Finite Group Databasebeta

← #11876978

Subgroups — #11876978

Order 1152.

1338 conjugacy classes of subgroups; only the 257 normal subgroups are shown.

normal subgroups only

This group has 1338 conjugacy classes of subgroups — too many to draw. Only its 257 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#10596196C212yesmaximal, complemented
2C32×#498C211yesmaximal, characteristic, complemented
3#10592787C212yesmaximal, complemented
4#10592568C214yesmaximal, complemented
5#10592564C214yesmaximal, complemented
6#10592394C211yesmaximal, characteristic, complemented
7C4×#3743C211yesmaximal, characteristic, complemented
8#81888—34nomaximal
9C2×#3832—22no—
10C32×C4⋊Q8C2212yes—
11#64156—22no—
12C2×#3745C2214yes—
13C2×#3743C2212yes—
14#64104—22no—
15#64104C2214yes—
16#64102—22no—
17#64102C2214yes—
18#64083C2212yes—
19C42×C3⋊D3C2211yescharacteristic
20C32×#106C2214yes—
21C32×C4×C8C2211yescharacteristic
22#63642C2212yes—
23#63636C2218yes—
24C4×C3⋊(C3⋊C8)C2211yescharacteristic
25#5725—38no—
26C3×#498D314yescomplemented
27#5088—38no—
28#4869—316no—
29#4865—316no—
30#4695—34no—
31C4×ΓL(1,𝔽25)—34no—
32C2×C32×Q8—22no—
33#3832—48no—
34C2×C4⋊(C3⋊D3)—24no—
35C2×C4⋊(C3⋊D3)—22no—
36C2×C4⋊(C3⋊D3)—22no—
37C2×C4⋊(C3⋊D3)C2314yes—
38C2×C4×C3⋊D3—24no—
39C2×C4×C3⋊D3D412yes—
40C2×C4×C3⋊D3C2311yescharacteristic
41C2×C32×C8C2312yes—
42C32×C4⋊C4—22no—
43C32×C4⋊C4C2314yes—
44C32×C42C2311yescharacteristic
45#3752—24no—
46#3752—24no—
47C4×C3⋊Dic3D412yes—
48C4×C3⋊Dic3C2311yescharacteristic
49C2×C3⋊(C3⋊C8)C2312yes—
50#3745—28no—
51#3743—24no—
52#3184—91noSylow
53C2×#239—68no—
54C3×C4⋊Q8C2×D318yes—
55#947—68no—
56C2×D24—316no—
57C2×ΓL(1,𝔽25)—38no—
58#895—316no—
59#895—68no—
60#893—316no—
61#893—68no—
62#874—38no—
63C42×D3—34no—
64C3×#106C2×D3116yes—
65C3×C4×C8C2×D314yes—
66#815—38no—
67#809—332no—
68C4×C3⋊C8—34no—
69C22×C3⋊D3—24no—
70C22×C3⋊D3C2×D411yescharacteristic
71C32×Q8—44no—
72C2×C32×C4—24no—
73C2×C32×C4C2×D412yes—
74C2×C32×C4C2411yescharacteristic
75C2×C3⋊Dic3C2×D411yescharacteristic
76C2×C3⋊Dic3C2×D412yes—
77C4⋊(C3⋊D3)—28no—
78C4⋊(C3⋊D3)—48no—
79C4⋊(C3⋊D3)—44no—
80C4⋊(C3⋊D3)—44no—
81C4×C3⋊D3—24no—
82C4×C3⋊D3—22no—
83C4×C3⋊D3—48no—
84C32×C8#4114yescomplemented
85C3⋊(C3⋊C8)—22no—
86#532—92no—
87#498C3⋊D311yescharacteristic, complemented
88#493—91no—
89#486—92no—
90#469—94no—
91#442—94no—
92C4×M16—91no—
93C2×C3×Q8—28no—
94#239—1232no—
95C2×D12—316no—
96C2×D12—616no—
97C2×D12—68no—
98C2×D12—68no—
99C2×C4×D3—38no—
100C2×C4×D3—34no—
101C2×C4×D3—616no—
102C2×C3×C8C22×D318yes—
103C3×C4⋊C4—28no—
104C3×C4⋊C4C22×D3116yes—
105C3×C42C22×D314yes—
106(C2×D3)⋊C4—616no—
107(C2×D3)⋊C4—616no—
108C4×Dic3—38no—
109C4×Dic3—34no—
110C2×C3⋊C8—38no—
111D24—632no—
112ΓL(1,𝔽25)—616no—
113C22×C32C22×D411yescharacteristic
114C2×C3⋊D3—21no—
115C2×C3⋊D3—22no—
116C2×C3⋊D3—44no—
117C2×C3⋊D3—44no—
118C2×C3⋊D3—44no—
119C32×C4—44no—
120C32×C4AGL(1,ℤ/8)14yes—
121C32×C4C2×#4112yes—
122C3⋊Dic3—21no—
123C3⋊Dic3—22no—
124C2×#41—182no—
125C2×D8—94no—
126C2×M16—92no—
127C4⋊Q8C2×C3⋊D312yes—
128#127—92no—
129#124—182no—
130#121—94no—
131#121—182no—
132C4×D4—94no—
133C4×D4—182no—
134C2×C42—91no—
135#106C2×C3⋊D314yes—
136#102—98no—
137#97—92no—
138C4×C8—91no—
139C4×C8C2×C3⋊D311yescharacteristic
140C22×D3—34no—
141C22×D3—616no—
142C3×Q8—416no—
143C2×C3×C4—216no—
144C2×C3×C4D3×D418yes—
145C2×C3×C4C23×D314yes—
146C2×Dic3—34no—
147C2×Dic3—38no—
148D12—632no—
149D12—1232no—
150D12—1216no—
151D12—1216no—
152C4×D3—616no—
153C4×D3—68no—
154C4×D3—1232no—
155C3×C8#239116yescomplemented
156C3⋊C8—68no—
157C2×C32#53211yescharacteristic
158C2×C32C2×AGL(1,ℤ/8)12yes—
159C3⋊D3—41no—
160C3⋊D3—84no—
161#41—368no—
162C2×Q8—22no—
163C2×D4—94no—
164C2×D4—184no—
165C2×D4—182no—
166C2×D4—182no—
167C22×C4—91no—
168C22×C4—92no—
169C22×C4—184no—
170D8—188no—
171M16—184no—
172C2×C8—92no—
173C2×C8C22×C3⋊D312yes—
174C4⋊C4—22no—
175C4⋊C4C22×C3⋊D314yes—
176C22⋊C4—184no—
177C22⋊C4—184no—
178C42—91no—
179C42—92no—
180C42C22×C3⋊D311yescharacteristic
181C22×C3C2×D3×D414yes—
182C2×D3—64no—
183C2×D3—68no—
184C2×D3—1216no—
185C2×D3—1216no—
186C2×D3—1216no—
187C3×C4—416no—
188C3×C4#914116yes—
189C3×C4C2×#23918yes—
190Dic3—64no—
191Dic3—68no—
192C32#318411yescharacteristic, complemented, Sylow
193C23—91no—
194C23—184no—
195Q8—44no—
196D4—188no—
197D4—368no—
198D4—364no—
199D4—364no—
200C2×C4—24no—
201C2×C4—91no—
202C2×C4—92no—
203C2×C4—182no—
204C2×C4—184no—
205C2×C4—368no—
206C2×C4D4×C3⋊D312yes—
207C2×C4C23×C3⋊D311yescharacteristic
208C8—182no—
209C8#383214yescomplemented
210C2×C3#572514yes—
211C2×C3C2×#91418yes—
212D3—124no—
213D3—2416no—
214C22—181no—
215C22—182no—
216C22—364no—
217C22—364no—
218C22—364no—
219C22C2×D4×C3⋊D311yescharacteristic
220C4—44no—
221C4—181no—
222C4—182no—
223C4#6412314yes—
224C4C2×#383212yes—
225C3#8188814yescomplemented
226C2—361no—
227C2—724no—
228C2#1059619611yescharacteristic
229C2C2×#6412312yes—
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#498C2
socleC22×C32C22×D4
hypercenter#498C3⋊D3
hypocenterC32#3184
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
1. #10596196C2semidirect
2. C32×#498C2semidirect
3. #10592787C2semidirect
4. #10592568C2semidirect
5. #10592564C2semidirect
6. #10592394C2semidirect
7. C4×#3743C2semidirect
26. C3×#498D3semidirect
84. C32×C8#41semidirect
87. #498C3⋊D3semidirect
155. C3×C8#239semidirect
192. C32#3184semidirect
209. C8#3832semidirect
225. C3#81888semidirect

Maximal subgroups

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

subgroupindex
#105961962
C32×#4982
#105927872
#105925682
#105925642
#105923942
C4×#37432
#818883