Finite Group Databasebeta

← #14650465

Subgroups — #14650465

Order 2816.

490 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079554C211yesmaximal, characteristic
2#13069440C211yesmaximal, characteristic
3#13067285C211yesmaximal, characteristic
4#13067180C211yesmaximal, characteristic, complemented
5#13066476C211yesmaximal, characteristic, complemented
6#13066447C211yesmaximal, characteristic, complemented
7C11×#2961C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×#66927C2211yescharacteristic
10C11×#446—22no—
11C11×#446—22no—
12C11×#424—21no—
13C11×#423C2211yescharacteristic
14C11×#405—21no—
15C2×C11×#97C2211yescharacteristic
16C2×#66885—21no—
17C2×#66885—21no—
18#10622701C412yescomplemented
19#10622698C412yescomplemented
20#10622659—22no—
21#10622640—22no—
22#10622549C2211yescharacteristic
23#10622538C2211yescharacteristic
24#10622538C2211yescharacteristic
25#10622176—22no—
26#10622123—22no—
27C22×D44—21no—
28C22×D44—21no—
29C22×D44—21no—
30C2×C11×M16—21no—
31C22×C8×C11D411yescharacteristic
32C22×C8×C11D411yescharacteristic
33C11×C4⋊Q8C2×C411yescharacteristic
34C11×C4⋊Q8C2×C411yescharacteristic
35C11×#125—21no—
36C11×C22⋊Q8—21no—
37C11×C22⋊Q8D412yes—
38C4×Q8×C11—21no—
39C4×Q8×C11D412yes—
40C11×#117—21no—
41C2×C42×C11C2311yescharacteristic
42C2×#4325—24no—
43C2×C4⋊Dic11—21no—
44#66927—21no—
45#66927—21no—
46#66927—21no—
47#66927C2×C412yes—
48C11×C4⋊C8—24no—
49C11×C4⋊C8—21no—
50C11×C4⋊C8D412yes—
51C11×#97—22no—
52C11×#97—21no—
53C11×#97—21no—
54C4×C8×C11—22no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C22⋊(C11⋊C8)—21no—
58C22⋊(C11⋊C8)—21no—
59#66885—42no—
60#66885—42no—
61#66873—24no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)—21no—
64C4×C11⋊C8—21no—
65C4×C11⋊C8C2×C412yes—
66#9294—111nomaximal, Sylow
67C23×D11—41no—
68C2×Q8×C11—21no—
69C2×Q8×C11C22⋊C412yes—
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11#4111yescharacteristic
73C22×Dic11—41no—
74C2×D44—22no—
75C2×D44—22no—
76C2×D44—22no—
77C2×D44—41no—
78C2×D44—41no—
79C2×D44—41no—
80C2×D44—41no—
81C2×D44—41no—
82C2×D44—41no—
83C2×D44—41no—
84C2×D44—82no—
85C2×D44—82no—
86C11×M16—41no—
87C11×M16—41no—
88C2×C8×C11—21no—
89C2×C8×C11—22no—
90C2×C8×C11—21no—
91C2×C8×C11—21no—
92C2×C8×C11—21no—
93C2×C8×C11—21no—
94C2×C8×C11SD1612yescomplemented
95C11×C4⋊C4—21no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—22no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4C22⋊C412yes—
101C11×C22⋊C4—22no—
102C42×C11—22no—
103C42×C11C22×C411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C42×C11#4111yescharacteristic
107#4325—84no—
108C4⋊Dic11—41no—
109C4⋊Dic11—41no—
110C2×C11⋊C8—22no—
111C2×C11⋊C8—41no—
112#3208—111no—
113#2961D1111yescharacteristic, complemented
114#1961—111no—
115#1545—111no—
116#1518—111no—
117#1286—111no—
118#1275—111no—
119C23×C11#12111yescharacteristic
120C22×D11—42no—
121C22×D11—82no—
122C22×D11—82no—
123C22×D11—81no—
124C22×D11—81no—
125Q8×C11—42no—
126Q8×C11—81no—
127C2×C4×C11—22no—
128C2×C4×C11—22no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11C2×C22⋊C411yescharacteristic
132C2×C4×C11C4×D411yescharacteristic
133C2×C4×C11C4×D411yescharacteristic
134C2×C4×C11#12011yescharacteristic
135C2×C4×C11#12111yescharacteristic
136C2×C4×C11#12311yescharacteristic
137C2×C4×C11C2×SD1611yescharacteristic
138C2×C4×C11#13511yescharacteristic
139C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C11#13711yescharacteristic
141C2×Dic11—81no—
142C2×Dic11—81no—
143C2×Dic11—81no—
144D44—44no—
145D44—42no—
146D44—42no—
147D44—82no—
148D44—82no—
149D44—82no—
150D44—81no—
151D44—81no—
152C8×C11—22no—
153C8×C11—41no—
154C8×C11—42no—
155C11⋊C8—42no—
156C11⋊C8—81no—
157#533C2×D1111yescharacteristic
158C2×#127—111no—
159#492—112no—
160#486—112no—
161#460—222no—
162#450—222no—
163#446—22no—
164#446—22no—
165#431—111no—
166#431—111no—
167#424—21no—
168#423C2×D1111yescharacteristic
169C2×#102—221no—
170C2×#102—221no—
171#405—21no—
172C2×#97C2×D1111yescharacteristic
173#382—111no—
174#331—222no—
175#328—222no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11#38611yescharacteristic
179C22×C11#46011yescharacteristic
180C22×C11#46411yescharacteristic
181C2×D11—82no—
182C2×D11—82no—
183C2×D11—82no—
184C2×D11—162no—
185C2×D11—162no—
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—42no—
191C4×C11—42no—
192C4×C11C4×SD1611yescharacteristic
193C4×C11#44011yescharacteristic
194C4×C11#44811yescharacteristic
195C4×C11#44911yescharacteristic
196Dic11—161no—
197C22×D4—221no—
198C22×D4—221no—
199C22×D4—221no—
200C2×SD16—224no—
201C2×M16—21no—
202C22×C8C22⋊D1111yescharacteristic
203C22×C8C22⋊D1111yescharacteristic
204C4⋊Q8C4×D1111yescharacteristic
205C4⋊Q8C4×D1111yescharacteristic
206#127—112no—
207#127—221no—
208#127—221no—
209#127—221no—
210#125—21no—
211C22⋊Q8—21no—
212C22⋊Q8D4412yes—
213C4×Q8—21no—
214C4×Q8C22⋊D1112yes—
215#117—21no—
216C2×C4⋊C4—221no—
217C2×C42C22×D1111yescharacteristic
218C4⋊C8—24no—
219C4⋊C8—21no—
220C4⋊C8—221no—
221C4⋊C8—221no—
222C4⋊C8C22⋊D1112yes—
223#102—224no—
224#102—442no—
225#102—442no—
226C22⋊C8—221no—
227C22⋊C8—221no—
228#97—22no—
229#97—21no—
230#97—21no—
231C4×C8—22no—
232C4×C8—112no—
233C4×C8—221no—
234#95—221no—
235#95—221no—
236C2×C11—21no—
237C2×C11—21no—
238C2×C11#188011yescharacteristic
239C2×C11#190311yescharacteristic
240C2×C11#191011yescharacteristic
241D11—162no—
242C24—441no—
243C2×Q8—21no—
244C2×Q8(C2×D11)⋊C412yes—
245C2×D4—222no—
246C2×D4—222no—
247C2×D4—222no—
248C2×D4—441no—
249C2×D4—441no—
250C2×D4—441no—
251C2×D4—441no—
252C2×D4—441no—
253C2×D4—441no—
254C2×D4—441no—
255C2×D4—882no—
256C2×D4—882no—
257C22×C4—441no—
258C22×C4C2×D4411yescharacteristic
259C22×C4#433911yescharacteristic
260C22×C4C2×C22⋊D1111yescharacteristic
261SD16—884no—
262M16—41no—
263M16—41no—
264C2×C8—21no—
265C2×C8—21no—
266C2×C8—21no—
267C2×C8—21no—
268C2×C8—22no—
269C2×C8—21no—
270C2×C8—222no—
271C2×C8—441no—
272C2×C8#432512yescomplemented
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—441no—
279C4⋊C4—441no—
280C4⋊C4(C2×D11)⋊C412yes—
281C22⋊C4—22no—
282C42—22no—
283C42C2×C4×D1111yescharacteristic
284C42#433911yescharacteristic
285C42C2×C22⋊D1111yescharacteristic
286C42C2×C22⋊D1111yescharacteristic
287C11#929411yescharacteristic, complemented, Sylow
288C23—442no—
289C23—882no—
290C23—882no—
291C23—881no—
292C23—881no—
293C23#6698311yescharacteristic
294Q8—42no—
295Q8—81no—
296D4—444no—
297D4—442no—
298D4—442no—
299D4—882no—
300D4—882no—
301D4—882no—
302D4—881no—
303D4—881no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—881no—
309C2×C4—881no—
310C2×C4—881no—
311C2×C4C2×(C2×D11)⋊C411yescharacteristic
312C2×C4C4×C22⋊D1111yescharacteristic
313C2×C4C4×C22⋊D1111yescharacteristic
314C2×C4#6698211yescharacteristic
315C2×C4#6698311yescharacteristic
316C2×C4C2×#432511yescharacteristic
317C2×C4#6699511yescharacteristic
318C2×C4#6700211yescharacteristic
319C2×C4#6700311yescharacteristic
320C2×C4#6700611yescharacteristic
321C8—22no—
322C8—41no—
323C8—42no—
324C8—442no—
325C8—881no—
326C22—21no—
327C22—21no—
328C22—882no—
329C22—882no—
330C22—882no—
331C22—1762no—
332C22—1762no—
333C22#1062264011yescharacteristic
334C22#1062264111yescharacteristic
335C22#1062282611yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—42no—
341C4—42no—
342C4—1761no—
343C4C4×#432511yescharacteristic
344C4#1062263911yescharacteristic
345C4#1062284011yescharacteristic
346C4#1062285111yescharacteristic
347C2—21no—
348C2—21no—
349C2—1762no—
350C2#1306897111yescharacteristic
351C2#1306909611yescharacteristic
352C2#1306914311yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2961C2
socleC22×C11#386
prime radicalC2×#66927C22
cosocleC2×C42×C11C23
hypercenter#2961D11
hypocenterC11#9294
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2961

Complements

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

NH ≅ G/Ntype
4. #13067180C2semidirect
5. #13066476C2semidirect
6. #13066447C2semidirect
7. C11×#2961C2semidirect
18. #10622701C4semidirect
19. #10622698C4semidirect
94. C2×C8×C11SD16semidirect
113. #2961D11semidirect
272. C2×C8#4325semidirect
287. C11#9294semidirect

Maximal subgroups

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

subgroupindex
#130795542
#130694402
#130672852
#130671802
#130664762
#130664472
C11×#29612
#929411