Finite Group Databasebeta

← #11782603

Subgroups — #11782603

Order 1152.

445 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 445 conjugacy classes of subgroups — too many to draw. Only its 114 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#10592791C211yesmaximal, characteristic
2C3×#5078C212yesmaximal
3#10590387C211yesmaximal, characteristic
4#10590311C212yesmaximal
5C3⋊C82C211yesmaximal, characteristic
6#71362—32nomaximal
7C32×C4⋊Q8C2211yescharacteristic
8C2×#3756—22no—
9#64078C2211yescharacteristic
10C3×#869C2212yes—
11C2×#3718—22no—
12C4×C3⋊(C3⋊C8)C2211yescharacteristic
13C3×#807—24no—
14C3×C4×C3⋊C8C2212yes—
15#63575—24no—
16C3×#500—32no—
17#5092—32no—
18#5092—32no—
19#5092—61no—
20#5078—32no—
21#5078D312yes—
22#4682—32no—
23C8×C3⋊C8—32no—
24C2×C32×Q8—21no—
25C2×#634—21no—
26C2×C3×Dic6—22no—
27C32×C4⋊C4—22no—
28C32×C42C2311yescharacteristic
29#3756—44no—
30C4⋊(C3⋊Dic3)—22no—
31C2×C3⋊(C3⋊C8)D412yes—
32C3×C4⋊Dic3—22no—
33C3×C4⋊Dic3—22no—
34C2×C3×C3⋊C8D414yes—
35#3718—44no—
36#1713—91noSylow
37C3×C4⋊Q8—21no—
38C3×C4⋊Q8—32no—
39C3×C4⋊Q8C2×D312yes—
40C2×#216—64no—
41C2×#216—64no—
42C2×#216—64no—
43#869—32no—
44#869—61no—
45#869C2×D312yes—
46C3×#107—64no—
47C3×C4×C8—32no—
48#818—64no—
49#807—24no—
50#807—64no—
51C4×C3⋊C8—32no—
52C4×C3⋊C8—61no—
53C4×C3⋊C8C2×D312yes—
54C32×Q8—42no—
55C2×C32×C4—41no—
56C2×C32×C4C2×D411yescharacteristic
57C2×C32×C4C2×D412yes—
58C2×C3⋊Dic3—41no—
59#634—42no—
60C2×C3×Dic3—42no—
61C3×Dic6—44no—
62C3⋊(C3⋊C8)D814yes—
63C3×C3⋊C8Q1618yescomplemented
64#500—32no—
65#500—92no—
66#494—91no—
67#494—91no—
68C82—91no—
69C2×C3×Q8—22no—
70C2×C3×Q8—22no—
71C2×C3×Q8—62no—
72C2×Dic6—22no—
73C2×Dic6—62no—
74C2×Dic6—62no—
75C2×C3×C8—34no—
76C3×C4⋊C4—22no—
77C3×C4⋊C4—22no—
78C3×C4⋊C4—42no—
79C3×C4⋊C4—62no—
80C3×C4⋊C4—62no—
81C3×C42—21no—
82C3×C42C22×D312yes—
83#216—128no—
84#216—128no—
85#216—128no—
86C4⋊Dic3—22no—
87C4⋊Dic3—22no—
88C4⋊Dic3—62no—
89C4⋊Dic3—62no—
90C4⋊Dic3—122no—
91C2×C3⋊C8—34no—
92C2×C3⋊C8—62no—
93C2×C3⋊C8#6714yes—
94C22×C32#12711yescharacteristic
95C32×C4—81no—
96C32×C4C2×D812yes—
97C32×C4C2×Q1614yes—
98C3⋊Dic3—81no—
99C3×Dic3—82no—
100C2×Q16—182no—
101C2×Q16—182no—
102C4⋊Q8—32no—
103C4⋊Q8—91no—
104C4⋊Q8D3211yescharacteristic
105#107—64no—
106#107—184no—
107C4×C8—32no—
108C4×C8—91no—
109C3×Q8—44no—
110C3×Q8—44no—
111C3×Q8—124no—
112C2×C3×C4—22no—
113C2×C3×C4—21no—
114C2×C3×C4—42no—
115C2×C3×C4—42no—
116C2×C3×C4—122no—
117C2×C3×C4D3×D412yes—
118C2×C3×C4D3×D412yes—
119C2×C3×C4C2×#6712yes—
120C2×Dic3—42no—
121C2×Dic3—122no—
122C2×Dic3—122no—
123Dic6—44no—
124Dic6—124no—
125Dic6—124no—
126C3×C8—38no—
127C3⋊C8—38no—
128C3⋊C8—64no—
129C3⋊C8#21618yescomplemented
130C2×C32#49311yescharacteristic
131C2×C32#49412yes—
132C2×Q8—21no—
133C2×Q8—62no—
134C2×Q8—181no—
135Q16—364no—
136Q16—364no—
137C2×C8—34no—
138C2×C8—92no—
139C4⋊C4—22no—
140C4⋊C4—62no—
141C4⋊C4—62no—
142C4⋊C4—182no—
143C42C2×D3211yescharacteristic
144C22×C3—21no—
145C22×C3#94012yes—
146C3×C4—22no—
147C3×C4—24no—
148C3×C4—82no—
149C3×C4—82no—
150C3×C4—242no—
151C3×C4D3×D814yes—
152C3×C4D3×Q1614yes—
153C3×C4C2×#21614yes—
154Dic3—82no—
155Dic3—242no—
156Dic3—242no—
157C32#171311yescharacteristic, complemented, Sylow
158Q8—42no—
159Q8—124no—
160Q8—362no—
161C2×C4—41no—
162C2×C4—122no—
163C2×C4—361no—
164C2×C4D3×#6712yes—
165C2×C4#381111yescharacteristic
166C8—38no—
167C8—94no—
168C2×C3—22no—
169C2×C3—21no—
170C2×C3#509212yes—
171C2×C3#515112yes—
172C2×C3#518312yes—
173C22#6397911yescharacteristic
174C4—81no—
175C4—242no—
176C4—721no—
177C4#6392612yes—
178C4D3×#21614yes—
179C3—21no—
180C3#7136212yescomplemented
181C2#1059148411yescharacteristic
182C2#1059162612yes—
subgroupG/H
centerC22#63979
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socle, prime radicalC22×C32#127
hypercenterC4⋊Q8D32
hypocenterC32#1713
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
63. C3×C3⋊C8Q16semidirect
129. C3⋊C8#216semidirect
157. C32#1713semidirect
180. C3#71362semidirect

Maximal subgroups

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

subgroupindex
#105927912
C3×#50782
#105903872
#105903112
C3⋊C822
#713623