Finite Group Databasebeta

← #11775705

Subgroups — #11775705

Order 1152.

702 conjugacy classes of subgroups.

The subgroup lattice has 276 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#529C211yesmaximal, characteristic
2C4×#3748C211yesmaximal, characteristic, complemented
3C2×#63630C211yesmaximal, characteristic, complemented
4#10589409C212yesmaximal, complemented
5#10589406C212yesmaximal, complemented
6#71746—34nomaximal
7C32×#126—21no—
8C32×#125C2211yescharacteristic
9C32×#124C2211yescharacteristic
10C32×#123—21no—
11C32×C22⋊Q8C411yescharacteristic
12C32×#121C411yescharacteristic
13C32×C4×Q8C411yescharacteristic
14C32×C4×D4—21no—
15C32×C4×D4C411yescharacteristic
16C32×#117—21no—
17C2×C32×C42C2211yescharacteristic
18C2×#3748—21no—
19C22×C3⋊(C3⋊C8)—21no—
20#63630—21no—
21#63630C2212yes—
22#63630C2212yes—
23C4×C3⋊(C3⋊C8)—21no—
24C3×#529D314yes—
25C4×#208—34no—
26C2×#803—34no—
27#4543—38no—
28#4540—38no—
29C2×C32×Q8C2×C411yescharacteristic
30C2×C32×D4—21no—
31C2×C32×D4C2×C411yescharacteristic
32C22×C32×C4—21no—
33C22×C32×C4C2×C411yescharacteristic
34C22×C32×C4D411yescharacteristic
35C22×C32×C4D411yescharacteristic
36C32×C4⋊C4—21no—
37C32×C4⋊C4—21no—
38C32×C4⋊C4—21no—
39C32×C4⋊C4—21no—
40C32×C4⋊C4C2×C411yescharacteristic
41C32×C4⋊C4C2×C411yescharacteristic
42C32×C22⋊C4—21no—
43C32×C22⋊C4—21no—
44C32×C22⋊C4—21no—
45C32×C22⋊C4—21no—
46C32×C22⋊C4—21no—
47C32×C42—21no—
48C32×C42C2×C411yescharacteristic
49C32×C42D411yescharacteristic
50C32×C42D411yescharacteristic
51C32×C42C2311yescharacteristic
52#3748—24no—
53C2×C3⋊(C3⋊C8)—24no—
54C2×C3⋊(C3⋊C8)—22no—
55C2×C3⋊(C3⋊C8)—22no—
56#1524—91noSylow
57C3×#126—24no—
58C3×#125C2×D314yes—
59C3×#124C2×D314yes—
60C3×#123—24no—
61C3×C22⋊Q8Dic314yes—
62C3×#121Dic314yes—
63C3×C4×Q8Dic314yes—
64C3×C4×D4—24no—
65C3×C4×D4Dic314yes—
66C3×#117—24no—
67C2×C3×C42C2×D314yes—
68C2×#208—64no—
69C22×C3⋊C8—64no—
70#803—38no—
71#803—38no—
72#803—64no—
73C4×C3⋊C8—64no—
74C23×C32—21no—
75C23×C32C22⋊C411yescharacteristic
76C32×Q8—41no—
77C32×D4—41no—
78C32×D4—42no—
79C2×C32×C4—22no—
80C2×C32×C4—22no—
81C2×C32×C4—21no—
82C2×C32×C4—21no—
83C2×C32×C4—21no—
84C2×C32×C4—41no—
85C2×C32×C4—42no—
86C2×C32×C4C22⋊C411yescharacteristic
87C2×C32×C4C22⋊C411yescharacteristic
88C2×C32×C4C22⋊C411yescharacteristic
89C2×C32×C4C22×C411yescharacteristic
90C2×C32×C4C2×D411yescharacteristic
91C2×C32×C4C2×D411yescharacteristic
92C3⋊(C3⋊C8)—24no—
93C3⋊(C3⋊C8)—24no—
94#529C3⋊D311yescharacteristic
95C4×M16—91no—
96C2×#97—91no—
97#330—92no—
98#329—92no—
99C2×C3×Q8C2×Dic314yes—
100C2×C3×D4—24no—
101C2×C3×D4C2×Dic314yes—
102C22×C3×C4—24no—
103C22×C3×C4C2×Dic314yes—
104C22×C3×C4#6714yes—
105C22×C3×C4#6714yes—
106C3×C4⋊C4—24no—
107C3×C4⋊C4—24no—
108C3×C4⋊C4—24no—
109C3×C4⋊C4—24no—
110C3×C4⋊C4C2×Dic314yes—
111C3×C4⋊C4C2×Dic314yes—
112C3×C22⋊C4—24no—
113C3×C22⋊C4—24no—
114C3×C22⋊C4—24no—
115C3×C22⋊C4—24no—
116C3×C22⋊C4—24no—
117C3×C42—24no—
118C3×C42C2×Dic314yes—
119C3×C42#6714yes—
120C3×C42#6714yes—
121C3×C42C22×D314yes—
122#208—616no—
123C2×C3⋊C8—616no—
124C2×C3⋊C8—68no—
125C2×C3⋊C8—68no—
126C22×C32—21no—
127C22×C32—21no—
128C22×C32—41no—
129C22×C32—41no—
130C22×C32—41no—
131C22×C32#10412yes—
132C22×C32C2×C22⋊C411yescharacteristic
133C32×C4—21no—
134C32×C4—21no—
135C32×C4—21no—
136C32×C4—21no—
137C32×C4—21no—
138C32×C4—41no—
139C32×C4—41no—
140C32×C4—41no—
141C32×C4#10412yes—
142C2×M16—181no—
143C22×C8—181no—
144#126—21no—
145#125C2×C3⋊D311yescharacteristic
146#124C2×C3⋊D311yescharacteristic
147#123—21no—
148C22⋊Q8C3⋊Dic311yescharacteristic
149#121C3⋊Dic311yescharacteristic
150C4×Q8C3⋊Dic311yescharacteristic
151C4×D4—21no—
152C4×D4C3⋊Dic311yescharacteristic
153#117—21no—
154C2×C42C2×C3⋊D311yescharacteristic
155#97—92no—
156#97—92no—
157#97—181no—
158C4×C8—181no—
159C23×C3—24no—
160C23×C3#21714yes—
161C3×Q8—44no—
162C3×D4—44no—
163C3×D4—48no—
164C2×C3×C4—28no—
165C2×C3×C4—28no—
166C2×C3×C4—24no—
167C2×C3×C4—24no—
168C2×C3×C4—24no—
169C2×C3×C4—44no—
170C2×C3×C4—48no—
171C2×C3×C4#21714yes—
172C2×C3×C4#21714yes—
173C2×C3×C4#21714yes—
174C2×C3×C4C22×Dic314yes—
175C2×C3×C4C2×#6714yes—
176C2×C3×C4C2×#6714yes—
177C3⋊C8—616no—
178C3⋊C8—616no—
179C2×C32—22no—
180C2×C32—81no—
181C2×C32#41311yescharacteristic
182C2×C32C2×#10411yescharacteristic
183C2×C32C2×#10411yescharacteristic
184C2×Q8C2×C3⋊Dic311yescharacteristic
185C2×D4—21no—
186C2×D4C2×C3⋊Dic311yescharacteristic
187C22×C4—21no—
188C22×C4C2×C3⋊Dic311yescharacteristic
189C22×C4#63811yescharacteristic
190C22×C4#63811yescharacteristic
191M16—184no—
192C2×C8—184no—
193C2×C8—182no—
194C2×C8—182no—
195C4⋊C4—21no—
196C4⋊C4—21no—
197C4⋊C4—21no—
198C4⋊C4—21no—
199C4⋊C4C2×C3⋊Dic311yescharacteristic
200C4⋊C4C2×C3⋊Dic311yescharacteristic
201C22⋊C4—21no—
202C22⋊C4—21no—
203C22⋊C4—21no—
204C22⋊C4—21no—
205C22⋊C4—21no—
206C42—21no—
207C42C2×C3⋊Dic311yescharacteristic
208C42#63811yescharacteristic
209C42#63811yescharacteristic
210C42C22×C3⋊D311yescharacteristic
211C22×C3—24no—
212C22×C3—24no—
213C22×C3—44no—
214C22×C3—44no—
215C22×C3—44no—
216C22×C3#83718yes—
217C22×C3C2×#21714yes—
218C3×C4—24no—
219C3×C4—24no—
220C3×C4—24no—
221C3×C4—24no—
222C3×C4—24no—
223C3×C4—44no—
224C3×C4—44no—
225C3×C4—44no—
226C3×C4#83718yes—
227C32#152411yescharacteristic, complemented, Sylow
228C23—21no—
229C23#375711yescharacteristic
230Q8—41no—
231D4—41no—
232D4—42no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—41no—
239C2×C4—42no—
240C2×C4#375711yescharacteristic
241C2×C4#375711yescharacteristic
242C2×C4#375711yescharacteristic
243C2×C4C22×C3⋊Dic311yescharacteristic
244C2×C4C2×#63811yescharacteristic
245C2×C4C2×#63811yescharacteristic
246C8—184no—
247C8—184no—
248C2×C3—28no—
249C2×C3—84no—
250C2×C3C2×#83714yes—
251C2×C3C2×#83714yes—
252C2×C3#523714yes—
253C22—21no—
254C22—21no—
255C22—41no—
256C22—41no—
257C22—41no—
258C22#6366412yes—
259C22C2×#375711yescharacteristic
260C4—21no—
261C4—21no—
262C4—21no—
263C4—21no—
264C4—21no—
265C4—41no—
266C4—41no—
267C4—41no—
268C4#6366412yes—
269C3#7174614yescomplemented
270C2—22no—
271C2—81no—
272C2C2×#6366411yescharacteristic
273C2C2×#6366411yescharacteristic
274C2#1059293611yescharacteristic
subgroupG/H
centerC2×C4#3757
commutatorC2×C32×C4C22×C4
FrattiniC42C22×C3⋊D3
FittingC32×#529C2
socleC22×C32C2×C22⋊C4
prime radicalC32×#121C4
cosocleC32×C42C23
hypercenter#529C3⋊D3
hypocenterC32#1524
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
2. C4×#3748C2semidirect
3. C2×#63630C2semidirect
4. #10589409C2semidirect
5. #10589406C2semidirect
227. C32#1524semidirect
269. C3#71746semidirect

Maximal subgroups

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

subgroupindex
C32×#5292
C4×#37482
C2×#636302
#105894092
#105894062
#717463