Finite Group Databasebeta

← #11790476

Subgroups — #11790476

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×#63768C211yesmaximal, 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#63768—21no—
14#63768—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⋊#157D412yes—
27C4×#157—21no—
28#3788C2×C414yes—
29#3788Q812yes—
30#3787—22no—
31#3787—21no—
32C2×C32×C8Q811yescharacteristic
33C2×C3⋊(C3⋊C8)Q811yescharacteristic
34C8×C3⋊D3C2×C411yescharacteristic
35C8×C3⋊D3C2×C411yescharacteristic
36C8×C3⋊D3D411yescharacteristic
37C8×C3⋊D3D411yescharacteristic
38#1951—91nomaximal, Sylow
39C2×D3×C8—121no—
40C22×C3⋊D3#4111yescharacteristic
41C2×#157—22no—
42C2×#157—42no—
43C2×#157—82no—
44C2×C32×C4C2×Q811yescharacteristic
45C2×C3⋊Dic3#4111yescharacteristic
46C4×C3⋊D3C22×C411yescharacteristic
47C4×C3⋊D3C2×D411yescharacteristic
48C4×C3⋊D3C2×D411yescharacteristic
49C4×C3⋊D3C2×Q811yescharacteristic
50#622—24no—
51#622—22no—
52C32×C8C4⋊C411yescharacteristic
53C32×C8C4⋊C411yescharacteristic
54C3⋊(C3⋊C8)C4⋊C411yescharacteristic
55C3⋊(C3⋊C8)C4⋊C411yescharacteristic
56C2×#108—91no—
57#428—92no—
58C2×#106—91no—
59#405—91no—
60#343—92no—
61C2×C4×D3—121no—
62C2×C3×C8—41no—
63C2×C3⋊C8—121no—
64D3×C8—121no—
65D3×C8—121no—
66D3×C8—121no—
67D3×C8—121no—
68C22×C32#12511yescharacteristic
69C2×C3⋊D3—22no—
70C2×C3⋊D3C4×Q811yescharacteristic
71C2×C3⋊D3#12111yescharacteristic
72#157—42no—
73#157—82no—
74C32×C4C2×C4⋊C411yescharacteristic
75C32×C4C4⋊Q811yescharacteristic
76C3⋊Dic3C4×D411yescharacteristic
77C3⋊Dic3C22⋊Q811yescharacteristic
78C2×M16—91no—
79C2×M16—92no—
80C22×C8—91no—
81#117—91no—
82C2×C4⋊C4—92no—
83#108—92no—
84#108—92no—
85#107—182no—
86#106—182no—
87#106—181no—
88#106—181no—
89#97—181no—
90C4×C8—181no—
91C22×D3—121no—
92C2×C3×C4—41no—
93C2×Dic3—121no—
94C4×D3—121no—
95C4×D3—121no—
96C4×D3—121no—
97C4×D3—121no—
98C3×C8—41no—
99C3×C8—41no—
100C3⋊C8—121no—
101C3⋊C8—121no—
102C2×C32—21no—
103C2×C32#38911yescharacteristic
104C3⋊D3—21no—
105C3⋊D3#47112yes—
106C22×C4—91no—
107C22×C4—182no—
108M16—94no—
109M16—92no—
110M16—181no—
111M16—182no—
112C2×C8—91no—
113C2×C8—91no—
114C2×C8—91no—
115C2×C8—91no—
116C2×C8—91no—
117C2×C8—181no—
118C2×C8—182no—
119C2×C8PSU(3,𝔽2)11yescharacteristic
120C4⋊C4—92no—
121C4⋊C4—182no—
122C4⋊C4—182no—
123C22⋊C4—181no—
124C42—181no—
125C22×C3—41no—
126C2×D3—121no—
127C2×D3—121no—
128C2×D3—124no—
129C3×C4—41no—
130C3×C4—41no—
131Dic3—121no—
132Dic3—121no—
133C32#195111yescharacteristic, complemented, Sylow
134C23—91no—
135C2×C4—91no—
136C2×C4—91no—
137C2×C4—91no—
138C2×C4—91no—
139C2×C4—91no—
140C2×C4—182no—
141C2×C4—362no—
142C2×C4—722no—
143C2×C4C2×PSU(3,𝔽2)11yescharacteristic
144C8—91no—
145C8—91no—
146C8—184no—
147C8—182no—
148C8#377711yescharacteristic
149C8#377711yescharacteristic
150C2×C3—42no—
151C2×C3—41no—
152D3—122no—
153D3—122no—
154C22—91no—
155C22—91no—
156C22—182no—
157C22#6424311yescharacteristic
158C4—91no—
159C4—91no—
160C4—362no—
161C4—722no—
162C4C4⋊PSU(3,𝔽2)11yescharacteristic
163C4C2×#377711yescharacteristic
164C3—41no—
165C2—21no—
166C2—92no—
167C2—181no—
168C2#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#1951
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
133. C32#1951semidirect

Maximal subgroups

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

subgroupindex
#105937712
C2×#637682
#105937652
#105935442
#105900942
#19519