Finite Group Databasebeta

← #11796855

Subgroups — #11796855

Order 1152.

490 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 62 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
1C2×#64128C211yesmaximal, characteristic
2#10593768C211yesmaximal, characteristic, complemented
3#10593762C211yesmaximal, characteristic, complemented
4#10590196C214yesmaximal, complemented
5C2×#3832—21no—
6#64286—21no—
7C2×C32×Q16C411yescharacteristic, complemented
8C2×#3755—21no—
9#64128—21no—
10#64128—21no—
11#64128C412yescomplemented
12#64128C2212yes—
13C2×#3745C411yescharacteristic, complemented
14C2×C8×C3⋊D3C2211yescharacteristic
15#63773—21no—
16#63769—21no—
17#63768C2212yescomplemented
18#63765C2212yescomplemented
19#63764—21no—
20C2×#919—62no—
21C2×C32×Q8—21no—
22#3832—22no—
23#3832—22no—
24#3832—41no—
25#3832—41no—
26C2×C4⋊(C3⋊D3)—21no—
27C2×C4⋊(C3⋊D3)—41no—
28C2×C4×C3⋊D3—41no—
29C2×C4×C3⋊D3D411yescharacteristic
30C22⋊#157—41no—
31C4⋊#157—22no—
32C4×#157—41no—
33C32×Q16—21no—
34C32×Q16C2×C412yes—
35C2×C32×C8C2×C411yescharacteristic
36#3755—22no—
37#3755—22no—
38C2×C3⋊(C3⋊C8)D411yescharacteristic
39#3745—21no—
40#3745C2×C412yes—
41C8×C3⋊D3C2×C411yescharacteristic
42C8×C3⋊D3D411yescharacteristic
43C8×C3⋊D3D411yescharacteristic
44C8×C3⋊D3C2311yescharacteristic
45#3708—22no—
46#2145—91nomaximal, Sylow
47C2×#239—64no—
48C2×C3×Q16—22no—
49C2×#215—64no—
50#919—64no—
51#919—64no—
52#919—64no—
53#919—64no—
54C2×D24—62no—
55C2×D3×C8—62no—
56C22×C3⋊D3—41no—
57C22×C3⋊D3D811yescharacteristic
58C2×#157—42no—
59C32×Q8—22no—
60C32×Q8—41no—
61C2×C32×C4—41no—
62C2×C32×C4C22⋊C411yescharacteristic
63C2×C3⋊Dic3SD1611yescharacteristic
64C4⋊(C3⋊D3)—22no—
65C4⋊(C3⋊D3)—42no—
66C4⋊(C3⋊D3)—42no—
67C4⋊(C3⋊D3)—41no—
68C4×C3⋊D3—42no—
69C4×C3⋊D3—42no—
70C4×C3⋊D3C22⋊C411yescharacteristic
71C4×C3⋊D3D811yescharacteristic
72C4×C3⋊D3SD1611yescharacteristic
73C4×C3⋊D3C2×D411yescharacteristic
74C32×C8C22⋊C411yescharacteristic
75C32×C8C22×C411yescharacteristic
76C3⋊(C3⋊C8)C22⋊C411yescharacteristic
77C3⋊(C3⋊C8)C2×D411yescharacteristic
78C2×#135—91no—
79C2×M32—91no—
80#427—91no—
81#360—94no—
82C2×C3×Q8—24no—
83#239—68no—
84#239—68no—
85#239—124no—
86#239—124no—
87C2×D12—64no—
88C2×D12—124no—
89C2×C4×D3—62no—
90C2×C4×D3—124no—
91C3×Q16—24no—
92C3×Q16—24no—
93C2×C3×C8—22no—
94#215—68no—
95#215—68no—
96C2×C3⋊C8—62no—
97D24—64no—
98D24—64no—
99D3×C8—62no—
100D3×C8—62no—
101D3×C8—62no—
102D3×C8—62no—
103C22×C32#10211yescharacteristic
104C2×C3⋊D3—41no—
105C2×C3⋊D3—42no—
106C2×C3⋊D3—82no—
107C2×C3⋊D3#10211yescharacteristic
108C2×C3⋊D3C2×D811yescharacteristic
109#157—82no—
110C32×C4—42no—
111C32×C4#10211yescharacteristic
112C32×C4C2×C22⋊C411yescharacteristic
113C3⋊Dic3#10211yescharacteristic
114C3⋊Dic3C2×SD1611yescharacteristic
115C2×#41—181no—
116#135—92no—
117#135—92no—
118#135—181no—
119#135—181no—
120C2×Q16#15711yescharacteristic, complemented
121C2×SD16—181no—
122C2×D8—91no—
123C22×C8—91no—
124#117—181no—
125M32—92no—
126M32—181no—
127C2×C16—181no—
128#107—181no—
129#106—92no—
130C22×D3—62no—
131C22×D3—124no—
132C3×Q8—28no—
133C3×Q8—44no—
134C2×C3×C4—22no—
135C2×C3×C4—44no—
136C2×Dic3—62no—
137D12—68no—
138D12—124no—
139D12—128no—
140D12—128no—
141C4×D3—62no—
142C4×D3—62no—
143C4×D3—62no—
144C4×D3—62no—
145C4×D3—128no—
146C4×D3—128no—
147C3×C8—22no—
148C3×C8—22no—
149C3⋊C8—62no—
150C3⋊C8—62no—
151C2×C32—21no—
152C2×C32C2×#10211yescharacteristic
153C3⋊D3—21no—
154C3⋊D3—21no—
155C3⋊D3—82no—
156#41—182no—
157#41—182no—
158#41—361no—
159#41—361no—
160C2×Q8—21no—
161C2×D4—181no—
162C2×D4—361no—
163C22×C4—91no—
164C22×C4—361no—
165Q16—21no—
166Q16C2×#15712yes—
167SD16—182no—
168SD16—182no—
169D8—92no—
170D8—181no—
171C2×C8—91no—
172C2×C8—91no—
173C2×C8—91no—
174C2×C8—91no—
175C2×C8—91no—
176C2×C8C2×#15711yescharacteristic
177C4⋊C4—182no—
178C22⋊C4—361no—
179C42—361no—
180C16—182no—
181C22×C3—22no—
182C2×D3—62no—
183C2×D3—62no—
184C2×D3—124no—
185C2×D3—128no—
186C2×D3—248no—
187C3×C4—22no—
188C3×C4—22no—
189C3×C4—48no—
190Dic3—62no—
191Dic3—62no—
192C32#214511yescharacteristic, complemented, Sylow
193C23—91no—
194C23—361no—
195Q8—22no—
196Q8—41no—
197D4—182no—
198D4—362no—
199D4—362no—
200D4—361no—
201C2×C4—41no—
202C2×C4—91no—
203C2×C4—91no—
204C2×C4—91no—
205C2×C4—91no—
206C2×C4—91no—
207C2×C4—362no—
208C2×C4—362no—
209C2×C4—362no—
210C2×C4C22⋊#15711yescharacteristic
211C8—91no—
212C8—91no—
213C8C22⋊#15711yescharacteristic
214C8C22×#15711yescharacteristic
215C2×C3—24no—
216C2×C3—22no—
217D3—122no—
218D3—122no—
219D3—248no—
220C22—91no—
221C22—91no—
222C22—361no—
223C22—362no—
224C22—722no—
225C22#6378211yescharacteristic
226C4—42no—
227C4—91no—
228C4—91no—
229C4—722no—
230C4#6378211yescharacteristic
231C4C2×C22⋊#15711yescharacteristic
232C3—22no—
233C2—21no—
234C2—181no—
235C2—181no—
236C2—722no—
237C2C2×#6378211yescharacteristic
subgroupG/H
centerC2C2×#63782
commutatorC32×C8C22×C4
FrattiniC8C22×#157
FittingC2×C32×Q16C4
socleC2×C32C2×#102
prime radicalC2×#64128C2
cosocleC8×C3⋊D3C23
hypercenterC2×Q16#157
hypocenterC32#2145
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
2. #10593768C2semidirect
3. #10593762C2semidirect
4. #10590196C2semidirect
7. C2×C32×Q16C4semidirect
11. #64128C4semidirect
13. C2×#3745C4semidirect
17. #63768C22semidirect
18. #63765C22semidirect
120. C2×Q16#157semidirect
192. C32#2145semidirect

Maximal subgroups

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

subgroupindex
C2×#641282
#105937682
#105937622
#105901962
#21459