Finite Group Databasebeta

← #11797988

Subgroups — #11797988

Order 1152.

272 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 43 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#10593334C211yesmaximal, characteristic
2#10590390C211yesmaximal, characteristic, complemented
3#10590344C211yesmaximal, characteristic, complemented
4#10590149C211yesmaximal, characteristic, complemented
5#10590067C211yesmaximal, characteristic, complemented
6#10590065C211yesmaximal, characteristic, complemented
7#10590064C211yesmaximal, characteristic, complemented
8C3×C4×D12—21no—
9#63822C2211yescharacteristic
10C2×#3713C2211yescharacteristic
11#63815—21no—
12#63773C2211yescharacteristic
13#63773C2211yescharacteristic
14#63735C412yescomplemented
15#63734C412yescomplemented
16#63630C2211yescharacteristic
17C3×#805—21no—
18#63578C2211yescharacteristic
19#63574C2211yescharacteristic
20#63562—21no—
21#5014—61no—
22#4823—61no—
23C3×#235—21no—
24C2×C3×D12—21no—
25C2×C3×C4×D3—41no—
26C32×C42D411yescharacteristic
27C2×C3⋊(C3⋊C8)D411yescharacteristic
28C2×C3⋊(C3⋊C8)C2311yescharacteristic
29C3×(C2×D3)⋊C4—41no—
30C3×C4⋊Dic3—21no—
31C3×#208—21no—
32#3718C2×C411yescharacteristic, complemented
33#3715—21no—
34#3713—21no—
35#3713C2×C412yes—
36#3713C2×C411yescharacteristic, complemented
37#3711—41no—
38D3×C3⋊C8—41no—
39#3708—21no—
40#3708C2×C412yescomplemented
41AGL(1,ℤ/16)—91nomaximal, Sylow
42C3×C4×D4—61no—
43#950—61no—
44#948—61no—
45C2×#213—61no—
46#907—61no—
47C4×D12—21no—
48C3×#104—61no—
49#832—61no—
50#822—61no—
51#809—61no—
52#808—61no—
53#805—21no—
54#803—61no—
55#803—61no—
56C22×C3×D3—41no—
57C2×C32×C4—21no—
58C2×C32×C4C2×D411yescharacteristic
59C3×#67—41no—
60C2×C3×Dic3—41no—
61C3×D12—22no—
62C3×D12—21no—
63C3×D12—41no—
64C3×C4×D3—41no—
65C3×C4×D3—82no—
66C3×Dic6—21no—
67C3⋊(C3⋊C8)—21no—
68C3⋊(C3⋊C8)C22×C411yescharacteristic
69C3⋊(C3⋊C8)#4111yescharacteristic
70C3×C3⋊C8—41no—
71#509—91no—
72#444—91no—
73#442—91no—
74#365—91no—
75#361—91no—
76#360—91no—
77#347—91no—
78C3×#41—61no—
79C2×C3×D4—61no—
80C22×C3×C4—121no—
81#235—21no—
82C2×D12—21no—
83C2×C4×D3—41no—
84C3×M16—61no—
85C3×C4⋊C4—61no—
86C3×C22⋊C4—121no—
87C3×C42—21no—
88C3×C42—21no—
89#216—61no—
90#215—61no—
91#214—61no—
92#213—62no—
93#213—61no—
94#213—62no—
95(C2×D3)⋊C4—41no—
96C4⋊Dic3—21no—
97#208—21no—
98#208—121no—
99C2×C3⋊C8—61no—
100C2×C3⋊C8—61no—
101C2×C3⋊C8—61no—
102C2×C3⋊C8—61no—
103C2×C3⋊C8—121no—
104ΓL(1,𝔽25)—121no—
105D3×C8—121no—
106C22×C32AGL(1,ℤ/8)11yescharacteristic
107C2×C3×D3—41no—
108C2×C3×D3—42no—
109C2×C3×D3—81no—
110C2×C3×D3—81no—
111C32×C4—41no—
112C32×C4C4×D411yescharacteristic
113C32×C4AGL(1,ℤ/8)11yescharacteristic
114C3×Dic3—41no—
115C3×Dic3—81no—
116#135—91no—
117C2×D8—91no—
118#131—181no—
119C4×D4—61no—
120SD32—92no—
121D16—92no—
122M32—91no—
123M32—91no—
124#108—91no—
125#106—91no—
126#104—61no—
127#102—181no—
128#97—91no—
129C23×C3—121no—
130C22×D3—41no—
131C3×Q8—61no—
132C3×D4—62no—
133C3×D4—61no—
134C3×D4—121no—
135C3×D4—121no—
136C2×C3×C4—21no—
137C2×C3×C4—21no—
138C2×C3×C4—21no—
139C2×C3×C4—21no—
140C2×C3×C4—41no—
141C2×C3×C4—121no—
142C2×C3×C4—121no—
143C2×C3×C4—242no—
144#67—41no—
145C2×Dic3—41no—
146D12—22no—
147D12—21no—
148D12—41no—
149C4×D3—41no—
150C4×D3—82no—
151Dic6—21no—
152C3×C8—121no—
153C3⋊C8—41no—
154C3⋊C8—61no—
155C3⋊C8—61no—
156C3⋊C8—61no—
157C3⋊C8—61no—
158C3⋊C8—61no—
159C3⋊C8—61no—
160C3⋊C8—121no—
161C2×C32—21no—
162C2×C32#44211yescharacteristic
163C3×D3—81no—
164C3×D3—82no—
165#41—61no—
166C2×D4—61no—
167C22×C4—121no—
168Q16—91no—
169SD16—181no—
170D8—91no—
171D8—92no—
172D8—181no—
173M16—61no—
174M16—361no—
175C2×C8—91no—
176C2×C8—91no—
177C2×C8—361no—
178C4⋊C4—61no—
179C22⋊C4—121no—
180C42GO+(4,𝔽2)11yescharacteristic
181C16—92no—
182C16—181no—
183C22×C3—21no—
184C22×C3—21no—
185C22×C3—121no—
186C22×C3—122no—
187C22×C3—241no—
188C22×C3—241no—
189C2×D3—41no—
190C2×D3—42no—
191C2×D3—81no—
192C2×D3—81no—
193C3×C4—21no—
194C3×C4—21no—
195C3×C4—21no—
196C3×C4—21no—
197C3×C4—41no—
198C3×C4—41no—
199C3×C4—81no—
200C3×C4—121no—
201C3×C4—241no—
202Dic3—41no—
203Dic3—81no—
204C32AGL(1,ℤ/16)11yescharacteristic, complemented, Sylow
205C23—121no—
206Q8—61no—
207D4—62no—
208D4—61no—
209D4—121no—
210D4—121no—
211C2×C4—21no—
212C2×C4—121no—
213C2×C4—121no—
214C2×C4—242no—
215C2×C4C2×GO+(4,𝔽2)11yescharacteristic
216C8—91no—
217C8—91no—
218C8—121no—
219C8—181no—
220C2×C3—21no—
221C2×C3—21no—
222C2×C3—21no—
223C2×C3—21no—
224C2×C3—41no—
225C2×C3—242no—
226C2×C3—241no—
227D3—82no—
228D3—81no—
229C22—121no—
230C22—122no—
231C22—241no—
232C22—241no—
233C22#6423611yescharacteristic
234C4—41no—
235C4—121no—
236C4—241no—
237C4#6422411yescharacteristic
238C4C4×GO+(4,𝔽2)11yescharacteristic
239C3—21no—
240C3—21no—
241C2—21no—
242C2—242no—
243C2—241no—
244C2#1059341911yescharacteristic
subgroupG/H
centerC2#10593419
commutatorC3⋊(C3⋊C8)C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socleC2×C32#442
prime radical#10593334C2
cosocleC2×C3⋊(C3⋊C8)C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32AGL(1,ℤ/16)
LCSG ▷ C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
2. #10590390C2semidirect
3. #10590344C2semidirect
4. #10590149C2semidirect
5. #10590067C2semidirect
6. #10590065C2semidirect
7. #10590064C2semidirect
14. #63735C4semidirect
15. #63734C4semidirect
32. #3718C2×C4semidirect
36. #3713C2×C4semidirect
40. #3708C2×C4semidirect
204. C32AGL(1,ℤ/16)semidirect

Maximal subgroups

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

subgroupindex
#105933342
#105903902
#105903442
#105901492
#105900672
#105900652
#105900642
AGL(1,ℤ/16)9