Finite Group Databasebeta

← #14657516

Subgroups — #14657516

Order 2816.

452 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 93 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#13078082C211yesmaximal, characteristic
2#13068627C211yesmaximal, characteristic, complemented
3#13067266C211yesmaximal, characteristic, complemented
4#13067177C211yesmaximal, characteristic, complemented
5#13066936C211yesmaximal, characteristic, complemented
6#13066476C211yesmaximal, characteristic, complemented
7C11×#1570C211yesmaximal, characteristic, complemented
8C2×#66961—21no—
9#10623008C2211yescharacteristic
10C2×C4×D44C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#423C2211yescharacteristic
13C2×C11×C4⋊C8C2211yescharacteristic
14#10622746—21no—
15C2×#66885—21no—
16#10622549C2211yescharacteristic
17#10622538C2211yescharacteristic
18#10622457—22no—
19#10622456—21no—
20#10622454—21no—
21C11×#334—22no—
22#10622189—21no—
23#10622123—21no—
24#10622120—21no—
25#10622108—22no—
26#10622106—22no—
27C2×#4339—21no—
28C22×D44D411yescharacteristic
29C22×C4×D11—21no—
30C2×C11×M16—21no—
31C22×C8×C11—21no—
32C2×C42×C11C2311yescharacteristic
33#66983—21no—
34#66983—21no—
35C2×(C2×D11)⋊C4—21no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11D411yescharacteristic
38#66961—42no—
39#66961—42no—
40C2×D88—22no—
41C2×#4314—22no—
42#66928—21no—
43#66927D411yescharacteristic
44C4×D44—21no—
45C4×D44—21no—
46C4×D44—21no—
47C4×D44—21no—
48C4×D44—21no—
49C4×D44—21no—
50#66922D411yescharacteristic
51C11×C4⋊C8—21no—
52C11×C4⋊C8—21no—
53C11×C4⋊C8—21no—
54C11×C4⋊C8—21no—
55C11×C4⋊C8D412yes—
56C11×C22⋊C8D412yes—
57C4×C8×C11—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C22⋊(C11⋊C8)—21no—
61#66885—22no—
62#66885—42no—
63#66880—22no—
64C4⋊(C11⋊C8)—21no—
65C4×C11⋊C8—21no—
66#10465—111nomaximal, Sylow
67C23×D11—21no—
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11#4111yescharacteristic
71C2×C22⋊D11—41no—
72C22×Dic11—21no—
73C22×Dic11—41no—
74#4339—41no—
75#4339—41no—
76#4339—41no—
77#4339—41no—
78C2×D44—21no—
79C2×D44—21no—
80C2×D44—21no—
81C2×D44—21no—
82C2×D44—21no—
83C2×D44—21no—
84C2×D44—21no—
85C2×D44—21no—
86C2×D44SD1612yes—
87C2×C4×D11—41no—
88C2×C4×D11—41no—
89C2×C4×D11—41no—
90C2×C4×D11—82no—
91C2×Dic22—21no—
92C11×M16—41no—
93C11×M16—41no—
94C2×C8×C11—22no—
95C2×C8×C11—22no—
96C2×C8×C11—41no—
97C2×C8×C11—41no—
98C2×C8×C11—41no—
99C42×C11C2×D411yescharacteristic
100C42×C11C2×D411yescharacteristic
101C42×C11#4111yescharacteristic
102C42×C11#4111yescharacteristic
103(C2×D11)⋊C4—41no—
104(C2×D11)⋊C4—41no—
105(C2×D11)⋊C4—41no—
106(C2×D11)⋊C4—41no—
107C4⋊Dic11—21no—
108C4⋊Dic11—21no—
109C4⋊Dic11—21no—
110C4⋊Dic11—21no—
111C4⋊Dic11—41no—
112C4⋊Dic11—41no—
113C2×C11⋊C8—41no—
114D88—44no—
115#4314—44no—
116#3036—111no—
117#1804—111no—
118#1570D1111yescharacteristic, complemented
119#1540—111no—
120#1517—111no—
121#1460—111no—
122#1286—111no—
123C23×C11#12111yescharacteristic
124C22×D11—22no—
125C22×D11—41no—
126C22×D11—41no—
127C22×D11—41no—
128C22×D11—81no—
129C22×D11—81no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11#12011yescharacteristic
133C2×C4×C11#12111yescharacteristic
134C2×C4×C11#12111yescharacteristic
135C2×C4×C11#12311yescharacteristic
136C2×C4×C11#12311yescharacteristic
137C2×C4×C11#12411yescharacteristic
138C2×C4×C11C2×SD1611yescharacteristic
139C2×C4×C11#13511yescharacteristic
140C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
142C22⋊D11—81no—
143C22⋊D11—81no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—81no—
147C2×Dic11—81no—
148C2×Dic11—81no—
149C2×Dic11—81no—
150D44—22no—
151D44—22no—
152D44—41no—
153D44—41no—
154D44—41no—
155D44—41no—
156D44—81no—
157D44—81no—
158C4×D11—82no—
159C4×D11—82no—
160C4×D11—81no—
161C4×D11—81no—
162Dic22—41no—
163Dic22—41no—
164C8×C11—42no—
165C8×C11—42no—
166C8×C11—81no—
167C11⋊C8—81no—
168C2×AGL(1,ℤ/8)—221no—
169#532—111no—
170C2×C4×D4—111no—
171#463—222no—
172#461—221no—
173#459—221no—
174#431—111no—
175#431C2×D1111yescharacteristic
176#423C2×D1111yescharacteristic
177C2×C4⋊C8C2×D1111yescharacteristic
178#417—221no—
179C2×#102—221no—
180#382—111no—
181#340—221no—
182#334—22no—
183#332—221no—
184#331—221no—
185#327—222no—
186#323—222no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11#39411yescharacteristic
190C22×C11#46511yescharacteristic
191C22×C11#46911yescharacteristic
192C2×D11—42no—
193C2×D11—82no—
194C2×D11—81no—
195C2×D11—81no—
196C2×D11—82no—
197C2×D11—81no—
198C2×D11—81no—
199C2×D11—81no—
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11#44911yescharacteristic
205C4×C11#45011yescharacteristic
206C4×C11#48111yescharacteristic
207C4×C11#48211yescharacteristic
208Dic11—81no—
209Dic11—81no—
210Dic11—161no—
211C2×#41—221no—
212C22×D4—111no—
213C23×C4—221no—
214AGL(1,ℤ/8)—442no—
215AGL(1,ℤ/8)—442no—
216C2×SD16—222no—
217C2×D8—222no—
218C2×M16—21no—
219C22×C8—21no—
220C4⋊Q8—111no—
221#127—111no—
222#124—221no—
223#121—221no—
224#121—221no—
225C4×D4—221no—
226C4×D4—221no—
227C4×D4—221no—
228C4×D4—221no—
229C4×D4—221no—
230C4×D4—221no—
231C2×C4⋊C4—111no—
232C2×C4⋊C4—221no—
233C2×C22⋊C4—221no—
234C2×C42C22×D1111yescharacteristic
235C4⋊C8—21no—
236C4⋊C8—21no—
237C4⋊C8—21no—
238C4⋊C8—21no—
239C4⋊C8—221no—
240C4⋊C8C22⋊D1112yes—
241#103—222no—
242#102—222no—
243#102—442no—
244C22⋊C8—221no—
245C22⋊C8D4412yes—
246C4×C8—21no—
247C4×C8—221no—
248#95—221no—
249#95—221no—
250C2×C11—21no—
251C2×C11—21no—
252C2×C11#203411yescharacteristic
253C2×C11#204811yescharacteristic
254C2×C11#205311yescharacteristic
255D11—82no—
256D11—161no—
257C24—221no—
258#41—441no—
259#41—441no—
260#41—441no—
261#41—441no—
262C2×Q8—221no—
263C2×D4—112no—
264C2×D4—221no—
265C2×D4—221no—
266C2×D4—221no—
267C2×D4—221no—
268C2×D4—221no—
269C2×D4—221no—
270C2×D4—221no—
271C2×D4—221no—
272C2×D4—441no—
273C22×C4—221no—
274C22×C4—441no—
275C22×C4—441no—
276C22×C4—441no—
277C22×C4—441no—
278C22×C4—882no—
279C22×C4C2×D4411yescharacteristic
280C22×C4D4×D1111yescharacteristic
281C22×C4#434311yescharacteristic
282SD16—444no—
283D8—444no—
284M16—41no—
285M16—41no—
286C2×C8—22no—
287C2×C8—22no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—441no—
292C4⋊C4—221no—
293C4⋊C4—221no—
294C4⋊C4—221no—
295C4⋊C4—221no—
296C4⋊C4—441no—
297C4⋊C4—441no—
298C22⋊C4—441no—
299C22⋊C4—441no—
300C22⋊C4—441no—
301C22⋊C4—441no—
302C42#433911yescharacteristic
303C42D4×D1111yescharacteristic
304C42#434311yescharacteristic
305C42C2×C22⋊D1111yescharacteristic
306C11#1046511yescharacteristic, complemented, Sylow
307C23—222no—
308C23—441no—
309C23—441no—
310C23—441no—
311C23—881no—
312C23—881no—
313C23#6694811yescharacteristic
314Q8—441no—
315Q8—441no—
316D4—222no—
317D4—222no—
318D4—441no—
319D4—441no—
320D4—441no—
321D4—441no—
322D4—881no—
323D4—881no—
324D4—881no—
325D4—881no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—441no—
329C2×C4—441no—
330C2×C4—882no—
331C2×C4—882no—
332C2×C4—881no—
333C2×C4—881no—
334C2×C4—881no—
335C2×C4—881no—
336C2×C4—881no—
337C2×C4—881no—
338C2×C4#6694711yescharacteristic
339C2×C4#6694711yescharacteristic
340C2×C4#6694811yescharacteristic
341C2×C4SD16×D1111yescharacteristic
342C2×C4#6696711yescharacteristic
343C2×C4#6696711yescharacteristic
344C2×C4#6696911yescharacteristic
345C2×C4#6698311yescharacteristic
346C2×C4#6699011yescharacteristic
347C2×C4#6700011yescharacteristic
348C8—42no—
349C8—42no—
350C8—81no—
351C8—881no—
352C22—21no—
353C22—21no—
354C22—442no—
355C22—882no—
356C22—882no—
357C22—881no—
358C22—881no—
359C22—881no—
360C22—881no—
361C22—881no—
362C22#1062247711yescharacteristic
363C22#1062247811yescharacteristic
364C22#1062260411yescharacteristic
365C4—21no—
366C4—21no—
367C4—21no—
368C4—21no—
369C4—881no—
370C4—881no—
371C4—1761no—
372C4#1062247611yescharacteristic
373C4#1062247911yescharacteristic
374C4#1062278211yescharacteristic
375C4#1062278511yescharacteristic
376C2—21no—
377C2—21no—
378C2—882no—
379C2—1761no—
380C2#1306980711yescharacteristic
381C2#1306989111yescharacteristic
382C2#1306992211yescharacteristic
subgroupG/H
centerC22#10622604
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1570C2
socleC22×C11#394
prime radical#13078082C2
hypercenter#1570D11
hypocenterC11#10465
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1570

Complements

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

NH ≅ G/Ntype
2. #13068627C2semidirect
3. #13067266C2semidirect
4. #13067177C2semidirect
5. #13066936C2semidirect
6. #13066476C2semidirect
7. C11×#1570C2semidirect
118. #1570D11semidirect
306. C11#10465semidirect

Maximal subgroups

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

subgroupindex
#130780822
#130686272
#130672662
#130671772
#130669362
#130664762
C11×#15702
#1046511