Finite Group Databasebeta

← #11798199

Subgroups — #11798199

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#10592887C211yesmaximal, characteristic
3C2×C3×#829C212yesmaximal, complemented
4#10589118C212yesmaximal, complemented
5#10589108C211yesmaximal, characteristic
6#71502—32nomaximal
7C2×#3797—21no—
8C2×C32×Q16C2211yescharacteristic
9#64155—21no—
10C2×C8×C3⋊D3C2211yescharacteristic
11C2×C3×Dic12C2212yes—
12C2×#3718—21no—
13#63802—24no—
14#63662—21no—
15#63645C2211yescharacteristic
16C3×#829—24no—
17C2×C3×C3⋊C16C2212yes—
18C2×D3×Q16—32no—
19C2×C3×Q32—32no—
20#5188—32no—
21#5188—61no—
22C2×#829D312yescomplemented
23#4564—32no—
24(C2×D3)⋊C16—32no—
25#4503—32no—
26C2×C32×Q8—21no—
27C2×C4×C3⋊D3D411yescharacteristic
28C2×C3×Dic6—22no—
29C2×#627—41no—
30C2×#624—41no—
31#3797—24no—
32#3797—42no—
33C32×Q16—22no—
34C2×C32×C8C2311yescharacteristic
35#3752—41no—
36C4⋊(C3⋊Dic3)—21no—
37#3750—41no—
38C2×C3⋊(C3⋊C8)D411yescharacteristic
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—21no—
47C2×C3×Q16—32no—
48C2×C3×Q16C2×D312yes—
49#946—62no—
50#946—62no—
51C2×#216—62no—
52D3×Q16—64no—
53D3×Q16—64no—
54C2×Dic12C2×D312yes—
55C2×D3×C8—32no—
56C2×D3×C8—61no—
57C3×Q32—64no—
58C2×C3×C16—32no—
59#835—62no—
60#835—62no—
61#829—24no—
62#818—32no—
63#818—61no—
64C2×C3⋊C16C2×D312yes—
65C22×C3⋊D3D811yescharacteristic
66C32×Q8—41no—
67C32×Q8—41no—
68C2×C32×C4—41no—
69C2×C32×C4C2×D411yescharacteristic
70C2×C3⋊Dic3—41no—
71C2×C3⋊Dic3D811yescharacteristic
72C4×C3⋊D3—21no—
73C4×C3⋊D3—21no—
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—32no—
83#467—91no—
84#358—92no—
85C22⋊C16—91no—
86C2×C3×Q8—22no—
87C2×C3×Q8—22no—
88C2×C3×Q8—62no—
89D3×Q8—68no—
90D3×Q8—124no—
91C2×C4×D3—32no—
92C2×C4×D3—61no—
93C2×C4×D3—122no—
94C2×Dic6—22no—
95C2×Dic6—122no—
96C3×Q16—22no—
97C3×Q16—22no—
98C3×Q16—34no—
99C3×Q16—42no—
100C3×Q16—62no—
101C2×C3×C8—21no—
102C2×C3×C8C22×D312yes—
103#216—68no—
104(C2×D3)⋊C4—122no—
105(C2×D3)⋊C4—122no—
106C4⋊Dic3—62no—
107C4⋊Dic3—62no—
108Dic3⋊C4—122no—
109Dic3⋊C4—122no—
110C2×C3⋊C8—32no—
111C2×C3⋊C8—61no—
112Dic12—22no—
113Dic12#6714yes—
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—181no—
132C2×Q16—184no—
133C2×Q16D3211yescharacteristic
134C22×C8—91no—
135C22⋊Q8—181no—
136Q32—64no—
137C2×C16—32no—
138#107—91no—
139#103—181no—
140C22×D3—32no—
141C22×D3—61no—
142C3×Q8—42no—
143C3×Q8—42no—
144C3×Q8—42no—
145C3×Q8—42no—
146C3×Q8—64no—
147C3×Q8—122no—
148C2×C3×C4—21no—
149C2×C3×C4—42no—
150C2×C3×C4—42no—
151C2×C3×C4—122no—
152C2×C3×C4D3×D412yes—
153C2×Dic3—32no—
154C2×Dic3—42no—
155C2×Dic3—61no—
156C2×Dic3—122no—
157C2×Dic3—122no—
158C4×D3—62no—
159C4×D3—62no—
160C4×D3—121no—
161C4×D3—121no—
162C4×D3—128no—
163Dic6—24no—
164Dic6—42no—
165Dic6—128no—
166C3×C8—22no—
167C3×C8D3×D412yes—
168C3×C8C2×#6712yes—
169C3⋊C8—62no—
170C3⋊C8—121no—
171C2×C32#44711yescharacteristic
172C2×C32C2×Q3211yescharacteristic
173C2×C32#51011yescharacteristic
174C3⋊D3—22no—
175C2×Q8—21no—
176C2×Q8—62no—
177C2×Q8—184no—
178C2×Q8—361no—
179C2×Q8—362no—
180C22×C4—91no—
181C22×C4—361no—
182Q16—22no—
183Q16—34no—
184Q16—62no—
185Q16—184no—
186C2×C8—91no—
187C2×C8—182no—
188C2×C8C2×D3211yescharacteristic
189C4⋊C4—181no—
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#91112yes—
207C3×C4#93712yes—
208Dic3—44no—
209Dic3—62no—
210Dic3—121no—
211Dic3—242no—
212Dic3—242no—
213C32#218811yescharacteristic, complemented, Sylow
214C23—91no—
215Q8—41no—
216Q8—41no—
217Q8—64no—
218Q8—122no—
219Q8—364no—
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×#6712yes—
230C2×C3—21no—
231C2×C3—21no—
232C2×C3—21no—
233C2×C3D3×Q3212yes—
234C2×C3#491812yes—
235C2×C3#515612yes—
236D3—64no—
237D3—122no—
238C22—92no—
239C22—181no—
240C22—181no—
241C22#6392611yescharacteristic
242C4—81no—
243C4—124no—
244C4—181no—
245C4—721no—
246C4#6392711yescharacteristic
247C4#6398311yescharacteristic
248C3—21no—
249C3#7150212yescomplemented
250C2—182no—
251C2#1059104311yescharacteristic
252C2#1059104411yescharacteristic
253C2#1059151611yescharacteristic
subgroupG/H
centerC22#63926
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC2×C32×Q16C22
socleC22×C32C2×D8
prime radicalC22×C3⋊D3D8
hypercenterC2×Q16D32
hypocenterC32#2188
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
3. C2×C3×#829C2semidirect
4. #10589118C2semidirect
22. C2×#829D3semidirect
122. C2×C3⋊D3Q32semidirect
213. C32#2188semidirect
249. C3#71502semidirect

Maximal subgroups

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

subgroupindex
C2×#638022
#105928872
C2×C3×#8292
#105891182
#105891082
#715023