Finite Group Databasebeta

← #11795337

Subgroups — #11795337

Order 1152.

528 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 167 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#10592820C211yesmaximal, characteristic
2#10592818C211yesmaximal, characteristic
3#10592663C211yesmaximal, characteristic
4C2×#63635C211yesmaximal, characteristic
5C32×#343C211yesmaximal, characteristic
6#10589424C211yesmaximal, characteristic
7#10589420C211yesmaximal, characteristic
8#68981—34nomaximal
9C2×C32×M16C2211yescharacteristic
10C2×C32×M16C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12#64135C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16#63645—21no—
17#63644—21no—
18#63641—22no—
19#63635—21no—
20#63635—22no—
21#63634—21no—
22#5121—34no—
23#5119—34no—
24#4964—34no—
25C2×#808—34no—
26C3×#343D314yes—
27#4558—34no—
28#4554—34no—
29C22×C32×C4—21no—
30C22×C32×C4C2311yescharacteristic
31C22×C3⋊Dic3—21no—
32C32×M16—21no—
33C32×M16—21no—
34C32×M16—21no—
35C32×M16Q812yes—
36C2×C32×C8—21no—
37C2×C32×C8—21no—
38C32×C4⋊C4—21no—
39C32×C4⋊C4—21no—
40#3757—21no—
41C4⋊(C3⋊Dic3)—21no—
42C4⋊(C3⋊Dic3)—21no—
43C4⋊(C3⋊Dic3)D411yescharacteristic
44C4⋊(C3⋊Dic3)D411yescharacteristic
45C4×C3⋊Dic3—21no—
46#3748—21no—
47#3748Q812yes—
48C2×C3⋊(C3⋊C8)—21no—
49C2×C3⋊(C3⋊C8)—21no—
50C2×C3⋊(C3⋊C8)—21no—
51C2×C3⋊(C3⋊C8)D412yes—
52#2090—91noSylow
53C2×C3×M16C2×D314yes—
54C2×C3×M16C2×D314yes—
55C2×C3×C4⋊C4C2×D314yes—
56#926—34no—
57C2×C4⋊Dic3—34no—
58C2×#208—34no—
59C22×C3⋊C8—34no—
60#818—64no—
61#817—64no—
62Dic3⋊C8—68no—
63#808—68no—
64#808—64no—
65#807—64no—
66C23×C32#4111yescharacteristic
67C2×C32×C4—41no—
68C2×C32×C4—81no—
69C2×C32×C4C2×D411yescharacteristic
70C2×C32×C4C2×D411yescharacteristic
71C2×C32×C4C2×Q811yescharacteristic
72C2×C32×C4C2×Q811yescharacteristic
73C2×C32×C4#4111yescharacteristic
74C2×C32×C4#4111yescharacteristic
75C2×C3⋊Dic3—21no—
76C2×C3⋊Dic3—21no—
77C2×C3⋊Dic3—41no—
78C2×C3⋊Dic3—81no—
79C32×C8—22no—
80C32×C8—41no—
81C3⋊(C3⋊C8)—22no—
82C3⋊(C3⋊C8)—22no—
83#428—91no—
84#428—91no—
85C2×#106—91no—
86#424—91no—
87#343—91no—
88#343C3⋊D311yescharacteristic
89#341—91no—
90C22×C3×C4—24no—
91C22×C3×C4C22×D314yes—
92C22×Dic3—64no—
93C3×M16—24no—
94C3×M16—24no—
95C3×M16—24no—
96C3×M16Dic618yes—
97C2×C3×C8—24no—
98C2×C3×C8—24no—
99C3×C4⋊C4—24no—
100C3×C4⋊C4—24no—
101#217—64no—
102C4⋊Dic3—34no—
103C4⋊Dic3—34no—
104C4⋊Dic3—64no—
105C4⋊Dic3—64no—
106C4×Dic3—64no—
107#208—38no—
108#208—64no—
109C2×C3⋊C8—38no—
110C2×C3⋊C8—64no—
111C2×C3⋊C8—64no—
112C2×C3⋊C8—64no—
113C22×C32—21no—
114C22×C32—21no—
115C22×C32#12111yescharacteristic
116C22×C32#12511yescharacteristic
117C22×C32#12511yescharacteristic
118C32×C4—81no—
119C32×C4C22⋊Q811yescharacteristic
120C32×C4C22⋊Q811yescharacteristic
121C32×C4#12311yescharacteristic
122C32×C4C4⋊Q811yescharacteristic
123C3⋊Dic3—41no—
124C3⋊Dic3—41no—
125C3⋊Dic3—81no—
126C2×M16—91no—
127C2×M16C2×C3⋊D311yescharacteristic
128C2×M16C2×C3⋊D311yescharacteristic
129C22×C8—91no—
130#117—91no—
131C2×C4⋊C4—91no—
132C2×C4⋊C4C2×C3⋊D311yescharacteristic
133#107—181no—
134#107—181no—
135#106—181no—
136#106—182no—
137#106—181no—
138C4⋊C8—182no—
139C23×C3#23514yes—
140C2×C3×C4—44no—
141C2×C3×C4—84no—
142C2×C3×C4C2×Dic614yes—
143C2×C3×C4#23514yes—
144C2×C3×C4D3×D414yes—
145C2×C3×C4D3×D414yes—
146C2×C3×C4#23714yes—
147C2×C3×C4D3×Q814yes—
148C2×Dic3—64no—
149C2×Dic3—64no—
150C2×Dic3—124no—
151C2×Dic3—244no—
152C3×C8—28no—
153C3×C8—44no—
154C3⋊C8—68no—
155C3⋊C8—68no—
156C2×C32—21no—
157C2×C32—21no—
158C2×C32#39811yescharacteristic
159C2×C32#47111yescharacteristic
160C2×C32#47111yescharacteristic
161C22×C4—21no—
162C22×C4—181no—
163C22×C4C22×C3⋊D311yescharacteristic
164M16—21no—
165M16—21no—
166M16—21no—
167M16—92no—
168M16—181no—
169M16#63412yes—
170C2×C8—21no—
171C2×C8—21no—
172C2×C8—92no—
173C2×C8—181no—
174C2×C8—181no—
175C2×C8—181no—
176C4⋊C4—21no—
177C4⋊C4—21no—
178C4⋊C4—91no—
179C4⋊C4—91no—
180C4⋊C4—181no—
181C4⋊C4—181no—
182C22⋊C4—181no—
183C42—181no—
184C22×C3—24no—
185C22×C3—24no—
186C22×C3#87014yes—
187C22×C3#88414yes—
188C22×C3#88914yes—
189C3×C4—84no—
190C3×C4#87814yes—
191C3×C4#88314yes—
192C3×C4#88814yes—
193C3×C4#89614yes—
194Dic3—124no—
195Dic3—124no—
196Dic3—244no—
197C32#209011yescharacteristic, complemented, Sylow
198C23#382811yescharacteristic
199C2×C4—41no—
200C2×C4—81no—
201C2×C4—181no—
202C2×C4—181no—
203C2×C4—361no—
204C2×C4—721no—
205C2×C4C2×#63411yescharacteristic
206C2×C4#382811yescharacteristic
207C2×C4D4×C3⋊D311yescharacteristic
208C2×C4D4×C3⋊D311yescharacteristic
209C2×C4#383011yescharacteristic
210C2×C4Q8×C3⋊D311yescharacteristic
211C8—22no—
212C8—41no—
213C8—182no—
214C8—182no—
215C2×C3—24no—
216C2×C3—24no—
217C2×C3#465714yes—
218C2×C3#474814yes—
219C2×C3#475414yes—
220C22—21no—
221C22—21no—
222C22#6407911yescharacteristic
223C22#6409311yescharacteristic
224C22#6409811yescharacteristic
225C4—81no—
226C4—361no—
227C4—361no—
228C4—721no—
229C4#6408711yescharacteristic
230C4#6409211yescharacteristic
231C4#6409711yescharacteristic
232C4#6410511yescharacteristic
233C3#6898114yescomplemented
234C2—21no—
235C2—21no—
236C2#1059235611yescharacteristic
237C2#1059244711yescharacteristic
238C2#1059245311yescharacteristic
subgroupG/H
centerC22#64093
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#343C2
socleC22×C32#121
prime radicalC23×C32#41
hypercenter#343C3⋊D3
hypocenterC32#2090
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
197. C32#2090semidirect
233. C3#68981semidirect

Maximal subgroups

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

subgroupindex
#105928202
#105928182
#105926632
C2×#636352
C32×#3432
#105894242
#105894202
#689813