Finite Group Databasebeta

← #11795429

Subgroups — #11795429

Order 1152.

870 conjugacy classes of subgroups; only the 249 normal subgroups are shown.

normal subgroups only

This group has 870 conjugacy classes of subgroups — too many to draw. Only its 249 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×#390C211yesmaximal, characteristic
2C2×#63659C212yesmaximal
3C2×#63634C212yesmaximal, complemented
4#10592634C211yesmaximal, characteristic, complemented
5#10589390C211yesmaximal, characteristic, complemented
6#69655—34nomaximal
7C22×C32×D4C2211yescharacteristic
8C2×C32×C4⋊C4C2211yescharacteristic
9C2×C32×C22⋊C4—22no—
10C2×C32×C42C2211yescharacteristic
11C2×C4⋊(C3⋊Dic3)—22no—
12C2×C4⋊(C3⋊Dic3)C2212yes—
13C22×C3⋊(C3⋊C8)C2212yes—
14#63659—24no—
15#63634—24no—
16C3×#390D314yes—
17C2×#832—38no—
18C2×#807—38no—
19#4935—34no—
20#4524—34no—
21C24×C32—21no—
22C2×C32×D4—22no—
23C2×C32×D4—22no—
24C2×C32×D4—21no—
25C2×C32×D4Q812yes—
26C22×C32×C4—21no—
27C22×C32×C4D412yes—
28C22×C32×C4C2311yescharacteristic
29C22×C3⋊Dic3—22no—
30C32×C4⋊C4—22no—
31C32×C22⋊C4—44no—
32C32×C42—22no—
33C4⋊(C3⋊Dic3)—22no—
34C4⋊(C3⋊Dic3)—22no—
35C4⋊(C3⋊Dic3)—44no—
36C2×C3⋊(C3⋊C8)—22no—
37C2×C3⋊(C3⋊C8)—22no—
38C2×C3⋊(C3⋊C8)D414yes—
39#2093—91noSylow
40C22×C3×D4C2×D314yes—
41C2×C3×C4⋊C4C2×D314yes—
42C2×C3×C22⋊C4—28no—
43C2×C3×C42C2×D314yes—
44C2×C4⋊Dic3—38no—
45C2×C4⋊Dic3—68no—
46C22×C3⋊C8—38no—
47#832—616no—
48#807—616no—
49C23×C32—22no—
50C23×C32—41no—
51C23×C32—41no—
52C23×C32—42no—
53C23×C32—42no—
54C23×C32C2×D411yescharacteristic
55C32×D4—24no—
56C32×D4—42no—
57C2×C32×C4—22no—
58C2×C32×C4—22no—
59C2×C32×C4—41no—
60C2×C32×C4—42no—
61C2×C32×C4D814yes—
62C2×C32×C4C2×D412yes—
63C2×C32×C4C2×Q811yescharacteristic
64C2×C32×C4#4111yescharacteristic
65C2×C32×C4#4112yes—
66C2×C3⋊Dic3—42no—
67C2×C3⋊Dic3—44no—
68C3⋊(C3⋊C8)—24no—
69C2×#107—92no—
70C2×#102—92no—
71#390C3⋊D311yescharacteristic
72#384—91no—
73#336—91no—
74C24×C3—24no—
75C2×C3×D4—24no—
76C2×C3×D4—28no—
77C2×C3×D4—28no—
78C2×C3×D4Dic618yes—
79C22×C3×C4—24no—
80C22×C3×C4#6718yes—
81C22×C3×C4C22×D314yes—
82C22×Dic3—68no—
83C3×C4⋊C4—28no—
84C3×C22⋊C4—416no—
85C3×C42—28no—
86C4⋊Dic3—68no—
87C4⋊Dic3—68no—
88C4⋊Dic3—1216no—
89C2×C3⋊C8—316no—
90C2×C3⋊C8—68no—
91C2×C3⋊C8—68no—
92C22×C32—42no—
93C22×C32—44no—
94C22×C32—82no—
95C22×C32—81no—
96C22×C32—81no—
97C22×C32C22⋊Q811yescharacteristic
98C22×C32#12311yescharacteristic
99C22×C32#12711yescharacteristic
100C22×C32C2×D812yes—
101C22×C32#13712yes—
102C32×C4—24no—
103C32×C4—81no—
104C32×C4C22⋊Q812yes—
105C32×C4#12312yes—
106C3⋊Dic3—82no—
107C22×D4C2×C3⋊D311yescharacteristic
108C22×C8—92no—
109C2×C4⋊C4—92no—
110C2×C4⋊C4—182no—
111C2×C4⋊C4C2×C3⋊D311yescharacteristic
112C2×C22⋊C4—22no—
113C2×C42C2×C3⋊D311yescharacteristic
114#107—184no—
115#102—184no—
116C23×C3—28no—
117C23×C3—48no—
118C23×C3—44no—
119C23×C3—44no—
120C23×C3—48no—
121C23×C3C2×#6714yes—
122C3×D4—216no—
123C3×D4—48no—
124C2×C3×C4—28no—
125C2×C3×C4—28no—
126C2×C3×C4—48no—
127C2×C3×C4—44no—
128C2×C3×C4#213116yes—
129C2×C3×C4C2×Dic614yes—
130C2×C3×C4#23514yes—
131C2×C3×C4D3×D418yes—
132C2×C3×C4#23718yes—
133C2×Dic3—1216no—
134C2×Dic3—128no—
135C3⋊C8—616no—
136C2×C32—82no—
137C2×C32#39911yescharacteristic
138C2×C32#47412yes—
139C2×C32#48012yes—
140C2×C32#49311yescharacteristic
141C2×C32#49711yescharacteristic
142C24—21no—
143C2×D4—21no—
144C2×D4—22no—
145C2×D4—22no—
146C2×D4#63412yes—
147C22×C4—21no—
148C22×C4—182no—
149C22×C4#63812yes—
150C22×C4C22×C3⋊D311yescharacteristic
151C2×C8—94no—
152C2×C8—182no—
153C2×C8—182no—
154C4⋊C4—22no—
155C4⋊C4—182no—
156C4⋊C4—182no—
157C4⋊C4—364no—
158C22⋊C4—44no—
159C42—22no—
160C22×C3—48no—
161C22×C3—416no—
162C22×C3—88no—
163C22×C3—84no—
164C22×C3—84no—
165C22×C3#92414yes—
166C22×C3C2×#21318yes—
167C22×C3#93514yes—
168C22×C3#94014yes—
169C22×C3#95118yes—
170C3×C4—216no—
171C3×C4—84no—
172C3×C4#87818yes—
173C3×C4#88318yes—
174Dic3—248no—
175C32#209311yescharacteristic, complemented, Sylow
176C23—22no—
177C23—42no—
178C23—41no—
179C23—41no—
180C23—42no—
181C23C2×#63811yescharacteristic
182D4—24no—
183D4—42no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—42no—
187C2×C4—41no—
188C2×C4—364no—
189C2×C4—362no—
190C2×C4#375314yes—
191C2×C4C2×#63411yescharacteristic
192C2×C4#382811yescharacteristic
193C2×C4D4×C3⋊D312yes—
194C2×C4#383012yes—
195C8—184no—
196C2×C3—88no—
197C2×C3#494914yes—
198C2×C3#500718yes—
199C2×C3#503318yes—
200C2×C3#506014yes—
201C2×C3#507314yes—
202C22—42no—
203C22—44no—
204C22—81no—
205C22—82no—
206C22—81no—
207C22#6413311yescharacteristic
208C22C2×#375312yes—
209C22#6414411yescharacteristic
210C22#6414911yescharacteristic
211C22#6416012yes—
212C4—24no—
213C4—81no—
214C4—722no—
215C4#6408712yes—
216C4#6409212yes—
217C3#6965514yescomplemented
218C2—82no—
219C2#1059264811yescharacteristic
220C2#1059270612yes—
221C2#1059273212yes—
222C2#1059275911yescharacteristic
223C2#1059277211yescharacteristic
subgroupG/H
centerC23C2×#638
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#390C2
socleC23×C32C2×D4
prime radicalC22×C32×D4C22
hypercenter#390C3⋊D3
hypocenterC32#2093
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42 ◁ #390

Complements

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

NH ≅ G/Ntype
3. C2×#63634C2semidirect
4. #10592634C2semidirect
5. #10589390C2semidirect
175. C32#2093semidirect
217. C3#69655semidirect

Maximal subgroups

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

subgroupindex
C32×#3902
C2×#636592
C2×#636342
#105926342
#105893902
#696553