Finite Group Databasebeta

← #11795354

Subgroups — #11795354

Order 1152.

210 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 49 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#10593774C211yesmaximal, characteristic
2#10593544C211yesmaximal, characteristic
3C2×#63745C211yesmaximal, characteristic
4#10593540C211yesmaximal, characteristic
5#10590190C211yesmaximal, characteristic
6#10590188C211yesmaximal, characteristic
7#10590094C211yesmaximal, characteristic
8#64286C2211yescharacteristic
9C2×C4⋊#157C2211yescharacteristic
10C2×C4⋊#157C2211yescharacteristic
11#64283C2211yescharacteristic
12#64283C2211yescharacteristic
13C2×#3787C2211yescharacteristic
14M16×C3⋊D3C2211yescharacteristic
15#63769—21no—
16#63768—21no—
17#63746—21no—
18#63745—21no—
19#63745—22no—
20#63744—22no—
21C22×#157—21no—
22C22×#157—21no—
23C2×C4×C3⋊D3C2311yescharacteristic
24C22⋊#157—21no—
25#3792—21no—
26#3792—21no—
27C2×#622—21no—
28C4⋊#157—21no—
29C4⋊#157—21no—
30C4⋊#157—21no—
31C4⋊#157—21no—
32C4⋊#157D411yescharacteristic
33C4⋊#157D411yescharacteristic
34C4×#157—21no—
35#3788—21no—
36#3788Q812yes—
37#3787—21no—
38#3787—21no—
39#3787—21no—
40#3787D412yes—
41C32×M16Q811yescharacteristic
42#3748Q811yescharacteristic
43#3743—21no—
44C8×C3⋊D3—21no—
45#2090—91nomaximal, Sylow
46D3×M16—121no—
47C22×C3⋊D3#4111yescharacteristic
48C2×#157—21no—
49C2×#157—21no—
50C2×#157—41no—
51C2×#157—41no—
52C2×#157—81no—
53C2×#157—81no—
54C2×C32×C4C2×Q811yescharacteristic
55C2×C3⋊Dic3#4111yescharacteristic
56C4×C3⋊D3C2×D411yescharacteristic
57C4×C3⋊D3C2×D411yescharacteristic
58C4×C3⋊D3C2×Q811yescharacteristic
59C4×C3⋊D3#4111yescharacteristic
60#622—22no—
61#622—22no—
62#622—41no—
63C32×C8—21no—
64C3⋊(C3⋊C8)—21no—
65#428—91no—
66#428—91no—
67C2×#106—91no—
68#424—91no—
69#343—91no—
70#343—91no—
71#341—91no—
72C2×C4×D3—121no—
73C3×M16—41no—
74#208—121no—
75ΓL(1,𝔽25)—122no—
76D3×C8—122no—
77C22×C32#12511yescharacteristic
78C2×C3⋊D3—21no—
79C2×C3⋊D3—21no—
80C2×C3⋊D3#12111yescharacteristic
81C2×C3⋊D3#12511yescharacteristic
82#157—41no—
83#157—41no—
84#157—81no—
85#157—81no—
86C32×C4C22⋊Q811yescharacteristic
87C32×C4C4⋊Q811yescharacteristic
88C3⋊Dic3C22⋊Q811yescharacteristic
89C3⋊Dic3#12311yescharacteristic
90C2×M16—91no—
91C2×M16—91no—
92C2×M16—91no—
93C22×C8—91no—
94#117—91no—
95C2×C4⋊C4—91no—
96C2×C4⋊C4—91no—
97#107—181no—
98#107—181no—
99#106—181no—
100#106—181no—
101#106—182no—
102C4⋊C8—182no—
103C22×D3—121no—
104C2×C3×C4—41no—
105C2×Dic3—121no—
106C4×D3—121no—
107C4×D3—121no—
108C4×D3—121no—
109C4×D3—121no—
110C3×C8—42no—
111C3⋊C8—122no—
112C2×C32—21no—
113C2×C32#39811yescharacteristic
114C3⋊D3—21no—
115C3⋊D3#47111yescharacteristic
116C3⋊D3#47111yescharacteristic
117C22×C4—91no—
118C22×C4—181no—
119C22×C4—181no—
120M16—92no—
121M16—91no—
122M16—181no—
123M16—181no—
124M16—181no—
125M16—181no—
126M16PSU(3,𝔽2)11yescharacteristic
127C2×C8—92no—
128C2×C8—181no—
129C2×C8—181no—
130C2×C8—181no—
131C2×C8—181no—
132C2×C8—181no—
133C4⋊C4—91no—
134C4⋊C4—91no—
135C4⋊C4—181no—
136C4⋊C4—181no—
137C4⋊C4—181no—
138C4⋊C4—181no—
139C22⋊C4—181no—
140C42—181no—
141C22×C3—41no—
142C2×D3—121no—
143C2×D3—121no—
144C2×D3—241no—
145C2×D3—241no—
146C3×C4—41no—
147C3×C4—41no—
148Dic3—121no—
149Dic3—121no—
150C32#209011yescharacteristic, complemented, Sylow
151C23—91no—
152C2×C4—91no—
153C2×C4—91no—
154C2×C4—91no—
155C2×C4—91no—
156C2×C4—91no—
157C2×C4—181no—
158C2×C4—181no—
159C2×C4—361no—
160C2×C4—361no—
161C2×C4—721no—
162C2×C4—721no—
163C2×C4C2×PSU(3,𝔽2)11yescharacteristic
164C8—21no—
165C8—182no—
166C8—182no—
167C8—181no—
168C8—361no—
169C2×C3—41no—
170C2×C3—81no—
171D3—121no—
172D3—121no—
173D3—241no—
174C22—91no—
175C22—91no—
176C22—181no—
177C22—181no—
178C22#6424311yescharacteristic
179C4—91no—
180C4—91no—
181C4—361no—
182C4—361no—
183C4—721no—
184C4—721no—
185C4C4⋊PSU(3,𝔽2)11yescharacteristic
186C4C22⋊PSU(3,𝔽2)11yescharacteristic
187C3—41no—
188C2—21no—
189C2—91no—
190C2—91no—
191C2—181no—
192C2#1059355211yescharacteristic
subgroupG/H
centerC2#10593552
commutator, cosocleC2×C4×C3⋊D3C23
FrattiniC2×C4C2×PSU(3,𝔽2)
FittingC32×M16Q8
socleC2×C32#398
prime radicalC22×C3⋊D3#41
hypercenterM16PSU(3,𝔽2)
hypocenterC32#2090
LCSG ▷ C2×C4×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ M16

Complements

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

NH ≅ G/Ntype
150. C32#2090semidirect

Maximal subgroups

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

subgroupindex
#105937742
#105935442
C2×#637452
#105935402
#105901902
#105901882
#105900942
#20909