Finite Group Databasebeta

← #14719694

Subgroups — #14719694

Order 2816.

1346 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077657C212yesmaximal, complemented
2#13066954C214yesmaximal, complemented
3#13066943C214yesmaximal, complemented
4#13066937C212yesmaximal, complemented
5#13066930C212yesmaximal, complemented
6C2×C11×#518C211yesmaximal, characteristic
7C23×D4×C11C411yescharacteristic
8C11×#518—28no—
9C2×C4×D4×C11C412yes—
10C2×C4×D4×C11C411yescharacteristic
11C2×C4×D4×C11C411yescharacteristic
12C2×C4×D4×C11C2212yes—
13C2×C4×D4×C11C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×C11×#117C411yescharacteristic
16C2×C11×#117C2211yescharacteristic
17C22×C11×C22⋊C4C412yes—
18C22×C11×C22⋊C4C2212yes—
19#10622820C2218yescomplemented
20#10622625—28no—
21#10622538C2214yescomplemented
22#10622166C2214yescomplemented
23#10622163C2214yes—
24#10622163C2218yescomplemented
25C25×C11C2×C412yes—
26C22×D4×C11—24no—
27C22×D4×C11—24no—
28C22×D4×C11—24no—
29C22×D4×C11C2×C412yes—
30C22×D4×C11C2×C411yescharacteristic
31C22×D4×C11C2×C411yescharacteristic
32C23×C4×C11C2×C411yescharacteristic
33C23×C4×C11C2×C412yes—
34C23×C4×C11C2×C412yes—
35C23×C4×C11C2×C412yes—
36C23×C4×C11C2312yes—
37C4×D4×C11—24no—
38C4×D4×C11—28no—
39C4×D4×C11—24no—
40C4×D4×C11—28no—
41C4×D4×C11—24no—
42C4×D4×C11D418yes—
43C11×#117—24no—
44C11×#117—24no—
45C2×C11×C4⋊C4C2×C411yescharacteristic
46C2×C11×C4⋊C4C2×C411yescharacteristic
47C2×C11×C4⋊C4C2×C411yescharacteristic
48C2×C11×C4⋊C4C2311yescharacteristic
49C2×C11×C22⋊C4—28no—
50C2×C11×C22⋊C4—28no—
51C2×C11×C22⋊C4C2×C411yescharacteristic
52C2×C11×C22⋊C4C2×C412yes—
53C2×C11×C22⋊C4C2×C412yes—
54C2×C11×C22⋊C4C2×C412yes—
55C2×C11×C22⋊C4C2×C412yes—
56C2×C11×C22⋊C4C2311yescharacteristic
57C2×C11×C22⋊C4C2312yes—
58C2×C42×C11C2×C412yes—
59C2×C42×C11C2×C411yescharacteristic
60C2×C42×C11C2311yescharacteristic
61C2×#4318—28no—
62C22⋊(C11⋊C8)—28no—
63C22⋊(C11⋊C8)C2318yes—
64C4⋊(C11⋊C8)—24no—
65C4×C11⋊C8—24no—
66#17369—111nomaximal, Sylow
67C24×C11—24no—
68C24×C11—24no—
69C24×C11—24no—
70C24×C11—82no—
71C24×C11—82no—
72C24×C11C22×C412yes—
73C24×C11C22×C411yescharacteristic
74C24×C11C22×C412yes—
75C2×D4×C11—232no—
76C2×D4×C11—24no—
77C2×D4×C11—24no—
78C2×D4×C11—22no—
79C2×D4×C11—24no—
80C2×D4×C11—22no—
81C2×D4×C11—22no—
82C2×D4×C11—22no—
83C2×D4×C11C22⋊C414yes—
84C2×D4×C11M1614yescomplemented
85C22×C4×C11—22no—
86C22×C4×C11—22no—
87C22×C4×C11—24no—
88C22×C4×C11—24no—
89C22×C4×C11—24no—
90C22×C4×C11—82no—
91C22×C4×C11—82no—
92C22×C4×C11—82no—
93C22×C4×C11—82no—
94C22×C4×C11M1614yescomplemented
95C22×C4×C11C22×C411yescharacteristic
96C22×C4×C11C22×C411yescharacteristic
97C22×C4×C11C22×C412yes—
98C22×C4×C11C22×C411yescharacteristic
99C22×C4×C11C22×C412yes—
100C22×C4×C11C22×C411yescharacteristic
101C22×C4×C11C22×C411yescharacteristic
102C22×C4×C11C2×D418yes—
103C22×C4×C11C2411yescharacteristic
104C11×C4⋊C4—22no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4C22⋊C414yes—
108C11×C22⋊C4—24no—
109C11×C22⋊C4—24no—
110C11×C22⋊C4—22no—
111C11×C22⋊C4—24no—
112C11×C22⋊C4—22no—
113C11×C22⋊C4—24no—
114C11×C22⋊C4C22⋊C418yes—
115C42×C11—24no—
116C42×C11—22no—
117C42×C11C2×D414yes—
118#4318—88no—
119C2×C11⋊C8—28no—
120C2×#518D1111yescharacteristic
121#2975—112no—
122#1465—114no—
123#1462—114no—
124#1460—112no—
125#1458—112no—
126C23×C11—216no—
127C23×C11—21no—
128C23×C11—22no—
129C23×C11—21no—
130C23×C11—22no—
131C23×C11—22no—
132C23×C11—22no—
133C23×C11—42no—
134C23×C11—42no—
135C23×C11—42no—
136C23×C11—42no—
137C23×C11—41no—
138C23×C11—41no—
139C23×C11—84no—
140C23×C11—84no—
141C23×C11—88no—
142C23×C11—88no—
143C23×C11C2×C22⋊C414yes—
144C23×C11C2×M1612yes—
145C23×C11C2×M1614yes—
146C23×C11C23×C411yescharacteristic
147D4×C11—216no—
148D4×C11—28no—
149D4×C11—28no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—28no—
153C2×C4×C11—21no—
154C2×C4×C11—22no—
155C2×C4×C11—21no—
156C2×C4×C11—48no—
157C2×C4×C11—42no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—42no—
162C2×C4×C11—41no—
163C2×C4×C11—84no—
164C2×C4×C11—84no—
165C2×C4×C11—84no—
166C2×C4×C11C2×C22⋊C414yes—
167C2×C4×C11C2×C22⋊C412yes—
168C2×C4×C11C2×C22⋊C412yes—
169C2×C4×C11C2×M1612yes—
170C2×C4×C11C2×M1612yes—
171C2×C4×C11C2×M1612yes—
172C2×C4×C11C22×D412yes—
173C11⋊C8—48no—
174C23×D4Dic1111yescharacteristic
175#518—28no—
176C2×C4×D4Dic1112yes—
177C2×C4×D4Dic1111yescharacteristic
178C2×C4×D4Dic1111yescharacteristic
179C2×C4×D4C2×D1111yescharacteristic
180C2×C4×D4C2×D1112yes—
181C2×C4×D4C2×D1111yescharacteristic
182C2×#117Dic1111yescharacteristic
183C2×#117C2×D1111yescharacteristic
184C22×C22⋊C4Dic1112yes—
185C22×C22⋊C4C2×D1112yes—
186#436—228no—
187#431—114no—
188#407—118no—
189#324—114no—
190#323—114no—
191#323—118no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—22no—
195C22×C11—24no—
196C22×C11—24no—
197C22×C11—24no—
198C22×C11—24no—
199C22×C11—42no—
200C22×C11—44no—
201C22×C11—44no—
202C22×C11—44no—
203C22×C11—44no—
204C22×C11—42no—
205C22×C11—42no—
206C22×C11—41no—
207C22×C11—42no—
208C22×C11—41no—
209C22×C11—816no—
210C22×C11C22×C22⋊C411yescharacteristic
211C22×C11C22×M1611yescharacteristic
212C22×C11C22×M1611yescharacteristic
213C4×C11—22no—
214C4×C11—22no—
215C4×C11—24no—
216C4×C11—22no—
217C4×C11—41no—
218C4×C11—42no—
219C4×C11—41no—
220C4×C11#40714yes—
221C25C2×Dic1112yes—
222C22×D4—24no—
223C22×D4—24no—
224C22×D4—24no—
225C22×D4C2×Dic1112yes—
226C22×D4C2×Dic1111yescharacteristic
227C22×D4C2×Dic1111yescharacteristic
228C23×C4C2×Dic1111yescharacteristic
229C23×C4C2×Dic1112yes—
230C23×C4C2×Dic1112yes—
231C23×C4C2×Dic1112yes—
232C23×C4C22×D1112yes—
233C2×M16—228no—
234C4×D4—24no—
235C4×D4—28no—
236C4×D4—24no—
237C4×D4—28no—
238C4×D4—24no—
239C4×D4C22⋊D1118yes—
240#117—24no—
241#117—24no—
242C2×C4⋊C4C2×Dic1111yescharacteristic
243C2×C4⋊C4C2×Dic1111yescharacteristic
244C2×C4⋊C4C2×Dic1111yescharacteristic
245C2×C4⋊C4C22×D1111yescharacteristic
246C2×C22⋊C4—28no—
247C2×C22⋊C4—28no—
248C2×C22⋊C4C2×Dic1111yescharacteristic
249C2×C22⋊C4C2×Dic1112yes—
250C2×C22⋊C4C2×Dic1112yes—
251C2×C22⋊C4C2×Dic1112yes—
252C2×C22⋊C4C2×Dic1112yes—
253C2×C22⋊C4C22×D1111yescharacteristic
254C2×C22⋊C4C22×D1112yes—
255C2×C42C2×Dic1112yes—
256C2×C42C2×Dic1111yescharacteristic
257C2×C42C22×D1111yescharacteristic
258C4⋊C8—224no—
259C22⋊C8—118no—
260C22⋊C8—228no—
261C4×C8—224no—
262C2×C11—21no—
263C2×C11—21no—
264C2×C11—44no—
265C2×C11—44no—
266C2×C11—42no—
267C2×C11C2×#40711yescharacteristic
268C2×C11#288311yescharacteristic
269C2×C11#288811yescharacteristic
270C24—24no—
271C24—24no—
272C24—24no—
273C24—82no—
274C24—82no—
275C24C22×Dic1111yescharacteristic
276C24C22×Dic1112yes—
277C24C22×Dic1112yes—
278C2×D4—232no—
279C2×D4—24no—
280C2×D4—24no—
281C2×D4—24no—
282C2×D4—22no—
283C2×D4—22no—
284C2×D4—22no—
285C2×D4—22no—
286C2×D4#431814yescomplemented
287C2×D4C22⋊Dic1114yes—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—24no—
291C22×C4—24no—
292C22×C4—24no—
293C22×C4—82no—
294C22×C4—82no—
295C22×C4—82no—
296C22×C4—82no—
297C22×C4#431814yescomplemented
298C22×C4C22×Dic1111yescharacteristic
299C22×C4C22×Dic1112yes—
300C22×C4C22×Dic1111yescharacteristic
301C22×C4C22×Dic1111yescharacteristic
302C22×C4C22×Dic1111yescharacteristic
303C22×C4C22×Dic1112yes—
304C22×C4C22×Dic1111yescharacteristic
305C22×C4C2×C22⋊D1118yes—
306C22×C4C23×D1111yescharacteristic
307M16—888no—
308C2×C8—228no—
309C4⋊C4—22no—
310C4⋊C4—22no—
311C4⋊C4—22no—
312C4⋊C4C22⋊Dic1114yes—
313C22⋊C4—24no—
314C22⋊C4—24no—
315C22⋊C4—22no—
316C22⋊C4—24no—
317C22⋊C4—22no—
318C22⋊C4—24no—
319C22⋊C4C22⋊Dic1118yes—
320C42—24no—
321C42—22no—
322C42C2×C22⋊D1114yes—
323C11#1736911yescharacteristic, complemented, Sylow
324C23—216no—
325C23—21no—
326C23—22no—
327C23—22no—
328C23—22no—
329C23—21no—
330C23—22no—
331C23—42no—
332C23—42no—
333C23—42no—
334C23—42no—
335C23—41no—
336C23—41no—
337C23—84no—
338C23—84no—
339C23—88no—
340C23—88no—
341C23C2×#431812yes—
342C23C2×#431814yes—
343C23C2×C22⋊Dic1114yes—
344C23C23×Dic1111yescharacteristic
345D4—216no—
346D4—28no—
347D4—28no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—28no—
351C2×C4—21no—
352C2×C4—22no—
353C2×C4—21no—
354C2×C4—48no—
355C2×C4—42no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—42no—
360C2×C4—41no—
361C2×C4—84no—
362C2×C4—84no—
363C2×C4—84no—
364C2×C4C2×#431812yes—
365C2×C4C2×#431812yes—
366C2×C4C2×#431812yes—
367C2×C4C2×C22⋊Dic1114yes—
368C2×C4C2×C22⋊Dic1112yes—
369C2×C4C2×C22⋊Dic1112yes—
370C2×C4C22×C22⋊D1112yes—
371C8—448no—
372C22—21no—
373C22—21no—
374C22—22no—
375C22—24no—
376C22—24no—
377C22—24no—
378C22—24no—
379C22—42no—
380C22—44no—
381C22—42no—
382C22—44no—
383C22—44no—
384C22—44no—
385C22—42no—
386C22—41no—
387C22—42no—
388C22—41no—
389C22—816no—
390C22C22×#431811yescharacteristic
391C22C22×#431811yescharacteristic
392C22C22×C22⋊Dic1111yescharacteristic
393C4—22no—
394C4—22no—
395C4—24no—
396C4—22no—
397C4—41no—
398C4—42no—
399C4—41no—
400C4#1062282014yes—
401C2—21no—
402C2—21no—
403C2—44no—
404C2—42no—
405C2—44no—
406C2C2×#1062282011yescharacteristic
407C2#1307707711yescharacteristic
408C2#1307709511yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#518C2
socleC22×C11C22×C22⋊C4
prime radicalC23×D4×C11C4
cosocleC22×C4×C11C24
hypercenterC2×#518D11
hypocenterC11#17369
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ C2×#518

Complements

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

NH ≅ G/Ntype
1. #13077657C2semidirect
2. #13066954C2semidirect
3. #13066943C2semidirect
4. #13066937C2semidirect
5. #13066930C2semidirect
19. #10622820C22semidirect
21. #10622538C22semidirect
22. #10622166C22semidirect
24. #10622163C22semidirect
84. C2×D4×C11M16semidirect
94. C22×C4×C11M16semidirect
286. C2×D4#4318semidirect
297. C22×C4#4318semidirect
323. C11#17369semidirect

Maximal subgroups

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

subgroupindex
#130776572
#130669542
#130669432
#130669372
#130669302
C2×C11×#5182
#1736911