Finite Group Databasebeta

← #11790084

Subgroups — #11790084

Order 1152.

302 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 79 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#10593726C211yesmaximal, characteristic
3#10593723C211yesmaximal, characteristic
4C2×#63744C212yesmaximal
5#10590090C212yesmaximal
6C2×C4⋊#157C412yes—
7C2×C4×#157C2212yes—
8C2×#3787C2212yes—
9C2×#3787C2211yescharacteristic
10C2×#3787C2211yescharacteristic
11C42×C3⋊D3C2211yescharacteristic
12#63781C411yescharacteristic
13#63781C411yescharacteristic
14#63779—21no—
15#63777—21no—
16#63777—21no—
17C4⋊#622—21no—
18#63744—24no—
19C22×#157C2×C412yes—
20C22×#157C2×C412yes—
21C2×C4×C3⋊D3C2×C411yescharacteristic
22C2×C4×C3⋊D3C2×C411yescharacteristic
23C2×C4×C3⋊D3C2311yescharacteristic
24C2×#622—21no—
25C2×#622—21no—
26C2×#622—22no—
27C4⋊#157—24no—
28C4×#157—22no—
29C4×#157—22no—
30#3787—21no—
31#3787—21no—
32#3787—22no—
33#3787—22no—
34#3787D412yes—
35#3787Q812yes—
36C32×C42Q811yescharacteristic
37C4×C3⋊Dic3D411yescharacteristic
38C4×C3⋊Dic3D411yescharacteristic
39C4×C3⋊Dic3Q811yescharacteristic
40#1940—91nomaximal, Sylow
41C42×D3—121no—
42C22×C3⋊D3C22×C411yescharacteristic
43C2×#157—22no—
44C2×#157—22no—
45C2×#157—22no—
46C2×#157—22no—
47C2×#157—22no—
48C2×#157M1614yes—
49C2×C32×C4C4⋊C411yescharacteristic
50C2×C32×C4C4⋊C411yescharacteristic
51C2×C32×C4C2×Q811yescharacteristic
52C2×C3⋊Dic3C4⋊C411yescharacteristic
53C2×C3⋊Dic3C4⋊C411yescharacteristic
54C2×C3⋊Dic3C2×D411yescharacteristic
55C4×C3⋊D3—22no—
56C4×C3⋊D3—22no—
57C4×C3⋊D3C2×D411yescharacteristic
58C4×C3⋊D3C2×Q811yescharacteristic
59C4×C3⋊D3#4111yescharacteristic
60C4×C3⋊D3#4111yescharacteristic
61#622—22no—
62#622—22no—
63#622—42no—
64C2×C4⋊C8—92no—
65C2×C4⋊C8—91no—
66C2×#97—91no—
67C4×C4⋊C4—91no—
68#336—92no—
69C2×C4×D3—121no—
70C2×C4×D3—121no—
71C2×C4×D3—121no—
72C3×C42—41no—
73C4×Dic3—121no—
74C4×Dic3—121no—
75C4×Dic3—121no—
76C22×C32C2×C4⋊C411yescharacteristic
77C2×C3⋊D3C4×D411yescharacteristic
78C2×C3⋊D3C4×Q811yescharacteristic
79C2×C3⋊D3C2×M1612yes—
80C2×C3⋊D3#13112yes—
81#157—24no—
82#157—42no—
83C32×C4—21no—
84C32×C4—21no—
85C32×C4#12511yescharacteristic
86C32×C4C4⋊Q811yescharacteristic
87C3⋊Dic3—21no—
88C3⋊Dic3—21no—
89C3⋊Dic3#12111yescharacteristic
90C3⋊Dic3C22⋊Q811yescharacteristic
91C22×C8—91no—
92C22×C8—91no—
93C22×C8—92no—
94C2×C4⋊C4—92no—
95C2×C42—91no—
96C2×C42—92no—
97C4⋊C8—181no—
98C4⋊C8—181no—
99C4⋊C8—184no—
100#97—181no—
101#97—181no—
102#95—91no—
103#95—91no—
104C22×D3—121no—
105C2×C3×C4—41no—
106C2×C3×C4—41no—
107C2×C3×C4—41no—
108C2×Dic3—121no—
109C2×Dic3—121no—
110C2×Dic3—121no—
111C4×D3—121no—
112C4×D3—121no—
113C4×D3—121no—
114C4×D3—121no—
115C4×D3—124no—
116C4×D3—124no—
117C2×C32#38911yescharacteristic
118C2×C32#42311yescharacteristic
119C2×C32#42411yescharacteristic
120C3⋊D3#43512yes—
121C3⋊D3#44612yes—
122C22×C4—91no—
123C22×C4—92no—
124C22×C4—91no—
125C22×C4—91no—
126C22×C4—92no—
127C2×C8—92no—
128C2×C8—92no—
129C2×C8—181no—
130C2×C8—181no—
131C2×C8—181no—
132C2×C8—181no—
133C2×C8—182no—
134C2×C8—182no—
135C2×C8—182no—
136C4⋊C4—184no—
137C42—91no—
138C42—91no—
139C42—91no—
140C42—182no—
141C42—182no—
142C42PSU(3,𝔽2)11yescharacteristic
143C22×C3—41no—
144C2×D3—121no—
145C2×D3—121no—
146C2×D3—122no—
147C2×D3—122no—
148C3×C4—42no—
149C3×C4—42no—
150C3×C4—41no—
151C3×C4—41no—
152Dic3—121no—
153Dic3—121no—
154Dic3—122no—
155Dic3—122no—
156C32#194011yescharacteristic, complemented, Sylow
157C23—91no—
158C2×C4—91no—
159C2×C4—91no—
160C2×C4—91no—
161C2×C4—91no—
162C2×C4—91no—
163C2×C4—94no—
164C2×C4—91no—
165C2×C4—91no—
166C2×C4—182no—
167C2×C4—182no—
168C2×C4—182no—
169C2×C4—182no—
170C2×C4—182no—
171C2×C4—182no—
172C2×C4—182no—
173C2×C4#377711yescharacteristic
174C2×C4#377711yescharacteristic
175C2×C4C2×PSU(3,𝔽2)11yescharacteristic
176C8—182no—
177C8—182no—
178C8—362no—
179C2×C3—41no—
180C2×C3—41no—
181C2×C3—41no—
182D3—122no—
183D3—122no—
184C22—92no—
185C22—92no—
186C22—91no—
187C22—91no—
188C22C2×#377711yescharacteristic
189C4—21no—
190C4—21no—
191C4—91no—
192C4—91no—
193C4—184no—
194C4—181no—
195C4—181no—
196C4—362no—
197C4#6424311yescharacteristic
198C4C4⋊PSU(3,𝔽2)11yescharacteristic
199C3—41no—
200C2—92no—
201C2—92no—
202C2#1059353911yescharacteristic
203C2#1059354011yescharacteristic
204C2#1059355411yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×PSU(3,𝔽2)
commutator, prime radicalC22×C3⋊D3C22×C4
FittingC32×C42Q8
socleC22×C32C2×C4⋊C4
cosocleC2×C4×C3⋊D3C23
hypercenterC42PSU(3,𝔽2)
hypocenterC32#1940
LCSG ▷ C22×C3⋊D3 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
156. C32#1940semidirect

Maximal subgroups

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

subgroupindex
C4×C4⋊#1572
#105937262
#105937232
C2×#637442
#105900902
#19409