Finite Group Databasebeta

← #11779995

Subgroups — #11779995

Order 1152.

600 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 600 conjugacy classes of subgroups — too many to draw. Only its 173 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
1C32×Q82C211yesmaximal, characteristic
2#10592778C211yesmaximal, characteristic
3#10592730C211yesmaximal, characteristic
4#10592719C211yesmaximal, characteristic
5#10589412C211yesmaximal, characteristic
6#10589401C211yesmaximal, characteristic
7#10589401C211yesmaximal, characteristic
8#71941—34nomaximal
9C32×C4⋊Q8—22no—
10C32×C4⋊Q8—21no—
11C32×C4⋊Q8—21no—
12C32×C4⋊Q8C2211yescharacteristic
13C32×C4×Q8—21no—
14C32×C4×Q8—21no—
15C32×C4×Q8C2211yescharacteristic
16C32×C4×Q8C2211yescharacteristic
17C2×#3756—21no—
18#64078C2211yescharacteristic
19#63662—22no—
20#63662—21no—
21#63637—21no—
22#63635—21no—
23C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
24C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
25C4×C3⋊(C3⋊C8)C2211yescharacteristic
26C3×Q82D314yes—
27#5079—34no—
28#5031—34no—
29#5020—34no—
30#4546—34no—
31#4535—34no—
32#4535—34no—
33C2×C32×Q8—22no—
34C2×C32×Q8D411yescharacteristic
35C2×C32×Q8D411yescharacteristic
36C2×C32×Q8D412yes—
37C2×#634—21no—
38C32×C4⋊C4—22no—
39C32×C4⋊C4—22no—
40C32×C4⋊C4—21no—
41C32×C4⋊C4—21no—
42C32×C4⋊C4—21no—
43C32×C4⋊C4—21no—
44C32×C4⋊C4D411yescharacteristic
45C32×C4⋊C4D411yescharacteristic
46C32×C42—22no—
47C32×C42—21no—
48C32×C42—21no—
49C32×C42C2311yescharacteristic
50#3756—42no—
51C4⋊(C3⋊Dic3)—21no—
52C4⋊(C3⋊Dic3)—21no—
53C2×C3⋊(C3⋊C8)—21no—
54C2×C3⋊(C3⋊C8)—21no—
55C2×C3⋊(C3⋊C8)—21no—
56#1645—91noSylow
57C3×C4⋊Q8—28no—
58C3×C4⋊Q8—24no—
59C3×C4⋊Q8—24no—
60C3×C4⋊Q8C2×D314yes—
61C3×C4×Q8—24no—
62C3×C4×Q8—24no—
63C3×C4×Q8C2×D314yes—
64C3×C4×Q8C2×D314yes—
65C2×#216—64no—
66#869—34no—
67#835—64no—
68#835—68no—
69#810—64no—
70#808—64no—
71C4⋊(C3⋊C8)—34no—
72C4⋊(C3⋊C8)—34no—
73C4×C3⋊C8—34no—
74C32×Q8—21no—
75C32×Q8—21no—
76C32×Q8—42no—
77C32×Q8—82no—
78C32×Q8SD1612yes—
79C32×Q8Q1612yescomplemented
80C2×C32×C4—21no—
81C2×C32×C4—21no—
82C2×C32×C4—22no—
83C2×C32×C4—21no—
84C2×C32×C4—21no—
85C2×C32×C4C2×D411yescharacteristic
86C2×C32×C4C2×D411yescharacteristic
87C2×C32×C4C2×D411yescharacteristic
88C2×C3⋊Dic3—41no—
89#634—41no—
90#634—41no—
91C3⋊(C3⋊C8)—41no—
92C3⋊(C3⋊C8)—41no—
93C3⋊(C3⋊C8)—41no—
94Q82C3⋊D311yescharacteristic
95#487—91no—
96#475—91no—
97#462—91no—
98#333—91no—
99Q8⋊C8—91no—
100Q8⋊C8—91no—
101C2×C3×Q8—28no—
102C2×C3×Q8#6714yes—
103C2×C3×Q8#6714yes—
104C2×C3×Q8#6718yes—
105C2×Dic6—64no—
106C3×C4⋊C4—28no—
107C3×C4⋊C4—28no—
108C3×C4⋊C4—24no—
109C3×C4⋊C4—24no—
110C3×C4⋊C4—24no—
111C3×C4⋊C4—24no—
112C3×C4⋊C4#6714yes—
113C3×C4⋊C4#6714yes—
114C3×C42—28no—
115C3×C42—24no—
116C3×C42—24no—
117C3×C42C22×D314yes—
118#216—128no—
119C4⋊Dic3—64no—
120C4⋊Dic3—64no—
121C2×C3⋊C8—64no—
122C2×C3⋊C8—64no—
123C2×C3⋊C8—64no—
124C22×C32#12011yescharacteristic
125C32×C4—22no—
126C32×C4—22no—
127C32×C4—21no—
128C32×C4—42no—
129C32×C4—41no—
130C32×C4—41no—
131C32×C4C2×SD1611yescharacteristic
132C32×C4C2×Q1611yescharacteristic
133C32×C4#13711yescharacteristic
134C32×C4#13711yescharacteristic
135C3⋊Dic3—81no—
136C2×Q16—181no—
137C4⋊Q8—22no—
138C4⋊Q8—21no—
139C4⋊Q8—21no—
140C4⋊Q8—91no—
141C4⋊Q8C2×C3⋊D311yescharacteristic
142C4×Q8—21no—
143C4×Q8—21no—
144C4×Q8C2×C3⋊D311yescharacteristic
145C4×Q8C2×C3⋊D311yescharacteristic
146#106—181no—
147C4⋊C8—91no—
148C4⋊C8—91no—
149#103—181no—
150#103—182no—
151#103—181no—
152C4×C8—91no—
153C3×Q8—24no—
154C3×Q8—24no—
155C3×Q8—48no—
156C3×Q8—88no—
157C3×Q8#21518yes—
158C3×Q8#21618yescomplemented
159C2×C3×C4—24no—
160C2×C3×C4—24no—
161C2×C3×C4—28no—
162C2×C3×C4—24no—
163C2×C3×C4—24no—
164C2×C3×C4C2×#6714yes—
165C2×C3×C4C2×#6714yes—
166C2×C3×C4C2×#6714yes—
167C2×Dic3—124no—
168Dic6—124no—
169Dic6—124no—
170C3⋊C8—124no—
171C3⋊C8—124no—
172C3⋊C8—124no—
173C2×C32#44811yescharacteristic
174C2×C32#45111yescharacteristic
175C2×C32#45511yescharacteristic
176C2×Q8—22no—
177C2×Q8—181no—
178C2×Q8#63811yescharacteristic
179C2×Q8#63811yescharacteristic
180C2×Q8#63812yes—
181Q16—362no—
182C2×C8—181no—
183C2×C8—181no—
184C2×C8—181no—
185C4⋊C4—22no—
186C4⋊C4—22no—
187C4⋊C4—21no—
188C4⋊C4—21no—
189C4⋊C4—21no—
190C4⋊C4—21no—
191C4⋊C4—181no—
192C4⋊C4—181no—
193C4⋊C4#63811yescharacteristic
194C4⋊C4#63811yescharacteristic
195C42—22no—
196C42—21no—
197C42—21no—
198C42C22×C3⋊D311yescharacteristic
199C22×C3#95314yes—
200C3×C4—28no—
201C3×C4—28no—
202C3×C4—24no—
203C3×C4—48no—
204C3×C4—44no—
205C3×C4—44no—
206C3×C4C2×#21514yes—
207C3×C4#94214yes—
208C3×C4#94214yes—
209C3×C4C2×#21614yes—
210Dic3—244no—
211C32#164511yescharacteristic, complemented, Sylow
212Q8—21no—
213Q8—21no—
214Q8—42no—
215Q8—82no—
216Q8—361no—
217Q8—361no—
218Q8#375512yes—
219Q8#375612yescomplemented
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—361no—
226C2×C4C2×#63811yescharacteristic
227C2×C4C2×#63811yescharacteristic
228C2×C4C2×#63811yescharacteristic
229C8—361no—
230C8—361no—
231C8—361no—
232C2×C3#522714yes—
233C2×C3#522814yes—
234C2×C3#524214yes—
235C22#6416211yescharacteristic
236C4—22no—
237C4—22no—
238C4—21no—
239C4—42no—
240C4—41no—
241C4—41no—
242C4—721no—
243C4C2×#375511yescharacteristic
244C4#6415111yescharacteristic
245C4#6415111yescharacteristic
246C4C2×#375611yescharacteristic
247C3#7194114yescomplemented
248C2#1059292611yescharacteristic
249C2#1059292711yescharacteristic
250C2#1059294111yescharacteristic
subgroupG/H
centerC22#64162
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×Q82C2
socle, prime radicalC22×C32#120
hypercenterQ82C3⋊D3
hypocenterC32#1645
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ Q82

Complements

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

NH ≅ G/Ntype
79. C32×Q8Q16semidirect
158. C3×Q8#216semidirect
211. C32#1645semidirect
219. Q8#3756semidirect
247. C3#71941semidirect

Maximal subgroups

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

subgroupindex
C32×Q822
#105927782
#105927302
#105927192
#105894122
#105894012
#719413