Finite Group Databasebeta

← #14647705

Subgroups — #14647705

Order 2816.

464 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13069334C211yesmaximal, characteristic
2C4×#66899C211yesmaximal, characteristic
3C2×#10622118C211yesmaximal, characteristic
4C2×Q8⋊(C11⋊C8)C211yesmaximal, characteristic
5#13066455C211yesmaximal, characteristic
6C11⋊#1273C211yesmaximal, characteristic
7C2×C8×Q8×C11C211yesmaximal, characteristic
8C2×C4×Q8×C11C2211yescharacteristic
9C8×Q8×C11—22no—
10C8×Q8×C11—22no—
11C2×C11×C4⋊C8—21no—
12C2×C11×C4⋊C8C2211yescharacteristic
13C2×C4×C8×C11—21no—
14C2×C4×C8×C11C2211yescharacteristic
15C2×#66899C411yescharacteristic
16C2×#66899C411yescharacteristic
17C2×Dic11⋊C8—21no—
18C4×C4⋊Dic11C2211yescharacteristic
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C2×C4×C11⋊C8C2211yescharacteristic
21C2×C4×C11⋊C8C2211yescharacteristic
22#10622188—21no—
23Q8⋊(C11⋊C8)—22no—
24#10622167C411yescharacteristic
25#10622167C411yescharacteristic
26#10622118—22no—
27C22×Q8×C11C2×C411yescharacteristic
28C22×C8×C11—21no—
29C22×C8×C11D411yescharacteristic
30C22×C8×C11D411yescharacteristic
31C4×Q8×C11—21no—
32C4×Q8×C11—21no—
33C4×Q8×C11D412yes—
34C4×Q8×C11Q812yes—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4C2×C411yescharacteristic
37C2×C42×C11—21no—
38C2×C42×C11C2311yescharacteristic
39C2×C4⋊Dic11C2×C411yescharacteristic
40C2×C4⋊Dic11C2×C411yescharacteristic
41C2×C4×Dic11—21no—
42C22×C11⋊C8—21no—
43C22×C11⋊C8—21no—
44C22×C11⋊C8C2×C411yescharacteristic
45C22×C11⋊C8C2×C411yescharacteristic
46C11×C4⋊C8—24no—
47C11×C4⋊C8—21no—
48C11×C4⋊C8D412yes—
49C4×C8×C11—24no—
50C4×C8×C11—21no—
51C4×C8×C11—21no—
52#66899—22no—
53#66899C814yescomplemented
54C11⋊#95—21no—
55Dic11⋊C8—42no—
56C4⋊(C11⋊C8)—21no—
57C4⋊(C11⋊C8)—21no—
58C4×C11⋊C8—21no—
59C4×C11⋊C8—21no—
60C4×C11⋊C8—21no—
61C4×C11⋊C8—21no—
62#8846—111nomaximal, Sylow
63C2×Q8×C11—21no—
64C2×Q8×C11—21no—
65C2×Q8×C11—21no—
66C2×Q8×C11C4⋊C412yes—
67C2×Q8×C11C2×C812yes—
68C2×Q8×C11M1612yes—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11C22×C411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11#4111yescharacteristic
74C22×Dic11—21no—
75C22×Dic11—21no—
76C2×C8×C11—21no—
77C2×C8×C11—21no—
78C2×C8×C11—22no—
79C2×C8×C11—21no—
80C2×C8×C11—21no—
81C2×C8×C11—21no—
82C2×C8×C11—41no—
83C2×C8×C11—41no—
84C2×C8×C11SD1612yes—
85C11×C4⋊C4—21no—
86C11×C4⋊C4—22no—
87C11×C4⋊C4—22no—
88C11×C4⋊C4C4⋊C412yes—
89C42×C11—22no—
90C42×C11—22no—
91C42×C11C2×D411yescharacteristic
92C42×C11C2×D411yescharacteristic
93C42×C11C2×Q811yescharacteristic
94C42×C11#4111yescharacteristic
95C4⋊Dic11—21no—
96C4⋊Dic11—21no—
97C4⋊Dic11—21no—
98C4⋊Dic11C2×C812yes—
99C4×Dic11—41no—
100C4×Dic11—41no—
101C2×C11⋊C8—22no—
102C2×C11⋊C8—21no—
103C2×C11⋊C8—21no—
104C2×C11⋊C8—21no—
105C2×C11⋊C8—21no—
106C2×C11⋊C8—21no—
107C2×C11⋊C8—41no—
108C2×C11⋊C8—41no—
109C2×C11⋊C8—41no—
110C2×C11⋊C8—41no—
111C2×C11⋊C8—41no—
112C2×C11⋊C8C2×C812yes—
113C2×C8×Q8D1111yescharacteristic
114#1939—111no—
115C4×#103—111no—
116C2×#334—111no—
117C2×Q8⋊C8—111no—
118#1279—111no—
119#1273—111no—
120C23×C11C4×D411yescharacteristic
121Q8×C11—22no—
122Q8×C11—22no—
123Q8×C11—22no—
124Q8×C11C4⋊C814yescomplemented
125C2×C4×C11—22no—
126C2×C4×C11—22no—
127C2×C4×C11—22no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—22no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11C2×C4⋊C411yescharacteristic
134C2×C4×C11C4×D411yescharacteristic
135C2×C4×C11#12011yescharacteristic
136C2×C4×C11C22⋊Q811yescharacteristic
137C2×C4×C11C22⋊Q811yescharacteristic
138C2×C4×C11#12311yescharacteristic
139C2×C4×C11C22×C811yescharacteristic
140C2×C4×C11C2×M1611yescharacteristic
141C2×C4×C11#13111yescharacteristic
142C2×C4×C11#13111yescharacteristic
143C2×C4×C11C2×SD1611yescharacteristic
144C2×C4×C11#13511yescharacteristic
145C2×C4×C11#13711yescharacteristic
146C2×C4×C11#13711yescharacteristic
147C2×Dic11—22no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C8×C11—22no—
154C8×C11—41no—
155C8×C11—42no—
156C11⋊C8—22no—
157C11⋊C8—42no—
158C11⋊C8—41no—
159C11⋊C8—81no—
160C2×C4×Q8C2×D1111yescharacteristic
161C8×Q8—22no—
162C8×Q8—22no—
163C2×C4⋊C8—21no—
164C2×C4⋊C8—111no—
165C2×C4⋊C8—221no—
166C2×C4⋊C8C2×D1111yescharacteristic
167C2×#103—111no—
168C2×#103—111no—
169C2×C4×C8—21no—
170C2×C4×C8—111no—
171C2×C4×C8—111no—
172C2×C4×C8C2×D1111yescharacteristic
173C4×C4⋊C4—111no—
174#340—111no—
175#340—111no—
176#336—221no—
177#334—222no—
178Q8⋊C8—222no—
179C22×C11#38511yescharacteristic
180C22×C11C8×D411yescharacteristic
181C22×C11#43511yescharacteristic
182C22×C11C4×SD1611yescharacteristic
183C22×C11#44111yescharacteristic
184C22×C11#44311yescharacteristic
185C22×C11#44411yescharacteristic
186C4×C11—24no—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—42no—
190C4×C11C2×C4⋊C811yescharacteristic
191C4×C11#42411yescharacteristic
192C4×C11C8×D411yescharacteristic
193C4×C11#43511yescharacteristic
194C4×C11#44811yescharacteristic
195C4×C11#45211yescharacteristic
196C4×C11#47511yescharacteristic
197C4×C11#47911yescharacteristic
198Dic11—42no—
199Dic11—81no—
200C22×Q8C4×D1111yescharacteristic
201C22×C8—21no—
202C22×C8—111no—
203C22×C8—111no—
204C22×C8—221no—
205C22×C8—221no—
206C22×C8C22⋊D1111yescharacteristic
207C22×C8C22⋊D1111yescharacteristic
208C4×Q8—21no—
209C4×Q8—21no—
210C4×Q8Dic2212yes—
211C4×Q8C22⋊D1112yes—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—111no—
214C2×C4⋊C4—111no—
215C2×C4⋊C4C4×D1111yescharacteristic
216C2×C42—21no—
217C2×C42—221no—
218C2×C42C22×D1111yescharacteristic
219C4⋊C8—24no—
220C4⋊C8—21no—
221C4⋊C8—221no—
222C4⋊C8—221no—
223C4⋊C8—442no—
224C4⋊C8C22⋊D1112yes—
225#103—114no—
226#103—222no—
227C4×C8—24no—
228C4×C8—21no—
229C4×C8—21no—
230C4×C8—221no—
231C4×C8—221no—
232C4×C8—221no—
233C4×C8—221no—
234#95—221no—
235C2×C11C8×SD1611yescharacteristic
236C2×C11#157911yescharacteristic
237C2×C11#158311yescharacteristic
238C2×C11#158711yescharacteristic
239C2×C11#185011yescharacteristic
240C2×C11#186511yescharacteristic
241C2×C11#186611yescharacteristic
242C2×Q8—21no—
243C2×Q8—21no—
244C2×Q8—21no—
245C2×Q8C8×D1112yes—
246C2×Q8#431312yes—
247C2×Q8Dic11⋊C412yes—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—221no—
251C22×C4—221no—
252C22×C4C2×C4×D1111yescharacteristic
253C22×C4#433911yescharacteristic
254C22×C4C2×C22⋊D1111yescharacteristic
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—21no—
258C2×C8—21no—
259C2×C8—21no—
260C2×C8—22no—
261C2×C8—41no—
262C2×C8—41no—
263C2×C8—112no—
264C2×C8—221no—
265C2×C8—221no—
266C2×C8—222no—
267C2×C8—221no—
268C2×C8—221no—
269C2×C8—221no—
270C2×C8—441no—
271C2×C8—441no—
272C2×C8—441no—
273C2×C8—441no—
274C2×C8—441no—
275C2×C8#432512yes—
276C4⋊C4—22no—
277C4⋊C4—21no—
278C4⋊C4—22no—
279C4⋊C4—112no—
280C4⋊C4—221no—
281C4⋊C4—221no—
282C4⋊C4—221no—
283C4⋊C4Dic11⋊C412yes—
284C42—22no—
285C42—22no—
286C42—441no—
287C42—441no—
288C42C2×Dic2211yescharacteristic
289C42#433911yescharacteristic
290C42C2×C22⋊D1111yescharacteristic
291C42C2×C22⋊D1111yescharacteristic
292C11#884611yescharacteristic, complemented, Sylow
293C23C4×C22⋊D1111yescharacteristic
294Q8—22no—
295Q8—22no—
296Q8—22no—
297Q8Dic11⋊C814yescomplemented
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—222no—
307C2×C4—441no—
308C2×C4—441no—
309C2×C4—441no—
310C2×C4—441no—
311C2×C4—441no—
312C2×C4C2×C8×D1111yescharacteristic
313C2×C4C2×#431311yescharacteristic
314C2×C4#6695411yescharacteristic
315C2×C4#6695411yescharacteristic
316C2×C4C2×Dic11⋊C411yescharacteristic
317C2×C4#6697711yescharacteristic
318C2×C4#6697711yescharacteristic
319C2×C4C4×C22⋊D1111yescharacteristic
320C2×C4#6698211yescharacteristic
321C2×C4C2×#432511yescharacteristic
322C2×C4#6699511yescharacteristic
323C2×C4#6700311yescharacteristic
324C2×C4#6700411yescharacteristic
325C2×C4#6700611yescharacteristic
326C8—22no—
327C8—41no—
328C8—42no—
329C8—222no—
330C8—442no—
331C8—441no—
332C8—881no—
333C22C4×#432511yescharacteristic
334C22#1062264311yescharacteristic
335C22C8×C22⋊D1111yescharacteristic
336C22#1062272411yescharacteristic
337C22#1062275711yescharacteristic
338C22#1062275811yescharacteristic
339C22#1062282311yescharacteristic
340C4—21no—
341C4—21no—
342C4—24no—
343C4—42no—
344C4—442no—
345C4—881no—
346C4#1062263311yescharacteristic
347C4#1062263511yescharacteristic
348C4C2×Dic11⋊C811yescharacteristic
349C4#1062271511yescharacteristic
350C4C8×C22⋊D1111yescharacteristic
351C4#1062272411yescharacteristic
352C4#1062284011yescharacteristic
353C4#1062285211yescharacteristic
354C2C8×#432511yescharacteristic
355C2#1306743311yescharacteristic
356C2#1306745911yescharacteristic
357C2#1306748711yescharacteristic
358C2#1306879411yescharacteristic
359C2#1306888411yescharacteristic
360C2#1306889111yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D11
commutatorC2×C4×C11C22×C8
FrattiniC2×C42C22×D11
FittingC2×C8×Q8×C11C2
socle, prime radicalC23×C11C4×D4
cosocleC2×C42×C11C23
hypercenterC2×C8×Q8D11
hypocenterC11#8846
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×C8×Q8

Complements

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

NH ≅ G/Ntype
53. #66899C8semidirect
124. Q8×C11C4⋊C8semidirect
292. C11#8846semidirect
297. Q8Dic11⋊C8semidirect

Maximal subgroups

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

subgroupindex
#130693342
C4×#668992
C2×#106221182
C2×Q8⋊(C11⋊C8)2
#130664552
C11⋊#12732
C2×C8×Q8×C112
#884611