Finite Group Databasebeta

← #14652898

Subgroups — #14652898

Order 2816.

856 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076961C211yesmaximal, characteristic
2C2×#10622108C214yesmaximal, complemented
3C4×C11⋊#95C211yesmaximal, characteristic, complemented
4C11×#1797C211yesmaximal, characteristic, complemented
5C22×C42×C11C2211yescharacteristic
6C2×#66983—21no—
7C2×#66983—21no—
8C2×#66983C2212yes—
9C22×C4×Dic11—21no—
10C2×#66927C411yescharacteristic, complemented
11C2×C11×C4⋊C8—21no—
12C2×C11×C22⋊C8C2212yes—
13C2×C11⋊#95—21no—
14C2×C11⋊#95C2212yes—
15#10622552—21no—
16#10622552—21no—
17#10622552C412yescomplemented
18#10622548C411yescharacteristic, complemented
19C11×#336—21no—
20#10622108—28no—
21C23×C4×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×C4×C11C2311yescharacteristic
24C22×C22⋊D11—22no—
25C23×Dic11—22no—
26C22×D44—21no—
27C22×D44—21no—
28C22×D44C2×C412yes—
29C22×C8×C11—22no—
30C2×C42×C11—42no—
31C2×C42×C11C2×C411yescharacteristic
32C2×C42×C11C2×C411yescharacteristic
33C2×C42×C11D411yescharacteristic
34C2×C42×C11D411yescharacteristic
35#66983—24no—
36#66983—24no—
37#66983—44no—
38#66983—42no—
39#66983—42no—
40C2×(C2×D11)⋊C4—22no—
41C2×(C2×D11)⋊C4—22no—
42C2×(C2×D11)⋊C4—22no—
43C2×C4⋊Dic11—21no—
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11C2×C412yes—
46C2×C4×Dic11—24no—
47C2×C4×Dic11—42no—
48C2×C4×Dic11—42no—
49#66927—42no—
50C11×C4⋊C8—42no—
51C11×C22⋊C8—24no—
52C11⋊#95—24no—
53C11⋊#95—22no—
54C11⋊#95D414yescomplemented
55#9712—111nomaximal, Sylow
56C24×C11C2×D411yescharacteristic
57C23×D11—22no—
58C22×C4×C11—22no—
59C22×C4×C11—22no—
60C22×C4×C11—22no—
61C22×C4×C11—22no—
62C22×C4×C11—41no—
63C22×C4×C11—41no—
64C22×C4×C11—41no—
65C22×C4×C11C22⋊C411yescharacteristic
66C22×C4×C11C22⋊C411yescharacteristic
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11D812yes—
70C22×C4×C11SD1612yes—
71C22×C4×C11C22×C411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D412yes—
74C22×C4×C11#4112yes—
75C2×C22⋊D11—44no—
76C2×C22⋊D11—42no—
77C2×C22⋊D11—42no—
78C2×C22⋊D11—44no—
79C22×Dic11—24no—
80C22×Dic11—24no—
81C22×Dic11—22no—
82C22×Dic11—24no—
83C22×Dic11—42no—
84C22×Dic11—42no—
85C22×Dic11—42no—
86C22×Dic11—42no—
87C2×D44—24no—
88C2×D44—42no—
89C2×D44—42no—
90C2×D44—42no—
91C2×D44—42no—
92C2×D44—42no—
93C2×D44—42no—
94C2×D44—42no—
95C2×D44—42no—
96C2×C8×C11—42no—
97C2×C8×C11—42no—
98C2×C8×C11—42no—
99C42×C11—22no—
100C42×C11—22no—
101C42×C11—41no—
102C42×C11—41no—
103(C2×D11)⋊C4—44no—
104(C2×D11)⋊C4—44no—
105(C2×D11)⋊C4—42no—
106(C2×D11)⋊C4—42no—
107C4⋊Dic11—24no—
108C4⋊Dic11—42no—
109C4⋊Dic11—42no—
110C4×Dic11—48no—
111#2856—111no—
112#1797D1111yescharacteristic, complemented
113C2×#327—114no—
114C4×#95—111no—
115C23×C11—21no—
116C23×C11—21no—
117C23×C11—21no—
118C23×C11—21no—
119C23×C11C2×C22⋊C411yescharacteristic
120C23×C11#12112yes—
121C23×C11C2×D811yescharacteristic
122C23×C11C2×SD1611yescharacteristic
123C23×C11AGL(1,ℤ/8)12yes—
124C22×D11—42no—
125C22×D11—42no—
126C22×D11—42no—
127C22×D11—42no—
128C22×D11—42no—
129C22×D11—42no—
130C22×D11—42no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—24no—
140C2×C4×C11—24no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—42no—
145C2×C4×C11—42no—
146C2×C4×C11—44no—
147C2×C4×C11#9912yes—
148C2×C4×C11#10212yes—
149C2×C4×C11#10212yes—
150C2×C4×C11#10412yes—
151C2×C4×C11#10412yes—
152C2×C4×C11C4×D412yes—
153C2×C4×C11#12411yescharacteristic
154C2×C4×C11#12711yescharacteristic
155C22⋊D11—84no—
156C22⋊D11—84no—
157C2×Dic11—28no—
158C2×Dic11—44no—
159C2×Dic11—44no—
160C2×Dic11—44no—
161C2×Dic11—44no—
162C2×Dic11—44no—
163C2×Dic11—44no—
164C2×Dic11—42no—
165C2×Dic11—42no—
166C2×Dic11—42no—
167D44—84no—
168D44—84no—
169D44—84no—
170C8×C11—82no—
171C2×#127—111no—
172C2×#121—112no—
173C2×#121—221no—
174C2×#121—221no—
175C22×C42—221no—
176C22×C42C2×D1111yescharacteristic
177C2×C4⋊C8—21no—
178C2×C22⋊C8C2×D1112yes—
179#390—112no—
180#390—221no—
181#390—221no—
182#384—111no—
183C2×#95—112no—
184C2×#95—221no—
185#336—21no—
186#327—228no—
187C22×C11—22no—
188C22×C11—22no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—22no—
194C22×C11—22no—
195C22×C11#39011yescharacteristic
196C22×C11C2×#9911yescharacteristic
197C22×C11#41011yescharacteristic
198C22×C11C2×#10211yescharacteristic
199C22×C11#41811yescharacteristic
200C22×C11C2×#10411yescharacteristic
201C22×C11C2×#10411yescharacteristic
202C22×C11#45912yes—
203C22×C11#46012yes—
204C2×D11—82no—
205C2×D11—82no—
206C2×D11—82no—
207C2×D11—82no—
208C2×D11—82no—
209C2×D11—82no—
210C2×D11—82no—
211C4×C11—22no—
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—22no—
215C4×C11—22no—
216C4×C11—41no—
217C4×C11#32714yescomplemented
218Dic11—48no—
219Dic11—82no—
220C22×D4—112no—
221C22×D4—222no—
222C22×D4—221no—
223C22×D4—221no—
224C23×C4—222no—
225C23×C4D4411yescharacteristic
226C23×C4D4411yescharacteristic
227C23×C4C22×D1111yescharacteristic
228C22×C8—22no—
229#127—442no—
230#121—224no—
231#121—224no—
232#121—444no—
233#121—442no—
234#121—442no—
235C2×C4⋊C4—112no—
236C2×C4⋊C4—221no—
237C2×C4⋊C4—221no—
238C2×C22⋊C4—222no—
239C2×C22⋊C4—222no—
240C2×C22⋊C4—222no—
241C2×C42—42no—
242C2×C42—224no—
243C2×C42—442no—
244C2×C42—442no—
245C2×C42C4×D1111yescharacteristic
246C2×C42C4×D1111yescharacteristic
247C2×C42C22⋊D1111yescharacteristic
248C2×C42C22⋊D1111yescharacteristic
249C4⋊C8—42no—
250C22⋊C8—24no—
251#95—114no—
252#95—224no—
253#95—222no—
254C2×C11—22no—
255C2×C11—22no—
256C2×C11C2×#32711yescharacteristic
257C2×C11#150211yescharacteristic
258C2×C11#150511yescharacteristic
259C2×C11#150711yescharacteristic
260C2×C11#196211yescharacteristic
261C2×C11#196411yescharacteristic
262C2×C11#198211yescharacteristic
263D11—162no—
264C24—222no—
265C24C2×D4411yescharacteristic
266C2×D4—224no—
267C2×D4—442no—
268C2×D4—442no—
269C2×D4—442no—
270C2×D4—442no—
271C2×D4—444no—
272C2×D4—442no—
273C2×D4—442no—
274C2×D4—444no—
275C2×D4—442no—
276C2×D4—442no—
277C2×D4—442no—
278C2×D4—442no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—224no—
287C22×C4—224no—
288C22×C4—224no—
289C22×C4—222no—
290C22×C4—442no—
291C22×C4—442no—
292C22×C4—442no—
293C22×C4—442no—
294C22×C4#431412yes—
295C22×C4D8812yes—
296C22×C4(C2×D11)⋊C411yescharacteristic
297C22×C4(C2×D11)⋊C411yescharacteristic
298C22×C4(C2×D11)⋊C411yescharacteristic
299C22×C4(C2×D11)⋊C411yescharacteristic
300C22×C4C2×C4×D1111yescharacteristic
301C22×C4D4×D1112yes—
302C22×C4#434312yes—
303C22×C4C2×C22⋊D1111yescharacteristic
304C2×C8—42no—
305C2×C8—42no—
306C2×C8—42no—
307C4⋊C4—224no—
308C4⋊C4—442no—
309C4⋊C4—442no—
310C22⋊C4—444no—
311C22⋊C4—444no—
312C22⋊C4—442no—
313C22⋊C4—442no—
314C42—22no—
315C42—22no—
316C42—41no—
317C42—41no—
318C42—448no—
319C11#971211yescharacteristic, complemented, Sylow
320C23—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—442no—
325C23—442no—
326C23—442no—
327C23—442no—
328C23—442no—
329C23—442no—
330C23—442no—
331C23#6694812yes—
332C23C2×#431411yescharacteristic
333C23C2×D8811yescharacteristic
334C23#6696112yes—
335C23C2×(C2×D11)⋊C411yescharacteristic
336D4—884no—
337D4—884no—
338D4—884no—
339D4—884no—
340D4—884no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—24no—
350C2×C4—24no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—44no—
357C2×C4—228no—
358C2×C4—444no—
359C2×C4—444no—
360C2×C4—444no—
361C2×C4—444no—
362C2×C4—444no—
363C2×C4—444no—
364C2×C4—442no—
365C2×C4—442no—
366C2×C4—442no—
367C2×C4#6687012yes—
368C2×C4#6688512yes—
369C2×C4#6688512yes—
370C2×C4#6688912yes—
371C2×C4#6688912yes—
372C2×C4#6694612yes—
373C2×C4#6699311yescharacteristic
374C2×C4#6700011yescharacteristic
375C8—82no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—22no—
381C22—22no—
382C22—22no—
383C22—22no—
384C22—882no—
385C22—882no—
386C22—882no—
387C22—882no—
388C22—882no—
389C22—882no—
390C22—882no—
391C22#1062245612yes—
392C22#1062246112yes—
393C22C2×#6687011yescharacteristic
394C22#1062260111yescharacteristic
395C22#1062261911yescharacteristic
396C22C2×#6688511yescharacteristic
397C22#1062274411yescharacteristic
398C22C2×#6688911yescharacteristic
399C22C2×#6688911yescharacteristic
400C4—22no—
401C4—22no—
402C4—21no—
403C4—22no—
404C4—21no—
405C4—41no—
406C4—448no—
407C4—882no—
408C4#1062210814yescomplemented
409C2—22no—
410C2—22no—
411C2—1762no—
412C2C2×#1062210811yescharacteristic
413C2#1306711211yescharacteristic
414C2#1306712511yescharacteristic
415C2#1306713311yescharacteristic
416C2#1306944311yescharacteristic
417C2#1306945111yescharacteristic
418C2#1306954211yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1797C2
socleC23×C11C2×C22⋊C4
prime radical#13076961C2
cosocleC23×C4×C11C23
hypercenter#1797D11
hypocenterC11#9712
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
2. C2×#10622108C2semidirect
3. C4×C11⋊#95C2semidirect
4. C11×#1797C2semidirect
10. C2×#66927C4semidirect
17. #10622552C4semidirect
18. #10622548C4semidirect
54. C11⋊#95D4semidirect
112. #1797D11semidirect
217. C4×C11#327semidirect
319. C11#9712semidirect
408. C4#10622108semidirect

Maximal subgroups

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

subgroupindex
#130769612
C2×#106221082
C4×C11⋊#952
C11×#17972
#971211