Finite Group Databasebeta

← #11783109

Subgroups — #11783109

Order 1152.

746 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 746 conjugacy classes of subgroups — too many to draw. Only its 146 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
1C22×#3788C211yesmaximal, characteristic
2C22×#3787C211yesmaximal, characteristic
3C2×#64101C211yesmaximal, characteristic
4#10590207C214yesmaximal, complemented
5C22×C4×C3⋊D3C2211yescharacteristic
6C22×#622C2212yes—
7C22×#622C2212yes—
8C2×#3788—22no—
9C2×#3788—22no—
10C2×#3788C414yescomplemented
11C2×#3787—22no—
12C2×#3787—22no—
13C2×#3787C414yescomplemented
14C2×C32×C4⋊C4C411yescharacteristic
15C2×#3752C412yes—
16C2×C4⋊(C3⋊Dic3)C411yescharacteristic
17C2×C4×C3⋊Dic3C2212yes—
18#64101—22no—
19#64101—22no—
20C2×#892—62no—
21C23×C3⋊D3C2×C411yescharacteristic
22C22×C32×C4C2×C412yes—
23C22×C32×C4C2×C411yescharacteristic
24C22×C3⋊Dic3C2×C412yes—
25C22×C3⋊Dic3C2311yescharacteristic
26C2×C4×C3⋊D3C2×C412yes—
27C2×C4×C3⋊D3C2×C412yes—
28C2×C4×C3⋊D3D412yes—
29C2×C4×C3⋊D3D412yes—
30C2×C4×C3⋊D3D412yes—
31C2×C4×C3⋊D3Q812yes—
32C2×#622—22no—
33C2×#622—22no—
34C2×#622—22no—
35C2×#622—22no—
36C2×#622C2×C414yes—
37C2×#622C2×C414yes—
38#3788—28no—
39#3787—28no—
40C32×C4⋊C4—22no—
41#3752—24no—
42C4⋊(C3⋊Dic3)—22no—
43C4×C3⋊Dic3—22no—
44C4×C3⋊Dic3—22no—
45#1729—91nomaximal, Sylow
46C22×C4×D3—62no—
47C2×C3×C4⋊C4—22no—
48C2×(C2×D3)⋊C4—64no—
49C2×C4⋊Dic3—62no—
50C2×C4×Dic3—64no—
51#892—68no—
52#892—68no—
53C23×C32C22×C411yescharacteristic
54C22×C3⋊D3—22no—
55C22×C3⋊D3—22no—
56C22×C3⋊D3C4212yes—
57C22×C3⋊D3C22⋊C412yes—
58C22×C3⋊D3C4⋊C412yes—
59C2×C32×C4—22no—
60C2×C32×C4—24no—
61C2×C32×C4C4212yes—
62C2×C32×C4C22⋊C412yes—
63C2×C32×C4C4⋊C412yes—
64C2×C3⋊Dic3—22no—
65C2×C3⋊Dic3—24no—
66C2×C3⋊Dic3C22×C411yescharacteristic
67C2×C3⋊Dic3C22×C411yescharacteristic
68C2×C3⋊Dic3C2×D411yescharacteristic
69C2×C3⋊Dic3C2×D411yescharacteristic
70C2×C3⋊Dic3C2×D411yescharacteristic
71C2×C3⋊Dic3C2×Q811yescharacteristic
72C4×C3⋊D3C22⋊C414yes—
73C4×C3⋊D3C22⋊C414yes—
74C4×C3⋊D3C4⋊C414yes—
75C4×C3⋊D3C4⋊C414yes—
76#622—24no—
77#622—24no—
78C22×M16—91no—
79C23×C8—91no—
80C2×#117—91no—
81#336—94no—
82C23×D3—62no—
83C22×C3×C4—22no—
84C22×C3×C4—24no—
85C22×Dic3—62no—
86C22×Dic3—64no—
87C2×C4×D3—64no—
88C2×C4×D3—64no—
89C2×C4×D3—64no—
90C2×C4×D3—64no—
91C2×C4×D3—64no—
92C2×C4×D3—64no—
93C3×C4⋊C4—28no—
94(C2×D3)⋊C4—616no—
95C4⋊Dic3—68no—
96C4×Dic3—68no—
97C4×Dic3—68no—
98C22×C32C2×C4211yescharacteristic
99C22×C32C2×C22⋊C411yescharacteristic
100C22×C32C2×C4⋊C411yescharacteristic
101C22×C32#13112yes—
102C22×C32#13112yes—
103C2×C3⋊D3—24no—
104C2×C3⋊D3—22no—
105C2×C3⋊D3—22no—
106C2×C3⋊D3—24no—
107C2×C3⋊D3#9514yes—
108C32×C4—42no—
109C32×C4#9514yes—
110C3⋊Dic3—42no—
111C3⋊Dic3C2×C22⋊C411yescharacteristic
112C3⋊Dic3C2×C22⋊C411yescharacteristic
113C3⋊Dic3C2×C4⋊C411yescharacteristic
114C3⋊Dic3C2×C4⋊C411yescharacteristic
115C23×C4—91no—
116C2×M16—94no—
117C2×M16—182no—
118C2×M16—182no—
119C22×C8—94no—
120C22×C8—92no—
121C22×C8—92no—
122C22×C8—182no—
123C22×C8—182no—
124#117—182no—
125#117—182no—
126C2×C4⋊C4—91no—
127C2×C4⋊C4#15711yescharacteristic
128C2×C22⋊C4—92no—
129C2×C42—92no—
130C23×C3—22no—
131C22×D3—64no—
132C22×D3—64no—
133C22×D3—64no—
134C22×D3—124no—
135C22×D3—124no—
136C2×C3×C4—28no—
137C2×C3×C4—24no—
138C2×C3×C4—24no—
139C2×C3×C4—24no—
140C2×C3×C4—48no—
141C2×Dic3—62no—
142C2×Dic3—62no—
143C2×Dic3—62no—
144C2×Dic3—62no—
145C2×Dic3—62no—
146C2×Dic3—62no—
147C2×Dic3—68no—
148C2×Dic3—128no—
149C4×D3—68no—
150C4×D3—68no—
151C4×D3—68no—
152C4×D3—68no—
153C2×C32C2×#9511yescharacteristic
154C2×C32#40512yes—
155C2×C32#40811yescharacteristic
156C2×C32#40811yescharacteristic
157C2×C32#42412yes—
158C3⋊D3—24no—
159C24—91no—
160C22×C4—91no—
161C22×C4—92no—
162C22×C4—92no—
163C22×C4—92no—
164C22×C4—92no—
165C22×C4—92no—
166C22×C4—92no—
167C22×C4—92no—
168C22×C4C2×#15712yes—
169C22×C4C2×#15711yescharacteristic
170M16—188no—
171C2×C8—94no—
172C2×C8—94no—
173C2×C8—188no—
174C2×C8—182no—
175C2×C8—182no—
176C2×C8—182no—
177C2×C8—182no—
178C4⋊C4—22no—
179C4⋊C4—182no—
180C22⋊C4—184no—
181C42—182no—
182C42—182no—
183C22×C3—22no—
184C22×C3—22no—
185C22×C3—24no—
186C22×C3—24no—
187C22×C3—22no—
188C2×D3—68no—
189C2×D3—124no—
190C2×D3—124no—
191C2×D3—128no—
192C2×D3—128no—
193C3×C4—28no—
194C3×C4—48no—
195Dic3—62no—
196Dic3—62no—
197Dic3—62no—
198Dic3—62no—
199Dic3—128no—
200C32#172911yescharacteristic, complemented, Sylow
201C23—92no—
202C23—92no—
203C23—92no—
204C23—182no—
205C23—182no—
206C23C22×#15711yescharacteristic
207C2×C4—24no—
208C2×C4—22no—
209C2×C4—91no—
210C2×C4—91no—
211C2×C4—91no—
212C2×C4—91no—
213C2×C4—91no—
214C2×C4—91no—
215C2×C4—94no—
216C2×C4—94no—
217C2×C4—94no—
218C2×C4—94no—
219C2×C4—184no—
220C2×C4—182no—
221C2×C4C4×#15712yes—
222C2×C4C4⋊#15712yes—
223C2×C4C22⋊#15712yes—
224C8—184no—
225C8—184no—
226C2×C3—22no—
227C2×C3—22no—
228C2×C3—22no—
229C2×C3—24no—
230C2×C3—24no—
231D3—128no—
232C22—94no—
233C22—182no—
234C22—182no—
235C22—184no—
236C22—184no—
237C22C2×C4×#15711yescharacteristic
238C22C2×C4⋊#15711yescharacteristic
239C22#6428712yes—
240C22#6428912yes—
241C22C2×C22⋊#15711yescharacteristic
242C4—42no—
243C4—91no—
244C4—91no—
245C4—91no—
246C4—91no—
247C4—362no—
248C4#6378114yes—
249C3—22no—
250C2—184no—
251C2#1059374812yes—
252C2#1059375512yes—
253C2C2×#6378111yescharacteristic
254C2#1059382311yescharacteristic
255C2#1059383411yescharacteristic
subgroupG/H
center, FrattiniC23C22×#157
commutatorC22×C32C2×C42
FittingC2×C32×C4⋊C4C4
socleC23×C32C22×C4
prime radicalC23×C3⋊D3C2×C4
cosocleC22×C3⋊Dic3C23
hypercenterC2×C4⋊C4#157
hypocenterC32#1729
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #10590207C2semidirect
10. C2×#3788C4semidirect
13. C2×#3787C4semidirect
200. C32#1729semidirect

Maximal subgroups

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

subgroupindex
C22×#37882
C22×#37872
C2×#641012
#105902072
#17299