Finite Group Databasebeta

← #11792402

Subgroups — #11792402

Order 1152.

1182 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 1182 conjugacy classes of subgroups — too many to draw. Only its 169 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
1#10596262C212yesmaximal, complemented
2#10596219C211yesmaximal, characteristic, complemented
3C32×#407C211yesmaximal, characteristic, complemented
4#10592838C212yesmaximal, complemented
5#10589423C211yesmaximal, characteristic, complemented
6#69993—34nomaximal
7C23×C32×C4C2211yescharacteristic
8C2×#3828C2212yes—
9C2×C32×M16C2211yescharacteristic
10C2×C32×M16C2211yescharacteristic
11#64162—22no—
12#64139—22no—
13#64138—22no—
14C4×#638—24no—
15#64135C2212yes—
16#64133—22no—
17#64118—22no—
18#64117—22no—
19#64113—22no—
20C32×C22⋊C8—22no—
21#63652—24no—
22#5791—38no—
23#5748—34no—
24C3×#407D314yescomplemented
25#5139—38no—
26#4557—34no—
27C24×C32D411yescharacteristic
28C22×C32×C4—22no—
29C22×C32×C4—22no—
30C22×C32×C4—21no—
31C22×C32×C4—21no—
32C22×C32×C4D411yescharacteristic
33C22×C32×C4C2311yescharacteristic
34C2×#638—24no—
35C2×#638—22no—
36#3828—22no—
37#3828—22no—
38#3828—22no—
39#3828—22no—
40C2×C4⋊(C3⋊D3)D412yescomplemented
41C2×C4×C3⋊D3—22no—
42C2×#634D412yescomplemented
43C32×M16—22no—
44C32×M16—22no—
45C2×C32×C8—21no—
46C2×C32×C8D412yescomplemented
47#3757—24no—
48#3757—22no—
49#3752—24no—
50C4⋊(C3⋊Dic3)—22no—
51#3750—24no—
52C4×C3⋊Dic3D414yescomplemented
53#3746—22no—
54#3745—22no—
55#3744—24no—
56#2010—91noSylow
57C23×C3×C4C2×D314yes—
58C2×#235—38no—
59C2×C3×M16C2×D314yes—
60C2×C3×M16C2×D314yes—
61#953—68no—
62#930—68no—
63#929—68no—
64C4×#67—616no—
65#926—38no—
66#924—68no—
67#909—68no—
68#908—68no—
69#904—68no—
70C3×C22⋊C8—28no—
71#825—616no—
72C23×C32—22no—
73C23×C32—21no—
74C23×C32—42no—
75C23×C32C2×D411yescharacteristic
76C22×C3⋊D3—22no—
77C2×C32×C4—22no—
78C2×C32×C4—21no—
79C2×C32×C4—41no—
80C2×C32×C4—42no—
81C2×C32×C4—41no—
82C2×C32×C4C2×D412yes—
83C2×C32×C4C2×D412yes—
84C2×C32×C4C2×D411yescharacteristic
85C2×C32×C4#4111yescharacteristic
86#638—48no—
87#638—42no—
88#638—42no—
89C2×C3⋊Dic3—24no—
90C2×C3⋊Dic3—22no—
91C4⋊(C3⋊D3)—22no—
92C4⋊(C3⋊D3)—22no—
93C4×C3⋊D3—42no—
94C4×C3⋊D3—42no—
95#634—22no—
96#634—22no—
97C32×C8—22no—
98C32×C8—41no—
99#575—91no—
100#525—92no—
101#421—92no—
102#407C3⋊D311yescharacteristic, complemented
103H(3,ℤ/4)—91no—
104C24×C3D1214yes—
105C22×C3×C4—24no—
106C22×C3×C4—28no—
107C22×C3×C4—28no—
108C22×C3×C4—24no—
109C22×C3×C4D1214yes—
110C22×C3×C4C22×D314yes—
111C2×#67—616no—
112C2×#67—68no—
113#235—68no—
114#235—68no—
115#235—68no—
116#235—68no—
117C2×D12—38no—
118C2×C4×D3—68no—
119C2×Dic6—38no—
120C3×M16—28no—
121C3×M16—28no—
122C2×C3×C8—24no—
123C2×C3×C8#6718yescomplemented
124#217—616no—
125#217—68no—
126(C2×D3)⋊C4—616no—
127C4⋊Dic3—68no—
128Dic3⋊C4—616no—
129C4×Dic3—316no—
130Dic12—68no—
131D24—68no—
132#204—616no—
133C22×C32—24no—
134C22×C32—22no—
135C22×C32—41no—
136C22×C32—42no—
137C22×C32—41no—
138C22×C32—41no—
139C22×C32#12012yes—
140C22×C32#12111yescharacteristic
141C2×C3⋊D3—44no—
142C2×C3⋊D3—42no—
143C32×C4—41no—
144C32×C4#12011yescharacteristic
145C32×C4#12112yes—
146C32×C4#12711yescharacteristic
147C3⋊Dic3—44no—
148C3⋊Dic3—42no—
149C2×#41—92no—
150C23×C4C2×C3⋊D311yescharacteristic
151#137—182no—
152AGL(1,ℤ/8)—182no—
153#135—182no—
154C2×M16C2×C3⋊D311yescharacteristic
155C2×M16C2×C3⋊D311yescharacteristic
156#123—182no—
157C22⋊Q8—182no—
158#121—182no—
159#120—182no—
160C4×D4—184no—
161#117—92no—
162#104—184no—
163C22⋊C8—22no—
164C23×C3—28no—
165C23×C3—24no—
166C23×C3—48no—
167C23×C3C2×D1214yes—
168C22×D3—68no—
169C2×C3×C4—28no—
170C2×C3×C4—24no—
171C2×C3×C4—48no—
172C2×C3×C4—44no—
173C2×C3×C4—44no—
174C2×C3×C4#23514yes—
175C2×C3×C4D3×D418yes—
176C2×C3×C4D3×D418yes—
177C2×C3×C4C2×#6714yes—
178#67—1232no—
179#67—128no—
180#67—128no—
181C2×Dic3—616no—
182C2×Dic3—68no—
183D12—68no—
184D12—68no—
185C4×D3—128no—
186C4×D3—128no—
187Dic6—68no—
188Dic6—68no—
189C3×C8—28no—
190C3×C8—44no—
191C2×C32—22no—
192C2×C32—21no—
193C2×C32—42no—
194C2×C32#39211yescharacteristic
195C3⋊D3—82no—
196C24C4⋊(C3⋊D3)11yescharacteristic
197#41—182no—
198#41—182no—
199#41—182no—
200#41—182no—
201C2×Q8—92no—
202C2×D4—92no—
203C2×D4—184no—
204C2×D4—182no—
205C22×C4—21no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—21no—
209C22×C4—182no—
210C22×C4C4⋊(C3⋊D3)11yescharacteristic
211C22×C4C22×C3⋊D311yescharacteristic
212Q16—182no—
213SD16—184no—
214D8—182no—
215M16—22no—
216M16—22no—
217C2×C8—21no—
218C2×C8#63812yescomplemented
219C4⋊C4—184no—
220C4⋊C4—182no—
221C22⋊C4—184no—
222C22⋊C4—184no—
223C22⋊C4—182no—
224C42—94no—
225C22×C3—216no—
226C22×C3—28no—
227C22×C3—44no—
228C22×C3—48no—
229C22×C3—44no—
230C22×C3—44no—
231C22×C3#88218yes—
232C22×C3#93014yes—
233C2×D3—1216no—
234C2×D3—128no—
235C3×C4—44no—
236C3×C4#88418yes—
237C3×C4#93714yes—
238C3×C4#94014yes—
239Dic3—1216no—
240Dic3—128no—
241C32#201011yescharacteristic, complemented, Sylow
242C23—22no—
243C23—21no—
244C23—42no—
245C23—182no—
246C23C2×C4⋊(C3⋊D3)11yescharacteristic
247Q8—182no—
248Q8—182no—
249D4—182no—
250D4—182no—
251D4—368no—
252D4—362no—
253D4—362no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—42no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—184no—
260C2×C4—182no—
261C2×C4—362no—
262C2×C4—362no—
263C2×C4#382811yescharacteristic
264C2×C4D4×C3⋊D312yes—
265C2×C4D4×C3⋊D312yes—
266C2×C4C2×#63811yescharacteristic
267C8—22no—
268C8—41no—
269C2×C3—28no—
270C2×C3—24no—
271C2×C3—48no—
272C2×C3#496014yes—
273D3—248no—
274C22—24no—
275C22—22no—
276C22—41no—
277C22—42no—
278C22—41no—
279C22—41no—
280C22—364no—
281C22—362no—
282C22#6409112yes—
283C22#6413911yescharacteristic
284C4—41no—
285C4—364no—
286C4—362no—
287C4#6409312yes—
288C4#6414611yescharacteristic
289C4#6414911yescharacteristic
290C3#6999314yescomplemented
291C2—22no—
292C2—21no—
293C2—42no—
294C2—722no—
295C2#1059265911yescharacteristic
subgroupG/H
centerC4#64149
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#407C2
socleC2×C32#392
hypercenter#407C3⋊D3
hypocenterC32#2010
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. #10596262C2semidirect
2. #10596219C2semidirect
3. C32×#407C2semidirect
4. #10592838C2semidirect
5. #10589423C2semidirect
24. C3×#407D3semidirect
40. C2×C4⋊(C3⋊D3)D4semidirect
42. C2×#634D4semidirect
46. C2×C32×C8D4semidirect
52. C4×C3⋊Dic3D4semidirect
102. #407C3⋊D3semidirect
123. C2×C3×C8#67semidirect
218. C2×C8#638semidirect
241. C32#2010semidirect
290. C3#69993semidirect

Maximal subgroups

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

subgroupindex
#105962622
#105962192
C32×#4072
#105928382
#105894232
#699933