Finite Group Databasebeta

← C3×#73847 #11856261

Subgroups — C3×#73847 #11856261

Order 1152.

2457 conjugacy classes of subgroups.

The subgroup lattice has 451 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C3×Dic3C211yesmaximal, characteristic, complemented
2C2×C3×#953C211yesmaximal, characteristic
3C2×C3×#886C212yesmaximal, complemented
4C32×#379C211yesmaximal, characteristic, complemented
5C3×#4958C214yesmaximal, complemented
6C3×#4950C214yesmaximal, complemented
7C3×#4943C212yesmaximal, complemented
8C3×#2849—31nomaximal
9#73847C311yesmaximal, characteristic, direct product factor
10C25×C32C2211yescharacteristic
11C22×C3×#67C2211yescharacteristic
12C22×C3×#67C2212yes—
13C23×C3×Dic3—28no—
14C23×C3×Dic3—24no—
15C23×C3×Dic3C2214yes—
16C23×C3×Dic3C2212yes—
17C2×C32×C22⋊C4C2212yes—
18C2×C32×C22⋊C4C2214yes—
19C3×#953—24no—
20C2×C3×#217C2211yescharacteristic
21C2×C3×#217C2212yes—
22C2×C3×(C2×D3)⋊C4C2214yescomplemented
23C2×C3×C4⋊Dic3C2214yescomplemented
24C3×#886—28no—
25C3×C3⋊#95C2218yescomplemented
26C24×C3×C4—31no—
27C24×Dic3C2×C311yescharacteristic, complemented
28C2×C3×#123—32no—
29C2×C3×#120—31no—
30C2×#953C2×C311yescharacteristic
31C2×#886C2×C312yescomplemented
32C3×#386—34no—
33C3×#385—34no—
34C3×#381—32no—
35C3×#379—21no—
36C3×#379D311yescharacteristic, complemented
37C3×#379C2×C311yescharacteristic, complemented
38#4958C2×C314yescomplemented
39#4950C2×C314yescomplemented
40#4943C2×C312yescomplemented
41C24×C32—24no—
42C24×C32—28no—
43C24×C32D414yes—
44C24×C32C2311yescharacteristic
45C24×C32C2312yes—
46C23×C3×D3C2311yescharacteristic
47C22×C32×C4C2314yes—
48C2×C3×#67—24no—
49C2×C3×#67—22no—
50C2×C3×#67—24no—
51C2×C3×#67—28no—
52C22×C3×Dic3—232no—
53C22×C3×Dic3—28no—
54C22×C3×Dic3—24no—
55C22×C3×Dic3—24no—
56C22×C3×Dic3—216no—
57C22×C3×Dic3D418yescomplemented
58C22×C3×Dic3C2311yescharacteristic
59C22×C3×Dic3C2312yes—
60C22×C3×Dic3C2314yes—
61C32×C22⋊C4—24no—
62C32×C22⋊C4—28no—
63C3×#217—22no—
64C3×#217—24no—
65C3×(C2×D3)⋊C4—28no—
66C3×C4⋊Dic3—28no—
67#2849—31noSylow
68C25×C3—21no—
69C25×C3C2×D311yescharacteristic
70C25×C3C22×C311yescharacteristic
71C22×C3×D4—32no—
72C22×C3×D4—31no—
73C23×C3×C4—32no—
74C23×C3×C4—34no—
75C23×C3×C4—68no—
76C23×C3×C4—64no—
77C22×#67C22×C312yes—
78C22×#67C22×C311yescharacteristic
79C23×Dic3—24no—
80C23×Dic3—28no—
81C23×Dic3C22×C314yes—
82C23×Dic3C22×C312yes—
83C3×#123—68no—
84C3×#120—64no—
85C2×C3×C4⋊C4—34no—
86C2×C3×C22⋊C4—22no—
87C2×C3×C22⋊C4—24no—
88C2×C3×C22⋊C4—31no—
89C2×C3×C22⋊C4—32no—
90C2×C3×C22⋊C4—34no—
91C2×C3×C22⋊C4C2×D312yes—
92C2×C3×C22⋊C4C2×D314yes—
93C2×C3×C22⋊C4C22×C312yes—
94C2×C3×C22⋊C4C22×C314yes—
95#953—24no—
96C2×#217C22×C311yescharacteristic
97C2×#217C22×C312yes—
98C2×(C2×D3)⋊C4C22×C314yescomplemented
99C2×C4⋊Dic3C22×C314yescomplemented
100#886—28no—
101C3×#95—38no—
102C3⋊#95C22×C318yescomplemented
103C23×C32—232no—
104C23×C32—28no—
105C23×C32—216no—
106C23×C32—24no—
107C23×C32—24no—
108C23×C32—24no—
109C23×C32C2×D412yes—
110C23×C32C2×D414yes—
111C23×C32C2×D414yes—
112C23×C32#4118yes—
113C23×C32C2411yescharacteristic
114C22×C3×D3—22no—
115C22×C3×D3—21no—
116C22×C3×D3—24no—
117C2×C32×C4—24no—
118C2×C32×C4—28no—
119C3×#67—44no—
120C3×#67—48no—
121C2×C3×Dic3—232no—
122C2×C3×Dic3—216no—
123C2×C3×Dic3—24no—
124C2×C3×Dic3—24no—
125C2×C3×Dic3—22no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3—22no—
128C2×C3×Dic3—24no—
129C2×C3×Dic3C2×D418yes—
130C24×C4—31no—
131C2×#123—32no—
132C2×#120—31no—
133#386—34no—
134#385—34no—
135#381—32no—
136#379C3×D311yescharacteristic, complemented
137C24×C3—24no—
138C24×C3—28no—
139C24×C3—24no—
140C24×C3—28no—
141C24×C3—24no—
142C24×C3—21no—
143C24×C3—22no—
144C24×C3—31no—
145C24×C3—44no—
146C24×C3—48no—
147C24×C3D1214yes—
148C24×C3C3×D414yes—
149C24×C3C22×D311yescharacteristic
150C24×C3C22×D312yes—
151C24×C3C23×C311yescharacteristic
152C24×C3C23×C312yes—
153C23×D3C23×C311yescharacteristic
154C2×C3×D4—62no—
155C2×C3×D4—64no—
156C2×C3×D4—64no—
157C2×C3×D4—68no—
158C22×C3×C4—24no—
159C22×C3×C4—38no—
160C22×C3×C4—34no—
161C22×C3×C4—32no—
162C22×C3×C4—31no—
163C22×C3×C4—616no—
164C22×C3×C4—632no—
165C22×C3×C4—68no—
166C22×C3×C4—64no—
167C22×C3×C4—64no—
168C22×C3×C4C22×D314yes—
169C22×C3×C4C23×C314yes—
170C2×#67—24no—
171C2×#67—22no—
172C2×#67—24no—
173C2×#67—28no—
174C22×Dic3—232no—
175C22×Dic3—28no—
176C22×Dic3—24no—
177C22×Dic3—24no—
178C22×Dic3—216no—
179C22×Dic3C3×D418yescomplemented
180C22×Dic3C23×C312yes—
181C22×Dic3C23×C311yescharacteristic
182C22×Dic3C23×C314yes—
183C3×C4⋊C4—68no—
184C3×C22⋊C4—24no—
185C3×C22⋊C4—28no—
186C3×C22⋊C4—24no—
187C3×C22⋊C4—28no—
188C3×C22⋊C4—44no—
189C3×C22⋊C4—48no—
190C3×C22⋊C4—68no—
191C3×C22⋊C4—62no—
192C3×C22⋊C4—64no—
193#217—22no—
194#217—24no—
195(C2×D3)⋊C4—28no—
196C4⋊Dic3—28no—
197C22×C32—232no—
198C22×C32—24no—
199C22×C32—24no—
200C22×C32—24no—
201C22×C32—28no—
202C22×C32—216no—
203C22×C32#12014yes—
204C22×C32#12318yescomplemented
205C22×C32C22×D411yescharacteristic
206C22×C32C22×D412yes—
207C22×C32C2×#4114yes—
208C2×C3×D3—41no—
209C2×C3×D3—42no—
210C2×C3×D3—44no—
211C32×C4—44no—
212C3×Dic3—28no—
213C3×Dic3—41no—
214C3×Dic3—42no—
215C25C2×C3×D311yescharacteristic
216C22×D4—31no—
217C22×D4—32no—
218C23×C4—32no—
219C23×C4—34no—
220C23×C4—68no—
221C23×C4—64no—
222#123—68no—
223#120—64no—
224C2×C4⋊C4—34no—
225C2×C22⋊C4—31no—
226C2×C22⋊C4—32no—
227C2×C22⋊C4—34no—
228C2×C22⋊C4C2×C3×D312yes—
229C2×C22⋊C4C2×C3×D314yes—
230#95—38no—
231C23×C3—232no—
232C23×C3—232no—
233C23×C3—28no—
234C23×C3—216no—
235C23×C3—28no—
236C23×C3—216no—
237C23×C3—24no—
238C23×C3—24no—
239C23×C3—24no—
240C23×C3—24no—
241C23×C3—24no—
242C23×C3—24no—
243C23×C3—21no—
244C23×C3—22no—
245C23×C3—24no—
246C23×C3—24no—
247C23×C3—28no—
248C23×C3—48no—
249C23×C3—416no—
250C23×C3—44no—
251C23×C3—44no—
252C23×C3—44no—
253C23×C3—432no—
254C23×C3—61no—
255C23×C3—62no—
256C23×C3—64no—
257C23×C3C2×D1212yes—
258C23×C3C2×D1214yes—
259C23×C3D3×D414yes—
260C23×C3#23718yes—
261C23×C3C2×C3×D412yes—
262C23×C3C2×C3×D414yes—
263C23×C3C2×C3×D414yes—
264C23×C3C3×#4118yes—
265C23×C3C23×D311yescharacteristic
266C23×C3C24×C311yescharacteristic
267C22×D3—22no—
268C22×D3—21no—
269C22×D3—24no—
270C3×D4—124no—
271C3×D4—128no—
272C2×C3×C4—24no—
273C2×C3×C4—28no—
274C2×C3×C4—24no—
275C2×C3×C4—28no—
276C2×C3×C4—38no—
277C2×C3×C4—44no—
278C2×C3×C4—48no—
279C2×C3×C4—632no—
280C2×C3×C4—616no—
281C2×C3×C4—64no—
282C2×C3×C4—64no—
283C2×C3×C4—61no—
284C2×C3×C4—62no—
285C2×C3×C4—62no—
286C2×C3×C4—64no—
287#67—44no—
288#67—48no—
289C2×Dic3—232no—
290C2×Dic3—216no—
291C2×Dic3—24no—
292C2×Dic3—24no—
293C2×Dic3—22no—
294C2×Dic3—21no—
295C2×Dic3—22no—
296C2×Dic3—24no—
297C2×Dic3C2×C3×D418yes—
298C2×C32—24no—
299C2×C32—28no—
300C2×C32C2×#12011yescharacteristic
301C2×C32C2×#12312yes—
302C2×C32#52514yes—
303C3×D3—81no—
304C24—24no—
305C24—28no—
306C24—31no—
307C24C3×D1214yes—
308C24C22×C3×D311yescharacteristic
309C24C22×C3×D312yes—
310C2×D4—62no—
311C2×D4—64no—
312C2×D4—64no—
313C2×D4—68no—
314C22×C4—34no—
315C22×C4—38no—
316C22×C4—32no—
317C22×C4—31no—
318C22×C4—616no—
319C22×C4—632no—
320C22×C4—68no—
321C22×C4—64no—
322C22×C4—64no—
323C22×C4C22×C3×D314yes—
324C4⋊C4—68no—
325C22⋊C4—24no—
326C22⋊C4—28no—
327C22⋊C4—68no—
328C22⋊C4—62no—
329C22⋊C4—64no—
330C22×C3—232no—
331C22×C3—232no—
332C22×C3—24no—
333C22×C3—24no—
334C22×C3—24no—
335C22×C3—28no—
336C22×C3—216no—
337C22×C3—24no—
338C22×C3—24no—
339C22×C3—24no—
340C22×C3—28no—
341C22×C3—216no—
342C22×C3—24no—
343C22×C3—28no—
344C22×C3—21no—
345C22×C3—22no—
346C22×C3—24no—
347C22×C3—44no—
348C22×C3—44no—
349C22×C3—44no—
350C22×C3—48no—
351C22×C3—416no—
352C22×C3—432no—
353C22×C3—121no—
354C22×C3—122no—
355C22×C3—124no—
356C22×C3#88214yes—
357C22×C3#88618yescomplemented
358C22×C3C3×#12014yes—
359C22×C3C3×#12318yescomplemented
360C22×C3C22×D1211yescharacteristic
361C22×C3C2×D3×D412yes—
362C22×C3C2×#23714yes—
363C22×C3C22×C3×D411yescharacteristic
364C22×C3C22×C3×D412yes—
365C22×C3C2×C3×#4114yes—
366C2×D3—41no—
367C2×D3—42no—
368C2×D3—44no—
369C3×C4—44no—
370C3×C4—44no—
371C3×C4—68no—
372C3×C4—84no—
373C3×C4—121no—
374C3×C4—122no—
375Dic3—28no—
376Dic3—41no—
377Dic3—42no—
378C32#284911yescharacteristic, complemented, Sylow
379C23—232no—
380C23—28no—
381C23—216no—
382C23—24no—
383C23—24no—
384C23—24no—
385C23—61no—
386C23—62no—
387C23—64no—
388C23C2×C3×D1212yes—
389C23C2×C3×D1214yes—
390C23C3×D3×D414yes—
391C23C3×#23718yes—
392C23C23×C3×D311yescharacteristic
393D4—124no—
394D4—128no—
395C2×C4—24no—
396C2×C4—28no—
397C2×C4—38no—
398C2×C4—632no—
399C2×C4—616no—
400C2×C4—64no—
401C2×C4—64no—
402C2×C4—61no—
403C2×C4—62no—
404C2×C4—62no—
405C2×C4—64no—
406C2×C3—24no—
407C2×C3—28no—
408C2×C3—24no—
409C2×C3—28no—
410C2×C3—21no—
411C2×C3—22no—
412C2×C3—24no—
413C2×C3—44no—
414C2×C3—48no—
415C2×C3—241no—
416C2×C3C2×#88211yescharacteristic
417C2×C3C2×#88612yes—
418C2×C3#558614yes—
419C2×C3C2×C3×#12011yescharacteristic
420C2×C3C2×C3×#12312yes—
421C2×C3C3×#52514yes—
422D3—81no—
423C22—232no—
424C22—24no—
425C22—24no—
426C22—24no—
427C22—28no—
428C22—216no—
429C22—121no—
430C22—122no—
431C22—124no—
432C22C3×#88214yes—
433C22C3×#88618yescomplemented
434C22C22×C3×D1211yescharacteristic
435C22C2×C3×D3×D412yes—
436C22C2×C3×#23714yes—
437C4—44no—
438C4—68no—
439C4—121no—
440C4—122no—
441C3—21no—
442C3#7384711yescharacteristic, direct product factor
443C3C3×#284911yescharacteristic, complemented
444C2—24no—
445C2—28no—
446C2—241no—
447C2C2×C3×#88211yescharacteristic
448C2C2×C3×#88612yes—
449C2C3×#558614yes—
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×#379C2
socleC23×C32C24
prime radicalC2×C3×#953C2
hypercenterC3×#379D3
hypocenterC3C3×#2849
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#379

Complements

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

NH ≅ G/Ntype
1. C24×C3×Dic3C2semidirect
3. C2×C3×#886C2semidirect
4. C32×#379C2semidirect
5. C3×#4958C2semidirect
6. C3×#4950C2semidirect
7. C3×#4943C2semidirect
9. #73847C3direct (N × H)
22. C2×C3×(C2×D3)⋊C4C22semidirect
23. C2×C3×C4⋊Dic3C22semidirect
25. C3×C3⋊#95C22semidirect
27. C24×Dic3C2×C3semidirect
31. C2×#886C2×C3semidirect
36. C3×#379D3semidirect
37. C3×#379C2×C3semidirect
38. #4958C2×C3semidirect
39. #4950C2×C3semidirect
40. #4943C2×C3semidirect
57. C22×C3×Dic3D4semidirect
98. C2×(C2×D3)⋊C4C22×C3semidirect
99. C2×C4⋊Dic3C22×C3semidirect
102. C3⋊#95C22×C3semidirect
136. #379C3×D3semidirect
179. C22×Dic3C3×D4semidirect
204. C22×C32#123semidirect
357. C22×C3#886semidirect
359. C22×C3C3×#123semidirect
378. C32#2849semidirect
433. C22C3×#886semidirect
442. C3#73847direct (N × H)
443. C3C3×#2849semidirect

Maximal subgroups

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

subgroupindex
C24×C3×Dic32
C2×C3×#9532
C2×C3×#8862
C32×#3792
C3×#49582
C3×#49502
C3×#49432
C3×#28493
#738473