Finite Group Databasebeta

← #14763259

Subgroups — #14763259

Order 2816.

1302 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66941C211yesmaximal, characteristic
2C2×#10622331C211yesmaximal, characteristic
3#13071018C211yesmaximal, characteristic
4#13069575C214yesmaximal, complemented
5#13069562C214yesmaximal, complemented
6#13068707C211yesmaximal, characteristic
7#13068706C211yesmaximal, characteristic
8#13068704C211yesmaximal, characteristic
9C11×#1824C211yesmaximal, characteristic
10C23×Dic22—21no—
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C4⋊Dic11C2211yescharacteristic
13C22×Dic11⋊C4—21no—
14C22×C4×Dic11C2211yescharacteristic
15C2×#66941—21no—
16C2×#66941—21no—
17C2×#66941—24no—
18C2×#66941C418yescomplemented
19C2×#66941C2212yes—
20C2×#66941C2212yes—
21C2×#66930—21no—
22C2×C11×C22⋊C8C2211yescharacteristic
23C11×#380C2211yescharacteristic
24#10622825C2211yescharacteristic
25C2×C22⋊(C11⋊C8)C2211yescharacteristic
26C2×Dic11⋊C8C2212yes—
27C2×C8×Dic11C2212yes—
28#10622589C2212yes—
29C4⋊C4×Dic11C2212yes—
30#10622555—21no—
31#10622331—24no—
32#10622263—21no—
33#10622262—21no—
34C11×#340C2214yes—
35#10622189C2214yes—
36#10622167C2214yes—
37#10622167C2214yes—
38C23×C4×C11—21no—
39C23×C4×C11C2311yescharacteristic
40C23×Dic11—21no—
41C23×Dic11D411yescharacteristic
42C23×Dic11D411yescharacteristic
43C22×Dic22—28no—
44C22×Dic22—22no—
45C22×Dic22—22no—
46C22×Dic22—48no—
47C22×C8×C11C2312yes—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4C2×C414yes—
51C2×C11×C4⋊C4C2312yes—
52C2×C11×C4⋊C4C2312yes—
53C2×C11×C22⋊C4—21no—
54C2×C22⋊Dic11—21no—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11—22no—
57C2×C4⋊Dic11C2×C414yes—
58C2×C4⋊Dic11C2312yes—
59C2×C4⋊Dic11C2312yes—
60C2×Dic11⋊C4—28no—
61C2×Dic11⋊C4—22no—
62C2×Dic11⋊C4—22no—
63C2×Dic11⋊C4—22no—
64C2×Dic11⋊C4—22no—
65C2×C4×Dic11—22no—
66C2×C4×Dic11C2×C414yes—
67C2×C4×Dic11D411yescharacteristic
68C2×C4×Dic11D411yescharacteristic
69C2×C4×Dic11D414yes—
70C2×C4×Dic11C2311yescharacteristic
71C2×C4×Dic11C2311yescharacteristic
72C22×C11⋊C8C2312yes—
73#66941—28no—
74#66941—28no—
75#66941—24no—
76#66941—24no—
77#66941C2×C418yes—
78#66941C2×C418yes—
79#66930—44no—
80C11×C22⋊C8—22no—
81C11×#95—21no—
82C11⋊#95—21no—
83C11⋊#95—22no—
84C22⋊(C11⋊C8)—22no—
85Dic11⋊C8—24no—
86C8×Dic11—24no—
87#21834—111nomaximal, Sylow
88C24×C11C2×D411yescharacteristic
89C22×C4×C11—24no—
90C22×C4×C11—24no—
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11—44no—
94C22×C4×C11C22×C412yes—
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D412yes—
97C22×C4×C11C2411yescharacteristic
98C22×Dic11—24no—
99C22×Dic11—24no—
100C22×Dic11—22no—
101C22×Dic11—22no—
102C22×Dic11—44no—
103C22×Dic11C22⋊C414yes—
104C22×Dic11C22⋊C414yes—
105C22×Dic11SD1614yes—
106C22×Dic11Q1614yes—
107C22×Dic11C2×D411yescharacteristic
108C22×Dic11C2×D411yescharacteristic
109C22×Dic11C2×D411yescharacteristic
110C22×Dic11C2×D411yescharacteristic
111C2×Dic22—28no—
112C2×Dic22—28no—
113C2×Dic22—432no—
114C2×Dic22—48no—
115C2×Dic22—48no—
116C2×C8×C11—22no—
117C2×C8×C11—24no—
118C11×C4⋊C4—24no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—24no—
121C11×C4⋊C4C22×C414yes—
122C11×C22⋊C4—42no—
123C22⋊Dic11—42no—
124C4⋊Dic11—24no—
125C4⋊Dic11—22no—
126C4⋊Dic11—24no—
127C4⋊Dic11C22×C414yes—
128Dic11⋊C4—28no—
129Dic11⋊C4—28no—
130Dic11⋊C4—44no—
131Dic11⋊C4—44no—
132C4×Dic11—44no—
133C4×Dic11C22⋊C414yes—
134C4×Dic11C22⋊C414yes—
135C4×Dic11C22×C412yes—
136C4×Dic11C22×C412yes—
137C4×Dic11C2×D412yes—
138C4×Dic11C2×D412yes—
139C2×C11⋊C8—22no—
140C2×C11⋊C8—24no—
141C22×C4⋊Q8—111no—
142C2×#431—111no—
143#2285—111no—
144#1990—114no—
145#1987—114no—
146#1824—111no—
147#1824—111no—
148#1824—111no—
149#1824D1111yescharacteristic
150C23×C11—22no—
151C23×C11—22no—
152C23×C11C2×C22⋊C412yes—
153C23×C11C2×SD1612yes—
154C23×C11C2×Q1612yes—
155C23×C11C22×D411yescharacteristic
156C2×C4×C11—22no—
157C2×C4×C11—24no—
158C2×C4×C11—24no—
159C2×C4×C11—24no—
160C2×C4×C11—48no—
161C2×C4×C11—44no—
162C2×C4×C11—42no—
163C2×C4×C11—42no—
164C2×C4×C11—42no—
165C2×C4×C11C2×C22⋊C412yes—
166C2×C4×C11C23×C411yescharacteristic
167C2×C4×C11C22×D411yescharacteristic
168C2×C4×C112−1+414yes—
169C2×Dic11—22no—
170C2×Dic11—28no—
171C2×Dic11—24no—
172C2×Dic11—48no—
173C2×Dic11—44no—
174C2×Dic11—42no—
175C2×Dic11—42no—
176C2×Dic11—42no—
177C2×Dic11#103116yes—
178C2×Dic11C2×C22⋊C412yes—
179C2×Dic11C2×C22⋊C412yes—
180C2×Dic11C2×C22⋊C412yes—
181C2×Dic11C2×C22⋊C412yes—
182C2×Dic11C2×SD1612yes—
183C2×Dic11C2×SD1612yes—
184C2×Dic11C2×Q1612yes—
185C2×Dic11C2×Q1612yes—
186C2×Dic11AGL(1,ℤ/8)14yes—
187Dic22—416no—
188Dic22—416no—
189C8×C11—42no—
190C11⋊C8—42no—
191C23×Q8—221no—
192C2×C4⋊Q8—112no—
193C2×C4⋊Q8—112no—
194C2×C4⋊Q8—118no—
195C2×C4⋊Q8—221no—
196C2×C4⋊Q8—221no—
197C2×C4⋊Q8—224no—
198C2×#117—221no—
199C22×C4⋊C4—111no—
200C22×C4⋊C4—221no—
201C22×C4⋊C4C2×D1111yescharacteristic
202C22×C42—111no—
203#431—224no—
204C2×C4⋊C8—112no—
205C2×C22⋊C8—111no—
206C2×C22⋊C8C2×D1111yescharacteristic
207C2×C4×C8—112no—
208#384—112no—
209#382—221no—
210#380—111no—
211#380—221no—
212#380C2×D1111yescharacteristic
213C4×C4⋊C4—112no—
214C4×C4⋊C4—221no—
215#340—114no—
216#340—114no—
217#340—114no—
218#340C2×D1114yes—
219C22×C11—22no—
220C22×C11—22no—
221C22×C11—24no—
222C22×C11—24no—
223C22×C11C2×#10314yes—
224C22×C11C22×C22⋊C411yescharacteristic
225C22×C11#53612yes—
226C22×C11C22×SD1611yescharacteristic
227C22×C11C22×Q1611yescharacteristic
228C22×C11C2×AGL(1,ℤ/8)12yes—
229C4×C11—22no—
230C4×C11—44no—
231C4×C11—82no—
232C4×C11#51912yes—
233C4×C11#53612yes—
234Dic11—22no—
235Dic11—44no—
236Dic11—82no—
237Dic11C2×#10314yes—
238Dic11C2×#10314yes—
239Dic11#41814yes—
240C22×Q8—228no—
241C22×Q8—222no—
242C22×Q8—222no—
243C22×Q8—448no—
244C23×C4—21no—
245C23×C4—111no—
246C23×C4—111no—
247C23×C4—221no—
248C23×C4C22×D1111yescharacteristic
249C22×C8—112no—
250C22×C8C22×D1112yes—
251C4⋊Q8—118no—
252C4⋊Q8—118no—
253C4⋊Q8—228no—
254C4⋊Q8—228no—
255C4⋊Q8—224no—
256C4⋊Q8—224no—
257#117—444no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—114no—
261C2×C4⋊C4—112no—
262C2×C4⋊C4—112no—
263C2×C4⋊C4—228no—
264C2×C4⋊C4—222no—
265C2×C4⋊C4—222no—
266C2×C4⋊C4—221no—
267C2×C4⋊C4—222no—
268C2×C4⋊C4—222no—
269C2×C4⋊C4—222no—
270C2×C4⋊C4C4×D1114yes—
271C2×C4⋊C4C22×D1112yes—
272C2×C4⋊C4C22×D1112yes—
273C2×C22⋊C4—21no—
274C2×C22⋊C4—221no—
275C2×C42—114no—
276C2×C42—111no—
277C2×C42—111no—
278C2×C42—114no—
279C2×C42—111no—
280C2×C42—111no—
281C2×C42—222no—
282C4⋊C8—224no—
283C22⋊C8—22no—
284C22⋊C8—222no—
285C4×C8—224no—
286#95—21no—
287#95—222no—
288#95—221no—
289C2×C11—24no—
290C2×C11#231011yescharacteristic
291C2×C11C22×#10311yescharacteristic
292C2×C11C2×#41811yescharacteristic
293C2×C11#322712yes—
294C2×C11#323012yes—
295C24D4×D1111yescharacteristic
296C2×Q8—228no—
297C2×Q8—228no—
298C2×Q8—448no—
299C2×Q8—4432no—
300C2×Q8—448no—
301C22×C4—24no—
302C22×C4—24no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—44no—
306C22×C4—114no—
307C22×C4—114no—
308C22×C4—114no—
309C22×C4—111no—
310C22×C4—111no—
311C22×C4—111no—
312C22×C4—114no—
313C22×C4—111no—
314C22×C4—224no—
315C22×C4—224no—
316C22×C4—222no—
317C22×C4—222no—
318C22×C4—444no—
319C22×C4C2×C4×D1112yes—
320C22×C4D4×D1111yescharacteristic
321C22×C4D4×D1112yes—
322C22×C4C23×D1111yescharacteristic
323C2×C8—22no—
324C2×C8—24no—
325C2×C8—222no—
326C2×C8—224no—
327C4⋊C4—24no—
328C4⋊C4—22no—
329C4⋊C4—24no—
330C4⋊C4—114no—
331C4⋊C4—228no—
332C4⋊C4—228no—
333C4⋊C4—224no—
334C4⋊C4—222no—
335C4⋊C4—224no—
336C4⋊C4—444no—
337C4⋊C4—444no—
338C4⋊C4C2×C4×D1114yes—
339C22⋊C4—42no—
340C22⋊C4—442no—
341C42—114no—
342C42—114no—
343C42—112no—
344C42—112no—
345C42—112no—
346C42—112no—
347C42—444no—
348C11#2183411yescharacteristic, complemented, Sylow
349C23—22no—
350C23—22no—
351C23C22⋊C4×D1112yes—
352C23SD16×D1112yes—
353C23Q16×D1112yes—
354C23C2×D4×D1111yescharacteristic
355Q8—4416no—
356Q8—4416no—
357C2×C4—22no—
358C2×C4—24no—
359C2×C4—24no—
360C2×C4—24no—
361C2×C4—48no—
362C2×C4—44no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—112no—
367C2×C4—112no—
368C2×C4—112no—
369C2×C4—112no—
370C2×C4—112no—
371C2×C4—112no—
372C2×C4—112no—
373C2×C4—114no—
374C2×C4—1116no—
375C2×C4—112no—
376C2×C4—228no—
377C2×C4—222no—
378C2×C4—224no—
379C2×C4—448no—
380C2×C4—444no—
381C2×C4—442no—
382C2×C4—442no—
383C2×C4—442no—
384C2×C4C22⋊C4×D1112yes—
385C2×C4C22×C4×D1111yescharacteristic
386C2×C4C2×D4×D1111yescharacteristic
387C2×C4#6704314yes—
388C8—42no—
389C8—442no—
390C22—22no—
391C22—22no—
392C22—24no—
393C22—24no—
394C22D11×#10314yes—
395C22C2×C22⋊C4×D1111yescharacteristic
396C22#1062317912yes—
397C22C2×SD16×D1111yescharacteristic
398C22C2×Q16×D1111yescharacteristic
399C22D11×AGL(1,ℤ/8)12yes—
400C4—22no—
401C4—44no—
402C4—82no—
403C4—114no—
404C4—114no—
405C4—114no—
406C4—222no—
407C4—444no—
408C4—882no—
409C4#1062304712yes—
410C4#1062317912yes—
411C2—24no—
412C2#1307120111yescharacteristic
413C2C2×D11×#10311yescharacteristic
414C2D11×#41811yescharacteristic
415C2#1307974212yes—
416C2#1307976512yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1824C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#1824D11
hypocenterC11#21834
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1824

Complements

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

NH ≅ G/Ntype
4. #13069575C2semidirect
5. #13069562C2semidirect
18. C2×#66941C4semidirect
348. C11#21834semidirect

Maximal subgroups

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

subgroupindex
C22×#669412
C2×#106223312
#130710182
#130695752
#130695622
#130687072
#130687062
#130687042
C11×#18242
#2183411