Finite Group Databasebeta

← C4×#63849 #11800784

Subgroups — C4×#63849 #11800784

Order 1152.

1753 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C42×C3⋊D3C211yesmaximal, characteristic
2C2×#63849C212yesmaximal
3C3×C4×C4⋊Dic3C212yesmaximal, complemented
4C4×#3722C212yesmaximal
5#10591274C212yesmaximal, complemented
6#10591260C212yesmaximal
7#10591252C212yesmaximal, complemented
8C4×Dic32C212yesmaximal, complemented
9C4×#892—32nomaximal
10C22×C4×C3⋊D3C2211yescharacteristic
11C22×C4×C3⋊D3C2211yescharacteristic
12C22×C4×C3⋊D3C2211yescharacteristic
13C2×C32×C42C2211yescharacteristic
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C42×C3⋊D3C418yescomplemented
18C2×C3×C4⋊Dic3C2214yes—
19C2×C3×C4×Dic3C2214yes—
20C2×#3722C2214yes—
21C2×Dic32C2214yes—
22C2×Dic32C2214yes—
23#63849C4116yesdirect product factor
24C3×C3⋊#95C2214yes—
25#63579C2214yes—
26C2×#892—34no—
27C2×C42×D3—32no—
28C2×C42×D3—61no—
29C3×C4×C4⋊C4—32no—
30Dic3×C4⋊C4—34no—
31C4×(C2×D3)⋊C4—34no—
32C4×C4⋊Dic3D312yescomplemented
33C42×Dic3—34no—
34#4666—34no—
35#4648—34no—
36C23×C3⋊D3C2311yescharacteristic
37C22×C32×C4C2311yescharacteristic
38C22×C32×C4C2311yescharacteristic
39C22×C32×C4C2311yescharacteristic
40C22×C3⋊Dic3C2311yescharacteristic
41C22×C3⋊Dic3C2311yescharacteristic
42C22×C3⋊Dic3C2311yescharacteristic
43C2×C4×C3⋊D3—24no—
44C2×C4×C3⋊D3—24no—
45C2×C4×C3⋊D3C2×C414yes—
46C2×C4×C3⋊D3C2×C414yes—
47C2×C4×C3⋊D3C2×C414yes—
48C2×C4×C3⋊D3C2×C418yes—
49C22×C3×Dic3C2318yes—
50C32×C42C2×C414yes—
51C4×C3⋊Dic3C2×C414yes—
52C4×C3⋊Dic3C2×C414yes—
53C4×C3⋊Dic3C2×C414yes—
54C3×C4⋊Dic3C2×C4116yescomplemented
55C3×C4×Dic3—28no—
56#3722C2×C4116yes—
57Dic32—28no—
58Dic32C2×C4116yescomplemented
59C4×#117—91noSylow
60C22×C4×D3—32no—
61C22×C4×D3—32no—
62C22×C4×D3—32no—
63C22×C4×D3—61no—
64C22×C4×D3—61no—
65C22×C4×D3—61no—
66C2×C3×C4⋊C4—34no—
67C2×C3×C42—21no—
68C2×C3×C42—34no—
69C2×C3×C42C2×D312yes—
70C2×(C2×D3)⋊C4—38no—
71C2×C4⋊Dic3C2×D314yes—
72C2×C4×Dic3—32no—
73C2×C4×Dic3—32no—
74C2×C4×Dic3—32no—
75C2×C4×Dic3—38no—
76C2×C4×Dic3—38no—
77C2×C4×Dic3—61no—
78C2×C4×Dic3—61no—
79C2×C4×Dic3—61no—
80C2×C4×Dic3C2×D314yes—
81#892—332no—
82C42×D3—316no—
83C42×D3—68no—
84C3×#95—34no—
85C3⋊#95—38no—
86C3⋊#95C2×D314yes—
87C23×C32C2411yescharacteristic
88C22×C3⋊D3—22no—
89C22×C3⋊D3—22no—
90C22×C3⋊D3C22×C414yes—
91C22×C3⋊D3C22×C412yes—
92C2×C32×C4—22no—
93C2×C32×C4C22×C412yes—
94C2×C32×C4C22×C414yes—
95C2×C32×C4C22×C412yes—
96C2×C32×C4C22×C412yes—
97C2×C32×C4#4114yes—
98C2×C3⋊Dic3—22no—
99C2×C3⋊Dic3C22×C412yes—
100C2×C3⋊Dic3C22×C414yes—
101C2×C3⋊Dic3C22×C412yes—
102C2×C3⋊Dic3C22×C412yes—
103C2×C3⋊Dic3#4114yes—
104C4×C3⋊D3—28no—
105C4×C3⋊D3—28no—
106C4×C3⋊D3C42116yescomplemented
107C2×C3×Dic3—28no—
108C2×C3×Dic3—28no—
109C2×C3×Dic3C22×C4116yes—
110C2×#117—92no—
111C22×C42—91no—
112C4×C4⋊C4—32no—
113C4×C4⋊C4—92no—
114C4×C22⋊C4—92no—
115C4×C22⋊C4—92no—
116#376—92no—
117C43—92no—
118C23×D3—32no—
119C23×D3—61no—
120C22×C3×C4—21no—
121C22×C3×C4—21no—
122C22×C3×C4—21no—
123C22×C3×C4—38no—
124C22×C3×C4C22×D312yes—
125C22×C3×C4C22×D312yes—
126C22×C3×C4C22×D312yes—
127C22×Dic3—32no—
128C22×Dic3—32no—
129C22×Dic3—32no—
130C22×Dic3—61no—
131C22×Dic3—61no—
132C22×Dic3—61no—
133C22×Dic3C22×D318yes—
134C2×C4×D3—38no—
135C2×C4×D3—316no—
136C2×C4×D3—38no—
137C2×C4×D3—38no—
138C2×C4×D3—64no—
139C2×C4×D3—64no—
140C2×C4×D3—64no—
141C2×C4×D3—68no—
142C2×C4×D3—68no—
143C2×C4×D3—68no—
144C2×C4×D3—68no—
145C2×C4×D3—64no—
146C2×C4×D3—64no—
147C3×C4⋊C4—316no—
148C3×C42—24no—
149C3×C42—68no—
150C3×C42C4×D318yes—
151(C2×D3)⋊C4—332no—
152C4⋊Dic3C4×D3116yescomplemented
153C4×Dic3—28no—
154C4×Dic3—38no—
155C4×Dic3—38no—
156C4×Dic3—38no—
157C4×Dic3—332no—
158C4×Dic3—64no—
159C4×Dic3—64no—
160C4×Dic3—64no—
161C4×Dic3—616no—
162C22×C32C23×C411yescharacteristic
163C22×C32C23×C412yes—
164C22×C32C2×#4112yes—
165C22×C32C2×#4112yes—
166C2×C3⋊D3—22no—
167C2×C3⋊D3—22no—
168C2×C3⋊D3—28no—
169C2×C3⋊D3C2×C4214yes—
170C32×C4—22no—
171C32×C4C2×C4214yes—
172C32×C4#11714yescomplemented
173C3⋊Dic3—22no—
174C3⋊Dic3C2×C4214yes—
175C3⋊Dic3#11714yescomplemented
176C3×Dic3—216no—
177C23×C4—91no—
178C23×C4—91no—
179C23×C4—91no—
180#117—916no—
181C2×C4⋊C4—34no—
182C2×C22⋊C4—94no—
183C2×C42—34no—
184C2×C42—94no—
185C2×C42—91no—
186C2×C42—91no—
187C2×C42—91no—
188C2×C42—98no—
189C2×C42—94no—
190C2×C42D3211yescharacteristic
191#95—34no—
192#95—94no—
193C23×C3—21no—
194C23×C3C23×D312yes—
195C22×D3—38no—
196C22×D3—34no—
197C22×D3—62no—
198C22×D3—64no—
199C22×D3—64no—
200C22×D3—64no—
201C22×D3—62no—
202C22×D3—62no—
203C22×D3—64no—
204C2×C3×C4—24no—
205C2×C3×C4—24no—
206C2×C3×C4—24no—
207C2×C3×C4—24no—
208C2×C3×C4—22no—
209C2×C3×C4—22no—
210C2×C3×C4—22no—
211C2×C3×C4—316no—
212C2×C3×C4—68no—
213C2×C3×C4—68no—
214C2×C3×C4C2×C4×D318yes—
215C2×C3×C4C2×C4×D314yes—
216C2×C3×C4C2×C4×D314yes—
217C2×C3×C4C2×C4×D314yes—
218C2×C3×C4#23714yes—
219C2×C3×C4#23914yes—
220C2×Dic3—28no—
221C2×Dic3—28no—
222C2×Dic3—38no—
223C2×Dic3—34no—
224C2×Dic3—34no—
225C2×Dic3—38no—
226C2×Dic3—34no—
227C2×Dic3—62no—
228C2×Dic3—62no—
229C2×Dic3—62no—
230C2×Dic3—64no—
231C2×Dic3—64no—
232C2×Dic3—64no—
233C2×Dic3—62no—
234C2×Dic3—62no—
235C2×Dic3C2×C4×D3116yes—
236C4×D3—332no—
237C4×D3—616no—
238C4×D3—616no—
239C4×D3—616no—
240C4×D3—616no—
241C4×D3—616no—
242C2×C32C22×C4211yescharacteristic
243C2×C32C2×#11711yescharacteristic
244C2×C32C2×#11711yescharacteristic
245C2×C32C4×#4114yes—
246C3⋊D3—24no—
247C24—91no—
248C22×C4—38no—
249C22×C4—91no—
250C22×C4—91no—
251C22×C4—98no—
252C22×C4—94no—
253C22×C4—91no—
254C22×C4—94no—
255C22×C4—94no—
256C22×C4—184no—
257C22×C4—184no—
258C22×C4C2×D3211yescharacteristic
259C22×C4C2×D3211yescharacteristic
260C22×C4C2×D3211yescharacteristic
261C4⋊C4—316no—
262C22⋊C4—916no—
263C42—68no—
264C42—916no—
265C42—94no—
266C42—94no—
267C42—94no—
268C42—188no—
269C42#62414yes—
270C22×C3—22no—
271C22×C3—22no—
272C22×C3—22no—
273C22×C3—21no—
274C22×C3C22×C4×D314yes—
275C22×C3C22×C4×D312yes—
276C22×C3C2×#23712yes—
277C22×C3C2×#23912yes—
278C22×C3D3×#4114yes—
279C2×D3—38no—
280C2×D3—64no—
281C2×D3—64no—
282C2×D3—64no—
283C2×D3—616no—
284C2×D3—64no—
285C2×D3—64no—
286C2×D3—68no—
287C2×D3—68no—
288C3×C4—24no—
289C3×C4—24no—
290C3×C4—24no—
291C3×C4—24no—
292C3×C4—616no—
293C3×C4C42×D318yes—
294C3×C4#89218yescomplemented
295Dic3—216no—
296Dic3—38no—
297Dic3—38no—
298Dic3—64no—
299Dic3—64no—
300Dic3—64no—
301Dic3—64no—
302C32C4×#11711yescharacteristic, complemented, Sylow
303C23—94no—
304C23—92no—
305C23—182no—
306C23—182no—
307C23C22×D3211yescharacteristic
308C2×C4—22no—
309C2×C4—316no—
310C2×C4—68no—
311C2×C4—68no—
312C2×C4—94no—
313C2×C4—94no—
314C2×C4—92no—
315C2×C4—92no—
316C2×C4—916no—
317C2×C4—92no—
318C2×C4—188no—
319C2×C4—182no—
320C2×C4—188no—
321C2×C4#379614yes—
322C2×C4C4×D3214yes—
323C2×C4C2×#62412yes—
324C2×C4C2×#62412yes—
325C2×C4C2×#62412yes—
326C2×C3—21no—
327C2×C3—21no—
328C2×C3—24no—
329C2×C3—21no—
330C2×C3C2×C42×D312yes—
331C2×C3C2×#89212yes—
332C2×C3D3×#11712yes—
333C2×C3C4×#23714yes—
334C2×C3C4×#23914yes—
335D3—68no—
336D3—68no—
337C22—94no—
338C22—182no—
339C22—188no—
340C22—182no—
341C22C2×#379612yes—
342C22C2×C4×D3212yes—
343C22#6430612yes—
344C22C22×#62411yescharacteristic
345C4—22no—
346C4—616no—
347C4—94no—
348C4—94no—
349C4—182no—
350C4#6384914yesdirect product factor
351C4C4×#62414yes—
352C3—21no—
353C3C4×#89212yescomplemented
354C2—184no—
355C2C4×#379614yes—
356C2C2×#6384911yescharacteristic
357C2C2×C4×#62411yescharacteristic
358C2#1059496911yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutatorC2×C32C22×C42
FrattiniC23C22×D32
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC2×C42D32
hypocenterC32C4×#117
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. C3×C4×C4⋊Dic3C2semidirect
5. #10591274C2semidirect
7. #10591252C2semidirect
8. C4×Dic32C2semidirect
17. C42×C3⋊D3C4semidirect
23. #63849C4direct (N × H)
32. C4×C4⋊Dic3D3semidirect
54. C3×C4⋊Dic3C2×C4semidirect
58. Dic32C2×C4semidirect
106. C4×C3⋊D3C42semidirect
152. C4⋊Dic3C4×D3semidirect
172. C32×C4#117semidirect
175. C3⋊Dic3#117semidirect
294. C3×C4#892semidirect
302. C32C4×#117semidirect
350. C4#63849direct (N × H)
353. C3C4×#892semidirect

Maximal subgroups

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

subgroupindex
C2×C42×C3⋊D32
C2×#638492
C3×C4×C4⋊Dic32
C4×#37222
#105912742
#105912602
#105912522
C4×Dic322
C4×#8923