Finite Group Databasebeta

← #11777077

Subgroups — #11777077

Order 1152.

278 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 62 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#10593730C211yesmaximal, characteristic
2#10593726C211yesmaximal, characteristic
3#10592532C211yesmaximal, characteristic
4#10590173C211yesmaximal, characteristic, complemented
5#10590172C211yesmaximal, characteristic, complemented
6#10590171C211yesmaximal, characteristic, complemented
7#10590170C211yesmaximal, characteristic, complemented
8C2×#3787—21no—
9C42×C3⋊D3C2211yescharacteristic
10#63779—21no—
11#63778—21no—
12#63777—21no—
13C4⋊#622C2211yescharacteristic
14C4⋊#622C2211yescharacteristic
15C4⋊#622C2211yescharacteristic
16C4⋊#622C2211yescharacteristic
17C32×C4⋊C8C411yescharacteristic
18#63647C411yescharacteristic
19#63647C411yescharacteristic
20C8×C3⋊Dic3C2211yescharacteristic
21C8×C3⋊Dic3C2211yescharacteristic
22C4⋊(C3⋊(C3⋊C8))C411yescharacteristic
23#4833—62no—
24C2×C4×C3⋊D3C2×C411yescharacteristic
25C2×C4×C3⋊D3D411yescharacteristic
26C2×C4×C3⋊D3Q811yescharacteristic
27C2×#622—21no—
28C2×#622—21no—
29C2×#622—21no—
30C2×#622—21no—
31#3787—42no—
32C2×C32×C8C2×C411yescharacteristic
33C2×C32×C8C2×C411yescharacteristic
34C32×C42C2×C411yescharacteristic
35C4×C3⋊Dic3D411yescharacteristic
36C4×C3⋊Dic3Q811yescharacteristic
37C4×C3⋊Dic3C2311yescharacteristic
38C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
39C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
40#1573—91nomaximal, Sylow
41C42×D3—62no—
42C3×C4⋊C8—22no—
43(C2×D3)⋊C8—62no—
44(C2×D3)⋊C8—62no—
45C8×Dic3—62no—
46C8×Dic3—62no—
47C4⋊(C3⋊C8)—62no—
48C22×C3⋊D3C4⋊C411yescharacteristic
49C2×C32×C4C4⋊C411yescharacteristic
50C2×C32×C4C4⋊C411yescharacteristic
51C2×C32×C4C22×C411yescharacteristic
52C2×C3⋊Dic3C4⋊C411yescharacteristic
53C2×C3⋊Dic3C2×D411yescharacteristic
54C2×C3⋊Dic3C2×Q811yescharacteristic
55C4×C3⋊D3—22no—
56C4×C3⋊D3—21no—
57C4×C3⋊D3—21no—
58C4×C3⋊D3—21no—
59C4×C3⋊D3—21no—
60#622—41no—
61#622—41no—
62#622—41no—
63#622—41no—
64C32×C8—21no—
65C32×C8—21no—
66C3⋊(C3⋊C8)—21no—
67C3⋊(C3⋊C8)—21no—
68#432—91no—
69#431—91no—
70C2×C4⋊C8—91no—
71#335—91no—
72#335—91no—
73#334—91no—
74#334—91no—
75C2×C4×D3—62no—
76C2×C4×D3—62no—
77C2×C4×D3—62no—
78C2×C3×C8—22no—
79C2×C3×C8—22no—
80C3×C42—22no—
81C4×Dic3—62no—
82C4×Dic3—62no—
83C4×Dic3—62no—
84C2×C3⋊C8—62no—
85C2×C3⋊C8—62no—
86C22×C32C2×C4⋊C411yescharacteristic
87C2×C3⋊D3—21no—
88C2×C3⋊D3—21no—
89C2×C3⋊D3#10812yes—
90C32×C4—21no—
91C32×C4—21no—
92C32×C4#13111yescharacteristic
93C32×C4#13111yescharacteristic
94C3⋊Dic3—21no—
95C3⋊Dic3—21no—
96C3⋊Dic3AGL(1,ℤ/8)11yescharacteristic
97C3⋊Dic3#13711yescharacteristic
98C22×C8—181no—
99C2×C42—91no—
100C4⋊C8—91no—
101C4⋊C8—91no—
102C4⋊C8—91no—
103C4⋊C8—91no—
104C4⋊C8—91no—
105C4⋊C8—181no—
106C4⋊C8#15711yescharacteristic
107C22⋊C8—91no—
108C22⋊C8—91no—
109C22⋊C8—181no—
110#97—181no—
111C4×C8—91no—
112C4×C8—91no—
113C22×D3—62no—
114C2×C3×C4—22no—
115C2×C3×C4—22no—
116C2×C3×C4—22no—
117C2×Dic3—62no—
118C2×Dic3—62no—
119C2×Dic3—62no—
120C4×D3—68no—
121C4×D3—122no—
122C4×D3—122no—
123C4×D3—122no—
124C4×D3—122no—
125C3×C8—42no—
126C3×C8—42no—
127C3⋊C8—122no—
128C3⋊C8—122no—
129C2×C32#42411yescharacteristic
130C2×C32#42811yescharacteristic
131C2×C32C2×#10811yescharacteristic
132C3⋊D3—22no—
133C22×C4—91no—
134C22×C4—91no—
135C22×C4—91no—
136C2×C8—91no—
137C2×C8—91no—
138C2×C8—181no—
139C2×C8—181no—
140C2×C8—181no—
141C2×C8—181no—
142C2×C8—362no—
143C2×C8C2×#15711yescharacteristic
144C2×C8C2×#15711yescharacteristic
145C42—91no—
146C42—91no—
147C42—91no—
148C42C2×#15711yescharacteristic
149C22×C3—22no—
150C2×D3—64no—
151C2×D3—122no—
152C2×D3—122no—
153C3×C4—24no—
154C3×C4—22no—
155C3×C4—22no—
156C3×C4—42no—
157Dic3—62no—
158Dic3—62no—
159Dic3—64no—
160Dic3—122no—
161C32#157311yescharacteristic, complemented, Sylow
162C23—91no—
163C2×C4—91no—
164C2×C4—91no—
165C2×C4—91no—
166C2×C4—181no—
167C2×C4—181no—
168C2×C4—182no—
169C2×C4—181no—
170C2×C4—181no—
171C2×C4C4⋊#15711yescharacteristic
172C2×C4C4⋊#15711yescharacteristic
173C2×C4C22×#15711yescharacteristic
174C8—21no—
175C8—21no—
176C8—181no—
177C8—181no—
178C8—361no—
179C8—361no—
180C8—361no—
181C8—361no—
182C2×C3—22no—
183C2×C3—22no—
184C2×C3—22no—
185D3—124no—
186C22—92no—
187C22—181no—
188C22—181no—
189C22C2×C4⋊#15711yescharacteristic
190C4—21no—
191C4—21no—
192C4—91no—
193C4—91no—
194C4—181no—
195C4—181no—
196C4#6428711yescharacteristic
197C4#6428911yescharacteristic
198C3—22no—
199C2—182no—
200C2#1059375511yescharacteristic
201C2#1059377111yescharacteristic
202C2#1059377411yescharacteristic
subgroupG/H
centerC22C2×C4⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×C4⋊C8C4
socleC22×C32C2×C4⋊C4
prime radicalC22×C3⋊D3C4⋊C4
cosocleC4×C3⋊Dic3C23
hypercenterC4⋊C8#157
hypocenterC32#1573
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
4. #10590173C2semidirect
5. #10590172C2semidirect
6. #10590171C2semidirect
7. #10590170C2semidirect
161. C32#1573semidirect

Maximal subgroups

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

subgroupindex
#105937302
#105937262
#105925322
#105901732
#105901722
#105901712
#105901702
#15739