Finite Group Databasebeta

← #11790356

Subgroups — #11790356

Order 1152.

302 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 81 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
1C4⋊C4×#157C211yesmaximal, characteristic
2#10593553C211yesmaximal, characteristic
3C2×#63745C212yesmaximal
4C2×#63744C211yesmaximal, characteristic
5#10590163C212yesmaximal
6C2×C4⋊#157C2212yes—
7C2×C4⋊#157C2211yescharacteristic
8C2×C4×#157—21no—
9C2×C4×#157C2211yescharacteristic
10C2×#3787C2212yes—
11C2×#3777—21no—
12C2×#3777—21no—
13C4⋊C4×C3⋊D3C2211yescharacteristic
14#63781—21no—
15#63745—24no—
16#63744C414yescomplemented
17C22×#157—21no—
18C22×#157—22no—
19C22×#157D411yescharacteristic
20C22×#157D411yescharacteristic
21C2×C4×C3⋊D3—21no—
22C2×C4×C3⋊D3C2311yescharacteristic
23C2×#622—22no—
24C4⋊#157—22no—
25C4⋊#157—21no—
26C4⋊#157—22no—
27C4⋊#157D412yes—
28C4×#157—42no—
29C4×#157C2×C412yes—
30C4×#157Q812yes—
31#3787—22no—
32#3787C2×C414yes—
33#3777—42no—
34#3777—42no—
35C32×C4⋊C4Q811yescharacteristic
36C4⋊(C3⋊Dic3)Q811yescharacteristic
37#3750—21no—
38#1948—91nomaximal, Sylow
39D3×C4⋊C4—121no—
40C22×C3⋊D3C2×D411yescharacteristic
41C2×#157—21no—
42C2×#157—21no—
43C2×#157—22no—
44C2×#157—41no—
45C2×#157—41no—
46C2×#157—42no—
47C2×#157—42no—
48C2×#157—42no—
49C2×#157C4⋊C412yes—
50C2×#157C4⋊C412yes—
51C2×#157SD1612yes—
52C2×#157SD1612yes—
53C2×C32×C4—21no—
54C2×C32×C4C2×Q811yescharacteristic
55C2×C3⋊Dic3—21no—
56C2×C3⋊Dic3#4111yescharacteristic
57C4×C3⋊D3—41no—
58C4×C3⋊D3—41no—
59C4×C3⋊D3C22×C411yescharacteristic
60C4×C3⋊D3C2×D411yescharacteristic
61C4×C3⋊D3C2×Q811yescharacteristic
62C4×C3⋊D3#4111yescharacteristic
63#622—24no—
64C2×#106—92no—
65C2×C4⋊C8—91no—
66#384—91no—
67C4×C4⋊C4—91no—
68#340—92no—
69C2×C4×D3—121no—
70C2×C4×D3—122no—
71C3×C4⋊C4—41no—
72C4⋊Dic3—121no—
73Dic3⋊C4—122no—
74C22×C32C22⋊Q811yescharacteristic
75C2×C3⋊D3C2×C4⋊C411yescharacteristic
76C2×C3⋊D3#12111yescharacteristic
77C2×C3⋊D3C2×SD1611yescharacteristic
78C2×C3⋊D3C2×SD1611yescharacteristic
79C2×C3⋊D3AGL(1,ℤ/8)11yescharacteristic
80C2×C3⋊D3#13711yescharacteristic
81#157—22no—
82#157—42no—
83#157—82no—
84#157#10614yescomplemented
85C32×C4—41no—
86C32×C4C4×Q811yescharacteristic
87C32×C4C4⋊Q811yescharacteristic
88C3⋊Dic3—41no—
89C3⋊Dic3C4×D411yescharacteristic
90C3⋊Dic3#12511yescharacteristic
91C22×C8—92no—
92C2×C4⋊C4—91no—
93C2×C4⋊C4—91no—
94C2×C4⋊C4—92no—
95C2×C4⋊C4—181no—
96C2×C4⋊C4—181no—
97C2×C42—91no—
98C2×C42—181no—
99#106—184no—
100C4⋊C8—94no—
101#95—181no—
102C22×D3—121no—
103C2×C3×C4—42no—
104C2×C3×C4—41no—
105C2×Dic3—121no—
106C2×Dic3—122no—
107C4×D3—121no—
108C4×D3—121no—
109C4×D3—121no—
110C4×D3—121no—
111C4×D3—242no—
112C4×D3—242no—
113C2×C32#38911yescharacteristic
114C2×C32#47511yescharacteristic
115C2×C32#47611yescharacteristic
116C3⋊D3C2×#10611yescharacteristic
117C3⋊D3#42811yescharacteristic
118C3⋊D3#46011yescharacteristic
119C3⋊D3#46111yescharacteristic
120C22×C4—91no—
121C22×C4—91no—
122C22×C4—91no—
123C22×C4—181no—
124C22×C4—181no—
125C22×C4—182no—
126C2×C8—94no—
127C2×C8—182no—
128C2×C8—182no—
129C4⋊C4—92no—
130C4⋊C4—91no—
131C4⋊C4—181no—
132C4⋊C4—181no—
133C4⋊C4—182no—
134C4⋊C4—182no—
135C4⋊C4—362no—
136C4⋊C4—362no—
137C4⋊C4PSU(3,𝔽2)11yescharacteristic
138C42—92no—
139C42—92no—
140C42—362no—
141C22×C3—41no—
142C2×D3—121no—
143C2×D3—121no—
144C2×D3—121no—
145C2×D3—121no—
146C2×D3—121no—
147C2×D3—121no—
148C3×C4—41no—
149C3×C4—41no—
150C3×C4—82no—
151Dic3—121no—
152Dic3—121no—
153Dic3—242no—
154C32#194811yescharacteristic, complemented, Sylow
155C23—91no—
156C2×C4—21no—
157C2×C4—92no—
158C2×C4—92no—
159C2×C4—92no—
160C2×C4—91no—
161C2×C4—91no—
162C2×C4—91no—
163C2×C4—91no—
164C2×C4—91no—
165C2×C4—92no—
166C2×C4—181no—
167C2×C4—181no—
168C2×C4—182no—
169C2×C4—181no—
170C2×C4—361no—
171C2×C4—361no—
172C2×C4—361no—
173C2×C4—361no—
174C2×C4—362no—
175C2×C4—362no—
176C2×C4—362no—
177C2×C4C2×PSU(3,𝔽2)11yescharacteristic
178C8—184no—
179C2×C3—41no—
180C2×C3—41no—
181C2×C3—41no—
182D3—121no—
183D3—121no—
184D3—121no—
185D3—121no—
186C22—91no—
187C22—91no—
188C22—91no—
189C22—91no—
190C22—91no—
191C22—91no—
192C22C22⋊PSU(3,𝔽2)11yescharacteristic
193C4—41no—
194C4—94no—
195C4—91no—
196C4—91no—
197C4—182no—
198C4—362no—
199C4—361no—
200C4—722no—
201C4C4×PSU(3,𝔽2)11yescharacteristic
202C4C4⋊PSU(3,𝔽2)11yescharacteristic
203C3—41no—
204C2—91no—
205C2—91no—
206C2—91no—
207C2—91no—
208C2#1059354811yescharacteristic
209C2#1059355911yescharacteristic
210C2#1059356111yescharacteristic
subgroupG/H
centerC22C22⋊PSU(3,𝔽2)
commutatorC4×C3⋊D3C22×C4
FrattiniC2×C4C2×PSU(3,𝔽2)
FittingC32×C4⋊C4Q8
socleC22×C32C22⋊Q8
prime radicalC22×C3⋊D3C2×D4
cosocleC2×C4×C3⋊D3C23
hypercenterC4⋊C4PSU(3,𝔽2)
hypocenterC32#1948
LCSG ▷ C4×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
16. #63744C4semidirect
84. #157#106semidirect
154. C32#1948semidirect

Maximal subgroups

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

subgroupindex
C4⋊C4×#1572
#105935532
C2×#637452
C2×#637442
#105901632
#19489