Finite Group Databasebeta

← #14652900

Subgroups — #14652900

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#13068596C211yesmaximal, characteristic, complemented
2C2×#10622175C214yesmaximal, complemented
3C4×C11⋊#95C211yesmaximal, characteristic, complemented
4C11×#2856C211yesmaximal, characteristic
5C2×C11×#127C411yescharacteristic, complemented
6C2×C11×#121—21no—
7C2×C11×#121—21no—
8C2×C11×#121C2212yes—
9C22×C42×C11C2211yescharacteristic
10C22×C4×Dic11—21no—
11C11×#390—21no—
12C11×#390—21no—
13C11×#390C412yescomplemented
14C11×#384C411yescharacteristic, complemented
15C2×C11⋊#95—21no—
16C2×C11⋊#95C2212yes—
17C2×C22⋊(C11⋊C8)C2212yes—
18C2×C4⋊(C11⋊C8)—21no—
19#10622175—28no—
20#10622162—21no—
21C22×D4×C11—22no—
22C22×D4×C11—21no—
23C22×D4×C11—21no—
24C22×D4×C11C2×C412yes—
25C23×C4×C11D411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C23×C4×C11C2311yescharacteristic
28C23×Dic11—22no—
29C11×#127—42no—
30C11×#121—24no—
31C11×#121—24no—
32C11×#121—44no—
33C11×#121—42no—
34C11×#121—42no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4C2×C412yes—
38C2×C11×C22⋊C4—22no—
39C2×C11×C22⋊C4—22no—
40C2×C11×C22⋊C4—22no—
41C2×C42×C11—42no—
42C2×C42×C11C2×C411yescharacteristic
43C2×C42×C11C2×C411yescharacteristic
44C2×C42×C11D411yescharacteristic
45C2×C42×C11D411yescharacteristic
46C2×C4×Dic11—24no—
47C2×C4×Dic11—42no—
48C2×C4×Dic11—42no—
49C22×C11⋊C8—22no—
50C11⋊#95—24no—
51C11⋊#95—22no—
52C11⋊#95D414yescomplemented
53C22⋊(C11⋊C8)—24no—
54C4⋊(C11⋊C8)—42no—
55#9712—111nomaximal, Sylow
56C24×C11—22no—
57C24×C11C2×D411yescharacteristic
58C2×D4×C11—24no—
59C2×D4×C11—42no—
60C2×D4×C11—42no—
61C2×D4×C11—42no—
62C2×D4×C11—42no—
63C2×D4×C11—44no—
64C2×D4×C11—42no—
65C2×D4×C11—42no—
66C2×D4×C11—44no—
67C2×D4×C11—42no—
68C2×D4×C11—42no—
69C2×D4×C11—42no—
70C2×D4×C11—42no—
71C22×C4×C11—22no—
72C22×C4×C11—22no—
73C22×C4×C11—22no—
74C22×C4×C11—22no—
75C22×C4×C11—22no—
76C22×C4×C11—41no—
77C22×C4×C11—41no—
78C22×C4×C11—41no—
79C22×C4×C11C22⋊C411yescharacteristic
80C22×C4×C11C22⋊C411yescharacteristic
81C22×C4×C11C22⋊C411yescharacteristic
82C22×C4×C11C22⋊C411yescharacteristic
83C22×C4×C11D812yes—
84C22×C4×C11SD1612yes—
85C22×C4×C11C22×C411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D412yes—
88C22×C4×C11#4112yes—
89C22×Dic11—24no—
90C22×Dic11—24no—
91C22×Dic11—24no—
92C22×Dic11—42no—
93C22×Dic11—42no—
94C22×Dic11—42no—
95C22×Dic11—42no—
96C11×C4⋊C4—24no—
97C11×C4⋊C4—42no—
98C11×C4⋊C4—42no—
99C11×C22⋊C4—44no—
100C11×C22⋊C4—44no—
101C11×C22⋊C4—42no—
102C11×C22⋊C4—42no—
103C42×C11—22no—
104C42×C11—22no—
105C42×C11—41no—
106C42×C11—41no—
107C4×Dic11—48no—
108C2×C11⋊C8—42no—
109C2×C11⋊C8—42no—
110C2×C11⋊C8—42no—
111#2856D1111yescharacteristic
112#1797—111no—
113C2×#327—114no—
114C4×#95—111no—
115C23×C11—21no—
116C23×C11—21no—
117C23×C11—21no—
118C23×C11—21no—
119C23×C11—42no—
120C23×C11—42no—
121C23×C11—42no—
122C23×C11—42no—
123C23×C11—42no—
124C23×C11—42no—
125C23×C11—42no—
126C23×C11C2×C22⋊C411yescharacteristic
127C23×C11#12112yes—
128C23×C11C2×D811yescharacteristic
129C23×C11C2×SD1611yescharacteristic
130C23×C11AGL(1,ℤ/8)12yes—
131D4×C11—84no—
132D4×C11—84no—
133D4×C11—84no—
134D4×C11—84no—
135D4×C11—84no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—24no—
145C2×C4×C11—24no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11—44no—
152C2×C4×C11—42no—
153C2×C4×C11—42no—
154C2×C4×C11—42no—
155C2×C4×C11#9912yes—
156C2×C4×C11#10212yes—
157C2×C4×C11#10212yes—
158C2×C4×C11#10412yes—
159C2×C4×C11#10412yes—
160C2×C4×C11C4×D412yes—
161C2×C4×C11#12411yescharacteristic
162C2×C4×C11#12711yescharacteristic
163C2×Dic11—28no—
164C2×Dic11—44no—
165C2×Dic11—44no—
166C2×Dic11—44no—
167C2×Dic11—44no—
168C2×Dic11—44no—
169C2×Dic11—44no—
170C11⋊C8—82no—
171C2×#127Dic1111yescharacteristic, complemented
172C2×#121—21no—
173C2×#121—21no—
174C2×#121C2×D1112yes—
175C22×C42—221no—
176C22×C42C2×D1111yescharacteristic
177C2×C4⋊C8—221no—
178C2×C22⋊C8—112no—
179#390—21no—
180#390—21no—
181#390Dic1112yescomplemented
182#384Dic1111yescharacteristic, complemented
183C2×#95—112no—
184C2×#95—221no—
185#336—221no—
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—82no—
196C22×C11—82no—
197C22×C11—82no—
198C22×C11—82no—
199C22×C11—82no—
200C22×C11—82no—
201C22×C11—82no—
202C22×C11#39011yescharacteristic
203C22×C11C2×#9911yescharacteristic
204C22×C11#41011yescharacteristic
205C22×C11C2×#10211yescharacteristic
206C22×C11#41811yescharacteristic
207C22×C11C2×#10411yescharacteristic
208C22×C11C2×#10411yescharacteristic
209C22×C11#45912yes—
210C22×C11#46012yes—
211C4×C11—22no—
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—22no—
215C4×C11—22no—
216C4×C11—41no—
217C4×C11—82no—
218C4×C11#32714yescomplemented
219Dic11—48no—
220C22×D4—22no—
221C22×D4—21no—
222C22×D4—21no—
223C22×D4C2×Dic1112yes—
224C23×C4—222no—
225C23×C4C22⋊D1111yescharacteristic
226C23×C4C22⋊D1111yescharacteristic
227C23×C4C22×D1111yescharacteristic
228C22×C8—222no—
229#127—42no—
230#121—24no—
231#121—24no—
232#121—44no—
233#121—42no—
234#121—42no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4C2×Dic1112yes—
238C2×C22⋊C4—22no—
239C2×C22⋊C4—22no—
240C2×C22⋊C4—22no—
241C2×C42—42no—
242C2×C42—224no—
243C2×C42—442no—
244C2×C42—442no—
245C2×C42C2×Dic1111yescharacteristic
246C2×C42C2×Dic1111yescharacteristic
247C2×C42C22⋊D1111yescharacteristic
248C2×C42C22⋊D1111yescharacteristic
249C4⋊C8—442no—
250C22⋊C8—224no—
251#95—114no—
252#95—224no—
253#95—222no—
254C2×C11—22no—
255C2×C11—22no—
256C2×C11—162no—
257C2×C11C2×#32711yescharacteristic
258C2×C11#150211yescharacteristic
259C2×C11#150511yescharacteristic
260C2×C11#150711yescharacteristic
261C2×C11#196211yescharacteristic
262C2×C11#196411yescharacteristic
263C2×C11#198211yescharacteristic
264C24—22no—
265C24C2×C22⋊D1111yescharacteristic
266C2×D4—24no—
267C2×D4—42no—
268C2×D4—42no—
269C2×D4—42no—
270C2×D4—42no—
271C2×D4—42no—
272C2×D4—44no—
273C2×D4—42no—
274C2×D4—44no—
275C2×D4—42no—
276C2×D4—42no—
277C2×D4—42no—
278C2×D4—42no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—224no—
288C22×C4—224no—
289C22×C4—224no—
290C22×C4—442no—
291C22×C4—442no—
292C22×C4—442no—
293C22×C4—442no—
294C22×C4#432312yes—
295C22×C4#432412yes—
296C22×C4C22⋊Dic1111yescharacteristic
297C22×C4C22⋊Dic1111yescharacteristic
298C22×C4C22⋊Dic1111yescharacteristic
299C22×C4C22⋊Dic1111yescharacteristic
300C22×C4D4×D1112yes—
301C22×C4#434112yes—
302C22×C4C22×Dic1111yescharacteristic
303C22×C4C2×C22⋊D1111yescharacteristic
304C2×C8—442no—
305C2×C8—442no—
306C2×C8—442no—
307C4⋊C4—24no—
308C4⋊C4—42no—
309C4⋊C4—42no—
310C22⋊C4—44no—
311C22⋊C4—44no—
312C22⋊C4—42no—
313C22⋊C4—42no—
314C42—22no—
315C42—22no—
316C42—41no—
317C42—41no—
318C42—448no—
319C11#971211yescharacteristic, complemented, Sylow
320C23—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—42no—
325C23—42no—
326C23—42no—
327C23—42no—
328C23—42no—
329C23—42no—
330C23—42no—
331C23C2×#432311yescharacteristic
332C23#6698512yes—
333C23C2×#432411yescharacteristic
334C23#6699112yes—
335C23C2×C22⋊Dic1111yescharacteristic
336D4—84no—
337D4—84no—
338D4—84no—
339D4—84no—
340D4—84no—
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—42no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—228no—
361C2×C4—444no—
362C2×C4—444no—
363C2×C4—444no—
364C2×C4—444no—
365C2×C4—444no—
366C2×C4—444no—
367C2×C4#6689612yes—
368C2×C4#6689612yes—
369C2×C4#6689812yes—
370C2×C4#6690112yes—
371C2×C4#6690112yes—
372C2×C4D4×Dic1112yes—
373C2×C4#6698911yescharacteristic
374C2×C4#6699311yescharacteristic
375C8—882no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—22no—
381C22—22no—
382C22—22no—
383C22—22no—
384C22—82no—
385C22—82no—
386C22—82no—
387C22—82no—
388C22—82no—
389C22—82no—
390C22—82no—
391C22#1062268512yes—
392C22#1062268812yes—
393C22C2×#6689611yescharacteristic
394C22#1062282811yescharacteristic
395C22C2×#6689811yescharacteristic
396C22#1062283411yescharacteristic
397C22C2×#6690111yescharacteristic
398C22C2×#6690111yescharacteristic
399C22#1062285311yescharacteristic
400C4—22no—
401C4—22no—
402C4—21no—
403C4—22no—
404C4—21no—
405C4—41no—
406C4—82no—
407C4—448no—
408C4#1062217514yescomplemented
409C2—22no—
410C2—22no—
411C2—162no—
412C2C2×#1062217511yescharacteristic
413C2#1306711111yescharacteristic
414C2#1306712411yescharacteristic
415C2#1306713211yescharacteristic
416C2#1306944511yescharacteristic
417C2#1306945311yescharacteristic
418C2#1306954411yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
Fitting, prime radicalC11×#2856C2
socleC23×C11C2×C22⋊C4
cosocleC23×C4×C11C23
hypercenter#2856D11
hypocenterC11#9712
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2856

Complements

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

NH ≅ G/Ntype
1. #13068596C2semidirect
2. C2×#10622175C2semidirect
3. C4×C11⋊#95C2semidirect
5. C2×C11×#127C4semidirect
13. C11×#390C4semidirect
14. C11×#384C4semidirect
52. C11⋊#95D4semidirect
171. C2×#127Dic11semidirect
181. #390Dic11semidirect
182. #384Dic11semidirect
218. C4×C11#327semidirect
319. C11#9712semidirect
408. C4#10622175semidirect

Maximal subgroups

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

subgroupindex
#130685962
C2×#106221752
C4×C11⋊#952
C11×#28562
#971211