Finite Group Databasebeta

← #11796670

Subgroups — #11796670

Order 1152.

696 conjugacy classes of subgroups; only the 217 normal subgroups are shown.

normal subgroups only

This group has 696 conjugacy classes of subgroups — too many to draw. Only its 217 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×#64113C211yesmaximal, characteristic
2C2×C32×#107C211yesmaximal, characteristic, complemented
3C2×#63639C211yesmaximal, characteristic, complemented
4#10589358C212yesmaximal, complemented
5#10589357C212yesmaximal, complemented
6#70598—34nomaximal
7C2×#3828—21no—
8C22×C32×C8C2211yescharacteristic
9C2×C32×C4⋊C4—21no—
10C2×#3746C2211yescharacteristic
11#64113—22no—
12#64113C414yescomplemented
13C2×#3745C2211yescharacteristic
14C2×#3744—21no—
15C32×#107—21no—
16C32×#107C2212yes—
17#63639—22no—
18C2×C3⋊(C3⋊C16)C2212yes—
19C2×#904—34no—
20C2×C3×#107D314yescomplemented
21C2×#812—34no—
22#4492—38no—
23#4491—38no—
24C22×C32×C4—41no—
25C22×C32×C4D411yescharacteristic
26C2×#638—41no—
27#3828—24no—
28#3828—42no—
29C2×C4⋊(C3⋊D3)—21no—
30C2×C4×C3⋊D3—41no—
31C2×#634—21no—
32C2×C32×C8C2×C412yes—
33C2×C32×C8D411yescharacteristic
34C2×C32×C8D412yes—
35C2×C32×C8C2311yescharacteristic
36C32×C4⋊C4—22no—
37C32×C4⋊C4—41no—
38#3746—21no—
39#3746C2×C412yescomplemented
40#3745—21no—
41#3745C2×C412yescomplemented
42#3744—24no—
43C3⋊(C3⋊C16)—22no—
44#2139—91noSylow
45C2×#235—64no—
46C22×C3×C8C2×D314yes—
47C2×C3×C4⋊C4—24no—
48C2×Dic12—34no—
49#904—316no—
50#904—68no—
51C2×D24—34no—
52C2×#204—64no—
53C3×#107—24no—
54C3×#107C2×D318yes—
55#812—68no—
56C2×C3⋊C16—38no—
57C23×C32D811yescharacteristic
58C22×C3⋊D3—41no—
59C2×C32×C4—42no—
60C2×C32×C4—82no—
61C2×C32×C4C22⋊C412yes—
62C2×C32×C4D811yescharacteristic
63C2×C32×C4SD1612yes—
64C2×C32×C4C2×D411yescharacteristic
65#638—44no—
66C2×C3⋊Dic3—41no—
67C4⋊(C3⋊D3)—22no—
68C4⋊(C3⋊D3)—41no—
69C4×C3⋊D3—44no—
70#634—22no—
71#634—41no—
72C32×C8C22⋊C412yes—
73C32×C8C22×C411yescharacteristic
74C32×C8C2×D411yescharacteristic
75C2×#135—91no—
76C2×M32—91no—
77C2×#107C3⋊D311yescharacteristic, complemented
78#358—92no—
79#357—92no—
80C22×C3×C4—44no—
81C22×C3×C4#6714yes—
82C2×#67—124no—
83#235—616no—
84#235—128no—
85C2×D12—64no—
86C2×C4×D3—124no—
87C2×Dic6—64no—
88C2×C3×C8C4×D318yes—
89C2×C3×C8D1218yes—
90C2×C3×C8#6714yes—
91C2×C3×C8C22×D314yes—
92C3×C4⋊C4—28no—
93C3×C4⋊C4—44no—
94Dic12—38no—
95Dic12—64no—
96D24—38no—
97D24—64no—
98#204—616no—
99C3⋊C16—68no—
100C22×C32—21no—
101C22×C32—21no—
102C22×C32#10212yes—
103C22×C32C2×D811yescharacteristic
104C2×C3⋊D3—42no—
105C2×C3⋊D3—81no—
106C2×C3⋊D3—81no—
107C32×C4—82no—
108C32×C4#10212yes—
109C32×C4C2×C22⋊C411yescharacteristic
110C32×C4C2×SD1611yescharacteristic
111C3⋊Dic3—42no—
112C2×#41—181no—
113#135—94no—
114#135—182no—
115C2×Q16—91no—
116C2×SD16—181no—
117C2×D8—91no—
118C22×C8C2×C3⋊D311yescharacteristic
119C2×C4⋊C4—21no—
120M32—182no—
121C2×C16—92no—
122#107—21no—
123#107C2×C3⋊D312yes—
124C23×C3#21314yes—
125C22×D3—124no—
126C2×C3×C4—48no—
127C2×C3×C4—88no—
128C2×C3×C4(C2×D3)⋊C418yes—
129C2×C3×C4#21314yes—
130C2×C3×C4#21518yes—
131C2×C3×C4C2×#6714yes—
132#67—1216no—
133C2×Dic3—124no—
134D12—68no—
135D12—124no—
136C4×D3—1216no—
137Dic6—68no—
138Dic6—124no—
139C3×C8(C2×D3)⋊C418yes—
140C3×C8C2×C4×D314yes—
141C3×C8C2×D1214yes—
142C2×C32—22no—
143C2×C32C2×#10211yescharacteristic
144C2×C32#50911yescharacteristic
145C2×C32#51011yescharacteristic
146C3⋊D3—82no—
147#41—184no—
148#41—362no—
149C2×Q8—181no—
150C2×D4—181no—
151C2×D4—361no—
152C22×C4—41no—
153C22×C4—361no—
154C22×C4#63811yescharacteristic
155Q16—92no—
156Q16—181no—
157SD16—184no—
158D8—92no—
159D8—181no—
160C2×C8C4×C3⋊D312yes—
161C2×C8C4⋊(C3⋊D3)12yes—
162C2×C8#63811yescharacteristic
163C2×C8C22×C3⋊D311yescharacteristic
164C4⋊C4—22no—
165C4⋊C4—41no—
166C16—182no—
167C22×C3—24no—
168C22×C3—24no—
169C22×C3#80918yes—
170C22×C3C2×#21314yes—
171C2×D3—128no—
172C2×D3—244no—
173C2×D3—244no—
174C3×C4—88no—
175C3×C4#80918yes—
176C3×C4C2×(C2×D3)⋊C414yes—
177C3×C4C2×#21514yes—
178Dic3—128no—
179C32#213911yescharacteristic, complemented, Sylow
180C23—361no—
181C23#375311yescharacteristic
182Q8—182no—
183Q8—361no—
184D4—182no—
185D4—364no—
186D4—361no—
187C2×C4—42no—
188C2×C4—82no—
189C2×C4—361no—
190C2×C4—364no—
191C2×C4#375212yes—
192C2×C4#375311yescharacteristic
193C2×C4#375512yes—
194C2×C4C2×#63811yescharacteristic
195C8#375212yes—
196C8C2×C4×C3⋊D311yescharacteristic
197C8C2×C4⋊(C3⋊D3)11yescharacteristic
198C2×C3—28no—
199C2×C3C2×#80914yes—
200C2×C3#514714yes—
201C2×C3#517914yes—
202D3—248no—
203C22—21no—
204C22—21no—
205C22—362no—
206C22—721no—
207C22—721no—
208C22#6363612yes—
209C22C2×#375311yescharacteristic
210C4—82no—
211C4—362no—
212C4#6363612yes—
213C4C2×#375211yescharacteristic
214C4C2×#375511yescharacteristic
215C3#7059814yescomplemented
216C2—22no—
217C2—722no—
218C2C2×#6363611yescharacteristic
219C2#1059284611yescharacteristic
220C2#1059287811yescharacteristic
subgroupG/H
centerC22C2×#3753
commutatorC32×C8C22×C4
FrattiniC2×C8C22×C3⋊D3
FittingC2×C32×#107C2
socleC22×C32C2×D8
prime radicalC2×#64113C2
cosocleC2×C32×C8C23
hypercenterC2×#107C3⋊D3
hypocenterC32#2139
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
2. C2×C32×#107C2semidirect
3. C2×#63639C2semidirect
4. #10589358C2semidirect
5. #10589357C2semidirect
12. #64113C4semidirect
20. C2×C3×#107D3semidirect
39. #3746C2×C4semidirect
41. #3745C2×C4semidirect
77. C2×#107C3⋊D3semidirect
179. C32#2139semidirect
215. C3#70598semidirect

Maximal subgroups

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

subgroupindex
C2×#641132
C2×C32×#1072
C2×#636392
#105893582
#105893572
#705983