Finite Group Databasebeta

← #11798210

Subgroups — #11798210

Order 1152.

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

normal subgroups only

This group has 489 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
1C2×#63802C211yesmaximal, characteristic
2#10592586C211yesmaximal, characteristic
3C2×#63551C212yesmaximal, complemented
4C3×#4492C212yesmaximal, complemented
5#10589108C211yesmaximal, characteristic
6#69225—32nomaximal
7C2×#3797—21no—
8C2×#3746C2211yescharacteristic
9C2×C8×C3⋊D3C2211yescharacteristic
10#64106—21no—
11C2×C3×Dic12C2212yes—
12C2×#3718—21no—
13#63802—24no—
14C32×#107C2211yescharacteristic
15#63637—21no—
16C2×C3×C3⋊C16C2212yes—
17#63551—24no—
18C2×D3×Q16—32no—
19C2×#829—32no—
20C2×Dic24—32no—
21#4887—32no—
22#4887—61no—
23C3×#358—32no—
24(C2×D3)⋊C16—32no—
25#4492D312yescomplemented
26C2×C4×C3⋊D3D411yescharacteristic
27C2×#634—21no—
28C2×C3×Dic6—22no—
29C2×#627—41no—
30C2×#624—41no—
31#3797—24no—
32#3797—42no—
33C2×C32×C8C2311yescharacteristic
34C32×C4⋊C4—21no—
35#3752—41no—
36C4⋊(C3⋊Dic3)—41no—
37C2×C3⋊(C3⋊C8)D411yescharacteristic
38#3746—22no—
39C8×C3⋊D3—22no—
40C3×Dic12—22no—
41C3×Dic12D414yes—
42#3718—24no—
43C3×C3⋊C16—22no—
44#2188—91noSylow
45C2×D3×Q8—62no—
46C2×C3×Q16—32no—
47C2×#216—62no—
48D3×Q16—64no—
49D3×Q16—64no—
50C2×Dic12—32no—
51C2×Dic12—61no—
52C2×Dic12C2×D312yes—
53C2×D3×C8—32no—
54C2×D3×C8—61no—
55#897—62no—
56#897—62no—
57C2×C3×C16—32no—
58C3×#107—21no—
59C3×#107C2×D312yes—
60#829—64no—
61C2×C3⋊C16C2×D312yes—
62#810—62no—
63#810—62no—
64Dic24—64no—
65C22×C3⋊D3D811yescharacteristic
66C2×C32×C4—41no—
67C2×C32×C4C2×D411yescharacteristic
68C2×C3⋊Dic3—41no—
69C2×C3⋊Dic3D811yescharacteristic
70C4×C3⋊D3—21no—
71C4×C3⋊D3—21no—
72#634—41no—
73#634—41no—
74C2×C3×Dic3—42no—
75C3×Dic6—24no—
76C3×Dic6—42no—
77#627—44no—
78#624—44no—
79C32×C8C2×D412yes—
80C3⋊(C3⋊C8)—21no—
81C22×Q16—91no—
82C2×Q32—92no—
83#467—91no—
84#358—32no—
85C22⋊C16—91no—
86C2×C3×Q8—62no—
87D3×Q8—68no—
88D3×Q8—124no—
89C2×C4×D3—32no—
90C2×C4×D3—61no—
91C2×C4×D3—122no—
92C2×Dic6—22no—
93C2×Dic6—62no—
94C2×Dic6—62no—
95C2×Dic6—122no—
96C3×Q16—34no—
97C3×Q16—62no—
98C2×C3×C8—21no—
99C2×C3×C8C22×D312yes—
100C3×C4⋊C4—22no—
101C3×C4⋊C4—22no—
102#216—68no—
103(C2×D3)⋊C4—122no—
104(C2×D3)⋊C4—122no—
105C4⋊Dic3—122no—
106C4⋊Dic3—122no—
107C2×C3⋊C8—32no—
108C2×C3⋊C8—61no—
109Dic12—22no—
110Dic12—62no—
111Dic12—62no—
112Dic12—122no—
113Dic12D1214yes—
114D3×C8—62no—
115D3×C8—62no—
116D3×C8—122no—
117C3×C16—62no—
118C3⋊C16—22no—
119C22×C32C2×D811yescharacteristic
120C2×C3⋊D3—21no—
121C2×C3⋊D3—21no—
122C2×C3⋊D3Q3212yescomplemented
123C32×C4—81no—
124C32×C4#12011yescharacteristic
125C32×C4AGL(1,ℤ/8)11yescharacteristic
126C3⋊Dic3—21no—
127C3⋊Dic3—81no—
128C3×Dic3—44no—
129C22×Q8—181no—
130C2×Q16—32no—
131C2×Q16—91no—
132C2×Q16—181no—
133C2×Q16—184no—
134C22×C8—91no—
135C22⋊Q8—181no—
136Q32—184no—
137C2×C16—32no—
138#107D3211yescharacteristic
139#103—181no—
140C22×D3—32no—
141C22×D3—61no—
142C3×Q8—64no—
143C3×Q8—122no—
144C2×C3×C4—21no—
145C2×C3×C4—42no—
146C2×C3×C4—42no—
147C2×C3×C4—122no—
148C2×C3×C4D3×D412yes—
149C2×Dic3—32no—
150C2×Dic3—42no—
151C2×Dic3—61no—
152C2×Dic3—122no—
153C2×Dic3—122no—
154C4×D3—62no—
155C4×D3—62no—
156C4×D3—121no—
157C4×D3—121no—
158C4×D3—128no—
159Dic6—24no—
160Dic6—42no—
161Dic6—128no—
162Dic6—122no—
163Dic6—122no—
164Dic6—122no—
165Dic6—122no—
166C3×C8—22no—
167C3×C8C2×D1212yes—
168C3×C8D3×D412yes—
169C3⋊C8—62no—
170C3⋊C8—121no—
171C2×C32#44711yescharacteristic
172C2×C32C2×Q3211yescharacteristic
173C2×C32#51011yescharacteristic
174C3⋊D3—22no—
175C2×Q8—62no—
176C2×Q8—184no—
177C2×Q8—181no—
178C2×Q8—361no—
179C2×Q8—362no—
180C22×C4—91no—
181C22×C4—361no—
182Q16—34no—
183Q16—62no—
184Q16—184no—
185Q16—182no—
186C2×C8—91no—
187C2×C8—182no—
188C2×C8C2×D3211yescharacteristic
189C4⋊C4—21no—
190C4⋊C4—361no—
191C22⋊C4—361no—
192C16—62no—
193C22×C3—21no—
194C22×C3D3×D812yes—
195C2×D3—34no—
196C2×D3—62no—
197C2×D3—62no—
198C2×D3—62no—
199C2×D3—121no—
200C2×D3—121no—
201C3×C4—21no—
202C3×C4—21no—
203C3×C4—82no—
204C3×C4—82no—
205C3×C4—124no—
206C3×C4#88212yes—
207C3×C4#91412yes—
208Dic3—44no—
209Dic3—62no—
210Dic3—121no—
211Dic3—242no—
212Dic3—242no—
213C32#218811yescharacteristic, complemented, Sylow
214C23—91no—
215Q8—64no—
216Q8—122no—
217Q8—364no—
218Q8—361no—
219Q8—361no—
220C2×C4—41no—
221C2×C4—91no—
222C2×C4—122no—
223C2×C4—181no—
224C2×C4—181no—
225C2×C4—364no—
226C2×C4—361no—
227C2×C4#381111yescharacteristic
228C8—181no—
229C8D3×D1212yes—
230C2×C3—21no—
231C2×C3—21no—
232C2×C3—21no—
233C2×C3#477312yes—
234C2×C3#491512yes—
235C2×C3D3×Q3212yes—
236D3—64no—
237D3—122no—
238C22—92no—
239C22—181no—
240C22—181no—
241C22#6392611yescharacteristic
242C4—81no—
243C4—124no—
244C4—181no—
245C4—721no—
246C4#6392311yescharacteristic
247C4#6394111yescharacteristic
248C3—21no—
249C3#6922512yescomplemented
250C2—182no—
251C2#1059059811yescharacteristic
252C2#1059103011yescharacteristic
253C2#1059104311yescharacteristic
subgroupG/H
centerC22#63926
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC32×#107C22
socleC22×C32C2×D8
prime radicalC22×C3⋊D3D8
hypercenter#107D32
hypocenterC32#2188
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #107

Complements

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

NH ≅ G/Ntype
3. C2×#63551C2semidirect
4. C3×#4492C2semidirect
25. #4492D3semidirect
122. C2×C3⋊D3Q32semidirect
213. C32#2188semidirect
249. C3#69225semidirect

Maximal subgroups

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

subgroupindex
C2×#638022
#105925862
C2×#635512
C3×#44922
#105891082
#692253