Finite Group Databasebeta

← C3×#82329 #11803843

Subgroups — C3×#82329 #11803843

Order 1152.

1693 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×D4C211yesmaximal, characteristic, complemented
2C2×C3×#940C211yesmaximal, characteristic
3C2×C3×C4×D12C211yesmaximal, characteristic, complemented
4C3×#5221C211yesmaximal, characteristic, complemented
5C3×#5213C214yesmaximal, complemented
6C3×#4988C211yesmaximal, characteristic, complemented
7C3×#4977C211yesmaximal, characteristic, complemented
8C3×#4956C214yesmaximal, complemented
9C3×#4932C211yesmaximal, characteristic, complemented
10C3×#2328—31nomaximal
11#82329C311yesmaximal, characteristic, direct product factor
12C22×C32×D4C2211yescharacteristic
13C23×C32×C4C2212yes—
14C22×C3×#67C2214yes—
15C22×C3×D12C2211yescharacteristic
16C22×C3×C4×D3C2212yes—
17C32×C4×D4—24no—
18C2×C32×C4⋊C4C2211yescharacteristic
19C2×C32×C22⋊C4C2212yes—
20C2×C32×C42C2211yescharacteristic
21C2×C3×#217C2214yes—
22C3×#940C418yescomplemented
23C2×C3×(C2×D3)⋊C4C2212yes—
24C2×C3×(C2×D3)⋊C4C2214yes—
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×C4×Dic3C2211yescharacteristic
27C2×C3×C4×Dic3C2211yescharacteristic
28C3×C4×D12—24no—
29C3×C3⋊#95C2212yes—
30C3×C3⋊#95C2212yes—
31C3×C3⋊#95C2214yes—
32C2×C3×#127—31no—
33C2×C3×C4×D4—21no—
34C2×C3×C4×D4—31no—
35C2×C3×C4×D4D311yescharacteristic, complemented
36C2×C3×C4×D4C2×C311yescharacteristic, complemented
37C2×#940C2×C311yescharacteristic
38C2×C4×D12C2×C311yescharacteristic, complemented
39C3×#390—31no—
40C3×#390—31no—
41C3×#386—34no—
42C3×#386—34no—
43C3×#382—31no—
44C3×#376—31no—
45#5221C2×C311yescharacteristic, complemented
46#5213C2×C314yescomplemented
47#4988C2×C311yescharacteristic, complemented
48#4977C2×C311yescharacteristic, complemented
49#4956C2×C314yescomplemented
50#4932C2×C311yescharacteristic, complemented
51C24×C32C2312yes—
52C23×C3×D3C2312yes—
53C2×C32×D4—22no—
54C2×C32×D4—22no—
55C2×C32×D4C2×C414yescomplemented
56C22×C32×C4—24no—
57C22×C32×C4—44no—
58C22×C32×C4C2312yes—
59C22×C32×C4C2311yescharacteristic
60C22×C32×C4C2311yescharacteristic
61C22×C32×C4C2311yescharacteristic
62C2×C3×#67—44no—
63C2×C3×#67—44no—
64C2×C3×#67C2×C4116yescomplemented
65C22×C3×Dic3C2312yes—
66C22×C3×Dic3C2312yes—
67C22×C3×Dic3C2312yes—
68C2×C3×D12—22no—
69C2×C3×D12—22no—
70C2×C3×D12C2×C414yescomplemented
71C2×C3×C4×D3—24no—
72C2×C3×C4×D3—44no—
73C32×C4⋊C4—22no—
74C32×C22⋊C4—24no—
75C32×C42D414yescomplemented
76C3×#217—44no—
77C3×(C2×D3)⋊C4—24no—
78C3×(C2×D3)⋊C4—44no—
79C3×C4⋊Dic3—22no—
80C3×C4×Dic3—22no—
81C3×C4×Dic3C2×C414yescomplemented
82#2328—31noSylow
83C22×C3×D4—21no—
84C22×C3×D4—34no—
85C22×C3×D4—31no—
86C22×C3×D4C2×D311yescharacteristic
87C22×C3×D4C22×C311yescharacteristic
88C23×C3×C4—22no—
89C23×C3×C4—32no—
90C23×C3×C4C2×D312yes—
91C23×C3×C4C22×C312yes—
92C22×#67C22×C314yes—
93C22×D12C22×C311yescharacteristic
94C22×C4×D3C22×C312yes—
95C3×#127—38no—
96C3×C4×D4—28no—
97C3×C4×D4—24no—
98C3×C4×D4—24no—
99C3×C4×D4—64no—
100C2×C3×C4⋊C4—21no—
101C2×C3×C4⋊C4—31no—
102C2×C3×C4⋊C4C2×D311yescharacteristic
103C2×C3×C4⋊C4C22×C311yescharacteristic
104C2×C3×C22⋊C4—22no—
105C2×C3×C22⋊C4—32no—
106C2×C3×C22⋊C4—34no—
107C2×C3×C22⋊C4—34no—
108C2×C3×C22⋊C4C2×D312yes—
109C2×C3×C22⋊C4C22×C312yes—
110C2×C3×C42—21no—
111C2×C3×C42—31no—
112C2×C3×C42—31no—
113C2×C3×C42C2×D311yescharacteristic
114C2×C3×C42C22×C311yescharacteristic
115C2×#217C22×C314yes—
116#940C3×C418yescomplemented
117C2×(C2×D3)⋊C4C22×C312yes—
118C2×(C2×D3)⋊C4C22×C314yes—
119C2×C4⋊Dic3C22×C311yescharacteristic
120C2×C4×Dic3C22×C311yescharacteristic
121C2×C4×Dic3C22×C311yescharacteristic
122C4×D12—24no—
123C3×#95—32no—
124C3×#95—32no—
125C3×#95—34no—
126C3⋊#95C22×C312yes—
127C3⋊#95C22×C312yes—
128C3⋊#95C22×C314yes—
129C23×C32—22no—
130C23×C32—22no—
131C23×C32—24no—
132C23×C32—24no—
133C23×C32C22×C414yes—
134C23×C32C2411yescharacteristic
135C22×C3×D3—22no—
136C22×C3×D3—22no—
137C22×C3×D3—24no—
138C22×C3×D3—24no—
139C22×C3×D3C22×C414yes—
140C32×D4—28no—
141C2×C32×C4—22no—
142C2×C32×C4—22no—
143C2×C32×C4—22no—
144C2×C32×C4—24no—
145C2×C32×C4—48no—
146C2×C32×C4C22×C412yes—
147C2×C32×C4C2×D412yes—
148C2×C32×C4C2×D412yes—
149C2×C32×C4C2×D412yes—
150C2×C32×C4#4112yes—
151C3×#67—416no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—24no—
159C2×C3×Dic3C22×C414yes—
160C3×D12—28no—
161C3×C4×D3—48no—
162C2×#127—31no—
163C2×C4×D4—31no—
164C2×C4×D4C3×D311yescharacteristic, complemented
165#390—31no—
166#390—31no—
167#386—34no—
168#386—34no—
169#382—31no—
170#376—31no—
171C24×C3—22no—
172C24×C3—32no—
173C24×C3C22×D312yes—
174C24×C3C23×C312yes—
175C23×D3C23×C312yes—
176C2×C3×D4—24no—
177C2×C3×D4—24no—
178C2×C3×D4—22no—
179C2×C3×D4—22no—
180C2×C3×D4—22no—
181C2×C3×D4—22no—
182C2×C3×D4—24no—
183C2×C3×D4—316no—
184C2×C3×D4—34no—
185C2×C3×D4—62no—
186C2×C3×D4—62no—
187C2×C3×D4—124no—
188C2×C3×D4—124no—
189C2×C3×D4C4×D314yescomplemented
190C2×C3×D4C2×C3×C414yescomplemented
191C22×C3×C4—28no—
192C22×C3×C4—24no—
193C22×C3×C4—24no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—22no—
198C22×C3×C4—32no—
199C22×C3×C4—32no—
200C22×C3×C4—32no—
201C22×C3×C4—44no—
202C22×C3×C4—44no—
203C22×C3×C4—48no—
204C22×C3×C4—64no—
205C22×C3×C4—124no—
206C22×C3×C4C22×D312yes—
207C22×C3×C4C22×D311yescharacteristic
208C22×C3×C4C22×D311yescharacteristic
209C22×C3×C4C22×D311yescharacteristic
210C22×C3×C4C23×C312yes—
211C22×C3×C4C23×C311yescharacteristic
212C22×C3×C4C23×C311yescharacteristic
213C22×C3×C4C23×C311yescharacteristic
214C2×#67—44no—
215C2×#67—44no—
216C2×#67C2×C3×C4116yescomplemented
217C22×Dic3C23×C312yes—
218C22×Dic3C23×C312yes—
219C22×Dic3C23×C312yes—
220C2×D12—22no—
221C2×D12—22no—
222C2×D12C2×C3×C414yescomplemented
223C2×C4×D3—24no—
224C2×C4×D3—44no—
225C3×C4⋊C4—24no—
226C3×C4⋊C4—22no—
227C3×C4⋊C4—22no—
228C3×C4⋊C4—62no—
229C3×C22⋊C4—28no—
230C3×C22⋊C4—24no—
231C3×C22⋊C4—24no—
232C3×C22⋊C4—64no—
233C3×C22⋊C4—124no—
234C3×C22⋊C4—124no—
235C3×C42—24no—
236C3×C42—34no—
237C3×C42—62no—
238C3×C42#6714yescomplemented
239C3×C42C3×D414yescomplemented
240#217—44no—
241(C2×D3)⋊C4—24no—
242(C2×D3)⋊C4—44no—
243C4⋊Dic3—22no—
244C4×Dic3—22no—
245C4×Dic3C2×C3×C414yescomplemented
246C22×C32—24no—
247C22×C32—28no—
248C22×C32—42no—
249C22×C32—42no—
250C22×C32—44no—
251C22×C32C23×C411yescharacteristic
252C22×C32C22×D411yescharacteristic
253C22×C32C2×#4111yescharacteristic
254C22×C32H(5,𝔽2)12yes—
255C22×C32H(5,𝔽2)12yes—
256C2×C3×D3—24no—
257C2×C3×D3—28no—
258C2×C3×D3—42no—
259C2×C3×D3—42no—
260C2×C3×D3—44no—
261C32×C4—22no—
262C32×C4—22no—
263C32×C4—42no—
264C32×C4C4×D414yes—
265C3×Dic3—24no—
266C3×Dic3—42no—
267C3×Dic3—42no—
268C22×D4—34no—
269C22×D4—31no—
270C22×D4C2×C3×D311yescharacteristic
271C23×C4—32no—
272C23×C4C2×C3×D312yes—
273#127—38no—
274C4×D4—24no—
275C4×D4—64no—
276C2×C4⋊C4—31no—
277C2×C4⋊C4C2×C3×D311yescharacteristic
278C2×C22⋊C4—32no—
279C2×C22⋊C4—34no—
280C2×C22⋊C4—34no—
281C2×C22⋊C4C2×C3×D312yes—
282C2×C42—31no—
283C2×C42—31no—
284C2×C42C2×C3×D311yescharacteristic
285#95—32no—
286#95—32no—
287#95—34no—
288C23×C3—24no—
289C23×C3—24no—
290C23×C3—22no—
291C23×C3—24no—
292C23×C3—24no—
293C23×C3—22no—
294C23×C3—22no—
295C23×C3—22no—
296C23×C3—24no—
297C23×C3—24no—
298C23×C3—21no—
299C23×C3—24no—
300C23×C3—34no—
301C23×C3—44no—
302C23×C3—44no—
303C23×C3—62no—
304C23×C3—64no—
305C23×C3—64no—
306C23×C3—62no—
307C23×C3C2×C4×D314yes—
308C23×C3C22×C3×C414yes—
309C23×C3C23×D311yescharacteristic
310C23×C3C24×C311yescharacteristic
311C22×D3—22no—
312C22×D3—22no—
313C22×D3—24no—
314C22×D3—24no—
315C22×D3C22×C3×C414yes—
316C3×D4—216no—
317C3×D4—28no—
318C3×D4—28no—
319C3×D4—68no—
320C3×D4—1216no—
321C2×C3×C4—24no—
322C2×C3×C4—22no—
323C2×C3×C4—22no—
324C2×C3×C4—22no—
325C2×C3×C4—22no—
326C2×C3×C4—24no—
327C2×C3×C4—24no—
328C2×C3×C4—22no—
329C2×C3×C4—22no—
330C2×C3×C4—24no—
331C2×C3×C4—22no—
332C2×C3×C4—22no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—34no—
337C2×C3×C4—42no—
338C2×C3×C4—44no—
339C2×C3×C4—416no—
340C2×C3×C4—48no—
341C2×C3×C4—48no—
342C2×C3×C4—62no—
343C2×C3×C4—62no—
344C2×C3×C4—62no—
345C2×C3×C4—62no—
346C2×C3×C4—62no—
347C2×C3×C4—64no—
348C2×C3×C4—62no—
349C2×C3×C4—128no—
350C2×C3×C4C2×C4×D312yes—
351C2×C3×C4#23512yes—
352C2×C3×C4C2×#6712yes—
353C2×C3×C4C2×#6712yes—
354C2×C3×C4C2×#6712yes—
355C2×C3×C4C22×C3×C412yes—
356C2×C3×C4C2×C3×D412yes—
357C2×C3×C4C2×C3×D412yes—
358C2×C3×C4C2×C3×D412yes—
359C2×C3×C4C3×#4112yes—
360#67—416no—
361C2×Dic3—22no—
362C2×Dic3—22no—
363C2×Dic3—22no—
364C2×Dic3—22no—
365C2×Dic3—22no—
366C2×Dic3—22no—
367C2×Dic3—24no—
368C2×Dic3C22×C3×C414yes—
369D12—28no—
370C4×D3—48no—
371C2×C32—44no—
372C2×C32C2×C4×D411yescharacteristic
373C2×C32#51812yes—
374C2×C32#53511yescharacteristic
375C2×C32#53511yescharacteristic
376C2×C32#54012yes—
377C3×D3—44no—
378C24—32no—
379C24C22×C3×D312yes—
380C2×D4—22no—
381C2×D4—22no—
382C2×D4—316no—
383C2×D4—34no—
384C2×D4—62no—
385C2×D4—62no—
386C2×D4—124no—
387C2×D4—124no—
388C2×D4C3×C4×D314yescomplemented
389C22×C4—24no—
390C22×C4—32no—
391C22×C4—32no—
392C22×C4—32no—
393C22×C4—44no—
394C22×C4—64no—
395C22×C4—124no—
396C22×C4C22×C3×D312yes—
397C22×C4C22×C3×D311yescharacteristic
398C22×C4C22×C3×D311yescharacteristic
399C22×C4C22×C3×D311yescharacteristic
400C4⋊C4—22no—
401C4⋊C4—62no—
402C22⋊C4—24no—
403C22⋊C4—64no—
404C22⋊C4—124no—
405C22⋊C4—124no—
406C42—34no—
407C42—62no—
408C42C3×#6714yescomplemented
409C22×C3—28no—
410C22×C3—24no—
411C22×C3—28no—
412C22×C3—24no—
413C22×C3—28no—
414C22×C3—21no—
415C22×C3—21no—
416C22×C3—22no—
417C22×C3—22no—
418C22×C3—21no—
419C22×C3—48no—
420C22×C3—44no—
421C22×C3—48no—
422C22×C3—44no—
423C22×C3—42no—
424C22×C3—44no—
425C22×C3—42no—
426C22×C3—42no—
427C22×C3—42no—
428C22×C3—44no—
429C22×C3—64no—
430C22×C3—68no—
431C22×C3—122no—
432C22×C3—124no—
433C22×C3—122no—
434C22×C3C22×C4×D311yescharacteristic
435C22×C3C2×#23511yescharacteristic
436C22×C3#100412yes—
437C22×C3#100912yes—
438C22×C3C22×#6711yescharacteristic
439C22×C3C23×C3×C411yescharacteristic
440C22×C3C22×C3×D411yescharacteristic
441C22×C3C2×C3×#4111yescharacteristic
442C22×C3C3×H(5,𝔽2)12yes—
443C22×C3C3×H(5,𝔽2)12yes—
444C2×D3—24no—
445C2×D3—28no—
446C2×D3—42no—
447C2×D3—42no—
448C2×D3—44no—
449C3×C4—24no—
450C3×C4—22no—
451C3×C4—22no—
452C3×C4—22no—
453C3×C4—22no—
454C3×C4—24no—
455C3×C4—42no—
456C3×C4—44no—
457C3×C4—42no—
458C3×C4—42no—
459C3×C4—64no—
460C3×C4—122no—
461C3×C4—122no—
462C3×C4C4×#6714yes—
463C3×C4C3×C4×D414yes—
464Dic3—24no—
465Dic3—42no—
466Dic3—42no—
467C32#232811yescharacteristic, complemented, Sylow
468C23—22no—
469C23—24no—
470C23—24no—
471C23—22no—
472C23—34no—
473C23—62no—
474C23—64no—
475C23—64no—
476C23—62no—
477C23C2×C3×C4×D314yes—
478C23C23×C3×D311yescharacteristic
479D4—28no—
480D4—68no—
481D4—1216no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—24no—
485C2×C4—22no—
486C2×C4—34no—
487C2×C4—48no—
488C2×C4—62no—
489C2×C4—62no—
490C2×C4—62no—
491C2×C4—62no—
492C2×C4—62no—
493C2×C4—64no—
494C2×C4—62no—
495C2×C4—128no—
496C2×C4C2×C3×C4×D312yes—
497C2×C4C3×#23512yes—
498C2×C4C2×C3×#6712yes—
499C2×C4C2×C3×#6712yes—
500C2×C4C2×C3×#6712yes—
501C2×C3—21no—
502C2×C3—22no—
503C2×C3—21no—
504C2×C3—22no—
505C2×C3—21no—
506C2×C3—48no—
507C2×C3—44no—
508C2×C3—44no—
509C2×C3—124no—
510C2×C3#554512yes—
511C2×C3#556212yes—
512C2×C3C2×C4×#6711yescharacteristic
513C2×C3#580511yescharacteristic
514C2×C3#583011yescharacteristic
515C2×C3C2×C3×C4×D411yescharacteristic
516C2×C3C3×#51812yes—
517C2×C3C3×#53511yescharacteristic
518C2×C3C3×#53511yescharacteristic
519C2×C3C3×#54012yes—
520D3—44no—
521C22—24no—
522C22—28no—
523C22—42no—
524C22—44no—
525C22—42no—
526C22—64no—
527C22—68no—
528C22—122no—
529C22—124no—
530C22—122no—
531C22C22×C3×C4×D311yescharacteristic
532C22C2×C3×#23511yescharacteristic
533C22C3×#100412yes—
534C22C3×#100912yes—
535C22C22×C3×#6711yescharacteristic
536C4—22no—
537C4—22no—
538C4—42no—
539C4—64no—
540C4—122no—
541C4—122no—
542C4C3×C4×#6714yes—
543C3—21no—
544C3#8232911yescharacteristic, direct product factor
545C3C3×#232811yescharacteristic, complemented
546C2—44no—
547C2—124no—
548C2C3×#554512yes—
549C2C3×#556212yes—
550C2C2×C3×C4×#6711yescharacteristic
551C2C3×#580511yescharacteristic
552C2C3×#583011yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC2×C32×C4×D4C2
socleC23×C32C24
prime radicalC2×C3×#940C2
cosocleC23×C3C24×C3
hypercenterC2×C3×C4×D4D3
hypocenterC3C3×#2328
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×C4×D4C2semidirect
3. C2×C3×C4×D12C2semidirect
4. C3×#5221C2semidirect
5. C3×#5213C2semidirect
6. C3×#4988C2semidirect
7. C3×#4977C2semidirect
8. C3×#4956C2semidirect
9. C3×#4932C2semidirect
11. #82329C3direct (N × H)
22. C3×#940C4semidirect
35. C2×C3×C4×D4D3semidirect
36. C2×C3×C4×D4C2×C3semidirect
38. C2×C4×D12C2×C3semidirect
45. #5221C2×C3semidirect
46. #5213C2×C3semidirect
47. #4988C2×C3semidirect
48. #4977C2×C3semidirect
49. #4956C2×C3semidirect
50. #4932C2×C3semidirect
55. C2×C32×D4C2×C4semidirect
64. C2×C3×#67C2×C4semidirect
70. C2×C3×D12C2×C4semidirect
75. C32×C42D4semidirect
81. C3×C4×Dic3C2×C4semidirect
116. #940C3×C4semidirect
164. C2×C4×D4C3×D3semidirect
189. C2×C3×D4C4×D3semidirect
190. C2×C3×D4C2×C3×C4semidirect
216. C2×#67C2×C3×C4semidirect
222. C2×D12C2×C3×C4semidirect
238. C3×C42#67semidirect
239. C3×C42C3×D4semidirect
245. C4×Dic3C2×C3×C4semidirect
388. C2×D4C3×C4×D3semidirect
408. C42C3×#67semidirect
467. C32#2328semidirect
544. C3#82329direct (N × H)
545. C3C3×#2328semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×D42
C2×C3×#9402
C2×C3×C4×D122
C3×#52212
C3×#52132
C3×#49882
C3×#49772
C3×#49562
C3×#49322
C3×#23283
#823293