Finite Group Databasebeta

← #11877031

Subgroups — #11877031

Order 1152.

1074 conjugacy classes of subgroups; only the 257 normal subgroups are shown.

normal subgroups only

This group has 1074 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#10596199C212yesmaximal
2C32×#498C211yesmaximal, characteristic, complemented
3#10592792C212yesmaximal, complemented
4#10592566C214yesmaximal
5#10592552C214yesmaximal, complemented
6#10592398C211yesmaximal, characteristic, complemented
7C4×#3743C211yesmaximal, characteristic
8#81889—34nomaximal
9C32×C4⋊Q8C2212yes—
10#64155—22no—
11Q8×C3⋊Dic3—22no—
12C2×#3746C2214yes—
13C2×#3743C2212yes—
14#64106C2214yes—
15#64101—22no—
16#64099—22no—
17#64096C2214yes—
18C42×C3⋊D3C2211yescharacteristic
19#64078C2212yes—
20C32×#106C2214yes—
21C32×C4×C8C2211yescharacteristic
22#63642C2212yes—
23#63637C2218yes—
24C4×C3⋊(C3⋊C8)C2211yescharacteristic
25#5728—38no—
26C3×#498D314yescomplemented
27#5093—38no—
28#4867—316no—
29#4853—316no—
30#4699—34no—
31C4×ΓL(1,𝔽25)—34no—
32C2×C32×Q8—22no—
33C2×C4×C3⋊D3D412yes—
34C2×C4×C3⋊D3C2311yescharacteristic
35C2×#634C2314yes—
36C2×C32×C8C2312yes—
37C32×C4⋊C4—22no—
38C32×C4⋊C4C2314yes—
39C32×C42C2311yescharacteristic
40#3752—24no—
41C4⋊(C3⋊Dic3)—22no—
42C4⋊(C3⋊Dic3)—22no—
43C4⋊(C3⋊Dic3)—24no—
44#3750—24no—
45C4×C3⋊Dic3—24no—
46C4×C3⋊Dic3D412yes—
47C4×C3⋊Dic3C2311yescharacteristic
48C2×C3⋊(C3⋊C8)C2312yes—
49#3746—28no—
50#3743—24no—
51#3185—91noSylow
52C3×C4⋊Q8C2×D318yes—
53#946—68no—
54Q8×Dic3—68no—
55C2×Dic12—316no—
56C2×ΓL(1,𝔽25)—38no—
57#897—316no—
58#892—68no—
59#890—68no—
60#887—316no—
61C42×D3—34no—
62#869—38no—
63C3×#106C2×D3116yes—
64C3×C4×C8C2×D314yes—
65#815—38no—
66#810—332no—
67C4×C3⋊C8—34no—
68C22×C3⋊D3C2×D411yescharacteristic
69C32×Q8—44no—
70C2×C32×C4—24no—
71C2×C32×C4C2×D412yes—
72C2×C32×C4C2411yescharacteristic
73C2×C3⋊Dic3—24no—
74C2×C3⋊Dic3C2×D412yes—
75C2×C3⋊Dic3C2×D411yescharacteristic
76C4×C3⋊D3—24no—
77C4×C3⋊D3—22no—
78#634—28no—
79C32×C8#4114yes—
80C3⋊(C3⋊C8)—22no—
81#533—92no—
82#498C3⋊D311yescharacteristic, complemented
83#494—91no—
84#487—92no—
85#470—94no—
86#441—94no—
87C4×M16—91no—
88C2×C3×Q8—28no—
89C2×C4×D3—38no—
90C2×C4×D3—34no—
91C2×Dic6—316no—
92C2×C3×C8C22×D318yes—
93C3×C4⋊C4—28no—
94C3×C4⋊C4C22×D3116yes—
95C3×C42C22×D314yes—
96(C2×D3)⋊C4—616no—
97C4⋊Dic3—616no—
98C4⋊Dic3—68no—
99C4⋊Dic3—68no—
100Dic3⋊C4—616no—
101C4×Dic3—38no—
102C4×Dic3—34no—
103C4×Dic3—616no—
104C2×C3⋊C8—38no—
105Dic12—632no—
106ΓL(1,𝔽25)—616no—
107C22×C32C22×D411yescharacteristic
108C2×C3⋊D3—21no—
109C2×C3⋊D3—22no—
110C32×C4—44no—
111C32×C4#13714yes—
112C32×C4C2×#4112yes—
113C3⋊Dic3—21no—
114C3⋊Dic3—22no—
115C3⋊Dic3—44no—
116C2×Q16—94no—
117C2×M16—92no—
118C4⋊Q8—92no—
119C4⋊Q8C2×C3⋊D312yes—
120#125—182no—
121C22⋊Q8—94no—
122C22⋊Q8—182no—
123C4×Q8—94no—
124C4×Q8—182no—
125#117—182no—
126C2×C42—91no—
127#106C2×C3⋊D314yes—
128#103—98no—
129#97—92no—
130C4×C8—91no—
131C4×C8C2×C3⋊D311yescharacteristic
132C22×D3—34no—
133C3×Q8—416no—
134C2×C3×C4—216no—
135C2×C3×C4D3×D418yes—
136C2×C3×C4C23×D314yes—
137C2×Dic3—38no—
138C2×Dic3—34no—
139C2×Dic3—616no—
140C4×D3—616no—
141C4×D3—68no—
142Dic6—632no—
143C3×C8#239116yes—
144C3⋊C8—68no—
145C2×C32#53211yescharacteristic
146C2×C32C2×#13712yes—
147C3⋊D3—41no—
148C2×Q8—22no—
149C2×Q8—94no—
150C22×C4—91no—
151C22×C4—92no—
152Q16—188no—
153M16—184no—
154C2×C8—92no—
155C2×C8C22×C3⋊D312yes—
156C4⋊C4—22no—
157C4⋊C4—184no—
158C4⋊C4—184no—
159C4⋊C4—182no—
160C4⋊C4—182no—
161C4⋊C4C22×C3⋊D314yes—
162C22⋊C4—184no—
163C42—91no—
164C42—92no—
165C42—184no—
166C42C22×C3⋊D311yescharacteristic
167C22×C3C2×D3×D414yes—
168C2×D3—64no—
169C2×D3—68no—
170C3×C4—416no—
171C3×C4#915116yes—
172C3×C4C2×#23918yes—
173Dic3—64no—
174Dic3—68no—
175Dic3—1216no—
176C32#318511yescharacteristic, complemented, Sylow
177C23—91no—
178Q8—44no—
179Q8—188no—
180C2×C4—24no—
181C2×C4—92no—
182C2×C4—91no—
183C2×C4—182no—
184C2×C4—184no—
185C2×C4—184no—
186C2×C4D4×C3⋊D312yes—
187C2×C4C23×C3⋊D311yescharacteristic
188C8—182no—
189C8#383214yes—
190C2×C3#572514yes—
191C2×C3C2×#91518yes—
192D3—124no—
193C22—181no—
194C22—182no—
195C22C2×D4×C3⋊D311yescharacteristic
196C4—44no—
197C4—181no—
198C4—182no—
199C4—364no—
200C4#6412414yes—
201C4C2×#383212yes—
202C3#8188914yescomplemented
203C2—361no—
204C2#1059619611yescharacteristic
205C2C2×#6412412yes—
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#498C2
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenter#498C3⋊D3
hypocenterC32#3185
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
2. C32×#498C2semidirect
3. #10592792C2semidirect
5. #10592552C2semidirect
6. #10592398C2semidirect
26. C3×#498D3semidirect
82. #498C3⋊D3semidirect
176. C32#3185semidirect
202. C3#81889semidirect

Maximal subgroups

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

subgroupindex
#105961992
C32×#4982
#105927922
#105925662
#105925522
#105923982
C4×#37432
#818893