Finite Group Databasebeta

← C3×#69500 #11792796

Subgroups — C3×#69500 #11792796

Order 1152.

1529 conjugacy classes of subgroups.

The subgroup lattice has 551 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#953C212yesmaximal, complemented
2C3×#5493C211yesmaximal, characteristic, complemented
3C32×#379C211yesmaximal, characteristic, complemented
4C2×C3×#806C212yesmaximal, complemented
5C3×#4526C211yesmaximal, characteristic, complemented
6C3×#2021—31nomaximal
7#69500C311yesmaximal, characteristic, direct product factor
8C25×C32C2211yescharacteristic
9C22×C3×#67—22no—
10C22×C3×#67C2212yes—
11C2×C32×C22⋊C4—22no—
12C2×C32×C22⋊C4C2211yescharacteristic
13C2×C32×C22⋊C4C2211yescharacteristic
14C3×#953—24no—
15C3×#953—24no—
16C2×C3×#217—22no—
17C2×C3×#217C2212yes—
18C3×#930—22no—
19C3×#886—22no—
20C3×#882—22no—
21C3×#806—24no—
22C3×#534—31no—
23C2×C3×#120—32no—
24C2×#953C2×C312yescomplemented
25#5493C2×C311yescharacteristic, complemented
26C2×C3×#99—32no—
27C3×#379—21no—
28C3×#379D311yescharacteristic, complemented
29C3×#379C2×C311yescharacteristic, complemented
30C2×#806C2×C312yescomplemented
31C3×#342—31no—
32#4526C2×C311yescharacteristic, complemented
33C24×C32—21no—
34C24×C32—22no—
35C24×C32—22no—
36C24×C32—21no—
37C24×C32—44no—
38C24×C32D412yescomplemented
39C24×C32C2311yescharacteristic
40C23×C3×D3D412yescomplemented
41C22×C32×C4—21no—
42C22×C32×C4D412yescomplemented
43C2×C3×#67—28no—
44C2×C3×#67—22no—
45C2×C3×#67—22no—
46C2×C3×#67—22no—
47C2×C3×#67—22no—
48C2×C3×#67—22no—
49C2×C3×#67—22no—
50C2×C3×#67—48no—
51C22×C3×Dic3—22no—
52C22×C3×Dic3D412yescomplemented
53C2×C3×D12—22no—
54C32×C22⋊C4—22no—
55C32×C22⋊C4—22no—
56C32×C22⋊C4—44no—
57C3×#217—28no—
58C3×#217—22no—
59C3×#217D414yescomplemented
60C3×(C2×D3)⋊C4—24no—
61C3×C4⋊Dic3—22no—
62#2021—31noSylow
63C25×C3—21no—
64C25×C3C2×D311yescharacteristic
65C25×C3C22×C311yescharacteristic
66C22×C3×D4—32no—
67C22×C3×D4—62no—
68C22×#67—22no—
69C22×#67C22×C312yes—
70C3×#123—62no—
71C3×#121—62no—
72C3×#120—62no—
73C3×#120—64no—
74C3×#120—64no—
75C2×C3×C22⋊C4—24no—
76C2×C3×C22⋊C4—22no—
77C2×C3×C22⋊C4—22no—
78C2×C3×C22⋊C4—21no—
79C2×C3×C22⋊C4—21no—
80C2×C3×C22⋊C4—32no—
81C2×C3×C22⋊C4—62no—
82C2×C3×C22⋊C4C2×D311yescharacteristic
83C2×C3×C22⋊C4C2×D311yescharacteristic
84C2×C3×C22⋊C4C22×C311yescharacteristic
85C2×C3×C22⋊C4C22×C311yescharacteristic
86#953—24no—
87#953—24no—
88C2×#217—22no—
89C2×#217C22×C312yes—
90#930—22no—
91#886—22no—
92#882—22no—
93C3×#99—64no—
94#806—24no—
95C23×C32—24no—
96C23×C32—22no—
97C23×C32—28no—
98C23×C32—24no—
99C23×C32—44no—
100C23×C32—42no—
101C23×C32—42no—
102C23×C32—44no—
103C23×C32—44no—
104C23×C32—48no—
105C23×C32—41no—
106C23×C32—42no—
107C23×C32—41no—
108C23×C32C2×D411yescharacteristic
109C23×C32C2×D412yes—
110C23×C32C2×D412yes—
111C23×C32C2×D411yescharacteristic
112C23×C32#4111yescharacteristic
113C22×C3×D3—22no—
114C22×C3×D3—22no—
115C22×C3×D3—22no—
116C22×C3×D3—44no—
117C2×C32×C4—22no—
118C2×C32×C4—42no—
119C2×C32×C4—42no—
120C2×C32×C4—41no—
121C3×#67—416no—
122C3×#67—42no—
123C3×#67—42no—
124C3×#67—42no—
125C3×#67—42no—
126C2×C3×Dic3—22no—
127C2×C3×Dic3—22no—
128C2×C3×Dic3—24no—
129C2×C3×Dic3—22no—
130C2×C3×Dic3—44no—
131C3×D12—82no—
132#534—31no—
133C2×#120—32no—
134C2×#99—32no—
135#379C3×D311yescharacteristic, complemented
136#342—31no—
137C24×C3—22no—
138C24×C3—22no—
139C24×C3—21no—
140C24×C3—22no—
141C24×C3—21no—
142C24×C3—22no—
143C24×C3—21no—
144C24×C3—22no—
145C24×C3—22no—
146C24×C3—21no—
147C24×C3—22no—
148C24×C3—21no—
149C24×C3—32no—
150C24×C3—42no—
151C24×C3—42no—
152C24×C3—44no—
153C24×C3—44no—
154C24×C3—48no—
155C24×C3D1212yescomplemented
156C24×C3C3×D412yescomplemented
157C24×C3C22×D311yescharacteristic
158C24×C3C23×C311yescharacteristic
159C23×D3C3×D412yescomplemented
160C2×C3×D4—62no—
161C2×C3×D4—68no—
162C2×C3×D4—62no—
163C2×C3×D4—62no—
164C2×C3×D4—62no—
165C2×C3×D4—62no—
166C2×C3×D4—62no—
167C2×C3×D4—62no—
168C2×C3×D4—128no—
169C22×C3×C4—22no—
170C22×C3×C4—21no—
171C22×C3×C4—21no—
172C22×C3×C4—22no—
173C22×C3×C4—32no—
174C22×C3×C4—62no—
175C22×C3×C4#6712yescomplemented
176C22×C3×C4C3×D412yescomplemented
177C2×#67—28no—
178C2×#67—22no—
179C2×#67—22no—
180C2×#67—22no—
181C2×#67—22no—
182C2×#67—22no—
183C2×#67—22no—
184C2×#67—48no—
185C22×Dic3—22no—
186C22×Dic3C3×D412yescomplemented
187C2×D12—22no—
188C3×C4⋊C4—62no—
189C3×C22⋊C4—22no—
190C3×C22⋊C4—22no—
191C3×C22⋊C4—22no—
192C3×C22⋊C4—22no—
193C3×C22⋊C4—34no—
194C3×C22⋊C4—42no—
195C3×C22⋊C4—42no—
196C3×C22⋊C4—44no—
197C3×C22⋊C4—44no—
198C3×C22⋊C4—48no—
199C3×C22⋊C4—64no—
200C3×C22⋊C4—68no—
201C3×C22⋊C4—62no—
202#217—28no—
203#217—22no—
204#217C3×D414yescomplemented
205(C2×D3)⋊C4—24no—
206C4⋊Dic3—22no—
207C22×C32—22no—
208C22×C32—24no—
209C22×C32—24no—
210C22×C32—28no—
211C22×C32—41no—
212C22×C32—42no—
213C22×C32—41no—
214C22×C32—44no—
215C22×C32—42no—
216C22×C32—44no—
217C22×C32—48no—
218C22×C32—42no—
219C22×C32—44no—
220C22×C32#12012yes—
221C22×C32#12011yescharacteristic
222C22×C32#12112yes—
223C22×C32#12111yescharacteristic
224C22×C32#12711yescharacteristic
225C2×C3×D3—44no—
226C2×C3×D3—42no—
227C2×C3×D3—44no—
228C2×C3×D3—82no—
229C32×C4—42no—
230C32×C4—81no—
231C3×Dic3—44no—
232C3×Dic3—42no—
233C25C2×C3×D311yescharacteristic
234C22×D4—32no—
235C22×D4—62no—
236#123—62no—
237#121—62no—
238#120—62no—
239#120—64no—
240#120—64no—
241C2×C22⋊C4—22no—
242C2×C22⋊C4—32no—
243C2×C22⋊C4—62no—
244C2×C22⋊C4C2×C3×D311yescharacteristic
245C2×C22⋊C4C2×C3×D311yescharacteristic
246#99—64no—
247C23×C3—28no—
248C23×C3—24no—
249C23×C3—24no—
250C23×C3—28no—
251C23×C3—28no—
252C23×C3—24no—
253C23×C3—24no—
254C23×C3—22no—
255C23×C3—24no—
256C23×C3—22no—
257C23×C3—21no—
258C23×C3—21no—
259C23×C3—22no—
260C23×C3—22no—
261C23×C3—21no—
262C23×C3—44no—
263C23×C3—48no—
264C23×C3—44no—
265C23×C3—44no—
266C23×C3—42no—
267C23×C3—42no—
268C23×C3—48no—
269C23×C3—44no—
270C23×C3—44no—
271C23×C3—42no—
272C23×C3—44no—
273C23×C3—44no—
274C23×C3—42no—
275C23×C3—48no—
276C23×C3—48no—
277C23×C3—44no—
278C23×C3—44no—
279C23×C3—48no—
280C23×C3—44no—
281C23×C3—42no—
282C23×C3—42no—
283C23×C3—48no—
284C23×C3—416no—
285C23×C3—42no—
286C23×C3—41no—
287C23×C3—41no—
288C23×C3—41no—
289C23×C3—42no—
290C23×C3—41no—
291C23×C3—62no—
292C23×C3—62no—
293C23×C3—62no—
294C23×C3—124no—
295C23×C3C2×D1211yescharacteristic
296C23×C3#23511yescharacteristic
297C23×C3D3×D412yes—
298C23×C3D3×D412yes—
299C23×C3C2×#6711yescharacteristic
300C23×C3C2×C3×D411yescharacteristic
301C23×C3C2×C3×D412yes—
302C23×C3C2×C3×D412yes—
303C23×C3C2×C3×D411yescharacteristic
304C23×C3C3×#4111yescharacteristic
305C22×D3—22no—
306C22×D3—22no—
307C22×D3—22no—
308C22×D3—44no—
309C3×D4—1216no—
310C3×D4—122no—
311C3×D4—122no—
312C3×D4—122no—
313C3×D4—122no—
314C3×D4—242no—
315C2×C3×C4—22no—
316C2×C3×C4—22no—
317C2×C3×C4—42no—
318C2×C3×C4—42no—
319C2×C3×C4—42no—
320C2×C3×C4—44no—
321C2×C3×C4—44no—
322C2×C3×C4—42no—
323C2×C3×C4—42no—
324C2×C3×C4—42no—
325C2×C3×C4—41no—
326C2×C3×C4—41no—
327C2×C3×C4—64no—
328C2×C3×C4—62no—
329C2×C3×C4—62no—
330C2×C3×C4—62no—
331C2×C3×C4—124no—
332#67—416no—
333#67—42no—
334#67—42no—
335#67—42no—
336#67—42no—
337C2×Dic3—22no—
338C2×Dic3—22no—
339C2×Dic3—24no—
340C2×Dic3—22no—
341C2×Dic3—44no—
342D12—82no—
343C2×C32—21no—
344C2×C32—21no—
345C2×C32—22no—
346C2×C32—22no—
347C2×C32—44no—
348C2×C32#39211yescharacteristic
349C2×C32B(4,𝔽2)12yes—
350C3×D3—82no—
351C24—22no—
352C24—21no—
353C24—21no—
354C24—22no—
355C24—32no—
356C24—44no—
357C24C3×D1212yescomplemented
358C24C22×C3×D311yescharacteristic
359C2×D4—62no—
360C2×D4—68no—
361C2×D4—62no—
362C2×D4—62no—
363C2×D4—62no—
364C2×D4—62no—
365C2×D4—62no—
366C2×D4—62no—
367C2×D4—128no—
368C22×C4—21no—
369C22×C4—32no—
370C22×C4—62no—
371C22×C4C3×#6712yescomplemented
372C4⋊C4—62no—
373C22⋊C4—22no—
374C22⋊C4—22no—
375C22⋊C4—34no—
376C22⋊C4—44no—
377C22⋊C4—64no—
378C22⋊C4—68no—
379C22⋊C4—62no—
380C22×C3—24no—
381C22×C3—22no—
382C22×C3—24no—
383C22×C3—24no—
384C22×C3—22no—
385C22×C3—28no—
386C22×C3—28no—
387C22×C3—28no—
388C22×C3—24no—
389C22×C3—24no—
390C22×C3—22no—
391C22×C3—22no—
392C22×C3—21no—
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—44no—
396C22×C3—48no—
397C22×C3—41no—
398C22×C3—41no—
399C22×C3—42no—
400C22×C3—41no—
401C22×C3—42no—
402C22×C3—41no—
403C22×C3—42no—
404C22×C3—42no—
405C22×C3—44no—
406C22×C3—48no—
407C22×C3—44no—
408C22×C3—44no—
409C22×C3—44no—
410C22×C3—48no—
411C22×C3—42no—
412C22×C3—44no—
413C22×C3—44no—
414C22×C3—42no—
415C22×C3—48no—
416C22×C3—44no—
417C22×C3—48no—
418C22×C3—48no—
419C22×C3—416no—
420C22×C3—42no—
421C22×C3—42no—
422C22×C3—44no—
423C22×C3—44no—
424C22×C3—124no—
425C22×C3—122no—
426C22×C3—124no—
427C22×C3—242no—
428C22×C3#88212yes—
429C22×C3#88412yes—
430C22×C3#93011yescharacteristic
431C22×C3#93711yescharacteristic
432C22×C3#94011yescharacteristic
433C22×C3C3×#12012yes—
434C22×C3C3×#12011yescharacteristic
435C22×C3C3×#12112yes—
436C22×C3C3×#12111yescharacteristic
437C22×C3C3×#12711yescharacteristic
438C2×D3—44no—
439C2×D3—42no—
440C2×D3—44no—
441C2×D3—82no—
442C3×C4—42no—
443C3×C4—42no—
444C3×C4—82no—
445C3×C4—82no—
446C3×C4—81no—
447C3×C4—81no—
448C3×C4—124no—
449C3×C4—122no—
450Dic3—44no—
451Dic3—42no—
452C32#202111yescharacteristic, complemented, Sylow
453C23—24no—
454C23—28no—
455C23—24no—
456C23—22no—
457C23—44no—
458C23—42no—
459C23—42no—
460C23—44no—
461C23—48no—
462C23—44no—
463C23—42no—
464C23—41no—
465C23—41no—
466C23—62no—
467C23—62no—
468C23—62no—
469C23—124no—
470C23C2×C3×D1211yescharacteristic
471C23C3×#23511yescharacteristic
472C23C3×D3×D412yes—
473C23C3×D3×D412yes—
474C23C2×C3×#6711yescharacteristic
475D4—1216no—
476D4—122no—
477D4—122no—
478D4—122no—
479D4—122no—
480D4—242no—
481C2×C4—22no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—41no—
485C2×C4—64no—
486C2×C4—62no—
487C2×C4—62no—
488C2×C4—62no—
489C2×C4—124no—
490C2×C3—22no—
491C2×C3—22no—
492C2×C3—22no—
493C2×C3—21no—
494C2×C3—22no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—22no—
498C2×C3—21no—
499C2×C3—22no—
500C2×C3—21no—
501C2×C3—22no—
502C2×C3—42no—
503C2×C3—42no—
504C2×C3—48no—
505C2×C3—44no—
506C2×C3—44no—
507C2×C3—242no—
508C2×C3#496011yescharacteristic
509C2×C3#503212yes—
510C2×C3C3×#39211yescharacteristic
511C2×C3C3×B(4,𝔽2)12yes—
512D3—82no—
513C22—22no—
514C22—24no—
515C22—28no—
516C22—24no—
517C22—41no—
518C22—41no—
519C22—42no—
520C22—44no—
521C22—44no—
522C22—42no—
523C22—48no—
524C22—42no—
525C22—44no—
526C22—124no—
527C22—122no—
528C22—124no—
529C22—242no—
530C22C3×#88212yes—
531C22C3×#88412yes—
532C22C3×#93011yescharacteristic
533C22C3×#93711yescharacteristic
534C22C3×#94011yescharacteristic
535C4—42no—
536C4—81no—
537C4—124no—
538C4—122no—
539C3—21no—
540C3#6950011yescharacteristic, direct product factor
541C3C3×#202111yescharacteristic, complemented
542C2—21no—
543C2—22no—
544C2—21no—
545C2—22no—
546C2—44no—
547C2—242no—
548C2C3×#496011yescharacteristic
549C2C3×#503212yes—
subgroupG/H
centerC22×C3#937
commutator, cosocleC24×C3C23×C3
FrattiniC24C22×C3×D3
FittingC32×#379C2
socleC22×C32#120
hypercenterC3×#379D3
hypocenterC3C3×#2021
LCSG ▷ C24×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C24×C3 ◁ C3×#379

Complements

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

NH ≅ G/Ntype
1. C2×C3×#953C2semidirect
2. C3×#5493C2semidirect
3. C32×#379C2semidirect
4. C2×C3×#806C2semidirect
5. C3×#4526C2semidirect
7. #69500C3direct (N × H)
24. C2×#953C2×C3semidirect
25. #5493C2×C3semidirect
28. C3×#379D3semidirect
29. C3×#379C2×C3semidirect
30. C2×#806C2×C3semidirect
32. #4526C2×C3semidirect
38. C24×C32D4semidirect
40. C23×C3×D3D4semidirect
42. C22×C32×C4D4semidirect
52. C22×C3×Dic3D4semidirect
59. C3×#217D4semidirect
135. #379C3×D3semidirect
155. C24×C3D12semidirect
156. C24×C3C3×D4semidirect
159. C23×D3C3×D4semidirect
175. C22×C3×C4#67semidirect
176. C22×C3×C4C3×D4semidirect
186. C22×Dic3C3×D4semidirect
204. #217C3×D4semidirect
357. C24C3×D12semidirect
371. C22×C4C3×#67semidirect
452. C32#2021semidirect
540. C3#69500direct (N × H)
541. C3C3×#2021semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9532
C3×#54932
C32×#3792
C2×C3×#8062
C3×#45262
C3×#20213
#695003