Finite Group Databasebeta

← #11918492

Subgroups — #11918492

Order 1152.

2350 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×C3⋊D3C211yesmaximal, characteristic
2#10596648C218yesmaximal, complemented
3#10596647C218yesmaximal, complemented
4#10596644C212yesmaximal, complemented
5#10596640C216yesmaximal, complemented
6C2×#64283C216yesmaximal, complemented
7C2×C32×#41C411yescharacteristic
8#41×C3⋊D3C414yes—
9#41×C3⋊D3C414yes—
10#41×C3⋊D3C2214yes—
11#41×C3⋊D3C2214yes—
12C2×#3832C2211yescharacteristic
13C2×Q8×C3⋊D3C411yescharacteristic
14C2×#3830C2213yes—
15C2×D4×C3⋊D3C413yes—
16C2×#3828C413yes—
17C22×C4×C3⋊D3C2213yes—
18C2×#3792C22112yescomplemented
19#64289C22116yescomplemented
20#64287C22148yescomplemented
21#64283C2214yes—
22#64283C22112yescomplemented
23#64283C22112yescomplemented
24#64283C22112yescomplemented
25C2×#3788C22112yescomplemented
26C2×#3787C22112yescomplemented
27C2×D3×#41—62no—
28C23×C3⋊D3C2×C413yes—
29C32×#41C2×C414yes—
30C32×#41C2×C414yes—
31C2×C32×Q8C2×C411yescharacteristic
32C2×C32×D4C2×C413yes—
33C22×C32×C4C2×C413yes—
34C2×#638C2×C416yes—
35C22×C3⋊Dic3C2313yes—
36#3832C2×C414yes—
37#3832C2314yes—
38Q8×C3⋊D3C2×C414yes—
39Q8×C3⋊D3C2×C414yes—
40#3830C2×C4112yes—
41#3830C23112yes—
42D4×C3⋊D3C2×C4112yes—
43D4×C3⋊D3C2×C4112yes—
44#3828C2×C4112yes—
45#3828C2×C4112yes—
46C2×C4⋊(C3⋊D3)C2×C413yes—
47C2×C4×C3⋊D3C2×C413yes—
48C2×C4×C3⋊D3C2×C413yes—
49C2×C4×C3⋊D3C2×C416yes—
50C2×C4×C3⋊D3C2×C416yes—
51C2×C4×C3⋊D3C2316yes—
52C2×C4×C3⋊D3C2316yes—
53C2×C4×C3⋊D3C2311yescharacteristic
54C2×C4×C3⋊D3C2313yes—
55C2×#634C2×C413yes—
56#3792C2318yes—
57#3792C23124yescomplemented
58C2×#622C23124yescomplemented
59#3788C2318yes—
60#3788C23124yescomplemented
61#3787C2318yes—
62#3787C23124yescomplemented
63C2×#568—91nomaximal, Sylow
64C2×C3×#41—22no—
65D3×#41—68no—
66D3×#41—68no—
67D3×#41—68no—
68D3×#41—68no—
69C2×#239—62no—
70C2×D3×Q8—62no—
71C2×#237—66no—
72C2×D3×D4—66no—
73C2×#235—66no—
74C22×C4×D3—66no—
75C23×C32C22×C413yes—
76C22×C3⋊D3—46no—
77C22×C3⋊D3C22×C411yescharacteristic
78C22×C3⋊D3C22×C416yes—
79C22×C3⋊D3C22×C413yes—
80C22×C3⋊D3C22×C416yes—
81C32×Q8C22×C414yes—
82C32×D4C22×C4112yes—
83C2×C32×C4C22×C413yes—
84C2×C32×C4C22×C411yescharacteristic
85C2×C32×C4C22×C416yes—
86C2×C32×C4C22×C416yes—
87#638C22×C4124yes—
88C2×C3⋊Dic3C22×C413yes—
89C2×C3⋊Dic3C22×C416yes—
90C2×C3⋊Dic3C2416yes—
91C2×C3⋊Dic3C2411yescharacteristic
92C4⋊(C3⋊D3)C22×C4112yes—
93C4×C3⋊D3C22×C411yescharacteristic
94C4×C3⋊D3C22×C411yescharacteristic
95C4×C3⋊D3C22×C416yes—
96C4×C3⋊D3C22×C416yes—
97C4×C3⋊D3C22×C416yes—
98C4×C3⋊D3C22×C416yes—
99C4×C3⋊D3C22×C416yes—
100C4×C3⋊D3C2411yescharacteristic
101C4×C3⋊D3C2416yes—
102C4×C3⋊D3C2411yescharacteristic
103#634C22×C4112yes—
104#622C24116yes—
105C22×#41—91no—
106#568—96no—
107#568—92no—
108#568—98no—
109C2×#131—98no—
110C22×M16—96no—
111C23×D3—66no—
112C3×#41—28no—
113C3×#41—28no—
114C2×C3×Q8—22no—
115C2×C3×D4—26no—
116C22×C3×C4—26no—
117C2×#67—612no—
118C22×Dic3—66no—
119#239—68no—
120#239—68no—
121D3×Q8—68no—
122D3×Q8—68no—
123#237—624no—
124#237—624no—
125D3×D4—624no—
126D3×D4—624no—
127#235—624no—
128#235—624no—
129C2×D12—66no—
130C2×C4×D3—62no—
131C2×C4×D3—66no—
132C2×C4×D3—66no—
133C2×C4×D3—66no—
134C2×C4×D3—612no—
135C2×C4×D3—612no—
136C2×C4×D3—612no—
137C2×C4×D3—612no—
138C2×Dic6—66no—
139C22×C32—43no—
140C22×C32C23×C411yescharacteristic
141C22×C32C23×C416yes—
142C2×C3⋊D3—22no—
143C2×C3⋊D3—212no—
144C2×C3⋊D3—46no—
145C2×C3⋊D3—43no—
146C2×C3⋊D3C23×C411yescharacteristic
147C2×C3⋊D3C23×C416yes—
148C2×C3⋊D3C23×C411yescharacteristic
149C32×C4C23×C416yes—
150C32×C4C23×C411yescharacteristic
151C32×C4C23×C411yescharacteristic
152C3⋊Dic3C23×C416yes—
153C3⋊Dic3C23×C411yescharacteristic
154C3⋊Dic3C2511yescharacteristic
155C2×#41—94no—
156C2×#41—94no—
157C2×#41—94no—
158C2×#41—94no—
159C2×#41—91no—
160C2×#41—93no—
161C2×#41—93no—
162C2×#41#15711yescharacteristic
163C22×Q8—91no—
164C22×D4—93no—
165C23×C4—93no—
166#131—948no—
167#131—916no—
168C2×M16—912no—
169C2×M16—94no—
170C2×M16—912no—
171C2×M16—912no—
172C2×M16—912no—
173C2×M16—912no—
174C22×C8—912no—
175C23×C3—26no—
176C22×D3—62no—
177C22×D3—66no—
178C22×D3—612no—
179C22×D3—612no—
180C22×D3—1224no—
181C3×Q8—28no—
182C3×D4—224no—
183C2×C3×C4—26no—
184C2×C3×C4—22no—
185C2×C3×C4—212no—
186C2×C3×C4—212no—
187#67—648no—
188C2×Dic3—66no—
189C2×Dic3—612no—
190C2×Dic3—62no—
191C2×Dic3—612no—
192D12—624no—
193C4×D3—62no—
194C4×D3—62no—
195C4×D3—612no—
196C4×D3—612no—
197C4×D3—612no—
198C4×D3—612no—
199C4×D3—612no—
200C4×D3—62no—
201C4×D3—62no—
202C4×D3—612no—
203Dic6—624no—
204C2×C32—21no—
205C2×C32—26no—
206C2×C32C24×C411yescharacteristic
207C3⋊D3—21no—
208C3⋊D3—26no—
209C3⋊D3#56812yescomplemented
210C24—93no—
211#41—94no—
212#41—94no—
213#41—912no—
214#41—912no—
215#41—912no—
216#41—912no—
217#41C2×#15714yes—
218#41C2×#15714yes—
219C2×Q8—94no—
220C2×Q8—94no—
221C2×Q8—93no—
222C2×Q8C2×#15711yescharacteristic
223C2×D4—96no—
224C2×D4—912no—
225C2×D4—912no—
226C2×D4—93no—
227C2×D4C2×#15713yes—
228C22×C4—93no—
229C22×C4—96no—
230C22×C4—91no—
231C22×C4—96no—
232C22×C4—93no—
233C22×C4—93no—
234C22×C4—93no—
235C22×C4—96no—
236C22×C4—96no—
237C22×C4C2×#15713yes—
238M16—98no—
239M16—98no—
240M16—924no—
241M16—924no—
242C2×C8—98no—
243C2×C8—924no—
244C2×C8—924no—
245C22×C3—22no—
246C22×C3—212no—
247C22×C3—412no—
248C2×D3—62no—
249C2×D3—62no—
250C2×D3—612no—
251C2×D3—68no—
252C2×D3—1224no—
253C2×D3—1224no—
254C2×D3—1212no—
255C3×C4—212no—
256C3×C4—22no—
257C3×C4—22no—
258Dic3—612no—
259Dic3—62no—
260Dic3—62no—
261C32C2×#56811yescharacteristic, complemented, Sylow
262C23—91no—
263C23—96no—
264C23—96no—
265C23—93no—
266C23—366no—
267C23C22×#15713yes—
268Q8—912no—
269Q8C22×#15714yes—
270D4—924no—
271D4—912no—
272D4C22×#157112yes—
273C2×C4—96no—
274C2×C4—91no—
275C2×C4—93no—
276C2×C4—96no—
277C2×C4—96no—
278C2×C4—91no—
279C2×C4—91no—
280C2×C4—96no—
281C2×C4—96no—
282C2×C4—96no—
283C2×C4—96no—
284C2×C4—91no—
285C2×C4—91no—
286C2×C4—96no—
287C2×C4C22×#15713yes—
288C2×C4C22×#15716yes—
289C2×C4C22×#15711yescharacteristic
290C2×C4C22×#15716yes—
291C8—916no—
292C2×C3—24no—
293C2×C3—22no—
294C2×C3—412no—
295D3—64no—
296D3—64no—
297D3—1212no—
298C22—43no—
299C22—91no—
300C22—91no—
301C22—96no—
302C22—182no—
303C22—1812no—
304C22—363no—
305C22—366no—
306C22C23×#15711yescharacteristic
307C22C23×#15716yes—
308C4—91no—
309C4—91no—
310C4—96no—
311C4C23×#15711yescharacteristic
312C4C23×#15716yes—
313C4C23×#15711yescharacteristic
314C3—22no—
315C2—21no—
316C2—26no—
317C2—92no—
318C2—181no—
319C2—186no—
320C2C24×#15711yescharacteristic
subgroupG/H
centerC4C23×#157
commutator, socleC2×C32C24×C4
FrattiniC2C24×#157
FittingC2×C32×#41C4
prime radicalC2×#41×C3⋊D3C2
cosocleC3⋊Dic3C25
hypercenterC2×#41#157
hypocenterC32C2×#568
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #10596648C2semidirect
3. #10596647C2semidirect
4. #10596644C2semidirect
5. #10596640C2semidirect
6. C2×#64283C2semidirect
18. C2×#3792C22semidirect
19. #64289C22semidirect
20. #64287C22semidirect
22. #64283C22semidirect
23. #64283C22semidirect
24. #64283C22semidirect
25. C2×#3788C22semidirect
26. C2×#3787C22semidirect
57. #3792C23semidirect
58. C2×#622C23semidirect
60. #3788C23semidirect
62. #3787C23semidirect
209. C3⋊D3#568semidirect
261. C32C2×#568semidirect

Maximal subgroups

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

subgroupindex
C2×#41×C3⋊D32
#105966482
#105966472
#105966442
#105966402
C2×#642832
C2×#5689