Finite Group Databasebeta

← #11779494

Subgroups — #11779494

Order 1152.

497 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 497 conjugacy classes of subgroups — too many to draw. Only its 86 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#10593988C211yesmaximal, characteristic
2#10592791C211yesmaximal, characteristic, complemented
3C3×#5084C212yesmaximal, complemented
4#10589096C211yesmaximal, characteristic, complemented
5#10589080C212yesmaximal, complemented
6#71145—32nomaximal
7C32×C4⋊Q8C2211yescharacteristic
8C2×#3756—22no—
9#64078C2211yescharacteristic
10C3×C4×D12C2212yes—
11#63913—22no—
12#63908—22no—
13#63841—22no—
14C4×C3⋊(C3⋊C8)C2211yescharacteristic
15C3×#809—22no—
16C3×#808—22no—
17C3×C4⋊(C3⋊C8)C2212yes—
18#5563—32no—
19C3×#476—32no—
20#5092—32no—
21#5092—61no—
22#5084D312yescomplemented
23D4⋊(C3⋊C8)—32no—
24#4483—32no—
25#4481—32no—
26C2×C32×Q8—21no—
27C2×#634D412yes—
28C2×C3×D12D412yes—
29C2×C3×C4×D3—22no—
30C2×#625—22no—
31C32×C4⋊C4—22no—
32C32×C42C2311yescharacteristic
33#3756—44no—
34C4⋊(C3⋊Dic3)—22no—
35C2×C3⋊(C3⋊C8)—21no—
36C3×(C2×D3)⋊C4—22no—
37C3×C4⋊Dic3D412yes—
38C2×C3×C3⋊C8—22no—
39(C2×D3)⋊Dic3—24no—
40Dic32—22no—
41#1634—91noSylow
42C3×C4⋊Q8—21no—
43C3×C4⋊Q8C2×D312yes—
44C3×C4×D4—32no—
45C2×#216—64no—
46C2×#216—64no—
47#938—62no—
48#930—62no—
49#926—62no—
50#892—62no—
51#885—64no—
52C4×D12C2×D312yes—
53#869—32no—
54#869—61no—
55C3×#106—62no—
56C3×C4⋊C8—32no—
57C3×#102—62no—
58#809—22no—
59#808—22no—
60C4⋊(C3⋊C8)C2×D312yes—
61C4×C3⋊C8—32no—
62C4×C3⋊C8—61no—
63C22×C3×D3—22no—
64C32×Q8—42no—
65C2×C32×C4—41no—
66C2×C32×C4C2×D411yescharacteristic
67C2×C32×C4C2×D412yes—
68C2×C3⋊Dic3—22no—
69#634—42no—
70C2×C3×Dic3—22no—
71C3×D12—22no—
72C3×D12—22no—
73C3×C4×D3—42no—
74C3×C4×D3—42no—
75#625—82no—
76C3⋊(C3⋊C8)—22no—
77C3×C3⋊C8—42no—
78#555—91no—
79#494—91no—
80#476—32no—
81#333—91no—
82D4⋊C8—92no—
83C2×C3×Q8—22no—
84C2×C3×Q8—22no—
85C2×C3×D4—32no—
86C22×C3×C4—62no—
87C2×#67—64no—
88C2×D12#6712yes—
89C2×C4×D3—22no—
90C2×Dic6—34no—
91C2×Dic6—62no—
92C2×C3×C8—62no—
93C3×C4⋊C4—22no—
94C3×C4⋊C4—22no—
95C3×C4⋊C4—32no—
96C3×C4⋊C4—42no—
97C3×C22⋊C4—62no—
98C3×C42—21no—
99C3×C42C22×D312yes—
100#217—64no—
101#216—128no—
102#216—128no—
103(C2×D3)⋊C4—22no—
104(C2×D3)⋊C4—64no—
105C4⋊Dic3—62no—
106C4⋊Dic3—62no—
107C4⋊Dic3—122no—
108C4⋊Dic3#6712yes—
109C4×Dic3—64no—
110C2×C3⋊C8—22no—
111C2×C3⋊C8—62no—
112C2×C3⋊C8—62no—
113C22×C32#12011yescharacteristic
114C2×C3×D3—42no—
115C2×C3×D3—42no—
116C2×C3×D3—42no—
117C32×C4—21no—
118C32×C4—81no—
119C32×C4#13512yes—
120C32×C4#13712yes—
121C3⋊Dic3—42no—
122C3×Dic3—42no—
123C2×Q16—182no—
124C4⋊Q8—91no—
125C4⋊Q8D3211yescharacteristic
126#124—182no—
127#121—182no—
128C4×D4—32no—
129#117—182no—
130#106—62no—
131C4⋊C8—32no—
132#102—62no—
133C4×C8—91no—
134C23×C3—62no—
135C22×D3—22no—
136C3×Q8—44no—
137C3×Q8—44no—
138C3×D4—62no—
139C3×D4—62no—
140C2×C3×C4—22no—
141C2×C3×C4—21no—
142C2×C3×C4—42no—
143C2×C3×C4—42no—
144C2×C3×C4—62no—
145C2×C3×C4—122no—
146C2×C3×C4—122no—
147C2×C3×C4D3×D412yes—
148C2×C3×C4D3×D412yes—
149C2×C3×C4C2×#6712yes—
150#67—244no—
151C2×Dic3—22no—
152C2×Dic3—64no—
153C2×Dic3—122no—
154D12—22no—
155D12—22no—
156C4×D3—42no—
157C4×D3—42no—
158Dic6—124no—
159Dic6—124no—
160C3×C8—122no—
161C3⋊C8—42no—
162C3⋊C8—64no—
163C3⋊C8—64no—
164C2×C32#45212yes—
165C2×C32#45311yescharacteristic
166C3×D3—82no—
167C2×Q8—21no—
168C2×Q8—92no—
169C2×D4—32no—
170C2×D4—182no—
171C22×C4—62no—
172Q16—364no—
173C2×C8—62no—
174C2×C8—181no—
175C4⋊C4—22no—
176C4⋊C4—32no—
177C4⋊C4—182no—
178C22⋊C4—62no—
179C22⋊C4—184no—
180C42—182no—
181C42C2×D3211yescharacteristic
182C22×C3—21no—
183C22×C3—122no—
184C22×C3—122no—
185C22×C3—122no—
186C22×C3#93712yes—
187C2×D3—42no—
188C2×D3—42no—
189C2×D3—42no—
190C3×C4—22no—
191C3×C4—22no—
192C3×C4—22no—
193C3×C4—22no—
194C3×C4—82no—
195C3×C4—82no—
196C3×C4—122no—
197C3×C4#91512yes—
198C3×C4#91612yes—
199C3×C4#94212yes—
200C3×C4#95012yes—
201Dic3—42no—
202Dic3—124no—
203Dic3—242no—
204C32#163411yescharacteristic, complemented, Sylow
205C23—62no—
206Q8—42no—
207Q8—362no—
208D4—62no—
209D4—62no—
210D4—722no—
211C2×C4—41no—
212C2×C4—62no—
213C2×C4—122no—
214C2×C4—122no—
215C2×C4—182no—
216C2×C4D3×#6712yes—
217C2×C4#381111yescharacteristic
218C8—122no—
219C8—182no—
220C2×C3—21no—
221C2×C3—22no—
222C2×C3—242no—
223C2×C3#504712yes—
224C2×C3#517312yes—
225C2×C3#519812yes—
226D3—82no—
227C22—122no—
228C22—122no—
229C22—122no—
230C22#6398311yescharacteristic
231C4—21no—
232C4—81no—
233C4—122no—
234C4—362no—
235C4#6394612yes—
236C4#6394712yes—
237C3—21no—
238C3#7114512yescomplemented
239C2—242no—
240C2#1059152211yescharacteristic
241C2#1059165512yes—
subgroupG/H
centerC22#63983
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32#120
prime radical#10593988C2
hypercenterC4⋊Q8D32
hypocenterC32#1634
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
2. #10592791C2semidirect
3. C3×#5084C2semidirect
4. #10589096C2semidirect
5. #10589080C2semidirect
22. #5084D3semidirect
204. C32#1634semidirect
238. C3#71145semidirect

Maximal subgroups

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

subgroupindex
#105939882
#105927912
C3×#50842
#105890962
#105890802
#711453