Finite Group Databasebeta

← #11789756

Subgroups — #11789756

Order 1152.

768 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#391C211yesmaximal, characteristic
2C2×#63662C211yesmaximal, characteristic
3C2×#63662C211yesmaximal, characteristic
4#10592627C211yesmaximal, characteristic
5C2×C4×C3⋊(C3⋊C8)C211yesmaximal, characteristic
6#10589395C211yesmaximal, characteristic
7#10589395C211yesmaximal, characteristic
8#69674—34nomaximal
9C22×C32×Q8C2211yescharacteristic
10C2×C32×C4⋊C4C2211yescharacteristic
11C2×C32×C42C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×#3750—21no—
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C32×#95—21no—
18C32×#95—21no—
19#63662—22no—
20#63662C414yescomplemented
21#63658—21no—
22C4×C3⋊(C3⋊C8)—22no—
23C3×#391D314yes—
24C2×#835—34no—
25C2×#835—34no—
26#4928—34no—
27C2×C4×C3⋊C8—34no—
28#4529—34no—
29#4529—34no—
30C2×C32×Q8—21no—
31C2×C32×Q8—21no—
32C2×C32×Q8—21no—
33C2×C32×Q8—21no—
34C2×C32×Q8—21no—
35C2×C32×Q8C2×C412yes—
36C22×C32×C4—21no—
37C22×C32×C4—21no—
38C22×C32×C4D411yescharacteristic
39C22×C32×C4D411yescharacteristic
40C22×C32×C4C2311yescharacteristic
41C22×C3⋊Dic3—21no—
42C22×C3⋊Dic3—21no—
43C32×C4⋊C4—21no—
44C32×C4⋊C4—21no—
45C32×C42—21no—
46C32×C42—21no—
47C4⋊(C3⋊Dic3)—21no—
48C4⋊(C3⋊Dic3)—21no—
49C4⋊(C3⋊Dic3)—21no—
50C4⋊(C3⋊Dic3)C2×C412yes—
51#3750—42no—
52C2×C3⋊(C3⋊C8)—21no—
53C2×C3⋊(C3⋊C8)—21no—
54C2×C3⋊(C3⋊C8)—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C2×C3⋊(C3⋊C8)C2×C412yes—
57C2×C3⋊(C3⋊C8)D412yes—
58#1933—91noSylow
59C22×C3×Q8C2×D314yes—
60C2×C3×C4⋊C4C2×D314yes—
61C2×C3×C42C2×D314yes—
62C2×C4⋊Dic3—34no—
63C2×C4⋊Dic3—34no—
64C2×Dic3⋊C4—64no—
65C22×C3⋊C8—34no—
66C22×C3⋊C8—34no—
67C3×#95—24no—
68C3×#95—24no—
69#835—316no—
70#835—68no—
71C3⋊#95—64no—
72C4×C3⋊C8—68no—
73C23×C32C2×D411yescharacteristic
74C32×Q8—22no—
75C32×Q8—22no—
76C32×Q8—41no—
77C32×Q8—41no—
78C2×C32×C4—21no—
79C2×C32×C4—21no—
80C2×C32×C4—21no—
81C2×C32×C4—21no—
82C2×C32×C4—22no—
83C2×C32×C4—41no—
84C2×C32×C4—41no—
85C2×C32×C4—41no—
86C2×C32×C4—41no—
87C2×C32×C4—41no—
88C2×C32×C4SD1612yes—
89C2×C32×C4Q1612yes—
90C2×C32×C4C22×C411yescharacteristic
91C2×C32×C4C2×D411yescharacteristic
92C2×C32×C4#4111yescharacteristic
93C2×C32×C4#4111yescharacteristic
94C2×C32×C4#4111yescharacteristic
95C2×C32×C4#4111yescharacteristic
96C2×C3⋊Dic3—22no—
97C2×C3⋊Dic3—41no—
98C2×C3⋊Dic3—41no—
99C2×C3⋊Dic3—41no—
100C2×C3⋊Dic3—41no—
101C2×C3⋊Dic3—41no—
102C3⋊(C3⋊C8)—22no—
103C3⋊(C3⋊C8)—22no—
104C2×#103—91no—
105C2×#103—91no—
106C2×C4×C8—91no—
107#391C3⋊D311yescharacteristic
108#389—91no—
109#340—91no—
110#340—91no—
111C2×C3×Q8—24no—
112C2×C3×Q8—24no—
113C2×C3×Q8—24no—
114C2×C3×Q8—24no—
115C2×C3×Q8—24no—
116C2×C3×Q8C4×D318yes—
117C22×C3×C4—24no—
118C22×C3×C4—24no—
119C22×C3×C4#6714yes—
120C22×C3×C4#6714yes—
121C22×C3×C4C22×D314yes—
122C22×Dic3—64no—
123C22×Dic3—64no—
124C3×C4⋊C4—24no—
125C3×C4⋊C4—24no—
126C3×C42—24no—
127C3×C42—24no—
128C4⋊Dic3—38no—
129C4⋊Dic3—64no—
130C4⋊Dic3—64no—
131C4⋊Dic3—64no—
132Dic3⋊C4—128no—
133C2×C3⋊C8—38no—
134C2×C3⋊C8—38no—
135C2×C3⋊C8—64no—
136C2×C3⋊C8—64no—
137C2×C3⋊C8—64no—
138C2×C3⋊C8—64no—
139C22×C32C4×D411yescharacteristic
140C22×C32#12111yescharacteristic
141C22×C32#12411yescharacteristic
142C22×C32C2×SD1611yescharacteristic
143C22×C32C2×Q1611yescharacteristic
144C22×C32#13511yescharacteristic
145C22×C32#13511yescharacteristic
146C32×C4—22no—
147C32×C4—22no—
148C32×C4—42no—
149C32×C4—81no—
150C32×C4#11711yescharacteristic
151C32×C4C4×D411yescharacteristic
152C32×C4#12311yescharacteristic
153C32×C4#12611yescharacteristic
154C3⋊Dic3—42no—
155C3⋊Dic3—81no—
156C22×Q8C2×C3⋊D311yescharacteristic
157C22×C8—91no—
158C22×C8—91no—
159C2×C4⋊C4—91no—
160C2×C4⋊C4—91no—
161C2×C4⋊C4—181no—
162C2×C4⋊C4C2×C3⋊D311yescharacteristic
163C2×C42C2×C3⋊D311yescharacteristic
164#103—94no—
165#103—182no—
166C4×C8—182no—
167#95—21no—
168#95—21no—
169#95—181no—
170C23×C3C2×#6714yes—
171C3×Q8—28no—
172C3×Q8—28no—
173C3×Q8—44no—
174C3×Q8—44no—
175C2×C3×C4—24no—
176C2×C3×C4—24no—
177C2×C3×C4—24no—
178C2×C3×C4—24no—
179C2×C3×C4—28no—
180C2×C3×C4—44no—
181C2×C3×C4—44no—
182C2×C3×C4—44no—
183C2×C3×C4—44no—
184C2×C3×C4—44no—
185C2×C3×C4#21518yes—
186C2×C3×C4#21618yes—
187C2×C3×C4C2×C4×D314yes—
188C2×C3×C4#23514yes—
189C2×C3×C4D3×D414yes—
190C2×C3×C4#23714yes—
191C2×C3×C4#23714yes—
192C2×C3×C4#23714yes—
193C2×Dic3—68no—
194C2×Dic3—124no—
195C2×Dic3—124no—
196C2×Dic3—124no—
197C2×Dic3—124no—
198C2×Dic3—124no—
199C3⋊C8—68no—
200C3⋊C8—68no—
201C2×C32#38811yescharacteristic
202C2×C32C4×SD1611yescharacteristic
203C2×C32C4×Q1611yescharacteristic
204C2×C32#46511yescharacteristic
205C2×C32#46711yescharacteristic
206C2×C32#48711yescharacteristic
207C2×C32#48811yescharacteristic
208C2×Q8—21no—
209C2×Q8—21no—
210C2×Q8—21no—
211C2×Q8—21no—
212C2×Q8—21no—
213C2×Q8C4×C3⋊D312yes—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—181no—
217C22×C4—181no—
218C22×C4#63811yescharacteristic
219C22×C4#63811yescharacteristic
220C22×C4C22×C3⋊D311yescharacteristic
221C2×C8—92no—
222C2×C8—92no—
223C2×C8—181no—
224C2×C8—181no—
225C2×C8—181no—
226C2×C8—181no—
227C4⋊C4—21no—
228C4⋊C4—21no—
229C4⋊C4—92no—
230C4⋊C4—181no—
231C4⋊C4—181no—
232C4⋊C4—181no—
233C4⋊C4—362no—
234C42—21no—
235C42—21no—
236C22×C3C4×#6714yes—
237C22×C3#93614yes—
238C22×C3#93914yes—
239C22×C3C2×#21514yes—
240C22×C3C2×#21614yes—
241C22×C3#95014yes—
242C22×C3#95014yes—
243C3×C4—28no—
244C3×C4—28no—
245C3×C4—48no—
246C3×C4—84no—
247C3×C4#87714yes—
248C3×C4#87914yes—
249C3×C4#67⋊C414yes—
250C3×C4#88314yes—
251Dic3—128no—
252Dic3—244no—
253C32#193311yescharacteristic, complemented, Sylow
254C23C2×#63811yescharacteristic
255Q8—22no—
256Q8—22no—
257Q8—41no—
258Q8—41no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—22no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—182no—
270C2×C4—361no—
271C2×C4—361no—
272C2×C4—361no—
273C2×C4—361no—
274C2×C4—361no—
275C2×C4#375512yes—
276C2×C4#375612yes—
277C2×C4C2×C4×C3⋊D311yescharacteristic
278C2×C4#382811yescharacteristic
279C2×C4D4×C3⋊D311yescharacteristic
280C2×C4#383011yescharacteristic
281C2×C4#383011yescharacteristic
282C2×C4#383011yescharacteristic
283C8—182no—
284C8—182no—
285C2×C3#494514yes—
286C2×C3C4×#21514yes—
287C2×C3C4×#21614yes—
288C2×C3#504814yes—
289C2×C3#505114yes—
290C2×C3#505614yes—
291C2×C3#507914yes—
292C22C4×#63811yescharacteristic
293C22#6414511yescharacteristic
294C22#6414811yescharacteristic
295C22C2×#375511yescharacteristic
296C22C2×#375611yescharacteristic
297C22#6415911yescharacteristic
298C22#6415911yescharacteristic
299C4—22no—
300C4—22no—
301C4—42no—
302C4—81no—
303C4—362no—
304C4—721no—
305C4#6408611yescharacteristic
306C4#6408811yescharacteristic
307C4#6409011yescharacteristic
308C4#6409211yescharacteristic
309C3#6967414yescomplemented
310C2#1059264411yescharacteristic
311C2C4×#375511yescharacteristic
312C2C4×#375611yescharacteristic
313C2#1059274711yescharacteristic
314C2#1059275011yescharacteristic
315C2#1059275511yescharacteristic
316C2#1059277811yescharacteristic
subgroupG/H
centerC23C2×#638
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#391C2
socle, prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenter#391C3⋊D3
hypocenterC32#1933
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
20. #63662C4semidirect
253. C32#1933semidirect
309. C3#69674semidirect

Maximal subgroups

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

subgroupindex
C32×#3912
C2×#636622
#105926272
C2×C4×C3⋊(C3⋊C8)2
#105893952
#696743