Finite Group Databasebeta

← #14647177

Subgroups — #14647177

Order 2816.

482 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071009C211yesmaximal, characteristic
2#13068379C211yesmaximal, characteristic
3#13068379C211yesmaximal, characteristic
4#13066498C211yesmaximal, characteristic, complemented
5#13066498C211yesmaximal, characteristic, complemented
6#13066497C211yesmaximal, characteristic, complemented
7C11×#1295C211yesmaximal, characteristic, complemented
8C2×C42×D11C2211yescharacteristic
9C2×C11×#97C2211yescharacteristic
10C2×C11×#97C2211yescharacteristic
11C11×#382C2211yescharacteristic
12C2×(C2×D11)⋊C8—21no—
13C2×(C2×D11)⋊C8—21no—
14#10622600C411yescharacteristic
15#10622600C411yescharacteristic
16C4⋊C4×Dic11C411yescharacteristic
17C4⋊C4×Dic11C411yescharacteristic
18#10622549C2211yescharacteristic
19C2×#66867C2211yescharacteristic
20C2×#66867C2211yescharacteristic
21#10622279—21no—
22#10622277—21no—
23#10622264—21no—
24#10622261—21no—
25#10622188—21no—
26#10622188—21no—
27C22×C4×D11C2×C411yescharacteristic
28C22×C4×D11D411yescharacteristic
29C22×C4×D11D411yescharacteristic
30C22×C8×C11—21no—
31C22×C8×C11—21no—
32C2×C11×C4⋊C4C2×C411yescharacteristic
33C2×C11×C4⋊C4C2×C411yescharacteristic
34C2×C42×C11C2311yescharacteristic
35C2×(C2×D11)⋊C4—21no—
36C2×(C2×D11)⋊C4—21no—
37C2×C4⋊Dic11C2×C411yescharacteristic
38C2×C4⋊Dic11C2×C411yescharacteristic
39C2×C4×Dic11—21no—
40C2×C4×Dic11—21no—
41C2×C4×Dic11C2×C411yescharacteristic
42C2×C4×Dic11D411yescharacteristic
43C2×C4×Dic11D411yescharacteristic
44C22×C11⋊C8—21no—
45C22×C11⋊C8—21no—
46C42×D11—21no—
47C42×D11—21no—
48C42×D11—21no—
49C42×D11—21no—
50C11×#97—21no—
51C11×#97—21no—
52C11×#97—21no—
53C11×#97—21no—
54C11×#95—21no—
55C11×#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95—21no—
62(C2×D11)⋊C8—24no—
63(C2×D11)⋊C8—24no—
64#66867—21no—
65#66867—21no—
66#66867—21no—
67#66867—21no—
68#8720—111nomaximal, Sylow
69C23×D11C22⋊C411yescharacteristic
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11C22×C411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×Dic11—21no—
76C22×Dic11—21no—
77C22×Dic11C22⋊C411yescharacteristic
78C22×Dic11C22⋊C411yescharacteristic
79C22×Dic11C22⋊C411yescharacteristic
80C2×C4×D11—22no—
81C2×C4×D11—22no—
82C2×C4×D11—21no—
83C2×C4×D11—21no—
84C2×C4×D11—21no—
85C2×C4×D11—21no—
86C2×C4×D11—21no—
87C2×C4×D11—21no—
88C2×C4×D11—41no—
89C2×C4×D11—41no—
90C2×C4×D11—41no—
91C2×C4×D11—41no—
92C2×C8×C11—22no—
93C2×C8×C11—22no—
94C2×C8×C11—41no—
95C2×C8×C11—41no—
96C2×C8×C11—41no—
97C2×C8×C11—41no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C42×C11#4111yescharacteristic
101C42×C11#4111yescharacteristic
102C42×C11#4111yescharacteristic
103C42×C11#4111yescharacteristic
104(C2×D11)⋊C4—42no—
105(C2×D11)⋊C4—42no—
106C4⋊Dic11—41no—
107C4⋊Dic11—41no—
108C4×Dic11—21no—
109C4×Dic11—21no—
110C4×Dic11—21no—
111C4×Dic11—21no—
112C4×Dic11—21no—
113C4×Dic11—21no—
114C4×Dic11—42no—
115C4×Dic11—42no—
116C2×C11⋊C8—22no—
117C2×C11⋊C8—22no—
118C2×C11⋊C8—41no—
119C2×C11⋊C8—41no—
120C2×C11⋊C8—41no—
121C2×C11⋊C8—41no—
122#2283—111no—
123#1749—111no—
124#1749—111no—
125#1295—111no—
126#1295—111no—
127#1295—111no—
128#1295D1111yescharacteristic, complemented
129C23×C11C2×C22⋊C411yescharacteristic
130C22×D11—21no—
131C22×D11—21no—
132C22×D11—21no—
133C22×D11—21no—
134C22×D11—21no—
135C22×D11—21no—
136C22×D11#10412yes—
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—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11#11711yescharacteristic
150C2×C4×C11#11711yescharacteristic
151C2×C4×C11#12311yescharacteristic
152C2×C4×C11#12311yescharacteristic
153C2×C4×C11#12311yescharacteristic
154C2×C4×C11#12311yescharacteristic
155C2×Dic11—21no—
156C2×Dic11—21no—
157C2×Dic11—21no—
158C2×Dic11—21no—
159C2×Dic11—21no—
160C2×Dic11—21no—
161C2×Dic11—21no—
162C2×Dic11—21no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11#10412yes—
170C4×D11—42no—
171C4×D11—42no—
172C4×D11—42no—
173C4×D11—42no—
174C4×D11—42no—
175C4×D11—42no—
176C8×C11—42no—
177C8×C11—42no—
178C11⋊C8—42no—
179C11⋊C8—42no—
180C22×C42—111no—
181C2×C22⋊C8—221no—
182C2×C22⋊C8—221no—
183C2×#97—111no—
184C2×#97—111no—
185C2×#97C2×D1111yescharacteristic
186C2×#97C2×D1111yescharacteristic
187#383—221no—
188#382—111no—
189#382C2×D1111yescharacteristic
190#381—221no—
191#380—111no—
192#380—111no—
193C4×C4⋊C4—111no—
194C4×C4⋊C4—111no—
195C4×C22⋊C4—221no—
196#376—221no—
197#336—221no—
198#336—221no—
199C22×C11#38111yescharacteristic
200C22×C11#41311yescharacteristic
201C22×C11#41311yescharacteristic
202C22×C11C2×#10411yescharacteristic
203C22×C11C2×#10411yescharacteristic
204C22×C11#42111yescharacteristic
205C22×C11#42111yescharacteristic
206C2×D11—22no—
207C2×D11—22no—
208C2×D11—22no—
209C2×D11—41no—
210C2×D11—41no—
211C2×D11—41no—
212C2×D11—41no—
213C4×C11—21no—
214C4×C11—21no—
215C4×C11—21no—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—21no—
219C4×C11—81no—
220C4×C11—81no—
221Dic11—22no—
222Dic11—41no—
223Dic11—41no—
224Dic11—81no—
225Dic11—81no—
226C23×C4—111no—
227C23×C4—111no—
228C23×C4—111no—
229C22×C8—21no—
230C22×C8—21no—
231C22×C8—221no—
232C22×C8—221no—
233C2×C4⋊C4—111no—
234C2×C4⋊C4—111no—
235C2×C4⋊C4C4×D1111yescharacteristic
236C2×C4⋊C4C4×D1111yescharacteristic
237C2×C22⋊C4—221no—
238C2×C22⋊C4—221no—
239C2×C42—111no—
240C2×C42—111no—
241C2×C42—111no—
242C2×C42—221no—
243C2×C42—221no—
244C2×C42—221no—
245C2×C42—221no—
246C2×C42—221no—
247C2×C42—221no—
248C2×C42C22×D1111yescharacteristic
249C22⋊C8—224no—
250C22⋊C8—224no—
251#97—21no—
252#97—21no—
253#97—21no—
254#97—21no—
255#97—221no—
256#97—221no—
257#97—221no—
258#97—221no—
259#95—21no—
260#95—21no—
261#95—221no—
262#95—221no—
263#95—221no—
264#95—221no—
265#95—221no—
266#95—221no—
267C2×C11#152411yescharacteristic
268C2×C11#152911yescharacteristic
269C2×C11#153211yescharacteristic
270C2×C11#153511yescharacteristic
271C2×C11#182211yescharacteristic
272C2×C11#182611yescharacteristic
273C2×C11#182611yescharacteristic
274D11—42no—
275C24—111no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—111no—
279C22×C4—111no—
280C22×C4—111no—
281C22×C4—222no—
282C22×C4—222no—
283C22×C4—221no—
284C22×C4—221no—
285C22×C4—221no—
286C22×C4—221no—
287C22×C4—221no—
288C22×C4—221no—
289C22×C4—221no—
290C22×C4—221no—
291C22×C4—441no—
292C22×C4—441no—
293C22×C4—441no—
294C22×C4—441no—
295C22×C4C2×C4×D1111yescharacteristic
296C22×C4D4×D1111yescharacteristic
297C22×C4D4×D1111yescharacteristic
298C2×C8—22no—
299C2×C8—22no—
300C2×C8—41no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—222no—
305C2×C8—222no—
306C2×C8—441no—
307C2×C8—441no—
308C2×C8—441no—
309C2×C8—441no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—441no—
313C4⋊C4—441no—
314C22⋊C4—442no—
315C22⋊C4—442no—
316C42—221no—
317C42—221no—
318C42—221no—
319C42—221no—
320C42—221no—
321C42—221no—
322C42—442no—
323C42—442no—
324C42#433911yescharacteristic
325C42#433911yescharacteristic
326C42#434111yescharacteristic
327C42#434311yescharacteristic
328C11#872011yescharacteristic, complemented, Sylow
329C23—112no—
330C23—221no—
331C23—221no—
332C23—221no—
333C23—221no—
334C23—221no—
335C23—221no—
336C23C22⋊C4×D1111yescharacteristic
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—112no—
350C2×C4—221no—
351C2×C4—221no—
352C2×C4—221no—
353C2×C4—221no—
354C2×C4—221no—
355C2×C4—221no—
356C2×C4—221no—
357C2×C4—221no—
358C2×C4—442no—
359C2×C4—442no—
360C2×C4—442no—
361C2×C4—442no—
362C2×C4—442no—
363C2×C4—442no—
364C2×C4—441no—
365C2×C4—441no—
366C2×C4—441no—
367C2×C4—441no—
368C2×C4—441no—
369C2×C4—441no—
370C2×C4#6692511yescharacteristic
371C2×C4#6693611yescharacteristic
372C2×C4#6693611yescharacteristic
373C2×C4#6694511yescharacteristic
374C2×C4#6694711yescharacteristic
375C2×C4#6694711yescharacteristic
376C8—42no—
377C8—42no—
378C8—442no—
379C8—442no—
380C22—222no—
381C22—222no—
382C22—222no—
383C22—441no—
384C22—441no—
385C22—441no—
386C22—441no—
387C22#1062227711yescharacteristic
388C22#1062235811yescharacteristic
389C22#1062236411yescharacteristic
390C22D11×#10411yescharacteristic
391C22D11×#10411yescharacteristic
392C22#1062243411yescharacteristic
393C22#1062243411yescharacteristic
394C4—21no—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—81no—
401C4—81no—
402C4—222no—
403C4—441no—
404C4—441no—
405C4—881no—
406C4—881no—
407C2—442no—
408C2#1306720111yescharacteristic
409C2#1306722211yescharacteristic
410C2#1306723511yescharacteristic
411C2#1306724411yescharacteristic
412C2#1306869811yescharacteristic
413C2#1306871411yescharacteristic
414C2#1306871411yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1295C2
socleC23×C11C2×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1295D11
hypocenterC11#8720
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
4. #13066498C2semidirect
5. #13066498C2semidirect
6. #13066497C2semidirect
7. C11×#1295C2semidirect
128. #1295D11semidirect
328. C11#8720semidirect

Maximal subgroups

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

subgroupindex
#130710092
#130683792
#130664982
#130664972
C11×#12952
#872011