Finite Group Databasebeta

← #14759010

Subgroups — #14759010

Order 2816.

1434 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623008C211yesmaximal, characteristic
2#13071014C211yesmaximal, characteristic, complemented
3#13069589C212yesmaximal, complemented
4#13069440C212yesmaximal, complemented
5#13069044C214yesmaximal, complemented
6#13068442C214yesmaximal, complemented
7C22×C11×#97C211yesmaximal, characteristic, complemented
8C22×#4339—21no—
9C23×C8×C11C2212yes—
10C22×C42×C11C2211yescharacteristic
11C2×#66983—21no—
12C2×#66983C2212yes—
13#10623008—24no—
14#10623008C418yescomplemented
15C2×#66928—21no—
16C2×#66927C2211yescharacteristic
17C2×C4×D44—21no—
18C2×C4×D44C2212yes—
19C2×#66922C2211yescharacteristic
20C2×C11×#97—24no—
21C2×C11×#97C2212yes—
22C2×C11×#97C2212yes—
23#10622825C2212yes—
24#10622824—21no—
25C4×C22⋊Dic11—21no—
26C2×#66885C2218yes—
27#10622550—21no—
28#10622549C2212yes—
29C4×C4⋊Dic11C2212yes—
30#10622545—21no—
31#10622189C2218yes—
32C23×C4×C11D411yescharacteristic
33C23×C4×C11D411yescharacteristic
34C23×C4×C11C2311yescharacteristic
35C22×C22⋊D11—22no—
36C2×#4339—28no—
37C2×#4339—48no—
38C22×D44—21no—
39C22×D44—21no—
40C22×D44C2312yes—
41C22×C4×D11—22no—
42C22×Dic22—21no—
43C22×C8×C11—24no—
44C22×C8×C11—28no—
45C22×C8×C11C2314yes—
46C2×C42×C11C2×C414yes—
47C2×C42×C11D411yescharacteristic
48C2×C42×C11D411yescharacteristic
49C2×C42×C11D414yes—
50C2×C42×C11C2311yescharacteristic
51C2×C42×C11C2311yescharacteristic
52C2×C22⋊Dic11—22no—
53#66983—28no—
54#66983—24no—
55#66983C2×C418yes—
56C2×(C2×D11)⋊C4—22no—
57C2×(C2×D11)⋊C4—22no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11C2314yes—
60C2×C4⋊Dic11C2312yes—
61C2×C4×Dic11—22no—
62#66928—28no—
63#66927—22no—
64#66927C2×C414yes—
65C4×D44—28no—
66C4×D44—24no—
67C4×D44C2×C418yes—
68#66922—22no—
69#66922C2×C414yes—
70C11×#97—24no—
71C11×#97—24no—
72C11⋊#95—22no—
73C11⋊#95—22no—
74C11⋊#95—22no—
75C11⋊#95—22no—
76#66885—216no—
77#21408—111nomaximal, Sylow
78C24×C11C2×D411yescharacteristic
79C23×D11—22no—
80C22×C4×C11—24no—
81C22×C4×C11—24no—
82C22×C4×C11—42no—
83C22×C4×C11C22⋊C414yes—
84C22×C4×C11C22⋊C414yes—
85C22×C4×C11C22×C412yes—
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D412yes—
92C22×C4×C11C2411yescharacteristic
93C2×C22⋊D11—28no—
94C2×C22⋊D11—48no—
95C22×Dic11—22no—
96C22×Dic11—24no—
97#4339—432no—
98C2×D44—24no—
99C2×D44—24no—
100C2×D44—22no—
101C2×D44—28no—
102C2×D44—44no—
103C2×D44—44no—
104C2×D44C22×C414yes—
105C2×C4×D11—28no—
106C2×C4×D11—48no—
107C2×Dic22—24no—
108C2×Dic22—44no—
109C2×C8×C11—216no—
110C2×C8×C11—24no—
111C2×C8×C11—24no—
112C2×C8×C11#4118yescomplemented
113C42×C11C22⋊C414yes—
114C42×C11C22⋊C414yes—
115C42×C11C22×C412yes—
116C42×C11C22×C412yes—
117C42×C11C2×D412yes—
118C42×C11C2×D412yes—
119C22⋊Dic11—44no—
120(C2×D11)⋊C4—28no—
121(C2×D11)⋊C4—28no—
122C4⋊Dic11—24no—
123C4⋊Dic11—22no—
124C4⋊Dic11—28no—
125C4⋊Dic11C22×C414yes—
126C4×Dic11—44no—
127C2×#532—111no—
128C22×#97D1111yescharacteristic, complemented
129#2283—111no—
130#1993—112no—
131#1961—112no—
132#1893—114no—
133#1762—114no—
134C23×C11—22no—
135C23×C11—22no—
136C23×C11C2×C22⋊C412yes—
137C23×C11AGL(1,ℤ/8)14yes—
138C23×C11C22×D411yescharacteristic
139C22×D11—24no—
140C22×D11—44no—
141C22×D11—44no—
142C22×D11—44no—
143C2×C4×C11—22no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—22no—
147C2×C4×C11—22no—
148C2×C4×C11—28no—
149C2×C4×C11—24no—
150C2×C4×C11—24no—
151C2×C4×C11—44no—
152C2×C4×C11C2×C22⋊C412yes—
153C2×C4×C11C2×C22⋊C412yes—
154C2×C4×C11C2×C22⋊C412yes—
155C2×C4×C11C2×C22⋊C412yes—
156C2×C4×C11C2×C22⋊C412yes—
157C2×C4×C11C23×C411yescharacteristic
158C2×C4×C11C22×D411yescharacteristic
159C2×C4×C11C2×#4114yes—
160C22⋊D11—416no—
161C2×Dic11—24no—
162C2×Dic11—44no—
163C2×Dic11—44no—
164C2×Dic11—44no—
165C2×Dic11—44no—
166D44—28no—
167D44—48no—
168D44—48no—
169D44—44no—
170C4×D11—416no—
171Dic22—48no—
172C8×C11—28no—
173C22×#41—221no—
174C23×C8C2×D1112yes—
175#532—118no—
176#532—224no—
177C2×C4⋊Q8—111no—
178C2×#127—111no—
179C2×#124—221no—
180C2×#121—112no—
181C2×#121—221no—
182C2×C4×D4—112no—
183C2×C4×D4—221no—
184C22×C42C2×D1111yescharacteristic
185C2×#102—118no—
186C2×#97—24no—
187C2×#97C2×D1112yes—
188C2×#97C2×D1112yes—
189#383—221no—
190#382—112no—
191#381—221no—
192#380—112no—
193C4×C4⋊C4—112no—
194C4×C22⋊C4—221no—
195#376—221no—
196#340—118no—
197C22×C11—22no—
198C22×C11—28no—
199C22×C11—22no—
200C22×C11#41814yes—
201C22×C11C22×C22⋊C411yescharacteristic
202C22×C11#53212yes—
203C22×C11C2×AGL(1,ℤ/8)12yes—
204C22×C11#57512yes—
205C2×D11—44no—
206C2×D11—44no—
207C2×D11—44no—
208C2×D11—88no—
209C4×C11—22no—
210C4×C11—22no—
211C4×C11—22no—
212C4×C11—22no—
213C4×C11—22no—
214C4×C11C4×#4112yes—
215C4×C11#52512yes—
216Dic11—44no—
217Dic11—84no—
218C2×#41—228no—
219C2×#41—448no—
220C22×Q8—221no—
221C22×D4—112no—
222C22×D4—222no—
223C22×D4—221no—
224C22×D4—221no—
225C23×C4—222no—
226C23×C4D4411yescharacteristic
227C23×C4D4411yescharacteristic
228C23×C4C22×D1111yescharacteristic
229C22×C8—24no—
230C22×C8—28no—
231C22×C8C22×D1114yes—
232C4⋊Q8—114no—
233C4⋊Q8—222no—
234#127—114no—
235#127—222no—
236#124—228no—
237#121—118no—
238#121—228no—
239#121—224no—
240C4×D4—118no—
241C4×D4—228no—
242C4×D4—224no—
243C2×C4⋊C4—112no—
244C2×C4⋊C4—114no—
245C2×C4⋊C4—221no—
246C2×C22⋊C4—222no—
247C2×C22⋊C4—222no—
248C2×C22⋊C4—222no—
249C2×C42—222no—
250C2×C42C4×D1114yes—
251C2×C42D4411yescharacteristic
252C2×C42D4411yescharacteristic
253C2×C42C22⋊D1114yes—
254C2×C42C22×D1111yescharacteristic
255C2×C42C22×D1111yescharacteristic
256#102—2216no—
257#97—24no—
258#97—24no—
259#95—222no—
260#95—222no—
261#95—222no—
262#95—222no—
263C2×C11—24no—
264C2×C11#229711yescharacteristic
265C2×C11C2×#41811yescharacteristic
266C2×C11#289611yescharacteristic
267C2×C11#318014yes—
268D11—84no—
269C24—222no—
270C24C2×D4411yescharacteristic
271#41—4432no—
272C2×Q8—224no—
273C2×Q8—444no—
274C2×D4—114no—
275C2×D4—228no—
276C2×D4—224no—
277C2×D4—224no—
278C2×D4—228no—
279C2×D4—222no—
280C2×D4—444no—
281C2×D4—444no—
282C2×D4—448no—
283C22×C4—24no—
284C22×C4—24no—
285C22×C4—42no—
286C22×C4—222no—
287C22×C4—228no—
288C22×C4—224no—
289C22×C4—448no—
290C22×C4(C2×D11)⋊C414yes—
291C22×C4(C2×D11)⋊C414yes—
292C22×C4C2×C4×D1112yes—
293C22×C4C2×D4411yescharacteristic
294C22×C4C2×D4411yescharacteristic
295C22×C4C2×D4411yescharacteristic
296C22×C4C2×D4411yescharacteristic
297C22×C4C2×D4411yescharacteristic
298C22×C4C2×C22⋊D1112yes—
299C22×C4C23×D1111yescharacteristic
300C2×C8—216no—
301C2×C8—24no—
302C2×C8—24no—
303C2×C8#433918yescomplemented
304C4⋊C4—114no—
305C4⋊C4—224no—
306C4⋊C4—222no—
307C4⋊C4—228no—
308C22⋊C4—228no—
309C22⋊C4—228no—
310C22⋊C4—444no—
311C42—444no—
312C42(C2×D11)⋊C414yes—
313C42(C2×D11)⋊C414yes—
314C42C2×C4×D1112yes—
315C42C2×C4×D1112yes—
316C42C2×C22⋊D1112yes—
317C42C2×C22⋊D1112yes—
318C11#2140811yescharacteristic, complemented, Sylow
319C23—22no—
320C23—22no—
321C23—224no—
322C23—444no—
323C23—444no—
324C23—444no—
325C23#6696114yes—
326C23C2×(C2×D11)⋊C412yes—
327C23C22×D4411yescharacteristic
328Q8—448no—
329D4—228no—
330D4—448no—
331D4—448no—
332D4—4416no—
333D4—444no—
334C2×C4—28no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—24no—
341C2×C4—24no—
342C2×C4—44no—
343C2×C4—224no—
344C2×C4—4416no—
345C2×C4—444no—
346C2×C4—444no—
347C2×C4—444no—
348C2×C4—444no—
349C2×C4C2×(C2×D11)⋊C412yes—
350C2×C4C2×(C2×D11)⋊C412yes—
351C2×C4C2×(C2×D11)⋊C412yes—
352C2×C4C2×(C2×D11)⋊C412yes—
353C2×C4C2×(C2×D11)⋊C412yes—
354C2×C4C22×C4×D1111yescharacteristic
355C2×C4C2×#433914yes—
356C2×C4C22×C22⋊D1111yescharacteristic
357C8—28no—
358C22—22no—
359C22—28no—
360C22—22no—
361C22—444no—
362C22—444no—
363C22—444no—
364C22—888no—
365C22#1062274414yes—
366C22#1062300812yes—
367C22C2×#6696112yes—
368C22#1062327912yes—
369C22C22×(C2×D11)⋊C411yescharacteristic
370C4—22no—
371C4—22no—
372C4—22no—
373C4—22no—
374C4—22no—
375C4—444no—
376C4—884no—
377C4C4×#433912yes—
378C4#1062332212yes—
379C2—24no—
380C2—884no—
381C2#1307110611yescharacteristic
382C2C2×#1062274411yescharacteristic
383C2#1307713611yescharacteristic
384C2#1307931414yes—
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×#97C2
socleC23×C11C22×D4
prime radicalC2×#10623008C2
cosocleC22×C4×C11C24
hypercenterC22×#97D11
hypocenterC11#21408
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×#97

Complements

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

NH ≅ G/Ntype
2. #13071014C2semidirect
3. #13069589C2semidirect
4. #13069440C2semidirect
5. #13069044C2semidirect
6. #13068442C2semidirect
7. C22×C11×#97C2semidirect
14. #10623008C4semidirect
112. C2×C8×C11#41semidirect
128. C22×#97D11semidirect
303. C2×C8#4339semidirect
318. C11#21408semidirect

Maximal subgroups

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

subgroupindex
C2×#106230082
#130710142
#130695892
#130694402
#130690442
#130684422
C22×C11×#972
#2140811