Finite Group Databasebeta

← #11786378

Subgroups — #11786378

Order 1152.

466 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 93 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×#3787C211yesmaximal, characteristic
2C4×C22⋊#157C211yesmaximal, characteristic
3#10593800C211yesmaximal, characteristic
4C2×#63744C212yesmaximal, complemented
5#10590090C212yesmaximal, complemented
6C22×C4×C3⋊D3C2211yescharacteristic
7C2×C22⋊#157C411yescharacteristic
8C2×C22⋊#157C411yescharacteristic
9C22×#622—21no—
10C2×C4×#157C2212yes—
11C2×#3787—21no—
12C2×#3787—24no—
13C2×#3787C2211yescharacteristic
14C2×#3787C2211yescharacteristic
15C2×#3787C2212yes—
16C22⋊#622—21no—
17#63781C412yes—
18#63778—21no—
19#63744—24no—
20C23×C3⋊D3C2×C411yescharacteristic
21C22×#157C2×C412yes—
22C22×#157C2×C412yes—
23C22×C32×C4Q811yescharacteristic
24C22×C3⋊Dic3D411yescharacteristic
25C2×C4×C3⋊D3—22no—
26C2×C4×C3⋊D3—22no—
27C2×C4×C3⋊D3C2×C411yescharacteristic
28C2×C4×C3⋊D3D411yescharacteristic
29C2×C4×C3⋊D3Q811yescharacteristic
30C2×C4×C3⋊D3C2311yescharacteristic
31C22⋊#157—22no—
32C22⋊#157C814yescomplemented
33C2×#622—24no—
34C2×#622—22no—
35C2×#622—21no—
36C2×#622—21no—
37C4×#157—22no—
38C4×#157—22no—
39#3787—24no—
40#3787—22no—
41#3787—22no—
42#3787—22no—
43#3787D414yes—
44#1850—91nomaximal, Sylow
45C22×C4×D3—121no—
46C23×C32C4⋊C411yescharacteristic
47C22×C3⋊D3—22no—
48C22×C3⋊D3—22no—
49C22×C3⋊D3C4⋊C411yescharacteristic
50C22×C3⋊D3C2×C812yes—
51C22×C3⋊D3M1612yes—
52C22×C3⋊D3C22×C411yescharacteristic
53C2×#157—22no—
54C2×#157—22no—
55C2×#157—22no—
56C2×#157—22no—
57C2×#157—22no—
58C2×#157C2×C814yescomplemented
59C2×C32×C4—22no—
60C2×C32×C4C4⋊C411yescharacteristic
61C2×C32×C4C2×Q811yescharacteristic
62C2×C3⋊Dic3—21no—
63C2×C3⋊Dic3—21no—
64C2×C3⋊Dic3C4⋊C411yescharacteristic
65C2×C3⋊Dic3C2×D411yescharacteristic
66C4×C3⋊D3—22no—
67C4×C3⋊D3—22no—
68C4×C3⋊D3—21no—
69C4×C3⋊D3—21no—
70C4×C3⋊D3C2×D412yes—
71C4×C3⋊D3#4112yes—
72#622—24no—
73#622—41no—
74#622—41no—
75C23×C8—91no—
76C2×C4⋊C8—92no—
77C2×C22⋊C8—91no—
78C4×C22⋊C4—91no—
79#336—92no—
80C23×D3—121no—
81C22×C3×C4—41no—
82C22×Dic3—121no—
83C2×C4×D3—121no—
84C2×C4×D3—121no—
85C2×C4×D3—121no—
86C2×C4×D3—121no—
87C2×C4×D3—124no—
88C2×C4×D3—124no—
89C22×C32—21no—
90C22×C32—21no—
91C22×C32C4⋊C812yescomplemented
92C22×C32C2×C4⋊C411yescharacteristic
93C2×C3⋊D3—21no—
94C2×C3⋊D3—21no—
95C2×C3⋊D3—24no—
96C2×C3⋊D3—24no—
97C2×C3⋊D3C4⋊C812yescomplemented
98C2×C3⋊D3C4×D412yes—
99C2×C3⋊D3C22×C811yescharacteristic
100C2×C3⋊D3C2×M1611yescharacteristic
101C2×C3⋊D3#13112yes—
102#157—24no—
103#157—42no—
104C32×C4—21no—
105C32×C4C22⋊Q812yes—
106C3⋊Dic3—21no—
107C3⋊Dic3#12011yescharacteristic
108C3⋊Dic3#12311yescharacteristic
109C23×C4—91no—
110C22×C8—92no—
111C22×C8—91no—
112C22×C8—91no—
113C22×C8—184no—
114C22×C8—181no—
115C22×C8—181no—
116C2×C22⋊C4—91no—
117C2×C22⋊C4—91no—
118C2×C42—92no—
119C4⋊C8—184no—
120C22⋊C8—181no—
121C22⋊C8—181no—
122#95—92no—
123C23×C3—41no—
124C22×D3—121no—
125C22×D3—122no—
126C22×D3—122no—
127C22×D3—121no—
128C22×D3—124no—
129C22×D3—124no—
130C2×C3×C4—44no—
131C2×C3×C4—41no—
132C2×C3×C4—41no—
133C2×Dic3—121no—
134C2×Dic3—121no—
135C2×Dic3—122no—
136C2×Dic3—122no—
137C4×D3—122no—
138C4×D3—122no—
139C4×D3—122no—
140C4×D3—122no—
141C4×D3—124no—
142C4×D3—124no—
143C2×C32—22no—
144C2×C32#38511yescharacteristic
145C2×C32C2×C4⋊C811yescharacteristic
146C2×C32#42411yescharacteristic
147C3⋊D3—22no—
148C3⋊D3C8×D412yes—
149C3⋊D3#43512yes—
150C24—91no—
151C22×C4—91no—
152C22×C4—92no—
153C22×C4—91no—
154C22×C4—91no—
155C22×C4—91no—
156C22×C4—91no—
157C22×C4—92no—
158C22×C4—182no—
159C22×C4—182no—
160C22×C4PSU(3,𝔽2)11yescharacteristic
161C2×C8—94no—
162C2×C8—182no—
163C2×C8—182no—
164C2×C8—184no—
165C2×C8—184no—
166C2×C8—181no—
167C2×C8—181no—
168C2×C8—182no—
169C2×C8—182no—
170C22⋊C4—94no—
171C22⋊C4—182no—
172C42—182no—
173C42—182no—
174C22×C3—42no—
175C22×C3—42no—
176C22×C3—42no—
177C22×C3—41no—
178C2×D3—122no—
179C2×D3—122no—
180C2×D3—121no—
181C2×D3—121no—
182C2×D3—122no—
183C2×D3—122no—
184C2×D3—128no—
185C2×D3—128no—
186C2×D3—122no—
187C3×C4—42no—
188C3×C4—42no—
189Dic3—121no—
190Dic3—121no—
191Dic3—122no—
192C32#185011yescharacteristic, complemented, Sylow
193C23—91no—
194C23—92no—
195C23—92no—
196C23—91no—
197C23—182no—
198C23—182no—
199C23#377711yescharacteristic
200C2×C4—22no—
201C2×C4—91no—
202C2×C4—92no—
203C2×C4—92no—
204C2×C4—94no—
205C2×C4—91no—
206C2×C4—181no—
207C2×C4—181no—
208C2×C4—182no—
209C2×C4—181no—
210C2×C4—181no—
211C2×C4—182no—
212C2×C4—182no—
213C2×C4—182no—
214C2×C4—182no—
215C2×C4—182no—
216C2×C4—182no—
217C2×C4#377711yescharacteristic
218C2×C4C2×PSU(3,𝔽2)11yescharacteristic
219C8—184no—
220C8—361no—
221C8—361no—
222C2×C3—44no—
223C2×C3—41no—
224C2×C3—41no—
225C2×C3—41no—
226D3—122no—
227D3—122no—
228D3—124no—
229C22—21no—
230C22—21no—
231C22—91no—
232C22—91no—
233C22—92no—
234C22—92no—
235C22—92no—
236C22—184no—
237C22—184no—
238C22—181no—
239C22—181no—
240C22#6374412yescomplemented
241C22C2×#377711yescharacteristic
242C4—21no—
243C4—91no—
244C4—91no—
245C4—184no—
246C4—181no—
247C4—362no—
248C4C22⋊PSU(3,𝔽2)12yes—
249C3—41no—
250C2—22no—
251C2—92no—
252C2—92no—
253C2—182no—
254C2C2×#6374411yescharacteristic
255C2#1059354011yescharacteristic
256C2#1059356911yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×PSU(3,𝔽2)
commutatorC2×C3⋊D3C22×C8
FittingC22×C32×C4Q8
socleC22×C32C2×C4⋊C4
prime radicalC23×C3⋊D3C2×C4
cosocleC2×C4×C3⋊D3C23
hypercenterC22×C4PSU(3,𝔽2)
hypocenterC32#1850
LCSG ▷ C2×C3⋊D3 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. C2×#63744C2semidirect
5. #10590090C2semidirect
32. C22⋊#157C8semidirect
58. C2×#157C2×C8semidirect
91. C22×C32C4⋊C8semidirect
97. C2×C3⋊D3C4⋊C8semidirect
192. C32#1850semidirect
240. C22#63744semidirect

Maximal subgroups

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

subgroupindex
C22×#37872
C4×C22⋊#1572
#105938002
C2×#637442
#105900902
#18509