Finite Group Databasebeta

← #11782711

Subgroups — #11782711

Order 1152.

413 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 413 conjugacy classes of subgroups — too many to draw. Only its 98 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×#5093C212yesmaximal
3#10590309C211yesmaximal, characteristic
4#10590303C212yesmaximal
5#10589079C211yesmaximal, characteristic
6#71217—32nomaximal
7C32×C4⋊Q8C2211yescharacteristic
8C2×#3756—22no—
9#64078C2211yescharacteristic
10C3×#869C2212yes—
11C4×C3⋊(C3⋊C8)C2211yescharacteristic
12C3×#810—24no—
13C3×C4×C3⋊C8C2212yes—
14#63574—22no—
15#63573—24no—
16C3×#487—32no—
17#5093D312yes—
18#5092—32no—
19#5092—61no—
20#5080—32no—
21#5080—32no—
22#4680—32no—
23#4454—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#1716—91noSylow
36C3×C4⋊Q8—21no—
37C3×C4⋊Q8—32no—
38C3×C4⋊Q8C2×D312yes—
39C2×#216—64no—
40C2×#216—64no—
41#869—32no—
42#869—61no—
43#869C2×D312yes—
44C3×#103—64no—
45C3×C4×C8—32no—
46#817—64no—
47#810—24no—
48#808—64no—
49#808—64no—
50C4×C3⋊C8—32no—
51C4×C3⋊C8—61no—
52C4×C3⋊C8C2×D312yes—
53C32×Q8—42no—
54C2×C32×C4—41no—
55C2×C32×C4C2×D411yescharacteristic
56C2×C32×C4C2×D412yes—
57C2×C3⋊Dic3—41no—
58#634—42no—
59C2×C3×Dic3—42no—
60C3×Dic6—44no—
61C3⋊(C3⋊C8)SD1614yes—
62C3×C3⋊C8—24no—
63#498—92no—
64#498—91no—
65#494—91no—
66#487—32no—
67#322—91no—
68C2×C3×Q8—22no—
69C2×C3×Q8—22no—
70C2×C3×Q8—62no—
71C2×Dic6—22no—
72C2×Dic6—62no—
73C2×Dic6—62no—
74C2×C3×C8—34no—
75C3×C4⋊C4—22no—
76C3×C4⋊C4—22no—
77C3×C4⋊C4—42no—
78C3×C4⋊C4—62no—
79C3×C4⋊C4—62no—
80C3×C42—21no—
81C3×C42C22×D312yes—
82#216—128no—
83#216—128no—
84C4⋊Dic3—22no—
85C4⋊Dic3—22no—
86C4⋊Dic3—62no—
87C4⋊Dic3—62no—
88C4⋊Dic3—122no—
89C2×C3⋊C8—34no—
90C2×C3⋊C8—62no—
91C2×C3⋊C8#6714yes—
92C22×C32#12711yescharacteristic
93C32×C4—81no—
94C32×C4C2×SD1612yes—
95C32×C4#13714yes—
96C3⋊Dic3—81no—
97C3×Dic3—82no—
98C2×Q16—182no—
99C4⋊Q8—32no—
100C4⋊Q8—91no—
101C4⋊Q8D3211yescharacteristic
102#106—182no—
103#106—184no—
104#103—64no—
105C4×C8—32no—
106C4×C8—91no—
107C3×Q8—44no—
108C3×Q8—44no—
109C3×Q8—124no—
110C2×C3×C4—22no—
111C2×C3×C4—21no—
112C2×C3×C4—42no—
113C2×C3×C4—42no—
114C2×C3×C4—122no—
115C2×C3×C4D3×D412yes—
116C2×C3×C4D3×D412yes—
117C2×C3×C4C2×#6712yes—
118C2×Dic3—42no—
119C2×Dic3—122no—
120C2×Dic3—122no—
121Dic6—44no—
122Dic6—124no—
123Dic6—124no—
124C3×C8—64no—
125C3⋊C8—24no—
126C3⋊C8—38no—
127C3⋊C8—64no—
128C2×C32#49211yescharacteristic
129C2×C32#49712yes—
130C2×Q8—21no—
131C2×Q8—62no—
132C2×Q8—181no—
133Q16—364no—
134C2×C8—34no—
135C2×C8—92no—
136C4⋊C4—22no—
137C4⋊C4—62no—
138C4⋊C4—62no—
139C4⋊C4—182no—
140C42C2×D3211yescharacteristic
141C22×C3—21no—
142C22×C3#94012yes—
143C3×C4—22no—
144C3×C4—24no—
145C3×C4—82no—
146C3×C4—82no—
147C3×C4—242no—
148C3×C4D3×SD1614yes—
149C3×C4#91814yes—
150C3×C4#95114yes—
151Dic3—82no—
152Dic3—242no—
153Dic3—242no—
154C32#171611yescharacteristic, complemented, Sylow
155Q8—42no—
156Q8—124no—
157Q8—362no—
158C2×C4—41no—
159C2×C4—122no—
160C2×C4—361no—
161C2×C4D3×#6712yes—
162C2×C4#381111yescharacteristic
163C8—64no—
164C8—94no—
165C2×C3—21no—
166C2×C3—22no—
167C2×C3#506012yes—
168C2×C3#517512yes—
169C2×C3#519012yes—
170C22#6397911yescharacteristic
171C4—81no—
172C4—242no—
173C4—721no—
174C4#6393012yes—
175C4#6394314yes—
176C3—21no—
177C3#7121712yescomplemented
178C2#1059149211yescharacteristic
179C2#1059162712yes—
subgroupG/H
centerC22#63979
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socle, prime radicalC22×C32#127
hypercenterC4⋊Q8D32
hypocenterC32#1716
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
154. C32#1716semidirect
177. C3#71217semidirect

Maximal subgroups

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

subgroupindex
#105927912
C3×#50932
#105903092
#105903032
#105890792
#712173