Finite Group Databasebeta

← C3×#73653 #11806889

Subgroups — C3×#73653 #11806889

Order 1152.

1761 conjugacy classes of subgroups.

The subgroup lattice has 535 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#893C212yesmaximal, complemented
2C2×C3×#874C211yesmaximal, characteristic
3C2×C3×C4×D12C212yesmaximal, complemented
4C32×C4×C4⋊C4C211yesmaximal, characteristic, complemented
5C3×#4988C212yesmaximal, complemented
6C3×#4939C212yesmaximal, complemented
7C3×C4×C4⋊Dic3C211yesmaximal, characteristic, complemented
8C3×#4665C214yesmaximal, complemented
9C3×#2366—31nomaximal
10#73653C311yesmaximal, characteristic, direct product factor
11C22×C3×D12C2212yes—
12C22×C3×D12C2212yes—
13C22×C3×D12C2212yes—
14C22×C3×C4×D3C2214yes—
15C2×C32×C4⋊C4C2211yescharacteristic
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×C32×C42C2212yes—
18C2×C32×C42C2211yescharacteristic
19C2×C3×(C2×D3)⋊C4C2214yes—
20C2×C3×(C2×D3)⋊C4C2214yes—
21C2×C3×(C2×D3)⋊C4C2214yes—
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×C4×Dic3C2212yes—
25C3×#893—28no—
26C3×#874C418yescomplemented
27C3×C4×D12—28no—
28C32×#95C2212yes—
29C3×C3⋊#95C2212yes—
30C2×C3×#127—31no—
31C2×C3×C4×D4—32no—
32C2×C3×C4×D4—32no—
33C2×#893C2×C312yescomplemented
34C2×#874C2×C311yescharacteristic
35C2×C4×D12C2×C312yescomplemented
36C3×#390—32no—
37C3×#390—32no—
38C3×#386—34no—
39C3×C4×C4⋊C4—21no—
40C3×C4×C4⋊C4—31no—
41C3×C4×C4⋊C4D311yescharacteristic, complemented
42C3×C4×C4⋊C4C2×C311yescharacteristic, complemented
43#4988C2×C312yescomplemented
44#4939C2×C312yescomplemented
45C4×C4⋊Dic3C2×C311yescharacteristic, complemented
46#4665C2×C314yescomplemented
47C23×C3×D3C2314yes—
48C22×C32×C4C2312yes—
49C22×C32×C4C2311yescharacteristic
50C22×C32×C4C2312yes—
51C22×C32×C4C2311yescharacteristic
52C22×C32×C4C2311yescharacteristic
53C22×C3×Dic3C2312yes—
54C22×C3×Dic3C2312yes—
55C2×C3×D12—24no—
56C2×C3×D12—24no—
57C2×C3×D12—24no—
58C2×C3×D12—24no—
59C2×C3×D12—42no—
60C2×C3×D12—42no—
61C2×C3×D12C2×C418yescomplemented
62C2×C3×D12C2×C418yescomplemented
63C2×C3×D12C2×C418yescomplemented
64C2×C3×C4×D3—28no—
65C2×C3×C4×D3—28no—
66C2×C3×C4×D3—44no—
67C32×C4⋊C4—22no—
68C32×C4⋊C4D414yescomplemented
69C32×C42—24no—
70C32×C42C2×C414yescomplemented
71C3×(C2×D3)⋊C4—28no—
72C3×(C2×D3)⋊C4—28no—
73C3×(C2×D3)⋊C4—44no—
74C3×C4⋊Dic3—22no—
75C3×C4⋊Dic3D414yescomplemented
76C3×C4×Dic3—24no—
77#2366—31noSylow
78C22×C3×D4—32no—
79C22×C3×D4—32no—
80C22×C3×D4—32no—
81C23×C3×C4—34no—
82C22×D12C22×C312yes—
83C22×D12C22×C312yes—
84C22×D12C22×C312yes—
85C22×C4×D3C22×C314yes—
86C3×#127—38no—
87C3×C4×D4—68no—
88C3×C4×D4—68no—
89C2×C3×C4⋊C4—21no—
90C2×C3×C4⋊C4—21no—
91C2×C3×C4⋊C4—31no—
92C2×C3×C4⋊C4—31no—
93C2×C3×C4⋊C4C2×D311yescharacteristic
94C2×C3×C4⋊C4C2×D311yescharacteristic
95C2×C3×C4⋊C4C22×C311yescharacteristic
96C2×C3×C4⋊C4C22×C311yescharacteristic
97C2×C3×C22⋊C4—34no—
98C2×C3×C22⋊C4—34no—
99C2×C3×C22⋊C4—34no—
100C2×C3×C42—21no—
101C2×C3×C42—22no—
102C2×C3×C42—32no—
103C2×C3×C42C2×D312yes—
104C2×C3×C42C2×D311yescharacteristic
105C2×C3×C42C22×C312yes—
106C2×C3×C42C22×C311yescharacteristic
107C2×(C2×D3)⋊C4C22×C314yes—
108C2×(C2×D3)⋊C4C22×C314yes—
109C2×(C2×D3)⋊C4C22×C314yes—
110C2×C4⋊Dic3C22×C311yescharacteristic
111C2×C4⋊Dic3C22×C311yescharacteristic
112C2×C4×Dic3C22×C312yes—
113#893—28no—
114#874C3×C418yescomplemented
115C4×D12—28no—
116C3×#95—22no—
117C3×#95—32no—
118C3×#95C2×D312yes—
119C3×#95C22×C312yes—
120C3⋊#95C22×C312yes—
121C23×C32C2411yescharacteristic
122C22×C3×D3—24no—
123C22×C3×D3—24no—
124C22×C3×D3—24no—
125C22×C3×D3—24no—
126C22×C3×D3—24no—
127C22×C3×D3—24no—
128C22×C3×D3C22×C418yes—
129C2×C32×C4—22no—
130C2×C32×C4—22no—
131C2×C32×C4—22no—
132C2×C32×C4—21no—
133C2×C32×C4—21no—
134C2×C32×C4—22no—
135C2×C32×C4—22no—
136C2×C32×C4C22×C412yes—
137C2×C32×C4C22×C412yes—
138C2×C32×C4C22×C412yes—
139C2×C32×C4C2×D414yes—
140C2×C32×C4C2×D412yes—
141C2×C32×C4C2×D412yes—
142C2×C32×C4#4112yes—
143C2×C32×C4#4112yes—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3C2×D414yes—
150C3×D12—216no—
151C3×D12—216no—
152C3×D12—48no—
153C3×C4×D3—416no—
154C2×#127—31no—
155C2×C4×D4—32no—
156C2×C4×D4—32no—
157#390—32no—
158#390—32no—
159#386—34no—
160C4×C4⋊C4—31no—
161C4×C4⋊C4C3×D311yescharacteristic, complemented
162C24×C3—34no—
163C23×D3C23×C314yes—
164C2×C3×D4—38no—
165C2×C3×D4—38no—
166C2×C3×D4—38no—
167C2×C3×D4—64no—
168C2×C3×D4—64no—
169C2×C3×D4—64no—
170C2×C3×D4—64no—
171C2×C3×D4—122no—
172C2×C3×D4—122no—
173C22×C3×C4—21no—
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—22no—
177C22×C3×C4—22no—
178C22×C3×C4—32no—
179C22×C3×C4—32no—
180C22×C3×C4—68no—
181C22×C3×C4—68no—
182C22×C3×C4—124no—
183C22×C3×C4C22×D312yes—
184C22×C3×C4C22×D311yescharacteristic
185C22×C3×C4C22×D312yes—
186C22×C3×C4C22×D311yescharacteristic
187C22×C3×C4C22×D311yescharacteristic
188C22×C3×C4C23×C312yes—
189C22×C3×C4C23×C311yescharacteristic
190C22×C3×C4C23×C312yes—
191C22×C3×C4C23×C311yescharacteristic
192C22×C3×C4C23×C311yescharacteristic
193C22×Dic3C23×C312yes—
194C22×Dic3C23×C312yes—
195C2×D12—24no—
196C2×D12—24no—
197C2×D12—24no—
198C2×D12—24no—
199C2×D12—42no—
200C2×D12—42no—
201C2×D12C2×C3×C418yescomplemented
202C2×D12C2×C3×C418yescomplemented
203C2×D12C2×C3×C418yescomplemented
204C2×C4×D3—28no—
205C2×C4×D3—28no—
206C2×C4×D3—44no—
207C3×C4⋊C4—24no—
208C3×C4⋊C4—22no—
209C3×C4⋊C4—22no—
210C3×C4⋊C4—24no—
211C3×C4⋊C4—34no—
212C3×C4⋊C4—62no—
213C3×C4⋊C4D1214yescomplemented
214C3×C4⋊C4C3×D414yescomplemented
215C3×C22⋊C4—68no—
216C3×C22⋊C4—68no—
217C3×C22⋊C4—124no—
218C3×C42—24no—
219C3×C42—24no—
220C3×C42—24no—
221C3×C42—44no—
222C3×C42—64no—
223C3×C42C4×D314yescomplemented
224C3×C42C2×C3×C414yescomplemented
225(C2×D3)⋊C4—28no—
226(C2×D3)⋊C4—28no—
227(C2×D3)⋊C4—44no—
228C4⋊Dic3—22no—
229C4⋊Dic3C3×D414yescomplemented
230C4×Dic3—24no—
231C22×C32C23×C411yescharacteristic
232C22×C32C22×D411yescharacteristic
233C22×C32C22×D411yescharacteristic
234C22×C32C2×#4111yescharacteristic
235C22×C32C2×#4111yescharacteristic
236C22×C32H(5,𝔽2)11yescharacteristic
237C22×C32H(5,𝔽2)11yescharacteristic
238C2×C3×D3—28no—
239C2×C3×D3—28no—
240C2×C3×D3—28no—
241C2×C3×D3—44no—
242C2×C3×D3—44no—
243C2×C3×D3—44no—
244C2×C3×D3—44no—
245C32×C4—22no—
246C32×C4—24no—
247C32×C4—42no—
248C32×C4C4×D414yescomplemented
249C32×C4C4×D414yescomplemented
250C3×Dic3—24no—
251C3×Dic3—42no—
252C22×D4—32no—
253C22×D4—32no—
254C22×D4—32no—
255C23×C4—34no—
256#127—38no—
257C4×D4—68no—
258C4×D4—68no—
259C2×C4⋊C4—31no—
260C2×C4⋊C4—31no—
261C2×C4⋊C4C2×C3×D311yescharacteristic
262C2×C4⋊C4C2×C3×D311yescharacteristic
263C2×C22⋊C4—34no—
264C2×C22⋊C4—34no—
265C2×C22⋊C4—34no—
266C2×C42—32no—
267C2×C42C2×C3×D312yes—
268C2×C42C2×C3×D311yescharacteristic
269#95—32no—
270#95C2×C3×D312yes—
271C23×C3—21no—
272C23×C3—38no—
273C23×C3—64no—
274C23×C3—64no—
275C23×C3—64no—
276C23×C3—64no—
277C23×C3—64no—
278C23×C3—64no—
279C23×C3C23×D311yescharacteristic
280C23×C3C24×C311yescharacteristic
281C22×D3—24no—
282C22×D3—24no—
283C22×D3—24no—
284C22×D3—24no—
285C22×D3—24no—
286C22×D3—24no—
287C22×D3C22×C3×C418yes—
288C3×D4—616no—
289C3×D4—616no—
290C3×D4—128no—
291C2×C3×C4—22no—
292C2×C3×C4—22no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—22no—
296C2×C3×C4—22no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—24no—
300C2×C3×C4—22no—
301C2×C3×C4—22no—
302C2×C3×C4—22no—
303C2×C3×C4—22no—
304C2×C3×C4—22no—
305C2×C3×C4—22no—
306C2×C3×C4—22no—
307C2×C3×C4—22no—
308C2×C3×C4—22no—
309C2×C3×C4—22no—
310C2×C3×C4—24no—
311C2×C3×C4—22no—
312C2×C3×C4—22no—
313C2×C3×C4—22no—
314C2×C3×C4—34no—
315C2×C3×C4—42no—
316C2×C3×C4—42no—
317C2×C3×C4—42no—
318C2×C3×C4—41no—
319C2×C3×C4—41no—
320C2×C3×C4—42no—
321C2×C3×C4—62no—
322C2×C3×C4—62no—
323C2×C3×C4—62no—
324C2×C3×C4—62no—
325C2×C3×C4—62no—
326C2×C3×C4—1216no—
327C2×C3×C4C2×C4×D312yes—
328C2×C3×C4C2×C4×D312yes—
329C2×C3×C4C2×C4×D312yes—
330C2×C3×C4C2×D1214yes—
331C2×C3×C4C2×D1212yes—
332C2×C3×C4#23512yes—
333C2×C3×C4D3×D412yes—
334C2×C3×C4#23912yes—
335C2×C3×C4C22×C3×C412yes—
336C2×C3×C4C22×C3×C412yes—
337C2×C3×C4C22×C3×C412yes—
338C2×C3×C4C2×C3×D414yes—
339C2×C3×C4C2×C3×D412yes—
340C2×C3×C4C2×C3×D412yes—
341C2×C3×C4C3×#4112yes—
342C2×C3×C4C3×#4112yes—
343C2×Dic3—22no—
344C2×Dic3—22no—
345C2×Dic3—22no—
346C2×Dic3—22no—
347C2×Dic3—22no—
348C2×Dic3C2×C3×D414yes—
349D12—216no—
350D12—216no—
351D12—48no—
352C4×D3—416no—
353C2×C32C2×C4×D411yescharacteristic
354C2×C32C2×C4×D411yescharacteristic
355C2×C32#51811yescharacteristic
356C2×C32D4211yescharacteristic
357C2×C32#55011yescharacteristic
358C2×C32#55011yescharacteristic
359C2×C32#55911yescharacteristic
360C3×D3—48no—
361C24—34no—
362C2×D4—38no—
363C2×D4—38no—
364C2×D4—38no—
365C2×D4—64no—
366C2×D4—64no—
367C2×D4—64no—
368C2×D4—64no—
369C2×D4—122no—
370C2×D4—122no—
371C22×C4—32no—
372C22×C4—32no—
373C22×C4—68no—
374C22×C4—68no—
375C22×C4—124no—
376C22×C4C22×C3×D312yes—
377C22×C4C22×C3×D311yescharacteristic
378C22×C4C22×C3×D312yes—
379C22×C4C22×C3×D311yescharacteristic
380C22×C4C22×C3×D311yescharacteristic
381C4⋊C4—22no—
382C4⋊C4—34no—
383C4⋊C4—62no—
384C4⋊C4C3×D1214yescomplemented
385C22⋊C4—68no—
386C22⋊C4—68no—
387C22⋊C4—124no—
388C42—24no—
389C42—64no—
390C42C3×C4×D314yescomplemented
391C22×C3—21no—
392C22×C3—21no—
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—68no—
399C22×C3—68no—
400C22×C3—68no—
401C22×C3—124no—
402C22×C3—124no—
403C22×C3—124no—
404C22×C3—124no—
405C22×C3C22×C4×D311yescharacteristic
406C22×C3C22×D1211yescharacteristic
407C22×C3C2×#23511yescharacteristic
408C22×C3C2×D3×D411yescharacteristic
409C22×C3C2×#23911yescharacteristic
410C22×C3#100911yescharacteristic
411C22×C3#100911yescharacteristic
412C22×C3C23×C3×C411yescharacteristic
413C22×C3C22×C3×D411yescharacteristic
414C22×C3C22×C3×D411yescharacteristic
415C22×C3C2×C3×#4111yescharacteristic
416C22×C3C2×C3×#4111yescharacteristic
417C22×C3C3×H(5,𝔽2)11yescharacteristic
418C22×C3C3×H(5,𝔽2)11yescharacteristic
419C2×D3—28no—
420C2×D3—28no—
421C2×D3—28no—
422C2×D3—44no—
423C2×D3—44no—
424C2×D3—44no—
425C2×D3—44no—
426C3×C4—22no—
427C3×C4—24no—
428C3×C4—22no—
429C3×C4—24no—
430C3×C4—24no—
431C3×C4—24no—
432C3×C4—42no—
433C3×C4—44no—
434C3×C4—44no—
435C3×C4—42no—
436C3×C4—42no—
437C3×C4—64no—
438C3×C4—122no—
439C3×C4C4×D1214yescomplemented
440C3×C4#89314yescomplemented
441C3×C4C3×C4×D414yescomplemented
442C3×C4C3×C4×D414yescomplemented
443Dic3—24no—
444Dic3—42no—
445C32#236611yescharacteristic, complemented, Sylow
446C23—38no—
447C23—64no—
448C23—64no—
449C23—64no—
450C23—64no—
451C23—64no—
452C23—64no—
453C23C23×C3×D311yescharacteristic
454D4—616no—
455D4—616no—
456D4—128no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—34no—
465C2×C4—62no—
466C2×C4—62no—
467C2×C4—62no—
468C2×C4—62no—
469C2×C4—62no—
470C2×C4—1216no—
471C2×C4C2×C3×C4×D312yes—
472C2×C4C2×C3×C4×D312yes—
473C2×C4C2×C3×C4×D312yes—
474C2×C4C2×C3×D1214yes—
475C2×C4C2×C3×D1212yes—
476C2×C4C3×#23512yes—
477C2×C4C3×D3×D412yes—
478C2×C4C3×#23912yes—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—21no—
484C2×C3—21no—
485C2×C3—21no—
486C2×C3—128no—
487C2×C3C2×C4×D1211yescharacteristic
488C2×C3C2×#89311yescharacteristic
489C2×C3#552111yescharacteristic
490C2×C3D4×D1211yescharacteristic
491C2×C3#555311yescharacteristic
492C2×C3#557711yescharacteristic
493C2×C3#558511yescharacteristic
494C2×C3C2×C3×C4×D411yescharacteristic
495C2×C3C2×C3×C4×D411yescharacteristic
496C2×C3C3×#51811yescharacteristic
497C2×C3C3×D4211yescharacteristic
498C2×C3C3×#55011yescharacteristic
499C2×C3C3×#55011yescharacteristic
500C2×C3C3×#55911yescharacteristic
501D3—48no—
502C22—68no—
503C22—68no—
504C22—68no—
505C22—124no—
506C22—124no—
507C22—124no—
508C22—124no—
509C22C22×C3×C4×D311yescharacteristic
510C22C22×C3×D1211yescharacteristic
511C22C2×C3×#23511yescharacteristic
512C22C2×C3×D3×D411yescharacteristic
513C22C2×C3×#23911yescharacteristic
514C22C3×#100911yescharacteristic
515C22C3×#100911yescharacteristic
516C4—22no—
517C4—24no—
518C4—42no—
519C4—64no—
520C4—122no—
521C4C3×C4×D1214yescomplemented
522C4C3×#89314yescomplemented
523C3—21no—
524C3#7365311yescharacteristic, direct product factor
525C3C3×#236611yescharacteristic, complemented
526C2—128no—
527C2C2×C3×C4×D1211yescharacteristic
528C2C2×C3×#89311yescharacteristic
529C2C3×#552111yescharacteristic
530C2C3×D4×D1211yescharacteristic
531C2C3×#555311yescharacteristic
532C2C3×#557711yescharacteristic
533C2C3×#558511yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×C4×C4⋊C4C2
socleC23×C32C24
prime radicalC2×C3×#874C2
cosocleC23×C3C24×C3
hypercenterC3×C4×C4⋊C4D3
hypocenterC3C3×#2366
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#893C2semidirect
3. C2×C3×C4×D12C2semidirect
4. C32×C4×C4⋊C4C2semidirect
5. C3×#4988C2semidirect
6. C3×#4939C2semidirect
7. C3×C4×C4⋊Dic3C2semidirect
8. C3×#4665C2semidirect
10. #73653C3direct (N × H)
26. C3×#874C4semidirect
33. C2×#893C2×C3semidirect
35. C2×C4×D12C2×C3semidirect
41. C3×C4×C4⋊C4D3semidirect
42. C3×C4×C4⋊C4C2×C3semidirect
43. #4988C2×C3semidirect
44. #4939C2×C3semidirect
45. C4×C4⋊Dic3C2×C3semidirect
46. #4665C2×C3semidirect
61. C2×C3×D12C2×C4semidirect
62. C2×C3×D12C2×C4semidirect
63. C2×C3×D12C2×C4semidirect
68. C32×C4⋊C4D4semidirect
70. C32×C42C2×C4semidirect
75. C3×C4⋊Dic3D4semidirect
114. #874C3×C4semidirect
161. C4×C4⋊C4C3×D3semidirect
201. C2×D12C2×C3×C4semidirect
202. C2×D12C2×C3×C4semidirect
203. C2×D12C2×C3×C4semidirect
213. C3×C4⋊C4D12semidirect
214. C3×C4⋊C4C3×D4semidirect
223. C3×C42C4×D3semidirect
224. C3×C42C2×C3×C4semidirect
229. C4⋊Dic3C3×D4semidirect
248. C32×C4C4×D4semidirect
249. C32×C4C4×D4semidirect
384. C4⋊C4C3×D12semidirect
390. C42C3×C4×D3semidirect
439. C3×C4C4×D12semidirect
440. C3×C4#893semidirect
441. C3×C4C3×C4×D4semidirect
442. C3×C4C3×C4×D4semidirect
445. C32#2366semidirect
521. C4C3×C4×D12semidirect
522. C4C3×#893semidirect
524. C3#73653direct (N × H)
525. C3C3×#2366semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8932
C2×C3×#8742
C2×C3×C4×D122
C32×C4×C4⋊C42
C3×#49882
C3×#49392
C3×C4×C4⋊Dic32
C3×#46652
C3×#23663
#736533