Finite Group Databasebeta

← #11790355

Subgroups — #11790355

Order 1152.

310 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 85 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#10593735C211yesmaximal, characteristic
2C4×C4⋊#157C211yesmaximal, characteristic
3#10593726C211yesmaximal, characteristic
4C2×#63745C212yesmaximal
5#10590093C212yesmaximal
6C2×C4⋊#157—21no—
7C2×C4⋊#157—21no—
8C2×C4⋊#157C2212yes—
9C2×C4⋊#157C2211yescharacteristic
10C2×C4⋊#157C2211yescharacteristic
11C2×C4×#157—21no—
12C2×#3787C2212yes—
13C42×C3⋊D3C2211yescharacteristic
14#63781—21no—
15#63779C412yescomplemented
16C4⋊#622C412yescomplemented
17#63745—24no—
18C22×#157—21no—
19C22×#157—21no—
20C22×#157—22no—
21C2×C4×C3⋊D3D411yescharacteristic
22C2×C4×C3⋊D3D411yescharacteristic
23C2×C4×C3⋊D3C2311yescharacteristic
24C2×#622C2×C414yes—
25C4⋊#157—22no—
26C4⋊#157—21no—
27C4⋊#157—21no—
28C4⋊#157—22no—
29C4⋊#157—42no—
30C4⋊#157—42no—
31C4⋊#157D412yes—
32C4⋊#157Q812yes—
33C4×#157—42no—
34#3787—22no—
35#3787—22no—
36C32×C42Q811yescharacteristic
37C4×C3⋊Dic3C2×C411yescharacteristic
38C4×C3⋊Dic3C2×C411yescharacteristic
39C4×C3⋊Dic3Q811yescharacteristic
40#1948—91nomaximal, Sylow
41C42×D3—121no—
42C22×C3⋊D3C2×D411yescharacteristic
43C2×#157—22no—
44C2×#157—22no—
45C2×#157—41no—
46C2×#157—41no—
47C2×#157—41no—
48C2×#157—41no—
49C2×#157—42no—
50C2×#157—42no—
51C2×#157—42no—
52C2×C32×C4C4⋊C411yescharacteristic
53C2×C32×C4C4⋊C411yescharacteristic
54C2×C32×C4C2×Q811yescharacteristic
55C2×C3⋊Dic3C4⋊C411yescharacteristic
56C2×C3⋊Dic3C4⋊C411yescharacteristic
57C2×C3⋊Dic3C22×C411yescharacteristic
58C4×C3⋊D3—21no—
59C4×C3⋊D3—21no—
60C4×C3⋊D3SD1612yes—
61C4×C3⋊D3SD1612yes—
62C4×C3⋊D3C2×D411yescharacteristic
63C4×C3⋊D3C2×Q811yescharacteristic
64C4×C3⋊D3#4111yescharacteristic
65C4×C3⋊D3#4111yescharacteristic
66#622—24no—
67C2×#106—92no—
68C2×C4⋊C8—91no—
69#384—91no—
70C4×C4⋊C4—91no—
71#340—92no—
72C2×C4×D3—121no—
73C2×C4×D3—121no—
74C2×C4×D3—121no—
75C3×C42—41no—
76C4×Dic3—121no—
77C4×Dic3—121no—
78C4×Dic3—121no—
79C22×C32C2×C4⋊C411yescharacteristic
80C2×C3⋊D3#12111yescharacteristic
81C2×C3⋊D3C22⋊Q811yescharacteristic
82C2×C3⋊D3C2×SD1611yescharacteristic
83C2×C3⋊D3C2×SD1611yescharacteristic
84C2×C3⋊D3AGL(1,ℤ/8)11yescharacteristic
85C2×C3⋊D3#13711yescharacteristic
86#157—42no—
87#157—42no—
88#157—82no—
89C32×C4—21no—
90C32×C4#10612yescomplemented
91C32×C4#12511yescharacteristic
92C32×C4C4⋊Q811yescharacteristic
93C3⋊Dic3—21no—
94C3⋊Dic3#10612yescomplemented
95C3⋊Dic3C4×D411yescharacteristic
96C3⋊Dic3C4×Q811yescharacteristic
97C22×C8—92no—
98C2×C4⋊C4—91no—
99C2×C4⋊C4—91no—
100C2×C4⋊C4—92no—
101C2×C4⋊C4—181no—
102C2×C4⋊C4—181no—
103C2×C42—91no—
104C2×C42—181no—
105#106—184no—
106C4⋊C8—92no—
107C4⋊C8—92no—
108#95—181no—
109C22×D3—121no—
110C2×C3×C4—41no—
111C2×C3×C4—41no—
112C2×C3×C4—41no—
113C2×Dic3—121no—
114C2×Dic3—121no—
115C2×Dic3—121no—
116C4×D3—122no—
117C4×D3—122no—
118C4×D3—121no—
119C4×D3—121no—
120C4×D3—121no—
121C4×D3—121no—
122C4×D3—122no—
123C4×D3—122no—
124C2×C32#38911yescharacteristic
125C2×C32C2×#10611yescharacteristic
126C2×C32#42811yescharacteristic
127C3⋊D3#46011yescharacteristic
128C3⋊D3#46111yescharacteristic
129C3⋊D3#47511yescharacteristic
130C3⋊D3#47611yescharacteristic
131C22×C4—91no—
132C22×C4—91no—
133C22×C4—91no—
134C22×C4—181no—
135C22×C4—181no—
136C22×C4—182no—
137C2×C8—94no—
138C2×C8—182no—
139C2×C8—182no—
140C4⋊C4—92no—
141C4⋊C4—92no—
142C4⋊C4—181no—
143C4⋊C4—181no—
144C4⋊C4—182no—
145C4⋊C4—182no—
146C4⋊C4—362no—
147C4⋊C4—362no—
148C42—91no—
149C42—91no—
150C42—91no—
151C42—362no—
152C42PSU(3,𝔽2)11yescharacteristic
153C22×C3—41no—
154C2×D3—121no—
155C2×D3—121no—
156C2×D3—121no—
157C2×D3—121no—
158C2×D3—121no—
159C2×D3—121no—
160C3×C4—42no—
161C3×C4—42no—
162C3×C4—41no—
163C3×C4—41no—
164Dic3—122no—
165Dic3—121no—
166Dic3—121no—
167Dic3—122no—
168C32#194811yescharacteristic, complemented, Sylow
169C23—91no—
170C2×C4—91no—
171C2×C4—91no—
172C2×C4—92no—
173C2×C4—92no—
174C2×C4—91no—
175C2×C4—91no—
176C2×C4—91no—
177C2×C4—91no—
178C2×C4—91no—
179C2×C4—181no—
180C2×C4—181no—
181C2×C4—182no—
182C2×C4—182no—
183C2×C4—361no—
184C2×C4—361no—
185C2×C4—361no—
186C2×C4—361no—
187C2×C4—362no—
188C2×C4—362no—
189C2×C4—362no—
190C2×C4#377711yescharacteristic
191C2×C4#377711yescharacteristic
192C2×C4C2×PSU(3,𝔽2)11yescharacteristic
193C8—184no—
194C2×C3—41no—
195C2×C3—41no—
196C2×C3—41no—
197D3—121no—
198D3—121no—
199D3—121no—
200D3—121no—
201C22—91no—
202C22—91no—
203C22—91no—
204C22—91no—
205C22—91no—
206C22—91no—
207C22C2×#377711yescharacteristic
208C4—21no—
209C4—92no—
210C4—91no—
211C4—91no—
212C4—181no—
213C4—362no—
214C4—362no—
215C4—722no—
216C4#6374512yescomplemented
217C4#6424311yescharacteristic
218C4C4⋊PSU(3,𝔽2)11yescharacteristic
219C3—41no—
220C2—91no—
221C2—91no—
222C2—91no—
223C2—91no—
224C2C2×#6374511yescharacteristic
225C2#1059354411yescharacteristic
226C2#1059355411yescharacteristic
subgroupG/H
centerC22C2×#3777
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×PSU(3,𝔽2)
FittingC32×C42Q8
socleC22×C32C2×C4⋊C4
prime radicalC22×C3⋊D3C2×D4
cosocleC2×C4×C3⋊D3C23
hypercenterC42PSU(3,𝔽2)
hypocenterC32#1948
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
15. #63779C4semidirect
16. C4⋊#622C4semidirect
90. C32×C4#106semidirect
94. C3⋊Dic3#106semidirect
168. C32#1948semidirect
216. C4#63745semidirect

Maximal subgroups

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

subgroupindex
#105937352
C4×C4⋊#1572
#105937262
C2×#637452
#105900932
#19489