Finite Group Databasebeta

← #14655869

Subgroups — #14655869

Order 2816.

546 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 101 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#13079923C211yesmaximal, characteristic
2#13079541C211yesmaximal, characteristic, complemented
3#13069565C211yesmaximal, characteristic, complemented
4#13069535C211yesmaximal, characteristic, complemented
5#13067111C211yesmaximal, characteristic, complemented
6#13066467C211yesmaximal, characteristic, complemented
7C11×#3141C211yesmaximal, characteristic, complemented
8C11×#532C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10#10623008C2211yescharacteristic
11C11×#489—22no—
12C11×#487—21no—
13C11×#486—21no—
14C11×#417—22no—
15C4×C11×M16C2211yescharacteristic
16#10622840—22no—
17C2×#66889—22no—
18#10622700—21no—
19#10622698—21no—
20#10622696—22no—
21#10622694—21no—
22#10622685—21no—
23#10622651—22no—
24#10622628—21no—
25#10622620—21no—
26C4×C4⋊Dic11C2211yescharacteristic
27#10622538C2211yescharacteristic
28C2×C4⋊(C11⋊C8)C2211yescharacteristic
29#10622175—22no—
30#10622167—22no—
31C2×C11×#41—21no—
32C22×Q8×C11—21no—
33C2×#4339—21no—
34C2×C11×M16D412yes—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8D412yes—
39C11×C4⋊Q8D411yescharacteristic
40C11×#127D411yescharacteristic
41C11×#124—21no—
42C11×#121—21no—
43C11×#121—21no—
44C4×D4×C11—21no—
45C4×D4×C11—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C42×C11C2311yescharacteristic
49C2×#4325—24no—
50C2×#4323—22no—
51#66983—21no—
52#66983—21no—
53C2×C4⋊Dic11—21no—
54C2×C4×Dic11—21no—
55C22×C11⋊C8D412yes—
56#66928—21no—
57#66927D411yescharacteristic
58C4×D44—21no—
59C4×D44—21no—
60#66922D411yescharacteristic
61C11×#103—24no—
62C11×#102—24no—
63C11×#97—21no—
64C4×C8×C11—21no—
65#66899—24no—
66#66896—22no—
67C11⋊#95—21no—
68C22⋊(C11⋊C8)D412yes—
69#66889—44no—
70#66873—22no—
71#66871—22no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)—21no—
75C4×C11⋊C8—21no—
76#10196—111nomaximal, Sylow
77C11×#41—42no—
78C11×#41—42no—
79C2×Q8×C11—22no—
80C2×Q8×C11—21no—
81C2×Q8×C11—41no—
82C2×Q8×C11—82no—
83C2×D4×C11—21no—
84C2×D4×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11—41no—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C2×C22⋊D11—41no—
93C22×Dic11—41no—
94#4339—42no—
95#4339—42no—
96C2×D44—21no—
97C2×D44—21no—
98C2×D44—21no—
99C2×C4×D11—41no—
100C2×Dic22—21no—
101C11×M16—22no—
102C11×M16—22no—
103C2×C8×C11—22no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C11×C22⋊C4—41no—
111C11×C22⋊C4—41no—
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11#4111yescharacteristic
116#4325—84no—
117#4323—82no—
118(C2×D11)⋊C4—41no—
119(C2×D11)⋊C4—41no—
120C4⋊Dic11—22no—
121C4⋊Dic11—21no—
122C4⋊Dic11—21no—
123C4⋊Dic11—41no—
124C4×Dic11—42no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—42no—
128#3245—111no—
129#3206—111no—
130#3141D1111yescharacteristic, complemented
131#1987—111no—
132#1980—111no—
133#1502—111no—
134#1283—111no—
135C23×C11—41no—
136C23×C11#12711yescharacteristic
137C22×D11—41no—
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—82no—
153C2×C4×C11—82no—
154C2×C4×C11#12011yescharacteristic
155C2×C4×C11#12011yescharacteristic
156C2×C4×C11#12011yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#12111yescharacteristic
159C2×C4×C11#12111yescharacteristic
160C2×C4×C11#13512yes—
161C2×C4×C11AGL(1,ℤ/8)12yes—
162C22⋊D11—81no—
163C22⋊D11—81no—
164C2×Dic11—42no—
165C2×Dic11—41no—
166C2×Dic11—81no—
167C2×Dic11—81no—
168D44—42no—
169D44—41no—
170D44—41no—
171D44—42no—
172C4×D11—82no—
173Dic22—42no—
174C8×C11—42no—
175C11⋊C8—42no—
176C11⋊C8—42no—
177#532—111no—
178#532C2×D1111yescharacteristic
179C2×C4⋊Q8C2×D1111yescharacteristic
180#492—221no—
181#489—22no—
182#487—21no—
183#487—221no—
184#486—21no—
185#474—221no—
186#474—221no—
187#466—222no—
188#461—222no—
189#459—221no—
190#459—221no—
191#448—222no—
192#431—111no—
193C2×C4⋊C8—111no—
194C2×#104—222no—
195#417—22no—
196C4×M16C2×D1111yescharacteristic
197C4×C4⋊C4—111no—
198#340—222no—
199#327—222no—
200C22×C11—21no—
201C22×C11—21no—
202C22×C11—81no—
203C22×C11—81no—
204C22×C11—81no—
205C22×C11#39211yescharacteristic
206C22×C11#49511yescharacteristic
207C22×C11#49611yescharacteristic
208C2×D11—81no—
209C2×D11—81no—
210C2×D11—81no—
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—82no—
215C4×C11—81no—
216C4×C11#44912yes—
217C4×C11#45511yescharacteristic
218C4×C11#45611yescharacteristic
219C4×C11#46312yes—
220Dic11—82no—
221Dic11—81no—
222C2×#41—21no—
223C2×#41—221no—
224C22×Q8—21no—
225C2×SD16—224no—
226C2×D8—222no—
227C2×M16C22⋊D1112yes—
228C22×C8—112no—
229C4⋊Q8—21no—
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8—111no—
233C4⋊Q8C22⋊D1112yes—
234C4⋊Q8C22⋊D1111yescharacteristic
235#127—111no—
236#127C22⋊D1111yescharacteristic
237#124—21no—
238#124—221no—
239#121—21no—
240#121—21no—
241#121—221no—
242#121—221no—
243C4×D4—21no—
244C4×D4—21no—
245C4×D4—221no—
246C4×D4—221no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—221no—
250C2×C42—221no—
251C2×C42C22×D1111yescharacteristic
252#107—222no—
253C4⋊C8—221no—
254C4⋊C8—221no—
255C4⋊C8—221no—
256#104—444no—
257#103—24no—
258#103—224no—
259#102—24no—
260#102—222no—
261#102—222no—
262C22⋊C8—112no—
263#97—21no—
264C4×C8—21no—
265C4×C8—221no—
266#95—221no—
267C2×C11—21no—
268C2×C11—21no—
269C2×C11—161no—
270C2×C11#200711yescharacteristic
271C2×C11#200811yescharacteristic
272C2×C11#201211yescharacteristic
273D11—161no—
274#41—42no—
275#41—42no—
276#41—442no—
277#41—442no—
278C2×Q8—22no—
279C2×Q8—21no—
280C2×Q8—41no—
281C2×Q8—82no—
282C2×Q8—221no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—41no—
287C2×D4—221no—
288C2×D4—221no—
289C2×D4—221no—
290C2×D4—441no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—441no—
294C22×C4—441no—
295C22×C4D4×D1111yescharacteristic
296C22×C4D4×D1111yescharacteristic
297C22×C4C2×C22⋊D1111yescharacteristic
298SD16—884no—
299D8—882no—
300M16—22no—
301M16—22no—
302C2×C8—22no—
303C2×C8—222no—
304C2×C8—222no—
305C2×C8—442no—
306C4⋊C4—21no—
307C4⋊C4—22no—
308C4⋊C4—21no—
309C4⋊C4—22no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—222no—
313C4⋊C4—221no—
314C4⋊C4—221no—
315C4⋊C4—441no—
316C22⋊C4—41no—
317C22⋊C4—41no—
318C22⋊C4—441no—
319C22⋊C4—441no—
320C42—442no—
321C42D4×D1111yescharacteristic
322C42#434111yescharacteristic
323C42C2×C22⋊D1111yescharacteristic
324C42C2×C22⋊D1111yescharacteristic
325C11#1019611yescharacteristic, complemented, Sylow
326C23—41no—
327C23—441no—
328C23#6699311yescharacteristic
329Q8—44no—
330Q8—42no—
331Q8—82no—
332Q8—442no—
333D4—41no—
334D4—41no—
335D4—42no—
336D4—81no—
337D4—81no—
338D4—81no—
339D4—442no—
340D4—441no—
341D4—441no—
342D4—442no—
343D4—881no—
344D4—881no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—42no—
350C2×C4—82no—
351C2×C4—82no—
352C2×C4—442no—
353C2×C4—441no—
354C2×C4—881no—
355C2×C4—881no—
356C2×C4—882no—
357C2×C4#6699011yescharacteristic
358C2×C4#6699011yescharacteristic
359C2×C4#6699111yescharacteristic
360C2×C4#6699211yescharacteristic
361C2×C4#6699211yescharacteristic
362C2×C4#6700212yes—
363C2×C4#6700312yes—
364C2×C4#6700611yescharacteristic
365C8—42no—
366C8—442no—
367C8—442no—
368C22—21no—
369C22—21no—
370C22—81no—
371C22—81no—
372C22—81no—
373C22—881no—
374C22—881no—
375C22—881no—
376C22#1062267111yescharacteristic
377C22#1062267211yescharacteristic
378C22#1062283611yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—82no—
383C4—81no—
384C4—882no—
385C4—881no—
386C4#1062267012yes—
387C4#1062281511yescharacteristic
388C4#1062281811yescharacteristic
389C4#1062285112yes—
390C2—21no—
391C2—21no—
392C2—161no—
393C2—1761no—
394C2#1306966111yescharacteristic
395C2#1306966711yescharacteristic
396C2#1306969311yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3141C2
socleC22×C11#392
prime radical#13079923C2
hypercenter#3141D11
hypocenterC11#10196
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3141

Complements

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

NH ≅ G/Ntype
2. #13079541C2semidirect
3. #13069565C2semidirect
4. #13069535C2semidirect
5. #13067111C2semidirect
6. #13066467C2semidirect
7. C11×#3141C2semidirect
130. #3141D11semidirect
325. C11#10196semidirect

Maximal subgroups

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

subgroupindex
#130799232
#130795412
#130695652
#130695352
#130671112
#130664672
C11×#31412
#1019611