Finite Group Databasebeta

← C22×#63562 #11857734

Subgroups — C22×#63562 #11857734

Order 1152.

2313 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×D12C211yesmaximal, characteristic
2C23×C3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
3C22×C3×C4⋊Dic3C211yesmaximal, characteristic, complemented
4C2×#63562C2112yesmaximal, direct product factor
5C22×#832—31nomaximal
6C22×#809—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—
14C22×C3⋊(C3⋊C8)—24no—
15C22×C3⋊(C3⋊C8)C2216yescomplemented
16C2×C3×C4⋊Dic3—23no—
17C2×C3×C4⋊Dic3C2216yescomplemented
18#63562C22116yesdirect product factor
19C23×C3×D4—31no—
20C23×D12D311yescharacteristic
21C22×C3×C4⋊C4—31no—
22C22×C4⋊Dic3D311yescharacteristic, complemented
23C23×C3⋊C8—31no—
24C23×C3⋊C8—31no—
25C23×C3⋊C8—61no—
26C2×#832—312no—
27C2×#809—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—
44C2×C3⋊(C3⋊C8)—212no—
45C2×C3⋊(C3⋊C8)C2314yescomplemented
46C3×C4⋊Dic3—26no—
47C3×C4⋊Dic3C2314yescomplemented
48C22×#102—91noSylow
49C25×C3—61no—
50C24×D3—21no—
51C22×C3×D4—38no—
52C22×C3×D4—36no—
53C22×C3×D4—64no—
54C22×C3×D4—63no—
55C23×C3×C4—21no—
56C23×C3×C4—61no—
57C23×C3×C4C2×D311yescharacteristic
58C23×C3×C4C2×D311yescharacteristic
59C23×Dic3—21no—
60C22×D12—23no—
61C22×D12—24no—
62C22×D12Dic318yescomplemented
63C22×D12C2×D316yes—
64C2×C3×C4⋊C4—36no—
65C2×C3×C4⋊C4—63no—
66C2×C4⋊Dic3—23no—
67C2×C4⋊Dic3C2×D316yescomplemented
68C22×C3⋊C8—36no—
69C22×C3⋊C8—36no—
70C22×C3⋊C8—66no—
71C22×C3⋊C8—68no—
72C22×C3⋊C8—64no—
73C22×C3⋊C8—64no—
74#832—316no—
75#809—316no—
76C23×C32C22⋊C414yes—
77C23×C32D814yes—
78C23×C32SD1614yes—
79C23×C32C2×D413yes—
80C22×C3×D3—224no—
81C22×C3×D3—24no—
82C22×C3×D3—432no—
83C22×C3×D3—412no—
84C22×C3×D3—412no—
85C2×C32×C4C22⋊C4112yes—
86C2×C32×C4C22×C416yes—
87C2×C32×C4C2×D416yes—
88C2×C32×C4C2×D413yes—
89C2×C32×C4C2411yescharacteristic
90C2×C3×Dic3—24no—
91C2×C3×Dic3—412no—
92C3×D12—224no—
93C3×D12—24no—
94C3×D12C22×C418yescomplemented
95C3⋊(C3⋊C8)—24no—
96C23×D4—31no—
97C23×C8—91no—
98C22×C4⋊C4—31no—
99C2×#102—912no—
100C24×C3—21no—
101C24×C3—68no—
102C24×C3—66no—
103C24×C3—124no—
104C24×C3—124no—
105C24×C3#6711yescharacteristic
106C24×C3#6711yescharacteristic
107C23×D3—28no—
108C23×D3—26no—
109C23×D3—44no—
110C23×D3—44no—
111C2×C3×D4—324no—
112C2×C3×D4—34no—
113C2×C3×D4—624no—
114C2×C3×D4—612no—
115C2×C3×D4—66no—
116C22×C3×C4—24no—
117C22×C3×C4—23no—
118C22×C3×C4—24no—
119C22×C3×C4—23no—
120C22×C3×C4—66no—
121C22×C3×C4—124no—
122C22×C3×C4C4×D314yes—
123C22×C3×C4D1214yes—
124C22×C3×C4C2×Dic314yes—
125C22×C3×C4#6713yes—
126C22×C3×C4#6713yes—
127C22×C3×C4#6714yes—
128C22×C3×C4C22×D313yes—
129C22×C3×C4C22×D313yes—
130C22×Dic3—26no—
131C22×Dic3—44no—
132C2×D12—224no—
133C2×D12—26no—
134C2×D12—212no—
135C2×D12C2×Dic3124yescomplemented
136C2×D12C22×D314yes—
137C3×C4⋊C4—34no—
138C3×C4⋊C4—66no—
139C4⋊Dic3—26no—
140C4⋊Dic3C22×D314yescomplemented
141C2×C3⋊C8—34no—
142C2×C3⋊C8—34no—
143C2×C3⋊C8—64no—
144C2×C3⋊C8—624no—
145C2×C3⋊C8—612no—
146C2×C3⋊C8—612no—
147C22×C32#102116yescomplemented
148C22×C32C2×C22⋊C416yes—
149C22×C32C2×D816yes—
150C22×C32C2×SD1616yes—
151C22×C32C22×D411yescharacteristic
152C2×C3×D3—28no—
153C2×C3×D3—44no—
154C2×C3×D3—44no—
155C2×C3×D3—448no—
156C32×C4C2×C22⋊C416yes—
157C32×C4C23×C411yescharacteristic
158C32×C4C22×D411yescharacteristic
159C3×Dic3—44no—
160C25—61no—
161C22×D4—38no—
162C22×D4—36no—
163C22×D4—63no—
164C22×D4—64no—
165C23×C4—61no—
166C23×C4D3211yescharacteristic
167C22×C8—96no—
168C22×C8—184no—
169C2×C4⋊C4—36no—
170C2×C4⋊C4—63no—
171#102—916no—
172C23×C3—24no—
173C23×C3—24no—
174C23×C3—24no—
175C23×C3—23no—
176C23×C3—624no—
177C23×C3—64no—
178C23×C3—1232no—
179C23×C3—1212no—
180C23×C3—1212no—
181C23×C3(C2×D3)⋊C414yes—
182C23×C3#21314yes—
183C23×C3#21314yes—
184C23×C3#21414yes—
185C23×C3#21514yes—
186C23×C3#21714yes—
187C23×C3C2×#6713yes—
188C23×C3C2×#6713yes—
189C22×D3—224no—
190C22×D3—24no—
191C22×D3—432no—
192C22×D3—412no—
193C22×D3—412no—
194C3×D4—38no—
195C3×D4—624no—
196C3×D4—64no—
197C2×C3×C4—21no—
198C2×C3×C4—212no—
199C2×C3×C4—26no—
200C2×C3×C4—23no—
201C2×C3×C4—26no—
202C2×C3×C4—64no—
203C2×C3×C4—1212no—
204C2×C3×C4(C2×D3)⋊C4112yes—
205C2×C3×C4#217112yes—
206C2×C3×C4C2×C4×D316yes—
207C2×C3×C4C2×D1216yes—
208C2×C3×C4C22×Dic316yes—
209C2×C3×C4C2×#6713yes—
210C2×C3×C4C2×#6713yes—
211C2×C3×C4C2×#6716yes—
212C2×C3×C4C23×D311yescharacteristic
213C2×C3×C4C23×D311yescharacteristic
214C2×Dic3—24no—
215C2×Dic3—412no—
216D12—224no—
217D12—24no—
218D12C22×Dic318yescomplemented
219C3⋊C8—68no—
220C3⋊C8—64no—
221C3⋊C8—64no—
222C2×C32C2×#102112yescomplemented
223C2×C32C22×C22⋊C411yescharacteristic
224C2×C32C22×D811yescharacteristic
225C2×C32C22×SD1611yescharacteristic
226C3×D3—48no—
227C24—68no—
228C24—66no—
229C24—124no—
230C24—124no—
231C24#62511yescharacteristic
232C2×D4—34no—
233C2×D4—324no—
234C2×D4—624no—
235C2×D4—66no—
236C2×D4—612no—
237C22×C4—66no—
238C22×C4—124no—
239C22×C4D3×Dic314yes—
240C22×C4#62513yes—
241C22×C4#62614yes—
242C22×C4C2×D3213yes—
243C2×C8—94no—
244C2×C8—1812no—
245C4⋊C4—34no—
246C4⋊C4—66no—
247C22×C3—21no—
248C22×C3—216no—
249C22×C3—26no—
250C22×C3—26no—
251C22×C3—26no—
252C22×C3—68no—
253C22×C3—1248no—
254C22×C3—124no—
255C22×C3—124no—
256C22×C3#809116yescomplemented
257C22×C3#832116yescomplemented
258C22×C3C2×(C2×D3)⋊C416yes—
259C22×C3C2×#21316yes—
260C22×C3C2×#21316yes—
261C22×C3C2×#21416yes—
262C22×C3C2×#21516yes—
263C22×C3C2×#21716yes—
264C22×C3C22×#6711yescharacteristic
265C22×C3C22×#6711yescharacteristic
266C2×D3—28no—
267C2×D3—448no—
268C2×D3—44no—
269C2×D3—44no—
270C3×C4—21no—
271C3×C4—21no—
272C3×C4—26no—
273C3×C4—124no—
274C3×C4C2×(C2×D3)⋊C416yes—
275C3×C4C2×#21716yes—
276C3×C4C22×C4×D311yescharacteristic
277C3×C4C22×D1211yescharacteristic
278C3×C4C23×Dic311yescharacteristic
279C3×C4C22×#6711yescharacteristic
280Dic3—44no—
281C32C22×#10211yescharacteristic, complemented, Sylow
282C23—64no—
283C23—624no—
284C23—1232no—
285C23—1212no—
286C23—1212no—
287C23#371314yes—
288C23#371514yes—
289C23(C2×D3)⋊Dic314yes—
290C23C2×#62513yes—
291D4—38no—
292D4—64no—
293D4—624no—
294C2×C4—64no—
295C2×C4—1212no—
296C2×C4(C2×D3)⋊Dic3112yes—
297C2×C4C2×D3×Dic316yes—
298C2×C4C2×#62513yes—
299C2×C4C2×#62616yes—
300C2×C4C22×D3211yescharacteristic
301C8—184no—
302C2×C3—212no—
303C2×C3—21no—
304C2×C3—21no—
305C2×C3—21no—
306C2×C3—128no—
307C2×C3C2×#809112yescomplemented
308C2×C3C2×#832112yescomplemented
309C2×C3C22×(C2×D3)⋊C411yescharacteristic
310C2×C3C22×#21311yescharacteristic
311C2×C3C22×#21311yescharacteristic
312C2×C3C22×#21411yescharacteristic
313C2×C3C22×#21511yescharacteristic
314C2×C3C22×#21711yescharacteristic
315D3—48no—
316C22—68no—
317C22—1248no—
318C22—124no—
319C22—124no—
320C22#63562116yesdirect product factor
321C22C2×#371316yes—
322C22C2×#371516yes—
323C22C2×(C2×D3)⋊Dic316yes—
324C22C22×#62511yescharacteristic
325C4—124no—
326C4C2×(C2×D3)⋊Dic316yes—
327C4C22×D3×Dic311yescharacteristic
328C4C22×#62611yescharacteristic
329C3—21no—
330C3C22×#80911yescharacteristic, complemented
331C3C22×#83211yescharacteristic, complemented
332C2—128no—
333C2C2×#63562112yesdirect product factor
334C2C22×#371311yescharacteristic
335C2C22×#371511yescharacteristic
336C2C22×(C2×D3)⋊Dic311yescharacteristic
subgroupG/H
centerC24#625
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. C23×C3⋊(C3⋊C8)C2semidirect
3. C22×C3×C4⋊Dic3C2semidirect
4. C2×#63562C2direct (N × H)
12. C22×C3×D12C4semidirect
15. C22×C3⋊(C3⋊C8)C22semidirect
17. C2×C3×C4⋊Dic3C22semidirect
18. #63562C22direct (N × H)
22. C22×C4⋊Dic3D3semidirect
42. C2×C3×D12C2×C4semidirect
45. C2×C3⋊(C3⋊C8)C23semidirect
47. C3×C4⋊Dic3C23semidirect
62. C22×D12Dic3semidirect
67. C2×C4⋊Dic3C2×D3semidirect
94. C3×D12C22×C4semidirect
135. C2×D12C2×Dic3semidirect
140. C4⋊Dic3C22×D3semidirect
147. C22×C32#102semidirect
218. D12C22×Dic3semidirect
222. C2×C32C2×#102semidirect
256. C22×C3#809semidirect
257. C22×C3#832semidirect
281. C32C22×#102semidirect
307. C2×C3C2×#809semidirect
308. C2×C3C2×#832semidirect
320. C22#63562direct (N × H)
330. C3C22×#809semidirect
331. C3C22×#832semidirect
333. C2C2×#63562direct (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
C23×C3⋊(C3⋊C8)2
C22×C3×C4⋊Dic32
C2×#635622
C22×#8323
C22×#8093