Finite Group Databasebeta

← #14724307

Subgroups — #14724307

Order 2816.

630 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079184C211yesmaximal, characteristic
2#13077588C212yesmaximal, complemented
3#13067512C211yesmaximal, characteristic, complemented
4#13067509C212yesmaximal, complemented
5#13067501C211yesmaximal, characteristic, complemented
6C8×Dic44C211yesmaximal, characteristic, complemented
7C8×#4324C212yesmaximal, complemented
8#13067378C211yesmaximal, characteristic, complemented
9#13067073C212yesmaximal, complemented
10C82×D11C211yesmaximal, characteristic, complemented
11C8×C11×D8C211yesmaximal, characteristic, complemented
12#10623088C2212yes—
13C4×C11×D8C2211yescharacteristic
14C8×D4×C11C2212yes—
15#10622770C411yescharacteristic
16#10622768C411yescharacteristic
17C8×C22⋊D11—22no—
18#10622714—22no—
19C4×#4324C2212yes—
20#10622625C2212yes—
21#10622500C411yescharacteristic
22#10622491C411yescharacteristic
23#10622448C2212yes—
24#10622444C2212yes—
25#10622391C412yes—
26#10622381C412yes—
27#10622341—22no—
28#10622333—22no—
29C4×Dic44C2211yescharacteristic
30C4×C8×D11C2211yescharacteristic
31C4×C8×D11C2211yescharacteristic
32C4×C8×D11C2211yescharacteristic
33C8×Dic22C2212yes—
34C11×#335C2211yescharacteristic
35C11×D4⋊C8C2212yes—
36C82×C11C2211yescharacteristic
37D4⋊(C11⋊C8)C2212yes—
38#10622122C2212yes—
39#10622118C2212yes—
40#10622096C2211yescharacteristic
41#10622094C2212yes—
42C8×C11⋊C8C2211yescharacteristic
43C8×C11⋊C8C2211yescharacteristic
44C8×C11⋊C8C2211yescharacteristic
45C2×C11×D8C2×C411yescharacteristic
46C22×C8×C11—22no—
47C4×D4×C11C2312yes—
48#66991C2×C412yes—
49#66989C2×C412yes—
50C2×#4324C2×C412yes—
51C4×C22⋊D11—22no—
52#66979—22no—
53C2×#4318—22no—
54C2×Dic44C2×C411yescharacteristic
55C2×C8×D11—21no—
56C2×C8×D11C2×C411yescharacteristic
57C2×C8×D11C2×C411yescharacteristic
58C2×C8×D11D411yescharacteristic
59C2×C8×D11D411yescharacteristic
60#66950C2×C412yes—
61#66943C2×C412yes—
62#66936—22no—
63#66932—22no—
64C42×D11C2311yescharacteristic
65C4×Dic22C2312yes—
66C11×#107C2×C411yescharacteristic
67C11×C4⋊C8C2312yes—
68C11×#102C2×C412yes—
69C11×C22⋊C8—22no—
70C4×C8×C11C2311yescharacteristic
71C4×C8×C11C2311yescharacteristic
72C4×C8×C11C2311yescharacteristic
73#66896C2×C412yes—
74C22⋊(C11⋊C8)—22no—
75(C2×D11)⋊C8—22no—
76#66882C2×C411yescharacteristic
77#66880C2×C412yes—
78#66879—22no—
79#66879—22no—
80Dic11⋊C8—22no—
81Dic11⋊C8—22no—
82C8×Dic11—22no—
83C8×Dic11—21no—
84C8×Dic11C2×C411yescharacteristic
85C8×Dic11C2×C411yescharacteristic
86C8×Dic11D411yescharacteristic
87C8×Dic11D411yescharacteristic
88#66874C2×C412yes—
89#66872C2×C412yes—
90C4⋊(C11⋊C8)C2312yes—
91C4×C11⋊C8C2311yescharacteristic
92C4×C11⋊C8C2311yescharacteristic
93C4×C11⋊C8C2311yescharacteristic
94#17959—111nomaximal, Sylow
95C2×D4×C11C22×C412yes—
96C22×C4×C11—22no—
97C2×C22⋊D11—22no—
98C2×C4×D11C22×C411yescharacteristic
99C2×C4×D11C2×D411yescharacteristic
100C2×C4×D11#4111yescharacteristic
101C2×Dic22C22×C412yes—
102C11×D8—22no—
103C2×C8×C11—22no—
104C2×C8×C11—21no—
105C2×C8×C11—44no—
106C2×C8×C11C22×C411yescharacteristic
107C2×C8×C11C22×C411yescharacteristic
108C2×C8×C11C2×D411yescharacteristic
109C2×C8×C11C2×D411yescharacteristic
110C11×C4⋊C4C22×C412yes—
111C11×C22⋊C4—22no—
112C42×C11C2411yescharacteristic
113C22⋊Dic11—22no—
114C22⋊Dic11—22no—
115C22⋊Dic11—22no—
116#4324—24no—
117(C2×D11)⋊C4—22no—
118C4⋊Dic11—22no—
119C4⋊Dic11—22no—
120C4⋊Dic11C22×C412yes—
121Dic11⋊C4—22no—
122Dic11⋊C4—22no—
123C4×Dic11—22no—
124C4×Dic11C22×C411yescharacteristic
125C4×Dic11C2×D411yescharacteristic
126C4×Dic11#4111yescharacteristic
127#4318—44no—
128C2×C11⋊C8—22no—
129C2×C11⋊C8—21no—
130C2×C11⋊C8C22×C411yescharacteristic
131C2×C11⋊C8C22×C411yescharacteristic
132C2×C11⋊C8C2×D411yescharacteristic
133C2×C11⋊C8C2×D411yescharacteristic
134Dic44—22no—
135C8×D11—24no—
136C8×D11—22no—
137C8×D11—22no—
138C8×D11—22no—
139C8×D11—22no—
140#3168—111no—
141#2966—112no—
142#1591—111no—
143#1590—112no—
144#1589—111no—
145C8×Q16—111no—
146C8×SD16—112no—
147C8×D8D1111yescharacteristic, complemented
148#1568—111no—
149#1494—112no—
150C2×C82—111no—
151C23×C11—22no—
152C22×D11C4×D411yescharacteristic
153D4×C11—22no—
154D4×C11—22no—
155C2×C4×C11—22no—
156C2×C4×C11—42no—
157C2×C4×C11—42no—
158C2×C4×C11C23×C411yescharacteristic
159C2×C4×C11C22×D411yescharacteristic
160C2×C4×C11C2×#4111yescharacteristic
161C22⋊D11—44no—
162C2×Dic11—22no—
163C2×Dic11—22no—
164C2×Dic11C4×D411yescharacteristic
165C2×Dic11C4×D411yescharacteristic
166C2×Dic11C4×D411yescharacteristic
167C4×D11—22no—
168C4×D11—21no—
169C4×D11—21no—
170C4×D11—21no—
171C4×D11—21no—
172Dic22—22no—
173Dic22—22no—
174C8×C11—22no—
175C8×C11—21no—
176C8×C11—21no—
177C8×C11—42no—
178C8×C11#13112yes—
179C8×C11#13512yes—
180C11⋊C8—22no—
181C11⋊C8—21no—
182C11⋊C8—21no—
183C11⋊C8—42no—
184C11⋊C8#13112yes—
185C11⋊C8#13512yes—
186#529—112no—
187#499—111no—
188#495—111no—
189#488—112no—
190#467—111no—
191#466—111no—
192#465—112no—
193#446—112no—
194C8×Q8—112no—
195C4×Q16—111no—
196C4×SD16—112no—
197C4×D8C2×D1111yescharacteristic
198#436—112no—
199#435—222no—
200C8×D4—222no—
201C8×D4C2×D1112yes—
202#433—222no—
203#432—112no—
204#405—222no—
205C2×C4×C8—111no—
206C2×C4×C8—111no—
207C2×C4×C8—111no—
208#335—111no—
209#335C2×D1111yescharacteristic
210#334—112no—
211Q8⋊C8—112no—
212Q8⋊C8—112no—
213D4⋊C8—112no—
214D4⋊C8C2×D1112yes—
215C82—111no—
216C82—111no—
217C82—111no—
218C82C2×D1111yescharacteristic
219C22×C11—42no—
220C22×C11—42no—
221C22×C11—42no—
222C22×C11C2×C4×D411yescharacteristic
223C2×D11—21no—
224C2×D11—21no—
225C2×D11#44312yes—
226C4×C11—21no—
227C4×C11—42no—
228C4×C11C2×#13111yescharacteristic
229C4×C11C2×#13111yescharacteristic
230C4×C11C2×#13511yescharacteristic
231C4×C11C2×#13511yescharacteristic
232Dic11—21no—
233Dic11—21no—
234Dic11—21no—
235Dic11—42no—
236Dic11—42no—
237C2×Q16—111no—
238C2×SD16—112no—
239C2×D8C4×D1111yescharacteristic
240C2×M16—222no—
241C22×C8—22no—
242C22×C8—111no—
243C22×C8—111no—
244C22×C8—111no—
245C22×C8—111no—
246C22×C8—221no—
247#126—222no—
248#125—112no—
249#124—112no—
250#123—222no—
251C22⋊Q8—112no—
252#121—112no—
253C4×Q8—112no—
254C4×D4—222no—
255C4×D4C22×D1112yes—
256#117—222no—
257C2×C42—111no—
258#107—111no—
259#107C4×D1111yescharacteristic
260#106—112no—
261C4⋊C8—112no—
262C4⋊C8—222no—
263C4⋊C8—222no—
264C4⋊C8C22×D1112yes—
265#103—112no—
266#103—112no—
267#102—112no—
268#102C4×D1112yes—
269C22⋊C8—22no—
270C22⋊C8—222no—
271C22⋊C8—222no—
272#97—222no—
273#97—222no—
274C4×C8—111no—
275C4×C8—111no—
276C4×C8—111no—
277C4×C8—111no—
278C4×C8—111no—
279C4×C8—111no—
280C4×C8—111no—
281C4×C8—221no—
282C4×C8—222no—
283C4×C8C22×D1111yescharacteristic
284C4×C8C22×D1111yescharacteristic
285C4×C8C22×D1111yescharacteristic
286C2×C11—82no—
287C2×C11#293111yescharacteristic
288C2×C11C4×#13511yescharacteristic
289C2×C11C2×#44311yescharacteristic
290D11—22no—
291C2×Q8—112no—
292C2×D4—222no—
293C2×D4C2×C4×D1112yes—
294C22×C4—22no—
295C22×C4—111no—
296C22×C4—111no—
297C22×C4—111no—
298Q16—222no—
299SD16—224no—
300D8—22no—
301M16—444no—
302C2×C8—21no—
303C2×C8—22no—
304C2×C8—44no—
305C2×C8—111no—
306C2×C8—111no—
307C2×C8—111no—
308C2×C8—111no—
309C2×C8—222no—
310C2×C8—222no—
311C2×C8—224no—
312C2×C8—221no—
313C2×C8—222no—
314C2×C8—222no—
315C2×C8—222no—
316C2×C8C2×C4×D1111yescharacteristic
317C2×C8C2×C4×D1111yescharacteristic
318C2×C8D4×D1111yescharacteristic
319C2×C8D4×D1111yescharacteristic
320C4⋊C4—112no—
321C4⋊C4—222no—
322C4⋊C4—222no—
323C4⋊C4—222no—
324C4⋊C4—222no—
325C4⋊C4C2×C4×D1112yes—
326C22⋊C4—22no—
327C22⋊C4—222no—
328C22⋊C4—222no—
329C22⋊C4—222no—
330C22⋊C4—222no—
331C42—111no—
332C42—111no—
333C42—111no—
334C42—222no—
335C42C23×D1111yescharacteristic
336C11#1795911yescharacteristic, complemented, Sylow
337C23—22no—
338C23—111no—
339Q8—222no—
340Q8—222no—
341D4—22no—
342D4—22no—
343D4—444no—
344C2×C4—22no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—111no—
348C2×C4—111no—
349C2×C4—111no—
350C2×C4—222no—
351C2×C4—221no—
352C2×C4—221no—
353C2×C4—221no—
354C2×C4—221no—
355C2×C4—222no—
356C2×C4—222no—
357C2×C4C22×C4×D1111yescharacteristic
358C2×C4C2×D4×D1111yescharacteristic
359C2×C4#41×D1111yescharacteristic
360C8—22no—
361C8—21no—
362C8—21no—
363C8—42no—
364C8—112no—
365C8—112no—
366C8—222no—
367C8—221no—
368C8—221no—
369C8—442no—
370C8#6695412yes—
371C8#6696512yes—
372C22—42no—
373C22—42no—
374C22—42no—
375C22—112no—
376C22—221no—
377C22—221no—
378C22C4×D4×D1111yescharacteristic
379C4—21no—
380C4—42no—
381C4—221no—
382C4—221no—
383C4—221no—
384C4—442no—
385C4—442no—
386C4C2×#6695411yescharacteristic
387C4D11×#13111yescharacteristic
388C4C2×#6696511yescharacteristic
389C4D11×#13511yescharacteristic
390C2—82no—
391C2—222no—
392C2#1307732311yescharacteristic
393C2C4×#6696511yescharacteristic
394C2D11×#44311yescharacteristic
subgroupG/H
centerC2×C8D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC8×C11×D8C2
socleC22×C11C2×C4×D4
prime radical#10622770C4
cosocleC42×C11C24
hypercenterC8×D8D11
hypocenterC11#17959
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C8 ◁ C4×C8 ◁ C8×D8

Complements

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

NH ≅ G/Ntype
2. #13077588C2semidirect
3. #13067512C2semidirect
4. #13067509C2semidirect
5. #13067501C2semidirect
6. C8×Dic44C2semidirect
7. C8×#4324C2semidirect
8. #13067378C2semidirect
9. #13067073C2semidirect
10. C82×D11C2semidirect
11. C8×C11×D8C2semidirect
147. C8×D8D11semidirect
336. C11#17959semidirect

Maximal subgroups

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

subgroupindex
#130791842
#130775882
#130675122
#130675092
#130675012
C8×Dic442
C8×#43242
#130673782
#130670732
C82×D112
C8×C11×D82
#1795911