Finite Group Databasebeta

← C22×#63563 #11857732

Subgroups — C22×#63563 #11857732

Order 1152.

2353 conjugacy classes of subgroups.

The subgroup lattice has 343 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×D12C211yesmaximal, characteristic
2C22×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
3C23×C3×C3⋊C8C211yesmaximal, characteristic, complemented
4C2×#63563C2112yesmaximal, direct product factor
5C22×#832—31nomaximal
6C22×#821—31nomaximal
7C24×C3×D3—21no—
8C23×C32×C4C2211yescharacteristic
9C23×C3⋊Dic3—21no—
10C22×C3×D12—24no—
11C22×C3×D12—23no—
12C22×C3×D12C418yescomplemented
13C22×C3×D12C2216yes—
14C2×C4⋊(C3⋊Dic3)—23no—
15C2×C4⋊(C3⋊Dic3)C2216yescomplemented
16C22×C3×C3⋊C8—24no—
17C22×C3×C3⋊C8C2216yescomplemented
18#63563C22116yesdirect product factor
19C23×C3×D4—31no—
20C23×D12D311yescharacteristic
21C23×C3×C8—31no—
22C22×C4⋊Dic3—31no—
23C22×C4⋊Dic3—31no—
24C22×C4⋊Dic3—61no—
25C23×C3⋊C8D311yescharacteristic, complemented
26C2×#832—312no—
27C2×#821—312no—
28C24×C32D411yescharacteristic
29C23×C3×D3—28no—
30C23×C3×D3—26no—
31C23×C3×D3—44no—
32C23×C3×D3—44no—
33C22×C32×C4C2×C414yes—
34C22×C32×C4D413yes—
35C22×C32×C4D414yes—
36C22×C32×C4C2313yes—
37C22×C3⋊Dic3—26no—
38C22×C3⋊Dic3—44no—
39C2×C3×D12—224no—
40C2×C3×D12—26no—
41C2×C3×D12—212no—
42C2×C3×D12C2×C4124yescomplemented
43C2×C3×D12C2314yes—
44C4⋊(C3⋊Dic3)—26no—
45C4⋊(C3⋊Dic3)C2314yescomplemented
46C2×C3×C3⋊C8—212no—
47C2×C3×C3⋊C8C2314yescomplemented
48C22×#102—91noSylow
49C25×C3—61no—
50C24×D3—21no—
51C22×C3×D4—38no—
52C22×C3×D4—36no—
53C22×C3×D4—63no—
54C22×C3×D4—64no—
55C23×C3×C4—21no—
56C23×C3×C4C2×D311yescharacteristic
57C23×C3×C4C2×D311yescharacteristic
58C23×Dic3—62no—
59C23×Dic3—61no—
60C23×Dic3—61no—
61C22×D12—24no—
62C22×D12—23no—
63C22×D12Dic318yescomplemented
64C22×D12C2×D316yes—
65C22×C3×C8—36no—
66C22×C3×C8—64no—
67C2×C4⋊Dic3—36no—
68C2×C4⋊Dic3—36no—
69C2×C4⋊Dic3—66no—
70C2×C4⋊Dic3—66no—
71C2×C4⋊Dic3—63no—
72C2×C4⋊Dic3—63no—
73C22×C3⋊C8—24no—
74C22×C3⋊C8C2×D316yescomplemented
75#832—316no—
76#821—316no—
77C23×C32C22⋊C414yes—
78C23×C32D814yes—
79C23×C32SD1614yes—
80C23×C32C2×D413yes—
81C22×C3×D3—224no—
82C22×C3×D3—24no—
83C22×C3×D3—432no—
84C22×C3×D3—412no—
85C22×C3×D3—412no—
86C2×C32×C4C22⋊C4112yes—
87C2×C32×C4C22×C416yes—
88C2×C32×C4C2×D413yes—
89C2×C32×C4C2×D416yes—
90C2×C32×C4C2411yescharacteristic
91C2×C3⋊Dic3—24no—
92C2×C3⋊Dic3—412no—
93C3×D12—224no—
94C3×D12—24no—
95C3×D12C22×C418yescomplemented
96C3×C3⋊C8—24no—
97C23×D4—31no—
98C23×C8—31no—
99C22×C4⋊C4—91no—
100C2×#102—912no—
101C24×C3—21no—
102C24×C3—68no—
103C24×C3—66no—
104C24×C3—124no—
105C24×C3—124no—
106C24×C3D1211yescharacteristic
107C24×C3#6711yescharacteristic
108C23×D3—28no—
109C23×D3—26no—
110C23×D3—44no—
111C23×D3—44no—
112C2×C3×D4—324no—
113C2×C3×D4—34no—
114C2×C3×D4—624no—
115C2×C3×D4—66no—
116C2×C3×D4—612no—
117C22×C3×C4—24no—
118C22×C3×C4—24no—
119C22×C3×C4—23no—
120C22×C3×C4—23no—
121C22×C3×C4C4×D314yes—
122C22×C3×C4D1213yes—
123C22×C3×C4C2×Dic314yes—
124C22×C3×C4#6714yes—
125C22×C3×C4#6714yes—
126C22×C3×C4#6713yes—
127C22×C3×C4C22×D313yes—
128C22×C3×C4C22×D313yes—
129C22×Dic3—612no—
130C22×Dic3—66no—
131C22×Dic3—66no—
132C22×Dic3—128no—
133C22×Dic3—124no—
134C22×Dic3—124no—
135C2×D12—224no—
136C2×D12—212no—
137C2×D12—26no—
138C2×D12C2×Dic3124yescomplemented
139C2×D12C22×D314yes—
140C2×C3×C8—34no—
141C2×C3×C8—612no—
142C4⋊Dic3—34no—
143C4⋊Dic3—34no—
144C4⋊Dic3—64no—
145C4⋊Dic3—612no—
146C4⋊Dic3—66no—
147C4⋊Dic3—66no—
148C2×C3⋊C8—212no—
149C2×C3⋊C8C22×D314yescomplemented
150C22×C32#102116yescomplemented
151C22×C32C2×C22⋊C416yes—
152C22×C32C2×D816yes—
153C22×C32C2×SD1616yes—
154C22×C32C22×D411yescharacteristic
155C2×C3×D3—28no—
156C2×C3×D3—44no—
157C2×C3×D3—44no—
158C2×C3×D3—448no—
159C32×C4C2×C22⋊C416yes—
160C32×C4C23×C411yescharacteristic
161C32×C4C22×D411yescharacteristic
162C3⋊Dic3—44no—
163C25—61no—
164C22×D4—38no—
165C22×D4—36no—
166C22×D4—64no—
167C22×D4—63no—
168C23×C4—181no—
169C23×C4D3211yescharacteristic
170C22×C8—36no—
171C22×C8—64no—
172C2×C4⋊C4—96no—
173C2×C4⋊C4—183no—
174#102—916no—
175C23×C3—24no—
176C23×C3—24no—
177C23×C3—24no—
178C23×C3—23no—
179C23×C3—624no—
180C23×C3—64no—
181C23×C3—1232no—
182C23×C3—1212no—
183C23×C3—1212no—
184C23×C3#20414yes—
185C23×C3D2414yes—
186C23×C3(C2×D3)⋊C414yes—
187C23×C3#21314yes—
188C23×C3#21414yes—
189C23×C3#21714yes—
190C23×C3C2×D1213yes—
191C23×C3C2×#6713yes—
192C22×D3—224no—
193C22×D3—24no—
194C22×D3—432no—
195C22×D3—412no—
196C22×D3—412no—
197C3×D4—38no—
198C3×D4—624no—
199C3×D4—64no—
200C2×C3×C4—21no—
201C2×C3×C4—212no—
202C2×C3×C4—26no—
203C2×C3×C4—26no—
204C2×C3×C4—23no—
205C2×C3×C4(C2×D3)⋊C4112yes—
206C2×C3×C4#217112yes—
207C2×C3×C4C2×C4×D316yes—
208C2×C3×C4C2×D1213yes—
209C2×C3×C4C22×Dic316yes—
210C2×C3×C4C2×#6716yes—
211C2×C3×C4C2×#6716yes—
212C2×C3×C4C2×#6713yes—
213C2×C3×C4C23×D311yescharacteristic
214C2×C3×C4C23×D311yescharacteristic
215C2×Dic3—68no—
216C2×Dic3—64no—
217C2×Dic3—64no—
218C2×Dic3—1224no—
219C2×Dic3—1212no—
220C2×Dic3—1212no—
221D12—224no—
222D12—24no—
223D12C22×Dic318yescomplemented
224C3×C8—64no—
225C3⋊C8—24no—
226C2×C32C2×#102112yescomplemented
227C2×C32C22×C22⋊C411yescharacteristic
228C2×C32C22×D811yescharacteristic
229C2×C32C22×SD1611yescharacteristic
230C3×D3—48no—
231C24—68no—
232C24—66no—
233C24—124no—
234C24—124no—
235C24#62611yescharacteristic
236C2×D4—34no—
237C2×D4—324no—
238C2×D4—624no—
239C2×D4—612no—
240C2×D4—66no—
241C22×C4—186no—
242C22×C4—364no—
243C22×C4D3×Dic314yes—
244C22×C4#62514yes—
245C22×C4#62613yes—
246C22×C4C2×D3213yes—
247C2×C8—34no—
248C2×C8—612no—
249C4⋊C4—94no—
250C4⋊C4—186no—
251C22×C3—21no—
252C22×C3—216no—
253C22×C3—26no—
254C22×C3—26no—
255C22×C3—26no—
256C22×C3—68no—
257C22×C3—124no—
258C22×C3—124no—
259C22×C3—1248no—
260C22×C3#821116yescomplemented
261C22×C3#832116yescomplemented
262C22×C3C2×#20416yes—
263C22×C3C2×D2416yes—
264C22×C3C2×(C2×D3)⋊C416yes—
265C22×C3C2×#21316yes—
266C22×C3C2×#21416yes—
267C22×C3C2×#21716yes—
268C22×C3C22×D1211yescharacteristic
269C22×C3C22×#6711yescharacteristic
270C2×D3—28no—
271C2×D3—448no—
272C2×D3—44no—
273C2×D3—44no—
274C3×C4—21no—
275C3×C4—21no—
276C3×C4—26no—
277C3×C4C2×(C2×D3)⋊C416yes—
278C3×C4C2×#21716yes—
279C3×C4C22×C4×D311yescharacteristic
280C3×C4C23×Dic311yescharacteristic
281C3×C4C22×#6711yescharacteristic
282C3×C4C22×#6711yescharacteristic
283Dic3—128no—
284Dic3—124no—
285Dic3—124no—
286C32C22×#10211yescharacteristic, complemented, Sylow
287C23—64no—
288C23—624no—
289C23—1232no—
290C23—1212no—
291C23—1212no—
292C23#371414yes—
293C23#371614yes—
294C23(C2×D3)⋊Dic314yes—
295C23C2×#62613yes—
296D4—38no—
297D4—64no—
298D4—624no—
299C2×C4—184no—
300C2×C4—3612no—
301C2×C4(C2×D3)⋊Dic3112yes—
302C2×C4C2×D3×Dic316yes—
303C2×C4C2×#62516yes—
304C2×C4C2×#62613yes—
305C2×C4C22×D3211yescharacteristic
306C8—64no—
307C2×C3—212no—
308C2×C3—21no—
309C2×C3—21no—
310C2×C3—21no—
311C2×C3—128no—
312C2×C3C2×#821112yescomplemented
313C2×C3C2×#832112yescomplemented
314C2×C3C22×#20411yescharacteristic
315C2×C3C22×D2411yescharacteristic
316C2×C3C22×(C2×D3)⋊C411yescharacteristic
317C2×C3C22×#21311yescharacteristic
318C2×C3C22×#21411yescharacteristic
319C2×C3C22×#21711yescharacteristic
320D3—48no—
321C22—68no—
322C22—1248no—
323C22—124no—
324C22—124no—
325C22#63563116yesdirect product factor
326C22C2×#371416yes—
327C22C2×#371616yes—
328C22C2×(C2×D3)⋊Dic316yes—
329C22C22×#62611yescharacteristic
330C4—364no—
331C4C2×(C2×D3)⋊Dic316yes—
332C4C22×D3×Dic311yescharacteristic
333C4C22×#62511yescharacteristic
334C3—21no—
335C3C22×#82111yescharacteristic, complemented
336C3C22×#83211yescharacteristic, complemented
337C2—128no—
338C2C2×#63563112yesdirect product factor
339C2C22×#371411yescharacteristic
340C2C22×#371611yescharacteristic
341C2C22×(C2×D3)⋊Dic311yescharacteristic
subgroupG/H
centerC24#626
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC23×C32×C4C22
socleC24×C32D4
prime radicalC23×C3×D12C2
cosocleC2×C32×C4C24
hypercenterC23×C4D32
hypocenterC32C22×#102
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊(C3⋊Dic3)C2semidirect
3. C23×C3×C3⋊C8C2semidirect
4. C2×#63563C2direct (N × H)
12. C22×C3×D12C4semidirect
15. C2×C4⋊(C3⋊Dic3)C22semidirect
17. C22×C3×C3⋊C8C22semidirect
18. #63563C22direct (N × H)
25. C23×C3⋊C8D3semidirect
42. C2×C3×D12C2×C4semidirect
45. C4⋊(C3⋊Dic3)C23semidirect
47. C2×C3×C3⋊C8C23semidirect
63. C22×D12Dic3semidirect
74. C22×C3⋊C8C2×D3semidirect
95. C3×D12C22×C4semidirect
138. C2×D12C2×Dic3semidirect
149. C2×C3⋊C8C22×D3semidirect
150. C22×C32#102semidirect
223. D12C22×Dic3semidirect
226. C2×C32C2×#102semidirect
260. C22×C3#821semidirect
261. C22×C3#832semidirect
286. C32C22×#102semidirect
312. C2×C3C2×#821semidirect
313. C2×C3C2×#832semidirect
325. C22#63563direct (N × H)
335. C3C22×#821semidirect
336. C3C22×#832semidirect
338. C2C2×#63563direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×D122
C22×C4⋊(C3⋊Dic3)2
C23×C3×C3⋊C82
C2×#635632
C22×#8323
C22×#8213