Finite Group Databasebeta

← #14641844

Subgroups — #14641844

Order 2816.

478 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071187C211yesmaximal, characteristic
2#13068731C211yesmaximal, characteristic
3#13068360C211yesmaximal, characteristic
4#13066440C211yesmaximal, characteristic
5#13066439C211yesmaximal, characteristic
6#13066438C211yesmaximal, characteristic
7C11×#1271C211yesmaximal, characteristic
8C2×#66941C411yescharacteristic
9C2×#66940—21no—
10C11×#389C2211yescharacteristic
11C2×Dic11⋊C8—21no—
12C2×C8×Dic11—21no—
13#10622589C411yescharacteristic
14C4⋊C4×Dic11C411yescharacteristic
15C4⋊C4×Dic11C411yescharacteristic
16#10622585—21no—
17C42×Dic11C2211yescharacteristic
18#10622541C2211yescharacteristic
19#10622262—21no—
20#10622259—21no—
21C11×#336C2211yescharacteristic
22C11×#336C2211yescharacteristic
23#10622188—21no—
24#10622188—21no—
25#10622162C2211yescharacteristic
26#10622162C2211yescharacteristic
27C22×Dic22—21no—
28C22×C8×C11—21no—
29C22×C8×C11—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4C2×C411yescharacteristic
32C2×C11×C4⋊C4C2×C411yescharacteristic
33C2×C42×C11C2311yescharacteristic
34C2×C4⋊Dic11C2×C411yescharacteristic
35C2×C4⋊Dic11C2×C411yescharacteristic
36C2×Dic11⋊C4—21no—
37C2×Dic11⋊C4—21no—
38C2×Dic11⋊C4—21no—
39C2×Dic11⋊C4—21no—
40C2×C4×Dic11—21no—
41C2×C4×Dic11—21no—
42C2×C4×Dic11C2×C411yescharacteristic
43C2×C4×Dic11C2×C411yescharacteristic
44C2×C4×Dic11D411yescharacteristic
45C2×C4×Dic11D411yescharacteristic
46C2×C4×Dic11D411yescharacteristic
47C2×C4×Dic11D411yescharacteristic
48C22×C11⋊C8—21no—
49C22×C11⋊C8—21no—
50#66941—22no—
51#66941C814yescomplemented
52#66940—42no—
53#66940—42no—
54C11×#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58Dic11⋊C8—42no—
59C8×Dic11—24no—
60#7591—111nomaximal, Sylow
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11C22×C411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C22×Dic11—21no—
67C22×Dic11—21no—
68C22×Dic11C22⋊C411yescharacteristic
69C22×Dic11C22⋊C411yescharacteristic
70C22×Dic11C22⋊C411yescharacteristic
71C22×Dic11C22⋊C411yescharacteristic
72C2×Dic22—24no—
73C2×Dic22—42no—
74C2×Dic22—42no—
75C2×C8×C11—22no—
76C2×C8×C11—41no—
77C2×C8×C11—41no—
78C2×C8×C11—41no—
79C2×C8×C11—41no—
80C2×C8×C11—41no—
81C11×C4⋊C4—21no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4C2×C812yes—
86C42×C11—41no—
87C4⋊Dic11—21no—
88C4⋊Dic11—41no—
89C4⋊Dic11C2×C812yes—
90Dic11⋊C4—24no—
91Dic11⋊C4—42no—
92Dic11⋊C4—42no—
93Dic11⋊C4—41no—
94Dic11⋊C4—41no—
95C4×Dic11—22no—
96C4×Dic11—22no—
97C4×Dic11—21no—
98C4×Dic11—21no—
99C4×Dic11—41no—
100C4×Dic11—42no—
101C4×Dic11—42no—
102C4×Dic11C2×C812yes—
103C4×Dic11M1612yes—
104C4×Dic11SD1612yes—
105C4×Dic11Q1612yes—
106C2×C11⋊C8—22no—
107C2×C11⋊C8—41no—
108C2×C11⋊C8—41no—
109C2×C11⋊C8—41no—
110C2×C11⋊C8—41no—
111C2×C11⋊C8—41no—
112C4×C4⋊Q8—111no—
113#1831—111no—
114#1744—111no—
115#1271—111no—
116#1271—111no—
117#1271—111no—
118#1271D1111yescharacteristic
119C23×C11C2×C22⋊C411yescharacteristic
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—22no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11C22×C811yescharacteristic
133C2×C4×C11C2×M1611yescharacteristic
134C2×C4×C11C2×SD1611yescharacteristic
135C2×C4×C11C2×Q1611yescharacteristic
136C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
138C2×Dic11—21no—
139C2×Dic11—21no—
140C2×Dic11—21no—
141C2×Dic11—21no—
142C2×Dic11—21no—
143C2×Dic11—21no—
144C2×Dic11—22no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11C22⋊C812yes—
151C2×Dic11C22⋊C812yes—
152C2×Dic11#10112yes—
153C2×Dic11#10312yes—
154C2×Dic11#10312yes—
155C2×Dic11#10412yes—
156Dic22—48no—
157C8×C11—42no—
158C8×C11—81no—
159C11⋊C8—42no—
160C11⋊C8—81no—
161C2×C4⋊Q8—111no—
162C2×C4×Q8—221no—
163C2×C4⋊C8—221no—
164C2×C4×C8—221no—
165#391—221no—
166#389—111no—
167#389—221no—
168#389C2×D1111yescharacteristic
169#384—111no—
170C4×C4⋊C4—111no—
171C4×C4⋊C4—111no—
172C4×C4⋊C4—221no—
173C43—111no—
174#336—111no—
175#336—111no—
176#336—221no—
177#336—221no—
178#336C2×D1111yescharacteristic
179#336C2×D1111yescharacteristic
180C22×C11C2×C22⋊C811yescharacteristic
181C22×C11#41011yescharacteristic
182C22×C11C2×#10111yescharacteristic
183C22×C11C2×#10311yescharacteristic
184C22×C11#41811yescharacteristic
185C22×C11C2×#10411yescharacteristic
186C22×C11#42111yescharacteristic
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—42no—
194C4×C11—81no—
195Dic11—22no—
196Dic11—22no—
197Dic11—22no—
198Dic11—42no—
199Dic11—81no—
200Dic11Q8⋊C814yes—
201C22×Q8—221no—
202C22×C8—21no—
203C22×C8—21no—
204C22×C8—221no—
205C22×C8—221no—
206C4⋊Q8—114no—
207C4⋊Q8—222no—
208C4×Q8—442no—
209C4×Q8—442no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—111no—
212C2×C4⋊C4—111no—
213C2×C4⋊C4—221no—
214C2×C4⋊C4—221no—
215C2×C4⋊C4—221no—
216C2×C4⋊C4—221no—
217C2×C4⋊C4C4×D1111yescharacteristic
218C2×C4⋊C4C4×D1111yescharacteristic
219C2×C42—111no—
220C2×C42—111no—
221C2×C42—111no—
222C2×C42—111no—
223C2×C42—111no—
224C2×C42—111no—
225C2×C42—221no—
226C2×C42—221no—
227C2×C42C22×D1111yescharacteristic
228C4⋊C8—442no—
229C4×C8—224no—
230#95—21no—
231#95—221no—
232#95—221no—
233#95—221no—
234C2×C11#146111yescharacteristic
235C2×C11C2×Q8⋊C811yescharacteristic
236C2×C11#147811yescharacteristic
237C2×C11#150511yescharacteristic
238C2×C11#151811yescharacteristic
239C2×C11#153111yescharacteristic
240C2×C11#154911yescharacteristic
241C2×Q8—224no—
242C2×Q8—442no—
243C2×Q8—442no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—111no—
247C22×C4—111no—
248C22×C4—111no—
249C22×C4—111no—
250C22×C4—221no—
251C22×C4—221no—
252C22×C4C2×C4×D1111yescharacteristic
253C22×C4D4×D1111yescharacteristic
254C22×C4D4×D1111yescharacteristic
255C2×C8—22no—
256C2×C8—41no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—41no—
261C2×C8—222no—
262C2×C8—441no—
263C2×C8—441no—
264C2×C8—441no—
265C2×C8—441no—
266C2×C8—441no—
267C4⋊C4—21no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—112no—
272C4⋊C4—224no—
273C4⋊C4—221no—
274C4⋊C4—441no—
275C4⋊C4—442no—
276C4⋊C4—442no—
277C4⋊C4—441no—
278C4⋊C4—441no—
279C4⋊C4C8×D1112yes—
280C42—41no—
281C42—112no—
282C42—112no—
283C42—112no—
284C42—112no—
285C42—222no—
286C42—222no—
287C42—221no—
288C42—221no—
289C42—441no—
290C42—442no—
291C42—442no—
292C11#759111yescharacteristic, complemented, Sylow
293C23C22⋊C4×D1111yescharacteristic
294Q8—448no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—22no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—112no—
308C2×C4—112no—
309C2×C4—112no—
310C2×C4—112no—
311C2×C4—112no—
312C2×C4—112no—
313C2×C4—221no—
314C2×C4—221no—
315C2×C4—221no—
316C2×C4—221no—
317C2×C4—221no—
318C2×C4—221no—
319C2×C4—222no—
320C2×C4—441no—
321C2×C4—441no—
322C2×C4—441no—
323C2×C4—441no—
324C2×C4—441no—
325C2×C4C2×C8×D1111yescharacteristic
326C2×C4M16×D1111yescharacteristic
327C2×C4#6696411yescharacteristic
328C2×C4SD16×D1111yescharacteristic
329C2×C4#6696711yescharacteristic
330C2×C4Q16×D1111yescharacteristic
331C8—42no—
332C8—81no—
333C8—442no—
334C8—881no—
335C22D11×C22⋊C811yescharacteristic
336C22#1062235311yescharacteristic
337C22D11×#10111yescharacteristic
338C22#1062238311yescharacteristic
339C22D11×#10311yescharacteristic
340C22D11×#10411yescharacteristic
341C22#1062243411yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—42no—
349C4—81no—
350C4—114no—
351C4—222no—
352C4—222no—
353C4—222no—
354C4—442no—
355C4—881no—
356C2#1306693811yescharacteristic
357C2D11×Q8⋊C811yescharacteristic
358C2#1306700511yescharacteristic
359C2#1306712211yescharacteristic
360C2#1306717811yescharacteristic
361C2#1306722911yescharacteristic
362C2#1306729911yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC2×C4×C11C22×C8
FrattiniC2×C42C22×D11
FittingC11×#1271C2
socle, prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1271D11
hypocenterC11#7591
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
51. #66941C8semidirect
292. C11#7591semidirect

Maximal subgroups

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

subgroupindex
#130711872
#130687312
#130683602
#130664402
#130664392
#130664382
C11×#12712
#759111