Finite Group Databasebeta

← #14652839

Subgroups — #14652839

Order 2816.

602 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#13076972C211yesmaximal, characteristic
2#13068732C211yesmaximal, characteristic, complemented
3C4⋊C8×Dic11C211yesmaximal, characteristic, complemented
4C2×#10622119C211yesmaximal, characteristic, complemented
5C2×#10622119C211yesmaximal, characteristic, complemented
6C2×#10622182C211yesmaximal, characteristic
7C2×C11×#331C211yesmaximal, characteristic
8C2×C11×#127C2211yescharacteristic
9C2×#66989C414yes—
10C2×#66922C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13#10622834—21no—
14#10622834—22no—
15#10622834—21no—
16C2×C8×Dic11—21no—
17C42×Dic11C2211yescharacteristic
18C2×C4⋊(C11⋊C8)C2211yescharacteristic
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C11×#331—22no—
21#10622188—21no—
22#10622188—22no—
23#10622182—22no—
24#10622119—22no—
25#10622119—22no—
26C22×D4×C11—21no—
27C22×D4×C11—21no—
28C22×D4×C11C2×C412yes—
29C22×Dic22C2×C412yes—
30C22×C8×C11—21no—
31C22×C8×C11—21no—
32C11×#127—21no—
33C11×#127—21no—
34C11×#127—21no—
35C11×#127—21no—
36C2×C42×C11C2311yescharacteristic
37C2×C22⋊Dic11—24no—
38C2×C22⋊Dic11—24no—
39#66989—48no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11—21no—
42C2×C4×Dic11C2×C412yes—
43C2×C4×Dic11D411yescharacteristic
44C2×C4×Dic11D412yes—
45C2×C4×Dic11D411yescharacteristic
46C22×C11⋊C8—21no—
47C22×C11⋊C8—21no—
48#66922—21no—
49#66922—21no—
50#66922—21no—
51#66922—21no—
52C11×C4⋊C8—21no—
53C11×C4⋊C8—21no—
54C11×C4⋊C8—21no—
55C11×C4⋊C8D412yes—
56C8×Dic11—42no—
57C4⋊(C11⋊C8)—21no—
58C4⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)D412yes—
61#9699—111nomaximal, Sylow
62C24×C11—22no—
63C2×D4×C11—22no—
64C2×D4×C11—22no—
65C2×D4×C11—44no—
66C2×D4×C11—41no—
67C2×D4×C11—41no—
68C2×D4×C11—41no—
69C2×D4×C11—41no—
70C2×D4×C11—41no—
71C2×D4×C11—42no—
72C2×D4×C11—41no—
73C2×D4×C11—42no—
74C2×D4×C11—41no—
75C2×D4×C11—41no—
76C22×C4×C11C22×C411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×Dic11—22no—
80C22×Dic11C22⋊C412yes—
81C22×Dic11C22⋊C412yes—
82C2×Dic22—22no—
83C2×Dic22—22no—
84C2×Dic22—44no—
85C2×C8×C11—22no—
86C2×C8×C11—41no—
87C2×C8×C11—41no—
88C2×C8×C11—42no—
89C2×C8×C11—41no—
90C42×C11C2×D411yescharacteristic
91C42×C11C2×D411yescharacteristic
92C42×C11#4111yescharacteristic
93C42×C11#4111yescharacteristic
94C22⋊Dic11—48no—
95C22⋊Dic11—48no—
96C4⋊Dic11—41no—
97C4⋊Dic11—41no—
98C4⋊Dic11—41no—
99C4⋊Dic11—41no—
100C4×Dic11—24no—
101C4×Dic11—21no—
102C4×Dic11—22no—
103C4×Dic11—21no—
104C4×Dic11—22no—
105C4×Dic11—21no—
106C4×Dic11—21no—
107C2×C11⋊C8—22no—
108C2×C11⋊C8—41no—
109C2×C11⋊C8—41no—
110C2×C11⋊C8—42no—
111C2×C11⋊C8—41no—
112#2858—111no—
113#1831—111no—
114C4×C4⋊C8—111no—
115C2×#333—111no—
116C2×#333—111no—
117C2×#331—111no—
118C2×#331D1111yescharacteristic
119C23×C11—42no—
120C23×C11—44no—
121C23×C11—42no—
122C23×C11—44no—
123C23×C11—42no—
124C23×C11C2×C22⋊C411yescharacteristic
125D4×C11—82no—
126D4×C11—82no—
127D4×C11—81no—
128D4×C11—81no—
129D4×C11—81no—
130D4×C11—81no—
131D4×C11—82no—
132D4×C11—81no—
133D4×C11—81no—
134C2×C4×C11—22no—
135C2×C4×C11C4×D411yescharacteristic
136C2×C4×C11C4×D411yescharacteristic
137C2×C4×C11#12111yescharacteristic
138C2×C4×C11#12111yescharacteristic
139C2×C4×C11#12411yescharacteristic
140C2×C4×C11#12711yescharacteristic
141C2×C4×C11#13511yescharacteristic
142C2×C4×C11#13512yes—
143C2×C4×C11#13511yescharacteristic
144C2×C4×C11#13512yes—
145C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C11#13711yescharacteristic
147C2×Dic11—22no—
148C2×Dic11—22no—
149C2×Dic11—22no—
150C2×Dic11—22no—
151C2×Dic11—22no—
152C2×Dic11—42no—
153C2×Dic11—44no—
154C2×Dic11#10014yes—
155Dic22—82no—
156Dic22—82no—
157C8×C11—42no—
158C8×C11—81no—
159C11⋊C8—42no—
160C11⋊C8—81no—
161C2×C4⋊Q8—111no—
162C2×#127C2×D1111yescharacteristic
163C2×#124—114no—
164C2×C4⋊C8—111no—
165C2×C4⋊C8—111no—
166C2×C4⋊C8C2×D1111yescharacteristic
167C2×C4⋊C8C2×D1111yescharacteristic
168C2×C4×C8—221no—
169#390—222no—
170#390—221no—
171#390—221no—
172C43—111no—
173#336—222no—
174#336—221no—
175#333—222no—
176#333—222no—
177#331—22no—
178#331—222no—
179C22×C11—84no—
180C22×C11—84no—
181C22×C11—82no—
182C22×C11—82no—
183C22×C11—82no—
184C22×C11#39011yescharacteristic
185C22×C11C2×#10012yes—
186C22×C11#41611yescharacteristic
187C22×C11#41612yes—
188C22×C11#41711yescharacteristic
189C4×C11—21no—
190C4×C11—21no—
191C4×C11#46311yescharacteristic
192C4×C11#46311yescharacteristic
193C4×C11#46411yescharacteristic
194C4×C11#46411yescharacteristic
195C4×C11#48812yes—
196C4×C11#49511yescharacteristic
197C4×C11#49511yescharacteristic
198Dic11—24no—
199Dic11—42no—
200Dic11—82no—
201C22×Q8—112no—
202C22×D4—21no—
203C22×D4—21no—
204C22×D4C4×D1112yes—
205C22×C8—21no—
206C22×C8—21no—
207C22×C8—221no—
208C22×C8—221no—
209C4⋊Q8—221no—
210C4⋊Q8—221no—
211C4⋊Q8—221no—
212C4⋊Q8—221no—
213#127—21no—
214#127—21no—
215#127—21no—
216#127—21no—
217#124—448no—
218C2×C4⋊C4—221no—
219C2×C4⋊C4—221no—
220C2×C22⋊C4—224no—
221C2×C22⋊C4—224no—
222C2×C42—112no—
223C2×C42—112no—
224C2×C42—111no—
225C2×C42—111no—
226C2×C42C22×D1111yescharacteristic
227C4⋊C8—21no—
228C4⋊C8—21no—
229C4⋊C8—21no—
230C4⋊C8—112no—
231C4⋊C8—221no—
232C4⋊C8—221no—
233C4⋊C8—221no—
234C4⋊C8C22⋊D1112yes—
235C4×C8—442no—
236C2×C11—162no—
237C2×C11#154312yes—
238C2×C11#155112yes—
239C2×C11#195811yescharacteristic
240C2×C11#196511yescharacteristic
241C2×C11#198311yescharacteristic
242C24—22no—
243C2×Q8—222no—
244C2×Q8—222no—
245C2×Q8—444no—
246C2×D4—22no—
247C2×D4—22no—
248C2×D4—44no—
249C2×D4—41no—
250C2×D4—41no—
251C2×D4—41no—
252C2×D4—41no—
253C2×D4—42no—
254C2×D4—41no—
255C2×D4—41no—
256C2×D4—42no—
257C2×D4—41no—
258C2×D4—41no—
259C22×C4—112no—
260C22×C4—112no—
261C22×C4—222no—
262C22×C4C2×C4×D1111yescharacteristic
263C22×C4D4×D1111yescharacteristic
264C22×C4D4×D1111yescharacteristic
265C2×C8—22no—
266C2×C8—41no—
267C2×C8—41no—
268C2×C8—42no—
269C2×C8—41no—
270C2×C8—222no—
271C2×C8—441no—
272C2×C8—441no—
273C2×C8—442no—
274C2×C8—441no—
275C4⋊C4—441no—
276C4⋊C4—441no—
277C4⋊C4—441no—
278C4⋊C4—441no—
279C22⋊C4—448no—
280C22⋊C4—448no—
281C42—224no—
282C42—221no—
283C42—222no—
284C42—221no—
285C42—221no—
286C42—222no—
287C42—221no—
288C42#433911yescharacteristic
289C42D4×D1111yescharacteristic
290C42#434111yescharacteristic
291C42C2×C22⋊D1111yescharacteristic
292C11#969911yescharacteristic, complemented, Sylow
293C23—42no—
294C23—44no—
295C23—42no—
296C23—42no—
297C23—44no—
298C23C22⋊C4×D1111yescharacteristic
299Q8—882no—
300Q8—882no—
301D4—82no—
302D4—82no—
303D4—81no—
304D4—81no—
305D4—81no—
306D4—81no—
307D4—81no—
308D4—82no—
309D4—81no—
310C2×C4—22no—
311C2×C4—114no—
312C2×C4—222no—
313C2×C4—222no—
314C2×C4—222no—
315C2×C4—222no—
316C2×C4—222no—
317C2×C4—442no—
318C2×C4—444no—
319C2×C4(C22⋊D11)⋊C411yescharacteristic
320C2×C4#6693711yescharacteristic
321C2×C4#6693811yescharacteristic
322C2×C4#6696411yescharacteristic
323C2×C4#6696511yescharacteristic
324C2×C4#6696512yes—
325C2×C4#6696811yescharacteristic
326C2×C4#6696911yescharacteristic
327C2×C4#6696912yes—
328C2×C4C4×C22⋊D1111yescharacteristic
329C2×C4#6699211yescharacteristic
330C2×C4#6699311yescharacteristic
331C8—42no—
332C8—81no—
333C8—442no—
334C8—881no—
335C22—84no—
336C22—84no—
337C22—82no—
338C22—82no—
339C22—82no—
340C22D11×#10012yes—
341C22#1062238411yescharacteristic
342C22#1062238511yescharacteristic
343C22#1062238512yes—
344C22#1062257011yescharacteristic
345C4—21no—
346C4—21no—
347C4—224no—
348C4—442no—
349C4—882no—
350C4#1062238011yescharacteristic
351C4#1062238112yes—
352C4#1062240011yescharacteristic
353C4#1062276611yescharacteristic
354C4#1062276811yescharacteristic
355C4#1062277911yescharacteristic
356C4#1062278111yescharacteristic
357C2—162no—
358C2#1306727512yes—
359C2#1306730812yes—
360C2#1306942611yescharacteristic
361C2#1306945411yescharacteristic
362C2#1306954711yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#331C2
socleC23×C11C2×C22⋊C4
prime radicalC2×C11×#127C22
cosocleC2×C42×C11C23
hypercenterC2×#331D11
hypocenterC11#9699
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#331

Complements

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

NH ≅ G/Ntype
2. #13068732C2semidirect
3. C4⋊C8×Dic11C2semidirect
4. C2×#10622119C2semidirect
5. C2×#10622119C2semidirect
292. C11#9699semidirect

Maximal subgroups

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

subgroupindex
#130769722
#130687322
C4⋊C8×Dic112
C2×#106221192
C2×#106221822
C2×C11×#3312
#969911