Finite Group Databasebeta

← #11790511

Subgroups — #11790511

Order 1152.

234 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 65 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#10593771C211yesmaximal, characteristic
2C2×#63769C211yesmaximal, characteristic
3#10593765C211yesmaximal, characteristic
4#10593544C212yesmaximal
5#10590094C212yesmaximal
6#64286C2211yescharacteristic
7C2×C4⋊#157C2212yes—
8#64283C2212yes—
9#64283C2211yescharacteristic
10C2×C8×C3⋊D3C2211yescharacteristic
11#63771C412yescomplemented
12#63770C412yescomplemented
13#63769—21no—
14#63769—21no—
15#63767—21no—
16C8×#157—21no—
17#63746—22no—
18#63745—22no—
19C22×#157—22no—
20C2×C4×C3⋊D3C2311yescharacteristic
21C22⋊#157—21no—
22#3792—22no—
23#3792—21no—
24C4⋊#157—22no—
25C4⋊#157—22no—
26C4⋊#157D411yescharacteristic
27C4⋊#157D411yescharacteristic
28C4×#157—21no—
29#3788C2×C414yes—
30#3788Q812yes—
31#3787—22no—
32#3787—21no—
33C2×C32×C8Q811yescharacteristic
34C2×C3⋊(C3⋊C8)Q811yescharacteristic
35C8×C3⋊D3C2×C411yescharacteristic
36C8×C3⋊D3C2×C411yescharacteristic
37C8×C3⋊D3D411yescharacteristic
38C8×C3⋊D3D411yescharacteristic
39#1952—91nomaximal, Sylow
40C2×D3×C8—121no—
41C22×C3⋊D3#4111yescharacteristic
42C2×#157—21no—
43C2×#157—21no—
44C2×#157—42no—
45C2×#157—82no—
46C2×C32×C4C2×Q811yescharacteristic
47C2×C3⋊Dic3#4111yescharacteristic
48C4×C3⋊D3C22×C411yescharacteristic
49C4×C3⋊D3C2×D411yescharacteristic
50C4×C3⋊D3C2×D411yescharacteristic
51C4×C3⋊D3C2×Q811yescharacteristic
52#622—24no—
53#622—22no—
54C32×C8C4⋊C411yescharacteristic
55C32×C8C4⋊C411yescharacteristic
56C3⋊(C3⋊C8)C4⋊C411yescharacteristic
57C3⋊(C3⋊C8)C4⋊C411yescharacteristic
58C2×#108—91no—
59#428—92no—
60C2×#107—91no—
61#405—91no—
62#343—92no—
63C2×C4×D3—121no—
64C2×C3×C8—41no—
65C2×C3⋊C8—121no—
66D3×C8—121no—
67D3×C8—121no—
68D3×C8—121no—
69D3×C8—121no—
70C22×C32#12511yescharacteristic
71C2×C3⋊D3—21no—
72C2×C3⋊D3—21no—
73C2×C3⋊D3C4×Q811yescharacteristic
74C2×C3⋊D3#12111yescharacteristic
75#157—41no—
76#157—41no—
77#157—82no—
78C32×C4C2×C4⋊C411yescharacteristic
79C32×C4C4⋊Q811yescharacteristic
80C3⋊Dic3C4×D411yescharacteristic
81C3⋊Dic3C22⋊Q811yescharacteristic
82C2×M16—91no—
83C2×M16—92no—
84C22×C8—91no—
85#117—91no—
86C2×C4⋊C4—92no—
87#108—92no—
88#108—92no—
89#107—182no—
90#107—181no—
91#107—181no—
92#106—182no—
93#97—181no—
94C4×C8—181no—
95C22×D3—121no—
96C2×C3×C4—41no—
97C2×Dic3—121no—
98C4×D3—121no—
99C4×D3—121no—
100C4×D3—121no—
101C4×D3—121no—
102C3×C8—41no—
103C3×C8—41no—
104C3⋊C8—121no—
105C3⋊C8—121no—
106C2×C32—21no—
107C2×C32#38911yescharacteristic
108C3⋊D3—21no—
109C3⋊D3#47211yescharacteristic
110C3⋊D3#47311yescharacteristic
111C22×C4—91no—
112C22×C4—182no—
113M16—94no—
114M16—92no—
115M16—181no—
116M16—182no—
117C2×C8—91no—
118C2×C8—91no—
119C2×C8—91no—
120C2×C8—91no—
121C2×C8—91no—
122C2×C8—181no—
123C2×C8—182no—
124C2×C8PSU(3,𝔽2)11yescharacteristic
125C4⋊C4—91no—
126C4⋊C4—91no—
127C4⋊C4—182no—
128C4⋊C4—182no—
129C22⋊C4—181no—
130C42—181no—
131C22×C3—41no—
132C2×D3—121no—
133C2×D3—121no—
134C2×D3—122no—
135C2×D3—122no—
136C3×C4—41no—
137C3×C4—41no—
138Dic3—121no—
139Dic3—121no—
140C32#195211yescharacteristic, complemented, Sylow
141C23—91no—
142C2×C4—91no—
143C2×C4—91no—
144C2×C4—91no—
145C2×C4—91no—
146C2×C4—91no—
147C2×C4—181no—
148C2×C4—181no—
149C2×C4—362no—
150C2×C4—722no—
151C2×C4C2×PSU(3,𝔽2)11yescharacteristic
152C8—91no—
153C8—91no—
154C8—184no—
155C8—182no—
156C8#377711yescharacteristic
157C8#377711yescharacteristic
158C2×C3—42no—
159C2×C3—41no—
160D3—121no—
161D3—121no—
162D3—122no—
163C22—91no—
164C22—91no—
165C22—181no—
166C22—181no—
167C22#6424311yescharacteristic
168C4—91no—
169C4—91no—
170C4—361no—
171C4—361no—
172C4—722no—
173C4C4⋊PSU(3,𝔽2)11yescharacteristic
174C4C2×#377711yescharacteristic
175C3—41no—
176C2—21no—
177C2—91no—
178C2—91no—
179C2—181no—
180C2#1059355411yescharacteristic
subgroupG/H
centerC2#10593554
commutatorC4×C3⋊D3C22×C4
FrattiniC2×C4C2×PSU(3,𝔽2)
FittingC2×C32×C8Q8
socleC2×C32#389
prime radicalC22×C3⋊D3#41
cosocleC2×C4×C3⋊D3C23
hypercenterC2×C8PSU(3,𝔽2)
hypocenterC32#1952
LCSG ▷ C4×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
11. #63771C4semidirect
12. #63770C4semidirect
140. C32#1952semidirect

Maximal subgroups

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

subgroupindex
#105937712
C2×#637692
#105937652
#105935442
#105900942
#19529