Finite Group Databasebeta

← #14762850

Subgroups — #14762850

Order 2816.

1466 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66977C211yesmaximal, characteristic
2C2×#10622820C211yesmaximal, characteristic
3#13069047C214yesmaximal, complemented
4#13068928C214yesmaximal, complemented
5#13068704C212yesmaximal, complemented
6#13068550C212yesmaximal, complemented
7C11×#2280C211yesmaximal, characteristic
8C24×C4×C11C2211yescharacteristic
9C23×Dic22C2211yescharacteristic
10C2×C11×#117C2212yes—
11C22×C22⋊Dic11—21no—
12C22×C4⋊Dic11C2211yescharacteristic
13C2×#66977—24no—
14C2×#66977—21no—
15C2×#66977—21no—
16C2×#66977C418yescomplemented
17C2×#66977C2212yes—
18C2×#66977C2212yes—
19C22×Dic11⋊C4—21no—
20C22×#4318C2212yes—
21C11×#381—21no—
22C11×#380C2212yes—
23C11×#380C2212yes—
24C11×#379—21no—
25C4×C11×C22⋊C4—21no—
26C4×C11×C22⋊C4—21no—
27#10622820—24no—
28C2×C22⋊(C11⋊C8)C2212yes—
29C2×C22⋊(C11⋊C8)C2212yes—
30C2×#66874C2218yescomplemented
31#10622167C2218yescomplemented
32C25×C11D411yescharacteristic
33C23×C4×C11—44no—
34C23×C4×C11C2×C414yes—
35C23×C4×C11D414yes—
36C23×C4×C11D411yescharacteristic
37C23×C4×C11D411yescharacteristic
38C23×C4×C11D411yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C23×Dic11—21no—
43C23×Dic11—21no—
44C22×Dic22—22no—
45C22×Dic22—21no—
46C22×Dic22—44no—
47C22×Dic22C2×C414yes—
48C22×Dic22C2312yes—
49C11×#117—44no—
50C2×C11×C4⋊C4C2314yes—
51C2×C11×C22⋊C4—22no—
52C2×C11×C22⋊C4—22no—
53C2×C11×C22⋊C4—22no—
54C2×C42×C11—22no—
55C2×C22⋊Dic11—28no—
56C2×C22⋊Dic11—22no—
57C2×C22⋊Dic11—22no—
58C2×C4⋊Dic11—22no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11C2×C414yes—
61C2×C4⋊Dic11C2312yes—
62#66977—28no—
63#66977—28no—
64#66977—24no—
65#66977—24no—
66#66977C2×C418yes—
67#66977C2×C418yes—
68C2×Dic11⋊C4—28no—
69C2×Dic11⋊C4—22no—
70C2×Dic11⋊C4—22no—
71C2×#4318—24no—
72C2×#4318—44no—
73C22×C11⋊C8C2314yes—
74C11×#95—22no—
75C11×#95—22no—
76C22⋊(C11⋊C8)—24no—
77C22⋊(C11⋊C8)—24no—
78#66874—48no—
79#21768—111nomaximal, Sylow
80C24×C11—24no—
81C24×C11—42no—
82C24×C11—42no—
83C24×C11C22⋊C414yes—
84C24×C11C2×D411yescharacteristic
85C24×C11C2×D411yescharacteristic
86C24×C11C2×D411yescharacteristic
87C22×C4×C11—24no—
88C22×C4×C11—24no—
89C22×C4×C11—24no—
90C22×C4×C11—24no—
91C22×C4×C11—48no—
92C22×C4×C11—48no—
93C22×C4×C11—42no—
94C22×C4×C11—42no—
95C22×C4×C11—42no—
96C22×C4×C11C22⋊C414yes—
97C22×C4×C11C22⋊C414yes—
98C22×C4×C11C22⋊C414yes—
99C22×C4×C11C22×C412yes—
100C22×C4×C11C22×C412yes—
101C22×C4×C11C22×C412yes—
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D412yes—
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2×D412yes—
108C22×C4×C11C2411yescharacteristic
109C22×Dic11—24no—
110C22×Dic11—24no—
111C22×Dic11—22no—
112C22×Dic11—22no—
113C22×Dic11—44no—
114C22×Dic11—44no—
115C2×Dic22—24no—
116C2×Dic22—22no—
117C2×Dic22—28no—
118C2×Dic22—48no—
119C2×Dic22—44no—
120C2×Dic22—48no—
121C2×Dic22C22×C414yes—
122C11×C4⋊C4—28no—
123C11×C22⋊C4—44no—
124C11×C22⋊C4—44no—
125C11×C22⋊C4—44no—
126C42×C11—44no—
127C22⋊Dic11—28no—
128C22⋊Dic11—28no—
129C4⋊Dic11—24no—
130C4⋊Dic11—22no—
131C4⋊Dic11C22×C414yes—
132Dic11⋊C4—28no—
133Dic11⋊C4—28no—
134#4318—48no—
135C2×C11⋊C8—24no—
136C2×C11⋊C8—28no—
137C22×C22⋊Q8—111no—
138C2×#407—111no—
139#2280D1111yescharacteristic
140#1894—114no—
141#1873—114no—
142#1824—112no—
143#1787—112no—
144C23×C11—22no—
145C23×C11—22no—
146C23×C11—22no—
147C23×C11—22no—
148C23×C11—22no—
149C23×C11—22no—
150C23×C11—22no—
151C23×C11—22no—
152C23×C11—28no—
153C23×C11—44no—
154C23×C11—44no—
155C23×C11—416no—
156C23×C11C2×C22⋊C412yes—
157C23×C11C2×C22⋊C412yes—
158C23×C11C2×C22⋊C412yes—
159C23×C11#13714yes—
160C23×C11C22×D411yescharacteristic
161C2×C4×C11—22no—
162C2×C4×C11—22no—
163C2×C4×C11—22no—
164C2×C4×C11—24no—
165C2×C4×C11—24no—
166C2×C4×C11—24no—
167C2×C4×C11—24no—
168C2×C4×C11—24no—
169C2×C4×C11—24no—
170C2×C4×C11—44no—
171C2×C4×C11—44no—
172C2×C4×C11—44no—
173C2×C4×C11—44no—
174C2×C4×C11—44no—
175C2×C4×C11—44no—
176C2×C4×C11C2×C22⋊C412yes—
177C2×C4×C11C2×C22⋊C412yes—
178C2×C4×C11C2×C22⋊C412yes—
179C2×C4×C11C23×C411yescharacteristic
180C2×C4×C11C22×D411yescharacteristic
181C2×C4×C11H(5,𝔽2)14yes—
182C2×Dic11—24no—
183C2×Dic11—24no—
184C2×Dic11—48no—
185C2×Dic11—48no—
186C2×Dic11—44no—
187C2×Dic11—44no—
188Dic22—28no—
189Dic22—48no—
190Dic22—44no—
191C11⋊C8—44no—
192C23×Q8—111no—
193C24×C4C2×D1111yescharacteristic
194C22×M16—112no—
195C2×C22⋊Q8—112no—
196C2×C22⋊Q8—112no—
197C2×C22⋊Q8—118no—
198C2×C22⋊Q8—224no—
199C2×C22⋊Q8—221no—
200C2×C22⋊Q8—221no—
201C2×#117C2×D1112yes—
202C22×C4⋊C4—111no—
203C22×C4⋊C4—221no—
204C22×C22⋊C4—221no—
205C2×#103—118no—
206#407—224no—
207C2×C22⋊C8—112no—
208C2×C22⋊C8—112no—
209#381—21no—
210#380C2×D1112yes—
211#380C2×D1112yes—
212#379—21no—
213C4×C22⋊C4—21no—
214C4×C22⋊C4—21no—
215#340—118no—
216C22×C11—22no—
217C22×C11—22no—
218C22×C11—28no—
219C22×C11—22no—
220C22×C11—22no—
221C22×C11—22no—
222C22×C11—22no—
223C22×C11—22no—
224C22×C11—22no—
225C22×C11—416no—
226C22×C11—44no—
227C22×C11—44no—
228C22×C11#41914yes—
229C22×C11C22×C22⋊C411yescharacteristic
230C22×C11#53412yes—
231C22×C11C2×#13712yes—
232C22×C11#57512yes—
233C4×C11—22no—
234C4×C11—22no—
235C4×C11—22no—
236C4×C11—84no—
237C4×C11#51812yes—
238C4×C11#53412yes—
239Dic11—44no—
240Dic11—44no—
241C25C22⋊D1111yescharacteristic
242C22×Q8—114no—
243C22×Q8—112no—
244C22×Q8—222no—
245C22×Q8—221no—
246C22×Q8—444no—
247C23×C4—44no—
248C23×C4—221no—
249C23×C4—221no—
250C23×C4C4×D1114yes—
251C23×C4D4414yes—
252C23×C4C22⋊D1111yescharacteristic
253C23×C4C22⋊D1111yescharacteristic
254C23×C4C22⋊D1111yescharacteristic
255C23×C4C22×D1111yescharacteristic
256C23×C4C22×D1111yescharacteristic
257C23×C4C22×D1111yescharacteristic
258C2×M16—224no—
259C2×M16—444no—
260C22×C8—114no—
261C22⋊Q8—118no—
262C22⋊Q8—118no—
263C22⋊Q8—228no—
264C22⋊Q8—228no—
265C22⋊Q8—224no—
266C22⋊Q8—224no—
267#117—44no—
268C2×C4⋊C4—114no—
269C2×C4⋊C4—112no—
270C2×C4⋊C4—228no—
271C2×C4⋊C4—222no—
272C2×C4⋊C4—221no—
273C2×C4⋊C4—222no—
274C2×C4⋊C4—222no—
275C2×C4⋊C4C22×D1114yes—
276C2×C22⋊C4—22no—
277C2×C22⋊C4—22no—
278C2×C22⋊C4—22no—
279C2×C22⋊C4—228no—
280C2×C22⋊C4—222no—
281C2×C22⋊C4—222no—
282C2×C42—22no—
283#103—448no—
284C22⋊C8—224no—
285C22⋊C8—224no—
286#95—22no—
287#95—22no—
288C2×C11—24no—
289C2×C11—42no—
290C2×C11—42no—
291C2×C11#230811yescharacteristic
292C2×C11C2×#41911yescharacteristic
293C2×C11#289611yescharacteristic
294C2×C11#319614yes—
295C24—24no—
296C24—42no—
297C24—42no—
298C24(C2×D11)⋊C414yes—
299C24C2×C22⋊D1111yescharacteristic
300C24C2×C22⋊D1111yescharacteristic
301C24C2×C22⋊D1111yescharacteristic
302C2×Q8—114no—
303C2×Q8—224no—
304C2×Q8—222no—
305C2×Q8—228no—
306C2×Q8—448no—
307C2×Q8—444no—
308C2×Q8—448no—
309C22×C4—24no—
310C22×C4—24no—
311C22×C4—24no—
312C22×C4—24no—
313C22×C4—48no—
314C22×C4—48no—
315C22×C4—42no—
316C22×C4—42no—
317C22×C4—42no—
318C22×C4—224no—
319C22×C4—224no—
320C22×C4—222no—
321C22×C4—222no—
322C22×C4—444no—
323C22×C4—444no—
324C22×C4(C2×D11)⋊C414yes—
325C22×C4(C2×D11)⋊C414yes—
326C22×C4(C2×D11)⋊C414yes—
327C22×C4C2×C4×D1112yes—
328C22×C4C2×C4×D1112yes—
329C22×C4C2×C4×D1112yes—
330C22×C4C2×D4412yes—
331C22×C4C2×D4412yes—
332C22×C4C2×D4412yes—
333C22×C4C2×C22⋊D1111yescharacteristic
334C22×C4C2×C22⋊D1111yescharacteristic
335C22×C4C2×C22⋊D1111yescharacteristic
336C22×C4C23×D1111yescharacteristic
337M16—448no—
338C2×C8—224no—
339C2×C8—228no—
340C4⋊C4—28no—
341C4⋊C4—114no—
342C4⋊C4—224no—
343C4⋊C4—228no—
344C4⋊C4—228no—
345C4⋊C4—222no—
346C22⋊C4—44no—
347C22⋊C4—44no—
348C22⋊C4—44no—
349C22⋊C4—228no—
350C22⋊C4—228no—
351C42—44no—
352C11#2176811yescharacteristic, complemented, Sylow
353C23—22no—
354C23—22no—
355C23—22no—
356C23—22no—
357C23—22no—
358C23—22no—
359C23—22no—
360C23—22no—
361C23—28no—
362C23—44no—
363C23—44no—
364C23—416no—
365C23C2×(C2×D11)⋊C412yes—
366C23C2×(C2×D11)⋊C412yes—
367C23C2×(C2×D11)⋊C412yes—
368C23#6700414yes—
369C23C22×C22⋊D1111yescharacteristic
370Q8—228no—
371Q8—448no—
372Q8—444no—
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—24no—
377C2×C4—24no—
378C2×C4—24no—
379C2×C4—24no—
380C2×C4—24no—
381C2×C4—24no—
382C2×C4—44no—
383C2×C4—44no—
384C2×C4—44no—
385C2×C4—44no—
386C2×C4—44no—
387C2×C4—44no—
388C2×C4—224no—
389C2×C4—224no—
390C2×C4—448no—
391C2×C4—448no—
392C2×C4—444no—
393C2×C4—444no—
394C2×C4C2×(C2×D11)⋊C412yes—
395C2×C4C2×(C2×D11)⋊C412yes—
396C2×C4C2×(C2×D11)⋊C412yes—
397C2×C4C22×C4×D1111yescharacteristic
398C2×C4C22×D4411yescharacteristic
399C2×C4#6703714yes—
400C8—444no—
401C22—22no—
402C22—22no—
403C22—28no—
404C22—22no—
405C22—22no—
406C22—22no—
407C22—22no—
408C22—22no—
409C22—22no—
410C22—416no—
411C22—44no—
412C22—44no—
413C22#1062261714yes—
414C22C22×(C2×D11)⋊C411yescharacteristic
415C22#1062333512yes—
416C22#1062335312yes—
417C22C2×#6700412yes—
418C4—22no—
419C4—22no—
420C4—22no—
421C4—84no—
422C4—444no—
423C4—444no—
424C4#1062301712yes—
425C4#1062302412yes—
426C2—24no—
427C2—42no—
428C2—42no—
429C2#1307119111yescharacteristic
430C2C2×#1062261711yescharacteristic
431C2#1307713311yescharacteristic
432C2#1307944214yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2280C2
socleC23×C11C22×D4
prime radicalC25×C11D4
cosocleC22×C4×C11C24
hypercenter#2280D11
hypocenterC11#21768
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ #2280

Complements

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

NH ≅ G/Ntype
3. #13069047C2semidirect
4. #13068928C2semidirect
5. #13068704C2semidirect
6. #13068550C2semidirect
16. C2×#66977C4semidirect
30. C2×#66874C22semidirect
31. #10622167C22semidirect
352. C11#21768semidirect

Maximal subgroups

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

subgroupindex
C22×#669772
C2×#106228202
#130690472
#130689282
#130687042
#130685502
C11×#22802
#2176811