Finite Group Databasebeta

← #14724334

Subgroups — #14724334

Order 2816.

734 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079192C211yesmaximal, characteristic
2#13077323C212yesmaximal, complemented
3#13067530C211yesmaximal, characteristic, complemented
4#13067529C211yesmaximal, characteristic, complemented
5#13067527C212yesmaximal, complemented
6#13067441C211yesmaximal, characteristic, complemented
7#13067438C212yesmaximal, complemented
8#13067370C211yesmaximal, characteristic, complemented
9#13067065C212yesmaximal, complemented
10D11×#322C211yesmaximal, characteristic, complemented
11C11×#1580C211yesmaximal, characteristic, complemented
12C2×#66954—22no—
13#10623079C2212yes—
14C4×C11×D8C2211yescharacteristic
15C8×D4×C11C2212yes—
16#10622770C411yescharacteristic
17#10622764C411yescharacteristic
18C8×C22⋊D11—22no—
19C4×#4323C2212yes—
20#10622625C2212yes—
21#10622496C411yescharacteristic
22#10622487C411yescharacteristic
23#10622451C2212yes—
24#10622450C2212yes—
25#10622388C412yes—
26#10622373C412yes—
27#10622342—22no—
28#10622340—22no—
29C4×D88C2211yescharacteristic
30C8×D44C2212yes—
31C4×C8×D11C2211yescharacteristic
32C4×C8×D11C2211yescharacteristic
33C4×C8×D11C2211yescharacteristic
34C11×#334C2211yescharacteristic
35C11×D4⋊C8C2212yes—
36C11×#322C2211yescharacteristic
37D4⋊(C11⋊C8)C2212yes—
38#10622121C2212yes—
39#10622118C2212yes—
40#10622097C2212yes—
41#10622095C2211yescharacteristic
42#10622093C2211yescharacteristic
43#10622092C2211yescharacteristic
44#10622092C2211yescharacteristic
45C2×#4339—22no—
46C2×C11×D8C2×C411yescharacteristic
47C22×C8×C11—22no—
48C4×D4×C11C2312yes—
49#66993C2×C412yes—
50#66991C2×C412yes—
51C2×#4323C2×C412yes—
52C4×C22⋊D11—22no—
53C2×#4318—22no—
54C2×D88C2×C411yescharacteristic
55#66954—48no—
56C2×#4313—22no—
57C2×#4313—22no—
58C2×C8×D11—21no—
59C2×C8×D11—22no—
60C2×C8×D11C2×C411yescharacteristic
61C2×C8×D11C2×C411yescharacteristic
62C2×C8×D11D412yes—
63#66948C2×C412yes—
64#66941C2×C412yes—
65#66938—22no—
66#66937—22no—
67C4×D44C2312yes—
68C42×D11C2311yescharacteristic
69C11×#107C2×C411yescharacteristic
70C11×C4⋊C8C2312yes—
71C11×#102C2×C412yes—
72C11×C22⋊C8—22no—
73C4×C8×C11C2311yescharacteristic
74C4×C8×C11C2311yescharacteristic
75C4×C8×C11C2311yescharacteristic
76#66896C2×C412yes—
77C22⋊(C11⋊C8)—22no—
78#66885C2×C412yes—
79(C2×D11)⋊C8—22no—
80(C2×D11)⋊C8—22no—
81#66882C2×C411yescharacteristic
82Dic11⋊C8—22no—
83C8×Dic11—21no—
84C8×Dic11C2×C411yescharacteristic
85C8×Dic11C2×C411yescharacteristic
86C8×Dic11D412yes—
87#66873C2×C412yes—
88#66871C2×C412yes—
89C4⋊(C11⋊C8)C2312yes—
90C4×C11⋊C8C2311yescharacteristic
91C4×C11⋊C8C2311yescharacteristic
92C4×C11⋊C8C2311yescharacteristic
93#17962—111nomaximal, Sylow
94C2×D4×C11C22×C412yes—
95C22×C4×C11—22no—
96C2×C22⋊D11—22no—
97C2×C22⋊D11—22no—
98C2×C22⋊D11—22no—
99#4339—44no—
100#4339—44no—
101C2×D44—22no—
102C2×D44C22×C412yes—
103C2×C4×D11—22no—
104C2×C4×D11C22×C411yescharacteristic
105C2×C4×D11C2×D411yescharacteristic
106C2×C4×D11#4111yescharacteristic
107C2×Dic22—22no—
108C11×D8—22no—
109C2×C8×C11—22no—
110C2×C8×C11—21no—
111C2×C8×C11—44no—
112C2×C8×C11C22×C411yescharacteristic
113C2×C8×C11C22×C411yescharacteristic
114C2×C8×C11C2×D412yes—
115C11×C4⋊C4C22×C412yes—
116C11×C22⋊C4—22no—
117C42×C11C2411yescharacteristic
118C22⋊Dic11—22no—
119#4323—24no—
120(C2×D11)⋊C4—22no—
121(C2×D11)⋊C4—22no—
122C4⋊Dic11C22×C412yes—
123Dic11⋊C4—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×D412yes—
133D88—22no—
134#4313—44no—
135#4313—44no—
136C8×D11—24no—
137C8×D11—22no—
138C8×D11—22no—
139C8×D11—44no—
140C8×D11—42no—
141#3169—111no—
142#2931—112no—
143#1594—111no—
144#1594—111no—
145#1594—112no—
146#1580—112no—
147#1580—111no—
148#1580D1111yescharacteristic, complemented
149#1566—111no—
150#1492—112no—
151C2×#322—111no—
152C23×C11—22no—
153C22×D11—22no—
154C22×D11C4×D411yescharacteristic
155D4×C11—22no—
156D4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—42no—
159C2×C4×C11—42no—
160C2×C4×C11C23×C411yescharacteristic
161C2×C4×C11C22×D411yescharacteristic
162C2×C4×C11C2×#4111yescharacteristic
163C22⋊D11—44no—
164C22⋊D11—44no—
165C22⋊D11—44no—
166C2×Dic11—22no—
167C2×Dic11C4×D411yescharacteristic
168C2×Dic11C4×D411yescharacteristic
169C2×Dic11C4×D411yescharacteristic
170D44—22no—
171D44—22no—
172D44—44no—
173C4×D11—21no—
174C4×D11—21no—
175C4×D11—22no—
176C4×D11—42no—
177C4×D11—42no—
178C4×D11AGL(1,ℤ/8)14yes—
179Dic22—44no—
180C8×C11—21no—
181C8×C11—22no—
182C8×C11—41no—
183C8×C11—42no—
184C8×C11#13112yescomplemented
185C11⋊C8—21no—
186C11⋊C8—22no—
187C11⋊C8—41no—
188C11⋊C8—42no—
189C11⋊C8#13112yescomplemented
190C2×#131—222no—
191#532—112no—
192#500—111no—
193#493—111no—
194#486—112no—
195#466—111no—
196#466—111no—
197#466—112no—
198C4×D8—112no—
199C4×D8—111no—
200C4×D8C2×D1111yescharacteristic
201#436—112no—
202#436—112no—
203#436—222no—
204C8×D4—112no—
205C8×D4—222no—
206C8×D4C2×D1112yes—
207#423—112no—
208#408—222no—
209C2×C4×C8—111no—
210C2×C4×C8—111no—
211C2×C4×C8—111no—
212#334—112no—
213#334—111no—
214#334C2×D1111yescharacteristic
215D4⋊C8—112no—
216D4⋊C8—112no—
217D4⋊C8—112no—
218D4⋊C8C2×D1112yes—
219#322—111no—
220#322—111no—
221#322—111no—
222#322C2×D1111yescharacteristic
223C22×C11—42no—
224C22×C11—42no—
225C22×C11—42no—
226C22×C11C2×C4×D411yescharacteristic
227C2×D11—21no—
228C2×D11—21no—
229C2×D11—42no—
230C2×D11—42no—
231C2×D11—42no—
232C2×D11#44212yes—
233C4×C11—21no—
234C4×C11—42no—
235C4×C11C2×#13111yescharacteristic
236C4×C11C2×#13111yescharacteristic
237C4×C11C2×AGL(1,ℤ/8)12yes—
238Dic11—21no—
239Dic11—42no—
240Dic11#44212yes—
241Dic11#44412yes—
242C2×#41—222no—
243C2×D8—112no—
244C2×D8—111no—
245C2×D8C4×D1111yescharacteristic
246#131—448no—
247C2×M16—222no—
248C2×M16—222no—
249C2×M16—222no—
250C22×C8—22no—
251C22×C8—111no—
252C22×C8—111no—
253C22×C8—112no—
254C22×C8—221no—
255C22×C8—222no—
256C4⋊Q8—112no—
257#127—112no—
258#124—222no—
259#121—112no—
260#121—112no—
261#121—222no—
262C4×D4—112no—
263C4×D4—222no—
264C4×D4C22×D1112yes—
265C2×C42—111no—
266#107—111no—
267#107—112no—
268#107C4×D1111yescharacteristic
269C4⋊C8—112no—
270C4⋊C8—222no—
271C4⋊C8C22×D1112yes—
272#102—112no—
273#102—112no—
274#102—112no—
275#102C4×D1112yes—
276C22⋊C8—22no—
277C22⋊C8—222no—
278C22⋊C8—222no—
279C22⋊C8—222no—
280C4×C8—111no—
281C4×C8—111no—
282C4×C8—112no—
283C4×C8—111no—
284C4×C8—111no—
285C4×C8—111no—
286C4×C8—221no—
287C4×C8C22×D1111yescharacteristic
288C4×C8C22×D1111yescharacteristic
289C4×C8C22×D1111yescharacteristic
290C2×C11—82no—
291C2×C11#293111yescharacteristic
292C2×C11C2×#44211yescharacteristic
293C2×C11C2×#44411yescharacteristic
294D11—22no—
295D11—82no—
296#41—444no—
297#41—444no—
298C2×Q8—222no—
299C2×D4—112no—
300C2×D4—222no—
301C2×D4—222no—
302C2×D4—222no—
303C2×D4—222no—
304C2×D4C2×C4×D1112yes—
305C22×C4—22no—
306C22×C4—111no—
307C22×C4—111no—
308C22×C4—111no—
309C22×C4—222no—
310D8—22no—
311D8—224no—
312D8—222no—
313M16—444no—
314M16—444no—
315M16—444no—
316C2×C8—22no—
317C2×C8—21no—
318C2×C8—44no—
319C2×C8—111no—
320C2×C8—111no—
321C2×C8—112no—
322C2×C8—222no—
323C2×C8—224no—
324C2×C8—222no—
325C2×C8—222no—
326C2×C8—221no—
327C2×C8—444no—
328C2×C8—442no—
329C2×C8C2×C4×D1111yescharacteristic
330C2×C8C2×C4×D1111yescharacteristic
331C2×C8D4×D1112yes—
332C4⋊C4—112no—
333C4⋊C4—222no—
334C4⋊C4C2×C4×D1112yes—
335C22⋊C4—22no—
336C22⋊C4—222no—
337C22⋊C4—222no—
338C22⋊C4—222no—
339C42—111no—
340C42—111no—
341C42—111no—
342C42C23×D1111yescharacteristic
343C11#1796211yescharacteristic, complemented, Sylow
344C23—22no—
345C23—111no—
346C23—222no—
347Q8—444no—
348D4—22no—
349D4—22no—
350D4—222no—
351D4—222no—
352D4—444no—
353D4—444no—
354D4—444no—
355D4—444no—
356C2×C4—22no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—111no—
360C2×C4—111no—
361C2×C4—114no—
362C2×C4—111no—
363C2×C4—222no—
364C2×C4—221no—
365C2×C4—221no—
366C2×C4—222no—
367C2×C4—442no—
368C2×C4—442no—
369C2×C4C22×C4×D1111yescharacteristic
370C2×C4C2×D4×D1111yescharacteristic
371C2×C4#41×D1111yescharacteristic
372C8—21no—
373C8—22no—
374C8—41no—
375C8—42no—
376C8—112no—
377C8—221no—
378C8—222no—
379C8—441no—
380C8—442no—
381C8#6695412yescomplemented
382C22—42no—
383C22—42no—
384C22—42no—
385C22—112no—
386C22—221no—
387C22—221no—
388C22—442no—
389C22—442no—
390C22—442no—
391C22C4×D4×D1111yescharacteristic
392C4—21no—
393C4—42no—
394C4—112no—
395C4—112no—
396C4—221no—
397C4—442no—
398C4C2×#6695411yescharacteristic
399C4D11×#13111yescharacteristic
400C4D11×AGL(1,ℤ/8)12yes—
401C2—82no—
402C2—222no—
403C2—882no—
404C2#1307732311yescharacteristic
405C2D11×#44211yescharacteristic
406C2D11×#44411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1580C2
socleC22×C11C2×C4×D4
prime radical#13079192C2
cosocleC42×C11C24
hypercenter#1580D11
hypocenterC11#17962
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1580

Complements

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

NH ≅ G/Ntype
2. #13077323C2semidirect
3. #13067530C2semidirect
4. #13067529C2semidirect
5. #13067527C2semidirect
6. #13067441C2semidirect
7. #13067438C2semidirect
8. #13067370C2semidirect
9. #13067065C2semidirect
10. D11×#322C2semidirect
11. C11×#1580C2semidirect
148. #1580D11semidirect
184. C8×C11#131semidirect
189. C11⋊C8#131semidirect
343. C11#17962semidirect
381. C8#66954semidirect

Maximal subgroups

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

subgroupindex
#130791922
#130773232
#130675302
#130675292
#130675272
#130674412
#130674382
#130673702
#130670652
D11×#3222
C11×#15802
#1796211