Finite Group Databasebeta

← #11796494

Subgroups — #11796494

Order 1152.

750 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 750 conjugacy classes of subgroups — too many to draw. Only its 107 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#10596196C211yesmaximal, characteristic
2#10592450C212yesmaximal, complemented
3C32×#356C211yesmaximal, characteristic, complemented
4#10589414C211yesmaximal, characteristic, complemented
5#10589343C212yesmaximal, complemented
6#69172—34nomaximal
7C2×#3832C411yescharacteristic
8C2×#3832C2211yescharacteristic
9C32×C4⋊Q8C2211yescharacteristic
10#64156C411yescharacteristic
11#64156C2211yescharacteristic
12M16×C3⋊D3—22no—
13#64104—22no—
14#64102—22no—
15#64083C411yescharacteristic
16C42×C3⋊D3C411yescharacteristic
17C32×#101C2212yes—
18#63663C2212yes—
19#63650—22no—
20#5725—34no—
21#4751—38no—
22C3×#356D314yescomplemented
23#4548—34no—
24#4477—38no—
25C2×C32×Q8C2×C411yescharacteristic
26C2×C32×Q8C2311yescharacteristic
27#3832—41no—
28#3832—41no—
29#3832—41no—
30#3832—41no—
31C2×C4⋊(C3⋊D3)—22no—
32C2×C4⋊(C3⋊D3)—21no—
33C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
34C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
35C2×C4⋊(C3⋊D3)D412yes—
36C2×C4×C3⋊D3—21no—
37C2×C4×C3⋊D3—21no—
38C2×C4×C3⋊D3C2×C411yescharacteristic
39C2×C4×C3⋊D3D412yes—
40C32×M16—22no—
41C32×C4⋊C4—22no—
42C32×C42C2×C411yescharacteristic
43#3752—22no—
44#3752—22no—
45C4×C3⋊Dic3—21no—
46C4×C3⋊Dic3C2×C411yescharacteristic
47#3748—22no—
48#3743—42no—
49C8×C3⋊D3—42no—
50#2132—91noSylow
51C2×#239—34no—
52C2×#239—34no—
53C3×C4⋊Q8C2×D314yes—
54#947—34no—
55#947—34no—
56D3×M16—68no—
57#895—68no—
58#893—68no—
59#874—34no—
60C42×D3—34no—
61C3×#101C2×D318yes—
62#836—38no—
63#823—68no—
64C22×C3⋊D3—21no—
65C22×C3⋊D3C22⋊C412yes—
66C22×C3⋊D3C22⋊C411yescharacteristic
67C32×Q8—41no—
68C32×Q8—41no—
69C2×C32×C4—21no—
70C2×C32×C4—21no—
71C2×C32×C4C22×C411yescharacteristic
72C2×C32×C4C2×D412yes—
73C2×C3⋊Dic3—21no—
74C2×C3⋊Dic3C22⋊C411yescharacteristic
75C4⋊(C3⋊D3)—41no—
76C4⋊(C3⋊D3)—42no—
77C4⋊(C3⋊D3)—41no—
78C4⋊(C3⋊D3)—44no—
79C4⋊(C3⋊D3)—42no—
80C4×C3⋊D3—22no—
81C4×C3⋊D3—22no—
82C4×C3⋊D3—21no—
83C4×C3⋊D3—21no—
84C4×C3⋊D3—42no—
85C4×C3⋊D3—41no—
86C4×C3⋊D3—41no—
87C32×C8—42no—
88C3⋊(C3⋊C8)—42no—
89#532—91no—
90#413—92no—
91#356—91no—
92#356C3⋊D311yescharacteristic, complemented
93#355—92no—
94C2×C3×Q8C4×D314yes—
95C2×C3×Q8C22×D314yes—
96#239—124no—
97#239—124no—
98#239—124no—
99#239—124no—
100C2×D12—34no—
101C2×D12—34no—
102C2×D12—38no—
103C2×D12—68no—
104C2×D12—64no—
105C2×C4×D3—34no—
106C2×C4×D3—38no—
107C2×C4×D3—64no—
108C2×C4×D3—64no—
109C3×M16—28no—
110C3×C4⋊C4—28no—
111C3×C42C4×D314yes—
112(C2×D3)⋊C4—68no—
113(C2×D3)⋊C4—68no—
114C4×Dic3—34no—
115C4×Dic3—64no—
116#208—68no—
117ΓL(1,𝔽25)—128no—
118D3×C8—128no—
119C22×C32C2×C22⋊C411yescharacteristic
120C2×C3⋊D3—21no—
121C2×C3⋊D3—22no—
122C2×C3⋊D3—41no—
123C2×C3⋊D3—42no—
124C2×C3⋊D3—42no—
125C2×C3⋊D3—41no—
126C32×C4—22no—
127C32×C4—22no—
128C32×C4—21no—
129C32×C4—41no—
130C3⋊Dic3—41no—
131C3⋊Dic3#9911yescharacteristic
132C3⋊Dic3#9911yescharacteristic
133C2×#41—91no—
134C2×#41—91no—
135C2×M16—182no—
136C4⋊Q8C2×C3⋊D311yescharacteristic
137#127—91no—
138#124—91no—
139#124—91no—
140#121—182no—
141C4×D4—182no—
142C2×C42—91no—
143#101—92no—
144#101C2×C3⋊D312yes—
145#100—182no—
146C22×D3—38no—
147C22×D3—34no—
148C22×D3—64no—
149C3×Q8—44no—
150C3×Q8—44no—
151C2×C3×C4—24no—
152C2×C3×C4—24no—
153C2×C3×C4C2×C4×D314yes—
154C2×C3×C4D3×D418yes—
155C2×Dic3—34no—
156C2×Dic3—64no—
157D12—128no—
158D12—124no—
159D12—124no—
160D12—1216no—
161D12—128no—
162C4×D3—68no—
163C4×D3—68no—
164C4×D3—64no—
165C4×D3—64no—
166C4×D3—124no—
167C4×D3—124no—
168C4×D3—128no—
169C3×C8—48no—
170C3⋊C8—128no—
171C2×C32—21no—
172C2×C32C2×#9911yescharacteristic
173C3⋊D3—41no—
174C3⋊D3—42no—
175C3⋊D3—81no—
176#41—361no—
177#41—361no—
178#41—361no—
179#41—361no—
180C2×Q8C4×C3⋊D311yescharacteristic
181C2×Q8C22×C3⋊D311yescharacteristic
182C2×D4—91no—
183C2×D4—91no—
184C2×D4—92no—
185C2×D4—182no—
186C2×D4—181no—
187C22×C4—91no—
188C22×C4—92no—
189C22×C4—181no—
190C22×C4—181no—
191M16—22no—
192M16—182no—
193M16—362no—
194C2×C8—362no—
195C4⋊C4—22no—
196C22⋊C4—182no—
197C22⋊C4—182no—
198C42—91no—
199C42—181no—
200C42C4×C3⋊D311yescharacteristic
201C22×C3D3×C22⋊C414yes—
202C2×D3—64no—
203C2×D3—68no—
204C2×D3—124no—
205C2×D3—128no—
206C2×D3—128no—
207C2×D3—124no—
208C3×C4—28no—
209C3×C4—28no—
210C3×C4—24no—
211C3×C4—44no—
212Dic3—34no—
213Dic3—34no—
214Dic3—124no—
215C32#213211yescharacteristic, complemented, Sylow
216C23—92no—
217C23—91no—
218C23—181no—
219Q8—41no—
220Q8—41no—
221D4—362no—
222D4—361no—
223D4—361no—
224D4—364no—
225D4—362no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—91no—
229C2×C4—182no—
230C2×C4—182no—
231C2×C4—181no—
232C2×C4—181no—
233C2×C4—181no—
234C2×C4—362no—
235C2×C4—361no—
236C2×C4—361no—
237C2×C4C2×C4×C3⋊D311yescharacteristic
238C2×C4D4×C3⋊D312yes—
239C8—42no—
240C8—362no—
241C2×C3—24no—
242C2×C3D3×#9914yes—
243D3—124no—
244D3—128no—
245D3—244no—
246C22—181no—
247C22—182no—
248C22—361no—
249C22—362no—
250C22—362no—
251C22—361no—
252C22C22⋊C4×C3⋊D311yescharacteristic
253C4—22no—
254C4—22no—
255C4—21no—
256C4—41no—
257C4—91no—
258C4—91no—
259C4—361no—
260C3#6917214yescomplemented
261C2—21no—
262C2—361no—
263C2—362no—
264C2—721no—
265C2C3⋊D3×#9911yescharacteristic
subgroupG/H
centerC2C3⋊D3×#99
commutatorC2×C32×C4C22×C4
FrattiniC2×Q8C22×C3⋊D3
FittingC32×#356C2
socleC2×C32C2×#99
prime radical#10596196C2
cosocleC2×C32×Q8C23
hypercenter#356C3⋊D3
hypocenterC32#2132
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #356

Complements

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

NH ≅ G/Ntype
2. #10592450C2semidirect
3. C32×#356C2semidirect
4. #10589414C2semidirect
5. #10589343C2semidirect
22. C3×#356D3semidirect
92. #356C3⋊D3semidirect
215. C32#2132semidirect
260. C3#69172semidirect

Maximal subgroups

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

subgroupindex
#105961962
#105924502
C32×#3562
#105894142
#105893432
#691723