Finite Group Databasebeta

← #11779562

Subgroups — #11779562

Order 1152.

564 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 131 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#10596038C211yesmaximal, characteristic
2C32×#477C211yesmaximal, characteristic
3#10592790C211yesmaximal, characteristic
4#10592778C211yesmaximal, characteristic
5#10589401C211yesmaximal, characteristic
6#10589350C211yesmaximal, characteristic
7#10589348C211yesmaximal, characteristic
8#71162—34nomaximal
9C32×C4⋊Q8C2211yescharacteristic
10C32×C4×Q8C2211yescharacteristic
11#64153—21no—
12#64098—22no—
13#64096—21no—
14#64079—21no—
15#64078C2211yescharacteristic
16C4×#634—21no—
17C4×#634C2211yescharacteristic
18C32×#107—21no—
19C32×C4⋊C8C2211yescharacteristic
20C32×#103—21no—
21#63662—22no—
22#63637—21no—
23#63634—21no—
24C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
25C4×C3⋊(C3⋊C8)C2211yescharacteristic
26#5567—34no—
27C3×#477D314yes—
28#5091—34no—
29#5079—34no—
30#4535—34no—
31#4484—34no—
32#4482—34no—
33C2×C32×Q8—21no—
34C2×C32×Q8D411yescharacteristic
35C2×#634—21no—
36C2×#634D411yescharacteristic
37C2×C32×C8—21no—
38C32×C4⋊C4—21no—
39C32×C4⋊C4—21no—
40C32×C4⋊C4—21no—
41C32×C4⋊C4D411yescharacteristic
42C32×C42—21no—
43C32×C42C2311yescharacteristic
44C4⋊(C3⋊Dic3)—21no—
45C4⋊(C3⋊Dic3)D411yescharacteristic
46C4⋊(C3⋊Dic3)D412yes—
47#3750—22no—
48#3750—22no—
49#3750—22no—
50#3750—21no—
51C4×C3⋊Dic3—22no—
52C4×C3⋊Dic3—21no—
53C2×C3⋊(C3⋊C8)—21no—
54C2×C3⋊(C3⋊C8)—21no—
55#1636—91noSylow
56C3×C4⋊Q8C2×D314yes—
57C3×C4×Q8C2×D314yes—
58#944—64no—
59#889—68no—
60#887—64no—
61#870—64no—
62#869—34no—
63C4×Dic6—34no—
64C4×Dic6—64no—
65C3×#107—24no—
66C3×C4⋊C8C2×D314yes—
67C3×#103—24no—
68#835—68no—
69#810—64no—
70#807—64no—
71C4⋊(C3⋊C8)—34no—
72C4×C3⋊C8—34no—
73C32×Q8—21no—
74C32×Q8—21no—
75C32×Q8—42no—
76C2×C32×C4—21no—
77C2×C32×C4—21no—
78C2×C32×C4—41no—
79C2×C32×C4C2×D411yescharacteristic
80C2×C32×C4C2×D411yescharacteristic
81C2×C32×C4C2×D411yescharacteristic
82C2×C3⋊Dic3—21no—
83C2×C3⋊Dic3—21no—
84C2×C3⋊Dic3—22no—
85#634—21no—
86#634—41no—
87#634—41no—
88#634Q1612yes—
89C32×C8—41no—
90C3⋊(C3⋊C8)—41no—
91C3⋊(C3⋊C8)—41no—
92#557—91no—
93#487—91no—
94#477—91no—
95#477C3⋊D311yescharacteristic
96#332—91no—
97Q8⋊C8—91no—
98Q8⋊C8—91no—
99C2×C3×Q8—24no—
100C2×C3×Q8#6714yes—
101C2×Dic6—34no—
102C2×Dic6—64no—
103C2×C3×C8—24no—
104C3×C4⋊C4—24no—
105C3×C4⋊C4—24no—
106C3×C4⋊C4—24no—
107C3×C4⋊C4#6714yes—
108C3×C42—24no—
109C3×C42C22×D314yes—
110C4⋊Dic3—34no—
111C4⋊Dic3—38no—
112C4⋊Dic3—64no—
113Dic3⋊C4—68no—
114Dic3⋊C4—68no—
115Dic3⋊C4—68no—
116Dic3⋊C4—64no—
117C4×Dic3—68no—
118C4×Dic3—64no—
119C2×C3⋊C8—64no—
120C2×C3⋊C8—64no—
121C22×C32#12011yescharacteristic
122C32×C4—21no—
123C32×C4—41no—
124C32×C4—41no—
125C32×C4—81no—
126C32×C4C2×Q1611yescharacteristic
127C32×C4#13511yescharacteristic
128C32×C4#13711yescharacteristic
129C32×C4#13711yescharacteristic
130C3⋊Dic3—22no—
131C3⋊Dic3—42no—
132C3⋊Dic3—41no—
133C4⋊Q8—91no—
134C4⋊Q8—181no—
135C4⋊Q8C2×C3⋊D311yescharacteristic
136#125—181no—
137#125—182no—
138C4×Q8—91no—
139C4×Q8—181no—
140C4×Q8—181no—
141C4×Q8C2×C3⋊D311yescharacteristic
142#107—21no—
143#107—181no—
144C4⋊C8—91no—
145C4⋊C8C2×C3⋊D311yescharacteristic
146#103—21no—
147#103—181no—
148#103—182no—
149C4×C8—91no—
150C3×Q8—24no—
151C3×Q8—24no—
152C3×Q8—48no—
153C2×C3×C4—24no—
154C2×C3×C4—24no—
155C2×C3×C4—44no—
156C2×C3×C4D3×D414yes—
157C2×C3×C4D3×D414yes—
158C2×C3×C4C2×#6714yes—
159C2×Dic3—64no—
160C2×Dic3—64no—
161C2×Dic3—68no—
162Dic6—38no—
163Dic6—64no—
164Dic6—124no—
165Dic6—124no—
166C3×C8—44no—
167C3⋊C8—124no—
168C3⋊C8—124no—
169C2×C32#45111yescharacteristic
170C2×C32#45211yescharacteristic
171C2×C32#45411yescharacteristic
172C2×Q8—21no—
173C2×Q8—91no—
174C2×Q8—181no—
175C2×Q8#63811yescharacteristic
176C2×C8—21no—
177C2×C8—181no—
178C2×C8—181no—
179C4⋊C4—21no—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—92no—
183C4⋊C4—91no—
184C4⋊C4—182no—
185C4⋊C4—182no—
186C4⋊C4—182no—
187C4⋊C4—181no—
188C4⋊C4—181no—
189C4⋊C4#63811yescharacteristic
190C42—21no—
191C42—182no—
192C42—181no—
193C42C22×C3⋊D311yescharacteristic
194C22×C3#93714yes—
195C3×C4—24no—
196C3×C4—44no—
197C3×C4—44no—
198C3×C4—84no—
199C3×C4D3×Q1614yes—
200C3×C4#91814yes—
201C3×C4#94214yes—
202C3×C4#95014yes—
203Dic3—68no—
204Dic3—124no—
205Dic3—128no—
206C32#163611yescharacteristic, complemented, Sylow
207Q8—21no—
208Q8—21no—
209Q8—42no—
210Q8—92no—
211Q8—181no—
212Q8—361no—
213Q8—361no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—41no—
217C2×C4—181no—
218C2×C4—181no—
219C2×C4—182no—
220C2×C4D4×C3⋊D311yescharacteristic
221C2×C4D4×C3⋊D311yescharacteristic
222C2×C4C2×#63811yescharacteristic
223C8—41no—
224C8—361no—
225C8—361no—
226C2×C3#504714yes—
227C2×C3#518614yes—
228C2×C3#520114yes—
229C22#6414611yescharacteristic
230C4—21no—
231C4—41no—
232C4—41no—
233C4—81no—
234C4—182no—
235C4—361no—
236C4—362no—
237C4Q16×C3⋊D311yescharacteristic
238C4#6412711yescharacteristic
239C4#6415111yescharacteristic
240C4#6415911yescharacteristic
241C3#7116214yescomplemented
242C2#1059274611yescharacteristic
243C2#1059288511yescharacteristic
244C2#1059290011yescharacteristic
subgroupG/H
centerC22#64146
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×#477C2
socle, prime radicalC22×C32#120
hypercenter#477C3⋊D3
hypocenterC32#1636
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
206. C32#1636semidirect
241. C3#71162semidirect

Maximal subgroups

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

subgroupindex
#105960382
C32×#4772
#105927902
#105927782
#105894012
#105893502
#105893482
#711623