Finite Group Databasebeta

← #14656253

Subgroups — #14656253

Order 2816.

580 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 580 conjugacy classes of subgroups — too many to draw. Only its 103 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#13078409C211yesmaximal, characteristic, complemented
2#13078076C211yesmaximal, characteristic
3#13069409C211yesmaximal, characteristic, complemented
4#13067071C211yesmaximal, characteristic, complemented
5#13067067C211yesmaximal, characteristic, complemented
6#13066491C211yesmaximal, characteristic, complemented
7C11×#3246C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C11×#532C2211yescharacteristic
10C2×#67002—21no—
11C2×C4×D44C2211yescharacteristic
12C11×#476—21no—
13C11×#475—21no—
14C11×#465—22no—
15C11×#461—21no—
16C11×#460—21no—
17C2×C11×C4⋊C8C2211yescharacteristic
18#10622845—21no—
19C2×(C2×D11)⋊C8—22no—
20#10622700—21no—
21#10622697—21no—
22#10622696—21no—
23#10622685—21no—
24#10622679—22no—
25#10622670—22no—
26#10622614—21no—
27#10622608—21no—
28#10622537C2211yescharacteristic
29#10622537C2211yescharacteristic
30C2×C4×C11⋊C8C2211yescharacteristic
31Q8⋊(C11⋊C8)—22no—
32D4⋊(C11⋊C8)—22no—
33C2×C11×#41—21no—
34C22×D44D411yescharacteristic
35C22×C4×D11—21no—
36C2×C11×SD16—22no—
37C22×C8×C11D412yes—
38C11×C4⋊Q8D411yescharacteristic
39C11×C4⋊Q8D411yescharacteristic
40C11×C4⋊Q8D411yescharacteristic
41C11×#127D411yescharacteristic
42C11×#125—21no—
43C11×#124—21no—
44C11×C22⋊Q8—21no—
45C11×C22⋊Q8—21no—
46C11×#121—21no—
47C11×#121—21no—
48C4×Q8×C11—21no—
49C4×Q8×C11—21no—
50C4×D4×C11—21no—
51C4×D4×C11—21no—
52C11×#117—21no—
53C2×C42×C11C2311yescharacteristic
54#67002—42no—
55#67002—42no—
56C2×#4325—22no—
57C2×#4323—22no—
58C2×(C2×D11)⋊C4—21no—
59C2×C4⋊Dic11D411yescharacteristic
60C2×#4318—21no—
61C2×#4318—21no—
62C22×C11⋊C8—21no—
63C4×D44—21no—
64C4×D44—21no—
65C4×D44—21no—
66C4×D44—21no—
67C11×#106—22no—
68C11×C4⋊C8—21no—
69C11×C4⋊C8—21no—
70C11×#103—22no—
71C11×#102—22no—
72#66899—22no—
73#66896—22no—
74(C2×D11)⋊C8—44no—
75#66873—22no—
76#66873—22no—
77#66872—22no—
78#66871—22no—
79C4⋊(C11⋊C8)—21no—
80C4⋊(C11⋊C8)—21no—
81C4⋊(C11⋊C8)D412yes—
82C4⋊(C11⋊C8)D412yes—
83C4×C11⋊C8—21no—
84C4×C11⋊C8—21no—
85#10256—111nomaximal, Sylow
86C23×D11—21no—
87C11×#41—41no—
88C11×#41—41no—
89C11×#41—41no—
90C11×#41—41no—
91C2×Q8×C11—21no—
92C2×Q8×C11—21no—
93C2×Q8×C11—21no—
94C2×D4×C11—21no—
95C2×D4×C11—21no—
96C2×D4×C11—21no—
97C2×D4×C11—41no—
98C22×C4×C11—41no—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11#4111yescharacteristic
102C22×Dic11—21no—
103C2×D44—21no—
104C2×D44—21no—
105C2×D44—21no—
106C2×D44—21no—
107C2×D44—21no—
108C2×D44SD1612yescomplemented
109C2×C4×D11—42no—
110C2×C4×D11—42no—
111C2×C4×D11—41no—
112C2×C4×D11—41no—
113C11×SD16—82no—
114C2×C8×C11—22no—
115C2×C8×C11—42no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—21no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—41no—
123C11×C4⋊C4—41no—
124C11×C22⋊C4—41no—
125C11×C22⋊C4—41no—
126C11×C22⋊C4—41no—
127C42×C11—41no—
128C42×C11C2×D411yescharacteristic
129C42×C11C2×D411yescharacteristic
130C42×C11C2×D411yescharacteristic
131C42×C11C2×D411yescharacteristic
132#4325—44no—
133#4323—44no—
134(C2×D11)⋊C4—41no—
135(C2×D11)⋊C4—41no—
136C4⋊Dic11—21no—
137C4⋊Dic11—21no—
138#4318—41no—
139#4318—41no—
140#4318—41no—
141#4318—41no—
142C2×C11⋊C8—22no—
143C2×C11⋊C8—22no—
144C2×C11⋊C8—22no—
145C2×C11⋊C8—41no—
146C2×C11⋊C8—41no—
147#3246D1111yescharacteristic, complemented
148#3077—111no—
149#3036—111no—
150#1954—111no—
151#1493—111no—
152#1492—111no—
153#1292—111no—
154C23×C11—41no—
155C23×C11#12111yescharacteristic
156C22×D11—22no—
157C22×D11—42no—
158C22×D11—42no—
159C22×D11—41no—
160C22×D11—41no—
161Q8×C11—42no—
162Q8×C11—41no—
163Q8×C11—41no—
164Q8×C11—41no—
165Q8×C11—41no—
166D4×C11—42no—
167D4×C11—41no—
168D4×C11—41no—
169D4×C11—41no—
170D4×C11—41no—
171D4×C11—81no—
172D4×C11—81no—
173C2×C4×C11—21no—
174C2×C4×C11—21no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—81no—
180C2×C4×C11—81no—
181C2×C4×C11#12011yescharacteristic
182C2×C4×C11#12011yescharacteristic
183C2×C4×C11#12011yescharacteristic
184C2×C4×C11#12111yescharacteristic
185C2×C4×C11#12111yescharacteristic
186C2×C4×C11#12711yescharacteristic
187C2×C4×C11C2×SD1611yescharacteristic
188C2×C4×C11#13511yescharacteristic
189C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
190C2×C4×C11#13711yescharacteristic
191C2×Dic11—42no—
192C2×Dic11—41no—
193D44—22no—
194D44—22no—
195D44—41no—
196D44—41no—
197C4×D11—82no—
198C4×D11—81no—
199C4×D11—81no—
200C8×C11—42no—
201C11⋊C8—42no—
202C11⋊C8—42no—
203C11⋊C8—42no—
204C2×AGL(1,ℤ/8)—221no—
205#533C2×D1111yescharacteristic
206#532C2×D1111yescharacteristic
207C2×C4×D4—111no—
208#478—222no—
209#476—21no—
210#476—221no—
211#475—21no—
212#474—221no—
213#465—22no—
214#463—222no—
215#461—21no—
216#461—221no—
217#460—21no—
218#459—221no—
219#428—221no—
220#423—111no—
221#423—111no—
222C2×C4⋊C8C2×D1111yescharacteristic
223#418—221no—
224#417—221no—
225C2×C22⋊C8—222no—
226C2×C4×C8—111no—
227Q8⋊C8—222no—
228D4⋊C8—222no—
229C22×C11—21no—
230C22×C11—21no—
231C22×C11—81no—
232C22×C11—81no—
233C22×C11—81no—
234C22×C11#39211yescharacteristic
235C22×C11#46511yescharacteristic
236C22×C11#46811yescharacteristic
237C2×D11—44no—
238C2×D11—42no—
239C2×D11—82no—
240C2×D11—81no—
241C2×D11—81no—
242C4×C11—21no—
243C4×C11—21no—
244C4×C11—21no—
245C4×C11—81no—
246C4×C11—81no—
247C4×C11—81no—
248C4×C11#44811yescharacteristic
249C4×C11#44911yescharacteristic
250C4×C11#45011yescharacteristic
251C4×C11#45211yescharacteristic
252C4×C11#45311yescharacteristic
253C4×C11#45411yescharacteristic
254Dic11—81no—
255C2×#41—21no—
256C22×D4—111no—
257C23×C4—221no—
258AGL(1,ℤ/8)—442no—
259AGL(1,ℤ/8)—442no—
260C2×SD16—22no—
261C2×SD16—222no—
262C2×D8—222no—
263C2×M16—221no—
264C2×M16—221no—
265C22×C8—221no—
266C22×C8C22⋊D1112yes—
267C4⋊Q8C22⋊D1111yescharacteristic
268C4⋊Q8C22⋊D1111yescharacteristic
269C4⋊Q8C22⋊D1111yescharacteristic
270#127C22⋊D1111yescharacteristic
271#125—21no—
272#124—21no—
273C22⋊Q8—21no—
274C22⋊Q8—21no—
275#121—21no—
276#121—21no—
277C4×Q8—21no—
278C4×Q8—21no—
279C4×D4—21no—
280C4×D4—21no—
281C4×D4—221no—
282C4×D4—221no—
283C4×D4—221no—
284C4×D4—221no—
285#117—21no—
286C2×C4⋊C4—111no—
287C2×C22⋊C4—221no—
288C2×C42C22×D1111yescharacteristic
289#107—222no—
290#106—22no—
291#106—222no—
292C4⋊C8—21no—
293C4⋊C8—21no—
294C4⋊C8—112no—
295C4⋊C8—112no—
296C4⋊C8—221no—
297C4⋊C8—221no—
298#103—22no—
299#103—222no—
300#102—22no—
301#102—222no—
302#102—222no—
303#102—222no—
304C22⋊C8—444no—
305C4×C8—221no—
306C4×C8—221no—
307C2×C11—21no—
308C2×C11—21no—
309C2×C11—161no—
310C2×C11#200011yescharacteristic
311C2×C11#200611yescharacteristic
312C2×C11#201711yescharacteristic
313D11—82no—
314C24—221no—
315#41—41no—
316#41—41no—
317#41—41no—
318#41—41no—
319C2×Q8—21no—
320C2×Q8—21no—
321C2×Q8—21no—
322C2×D4—21no—
323C2×D4—21no—
324C2×D4—21no—
325C2×D4—41no—
326C2×D4—112no—
327C2×D4—221no—
328C2×D4—221no—
329C2×D4—221no—
330C2×D4—221no—
331C2×D4—221no—
332C22×C4—41no—
333C22×C4—221no—
334C22×C4—442no—
335C22×C4—442no—
336C22×C4—441no—
337C22×C4—441no—
338C22×C4D4×D1111yescharacteristic
339C22×C4#434111yescharacteristic
340C22×C4C2×C22⋊D1111yescharacteristic
341SD16—82no—
342SD16—444no—
343D8—444no—
344M16—441no—
345M16—441no—
346M16—441no—
347M16—441no—
348C2×C8—22no—
349C2×C8—42no—
350C2×C8—222no—
351C2×C8—222no—
352C2×C8—222no—
353C2×C8—441no—
354C2×C8—441no—
355C4⋊C4—21no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—41no—
362C4⋊C4—41no—
363C4⋊C4—221no—
364C4⋊C4—221no—
365C22⋊C4—41no—
366C22⋊C4—41no—
367C22⋊C4—41no—
368C22⋊C4—441no—
369C22⋊C4—441no—
370C42—41no—
371C42D4×D1111yescharacteristic
372C42D4×D1111yescharacteristic
373C42C2×C22⋊D1111yescharacteristic
374C42C2×C22⋊D1111yescharacteristic
375C11#1025611yescharacteristic, complemented, Sylow
376C23—41no—
377C23—222no—
378C23—442no—
379C23—442no—
380C23—441no—
381C23—441no—
382C23#6699111yescharacteristic
383Q8—42no—
384Q8—41no—
385Q8—41no—
386Q8—41no—
387Q8—41no—
388D4—42no—
389D4—41no—
390D4—41no—
391D4—41no—
392D4—41no—
393D4—81no—
394D4—81no—
395D4—222no—
396D4—222no—
397D4—441no—
398D4—441no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—81no—
406C2×C4—81no—
407C2×C4—442no—
408C2×C4—441no—
409C2×C4—882no—
410C2×C4—881no—
411C2×C4—881no—
412C2×C4SD16×D1111yescharacteristic
413C2×C4#6696711yescharacteristic
414C2×C4#6696811yescharacteristic
415C2×C4#6696911yescharacteristic
416C2×C4#6699011yescharacteristic
417C2×C4#6699011yescharacteristic
418C2×C4#6699211yescharacteristic
419C2×C4#6699211yescharacteristic
420C2×C4#6699311yescharacteristic
421C2×C4#6700611yescharacteristic
422C8—42no—
423C8—442no—
424C8—442no—
425C8—442no—
426C22—21no—
427C22—21no—
428C22—81no—
429C22—81no—
430C22—81no—
431C22—444no—
432C22—442no—
433C22—882no—
434C22—881no—
435C22—881no—
436C22#1062278411yescharacteristic
437C22#1062278711yescharacteristic
438C22#1062283611yescharacteristic
439C4—21no—
440C4—21no—
441C4—21no—
442C4—81no—
443C4—81no—
444C4—81no—
445C4—881no—
446C4#1062278211yescharacteristic
447C4#1062278311yescharacteristic
448C4#1062278511yescharacteristic
449C4#1062278611yescharacteristic
450C4#1062285411yescharacteristic
451C4#1062285811yescharacteristic
452C2—21no—
453C2—21no—
454C2—161no—
455C2—882no—
456C2#1306961611yescharacteristic
457C2#1306965811yescharacteristic
458C2#1306971911yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3246C2
socleC22×C11#392
prime radical#13078076C2
hypercenter#3246D11
hypocenterC11#10256
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3246

Complements

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

NH ≅ G/Ntype
1. #13078409C2semidirect
3. #13069409C2semidirect
4. #13067071C2semidirect
5. #13067067C2semidirect
6. #13066491C2semidirect
7. C11×#3246C2semidirect
108. C2×D44SD16semidirect
147. #3246D11semidirect
375. C11#10256semidirect

Maximal subgroups

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

subgroupindex
#130784092
#130780762
#130694092
#130670712
#130670672
#130664912
C11×#32462
#1025611