Finite Group Databasebeta

← #11779989

Subgroups — #11779989

Order 1152.

600 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 600 conjugacy classes of subgroups — too many to draw. Only its 143 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
1Q8×#634C211yesmaximal, characteristic
2C32×#462C211yesmaximal, characteristic
3#10592793C211yesmaximal, characteristic
4#10592792C211yesmaximal, characteristic
5#10589401C211yesmaximal, characteristic
6#10589350C211yesmaximal, characteristic
7#10589347C211yesmaximal, characteristic
8#71063—34nomaximal
9C2×C32×Q16—21no—
10C32×C4⋊Q8C2211yescharacteristic
11C32×C4×Q8C2211yescharacteristic
12Q8×C3⋊Dic3—21no—
13#64097—22no—
14#64097—21no—
15#64078—21no—
16#64078C2211yescharacteristic
17C4×#634—21no—
18C4×#634C2211yescharacteristic
19C32×C4⋊C8C2211yescharacteristic
20C32×#103—21no—
21#63637—22no—
22#63637—21no—
23#63635—21no—
24C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
25C4×C3⋊(C3⋊C8)C2211yescharacteristic
26Q8×Dic6—34no—
27C3×#462D314yes—
28#5094—34no—
29#5093—34no—
30#4535—34no—
31#4484—34no—
32#4481—34no—
33C2×C32×Q8—21no—
34C2×C32×Q8D411yescharacteristic
35C2×#634—22no—
36C2×#634D411yescharacteristic
37C2×#634D412yes—
38C32×Q16—42no—
39C2×C32×C8—21no—
40C32×C4⋊C4—21no—
41C32×C4⋊C4—21no—
42C32×C4⋊C4—21no—
43C32×C4⋊C4D411yescharacteristic
44C32×C42—21no—
45C32×C42C2311yescharacteristic
46C4⋊(C3⋊Dic3)—22no—
47C4⋊(C3⋊Dic3)—21no—
48C4⋊(C3⋊Dic3)—21no—
49C4⋊(C3⋊Dic3)D411yescharacteristic
50#3750—22no—
51#3750—21no—
52C4×C3⋊Dic3—22no—
53C4×C3⋊Dic3—21no—
54C2×C3⋊(C3⋊C8)—21no—
55C2×C3⋊(C3⋊C8)—21no—
56#1645—91noSylow
57C2×C3×Q16—24no—
58C3×C4⋊Q8C2×D314yes—
59C3×C4×Q8C2×D314yes—
60Q8×Dic3—64no—
61#888—68no—
62#888—64no—
63#869—34no—
64#869—64no—
65C4×Dic6—34no—
66C4×Dic6—64no—
67C3×C4⋊C8C2×D314yes—
68C3×#103—24no—
69#810—68no—
70#810—64no—
71#808—64no—
72C4⋊(C3⋊C8)—34no—
73C4×C3⋊C8—34no—
74C32×Q8—21no—
75C32×Q8—41no—
76C32×Q8—41no—
77C32×Q8SD1612yes—
78C2×C32×C4—21no—
79C2×C32×C4—21no—
80C2×C32×C4—41no—
81C2×C32×C4C2×D411yescharacteristic
82C2×C32×C4C2×D411yescharacteristic
83C2×C32×C4C2×D411yescharacteristic
84C2×C3⋊Dic3—21no—
85C2×C3⋊Dic3—22no—
86C2×C3⋊Dic3—21no—
87#634—21no—
88#634—42no—
89#634—82no—
90#634Q1612yescomplemented
91C32×C8—41no—
92C3⋊(C3⋊C8)—41no—
93C3⋊(C3⋊C8)—41no—
94Q82—91no—
95#487—91no—
96#475—91no—
97#462C3⋊D311yescharacteristic
98#333—91no—
99Q8⋊C8—91no—
100Q8⋊C8—91no—
101C2×C3×Q8—24no—
102C2×C3×Q8#6714yes—
103C2×Dic6—34no—
104C2×Dic6—38no—
105C2×Dic6—68no—
106C3×Q16—48no—
107C2×C3×C8—24no—
108C3×C4⋊C4—24no—
109C3×C4⋊C4—24no—
110C3×C4⋊C4—24no—
111C3×C4⋊C4#6714yes—
112C3×C42—24no—
113C3×C42C22×D314yes—
114C4⋊Dic3—34no—
115C4⋊Dic3—68no—
116C4⋊Dic3—64no—
117C4⋊Dic3—64no—
118Dic3⋊C4—68no—
119Dic3⋊C4—64no—
120C4×Dic3—68no—
121C4×Dic3—64no—
122C2×C3⋊C8—64no—
123C2×C3⋊C8—64no—
124C22×C32#12011yescharacteristic
125C32×C4—22no—
126C32×C4—21no—
127C32×C4—41no—
128C32×C4—81no—
129C32×C4C2×SD1611yescharacteristic
130C32×C4C2×Q1611yescharacteristic
131C32×C4#13711yescharacteristic
132C32×C4#13711yescharacteristic
133C3⋊Dic3—22no—
134C3⋊Dic3—42no—
135C3⋊Dic3—41no—
136C2×Q16—21no—
137C4⋊Q8—91no—
138C4⋊Q8—181no—
139C4⋊Q8—182no—
140C4⋊Q8—181no—
141C4⋊Q8C2×C3⋊D311yescharacteristic
142C4×Q8—91no—
143C4×Q8—181no—
144C4×Q8—181no—
145C4×Q8C2×C3⋊D311yescharacteristic
146#106—181no—
147C4⋊C8—91no—
148C4⋊C8C2×C3⋊D311yescharacteristic
149#103—21no—
150#103—181no—
151#103—182no—
152C4×C8—91no—
153C3×Q8—24no—
154C3×Q8—44no—
155C3×Q8—44no—
156C3×Q8#21418yes—
157C2×C3×C4—24no—
158C2×C3×C4—24no—
159C2×C3×C4—44no—
160C2×C3×C4D3×D414yes—
161C2×C3×C4D3×D414yes—
162C2×C3×C4C2×#6714yes—
163C2×Dic3—64no—
164C2×Dic3—64no—
165C2×Dic3—68no—
166Dic6—38no—
167Dic6—64no—
168Dic6—128no—
169Dic6—248no—
170C3×C8—44no—
171C3⋊C8—124no—
172C3⋊C8—124no—
173C2×C32#44811yescharacteristic
174C2×C32#45111yescharacteristic
175C2×C32#45511yescharacteristic
176C2×Q8—21no—
177C2×Q8—91no—
178C2×Q8—92no—
179C2×Q8—182no—
180C2×Q8#63811yescharacteristic
181Q16—42no—
182C2×C8—21no—
183C2×C8—181no—
184C2×C8—181no—
185C4⋊C4—21no—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—91no—
189C4⋊C4—182no—
190C4⋊C4—182no—
191C4⋊C4—181no—
192C4⋊C4—181no—
193C4⋊C4—181no—
194C4⋊C4#63811yescharacteristic
195C42—21no—
196C42—182no—
197C42—181no—
198C42C22×C3⋊D311yescharacteristic
199C22×C3#93714yes—
200C3×C4—24no—
201C3×C4—28no—
202C3×C4—44no—
203C3×C4—84no—
204C3×C4D3×Q1614yes—
205C3×C4#91814yes—
206C3×C4C2×#21414yes—
207C3×C4#95114yes—
208Dic3—68no—
209Dic3—128no—
210Dic3—124no—
211C32#164511yescharacteristic, complemented, Sylow
212Q8—21no—
213Q8—41no—
214Q8—41no—
215Q8—92no—
216Q8—181no—
217Q8—362no—
218Q8—722no—
219Q8#375412yes—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—41no—
223C2×C4—181no—
224C2×C4—181no—
225C2×C4—182no—
226C2×C4D4×C3⋊D311yescharacteristic
227C2×C4D4×C3⋊D311yescharacteristic
228C2×C4C2×#63811yescharacteristic
229C8—41no—
230C8—361no—
231C8—361no—
232C2×C3#504014yes—
233C2×C3#518614yes—
234C2×C3#520214yes—
235C22#6414611yescharacteristic
236C4—21no—
237C4—22no—
238C4—41no—
239C4—81no—
240C4—182no—
241C4—362no—
242C4—361no—
243C4Q16×C3⋊D311yescharacteristic
244C4#6412711yescharacteristic
245C4C2×#375411yescharacteristic
246C4#6416011yescharacteristic
247C3#7106314yescomplemented
248C2#1059273911yescharacteristic
249C2#1059288511yescharacteristic
250C2#1059290111yescharacteristic
subgroupG/H
centerC22#64146
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×#462C2
socle, prime radicalC22×C32#120
hypercenter#462C3⋊D3
hypocenterC32#1645
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
90. #634Q16semidirect
211. C32#1645semidirect
247. C3#71063semidirect

Maximal subgroups

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

subgroupindex
Q8×#6342
C32×#4622
#105927932
#105927922
#105894012
#105893502
#105893472
#710633