Finite Group Databasebeta

← #11785271

Subgroups — #11785271

Order 1152.

876 conjugacy classes of subgroups.

The subgroup lattice has 327 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64096C211yesmaximal, characteristic
2C2×#63643C211yesmaximal, characteristic
3C2×#63641C211yesmaximal, characteristic
4#10592676C211yesmaximal, characteristic
5C2×#63637C211yesmaximal, characteristic
6C32×#340C211yesmaximal, characteristic
7#10589395C211yesmaximal, characteristic
8#68905—34nomaximal
9C22×#634C2211yescharacteristic
10C22×C32×C8C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×#3750—21no—
15C2×C4×C3⋊Dic3—21no—
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18#64096—22no—
19#64096C414yescomplemented
20#63658—21no—
21#63658—21no—
22#63643—22no—
23#63641—22no—
24#63637—22no—
25C2×#887—34no—
26C2×#816—34no—
27C2×Dic3⋊C8—34no—
28#4977—34no—
29C2×#810—34no—
30C3×#340D314yes—
31#4529—34no—
32C22×C32×C4—21no—
33C22×C32×C4—21no—
34C22×C32×C4C2311yescharacteristic
35C22×C3⋊Dic3—21no—
36C22×C3⋊Dic3—21no—
37C22×C3⋊Dic3D411yescharacteristic
38C22×C3⋊Dic3D411yescharacteristic
39C2×#634—21no—
40C2×#634—21no—
41C2×#634—21no—
42C2×#634C2×C412yes—
43C2×#634D412yes—
44C2×#634Q812yes—
45C2×C32×C8—21no—
46C2×C32×C8—21no—
47C2×C32×C8—21no—
48C32×C4⋊C4—21no—
49C32×C4⋊C4—21no—
50C32×C4⋊C4—21no—
51C32×C4⋊C4C2×C412yes—
52C4⋊(C3⋊Dic3)—21no—
53C4⋊(C3⋊Dic3)—21no—
54#3750—24no—
55C4×C3⋊Dic3—24no—
56C4×C3⋊Dic3C2×C412yes—
57C4×C3⋊Dic3D412yes—
58C2×C3⋊(C3⋊C8)—21no—
59C2×C3⋊(C3⋊C8)—21no—
60C2×C3⋊(C3⋊C8)—21no—
61#1805—91noSylow
62C22×Dic6—34no—
63C22×C3×C8C2×D314yes—
64C2×C3×C4⋊C4C2×D314yes—
65C2×C3×C4⋊C4C2×D314yes—
66C2×C4⋊Dic3—34no—
67C2×Dic3⋊C4—64no—
68C2×C4×Dic3—34no—
69C2×C4×Dic3—64no—
70C22×C3⋊C8—34no—
71#887—316no—
72#887—68no—
73C3⋊#95—64no—
74C3⋊#95—64no—
75#816—68no—
76Dic3⋊C8—68no—
77#810—68no—
78C23×C32C2×D411yescharacteristic
79C2×C32×C4—22no—
80C2×C32×C4—41no—
81C2×C32×C4—41no—
82C2×C32×C4—41no—
83C2×C32×C4—41no—
84C2×C32×C4—41no—
85C2×C32×C4C22×C411yescharacteristic
86C2×C32×C4C2×D411yescharacteristic
87C2×C32×C4C2×D411yescharacteristic
88C2×C32×C4C2×Q811yescharacteristic
89C2×C32×C4#4111yescharacteristic
90C2×C32×C4#4111yescharacteristic
91C2×C3⋊Dic3—22no—
92C2×C3⋊Dic3—22no—
93C2×C3⋊Dic3—22no—
94C2×C3⋊Dic3—21no—
95C2×C3⋊Dic3—21no—
96C2×C3⋊Dic3—21no—
97C2×C3⋊Dic3—21no—
98C2×C3⋊Dic3—41no—
99C2×C3⋊Dic3—41no—
100C2×C3⋊Dic3—41no—
101C2×C3⋊Dic3C22⋊C412yes—
102C2×C3⋊Dic3C22⋊C412yes—
103#634—22no—
104#634—22no—
105#634—22no—
106#634C4⋊C414yes—
107C32×C8—41no—
108C3⋊(C3⋊C8)—41no—
109C2×C4×Q8—91no—
110C2×C4⋊C8—91no—
111C2×#103—91no—
112C2×#103—91no—
113#382—91no—
114#340—91no—
115#340C3⋊D311yescharacteristic
116C22×C3×C4—24no—
117C22×C3×C4—24no—
118C22×C3×C4C22×D314yes—
119C22×Dic3—34no—
120C22×Dic3—34no—
121C22×Dic3—64no—
122C22×Dic3—64no—
123C2×Dic6—38no—
124C2×Dic6—38no—
125C2×Dic6—38no—
126C2×Dic6—64no—
127C2×Dic6—64no—
128C2×Dic6—64no—
129C2×C3×C8—24no—
130C2×C3×C8—24no—
131C2×C3×C8—24no—
132C3×C4⋊C4—24no—
133C3×C4⋊C4—24no—
134C3×C4⋊C4—24no—
135C3×C4⋊C4C4×D318yes—
136C4⋊Dic3—64no—
137C4⋊Dic3—64no—
138Dic3⋊C4—616no—
139C4×Dic3—38no—
140C4×Dic3—38no—
141C4×Dic3—616no—
142C2×C3⋊C8—64no—
143C2×C3⋊C8—64no—
144C2×C3⋊C8—64no—
145C22×C32C2×C22⋊C411yescharacteristic
146C22×C32#12111yescharacteristic
147C22×C32C22⋊Q811yescharacteristic
148C22×C32#13511yescharacteristic
149C22×C32#13511yescharacteristic
150C22×C32#13711yescharacteristic
151C22×C32#13711yescharacteristic
152C32×C4—42no—
153C32×C4—81no—
154C32×C4C2×C4⋊C411yescharacteristic
155C32×C4#11711yescharacteristic
156C32×C4#12111yescharacteristic
157C32×C4C22⋊Q811yescharacteristic
158C3⋊Dic3—24no—
159C3⋊Dic3—22no—
160C3⋊Dic3—22no—
161C3⋊Dic3—81no—
162C22×Q8—91no—
163C22×C8—91no—
164C22×C8C2×C3⋊D311yescharacteristic
165C4×Q8—94no—
166C4×Q8—182no—
167C2×C4⋊C4—91no—
168C2×C4⋊C4—181no—
169C2×C4⋊C4C2×C3⋊D311yescharacteristic
170C2×C4⋊C4C2×C3⋊D311yescharacteristic
171C2×C42—91no—
172C2×C42—181no—
173C4⋊C8—182no—
174#103—182no—
175#103—182no—
176#95—181no—
177#95—181no—
178C23×C3D3×D414yes—
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×C4C2×C4×D314yes—
186C2×C3×C4#23514yes—
187C2×C3×C4#23514yes—
188C2×C3×C4D3×D414yes—
189C2×C3×C4D3×D414yes—
190C2×C3×C4D3×Q814yes—
191C2×Dic3—38no—
192C2×Dic3—38no—
193C2×Dic3—68no—
194C2×Dic3—68no—
195C2×Dic3—68no—
196C2×Dic3—64no—
197C2×Dic3—64no—
198C2×Dic3—64no—
199C2×Dic3—64no—
200C2×Dic3—124no—
201C2×Dic3—124no—
202C2×Dic3—124no—
203Dic6—316no—
204Dic6—68no—
205Dic6—68no—
206Dic6—68no—
207C3×C8—44no—
208C3⋊C8—124no—
209C2×C32#38011yescharacteristic
210C2×C32#41611yescharacteristic
211C2×C32#41911yescharacteristic
212C2×C32#46411yescharacteristic
213C2×C32#46411yescharacteristic
214C2×C32#47911yescharacteristic
215C2×C32#47911yescharacteristic
216C2×Q8—92no—
217C2×Q8—92no—
218C2×Q8—92no—
219C2×Q8—181no—
220C2×Q8—181no—
221C2×Q8—181no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—91no—
225C22×C4—91no—
226C22×C4—181no—
227C22×C4—181no—
228C22×C4C22×C3⋊D311yescharacteristic
229C2×C8—21no—
230C2×C8—21no—
231C2×C8—21no—
232C2×C8—181no—
233C2×C8—181no—
234C2×C8—181no—
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—184no—
239C4⋊C4—181no—
240C4⋊C4—181no—
241C4⋊C4C4×C3⋊D312yes—
242C42—92no—
243C42—92no—
244C42—184no—
245C22×C3D3×C22⋊C414yes—
246C22×C3#88414yes—
247C22×C3#89614yes—
248C22×C3#91214yes—
249C22×C3#91514yes—
250C22×C3#91614yes—
251C22×C3#91814yes—
252C3×C4—48no—
253C3×C4—84no—
254C3×C4#87214yes—
255C3×C4#88414yes—
256C3×C4D3×C4⋊C414yes—
257C3×C4#89614yes—
258Dic3—616no—
259Dic3—68no—
260Dic3—68no—
261Dic3—244no—
262C32#180511yescharacteristic, complemented, Sylow
263C23D4×C3⋊D311yescharacteristic
264Q8—94no—
265Q8—182no—
266Q8—182no—
267Q8—182no—
268C2×C4—22no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—92no—
275C2×C4—92no—
276C2×C4—182no—
277C2×C4—182no—
278C2×C4—182no—
279C2×C4—181no—
280C2×C4—181no—
281C2×C4—181no—
282C2×C4—181no—
283C2×C4—361no—
284C2×C4—361no—
285C2×C4—361no—
286C2×C4C2×C4×C3⋊D311yescharacteristic
287C2×C4#382811yescharacteristic
288C2×C4#382811yescharacteristic
289C2×C4D4×C3⋊D311yescharacteristic
290C2×C4D4×C3⋊D311yescharacteristic
291C2×C4Q8×C3⋊D311yescharacteristic
292C8—41no—
293C8—361no—
294C2×C3#466714yes—
295C2×C3#476714yes—
296C2×C3#477214yes—
297C2×C3#479814yes—
298C2×C3#480214yes—
299C2×C3#485714yes—
300C2×C3#487714yes—
301C22C22⋊C4×C3⋊D311yescharacteristic
302C22#6409311yescharacteristic
303C22#6410511yescharacteristic
304C22#6412111yescharacteristic
305C22#6412411yescharacteristic
306C22#6412511yescharacteristic
307C22#6412711yescharacteristic
308C4—42no—
309C4—81no—
310C4—184no—
311C4—182no—
312C4—182no—
313C4—721no—
314C4#6408111yescharacteristic
315C4#6409311yescharacteristic
316C4C4⋊C4×C3⋊D311yescharacteristic
317C4#6410511yescharacteristic
318C3#6890514yescomplemented
319C2#1059236611yescharacteristic
320C2#1059246611yescharacteristic
321C2#1059247111yescharacteristic
322C2#1059249711yescharacteristic
323C2#1059250111yescharacteristic
324C2#1059255611yescharacteristic
325C2#1059257611yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#340C2
socle, prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenter#340C3⋊D3
hypocenterC32#1805
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
19. #64096C4semidirect
262. C32#1805semidirect
318. C3#68905semidirect

Maximal subgroups

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

subgroupindex
C2×#640962
C2×#636432
C2×#636412
#105926762
C2×#636372
C32×#3402
#105893952
#689053