Finite Group Databasebeta

← #11781817

Subgroups — #11781817

Order 1152.

351 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 351 conjugacy classes of subgroups — too many to draw. Only its 82 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#10592530C211yesmaximal, characteristic
2#10590387C211yesmaximal, characteristic
3#10590307C212yesmaximal
4C3×#4482C212yesmaximal
5#10589098C211yesmaximal, characteristic
6#68473—32nomaximal
7C4×#634C2211yescharacteristic
8C3×#869C2212yes—
9C2×#3718—21no—
10C2×#3718—21no—
11C32×C4⋊C8C2211yescharacteristic
12#63642—21no—
13#63641—21no—
14C4×C3⋊(C3⋊C8)C2211yescharacteristic
15C3×C4⋊(C3⋊C8)C2212yes—
16#63573—22no—
17#63567—22no—
18#5094—32no—
19#5092—32no—
20#4851—32no—
21#4831—32no—
22#4831—61no—
23C3×#332—32no—
24#4482D312yes—
25#4480—32no—
26C2×#634D411yescharacteristic
27C2×C3×Dic6—22no—
28C2×C32×C8—21no—
29C32×C42C2311yescharacteristic
30C4⋊(C3⋊Dic3)D411yescharacteristic
31#3750—21no—
32C4×C3⋊Dic3—21no—
33C2×C3⋊(C3⋊C8)D411yescharacteristic
34C2×C3⋊(C3⋊C8)D411yescharacteristic
35C3×C4⋊Dic3—22no—
36C3×C4⋊Dic3—22no—
37C2×C3×C3⋊C8—22no—
38#3718—42no—
39#3718—42no—
40#1690—91noSylow
41C3×C4⋊Q8—32no—
42C2×#216—62no—
43C2×#216—62no—
44#869C2×D312yes—
45C4×Dic6—32no—
46C4×Dic6—61no—
47C3×C4⋊C8—21no—
48C3×C4⋊C8—32no—
49C3×C4⋊C8C2×D312yes—
50#817—62no—
51#816—62no—
52#815—62no—
53#815—62no—
54Dic3⋊C8—62no—
55Dic3⋊C8—62no—
56#810—62no—
57#808—62no—
58C4⋊(C3⋊C8)C2×D312yes—
59C4×C3⋊C8—32no—
60C4×C3⋊C8—61no—
61C2×C32×C4C2×D411yescharacteristic
62C2×C32×C4C2×D411yescharacteristic
63C2×C32×C4#4111yescharacteristic
64C2×C3⋊Dic3—21no—
65C2×C3⋊Dic3—21no—
66#634—22no—
67C2×C3×Dic3—42no—
68C3×Dic6—42no—
69C3×Dic6—42no—
70C32×C8—41no—
71C3⋊(C3⋊C8)—21no—
72C3⋊(C3⋊C8)SD1612yes—
73C3×C3⋊C8—42no—
74#494—91no—
75#475—92no—
76#446—91no—
77#334—91no—
78#332—32no—
79C2×C3×Q8—62no—
80C2×Dic6—22no—
81C2×Dic6—32no—
82C2×Dic6—61no—
83C2×C3×C8—22no—
84C2×C3×C8—22no—
85C2×C3×C8—62no—
86C3×C4⋊C4—62no—
87C3×C4⋊C4—62no—
88C3×C42—21no—
89C3×C42C22×D312yes—
90#216—124no—
91#216—124no—
92C4⋊Dic3—22no—
93C4⋊Dic3—22no—
94C4⋊Dic3—32no—
95C4⋊Dic3—61no—
96Dic3⋊C4—62no—
97Dic3⋊C4—62no—
98C4×Dic3—62no—
99C4×Dic3—62no—
100C2×C3⋊C8—22no—
101C2×C3⋊C8—32no—
102C2×C3⋊C8—32no—
103C2×C3⋊C8—61no—
104C2×C3⋊C8—61no—
105C22×C32#12111yescharacteristic
106C32×C4—21no—
107C32×C4C2×SD1611yescharacteristic
108C32×C4AGL(1,ℤ/8)11yescharacteristic
109C32×C4#13712yes—
110C3⋊Dic3—41no—
111C3⋊Dic3—41no—
112C3×Dic3—82no—
113C2×Q16—181no—
114C2×Q16—181no—
115C4⋊Q8—32no—
116C4×Q8—91no—
117#106—182no—
118C4⋊C8—32no—
119C4⋊C8—181no—
120C4⋊C8D3211yescharacteristic
121#103—182no—
122#97—181no—
123C4×C8—91no—
124C3×Q8—122no—
125C3×Q8—122no—
126C2×C3×C4—21no—
127C2×C3×C4—21no—
128C2×C3×C4—21no—
129C2×C3×C4—122no—
130C2×C3×C4#23512yes—
131C2×C3×C4D3×D412yes—
132C2×C3×C4D3×D412yes—
133C2×Dic3—42no—
134C2×Dic3—62no—
135C2×Dic3—62no—
136C2×Dic3—62no—
137C2×Dic3—62no—
138Dic6—42no—
139Dic6—42no—
140Dic6—62no—
141Dic6—62no—
142Dic6—122no—
143C3×C8—42no—
144C3×C8—42no—
145C3×C8—122no—
146C3⋊C8—34no—
147C3⋊C8—42no—
148C3⋊C8—62no—
149C3⋊C8—62no—
150C3⋊C8—121no—
151C2×C32#46011yescharacteristic
152C2×C32#47011yescharacteristic
153C2×C32#47311yescharacteristic
154C2×Q8—62no—
155C2×Q8—91no—
156Q16—362no—
157Q16—362no—
158C2×C8—21no—
159C2×C8—62no—
160C2×C8—91no—
161C2×C8—91no—
162C4⋊C4—62no—
163C4⋊C4—62no—
164C4⋊C4—91no—
165C4⋊C4—181no—
166C42—181no—
167C42C2×D3211yescharacteristic
168C22×C3—21no—
169C22×C3#88412yes—
170C3×C4—22no—
171C3×C4—22no—
172C3×C4—21no—
173C3×C4—21no—
174C3×C4—41no—
175C3×C4—242no—
176C3×C4#91112yes—
177C3×C4D3×SD1612yes—
178C3×C4#91512yes—
179C3×C4#91812yes—
180Dic3—82no—
181Dic3—122no—
182Dic3—122no—
183Dic3—122no—
184Dic3—122no—
185C32#169011yescharacteristic, complemented, Sylow
186Q8—122no—
187Q8—122no—
188Q8—182no—
189C2×C4—122no—
190C2×C4—181no—
191C2×C4—181no—
192C2×C4#379811yescharacteristic
193C2×C4#380211yescharacteristic
194C2×C4#381111yescharacteristic
195C8—41no—
196C8—92no—
197C8—122no—
198C8—181no—
199C2×C3—21no—
200C2×C3—21no—
201C2×C3—21no—
202C2×C3#475512yes—
203C2×C3#476212yes—
204C2×C3#481612yes—
205C22#6391211yescharacteristic
206C4—21no—
207C4—242no—
208C4—361no—
209C4—361no—
210C4#6381112yes—
211C4#6392711yescharacteristic
212C4#6394011yescharacteristic
213C3—21no—
214C3#6847312yescomplemented
215C2#1059055311yescharacteristic
216C2#1059085611yescharacteristic
217C2#1059099311yescharacteristic
subgroupG/H
centerC22#63912
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socle, prime radicalC22×C32#121
hypercenterC4⋊C8D32
hypocenterC32#1690
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
185. C32#1690semidirect
214. C3#68473semidirect

Maximal subgroups

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

subgroupindex
#105925302
#105903872
#105903072
C3×#44822
#105890982
#684733