Finite Group Databasebeta

← #14719823

Subgroups — #14719823

Order 2816.

1040 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623093C211yesmaximal, characteristic
2#13077640C211yesmaximal, characteristic, complemented
3#13066977C214yesmaximal, complemented
4#13066965C214yesmaximal, complemented
5#13066936C212yesmaximal, complemented
6#13066928C212yesmaximal, complemented
7C11×#2975C211yesmaximal, characteristic, complemented
8C2×C4×D4×C11C2211yescharacteristic
9C2×#66993C411yescharacteristic
10C2×#66991C411yescharacteristic
11C2×#66983C2212yes—
12C2×#66982C2212yes—
13#10623093—24no—
14#10623093—24no—
15C2×#66948C411yescharacteristic
16C2×#66943C411yescharacteristic
17C2×#66937C412yes—
18C2×#66936C412yes—
19C2×C4×D44C2211yescharacteristic
20C2×#66925C2211yescharacteristic
21C11×#436—24no—
22C11×#431C2212yes—
23C11×#407C2214yes—
24C2×C22⋊(C11⋊C8)C2214yes—
25D4×C11⋊C8—24no—
26#10622538C2212yes—
27#10622107C2214yes—
28#10622106C2214yes—
29#10622106C2218yes—
30C22×D4×C11C2×C411yescharacteristic
31C23×C4×C11C2312yes—
32C22×C22⋊D11C2×C412yes—
33C22×C22⋊D11C2×C412yes—
34C22×C22⋊D11C2×C412yes—
35C22×D44C2×C411yescharacteristic
36C22×D44C2×C412yes—
37C22×C4×D11C2×C411yescharacteristic
38C22×C4×D11C2×C412yes—
39C2×C11×M16—24no—
40C4×D4×C11D414yes—
41C4×D4×C11D414yes—
42C2×C11×C4⋊C4C2×C411yescharacteristic
43C2×C11×C22⋊C4C2×C412yes—
44C2×C42×C11C2311yescharacteristic
45C2×C22⋊Dic11C2×C412yes—
46#66993—24no—
47#66991—24no—
48#66983—24no—
49#66983—24no—
50#66982—24no—
51#66982—24no—
52C2×(C2×D11)⋊C4C2×C411yescharacteristic
53C2×(C2×D11)⋊C4C2×C412yes—
54C2×(C2×D11)⋊C4C2311yescharacteristic
55C2×(C2×D11)⋊C4C2312yes—
56C2×C4⋊Dic11C2×C411yescharacteristic
57C2×C4⋊Dic11C2×C412yes—
58C2×Dic11⋊C4C2×C411yescharacteristic
59C2×Dic11⋊C4C2×C412yes—
60C2×Dic11⋊C4C2311yescharacteristic
61C2×C4×Dic11C2×C411yescharacteristic
62C22×C11⋊C8—24no—
63#66948—24no—
64#66943—24no—
65#66937—28no—
66#66936—28no—
67C4×D44—22no—
68C4×D44—22no—
69#66925—22no—
70#66925—22no—
71C11×C4⋊C8—22no—
72C11×C22⋊C8—24no—
73C11×C22⋊C8C2314yes—
74C4×C8×C11—22no—
75C22⋊(C11⋊C8)—24no—
76C22⋊(C11⋊C8)C2314yes—
77C4⋊(C11⋊C8)—22no—
78C4×C11⋊C8—22no—
79#17389—111nomaximal, Sylow
80C24×C11C22×C412yes—
81C23×D11C22×C411yescharacteristic
82C23×D11C22×C412yes—
83C2×D4×C11—24no—
84C2×D4×C11C22⋊C414yes—
85C22×C4×C11—82no—
86C22×C4×C11C22×C412yes—
87C22×C4×C11C22×C411yescharacteristic
88C22×C4×C11C22×C411yescharacteristic
89C22×C4×C11C2×D414yes—
90C22×C4×C11C2×D414yes—
91C22×C4×C11C2411yescharacteristic
92C2×C22⋊D11—24no—
93C2×C22⋊D11—24no—
94C2×C22⋊D11—24no—
95C2×C22⋊D11—82no—
96C2×C22⋊D11—82no—
97C2×C22⋊D11—82no—
98C22×Dic11C22×C411yescharacteristic
99C22×Dic11C22×C411yescharacteristic
100C22×Dic11C22×C411yescharacteristic
101C22×Dic11C22×C412yes—
102C2×D44—22no—
103C2×D44—24no—
104C2×D44—24no—
105C2×D44—82no—
106C2×C4×D11—22no—
107C2×C4×D11—24no—
108C2×C4×D11—24no—
109C2×C4×D11—82no—
110C11×M16—84no—
111C2×C8×C11—24no—
112C11×C4⋊C4C22⋊C414yes—
113C11×C22⋊C4C22⋊C418yes—
114C42×C11C2×D412yes—
115C42×C11C2×D412yes—
116C22⋊Dic11—24no—
117(C2×D11)⋊C4—22no—
118(C2×D11)⋊C4—24no—
119(C2×D11)⋊C4—21no—
120(C2×D11)⋊C4—21no—
121(C2×D11)⋊C4—22no—
122(C2×D11)⋊C4—22no—
123C4⋊Dic11—22no—
124C4⋊Dic11—24no—
125Dic11⋊C4—22no—
126Dic11⋊C4—24no—
127Dic11⋊C4—21no—
128Dic11⋊C4—21no—
129C4×Dic11—22no—
130C2×C11⋊C8—24no—
131C2×C11⋊C8—84no—
132C2×#540—111no—
133#2975D1111yescharacteristic, complemented
134#2972—111no—
135#1471—114no—
136#1468—114no—
137#1460—112no—
138#1458—112no—
139C23×C11—24no—
140C23×C11—42no—
141C23×C11—42no—
142C23×C11C2×C22⋊C414yes—
143C23×C11C23×C411yescharacteristic
144C22×D11—21no—
145C22×D11—22no—
146C22×D11—22no—
147C22×D11—24no—
148C22×D11—42no—
149C22×D11—41no—
150C22×D11—42no—
151C22×D11—41no—
152D4×C11—28no—
153C2×C4×C11—44no—
154C2×C4×C11—44no—
155C2×C4×C11—41no—
156C2×C4×C11—42no—
157C2×C4×C11—41no—
158C2×C4×C11C2×C22⋊C414yes—
159C2×C4×C11C2×C22⋊C412yes—
160C2×C4×C11C2×C22⋊C412yes—
161C2×C4×C11#13114yes—
162C2×C4×C11C22×D411yescharacteristic
163C2×C4×C11C22×D411yescharacteristic
164C22⋊D11—84no—
165C22⋊D11—84no—
166C22⋊D11—84no—
167C2×Dic11—21no—
168C2×Dic11—21no—
169C2×Dic11—21no—
170C2×Dic11—22no—
171C2×Dic11—22no—
172C2×Dic11—42no—
173C2×Dic11—41no—
174C2×Dic11—41no—
175D44—44no—
176D44—84no—
177C4×D11—44no—
178C4×D11—84no—
179C8×C11—44no—
180C11⋊C8—44no—
181#540—224no—
182#540—224no—
183C2×#127—111no—
184C2×#125—111no—
185C2×#123—112no—
186C2×#123—112no—
187C2×#121—111no—
188C2×#121—112no—
189C2×#121—111no—
190C2×#121—112no—
191C2×C4×D4—111no—
192C2×C4×D4C2×D1111yescharacteristic
193C2×#117—111no—
194#436—24no—
195C8×D4—224no—
196#431—112no—
197#431C2×D1112yes—
198#407C2×D1114yes—
199C2×C22⋊C8—114no—
200#324—114no—
201#323—114no—
202#323—118no—
203C22×C11—21no—
204C22×C11—21no—
205C22×C11—24no—
206C22×C11—24no—
207C22×C11—24no—
208C22×C11—84no—
209C22×C11C22×C22⋊C411yescharacteristic
210C22×C11C2×#13112yes—
211C2×D11—41no—
212C2×D11—42no—
213C2×D11—41no—
214C2×D11—42no—
215C2×D11—42no—
216C2×D11—41no—
217C2×D11—82no—
218C2×D11—84no—
219C4×C11—21no—
220C4×C11—21no—
221C4×C11—24no—
222C4×C11—22no—
223C4×C11#40814yes—
224Dic11—41no—
225Dic11—41no—
226Dic11—42no—
227Dic11—41no—
228C22×D4—112no—
229C22×D4—112no—
230C22×D4—112no—
231C22×D4—111no—
232C22×D4—112no—
233C22×D4C4×D1111yescharacteristic
234C23×C4—111no—
235C23×C4—112no—
236C23×C4C22×D1112yes—
237C2×M16—24no—
238C22×C8—224no—
239#127—224no—
240#125—224no—
241#123—224no—
242#123—224no—
243#123—228no—
244#121—224no—
245#121—224no—
246#121—224no—
247#121—224no—
248#121—228no—
249C4×D4—222no—
250C4×D4—222no—
251C4×D4D4414yes—
252C4×D4C22⋊D1114yes—
253#117—222no—
254#117—222no—
255C2×C4⋊C4—111no—
256C2×C4⋊C4—111no—
257C2×C4⋊C4—112no—
258C2×C4⋊C4—112no—
259C2×C4⋊C4—111no—
260C2×C4⋊C4C4×D1111yescharacteristic
261C2×C22⋊C4—112no—
262C2×C22⋊C4—111no—
263C2×C22⋊C4—112no—
264C2×C22⋊C4—111no—
265C2×C22⋊C4—112no—
266C2×C22⋊C4C4×D1112yes—
267C2×C42—111no—
268C2×C42C22×D1111yescharacteristic
269C4⋊C8—22no—
270C4⋊C8—222no—
271C22⋊C8—24no—
272C22⋊C8—114no—
273C22⋊C8—224no—
274C22⋊C8C22×D1114yes—
275C4×C8—22no—
276C4×C8—222no—
277C2×C11—22no—
278C2×C11—44no—
279C2×C11C2×#40811yescharacteristic
280C2×C11#288311yescharacteristic
281C2×C11#288811yescharacteristic
282D11—81no—
283D11—82no—
284C24—111no—
285C24—112no—
286C24C2×C4×D1112yes—
287C2×D4—24no—
288C2×D4—224no—
289C2×D4—224no—
290C2×D4—224no—
291C2×D4—224no—
292C2×D4—222no—
293C2×D4—224no—
294C2×D4—882no—
295C2×D4—882no—
296C2×D4—882no—
297C2×D4—882no—
298C2×D4(C2×D11)⋊C414yes—
299C22×C4—82no—
300C22×C4—111no—
301C22×C4—111no—
302C22×C4—111no—
303C22×C4—112no—
304C22×C4—224no—
305C22×C4—222no—
306C22×C4—224no—
307C22×C4—882no—
308C22×C4C2×C4×D1111yescharacteristic
309C22×C4C2×C4×D1112yes—
310C22×C4C2×C4×D1111yescharacteristic
311C22×C4C2×D4414yes—
312C22×C4C2×C22⋊D1114yes—
313C22×C4C23×D1111yescharacteristic
314M16—84no—
315C2×C8—24no—
316C2×C8—224no—
317C2×C8—884no—
318C4⋊C4—222no—
319C4⋊C4—222no—
320C4⋊C4—224no—
321C4⋊C4—224no—
322C4⋊C4—221no—
323C4⋊C4—221no—
324C4⋊C4(C2×D11)⋊C414yes—
325C22⋊C4—224no—
326C22⋊C4—222no—
327C22⋊C4—224no—
328C22⋊C4—221no—
329C22⋊C4—222no—
330C22⋊C4—221no—
331C22⋊C4—222no—
332C22⋊C4(C2×D11)⋊C418yes—
333C42—222no—
334C42C2×D4412yes—
335C42C2×C22⋊D1112yes—
336C11#1738911yescharacteristic, complemented, Sylow
337C23—24no—
338C23—42no—
339C23—42no—
340C23—221no—
341C23—222no—
342C23—222no—
343C23—224no—
344C23—442no—
345C23—441no—
346C23—442no—
347C23—441no—
348C23C2×(C2×D11)⋊C414yes—
349C23C22×C4×D1111yescharacteristic
350D4—28no—
351D4—444no—
352D4—884no—
353D4—884no—
354D4—884no—
355D4—884no—
356C2×C4—44no—
357C2×C4—44no—
358C2×C4—41no—
359C2×C4—42no—
360C2×C4—41no—
361C2×C4—222no—
362C2×C4—221no—
363C2×C4—221no—
364C2×C4—221no—
365C2×C4—222no—
366C2×C4—444no—
367C2×C4—442no—
368C2×C4—441no—
369C2×C4—441no—
370C2×C4—884no—
371C2×C4#6696014yes—
372C2×C4C2×(C2×D11)⋊C412yes—
373C2×C4C2×(C2×D11)⋊C414yes—
374C2×C4C2×(C2×D11)⋊C412yes—
375C2×C4C22×D4411yescharacteristic
376C2×C4C22×C22⋊D1111yescharacteristic
377C8—44no—
378C8—444no—
379C22—21no—
380C22—21no—
381C22—24no—
382C22—24no—
383C22—24no—
384C22—84no—
385C22—441no—
386C22—442no—
387C22—441no—
388C22—442no—
389C22—442no—
390C22—441no—
391C22—882no—
392C22—884no—
393C22C2×#6696012yes—
394C22C22×(C2×D11)⋊C411yescharacteristic
395C4—21no—
396C4—21no—
397C4—24no—
398C4—22no—
399C4—441no—
400C4—441no—
401C4—442no—
402C4—441no—
403C4#1062274214yes—
404C2—22no—
405C2—44no—
406C2—881no—
407C2—882no—
408C2C2×#1062274211yescharacteristic
409C2#1307707611yescharacteristic
410C2#1307709411yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2975C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#10623093C2
cosocleC22×C4×C11C24
hypercenter#2975D11
hypocenterC11#17389
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2975

Complements

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

NH ≅ G/Ntype
2. #13077640C2semidirect
3. #13066977C2semidirect
4. #13066965C2semidirect
5. #13066936C2semidirect
6. #13066928C2semidirect
7. C11×#2975C2semidirect
133. #2975D11semidirect
336. C11#17389semidirect

Maximal subgroups

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

subgroupindex
C2×#106230932
#130776402
#130669772
#130669652
#130669362
#130669282
C11×#29752
#1738911