Finite Group Databasebeta

← #14757276

Subgroups — #14757276

Order 2816.

990 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622734C211yesmaximal, characteristic
2C22×#66881C211yesmaximal, characteristic
3#13071239C211yesmaximal, characteristic
4#13070972C211yesmaximal, characteristic
5#13069386C214yesmaximal, complemented
6#13069380C214yesmaximal, complemented
7#13068336C211yesmaximal, characteristic
8#13068333C211yesmaximal, characteristic
9C2×C11×#424C211yesmaximal, characteristic
10C22×C11×M16C2211yescharacteristic
11C23×C8×C11C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13C2×#66979C2211yescharacteristic
14C2×#66979C2211yescharacteristic
15C22×C4⋊Dic11C2211yescharacteristic
16C22×C4⋊Dic11C2211yescharacteristic
17C11×#424C418yescomplemented
18C2×C11×C4⋊C8C2214yes—
19#10622734—24no—
20C2×#66882C2212yes—
21C2×#66881—24no—
22C2×#66881C2212yes—
23C2×#66881C2214yes—
24#10622598—22no—
25C4⋊C4×Dic11—22no—
26#10622563—22no—
27C22⋊C4×Dic11—22no—
28#10622549C2212yes—
29#10622548C2212yes—
30C4×C4⋊Dic11C2214yes—
31#10622189C2212yes—
32#10622189C2212yes—
33#10622189C2214yes—
34C23×C4×C11C2311yescharacteristic
35C23×Dic11—21no—
36C23×Dic11—21no—
37C2×C11×M16—22no—
38C2×C11×M16—22no—
39C2×C11×M16C2×C414yes—
40C22×C8×C11—22no—
41C22×C8×C11—22no—
42C22×C8×C11C2×C414yes—
43C22×C8×C11C2312yes—
44C22×C8×C11C2312yes—
45C11×#117C2×C414yes—
46C11×#117Q814yes—
47C2×C11×C4⋊C4D412yes—
48C2×C11×C22⋊C4D412yes—
49C2×C42×C11C2312yes—
50C2×C22⋊Dic11—21no—
51C2×C22⋊Dic11—21no—
52#66979—22no—
53#66979—22no—
54#66979—22no—
55#66979Q814yes—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11—22no—
58C2×C4⋊Dic11—22no—
59C2×C4⋊Dic11—22no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11—24no—
62C2×C4⋊Dic11D414yes—
63C2×C4⋊Dic11C2311yescharacteristic
64C2×C4⋊Dic11C2312yes—
65C2×C4⋊Dic11C2311yescharacteristic
66C2×C4⋊Dic11C2312yes—
67C2×C4⋊Dic11C2312yes—
68C2×C4×Dic11—21no—
69C2×C4×Dic11—21no—
70C2×C4×Dic11—24no—
71C11×C4⋊C8C2×C4116yescomplemented
72C11⋊#95—24no—
73C11⋊#95—24no—
74#66882—24no—
75#66881—24no—
76#66881—28no—
77#21174—111nomaximal, Sylow
78C24×C11C2×D411yescharacteristic
79C22×C4×C11C22×C412yes—
80C22×C4×C11C2×D414yes—
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D412yes—
83C22×C4×C11C2×Q812yes—
84C22×C4×C11C2×Q812yes—
85C22×C4×C11#4112yes—
86C22×C4×C11#4112yes—
87C22×C4×C11C2411yescharacteristic
88C22×Dic11—24no—
89C22×Dic11—22no—
90C22×Dic11—22no—
91C22×Dic11—21no—
92C22×Dic11—22no—
93C22×Dic11—21no—
94C22×Dic11—42no—
95C22×Dic11—82no—
96C22×Dic11—82no—
97C11×M16—28no—
98C2×C8×C11—28no—
99C2×C8×C11—22no—
100C2×C8×C11—22no—
101C2×C8×C11—22no—
102C2×C8×C11—22no—
103C2×C8×C11C22×C414yes—
104C2×C8×C11C22×C414yes—
105C11×C4⋊C4C4⋊C418yes—
106C11×C22⋊C4C4⋊C418yes—
107C42×C11C22×C414yes—
108C42×C11C2×Q814yes—
109C22⋊Dic11—24no—
110C22⋊Dic11—42no—
111C4⋊Dic11—24no—
112C4⋊Dic11—22no—
113C4⋊Dic11—21no—
114C4⋊Dic11—21no—
115C4⋊Dic11—22no—
116C4⋊Dic11—22no—
117C4⋊Dic11—22no—
118C4⋊Dic11—21no—
119C4⋊Dic11—21no—
120C4⋊Dic11—42no—
121C4⋊Dic11—84no—
122C4⋊Dic11C2×D414yes—
123C4⋊Dic11C2×Q814yes—
124C4×Dic11—24no—
125C4×Dic11—42no—
126C4×Dic11—84no—
127C2×#428—111no—
128C22×#106—111no—
129C2×#424D1111yescharacteristic
130#2317—111no—
131#2274—111no—
132#1949—114no—
133#1948—114no—
134#1736—111no—
135#1735—111no—
136C23×C11—22no—
137C23×C11—22no—
138C23×C11C2×C4⋊C412yes—
139C23×C11#12112yes—
140C23×C11C22⋊Q812yes—
141C23×C11C22×D411yescharacteristic
142C2×C4×C11—24no—
143C2×C4×C11—24no—
144C2×C4×C11C2×C4⋊C418yes—
145C2×C4×C11C2×C4⋊C412yes—
146C2×C4×C11C4×D414yes—
147C2×C4×C11C4×Q814yes—
148C2×C4×C11#12112yes—
149C2×C4×C11C22⋊Q812yes—
150C2×C4×C11#12514yes—
151C2×C4×C11C4⋊Q814yes—
152C2×C4×C11C23×C411yescharacteristic
153C2×C4×C11C22×D411yescharacteristic
154C2×C4×C11C22×Q811yescharacteristic
155C2×C4×C11C22×Q811yescharacteristic
156C2×C4×C11C2×#4111yescharacteristic
157C2×C4×C11C2×#4111yescharacteristic
158C2×Dic11—24no—
159C2×Dic11—24no—
160C2×Dic11—42no—
161C2×Dic11—44no—
162C2×Dic11—42no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—42no—
166C2×Dic11—42no—
167C2×Dic11—44no—
168C2×Dic11—42no—
169C2×Dic11—84no—
170C2×Dic11—84no—
171C8×C11—24no—
172C8×C11—24no—
173C22×M16C2×D1111yescharacteristic
174C23×C8C2×D1111yescharacteristic
175C2×#117—111no—
176C2×#117—111no—
177C2×#117C2×D1111yescharacteristic
178C22×C4⋊C4—111no—
179C22×C4⋊C4—111no—
180#428—224no—
181C2×#107—112no—
182C2×#106—114no—
183C2×#106—112no—
184C2×#106—224no—
185#424Dic1118yescomplemented
186C2×C4⋊C8C2×D1114yes—
187#389—222no—
188#385—222no—
189#384—112no—
190#382—112no—
191C4×C4⋊C4—114no—
192C4×C4⋊C4—222no—
193C4×C22⋊C4—222no—
194#340—112no—
195#340—114no—
196#340—112no—
197C22×C11—24no—
198C22×C11—24no—
199C22×C11—22no—
200C22×C11—22no—
201C22×C11#38914yes—
202C22×C11C22×C4⋊C411yescharacteristic
203C22×C11C2×#12111yescharacteristic
204C22×C11C2×C22⋊Q811yescharacteristic
205C22×C11#57712yes—
206C22×C11#57712yes—
207C4×C11—28no—
208C4×C11#38914yes—
209C4×C11C2×C4×D411yescharacteristic
210C4×C11C2×C4×Q811yescharacteristic
211C4×C11C2×#12511yescharacteristic
212C4×C11C2×C4⋊Q811yescharacteristic
213Dic11—44no—
214Dic11—44no—
215Dic11—81no—
216Dic11—81no—
217Dic11—82no—
218C23×C4—221no—
219C23×C4—221no—
220C23×C4C22×D1111yescharacteristic
221C2×M16—22no—
222C2×M16—22no—
223C2×M16C2×Dic1114yes—
224C22×C8—22no—
225C22×C8—22no—
226C22×C8C2×Dic1114yes—
227C22×C8C22×D1112yes—
228C22×C8C22×D1112yes—
229#117—114no—
230#117—222no—
231#117—222no—
232#117—222no—
233#117Dic2214yes—
234#117C2×Dic1114yes—
235C2×C4⋊C4—114no—
236C2×C4⋊C4—112no—
237C2×C4⋊C4—112no—
238C2×C4⋊C4—112no—
239C2×C4⋊C4—111no—
240C2×C4⋊C4—111no—
241C2×C4⋊C4—221no—
242C2×C4⋊C4—222no—
243C2×C4⋊C4—222no—
244C2×C4⋊C4—222no—
245C2×C4⋊C4—221no—
246C2×C4⋊C4—224no—
247C2×C4⋊C4D4412yes—
248C2×C22⋊C4—221no—
249C2×C22⋊C4—221no—
250C2×C22⋊C4D4412yes—
251C2×C42—221no—
252C2×C42—221no—
253C2×C42—224no—
254C2×C42C22×D1112yes—
255#107—224no—
256#106—228no—
257#106—224no—
258C4⋊C8C2×Dic11116yescomplemented
259#95—224no—
260#95—224no—
261C2×C11—24no—
262C2×C11C2×#38911yescharacteristic
263C2×C11#291212yes—
264C2×C11#304211yescharacteristic
265C2×C11#304311yescharacteristic
266C2×C11#308412yes—
267C24C2×D4411yescharacteristic
268C22×C4—222no—
269C22×C4—222no—
270C22×C4—224no—
271C22×C4—221no—
272C22×C4—222no—
273C22×C4—221no—
274C22×C4—442no—
275C22×C4—882no—
276C22×C4—882no—
277C22×C4C2×Dic2212yes—
278C22×C4C2×D4414yes—
279C22×C4C2×D4411yescharacteristic
280C22×C4D4×D1112yes—
281C22×C4#434112yes—
282C22×C4Q8×D1112yes—
283C22×C4#434312yes—
284C22×C4C22×Dic1112yes—
285C22×C4C23×D1111yescharacteristic
286M16—28no—
287C2×C8—28no—
288C2×C8—22no—
289C2×C8—22no—
290C2×C8—22no—
291C2×C8—22no—
292C2×C8C22×Dic1114yes—
293C2×C8C22×Dic1114yes—
294C4⋊C4—114no—
295C4⋊C4—114no—
296C4⋊C4—224no—
297C4⋊C4—222no—
298C4⋊C4—222no—
299C4⋊C4—222no—
300C4⋊C4—221no—
301C4⋊C4—221no—
302C4⋊C4—222no—
303C4⋊C4—221no—
304C4⋊C4—221no—
305C4⋊C4—442no—
306C4⋊C4—884no—
307C4⋊C4C4⋊Dic1118yes—
308C22⋊C4—224no—
309C22⋊C4—442no—
310C22⋊C4C4⋊Dic1118yes—
311C42—224no—
312C42—442no—
313C42—884no—
314C42C2×Dic2214yes—
315C42C22×Dic1114yes—
316C11#2117411yescharacteristic, complemented, Sylow
317C23—22no—
318C23—22no—
319C23#6694812yes—
320C23#6695012yes—
321C23C2×C4⋊Dic1112yes—
322C23C22×D4411yescharacteristic
323C2×C4—24no—
324C2×C4—24no—
325C2×C4—224no—
326C2×C4—224no—
327C2×C4—442no—
328C2×C4—444no—
329C2×C4—442no—
330C2×C4—442no—
331C2×C4—444no—
332C2×C4—442no—
333C2×C4—441no—
334C2×C4—441no—
335C2×C4—442no—
336C2×C4—884no—
337C2×C4—884no—
338C2×C4#6694114yes—
339C2×C4#6694314yes—
340C2×C4#6694812yes—
341C2×C4#6695012yes—
342C2×C4C2×C4⋊Dic1118yes—
343C2×C4C2×C4⋊Dic1112yes—
344C2×C4D4×Dic1114yes—
345C2×C4Q8×Dic1114yes—
346C2×C4C22×Dic2211yescharacteristic
347C2×C4C2×D4×D1111yescharacteristic
348C2×C4C2×#434111yescharacteristic
349C2×C4C2×Q8×D1111yescharacteristic
350C2×C4C2×#434311yescharacteristic
351C2×C4C23×Dic1111yescharacteristic
352C8—24no—
353C8—24no—
354C22—22no—
355C22—22no—
356C22—24no—
357C22—24no—
358C22#1062259814yes—
359C22C2×#6694811yescharacteristic
360C22C2×#6695011yescharacteristic
361C22#1062328212yes—
362C22#1062328212yes—
363C22C22×C4⋊Dic1111yescharacteristic
364C4—28no—
365C4—444no—
366C4—444no—
367C4—881no—
368C4—882no—
369C4—881no—
370C4#1062259814yes—
371C4C2×#6694111yescharacteristic
372C4C2×#6694311yescharacteristic
373C4C2×D4×Dic1111yescharacteristic
374C4C2×Q8×Dic1111yescharacteristic
375C2—24no—
376C2C2×#1062259811yescharacteristic
377C2#1307721112yes—
378C2#1307812911yescharacteristic
379C2#1307813811yescharacteristic
380C2#1307848012yes—
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#424C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC2×#424D11
hypocenterC11#21174
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#424

Complements

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

NH ≅ G/Ntype
5. #13069386C2semidirect
6. #13069380C2semidirect
17. C11×#424C4semidirect
71. C11×C4⋊C8C2×C4semidirect
185. #424Dic11semidirect
258. C4⋊C8C2×Dic11semidirect
316. C11#21174semidirect

Maximal subgroups

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

subgroupindex
C2×#106227342
C22×#668812
#130712392
#130709722
#130693862
#130693802
#130683362
#130683332
C2×C11×#4242
#2117411