Finite Group Databasebeta

← #11785469

Subgroups — #11785469

Order 1152.

693 conjugacy classes of subgroups; only the 156 normal subgroups are shown.

normal subgroups only

This group has 693 conjugacy classes of subgroups — too many to draw. Only its 156 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
1C22×#3748C211yesmaximal, characteristic
2C3×#5207C212yesmaximal
3C2×#63578C212yesmaximal, complemented
4#10589165C212yesmaximal, complemented
5#69983—32nomaximal
6C23×C32×C4C2211yescharacteristic
7C2×#3748—24no—
8C2×#3748C414yes—
9C22×C3⋊(C3⋊C8)C2211yescharacteristic
10C22×C3⋊(C3⋊C8)C2211yescharacteristic
11C2×C3×#208C2214yes—
12C3×#830—24no—
13#63578—24no—
14C22×#208—32no—
15C22×#208—61no—
16C3×#407—32no—
17#5207D312yes—
18C2×#822—34no—
19#4558—34no—
20C24×C32Q811yescharacteristic
21C22×C32×C4—22no—
22C22×C32×C4—22no—
23C22×C32×C4C2×C412yes—
24C22×C32×C4D412yes—
25C22×C32×C4Q811yescharacteristic
26C22×C32×C4C2311yescharacteristic
27#3748—28no—
28C2×C3⋊(C3⋊C8)—22no—
29C2×C3⋊(C3⋊C8)C2×C412yes—
30C2×C3⋊(C3⋊C8)C2×C412yes—
31C2×C3⋊(C3⋊C8)D414yes—
32C3×#208—24no—
33C3×#208—24no—
34C2×C3×C3⋊C8—24no—
35#1811—91noSylow
36C23×C3×C4—21no—
37C23×C3×C4C2×D312yes—
38C2×C3×M16—34no—
39C2×#208—38no—
40C2×#208—64no—
41C2×#208—68no—
42C2×#208—68no—
43C2×#208C2×D314yes—
44C22×C3⋊C8—32no—
45C22×C3⋊C8—32no—
46C22×C3⋊C8—61no—
47C22×C3⋊C8—61no—
48C3×C22⋊C8—64no—
49#830—24no—
50#822—68no—
51C23×C32—22no—
52C23×C32—42no—
53C23×C32C4⋊C412yes—
54C23×C32C2×Q811yescharacteristic
55C2×C32×C4—22no—
56C2×C32×C4—22no—
57C2×C32×C4—22no—
58C2×C32×C4—24no—
59C2×C32×C4C4⋊C412yes—
60C2×C32×C4C22×C411yescharacteristic
61C2×C32×C4C2×D412yes—
62C2×C32×C4C2×D411yescharacteristic
63C2×C32×C4#4112yes—
64C3⋊(C3⋊C8)—22no—
65C3⋊(C3⋊C8)C22⋊C414yes—
66C3×C3⋊C8—44no—
67C22×M16—91no—
68C2×#108—92no—
69#407—32no—
70#341—92no—
71C24×C3—21no—
72C24×C3Dic612yes—
73C22×C3×C4—24no—
74C22×C3×C4—24no—
75C22×C3×C4—24no—
76C22×C3×C4—24no—
77C22×C3×C4—22no—
78C22×C3×C4—22no—
79C22×C3×C4—21no—
80C22×C3×C4—21no—
81C22×C3×C4Dic612yes—
82C22×C3×C4C4×D314yes—
83C22×C3×C4#6714yes—
84C22×C3×C4C22×D312yes—
85C3×M16—64no—
86C3×M16—64no—
87C2×C3×C8—64no—
88#208—24no—
89#208—24no—
90#208—616no—
91#208—616no—
92C2×C3⋊C8—24no—
93C2×C3⋊C8—34no—
94C2×C3⋊C8—38no—
95C2×C3⋊C8—34no—
96C2×C3⋊C8—62no—
97C2×C3⋊C8—62no—
98C2×C3⋊C8—64no—
99C2×C3⋊C8—64no—
100C2×C3⋊C8—64no—
101C22×C32—22no—
102C22×C32—22no—
103C22×C32—24no—
104C22×C32—44no—
105C22×C32C2×C4⋊C411yescharacteristic
106C22×C32C22⋊Q812yes—
107C32×C4—22no—
108C32×C4C2×C22⋊C411yescharacteristic
109C32×C4#11711yescharacteristic
110C32×C4#12112yes—
111C23×C4D3211yescharacteristic
112C2×M16—34no—
113C2×M16—94no—
114C2×M16—184no—
115C22×C8—91no—
116C22×C8—91no—
117#108—184no—
118C22⋊C8—64no—
119C23×C3—24no—
120C23×C3—24no—
121C23×C3—22no—
122C23×C3—21no—
123C23×C3—44no—
124C23×C3—44no—
125C23×C3Dic3⋊C414yes—
126C23×C3C2×Dic612yes—
127C2×C3×C4—24no—
128C2×C3×C4—24no—
129C2×C3×C4—24no—
130C2×C3×C4—28no—
131C2×C3×C4—24no—
132C2×C3×C4—24no—
133C2×C3×C4—24no—
134C2×C3×C4—28no—
135C2×C3×C4—22no—
136C2×C3×C4—22no—
137C2×C3×C4—21no—
138C2×C3×C4—21no—
139C2×C3×C4—22no—
140C2×C3×C4Dic3⋊C414yes—
141C2×C3×C4C2×C4×D312yes—
142C2×C3×C4D3×D414yes—
143C2×C3×C4#23714yes—
144C2×C3×C4C2×#6712yes—
145C3×C8—124no—
146C3⋊C8—38no—
147C3⋊C8—44no—
148C3⋊C8—64no—
149C3⋊C8—64no—
150C3⋊C8—64no—
151C2×C32—22no—
152C2×C32—42no—
153C2×C32#38011yescharacteristic
154C2×C32#43012yes—
155C24#62711yescharacteristic
156C22×C4—22no—
157C22×C4—22no—
158C22×C4#62412yes—
159C22×C4#62512yes—
160C22×C4#62711yescharacteristic
161C22×C4C2×D3211yescharacteristic
162M16—64no—
163M16—64no—
164M16—188no—
165C2×C8—64no—
166C2×C8—92no—
167C2×C8—94no—
168C2×C8—92no—
169C2×C8—182no—
170C22×C3—24no—
171C22×C3—24no—
172C22×C3—24no—
173C22×C3—28no—
174C22×C3—24no—
175C22×C3—21no—
176C22×C3—22no—
177C22×C3—44no—
178C22×C3—48no—
179C22×C3—48no—
180C22×C3#87814yes—
181C22×C3C2×Dic3⋊C412yes—
182C3×C4—24no—
183C3×C4—24no—
184C3×C4—21no—
185C3×C4—21no—
186C3×C4—22no—
187C3×C4#87712yes—
188C3×C4D3×C22⋊C412yes—
189C3×C4#93914yes—
190C32#181111yescharacteristic, complemented, Sylow
191C23—22no—
192C23—42no—
193C23#372412yes—
194C23C2×#62711yescharacteristic
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—24no—
199C2×C4#372412yes—
200C2×C4#380512yes—
201C2×C4C2×#62411yescharacteristic
202C2×C4C2×#62511yescharacteristic
203C2×C4#381112yes—
204C8—94no—
205C8—124no—
206C8—182no—
207C2×C3—24no—
208C2×C3—24no—
209C2×C3—22no—
210C2×C3—21no—
211C2×C3—44no—
212C2×C3—44no—
213C2×C3#494212yes—
214C2×C3#512414yes—
215C22—22no—
216C22—24no—
217C22—22no—
218C22—44no—
219C22C2×#372411yescharacteristic
220C22#6398212yes—
221C4—22no—
222C4#6395711yescharacteristic
223C4#6397411yescharacteristic
224C4#6398012yes—
225C3—21no—
226C3#6998312yescomplemented
227C2—22no—
228C2—42no—
229C2#1059114312yes—
230C2#1059172011yescharacteristic
subgroupG/H
centerC2×C4C2×#625
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC23×C32×C4C22
socleC22×C32C2×C4⋊C4
prime radicalC24×C32Q8
cosocleC22×C32×C4C23
hypercenterC23×C4D32
hypocenterC32#1811
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
3. C2×#63578C2semidirect
4. #10589165C2semidirect
190. C32#1811semidirect
226. C3#69983semidirect

Maximal subgroups

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

subgroupindex
C22×#37482
C3×#52072
C2×#635782
#105891652
#699833