Finite Group Databasebeta

← #14781142

Subgroups — #14781142

Order 2816.

1222 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077133C212yesmaximal
2#13071104C211yesmaximal, characteristic
3#13069774C214yesmaximal, complemented
4#13069769C214yesmaximal, complemented
5#13068355C211yesmaximal, characteristic, complemented
6C2×#10622170C212yesmaximal, complemented
7C11×#3458C211yesmaximal, characteristic, complemented
8C22×#4339C2211yescharacteristic
9C11×#544—24no—
10C11×#544C2214yes—
11C11×#543—22no—
12C11×#533—24no—
13C11×#533—22no—
14C2×C11×#117C2212yes—
15C2×C11×#117C2211yescharacteristic
16C22×C4×Dic11C2211yescharacteristic
17C22×#4318C2212yes—
18#10622617C2214yes—
19#10622615—24no—
20#10622614C2214yes—
21#10622601C2212yes—
22#10622587C2212yes—
23#10622579—24no—
24#10622571—22no—
25C4×(C2×D11)⋊C4—22no—
26#10622170C2218yes—
27#10622168C2214yes—
28C23×C4×C11C2311yescharacteristic
29C22×C22⋊D11—21no—
30C23×Dic11—21no—
31C2×#4339—22no—
32C2×#4339—22no—
33C2×#4339—22no—
34C2×#4339—24no—
35C2×#4339Q814yescomplemented
36C22×D44C2311yescharacteristic
37C22×C4×D11—21no—
38C22×Dic22C2311yescharacteristic
39C11×C4⋊Q8—24no—
40C11×C4⋊Q8—28no—
41C11×#125—24no—
42C11×#125—28no—
43C11×C22⋊Q8—216no—
44C11×C22⋊Q8—28no—
45C4×Q8×C11—28no—
46C11×#117—22no—
47C11×#117—22no—
48C11×#117—22no—
49C11×#117—22no—
50C11×#117D414yes—
51C11×#117C2314yes—
52C2×C11×C4⋊C4D414yes—
53C2×C11×C4⋊C4C2312yes—
54C2×C11×C22⋊C4—22no—
55C2×C11×C22⋊C4D412yes—
56C2×C42×C11—22no—
57C2×C42×C11D412yes—
58C2×(C2×D11)⋊C4—24no—
59C2×C4×Dic11—24no—
60C2×C4×Dic11—21no—
61C2×C4×Dic11C2312yes—
62C2×#4318—22no—
63C2×#4318—24no—
64C2×#4318—24no—
65C2×#4318C2314yes—
66C22×C11⋊C8—22no—
67C11⋊#95—24no—
68#66874—28no—
69#66873—28no—
70#23461—111nomaximal, Sylow
71C24×C11C2×D411yescharacteristic
72C23×D11—21no—
73C2×Q8×C11—28no—
74C22×C4×C11—24no—
75C22×C4×C11C2×D414yes—
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D412yes—
78C22×C4×C11C2×D412yes—
79C22×C4×C11C2×Q812yes—
80C22×C4×C11#4114yes—
81C22×C4×C11#4112yes—
82C22×C4×C11C2411yescharacteristic
83C2×C22⋊D11—24no—
84C2×C22⋊D11—42no—
85C2×C22⋊D11—42no—
86C22×Dic11—21no—
87C22×Dic11—22no—
88C22×Dic11—44no—
89C22×Dic11—42no—
90#4339—28no—
91#4339—28no—
92#4339—44no—
93#4339—44no—
94C2×D44—22no—
95C2×D44—21no—
96C2×D44—22no—
97C2×D44C2×Q812yes—
98C2×C4×D11—24no—
99C2×C4×D11—41no—
100C2×C4×D11—41no—
101C2×C4×D11—42no—
102C2×Dic22—22no—
103C2×Dic22—22no—
104C2×Dic22—21no—
105C2×Dic22C2×Q812yes—
106C11×C4⋊C4—216no—
107C11×C4⋊C4—28no—
108C11×C4⋊C4—24no—
109C11×C4⋊C4—24no—
110C11×C4⋊C4C2×D418yes—
111C11×C22⋊C4—24no—
112C11×C22⋊C4—24no—
113C11×C22⋊C4—24no—
114C42×C11—24no—
115C42×C11—22no—
116C42×C11—22no—
117C42×C11—24no—
118(C2×D11)⋊C4—48no—
119C4×Dic11—24no—
120C4×Dic11—42no—
121#4318—24no—
122#4318—24no—
123#4318—44no—
124C2×C11⋊C8—24no—
125C2×C11⋊C8—44no—
126#3458D1111yescharacteristic, complemented
127#2896—112no—
128#2297—111no—
129#2028—114no—
130#2027—114no—
131#1742—111no—
132C2×#339—112no—
133C23×C11—42no—
134C23×C11#12012yes—
135C23×C11C22⋊Q812yes—
136C23×C11#12412yes—
137C23×C11C22×D411yescharacteristic
138C22×D11—22no—
139C22×D11—44no—
140C22×D11—41no—
141C22×D11—41no—
142Q8×C11—88no—
143C2×C4×C11—24no—
144C2×C4×C11—28no—
145C2×C4×C11—44no—
146C2×C4×C11—84no—
147C2×C4×C11#12011yescharacteristic
148C2×C4×C11#12011yescharacteristic
149C2×C4×C11C22⋊Q814yes—
150C2×C4×C11C22⋊Q814yes—
151C2×C4×C11C22⋊Q812yes—
152C2×C4×C11#12414yes—
153C2×C4×C11#12414yes—
154C2×C4×C11#12412yes—
155C2×C4×C11C22×D412yes—
156C2×C4×C11C22×Q811yescharacteristic
157C2×C4×C11C2×#4112yes—
158C2×C4×C11C2×#4111yescharacteristic
159C22⋊D11—48no—
160C2×Dic11—24no—
161C2×Dic11—22no—
162C2×Dic11—42no—
163C2×Dic11—48no—
164C2×Dic11—41no—
165C2×Dic11—42no—
166C2×Dic11—41no—
167D44—24no—
168D44—42no—
169C4×D11—44no—
170C4×D11—44no—
171Dic22—24no—
172Dic22—42no—
173C11⋊C8—44no—
174C22×#41—111no—
175C22×M16—112no—
176#544—24no—
177#544C2×D1114yes—
178#543—22no—
179#533—24no—
180#533—22no—
181C2×#117C2×D1112yes—
182C2×#117C2×D1111yescharacteristic
183C22×C42—111no—
184#419—114no—
185#418—114no—
186#417—224no—
187#416—224no—
188#391—112no—
189#390—112no—
190#386—222no—
191C4×C22⋊C4—222no—
192#343—114no—
193#339—118no—
194C22×C11—22no—
195C22×C11—24no—
196C22×C11—42no—
197C22×C11—42no—
198C22×C11#39314yes—
199C22×C11C2×#12011yescharacteristic
200C22×C11C2×C22⋊Q811yescharacteristic
201C22×C11C2×#12411yescharacteristic
202C2×D11—44no—
203C2×D11—42no—
204C2×D11—82no—
205C2×D11—82no—
206C4×C11—44no—
207C4×C11—48no—
208C4×C11#39312yes—
209C4×C11#39312yes—
210C4×C11C2×C22⋊Q812yes—
211C4×C11C2×#12412yes—
212Dic11—44no—
213Dic11—42no—
214C2×#41—114no—
215C2×#41—222no—
216C2×#41—224no—
217C2×#41—222no—
218C2×#41—222no—
219C22×Q8—111no—
220C22×D4—111no—
221C22×D4—221no—
222C23×C4—221no—
223C23×C4—221no—
224C23×C4C22×D1111yescharacteristic
225C2×M16—114no—
226C2×M16—222no—
227C2×M16—224no—
228C2×M16—224no—
229C22×C8—222no—
230C4⋊Q8—24no—
231C4⋊Q8—28no—
232#125—24no—
233#125—28no—
234C22⋊Q8—216no—
235C22⋊Q8—28no—
236C4×Q8—28no—
237#117—22no—
238#117—22no—
239#117—22no—
240#117—22no—
241#117C22⋊D1114yes—
242#117C22×D1114yes—
243C2×C4⋊C4C22⋊D1114yes—
244C2×C4⋊C4C22×D1112yes—
245C2×C22⋊C4—22no—
246C2×C22⋊C4—224no—
247C2×C22⋊C4C22⋊D1112yes—
248C2×C42—22no—
249C2×C42—112no—
250C2×C42—224no—
251C2×C42—221no—
252C2×C42C22⋊D1112yes—
253#103—228no—
254#102—228no—
255#95—224no—
256C2×C11—21no—
257C2×C11—21no—
258C2×C11—24no—
259C2×C11C2×#39311yescharacteristic
260C2×C11#301812yes—
261D11—82no—
262C24—221no—
263C24C2×C22⋊D1111yescharacteristic
264#41—228no—
265#41—228no—
266#41—444no—
267#41—444no—
268C2×Q8—28no—
269C2×Q8—112no—
270C2×Q8—221no—
271C2×Q8—222no—
272C2×Q8—222no—
273C2×D4—112no—
274C2×D4—224no—
275C2×D4—222no—
276C2×D4—221no—
277C2×D4—222no—
278C2×D4—442no—
279C2×D4—442no—
280C22×C4—24no—
281C22×C4—221no—
282C22×C4—222no—
283C22×C4—224no—
284C22×C4—444no—
285C22×C4—442no—
286C22×C4—442no—
287C22×C4—441no—
288C22×C4—441no—
289C22×C4Q8×D1112yes—
290C22×C4#434314yes—
291C22×C4#434312yes—
292C22×C4C2×C22⋊D1114yes—
293C22×C4C2×C22⋊D1111yescharacteristic
294C22×C4C2×C22⋊D1112yes—
295C22×C4C2×C22⋊D1112yes—
296C22×C4C23×D1111yescharacteristic
297M16—224no—
298M16—224no—
299M16—444no—
300C2×C8—224no—
301C2×C8—444no—
302C4⋊C4—216no—
303C4⋊C4—28no—
304C4⋊C4—24no—
305C4⋊C4—24no—
306C4⋊C4C2×C22⋊D1118yes—
307C22⋊C4—24no—
308C22⋊C4—24no—
309C22⋊C4—24no—
310C22⋊C4—448no—
311C42—22no—
312C42—24no—
313C42—22no—
314C42—24no—
315C42—224no—
316C42—442no—
317C11#2346111yescharacteristic, complemented, Sylow
318C23—42no—
319C23—222no—
320C23—444no—
321C23—441no—
322C23—441no—
323C23#6699912yes—
324C23#6700012yes—
325C23#6700612yes—
326C23C22×C22⋊D1111yescharacteristic
327Q8—88no—
328Q8—224no—
329Q8—442no—
330D4—224no—
331D4—448no—
332D4—442no—
333C2×C4—24no—
334C2×C4—28no—
335C2×C4—44no—
336C2×C4—84no—
337C2×C4—224no—
338C2×C4—222no—
339C2×C4—442no—
340C2×C4—448no—
341C2×C4—442no—
342C2×C4—441no—
343C2×C4—441no—
344C2×C4—444no—
345C2×C4—444no—
346C2×C4#6699914yes—
347C2×C4#6699914yes—
348C2×C4#6699912yes—
349C2×C4#6700014yes—
350C2×C4#6700014yes—
351C2×C4#6700012yes—
352C2×C4#6700611yescharacteristic
353C2×C4#6700611yescharacteristic
354C2×C4C2×Q8×D1111yescharacteristic
355C2×C4C2×#434312yes—
356C2×C4C2×#434311yescharacteristic
357C2×C4C22×C22⋊D1112yes—
358C8—444no—
359C22—22no—
360C22—24no—
361C22—42no—
362C22—42no—
363C22—444no—
364C22—442no—
365C22—882no—
366C22—882no—
367C22#1062284414yes—
368C22C2×#6699911yescharacteristic
369C22C2×#6700011yescharacteristic
370C22C2×#6700611yescharacteristic
371C4—44no—
372C4—48no—
373C4—444no—
374C4—442no—
375C4#1062284412yes—
376C4#1062284412yes—
377C4C2×#6699912yes—
378C4C2×#6700012yes—
379C2—21no—
380C2—21no—
381C2—24no—
382C2—882no—
383C2C2×#1062284411yescharacteristic
384C2#1307796512yes—
subgroupG/H
centerC2×C4#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3458C2
socleC22×C11C2×#120
prime radicalC22×#4339C22
hypercenter#3458D11
hypocenterC11#23461
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #3458

Complements

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

NH ≅ G/Ntype
3. #13069774C2semidirect
4. #13069769C2semidirect
5. #13068355C2semidirect
6. C2×#10622170C2semidirect
7. C11×#3458C2semidirect
35. C2×#4339Q8semidirect
126. #3458D11semidirect
317. C11#23461semidirect

Maximal subgroups

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

subgroupindex
#130771332
#130711042
#130697742
#130697692
#130683552
C2×#106221702
C11×#34582
#2346111