Finite Group Databasebeta

← #11795432

Subgroups — #11795432

Order 1152.

870 conjugacy classes of subgroups; only the 239 normal subgroups are shown.

normal subgroups only

This group has 870 conjugacy classes of subgroups — too many to draw. Only its 239 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
1C32×#384C211yesmaximal, characteristic, complemented
2C2×#63636C212yesmaximal
3C2×#63634C212yesmaximal, complemented
4#10592638C211yesmaximal, characteristic
5#10589390C211yesmaximal, characteristic, complemented
6#69586—34nomaximal
7C22×C4⋊(C3⋊D3)C2211yescharacteristic
8C2×C32×C4⋊C4—22no—
9C2×C32×C4⋊C4C2212yes—
10C2×C32×C42C2211yescharacteristic
11C2×#3752—22no—
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2212yes—
14#63636—24no—
15#63634—24no—
16C3×#384D314yescomplemented
17C2×#809—38no—
18C2×#807—38no—
19#4939—34no—
20#4524—34no—
21C23×C3⋊D3—21no—
22C22×C32×C4—22no—
23C22×C32×C4D412yes—
24C22×C32×C4C2311yescharacteristic
25C22×C3⋊Dic3—21no—
26C2×C4⋊(C3⋊D3)—22no—
27C2×C4⋊(C3⋊D3)—22no—
28C2×C4⋊(C3⋊D3)—21no—
29C2×C4⋊(C3⋊D3)Q812yes—
30C32×C4⋊C4—22no—
31C32×C4⋊C4—22no—
32C32×C4⋊C4—44no—
33C32×C42—22no—
34#3752—44no—
35C4⋊(C3⋊Dic3)—22no—
36C2×C3⋊(C3⋊C8)—22no—
37C2×C3⋊(C3⋊C8)—22no—
38C2×C3⋊(C3⋊C8)D414yes—
39#2093—91noSylow
40C22×D12—34no—
41C2×C3×C4⋊C4—28no—
42C2×C3×C4⋊C4C2×D318yes—
43C2×C3×C42C2×D314yes—
44C2×(C2×D3)⋊C4—68no—
45C2×C4⋊Dic3—34no—
46C22×C3⋊C8—38no—
47#809—616no—
48#807—616no—
49C23×C32C2×D411yescharacteristic
50C22×C3⋊D3—22no—
51C22×C3⋊D3—41no—
52C22×C3⋊D3—41no—
53C22×C3⋊D3—42no—
54C22×C3⋊D3—42no—
55C2×C32×C4—22no—
56C2×C32×C4—22no—
57C2×C32×C4—42no—
58C2×C32×C4—44no—
59C2×C32×C4D814yes—
60C2×C32×C4C2×D412yes—
61C2×C32×C4C2×Q811yescharacteristic
62C2×C32×C4#4112yes—
63C2×C32×C4#4111yescharacteristic
64C2×C3⋊Dic3—41no—
65C2×C3⋊Dic3—42no—
66C4⋊(C3⋊D3)—24no—
67C4⋊(C3⋊D3)—42no—
68C3⋊(C3⋊C8)—24no—
69C2×#107—92no—
70C2×#102—92no—
71#390—91no—
72#384C3⋊D311yescharacteristic, complemented
73#336—91no—
74C23×D3—64no—
75C22×C3×C4—28no—
76C22×C3×C4#6718yes—
77C22×C3×C4C22×D314yes—
78C22×Dic3—64no—
79C2×D12—38no—
80C2×D12—68no—
81C2×D12—68no—
82C2×D12—64no—
83C3×C4⋊C4—28no—
84C3×C4⋊C4—28no—
85C3×C4⋊C4—416no—
86C3×C42—28no—
87(C2×D3)⋊C4—1216no—
88C4⋊Dic3—68no—
89C2×C3⋊C8—316no—
90C2×C3⋊C8—68no—
91C2×C3⋊C8—68no—
92C22×C32C22⋊Q811yescharacteristic
93C22×C32#12311yescharacteristic
94C22×C32#12711yescharacteristic
95C22×C32C2×D812yes—
96C22×C32#13712yes—
97C2×C3⋊D3—42no—
98C2×C3⋊D3—44no—
99C2×C3⋊D3—82no—
100C2×C3⋊D3—81no—
101C2×C3⋊D3—81no—
102C32×C4—24no—
103C32×C4—82no—
104C32×C4C22⋊Q812yes—
105C32×C4#12312yes—
106C3⋊Dic3—81no—
107C22×D4—91no—
108C22×C8—92no—
109C2×C4⋊C4—22no—
110C2×C4⋊C4—91no—
111C2×C4⋊C4C2×C3⋊D312yes—
112C2×C22⋊C4—182no—
113C2×C42C2×C3⋊D311yescharacteristic
114#107—184no—
115#102—184no—
116C23×C3C2×#6714yes—
117C22×D3—68no—
118C22×D3—124no—
119C22×D3—128no—
120C22×D3—124no—
121C22×D3—128no—
122C2×C3×C4—28no—
123C2×C3×C4—28no—
124C2×C3×C4—416no—
125C2×C3×C4—48no—
126C2×C3×C4#213116yes—
127C2×C3×C4#23518yes—
128C2×C3×C4D3×D418yes—
129C2×C3×C4D3×Q814yes—
130C2×C3×C4#23914yes—
131C2×Dic3—128no—
132C2×Dic3—124no—
133D12—616no—
134D12—128no—
135C3⋊C8—616no—
136C2×C32#39911yescharacteristic
137C2×C32#47412yes—
138C2×C32#48012yes—
139C2×C32#49311yescharacteristic
140C2×C32#49711yescharacteristic
141C3⋊D3—82no—
142C24—181no—
143C2×D4—92no—
144C2×D4—182no—
145C2×D4—182no—
146C2×D4—181no—
147C22×C4—22no—
148C22×C4—181no—
149C22×C4#63812yes—
150C22×C4C22×C3⋊D311yescharacteristic
151C2×C8—94no—
152C2×C8—182no—
153C2×C8—182no—
154C4⋊C4—22no—
155C4⋊C4—22no—
156C4⋊C4—44no—
157C4⋊C4—182no—
158C22⋊C4—364no—
159C42—22no—
160C22×C3#92914yes—
161C22×C3C2×#21318yes—
162C22×C3#94014yes—
163C22×C3#94218yes—
164C22×C3#94614yes—
165C2×D3—128no—
166C2×D3—1216no—
167C2×D3—248no—
168C2×D3—244no—
169C2×D3—244no—
170C3×C4—216no—
171C3×C4—88no—
172C3×C4#89418yes—
173C3×C4#89618yes—
174Dic3—244no—
175C32#209311yescharacteristic, complemented, Sylow
176C23—182no—
177C23—361no—
178C23—362no—
179C23—361no—
180C23—362no—
181C23C2×#63811yescharacteristic
182D4—184no—
183D4—362no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—44no—
187C2×C4—42no—
188C2×C4—362no—
189C2×C4—361no—
190C2×C4#375314yes—
191C2×C4#382812yes—
192C2×C4D4×C3⋊D312yes—
193C2×C4Q8×C3⋊D311yescharacteristic
194C2×C4#383211yescharacteristic
195C8—184no—
196C2×C3#496718yes—
197C2×C3#499314yes—
198C2×C3#507314yes—
199C2×C3#508614yes—
200C2×C3#508718yes—
201D3—248no—
202C22—364no—
203C22—362no—
204C22—721no—
205C22—721no—
206C22—722no—
207C22#6413811yescharacteristic
208C22C2×#375312yes—
209C22#6414911yescharacteristic
210C22#6415112yes—
211C22#6415511yescharacteristic
212C4—24no—
213C4—82no—
214C4—721no—
215C4#6410312yes—
216C4#6410512yes—
217C3#6958614yescomplemented
218C2—722no—
219C2#1059266612yes—
220C2#1059269211yescharacteristic
221C2#1059277211yescharacteristic
222C2#1059278511yescharacteristic
223C2#1059278612yes—
subgroupG/H
centerC23C2×#638
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#384C2
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenter#384C3⋊D3
hypocenterC32#2093
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
1. C32×#384C2semidirect
3. C2×#63634C2semidirect
5. #10589390C2semidirect
16. C3×#384D3semidirect
72. #384C3⋊D3semidirect
175. C32#2093semidirect
217. C3#69586semidirect

Maximal subgroups

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

subgroupindex
C32×#3842
C2×#636362
C2×#636342
#105926382
#105893902
#695863