Finite Group Databasebeta

← #14719940

Subgroups — #14719940

Order 2816.

1012 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077645C212yesmaximal, complemented
2#13066976C214yesmaximal, complemented
3#13066964C214yesmaximal, complemented
4#13066957C212yesmaximal, complemented
5#13066950C212yesmaximal, complemented
6C2×C11×#540C211yesmaximal, characteristic
7C11×#540—28no—
8C2×C11×#127C411yescharacteristic
9C2×C11×#125C411yescharacteristic
10C2×C11×#123C412yes—
11C2×C11×#123C2212yes—
12C2×C11×#121C412yes—
13C2×C11×#121C411yescharacteristic
14C2×C11×#121C411yescharacteristic
15C2×C11×#121C2212yes—
16C2×C4×D4×C11C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19#10622820C2214yes—
20C2×C22⋊(C11⋊C8)C2214yes—
21#10622624—28no—
22#10622539C2214yes—
23#10622166C2214yes—
24#10622163C2214yes—
25#10622163C2218yes—
26C22×D4×C11C2×C411yescharacteristic
27C22×D4×C11C2×C412yes—
28C22×D4×C11C2×C412yes—
29C22×D4×C11C2×C412yes—
30C22×D4×C11C2×C412yes—
31C22×D4×C11C2×C411yescharacteristic
32C23×C4×C11C2×C411yescharacteristic
33C23×C4×C11C2×C412yes—
34C23×C4×C11C2312yes—
35C11×#127—24no—
36C11×#125—24no—
37C11×#123—24no—
38C11×#123—24no—
39C11×#123—28no—
40C11×#121—24no—
41C11×#121—24no—
42C11×#121—24no—
43C11×#121—24no—
44C11×#121—28no—
45C4×D4×C11—24no—
46C4×D4×C11D418yes—
47C11×#117—24no—
48C2×C11×C4⋊C4C2×C411yescharacteristic
49C2×C11×C4⋊C4C2×C411yescharacteristic
50C2×C11×C4⋊C4C2×C412yes—
51C2×C11×C4⋊C4C2×C412yes—
52C2×C11×C4⋊C4C2×C411yescharacteristic
53C2×C11×C4⋊C4C2311yescharacteristic
54C2×C11×C22⋊C4C2×C411yescharacteristic
55C2×C11×C22⋊C4C2×C412yes—
56C2×C11×C22⋊C4C2×C412yes—
57C2×C11×C22⋊C4C2×C412yes—
58C2×C11×C22⋊C4C2311yescharacteristic
59C2×C11×C22⋊C4C2312yes—
60C2×C42×C11C2×C411yescharacteristic
61C2×C42×C11C2311yescharacteristic
62C2×#4318—24no—
63C22×C11⋊C8—24no—
64C22⋊(C11⋊C8)—24no—
65C22⋊(C11⋊C8)—24no—
66C22⋊(C11⋊C8)C2318yes—
67C4⋊(C11⋊C8)—24no—
68#66867—24no—
69#17408—111nomaximal, Sylow
70C24×C11C22×C411yescharacteristic
71C24×C11C22×C412yes—
72C24×C11C22×C412yes—
73C2×D4×C11—24no—
74C2×D4×C11—24no—
75C2×D4×C11—24no—
76C2×D4×C11—22no—
77C2×D4×C11—24no—
78C2×D4×C11—42no—
79C2×D4×C11—42no—
80C2×D4×C11—82no—
81C2×D4×C11—82no—
82C2×D4×C11—82no—
83C2×D4×C11—82no—
84C2×D4×C11C22⋊C414yes—
85C22×C4×C11—22no—
86C22×C4×C11—24no—
87C22×C4×C11—42no—
88C22×C4×C11—82no—
89C22×C4×C11—82no—
90C22×C4×C11C22×C411yescharacteristic
91C22×C4×C11C22×C411yescharacteristic
92C22×C4×C11C22×C411yescharacteristic
93C22×C4×C11C22×C411yescharacteristic
94C22×C4×C11C22×C412yes—
95C22×C4×C11C22×C411yescharacteristic
96C22×C4×C11C22×C412yes—
97C22×C4×C11C2×D414yes—
98C22×C4×C11C2×D414yes—
99C22×C4×C11C2411yescharacteristic
100C11×C4⋊C4—22no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—24no—
103C11×C4⋊C4—24no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4C22⋊C414yes—
106C11×C22⋊C4—24no—
107C11×C22⋊C4—22no—
108C11×C22⋊C4—24no—
109C11×C22⋊C4—22no—
110C11×C22⋊C4—22no—
111C11×C22⋊C4—22no—
112C11×C22⋊C4C22⋊C418yes—
113C42×C11—22no—
114C42×C11C2×D414yes—
115#4318—84no—
116C2×C11⋊C8—28no—
117C2×C11⋊C8—84no—
118C2×#540D1111yescharacteristic
119#2973—112no—
120#1471—114no—
121#1468—114no—
122#1466—112no—
123#1464—112no—
124C23×C11—24no—
125C23×C11—21no—
126C23×C11—22no—
127C23×C11—22no—
128C23×C11—24no—
129C23×C11—42no—
130C23×C11—42no—
131C23×C11—42no—
132C23×C11—41no—
133C23×C11—42no—
134C23×C11—41no—
135C23×C11C2×C22⋊C414yes—
136C23×C11C23×C411yescharacteristic
137D4×C11—44no—
138D4×C11—44no—
139D4×C11—84no—
140D4×C11—84no—
141D4×C11—84no—
142D4×C11—84no—
143C2×C4×C11—22no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—22no—
148C2×C4×C11—22no—
149C2×C4×C11—44no—
150C2×C4×C11—44no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—42no—
154C2×C4×C11—44no—
155C2×C4×C11—42no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—84no—
159C2×C4×C11C2×C22⋊C412yes—
160C2×C4×C11C2×C22⋊C412yes—
161C2×C4×C11C2×C22⋊C414yes—
162C2×C4×C11C22×D412yes—
163C11⋊C8—48no—
164#540—28no—
165C2×#127Dic1111yescharacteristic
166C2×#125Dic1111yescharacteristic
167C2×#123Dic1112yes—
168C2×#123C2×D1112yes—
169C2×#121Dic1112yes—
170C2×#121Dic1111yescharacteristic
171C2×#121Dic1111yescharacteristic
172C2×#121C2×D1112yes—
173C2×C4×D4C2×D1111yescharacteristic
174C2×C4×D4C2×D1111yescharacteristic
175C2×#117C2×D1111yescharacteristic
176#435—228no—
177#432—114no—
178#407—114no—
179C2×C22⋊C8—114no—
180#324—114no—
181#323—114no—
182#323—118no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11—24no—
186C22×C11—24no—
187C22×C11—24no—
188C22×C11—41no—
189C22×C11—42no—
190C22×C11—41no—
191C22×C11—42no—
192C22×C11—42no—
193C22×C11—41no—
194C22×C11—84no—
195C22×C11—82no—
196C22×C11—84no—
197C22×C11C22×C22⋊C411yescharacteristic
198C22×C11#56812yes—
199C4×C11—22no—
200C4×C11—22no—
201C4×C11—24no—
202C4×C11—22no—
203C4×C11—41no—
204C4×C11—41no—
205C4×C11—42no—
206C4×C11—41no—
207C22×D4C2×Dic1111yescharacteristic
208C22×D4C2×Dic1112yes—
209C22×D4C2×Dic1112yes—
210C22×D4C2×Dic1112yes—
211C22×D4C2×Dic1112yes—
212C22×D4C2×Dic1111yescharacteristic
213C23×C4C2×Dic1111yescharacteristic
214C23×C4C2×Dic1112yes—
215C23×C4C22×D1112yes—
216C2×M16—224no—
217C22×C8—224no—
218#127—24no—
219#125—24no—
220#123—24no—
221#123—24no—
222#123—28no—
223#121—24no—
224#121—24no—
225#121—24no—
226#121—24no—
227#121—28no—
228C4×D4—24no—
229C4×D4C22⋊D1118yes—
230#117—24no—
231C2×C4⋊C4C2×Dic1111yescharacteristic
232C2×C4⋊C4C2×Dic1111yescharacteristic
233C2×C4⋊C4C2×Dic1112yes—
234C2×C4⋊C4C2×Dic1112yes—
235C2×C4⋊C4C2×Dic1111yescharacteristic
236C2×C4⋊C4C22×D1111yescharacteristic
237C2×C22⋊C4C2×Dic1111yescharacteristic
238C2×C22⋊C4C2×Dic1112yes—
239C2×C22⋊C4C2×Dic1112yes—
240C2×C22⋊C4C2×Dic1112yes—
241C2×C22⋊C4C22×D1111yescharacteristic
242C2×C22⋊C4C22×D1112yes—
243C2×C42C2×Dic1111yescharacteristic
244C2×C42C22×D1111yescharacteristic
245C4⋊C8—224no—
246C22⋊C8—118no—
247C22⋊C8—224no—
248C22⋊C8—224no—
249#97—224no—
250C2×C11—22no—
251C2×C11—44no—
252C2×C11—81no—
253C2×C11—82no—
254C2×C11#287911yescharacteristic
255C2×C11#288311yescharacteristic
256C2×C11#288811yescharacteristic
257C24C22×Dic1111yescharacteristic
258C24C22×Dic1112yes—
259C24C22×Dic1112yes—
260C2×D4—24no—
261C2×D4—24no—
262C2×D4—24no—
263C2×D4—22no—
264C2×D4—24no—
265C2×D4—42no—
266C2×D4—42no—
267C2×D4—82no—
268C2×D4—82no—
269C2×D4—82no—
270C2×D4—82no—
271C2×D4C22⋊Dic1114yes—
272C22×C4—22no—
273C22×C4—24no—
274C22×C4—42no—
275C22×C4—82no—
276C22×C4—82no—
277C22×C4C22×Dic1111yescharacteristic
278C22×C4C22×Dic1111yescharacteristic
279C22×C4C22×Dic1111yescharacteristic
280C22×C4C22×Dic1111yescharacteristic
281C22×C4C22×Dic1112yes—
282C22×C4C22×Dic1111yescharacteristic
283C22×C4C22×Dic1112yes—
284C22×C4C2×C22⋊D1114yes—
285C22×C4C2×C22⋊D1114yes—
286C22×C4C23×D1111yescharacteristic
287M16—884no—
288C2×C8—228no—
289C2×C8—884no—
290C4⋊C4—22no—
291C4⋊C4—22no—
292C4⋊C4—24no—
293C4⋊C4—24no—
294C4⋊C4—22no—
295C4⋊C4C22⋊Dic1114yes—
296C22⋊C4—24no—
297C22⋊C4—22no—
298C22⋊C4—24no—
299C22⋊C4—22no—
300C22⋊C4—22no—
301C22⋊C4—22no—
302C22⋊C4C22⋊Dic1118yes—
303C42—22no—
304C42C2×C22⋊D1114yes—
305C11#1740811yescharacteristic, complemented, Sylow
306C23—24no—
307C23—21no—
308C23—22no—
309C23—22no—
310C23—24no—
311C23—42no—
312C23—42no—
313C23—42no—
314C23—41no—
315C23—42no—
316C23—41no—
317C23C2×C22⋊Dic1114yes—
318C23C23×Dic1111yescharacteristic
319D4—44no—
320D4—44no—
321D4—84no—
322D4—84no—
323D4—84no—
324D4—84no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—22no—
331C2×C4—44no—
332C2×C4—44no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—44no—
337C2×C4—42no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—84no—
341C2×C4C2×C22⋊Dic1112yes—
342C2×C4C2×C22⋊Dic1112yes—
343C2×C4C2×C22⋊Dic1114yes—
344C2×C4C22×C22⋊D1112yes—
345C8—448no—
346C22—21no—
347C22—21no—
348C22—24no—
349C22—24no—
350C22—24no—
351C22—41no—
352C22—42no—
353C22—41no—
354C22—42no—
355C22—42no—
356C22—41no—
357C22—84no—
358C22—82no—
359C22—84no—
360C22#1062335012yes—
361C22C22×C22⋊Dic1111yescharacteristic
362C4—22no—
363C4—22no—
364C4—24no—
365C4—22no—
366C4—41no—
367C4—41no—
368C4—42no—
369C4—41no—
370C2—22no—
371C2—44no—
372C2—81no—
373C2—82no—
374C2#1307706111yescharacteristic
375C2#1307707711yescharacteristic
376C2#1307709511yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#540C2
socleC22×C11C22×C22⋊C4
cosocleC22×C4×C11C24
hypercenterC2×#540D11
hypocenterC11#17408
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
1. #13077645C2semidirect
2. #13066976C2semidirect
3. #13066964C2semidirect
4. #13066957C2semidirect
5. #13066950C2semidirect
305. C11#17408semidirect

Maximal subgroups

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

subgroupindex
#130776452
#130669762
#130669642
#130669572
#130669502
C2×C11×#5402
#1740811