Finite Group Databasebeta

← C3×#82338 #11806035

Subgroups — C3×#82338 #11806035

Order 1152.

1333 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×D4C211yesmaximal, characteristic
2C3×#5221C212yesmaximal
3C3×#5211C212yesmaximal, complemented
4C3×C4×#217C212yesmaximal, complemented
5C3×Dic3×C4⋊C4C212yesmaximal, complemented
6C3×#4951C214yesmaximal, complemented
7C3×#4936C211yesmaximal, characteristic, complemented
8C3×C4×C4⋊Dic3C211yesmaximal, characteristic, complemented
9C3×#2357—31nomaximal
10#82338C311yesmaximal, characteristic, direct product factor
11C22×C32×D4C2211yescharacteristic
12C23×C32×C4C2212yes—
13C32×C4×D4C418yescomplemented
14C2×C32×C4⋊C4C2211yescharacteristic
15C2×C32×C22⋊C4C2212yes—
16C2×C32×C42C2211yescharacteristic
17C2×C3×#217C2214yes—
18C2×C3×#217C2214yes—
19C2×C3×C4⋊Dic3C2212yes—
20C2×C3×C4⋊Dic3C2212yes—
21C2×C3×C4×Dic3C2212yes—
22C2×C3×C4×Dic3C2214yes—
23C3×C3⋊#95C2211yescharacteristic
24C3×C3⋊#95C2211yescharacteristic
25C3×C3⋊#95C2212yes—
26C3×C3⋊#95C2212yes—
27C3×C3⋊#95C2214yes—
28C2×C3×C4×D4—21no—
29C2×C3×C4×D4D311yescharacteristic
30C2×C3×C4×D4C2×C311yescharacteristic
31C3×#390—32no—
32C3×#388—34no—
33C3×#382—31no—
34C3×#381—32no—
35C3×C4×C4⋊C4—32no—
36C3×C4×C4⋊C4—31no—
37C3×C4×C22⋊C4—32no—
38#5221C2×C312yes—
39#5211C2×C312yescomplemented
40C4×#217C2×C312yescomplemented
41Dic3×C4⋊C4C2×C312yescomplemented
42#4951C2×C314yescomplemented
43#4936C2×C311yescharacteristic, complemented
44C4×C4⋊Dic3C2×C311yescharacteristic, complemented
45C24×C32C2312yes—
46C2×C32×D4—22no—
47C2×C32×D4—22no—
48C2×C32×D4C2×C414yes—
49C22×C32×C4—44no—
50C22×C32×C4C2×C418yes—
51C22×C32×C4C2312yes—
52C22×C32×C4C2311yescharacteristic
53C22×C32×C4C2311yescharacteristic
54C22×C32×C4C2311yescharacteristic
55C22×C3×Dic3C2312yes—
56C22×C3×Dic3C2314yes—
57C22×C3×Dic3C2312yes—
58C32×C4⋊C4C2×C414yes—
59C32×C22⋊C4C2×C418yes—
60C32×C42C2×C414yes—
61C3×#217—28no—
62C3×#217—44no—
63C3×C4⋊Dic3—24no—
64C3×C4⋊Dic3—24no—
65C3×C4×Dic3—24no—
66C3×C4×Dic3—44no—
67#2357—31noSylow
68C22×C3×D4—21no—
69C22×C3×D4C2×D311yescharacteristic
70C22×C3×D4C22×C311yescharacteristic
71C23×C3×C4—22no—
72C23×C3×C4C2×D312yes—
73C23×C3×C4C22×C312yes—
74C3×C4×D4—28no—
75C3×C4×D4Dic318yescomplemented
76C3×C4×D4C3×C418yescomplemented
77C2×C3×C4⋊C4—21no—
78C2×C3×C4⋊C4—32no—
79C2×C3×C4⋊C4—32no—
80C2×C3×C4⋊C4C2×D311yescharacteristic
81C2×C3×C4⋊C4C22×C311yescharacteristic
82C2×C3×C22⋊C4—22no—
83C2×C3×C22⋊C4—34no—
84C2×C3×C22⋊C4—34no—
85C2×C3×C22⋊C4C2×D312yes—
86C2×C3×C22⋊C4C22×C312yes—
87C2×C3×C42—21no—
88C2×C3×C42—32no—
89C2×C3×C42—34no—
90C2×C3×C42C2×D311yescharacteristic
91C2×C3×C42C22×C311yescharacteristic
92C2×#217C22×C314yes—
93C2×#217C22×C314yes—
94C2×C4⋊Dic3C22×C312yes—
95C2×C4⋊Dic3C22×C312yes—
96C2×C4×Dic3C22×C312yes—
97C2×C4×Dic3C22×C314yes—
98C3×#95—31no—
99C3×#95—32no—
100C3×#95—31no—
101C3×#95—34no—
102C3×#95—32no—
103C3⋊#95C22×C311yescharacteristic
104C3⋊#95C22×C311yescharacteristic
105C3⋊#95C22×C312yes—
106C3⋊#95C22×C312yes—
107C3⋊#95C22×C314yes—
108C23×C32—22no—
109C23×C32—22no—
110C23×C32—24no—
111C23×C32—24no—
112C23×C32C22×C414yes—
113C23×C32C2411yescharacteristic
114C32×D4—28no—
115C2×C32×C4—22no—
116C2×C32×C4—22no—
117C2×C32×C4—24no—
118C2×C32×C4—48no—
119C2×C32×C4C22×C412yes—
120C2×C32×C4C22×C412yes—
121C2×C32×C4C22×C414yes—
122C2×C32×C4C22×C412yes—
123C2×C32×C4#4112yes—
124C2×C32×C4#4112yes—
125C2×C3×Dic3—22no—
126C2×C3×Dic3—22no—
127C2×C3×Dic3—22no—
128C2×C3×Dic3—24no—
129C2×C3×Dic3—22no—
130C2×C3×Dic3—24no—
131C2×C3×Dic3—24no—
132C2×C3×Dic3—22no—
133C2×C3×Dic3#4114yes—
134C2×C4×D4C3×D311yescharacteristic
135#390—32no—
136#388—34no—
137#382—31no—
138#381—32no—
139C4×C4⋊C4—32no—
140C4×C4⋊C4—31no—
141C4×C22⋊C4—32no—
142C24×C3—22no—
143C24×C3C22×D312yes—
144C24×C3C23×C312yes—
145C2×C3×D4—24no—
146C2×C3×D4—24no—
147C2×C3×D4—22no—
148C2×C3×D4—22no—
149C2×C3×D4—22no—
150C2×C3×D4—22no—
151C2×C3×D4—24no—
152C2×C3×D4C2×Dic314yes—
153C2×C3×D4C2×C3×C414yes—
154C22×C3×C4—28no—
155C22×C3×C4—21no—
156C22×C3×C4—21no—
157C22×C3×C4—21no—
158C22×C3×C4—22no—
159C22×C3×C4—32no—
160C22×C3×C4—32no—
161C22×C3×C4—34no—
162C22×C3×C4—44no—
163C22×C3×C4—44no—
164C22×C3×C4—48no—
165C22×C3×C4C2×Dic318yes—
166C22×C3×C4C2×C3×C418yes—
167C22×C3×C4C22×D311yescharacteristic
168C22×C3×C4C22×D312yes—
169C22×C3×C4C22×D311yescharacteristic
170C22×C3×C4C22×D311yescharacteristic
171C22×C3×C4C23×C311yescharacteristic
172C22×C3×C4C23×C312yes—
173C22×C3×C4C23×C311yescharacteristic
174C22×C3×C4C23×C311yescharacteristic
175C22×Dic3C23×C312yes—
176C22×Dic3C23×C314yes—
177C22×Dic3C23×C312yes—
178C3×C4⋊C4—24no—
179C3×C4⋊C4—64no—
180C3×C4⋊C4—64no—
181C3×C4⋊C4C2×Dic314yes—
182C3×C4⋊C4C2×C3×C414yes—
183C3×C22⋊C4—28no—
184C3×C22⋊C4—68no—
185C3×C22⋊C4—124no—
186C3×C22⋊C4C2×Dic318yes—
187C3×C22⋊C4C2×C3×C418yes—
188C3×C42—24no—
189C3×C42—64no—
190C3×C42—124no—
191C3×C42C2×Dic314yes—
192C3×C42C2×C3×C414yes—
193#217—28no—
194#217—44no—
195C4⋊Dic3—24no—
196C4⋊Dic3—24no—
197C4×Dic3—24no—
198C4×Dic3—44no—
199C22×C32—24no—
200C22×C32—24no—
201C22×C32—24no—
202C22×C32—44no—
203C22×C32—44no—
204C22×C32C23×C411yescharacteristic
205C22×C32C2×#4111yescharacteristic
206C22×C32C2×#4111yescharacteristic
207C22×C32C2×#4112yes—
208C22×C32H(5,𝔽2)12yes—
209C32×C4—22no—
210C32×C4—22no—
211C32×C4—24no—
212C32×C4#11714yes—
213C3×Dic3—24no—
214C3×Dic3—42no—
215C3×Dic3—44no—
216C22×D4C2×C3×D311yescharacteristic
217C23×C4C2×C3×D312yes—
218C4×D4C3×Dic318yescomplemented
219C2×C4⋊C4—32no—
220C2×C4⋊C4—32no—
221C2×C4⋊C4C2×C3×D311yescharacteristic
222C2×C22⋊C4—34no—
223C2×C22⋊C4—34no—
224C2×C22⋊C4C2×C3×D312yes—
225C2×C42—32no—
226C2×C42—34no—
227C2×C42C2×C3×D311yescharacteristic
228#95—31no—
229#95—32no—
230#95—31no—
231#95—34no—
232#95—32no—
233C23×C3—24no—
234C23×C3—24no—
235C23×C3—22no—
236C23×C3—22no—
237C23×C3—24no—
238C23×C3—24no—
239C23×C3—24no—
240C23×C3—22no—
241C23×C3—22no—
242C23×C3—24no—
243C23×C3—21no—
244C23×C3—24no—
245C23×C3—44no—
246C23×C3—44no—
247C23×C3C22×Dic314yes—
248C23×C3C22×C3×C414yes—
249C23×C3C23×D311yescharacteristic
250C23×C3C24×C311yescharacteristic
251C3×D4—216no—
252C3×D4—28no—
253C3×D4—28no—
254C2×C3×C4—24no—
255C2×C3×C4—24no—
256C2×C3×C4—22no—
257C2×C3×C4—22no—
258C2×C3×C4—22no—
259C2×C3×C4—24no—
260C2×C3×C4—22no—
261C2×C3×C4—22no—
262C2×C3×C4—22no—
263C2×C3×C4—22no—
264C2×C3×C4—22no—
265C2×C3×C4—22no—
266C2×C3×C4—24no—
267C2×C3×C4—34no—
268C2×C3×C4—42no—
269C2×C3×C4—44no—
270C2×C3×C4—48no—
271C2×C3×C4—48no—
272C2×C3×C4—416no—
273C2×C3×C4—62no—
274C2×C3×C4—62no—
275C2×C3×C4—62no—
276C2×C3×C4—64no—
277C2×C3×C4—64no—
278C2×C3×C4—62no—
279C2×C3×C4—64no—
280C2×C3×C4—62no—
281C2×C3×C4#23512yes—
282C2×C3×C4#23512yes—
283C2×C3×C4C22×Dic312yes—
284C2×C3×C4C22×Dic312yes—
285C2×C3×C4C22×Dic314yes—
286C2×C3×C4C22×Dic312yes—
287C2×C3×C4C22×C3×C412yes—
288C2×C3×C4C22×C3×C412yes—
289C2×C3×C4C22×C3×C414yes—
290C2×C3×C4C22×C3×C412yes—
291C2×C3×C4C3×#4112yes—
292C2×C3×C4C3×#4112yes—
293C2×Dic3—22no—
294C2×Dic3—22no—
295C2×Dic3—22no—
296C2×Dic3—24no—
297C2×Dic3—22no—
298C2×Dic3—24no—
299C2×Dic3—24no—
300C2×Dic3—22no—
301C2×Dic3C3×#4114yes—
302C2×C32—44no—
303C2×C32C2×#11711yescharacteristic
304C2×C32C4×#4111yescharacteristic
305C2×C32#51811yescharacteristic
306C2×C32#55312yes—
307C2×C32#55912yes—
308C24C22×C3×D312yes—
309C2×D4—22no—
310C2×D4—22no—
311C2×D4C2×C3×Dic314yes—
312C22×C4—32no—
313C22×C4—32no—
314C22×C4—34no—
315C22×C4—44no—
316C22×C4C2×C3×Dic318yes—
317C22×C4C22×C3×D311yescharacteristic
318C22×C4C22×C3×D312yes—
319C22×C4C22×C3×D311yescharacteristic
320C22×C4C22×C3×D311yescharacteristic
321C4⋊C4—64no—
322C4⋊C4—64no—
323C4⋊C4C2×C3×Dic314yes—
324C22⋊C4—68no—
325C22⋊C4—124no—
326C22⋊C4C2×C3×Dic318yes—
327C42—64no—
328C42—124no—
329C42C2×C3×Dic314yes—
330C22×C3—28no—
331C22×C3—24no—
332C22×C3—24no—
333C22×C3—24no—
334C22×C3—24no—
335C22×C3—24no—
336C22×C3—24no—
337C22×C3—21no—
338C22×C3—21no—
339C22×C3—22no—
340C22×C3—22no—
341C22×C3—21no—
342C22×C3—44no—
343C22×C3—44no—
344C22×C3—48no—
345C22×C3—48no—
346C22×C3—44no—
347C22×C3—44no—
348C22×C3—44no—
349C22×C3—44no—
350C22×C3C2×#23511yescharacteristic
351C22×C3C2×#23511yescharacteristic
352C22×C3#100412yes—
353C22×C3D3×#4112yes—
354C22×C3C23×Dic311yescharacteristic
355C22×C3C23×C3×C411yescharacteristic
356C22×C3C2×C3×#4111yescharacteristic
357C22×C3C2×C3×#4111yescharacteristic
358C22×C3C2×C3×#4112yes—
359C22×C3C3×H(5,𝔽2)12yes—
360C3×C4—24no—
361C3×C4—22no—
362C3×C4—24no—
363C3×C4—22no—
364C3×C4—22no—
365C3×C4—22no—
366C3×C4—24no—
367C3×C4—24no—
368C3×C4—44no—
369C3×C4—42no—
370C3×C4—64no—
371C3×C4—122no—
372C3×C4—124no—
373C3×C4#92614yes—
374C3×C4C3×#11714yes—
375Dic3—24no—
376Dic3—44no—
377Dic3—42no—
378C32#235711yescharacteristic, complemented, Sylow
379C23—22no—
380C23—22no—
381C23—24no—
382C23—24no—
383C23C22×C3×Dic314yes—
384C23C23×C3×D311yescharacteristic
385D4—28no—
386C2×C4—24no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—34no—
390C2×C4—48no—
391C2×C4—62no—
392C2×C4—62no—
393C2×C4—62no—
394C2×C4—64no—
395C2×C4—64no—
396C2×C4—62no—
397C2×C4—64no—
398C2×C4—62no—
399C2×C4C3×#23512yes—
400C2×C4C3×#23512yes—
401C2×C4C22×C3×Dic312yes—
402C2×C4C22×C3×Dic312yes—
403C2×C4C22×C3×Dic314yes—
404C2×C4C22×C3×Dic312yes—
405C2×C3—21no—
406C2×C3—21no—
407C2×C3—22no—
408C2×C3—22no—
409C2×C3—21no—
410C2×C3—48no—
411C2×C3—44no—
412C2×C3—44no—
413C2×C3#555812yes—
414C2×C3#555912yes—
415C2×C3C2×#92611yescharacteristic
416C2×C3#579811yescharacteristic
417C2×C3Dic3×#4111yescharacteristic
418C2×C3C2×C3×#11711yescharacteristic
419C2×C3C3×C4×#4111yescharacteristic
420C2×C3C3×#51811yescharacteristic
421C2×C3C3×#55312yes—
422C2×C3C3×#55912yes—
423C22—24no—
424C22—24no—
425C22—24no—
426C22—44no—
427C22—44no—
428C22C2×C3×#23511yescharacteristic
429C22C2×C3×#23511yescharacteristic
430C22C3×#100412yes—
431C22C3×D3×#4112yes—
432C22C23×C3×Dic311yescharacteristic
433C4—22no—
434C4—24no—
435C4—22no—
436C4—64no—
437C4—122no—
438C4—124no—
439C4C3×#92614yes—
440C3—21no—
441C3#8233811yescharacteristic, direct product factor
442C3C3×#235711yescharacteristic, complemented
443C2—44no—
444C2C3×#555812yes—
445C2C3×#555912yes—
446C2C2×C3×#92611yescharacteristic
447C2C3×#579811yescharacteristic
448C2C3×Dic3×#4111yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC2×C32×C4×D4C2
socleC23×C32C24
prime radicalC22×C32×D4C22
cosocleC23×C3C24×C3
hypercenterC2×C3×C4×D4D3
hypocenterC3C3×#2357
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
3. C3×#5211C2semidirect
4. C3×C4×#217C2semidirect
5. C3×Dic3×C4⋊C4C2semidirect
6. C3×#4951C2semidirect
7. C3×#4936C2semidirect
8. C3×C4×C4⋊Dic3C2semidirect
10. #82338C3direct (N × H)
13. C32×C4×D4C4semidirect
39. #5211C2×C3semidirect
40. C4×#217C2×C3semidirect
41. Dic3×C4⋊C4C2×C3semidirect
42. #4951C2×C3semidirect
43. #4936C2×C3semidirect
44. C4×C4⋊Dic3C2×C3semidirect
75. C3×C4×D4Dic3semidirect
76. C3×C4×D4C3×C4semidirect
218. C4×D4C3×Dic3semidirect
378. C32#2357semidirect
441. C3#82338direct (N × H)
442. C3C3×#2357semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×D42
C3×#52212
C3×#52112
C3×C4×#2172
C3×Dic3×C4⋊C42
C3×#49512
C3×#49362
C3×C4×C4⋊Dic32
C3×#23573
#823383