Finite Group Databasebeta

← #11808187

Subgroups — #11808187

Order 1152.

2241 conjugacy classes of subgroups; only the 292 normal subgroups are shown.

normal subgroups only

This group has 2241 conjugacy classes of subgroups — too many to draw. Only its 292 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×C3⋊D3C211yesmaximal, characteristic
2C2×#63883C213yesmaximal
3C3×#5230C212yesmaximal, complemented
4#10591370C213yesmaximal
5#10591354C216yesmaximal, complemented
6D3×#395—32nomaximal
7C22×C32×Q8C2211yescharacteristic
8C2×Q8×C3⋊D3—212no—
9C22×C4×C3⋊D3C2213yes—
10C22×#634C2213yes—
11C22×#624C2211yescharacteristic
12C22×#624C2213yes—
13C2×C3×Dic3⋊C4C2216yes—
14C2×Dic3⋊Dic3C2216yes—
15#63883—212no—
16C3×C3⋊#95C2216yes—
17#63579C2216yes—
18C22×D3×Q8—32no—
19C22×D3×Q8—61no—
20C2×D3×C4⋊C4—36no—
21C3×#395—32no—
22#5230D312yescomplemented
23#4979—36no—
24D3×#95—36no—
25#4656—36no—
26C23×C3⋊D3C2311yescharacteristic
27C2×C32×Q8—26no—
28C22×C32×C4C2313yes—
29C22×C3⋊Dic3C2313yes—
30Q8×C3⋊D3—232no—
31C2×C4×C3⋊D3—212no—
32C2×C4×C3⋊D3D4112yes—
33C2×#634—26no—
34C2×#634—212no—
35C22×C3×Dic3C2312yes—
36C22×C3×Dic3C2316yes—
37C2×#624—26no—
38C2×#624—26no—
39C2×#624—26no—
40C2×#624Q8112yescomplemented
41C3×Dic3⋊C4—212no—
42Dic3⋊Dic3—212no—
43C2×#395—91noSylow
44C22×C3×Q8—21no—
45C22×C3×Q8C2×D312yes—
46C2×D3×Q8—624no—
47C2×D3×Q8—624no—
48C22×C4×D3—36no—
49C22×C4×D3—36no—
50C22×C4×D3—32no—
51C22×C4×D3—63no—
52C22×Dic6—36no—
53C22×Dic6—63no—
54C2×C3×C4⋊C4—36no—
55C2×C4⋊Dic3—36no—
56C2×Dic3⋊C4—36no—
57C2×Dic3⋊C4C2×D316yes—
58D3×C4⋊C4—624no—
59C3×#95—36no—
60C3⋊#95—312no—
61C3⋊#95C2×D316yes—
62C23×C32C2411yescharacteristic
63C22×C3⋊D3C2×D416yes—
64C22×C3⋊D3C2×Q816yes—
65C22×C3⋊D3#4112yes—
66C32×Q8—28no—
67C2×C32×C4—26no—
68C2×C32×C4C2×D416yes—
69C2×C3⋊Dic3—26no—
70C2×C3⋊Dic3C2×D416yes—
71C4×C3⋊D3—224no—
72#634—224no—
73C2×C3×Dic3—26no—
74C2×C3×Dic3—26no—
75C2×C3×Dic3—26no—
76C2×C3×Dic3C2×Q8112yescomplemented
77#624—224no—
78#624—44no—
79C23×Q8—91no—
80C22×C4⋊C4—93no—
81#395—32no—
82#395—96no—
83C2×#95—93no—
84C23×D3—32no—
85C23×D3—61no—
86C2×C3×Q8—212no—
87C2×C3×Q8—212no—
88C22×C3×C4—23no—
89C22×C3×C4—36no—
90C22×C3×C4—32no—
91C22×C3×C4C22×D316yes—
92C22×Dic3—36no—
93C22×Dic3—63no—
94C22×Dic3C22×D312yes—
95C22×Dic3C22×D316yes—
96D3×Q8—664no—
97D3×Q8—664no—
98C2×C4×D3—324no—
99C2×C4×D3—324no—
100C2×C4×D3—612no—
101C2×C4×D3—612no—
102C2×C4×D3—612no—
103C2×C4×D3—624no—
104C2×C4×D3—624no—
105C2×C4×D3—612no—
106C2×Dic6—624no—
107C2×Dic6—624no—
108C2×Dic6—612no—
109C2×Dic6—612no—
110C3×C4⋊C4—612no—
111C4⋊Dic3—612no—
112Dic3⋊C4—212no—
113Dic3⋊C4—612no—
114C22×C32C22×D413yes—
115C22×C32C22×Q813yes—
116C22×C32C2×#4111yescharacteristic
117C2×C3⋊D3#12014yes—
118C2×C3⋊D3C22⋊Q8112yes—
119C2×C3⋊D3C4⋊Q8112yes—
120C32×C4—26no—
121C3⋊Dic3—26no—
122C3×Dic3—212no—
123C3×Dic3—42no—
124C22×Q8—93no—
125C22×Q8—1812no—
126C22×Q8D3211yescharacteristic
127C23×C4—93no—
128C23×C4—91no—
129C23×C4—93no—
130C2×C4⋊C4—36no—
131C2×C4⋊C4—96no—
132C2×C4⋊C4—1812no—
133#95—36no—
134#95—96no—
135C23×C3—21no—
136C23×C3C23×D312yes—
137C22×D3—312no—
138C22×D3—312no—
139C22×D3—34no—
140C22×D3—66no—
141C22×D3—66no—
142C22×D3—62no—
143C3×Q8—216no—
144C3×Q8—216no—
145C2×C3×C4—212no—
146C2×C3×C4—212no—
147C2×C3×C4—26no—
148C2×C3×C4—312no—
149C2×C3×C4—66no—
150C2×C3×C4—66no—
151C2×C3×C4—66no—
152C2×C3×C4D3×D4112yes—
153C2×Dic3—26no—
154C2×Dic3—26no—
155C2×Dic3—26no—
156C2×Dic3—312no—
157C2×Dic3—66no—
158C2×Dic3—612no—
159C2×Dic3—612no—
160C2×Dic3D3×Q8112yescomplemented
161C4×D3—648no—
162C4×D3—648no—
163C4×D3—648no—
164C4×D3—128no—
165Dic6—648no—
166Dic6—648no—
167C2×C32C2×#12011yescharacteristic
168C2×C32C2×C22⋊Q813yes—
169C2×C32C2×C4⋊Q813yes—
170C3⋊D3#39518yescomplemented
171C24—91no—
172C2×Q8—26no—
173C2×Q8—1812no—
174C2×Q8—1832no—
175C2×Q8—186no—
176C22×C4—36no—
177C22×C4—32no—
178C22×C4—912no—
179C22×C4—93no—
180C22×C4—912no—
181C22×C4—1812no—
182C22×C4—186no—
183C22×C4—186no—
184C22×C4—186no—
185C22×C4C2×D3213yes—
186C4⋊C4—612no—
187C4⋊C4—1812no—
188C22×C3—23no—
189C22×C3—21no—
190C22×C3—23no—
191C22×C3C2×D3×D416yes—
192C22×C3C2×D3×Q816yes—
193C22×C3D3×#4112yes—
194C2×D3—324no—
195C2×D3—38no—
196C2×D3—324no—
197C2×D3—64no—
198C2×D3—612no—
199C2×D3—612no—
200C3×C4—212no—
201C3×C4—212no—
202C3×C4—612no—
203C3×C4—122no—
204Dic3—212no—
205Dic3—42no—
206Dic3—612no—
207Dic3—612no—
208C32C2×#39511yescharacteristic, complemented, Sylow
209C23—96no—
210C23—92no—
211C23—96no—
212C23C22×D3211yescharacteristic
213Q8—28no—
214Q8—1824no—
215C2×C4—26no—
216C2×C4—312no—
217C2×C4—66no—
218C2×C4—66no—
219C2×C4—66no—
220C2×C4—96no—
221C2×C4—1824no—
222C2×C4—1824no—
223C2×C4—186no—
224C2×C4—364no—
225C2×C4#381116yes—
226C2×C3—23no—
227C2×C3—23no—
228C2×C3—21no—
229C2×C3D3×#12012yes—
230C2×C3D3×C22⋊Q816yes—
231C2×C3D3×C4⋊Q816yes—
232D3—316no—
233D3—68no—
234C22—912no—
235C22—912no—
236C22—94no—
237C22D32×Q813yes—
238C22#6431911yescharacteristic
239C22C2×#381113yes—
240C4—26no—
241C4—612no—
242C4—122no—
243C4—186no—
244C3—21no—
245C3D3×#39512yescomplemented
246C2—98no—
247C2#1059536513yes—
248C2#1059542913yes—
249C2#1059552711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC22×C32×Q8C22
prime radicalC23×C3⋊D3C23
hypercenterC22×Q8D32
hypocenterC32C2×#395
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
3. C3×#5230C2semidirect
5. #10591354C2semidirect
22. #5230D3semidirect
40. C2×#624Q8semidirect
76. C2×C3×Dic3C2×Q8semidirect
160. C2×Dic3D3×Q8semidirect
170. C3⋊D3#395semidirect
208. C32C2×#395semidirect
245. C3D3×#395semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×C3⋊D32
C2×#638832
C3×#52302
#105913702
#105913542
D3×#3953