect
28. C2×#806C2×C3semidirect
63. C24×D3C3×C4semidirect
73. C22×#67C3×C4semidirect
75. C23×Dic3C3×C4semidirect
82. C2×C3×C22⋊C4C2×D3semidirect
83. C2×C3×C22⋊C4C22×C3semidirect
85. C2×#217C22×C3semidirect
113. C22×C3×D3C22⋊C4semidirect
124. C2×C3×Dic3C22⋊C4semidirect
128. #379C3×D3semidirect
210. C22×C32#99semidirect
234. C2×C22⋊C4C2×C3×D3semidirect
305. C22×D3C3×C22⋊C4semidirect
329. C2×Dic3C3×C22⋊C4semidirect
416. C22×C3#806semidirect
417. C22×C3C3×#99semidirect
438. C32#1781semidirect
517. C22C3×#806semidirect
526. C3#69498direct (N × H)
527. C3C3×#1781semidirect

Maximal subgroups

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

subgroupindex
C23×C3×#672
C32×#3792
C3×#52472
C2×C3×#8062
C3×#17813
#694983