Finite Group Databasebeta

← #11906255

Subgroups — #11906255

Order 1152.

2892 conjugacy classes of subgroups.

The subgroup lattice has 267 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#519C211yesmaximal, characteristic
2#10596283C211yesmaximal, characteristic
3C2×Q8×C3⋊Dic3C211yesmaximal, characteristic
4#10596041C214yesmaximal, complemented
5#10596040C214yesmaximal, complemented
6#10596040C214yesmaximal, complemented
7Q8×#634C214yesmaximal, complemented
8#10595990C216yesmaximal
9#10595988C216yesmaximal
10#85875—34nomaximal
11C22×C32×Q8C2211yescharacteristic
12C32×C4×Q8C2214yes—
13C32×C4×Q8C2214yes—
14C32×#117C2216yes—
15Q8×C3⋊Dic3C2214yes—
16Q8×C3⋊Dic3C2214yes—
17Q8×C3⋊Dic3C2214yes—
18Q8×C3⋊Dic3C2214yes—
19#64135C2216yes—
20C2×C4⋊(C3⋊Dic3)C2213yes—
21C2×C4×C3⋊Dic3C2213yes—
22#64099C2216yes—
23#64099C2216yes—
24#64099C22112yes—
25#64097C2216yes—
26#64097C2216yes—
27#64097C22112yes—
28#64087C2214yes—
29#64087C22112yes—
30#64079C22112yes—
31#64078C22112yes—
32C4×#634C22112yes—
33C4×#634C22112yes—
34C3×#519D314yes—
35#5812—34no—
36C2×Q8×Dic3—34no—
37#5570—316no—
38#5569—316no—
39#5569—316no—
40Q8×Dic6—316no—
41#5519—324no—
42#5517—324no—
43C2×C32×Q8Q818yescomplemented
44C2×C32×Q8C2314yes—
45C22×C32×C4C2313yes—
46C22×C3⋊Dic3C2311yescharacteristic
47C22×C3⋊Dic3C2313yes—
48C2×#634C2314yes—
49C2×#634C23112yes—
50C32×C4⋊C4C2316yes—
51C32×C4⋊C4C2316yes—
52C32×C22⋊C4C2314yes—
53C32×C42C23112yes—
54#3757C2314yes—
55C4⋊(C3⋊Dic3)C2314yes—
56C4⋊(C3⋊Dic3)C23112yes—
57C4⋊(C3⋊Dic3)C2316yes—
58C4⋊(C3⋊Dic3)C23112yes—
59C4⋊(C3⋊Dic3)C2316yes—
60#3750C2314yes—
61#3750C2314yes—
62#3750C23112yes—
63#3750C23112yes—
64C4×C3⋊Dic3C2316yes—
65C4×C3⋊Dic3C23112yes—
66C4×C3⋊Dic3C2316yes—
67#3502—91noSylow
68C22×C3×Q8C2×D314yes—
69C3×C4×Q8C2×D3116yes—
70C3×C4×Q8C2×D3116yes—
71C3×#117C2×D3124yes—
72Q8×Dic3—316no—
73Q8×Dic3—316no—
74Q8×Dic3—316no—
75Q8×Dic3—316no—
76#926—324no—
77C2×C4⋊Dic3—312no—
78C2×C4×Dic3—312no—
79#890—324no—
80#890—324no—
81#890—348no—
82#888—324no—
83#888—324no—
84#888—348no—
85#878—316no—
86#878—348no—
87#870—348no—
88#869—348no—
89C4×Dic6—348no—
90C4×Dic6—348no—
91C23×C32C2411yescharacteristic
92C32×Q8C2×Q8116yes—
93C2×C32×C4C2×Q8112yes—
94C2×C32×C4C2414yes—
95C2×C32×C4C2414yes—
96C2×C32×C4C2416yes—
97C2×C3⋊Dic3—22no—
98C2×C3⋊Dic3—43no—
99C2×C3⋊Dic3C2411yescharacteristic
100C2×C3⋊Dic3C2414yes—
101C2×C3⋊Dic3C2414yes—
102C2×C3⋊Dic3C2416yes—
103C2×C3⋊Dic3C2411yescharacteristic
104#634—28no—
105#634—412no—
106Q82—94no—
107#557—94no—
108#557—94no—
109#557—94no—
110#544—96no—
111#533—96no—
112#519—91no—
113#519C3⋊D311yescharacteristic
114C2×C4×Q8—91no—
115C2×C3×Q8Dic6132yescomplemented
116C2×C3×Q8C22×D3116yes—
117C22×C3×C4C22×D3112yes—
118C22×Dic3—34no—
119C22×Dic3—312no—
120C2×Dic6—316no—
121C2×Dic6—348no—
122C3×C4⋊C4C22×D3124yes—
123C3×C4⋊C4C22×D3124yes—
124C3×C22⋊C4C22×D3116yes—
125C3×C42C22×D3148yes—
126#217—316no—
127C4⋊Dic3—316no—
128C4⋊Dic3—348no—
129C4⋊Dic3—324no—
130C4⋊Dic3—348no—
131C4⋊Dic3—324no—
132Dic3⋊C4—316no—
133Dic3⋊C4—316no—
134Dic3⋊C4—348no—
135Dic3⋊C4—348no—
136C4×Dic3—324no—
137C4×Dic3—348no—
138C4×Dic3—324no—
139C22×C32—21no—
140C22×C32—21no—
141C22×C32C22×Q812yes—
142C22×C32C2511yescharacteristic
143C32×C4—24no—
144C32×C4—24no—
145C32×C4C22×Q8112yes—
146C3⋊Dic3—24no—
147C3⋊Dic3—21no—
148C3⋊Dic3—24no—
149C3⋊Dic3—26no—
150C3⋊Dic32−1+412yes—
151C22×Q8C2×C3⋊D311yescharacteristic
152C4⋊Q8—96no—
153C4⋊Q8—96no—
154C4⋊Q8—912no—
155C4⋊Q8—912no—
156#125—96no—
157#125—96no—
158#125—912no—
159#125—912no—
160C22⋊Q8—94no—
161C22⋊Q8—912no—
162C4×Q8—94no—
163C4×Q8—94no—
164C4×Q8—94no—
165C4×Q8—94no—
166C4×Q8—912no—
167C4×Q8—912no—
168C4×Q8C2×C3⋊D314yes—
169C4×Q8C2×C3⋊D314yes—
170#117—96no—
171#117C2×C3⋊D316yes—
172C2×C4⋊C4—93no—
173C2×C42—93no—
174C23×C3C23×D314yes—
175C3×Q8C2×Dic6164yes—
176C2×C3×C4C2×Dic6148yes—
177C2×C3×C4C23×D3116yes—
178C2×C3×C4C23×D3116yes—
179C2×C3×C4C23×D3124yes—
180C2×Dic3—34no—
181C2×Dic3—34no—
182C2×Dic3—316no—
183C2×Dic3—316no—
184C2×Dic3—324no—
185C2×Dic3—68no—
186C2×Dic3—1212no—
187Dic6—632no—
188Dic6—1248no—
189C2×C32—22no—
190C2×C32C23×Q811yescharacteristic
191C2×C32C2×2−1+411yescharacteristic
192C2×C32#58511yescharacteristic
193C2×Q8—94no—
194C2×Q8—912no—
195C2×Q8#63418yescomplemented
196C2×Q8C22×C3⋊D314yes—
197C22×C4—91no—
198C22×C4—93no—
199C22×C4C22×C3⋊D313yes—
200C4⋊C4—912no—
201C4⋊C4—96no—
202C4⋊C4—96no—
203C4⋊C4—94no—
204C4⋊C4—94no—
205C4⋊C4—94no—
206C4⋊C4—912no—
207C4⋊C4—912no—
208C4⋊C4—912no—
209C4⋊C4C22×C3⋊D316yes—
210C4⋊C4C22×C3⋊D316yes—
211C22⋊C4—94no—
212C22⋊C4C22×C3⋊D314yes—
213C42—96no—
214C42—96no—
215C42—912no—
216C42C22×C3⋊D3112yes—
217C22×C3—24no—
218C22×C3—24no—
219C22×C3C22×Dic618yes—
220C22×C3C24×D314yes—
221C3×C4—216no—
222C3×C4—216no—
223C3×C4C22×Dic6148yes—
224Dic3—38no—
225Dic3—616no—
226Dic3—64no—
227Dic3—616no—
228Dic3—624no—
229C32#350211yescharacteristic, complemented, Sylow
230C23C23×C3⋊D311yescharacteristic
231Q8—188no—
232Q8—3612no—
233Q8C2×#634116yes—
234C2×C4—91no—
235C2×C4—91no—
236C2×C4—94no—
237C2×C4—94no—
238C2×C4—96no—
239C2×C4—182no—
240C2×C4—363no—
241C2×C4C2×#634112yes—
242C2×C4C23×C3⋊D314yes—
243C2×C4C23×C3⋊D314yes—
244C2×C4C23×C3⋊D316yes—
245C2×C3—28no—
246C2×C3C23×Dic614yes—
247C2×C3D3×2−1+414yes—
248C2×C3#596814yes—
249C22—21no—
250C22—21no—
251C22C22×#63412yes—
252C22C24×C3⋊D311yescharacteristic
253C4—24no—
254C4—24no—
255C4—92no—
256C4—181no—
257C4—184no—
258C4—186no—
259C4—184no—
260C4C22×#634112yes—
261C3#8587514yescomplemented
262C2—22no—
263C2C23×#63411yescharacteristic
264C2C3⋊D3×2−1+411yescharacteristic
265C2#1059676011yescharacteristic
subgroupG/H
center, FrattiniC22C24×C3⋊D3
commutator, socle, cosocleC22×C32C25
FittingC32×#519C2
prime radicalC23×C32C24
hypercenter#519C3⋊D3
hypocenterC32#3502
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #519

Complements

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

NH ≅ G/Ntype
4. #10596041C2semidirect
5. #10596040C2semidirect
6. #10596040C2semidirect
7. Q8×#634C2semidirect
43. C2×C32×Q8Q8semidirect
115. C2×C3×Q8Dic6semidirect
195. C2×Q8#634semidirect
229. C32#3502semidirect
261. C3#85875semidirect

Maximal subgroups

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

subgroupindex
C32×#5192
#105962832
C2×Q8×C3⋊Dic32
#105960412
#105960402
Q8×#6342
#105959902
#105959882
#858753