Finite Group Databasebeta

← #11784227

Subgroups — #11784227

Order 1152.

609 conjugacy classes of subgroups; only the 188 normal subgroups are shown.

normal subgroups only

This group has 609 conjugacy classes of subgroups — too many to draw. Only its 188 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#10592631C211yesmaximal, characteristic
2C2×#63572C212yesmaximal
3C2×#63555C211yesmaximal, characteristic
4C2×#63553C211yesmaximal, characteristic
5C3×#4524C212yesmaximal
6#68604—32nomaximal
7C2×C32×C42C2211yescharacteristic
8C2×C4×C3⋊Dic3C2211yescharacteristic
9C2×C4×C3⋊Dic3C2211yescharacteristic
10C22×C3×C3⋊C8C2212yes—
11C22×C3×C3⋊C8C2212yes—
12#63658C414yes—
13#63572C418yescomplemented
14#63555—22no—
15#63553—22no—
16C2×#815—32no—
17C2×Dic3⋊C8—32no—
18C2×Dic3⋊C8—32no—
19C2×C8×Dic3—32no—
20#4932—32no—
21#4932—61no—
22C3×#336—32no—
23#4524D312yes—
24C22×C32×C4C2×C412yes—
25C22×C32×C4C2311yescharacteristic
26C22×C3⋊Dic3C2×C412yes—
27C22×C3⋊Dic3C2×C412yes—
28C32×C42—22no—
29C4×C3⋊Dic3C2×C414yes—
30C4×C3⋊Dic3D412yes—
31C4×C3⋊Dic3Q812yes—
32C2×C3×C3⋊C8—22no—
33C2×C3×C3⋊C8—22no—
34C2×C3×C3⋊C8—22no—
35C2×C3×C3⋊C8—22no—
36C2×C3×C3⋊C8C2×C414yes—
37C2×C3×C3⋊C8C2×C414yes—
38#1768—91noSylow
39C22×C3×C8—32no—
40C22×C3×C8—32no—
41C2×C3×C42—21no—
42C2×C3×C42C2×D312yes—
43C2×C4×Dic3—32no—
44C2×C4×Dic3—32no—
45C2×C4×Dic3—61no—
46C2×C4×Dic3—61no—
47C22×C3⋊C8C2×D312yes—
48C22×C3⋊C8C2×D312yes—
49C3⋊#95—34no—
50C3⋊#95—34no—
51C3⋊#95—64no—
52#815—64no—
53Dic3⋊C8—38no—
54Dic3⋊C8—38no—
55C8×Dic3—64no—
56C23×C32C22×C411yescharacteristic
57C2×C32×C4—22no—
58C2×C32×C4—24no—
59C2×C32×C4C22×C412yes—
60C2×C32×C4C2×D411yescharacteristic
61C2×C32×C4C2×Q811yescharacteristic
62C2×C32×C4#4112yes—
63C2×C3⋊Dic3—24no—
64C2×C3⋊Dic3—24no—
65C2×C3⋊Dic3C4214yes—
66C2×C3⋊Dic3C4⋊C414yes—
67C3×C3⋊C8—24no—
68C3×C3⋊C8—24no—
69C2×C4⋊C8—92no—
70C2×#97—91no—
71C2×C4×C8—91no—
72#376—91no—
73#336—32no—
74C22×C3×C4—22no—
75C22×C3×C4—21no—
76C22×C3×C4C4×D314yes—
77C22×C3×C4C22×D312yes—
78C22×Dic3—32no—
79C22×Dic3—32no—
80C22×Dic3—34no—
81C22×Dic3—62no—
82C22×Dic3—62no—
83C2×C3×C8—34no—
84C2×C3×C8—34no—
85C2×C3×C8—62no—
86C2×C3×C8—62no—
87C2×C3×C8—62no—
88C2×C3×C8—62no—
89C3×C42—24no—
90C3×C42—22no—
91C3×C42—22no—
92C4×Dic3—34no—
93C4×Dic3—34no—
94C4×Dic3—34no—
95C4×Dic3—34no—
96C4×Dic3—64no—
97C4×Dic3—62no—
98C4×Dic3—62no—
99C2×C3⋊C8—22no—
100C2×C3⋊C8—22no—
101C2×C3⋊C8—22no—
102C2×C3⋊C8—22no—
103C2×C3⋊C8C4×D314yes—
104C2×C3⋊C8C4×D314yes—
105C22×C32C2×C4211yescharacteristic
106C22×C32C2×C4⋊C411yescharacteristic
107C22×C32#11711yescharacteristic
108C22×C32#13114yes—
109C32×C4—42no—
110C32×C4C4×D412yes—
111C32×C4C4×Q812yes—
112C3⋊Dic3—24no—
113C3⋊Dic3—24no—
114C22×C8—32no—
115C22×C8—32no—
116C2×C42—91no—
117C2×C42—91no—
118C2×C42D3211yescharacteristic
119C4⋊C8—98no—
120#97—182no—
121C4×C8—182no—
122#95—94no—
123C23×C3—21no—
124C23×C3C2×C4×D312yes—
125C2×C3×C4—24no—
126C2×C3×C4—24no—
127C2×C3×C4—24no—
128C2×C3×C4—24no—
129C2×C3×C4—21no—
130C2×C3×C4—22no—
131C2×C3×C4—21no—
132C2×C3×C4—22no—
133C2×C3×C4—44no—
134C2×C3×C4C2×C4×D312yes—
135C2×C3×C4C2×C4×D312yes—
136C2×C3×C4D3×D412yes—
137C2×C3×C4#23712yes—
138C2×C3×C4#23712yes—
139C2×C3×C4D3×Q812yes—
140C2×Dic3—34no—
141C2×Dic3—34no—
142C2×Dic3—38no—
143C2×Dic3—64no—
144C2×Dic3—64no—
145C2×Dic3—64no—
146C2×Dic3—64no—
147C2×Dic3—64no—
148C2×Dic3—64no—
149C2×Dic3—124no—
150C2×Dic3—124no—
151C3×C8—64no—
152C3×C8—64no—
153C3⋊C8—24no—
154C3⋊C8—24no—
155C2×C32C4×C4⋊C411yescharacteristic
156C2×C32#40512yes—
157C2×C32#42412yes—
158C2×C32#43312yes—
159C22×C4—92no—
160C22×C4—92no—
161C22×C4#62412yes—
162C22×C4C2×D3211yescharacteristic
163C2×C8—34no—
164C2×C8—34no—
165C2×C8—62no—
166C2×C8—62no—
167C2×C8—62no—
168C2×C8—62no—
169C42—22no—
170C42—92no—
171C42—94no—
172C42—92no—
173C22×C3—24no—
174C22×C3—21no—
175C22×C3—21no—
176C22×C3—21no—
177C22×C3C42×D312yes—
178C22×C3#87712yes—
179C22×C3D3×C4⋊C412yes—
180C22×C3#90114yes—
181C22×C3#90714yes—
182C3×C4—22no—
183C3×C4—22no—
184C3×C4—44no—
185C3×C4—44no—
186C3×C4#67⋊C412yes—
187C3×C4#67⋊C412yes—
188C3×C4#88712yes—
189C3×C4#88712yes—
190Dic3—64no—
191Dic3—64no—
192Dic3—68no—
193Dic3—124no—
194Dic3—124no—
195C32#176811yescharacteristic, complemented, Sylow
196C23C2×#62411yescharacteristic
197C2×C4—24no—
198C2×C4—22no—
199C2×C4—94no—
200C2×C4—94no—
201C2×C4—184no—
202C2×C4—184no—
203C2×C4#379711yescharacteristic
204C2×C4C4×D3212yes—
205C2×C4#380211yescharacteristic
206C2×C4#380512yes—
207C8—64no—
208C8—64no—
209C2×C3—21no—
210C2×C3—22no—
211C2×C3—22no—
212C2×C3—22no—
213C2×C3#464912yes—
214C2×C3#468912yes—
215C2×C3#470812yes—
216C2×C3#472014yes—
217C2×C3#483914yes—
218C22#6381714yes—
219C22C4×#62411yescharacteristic
220C22#6390011yescharacteristic
221C22#6395711yescharacteristic
222C4—42no—
223C4—184no—
224C4—184no—
225C4#6383812yes—
226C4#6390212yes—
227C3—21no—
228C3#6860412yescomplemented
229C2#1059032112yes—
230C2#1059033212yes—
231C2#1059106212yes—
232C2#1059125711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C2×D32
commutatorC22×C32C2×C42
FittingC2×C32×C42C22
socle, prime radicalC23×C32C22×C4
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1768
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
13. #63572C4semidirect
195. C32#1768semidirect
228. C3#68604semidirect

Maximal subgroups

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

subgroupindex
#105926312
C2×#635722
C2×#635552
C2×#635532
C3×#45242
#686043