Finite Group Databasebeta

← #14648973

Subgroups — #14648973

Order 2816.

476 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078620C211yesmaximal, characteristic
2#13069414C211yesmaximal, characteristic
3#13067273C211yesmaximal, characteristic, complemented
4#13067040C211yesmaximal, characteristic
5#13066511C211yesmaximal, characteristic, complemented
6#13066461C211yesmaximal, characteristic, complemented
7C11×#2961C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C4×D44C2211yescharacteristic
10C11×#446—22no—
11C11×#446—22no—
12C11×#424—21no—
13C11×#423C2211yescharacteristic
14C11×#405—21no—
15C2×C11×#97C2211yescharacteristic
16C2×(C2×D11)⋊C8—21no—
17C2×(C2×D11)⋊C8—21no—
18#10622697—21no—
19#10622696—21no—
20#10622659C412yes—
21#10622656C412yes—
22C4×#4325—22no—
23#10622538C2211yescharacteristic
24#10622538C2211yescharacteristic
25C2×C4⋊(C11⋊C8)C2211yescharacteristic
26#10622185—21no—
27#10622184—21no—
28#10622121—22no—
29C22×D44C2×C411yescharacteristic
30C22×C4×D11—21no—
31C2×C11×M16—21no—
32C22×C8×C11D411yescharacteristic
33C22×C8×C11D411yescharacteristic
34C11×C4⋊Q8D411yescharacteristic
35C11×C4⋊Q8D411yescharacteristic
36C11×#125—21no—
37C11×C22⋊Q8—21no—
38C11×C22⋊Q8C2×C412yes—
39C4×Q8×C11—21no—
40C4×Q8×C11D412yes—
41C11×#117—21no—
42C2×C42×C11C2311yescharacteristic
43C2×#4325—22no—
44C2×(C2×D11)⋊C4—21no—
45C2×C4⋊Dic11C2×C411yescharacteristic
46C22×C11⋊C8—21no—
47C4×D44—21no—
48C4×D44—21no—
49C4×D44—21no—
50C4×D44—21no—
51C11×C4⋊C8—24no—
52C11×C4⋊C8—21no—
53C11×C4⋊C8D412yes—
54C11×#97—22no—
55C11×#97—21no—
56C11×#97—21no—
57C4×C8×C11—22no—
58#66899—22no—
59C22⋊(C11⋊C8)—21no—
60C22⋊(C11⋊C8)C2×C412yes—
61(C2×D11)⋊C8—42no—
62(C2×D11)⋊C8—42no—
63#66873—22no—
64#66872—22no—
65C4⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)—21no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)—21no—
69C4×C11⋊C8—21no—
70C4×C11⋊C8—21no—
71#9050—111nomaximal, Sylow
72C23×D11—21no—
73C2×Q8×C11—21no—
74C2×Q8×C11C22⋊C412yes—
75C22×C4×C11C22×C411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11#4111yescharacteristic
78C22×Dic11—21no—
79C2×D44—21no—
80C2×D44—21no—
81C2×D44—42no—
82C2×C4×D11—41no—
83C2×C4×D11—41no—
84C2×C4×D11—41no—
85C2×C4×D11—41no—
86C2×C4×D11—41no—
87C2×C4×D11—41no—
88C11×M16—41no—
89C11×M16—41no—
90C2×C8×C11—21no—
91C2×C8×C11—22no—
92C2×C8×C11—21no—
93C2×C8×C11—21no—
94C2×C8×C11—21no—
95C2×C8×C11—21no—
96C2×C8×C11SD1612yescomplemented
97C11×C4⋊C4—22no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4C22⋊C412yes—
103C11×C22⋊C4—22no—
104C42×C11—22no—
105C42×C11C2×D411yescharacteristic
106C42×C11C2×D411yescharacteristic
107C42×C11C2×D411yescharacteristic
108C42×C11#4111yescharacteristic
109#4325—44no—
110(C2×D11)⋊C4—41no—
111(C2×D11)⋊C4—41no—
112C4⋊Dic11—21no—
113C4⋊Dic11—21no—
114C2×C11⋊C8—22no—
115C2×C11⋊C8—41no—
116C2×C11⋊C8—41no—
117C2×C11⋊C8—41no—
118C2×C11⋊C8—41no—
119#3101—111no—
120#2961D1111yescharacteristic, complemented
121#1955—111no—
122#1542—111no—
123#1486—111no—
124#1301—111no—
125#1281—111no—
126C23×C11C4×D411yescharacteristic
127C22×D11—22no—
128C22×D11—41no—
129C22×D11—41no—
130C22×D11—41no—
131C22×D11—41no—
132C22×D11—41no—
133C22×D11—41no—
134Q8×C11—42no—
135Q8×C11—81no—
136C2×C4×C11—22no—
137C2×C4×C11—22no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11C2×C22⋊C411yescharacteristic
141C2×C4×C11C4×D411yescharacteristic
142C2×C4×C11#12011yescharacteristic
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11#12111yescharacteristic
145C2×C4×C11#12311yescharacteristic
146C2×C4×C11C2×SD1611yescharacteristic
147C2×C4×C11#13511yescharacteristic
148C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C11#13711yescharacteristic
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153D44—22no—
154D44—22no—
155D44—41no—
156D44—41no—
157C4×D11—81no—
158C4×D11—81no—
159C4×D11—81no—
160C4×D11—81no—
161C8×C11—22no—
162C8×C11—41no—
163C8×C11—42no—
164C11⋊C8—42no—
165C11⋊C8—81no—
166C11⋊C8—81no—
167#533C2×D1111yescharacteristic
168C2×C4×D4—111no—
169#483—112no—
170#476—221no—
171#461—221no—
172#450—112no—
173#446—22no—
174#446—22no—
175C4×SD16—222no—
176#431—111no—
177#431—111no—
178#424—21no—
179#423C2×D1111yescharacteristic
180C2×C4⋊C8—111no—
181C2×C22⋊C8—221no—
182C2×C22⋊C8—221no—
183#405—21no—
184C2×#97C2×D1111yescharacteristic
185#333—221no—
186#332—221no—
187D4⋊C8—222no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11#38611yescharacteristic
191C22×C11C4×SD1611yescharacteristic
192C22×C11#44011yescharacteristic
193C2×D11—42no—
194C2×D11—42no—
195C2×D11—42no—
196C2×D11—81no—
197C2×D11—81no—
198C2×D11—81no—
199C2×D11—81no—
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—42no—
205C4×C11—42no—
206C4×C11#44811yescharacteristic
207C4×C11#44911yescharacteristic
208C4×C11#46011yescharacteristic
209C4×C11#46411yescharacteristic
210Dic11—81no—
211C22×D4—111no—
212C23×C4—221no—
213C2×SD16—222no—
214C2×M16—21no—
215C22×C8—221no—
216C22×C8C22⋊D1111yescharacteristic
217C22×C8C22⋊D1111yescharacteristic
218C4⋊Q8D4411yescharacteristic
219C4⋊Q8D4411yescharacteristic
220#125—21no—
221C22⋊Q8—21no—
222C22⋊Q8C4×D1112yes—
223C4×Q8—21no—
224C4×Q8C22⋊D1112yes—
225C4×D4—221no—
226C4×D4—221no—
227C4×D4—221no—
228C4×D4—221no—
229#117—21no—
230C2×C4⋊C4—111no—
231C2×C22⋊C4—221no—
232C2×C42C22×D1111yescharacteristic
233#106—222no—
234C4⋊C8—24no—
235C4⋊C8—21no—
236C4⋊C8—221no—
237C4⋊C8—221no—
238C4⋊C8—221no—
239C4⋊C8—221no—
240C4⋊C8C22⋊D1112yes—
241#103—222no—
242#102—222no—
243C22⋊C8—112no—
244C22⋊C8—221no—
245C22⋊C8—442no—
246C22⋊C8—442no—
247#97—22no—
248#97—21no—
249#97—21no—
250C4×C8—22no—
251C4×C8—221no—
252C4×C8—221no—
253C2×C11—21no—
254C2×C11—21no—
255C2×C11#188011yescharacteristic
256C2×C11#188111yescharacteristic
257C2×C11#189111yescharacteristic
258D11—82no—
259C24—221no—
260C2×Q8—21no—
261C2×Q8(C2×D11)⋊C412yes—
262C2×D4—221no—
263C2×D4—221no—
264C2×D4—442no—
265C22×C4—221no—
266C22×C4—441no—
267C22×C4—441no—
268C22×C4—441no—
269C22×C4—441no—
270C22×C4—441no—
271C22×C4—441no—
272C22×C4C2×C4×D1111yescharacteristic
273C22×C4#433911yescharacteristic
274C22×C4C2×C22⋊D1111yescharacteristic
275SD16—444no—
276M16—41no—
277M16—41no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—22no—
283C2×C8—21no—
284C2×C8—222no—
285C2×C8—441no—
286C2×C8—441no—
287C2×C8—441no—
288C2×C8—441no—
289C2×C8#432512yescomplemented
290C4⋊C4—22no—
291C4⋊C4—22no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—221no—
296C4⋊C4—221no—
297C4⋊C4(C2×D11)⋊C412yes—
298C22⋊C4—22no—
299C22⋊C4—441no—
300C22⋊C4—441no—
301C42—22no—
302C42C2×D4411yescharacteristic
303C42#433911yescharacteristic
304C42C2×C22⋊D1111yescharacteristic
305C42C2×C22⋊D1111yescharacteristic
306C11#905011yescharacteristic, complemented, Sylow
307C23—222no—
308C23—441no—
309C23—441no—
310C23—441no—
311C23—441no—
312C23—441no—
313C23—441no—
314C23C4×C22⋊D1111yescharacteristic
315Q8—42no—
316Q8—81no—
317D4—222no—
318D4—222no—
319D4—441no—
320D4—441no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—441no—
326C2×C4—441no—
327C2×C4—441no—
328C2×C4—881no—
329C2×C4—881no—
330C2×C4—881no—
331C2×C4—881no—
332C2×C4C2×(C2×D11)⋊C411yescharacteristic
333C2×C4C4×C22⋊D1111yescharacteristic
334C2×C4#6698211yescharacteristic
335C2×C4#6698311yescharacteristic
336C2×C4#6698311yescharacteristic
337C2×C4C2×#432511yescharacteristic
338C2×C4#6699511yescharacteristic
339C2×C4#6700211yescharacteristic
340C2×C4#6700311yescharacteristic
341C2×C4#6700611yescharacteristic
342C8—22no—
343C8—41no—
344C8—42no—
345C8—442no—
346C8—881no—
347C8—881no—
348C22—21no—
349C22—21no—
350C22—442no—
351C22—442no—
352C22—442no—
353C22—881no—
354C22—881no—
355C22—881no—
356C22—881no—
357C22C4×#432511yescharacteristic
358C22#1062263911yescharacteristic
359C22#1062282611yescharacteristic
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—42no—
365C4—42no—
366C4—881no—
367C4#1062264011yescharacteristic
368C4#1062264111yescharacteristic
369C4#1062284011yescharacteristic
370C4#1062285111yescharacteristic
371C2—21no—
372C2—21no—
373C2—882no—
374C2#1306897111yescharacteristic
375C2#1306897811yescharacteristic
376C2#1306903411yescharacteristic
subgroupG/H
centerC2×C4#67006
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2961C2
socleC22×C11#386
prime radicalC22×D44C2×C4
cosocleC2×C42×C11C23
hypercenter#2961D11
hypocenterC11#9050
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2961

Complements

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

NH ≅ G/Ntype
3. #13067273C2semidirect
5. #13066511C2semidirect
6. #13066461C2semidirect
7. C11×#2961C2semidirect
96. C2×C8×C11SD16semidirect
120. #2961D11semidirect
289. C2×C8#4325semidirect
306. C11#9050semidirect

Maximal subgroups

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

subgroupindex
#130786202
#130694142
#130672732
#130670402
#130665112
#130664612
C11×#29612
#905011