Finite Group Databasebeta

← #14655939

Subgroups — #14655939

Order 2816.

560 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079932C211yesmaximal, characteristic
2#13079760C211yesmaximal, characteristic, complemented
3#13069569C211yesmaximal, characteristic, complemented
4#13069560C211yesmaximal, characteristic, complemented
5#13067111C211yesmaximal, characteristic
6#13066467C211yesmaximal, characteristic, complemented
7C11×#3152C211yesmaximal, characteristic
8C2×C11×#137—22no—
9C11×#532C2211yescharacteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11#10623001C2211yescharacteristic
12C11×#497—22no—
13C11×#494—21no—
14C11×#492—21no—
15C4×C11×M16C2211yescharacteristic
16#10622707—21no—
17#10622707—22no—
18#10622706—21no—
19#10622692—21no—
20#10622688—21no—
21#10622654—22no—
22#10622632—21no—
23#10622621—21no—
24#10622584—22no—
25C4×C4⋊Dic11C2211yescharacteristic
26#10622538C2211yescharacteristic
27C2×C4⋊(C11⋊C8)C2211yescharacteristic
28#10622193—22no—
29#10622175—22no—
30#10622167—22no—
31C2×C11×#41—21no—
32C22×Q8×C11—21no—
33C11×#137—44no—
34C11×#137—44no—
35C2×C11×Q16—24no—
36C2×C11×SD16—24no—
37C2×C11×M16D412yes—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8D411yescharacteristic
42C11×C4⋊Q8D412yes—
43C11×#127D411yescharacteristic
44C11×#124—21no—
45C11×#121—21no—
46C11×#121—21no—
47C4×D4×C11—21no—
48C4×D4×C11—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C42×C11C2311yescharacteristic
52C2×#4324—22no—
53#66979—21no—
54C2×C4⋊Dic11—21no—
55#66977—21no—
56#66977—21no—
57C2×C4×Dic11—21no—
58C22×C11⋊C8D412yes—
59#66923—21no—
60#66922D411yescharacteristic
61#66922D411yescharacteristic
62C4×Dic22—21no—
63C4×Dic22—21no—
64C11×#97—21no—
65C4×C8×C11—21no—
66#66896—22no—
67C11⋊#95—21no—
68C22⋊(C11⋊C8)D412yes—
69#66874—24no—
70#66874—22no—
71#66872—24no—
72#66872—22no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)—21no—
75C4⋊(C11⋊C8)—21no—
76C4×C11⋊C8—21no—
77#10206—111nomaximal, Sylow
78C11×#41—42no—
79C11×#41—42no—
80C2×Q8×C11—21no—
81C2×Q8×C11—22no—
82C2×Q8×C11—41no—
83C2×Q8×C11—42no—
84C2×Q8×C11—42no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—41no—
89C22×C4×C11—41no—
90C22×C4×C11—41no—
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×Dic11—41no—
95C2×Dic22—21no—
96C2×Dic22—21no—
97C11×Q16—48no—
98C11×SD16—48no—
99C11×M16—22no—
100C11×M16SD1614yescomplemented
101C2×C8×C11—22no—
102C11×C4⋊C4—22no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C22⋊C4—41no—
109C11×C22⋊C4—41no—
110C42×C11C2×D411yescharacteristic
111C42×C11C2×D411yescharacteristic
112C42×C11C2×D411yescharacteristic
113C42×C11#4111yescharacteristic
114C22⋊Dic11—41no—
115#4324—82no—
116C4⋊Dic11—22no—
117C4⋊Dic11—21no—
118C4⋊Dic11—21no—
119C4⋊Dic11—21no—
120C4⋊Dic11—21no—
121C4⋊Dic11—41no—
122Dic11⋊C4—41no—
123Dic11⋊C4—41no—
124C4×Dic11—41no—
125C4×Dic11—42no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—42no—
129#3246—111no—
130#3229—111no—
131#3152D1111yescharacteristic
132#1988—111no—
133#1986—111no—
134#1502—111no—
135#1283—111no—
136C23×C11—41no—
137C23×C11#12711yescharacteristic
138Q8×C11—44no—
139Q8×C11—42no—
140Q8×C11—82no—
141D4×C11—42no—
142D4×C11—41no—
143D4×C11—41no—
144D4×C11—81no—
145D4×C11—81no—
146D4×C11—81no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—42no—
152C2×C4×C11—81no—
153C2×C4×C11—81no—
154C2×C4×C11—82no—
155C2×C4×C11#12011yescharacteristic
156C2×C4×C11#12011yescharacteristic
157C2×C4×C11#12011yescharacteristic
158C2×C4×C11#12111yescharacteristic
159C2×C4×C11#12111yescharacteristic
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11C2×SD1612yes—
162C2×C4×C11AGL(1,ℤ/8)12yes—
163C2×Dic11—42no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11—81no—
167C2×Dic11—81no—
168Dic22—42no—
169Dic22—41no—
170Dic22—41no—
171C8×C11—24no—
172C11⋊C8—42no—
173C11⋊C8—42no—
174C2×#137—22no—
175#533—111no—
176#532C2×D1111yescharacteristic
177C2×C4⋊Q8C2×D1111yescharacteristic
178#498—221no—
179#497—22no—
180#494—21no—
181#492—21no—
182#487—221no—
183#483—222no—
184#476—221no—
185#475—222no—
186#475—221no—
187#465—222no—
188#461—221no—
189#460—221no—
190#431—111no—
191C2×C4⋊C8—111no—
192C4×M16C2×D1111yescharacteristic
193C4×C4⋊C4—111no—
194#340—222no—
195#339—222no—
196#327—222no—
197C22×C11—21no—
198C22×C11—21no—
199C22×C11—81no—
200C22×C11—81no—
201C22×C11—81no—
202C22×C11#39211yescharacteristic
203C22×C11#49211yescharacteristic
204C22×C11#49611yescharacteristic
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—21no—
208C4×C11—81no—
209C4×C11—82no—
210C4×C11#45012yes—
211C4×C11#45511yescharacteristic
212C4×C11#45611yescharacteristic
213C4×C11#46012yes—
214Dic11—82no—
215Dic11—81no—
216Dic11—81no—
217C2×#41—21no—
218C22×Q8—21no—
219#137—44no—
220#137—44no—
221C2×Q16—24no—
222C2×SD16—24no—
223C2×SD16—222no—
224C2×M16C22⋊D1112yes—
225C22×C8—112no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8—111no—
230C4⋊Q8—111no—
231C4⋊Q8C22⋊D1112yes—
232C4⋊Q8C22⋊D1111yescharacteristic
233#127C22⋊D1111yescharacteristic
234#125—221no—
235#124—21no—
236C22⋊Q8—221no—
237C22⋊Q8—221no—
238#121—21no—
239#121—21no—
240C4×Q8—221no—
241C4×Q8—221no—
242C4×D4—21no—
243C4×D4—21no—
244#117—221no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—221no—
248C2×C42—221no—
249C2×C42C22×D1111yescharacteristic
250#106—222no—
251#106—224no—
252C4⋊C8—221no—
253C4⋊C8—221no—
254C4⋊C8—221no—
255#103—222no—
256#103—224no—
257#102—222no—
258C22⋊C8—112no—
259#97—21no—
260C4×C8—21no—
261C4×C8—221no—
262#95—221no—
263C2×C11—21no—
264C2×C11—21no—
265C2×C11—161no—
266C2×C11#200711yescharacteristic
267C2×C11#200911yescharacteristic
268C2×C11#201411yescharacteristic
269#41—42no—
270#41—42no—
271C2×Q8—21no—
272C2×Q8—22no—
273C2×Q8—41no—
274C2×Q8—42no—
275C2×Q8—42no—
276C2×Q8—221no—
277C2×Q8—221no—
278C2×D4—21no—
279C2×D4—21no—
280C2×D4—21no—
281C2×D4—41no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—441no—
285C22×C4D4×D1111yescharacteristic
286C22×C4D4×D1111yescharacteristic
287C22×C4C2×C22⋊D1111yescharacteristic
288Q16—48no—
289SD16—48no—
290SD16—882no—
291M16—22no—
292M16#432414yescomplemented
293C2×C8—22no—
294C2×C8—222no—
295C2×C8—222no—
296C2×C8—442no—
297C4⋊C4—22no—
298C4⋊C4—21no—
299C4⋊C4—22no—
300C4⋊C4—21no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—222no—
304C4⋊C4—221no—
305C4⋊C4—221no—
306C4⋊C4—221no—
307C4⋊C4—221no—
308C4⋊C4—441no—
309C4⋊C4—441no—
310C4⋊C4—441no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C22⋊C4—441no—
314C42—441no—
315C42—442no—
316C42D4×D1111yescharacteristic
317C42#434111yescharacteristic
318C42C2×C22⋊D1111yescharacteristic
319C42C2×C22⋊D1111yescharacteristic
320C11#1020611yescharacteristic, complemented, Sylow
321C23—41no—
322C23#6699311yescharacteristic
323Q8—44no—
324Q8—42no—
325Q8—82no—
326Q8—442no—
327Q8—441no—
328Q8—441no—
329D4—41no—
330D4—41no—
331D4—42no—
332D4—81no—
333D4—81no—
334D4—81no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4—82no—
343C2×C4—442no—
344C2×C4—441no—
345C2×C4—441no—
346C2×C4—881no—
347C2×C4—881no—
348C2×C4#6698512yes—
349C2×C4C2×#432412yes—
350C2×C4#6699011yescharacteristic
351C2×C4#6699011yescharacteristic
352C2×C4#6699111yescharacteristic
353C2×C4#6699211yescharacteristic
354C2×C4#6699211yescharacteristic
355C2×C4#6700611yescharacteristic
356C8—24no—
357C8—442no—
358C8—442no—
359C22—21no—
360C22—21no—
361C22—81no—
362C22—81no—
363C22—81no—
364C22#1062268711yescharacteristic
365C22#1062268911yescharacteristic
366C22#1062283611yescharacteristic
367C4—21no—
368C4—21no—
369C4—21no—
370C4—81no—
371C4—82no—
372C4—882no—
373C4—881no—
374C4—881no—
375C4#1062268812yes—
376C4#1062281511yescharacteristic
377C4#1062281811yescharacteristic
378C4#1062283112yes—
379C2—21no—
380C2—21no—
381C2—161no—
382C2#1306966111yescharacteristic
383C2#1306967411yescharacteristic
384C2#1306970411yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3152C2
socleC22×C11#392
prime radicalC11×#532C22
hypercenter#3152D11
hypocenterC11#10206
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3152

Complements

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

NH ≅ G/Ntype
2. #13079760C2semidirect
3. #13069569C2semidirect
4. #13069560C2semidirect
6. #13066467C2semidirect
100. C11×M16SD16semidirect
292. M16#4324semidirect
320. C11#10206semidirect

Maximal subgroups

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

subgroupindex
#130799322
#130797602
#130695692
#130695602
#130671112
#130664672
C11×#31522
#1020611