Finite Group Databasebeta

← #14656158

Subgroups — #14656158

Order 2816.

658 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 658 conjugacy classes of subgroups — too many to draw. Only its 105 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#13079531C211yesmaximal, characteristic
2#13073615C211yesmaximal, characteristic, complemented
3#13067285C211yesmaximal, characteristic, complemented
4#13067111C211yesmaximal, characteristic, complemented
5#13067011C211yesmaximal, characteristic, complemented
6#13066517C211yesmaximal, characteristic, complemented
7C11×#3037C211yesmaximal, characteristic, complemented
8C2×C11×#137—21no—
9C11×#532C2211yescharacteristic
10C2×C4×Q8×C11C2211yescharacteristic
11C2×#67000—21no—
12C2×#66927C2211yescharacteristic
13C11×#464—22no—
14C11×#462—21no—
15C11×#460—21no—
16C11×#423C2211yescharacteristic
17C11×#417—21no—
18#10622701—21no—
19#10622686—21no—
20#10622649—22no—
21#10622628—22no—
22#10622604—22no—
23#10622601—21no—
24#10622552—22no—
25C4×C4⋊Dic11C2211yescharacteristic
26#10622538C2211yescharacteristic
27#10622538C2211yescharacteristic
28#10622175—22no—
29Q8⋊(C11⋊C8)—22no—
30#10622123—22no—
31C2×C11×#41—21no—
32C22×Q8×C11D411yescharacteristic
33C22×D44—21no—
34C22×D44—21no—
35C22×D44D412yes—
36C11×#137—42no—
37C11×#137—42no—
38C2×C11×Q16—22no—
39C2×C11×SD16—22no—
40C2×C11×M16—21no—
41C11×C4⋊Q8D411yescharacteristic
42C11×#127D411yescharacteristic
43C11×#124—21no—
44C11×#121—21no—
45C11×#121—21no—
46C4×Q8×C11—21no—
47C4×Q8×C11—21no—
48C4×Q8×C11—21no—
49C4×Q8×C11—21no—
50C4×D4×C11—21no—
51C4×D4×C11—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4D411yescharacteristic
54C2×C42×C11—21no—
55C2×C42×C11C2311yescharacteristic
56#67000—42no—
57#67000—42no—
58C2×#4323—24no—
59C2×(C2×D11)⋊C4—24no—
60C2×(C2×D11)⋊C4—24no—
61C2×C4⋊Dic11—21no—
62C2×C4×Dic11—21no—
63#66927—21no—
64#66927—21no—
65#66927—21no—
66#66927—21no—
67C11×C4⋊C8—21no—
68C11×C4⋊C8D412yes—
69C11×#103—22no—
70C11×#102—22no—
71C11⋊#95D412yes—
72C22⋊(C11⋊C8)—21no—
73C22⋊(C11⋊C8)—21no—
74#66873—24no—
75C4⋊(C11⋊C8)—21no—
76C4⋊(C11⋊C8)D412yes—
77C4×C11⋊C8—21no—
78C4×C11⋊C8—21no—
79#10242—111nomaximal, Sylow
80C23×D11—22no—
81C11×#41—41no—
82C11×#41—41no—
83C11×#41—41no—
84C11×#41—41no—
85C2×Q8×C11—21no—
86C2×Q8×C11—21no—
87C2×Q8×C11—21no—
88C2×Q8×C11—21no—
89C2×Q8×C11—21no—
90C2×Q8×C11—21no—
91C2×Q8×C11D812yescomplemented
92C2×D4×C11—21no—
93C2×D4×C11—21no—
94C2×D4×C11—21no—
95C2×D4×C11—41no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—41no—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×Dic11—22no—
103C2×D44—22no—
104C2×D44—22no—
105C2×D44—44no—
106C2×D44—41no—
107C2×D44—41no—
108C2×D44—41no—
109C2×D44—41no—
110C2×D44—41no—
111C2×D44—41no—
112C2×D44—41no—
113C2×D44—41no—
114C2×D44—82no—
115C11×Q16—44no—
116C11×SD16—44no—
117C11×M16—41no—
118C11×M16—41no—
119C2×C8×C11—22no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—41no—
125C11×C4⋊C4—41no—
126C11×C22⋊C4—41no—
127C11×C22⋊C4—41no—
128C42×C11—41no—
129C42×C11—41no—
130C42×C11C2×D411yescharacteristic
131C42×C11C2×D411yescharacteristic
132C42×C11C2×D411yescharacteristic
133C42×C11#4111yescharacteristic
134#4323—84no—
135(C2×D11)⋊C4—48no—
136(C2×D11)⋊C4—84no—
137C4⋊Dic11—42no—
138C4×Dic11—41no—
139C4×Dic11—41no—
140C2×C11⋊C8—22no—
141C2×C11⋊C8—41no—
142#3205—111no—
143#3037D1111yescharacteristic, complemented
144#2548—111no—
145#1545—111no—
146#1502—111no—
147#1479—111no—
148#1303—111no—
149C23×C11—41no—
150C23×C11#12011yescharacteristic
151C22×D11—44no—
152C22×D11—44no—
153C22×D11—42no—
154C22×D11—42no—
155C22×D11—42no—
156Q8×C11—22no—
157Q8×C11—22no—
158Q8×C11—41no—
159Q8×C11—41no—
160Q8×C11—41no—
161Q8×C11—41no—
162D4×C11—41no—
163D4×C11—41no—
164D4×C11—42no—
165D4×C11—81no—
166D4×C11—81no—
167D4×C11—81no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—42no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—81no—
177C2×C4×C11—81no—
178C2×C4×C11#12011yescharacteristic
179C2×C4×C11#12011yescharacteristic
180C2×C4×C11#12111yescharacteristic
181C2×C4×C11#12111yescharacteristic
182C2×C4×C11#12111yescharacteristic
183C2×C4×C11#12711yescharacteristic
184C2×C4×C11C2×D811yescharacteristic
185C2×C4×C11#13511yescharacteristic
186C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
187C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
188C2×Dic11—42no—
189C2×Dic11—42no—
190C2×Dic11—42no—
191D44—44no—
192D44—82no—
193D44—82no—
194D44—82no—
195D44—81no—
196D44—81no—
197D44—81no—
198D44—81no—
199C8×C11—42no—
200C11⋊C8—42no—
201C11⋊C8—81no—
202C2×#137—21no—
203#532C2×D1111yescharacteristic
204C2×#127—111no—
205C2×#124—221no—
206C2×C4×Q8C2×D1111yescharacteristic
207#493—221no—
208#486—221no—
209#464—22no—
210#462—21no—
211#460—21no—
212#459—222no—
213#447—222no—
214#431—111no—
215#431—111no—
216#423C2×D1111yescharacteristic
217#417—21no—
218#394—222no—
219#390—222no—
220#390—221no—
221C4×C4⋊C4—111no—
222#331—222no—
223#327—222no—
224Q8⋊C8—222no—
225C22×C11—21no—
226C22×C11—21no—
227C22×C11—81no—
228C22×C11—81no—
229C22×C11—81no—
230C22×C11#39211yescharacteristic
231C22×C11#44711yescharacteristic
232C22×C11#44911yescharacteristic
233C2×D11—84no—
234C2×D11—84no—
235C2×D11—82no—
236C2×D11—82no—
237C2×D11—82no—
238C4×C11—21no—
239C4×C11—21no—
240C4×C11—21no—
241C4×C11—42no—
242C4×C11—81no—
243C4×C11—81no—
244C4×C11#44711yescharacteristic
245C4×C11#44911yescharacteristic
246C4×C11#45512yes—
247C4×C11#46611yescharacteristic
248C4×C11#46911yescharacteristic
249Dic11—82no—
250C2×#41—21no—
251C22×Q8C22⋊D1111yescharacteristic
252C22×D4—112no—
253C22×D4—221no—
254C22×D4—221no—
255#137—42no—
256#137—42no—
257C2×Q16—22no—
258C2×SD16—22no—
259C2×D8—224no—
260C2×M16—21no—
261C4⋊Q8C22⋊D1111yescharacteristic
262#127—221no—
263#127—221no—
264#127—221no—
265#127—221no—
266#127C22⋊D1111yescharacteristic
267#124—21no—
268#124—442no—
269#124—442no—
270#121—21no—
271#121—21no—
272C4×Q8—21no—
273C4×Q8—21no—
274C4×Q8—21no—
275C4×Q8—21no—
276C4×D4—21no—
277C4×D4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—221no—
280C2×C4⋊C4C22⋊D1111yescharacteristic
281C2×C22⋊C4—224no—
282C2×C22⋊C4—224no—
283C2×C42—21no—
284C2×C42—221no—
285C2×C42C22×D1111yescharacteristic
286C4⋊C8—21no—
287C4⋊C8—112no—
288C4⋊C8—221no—
289C4⋊C8C22⋊D1112yes—
290#103—22no—
291#102—22no—
292#102—224no—
293C22⋊C8—221no—
294C22⋊C8—221no—
295C4×C8—221no—
296C4×C8—221no—
297#95—112no—
298C2×C11—21no—
299C2×C11—21no—
300C2×C11—161no—
301C2×C11#199911yescharacteristic
302C2×C11#200411yescharacteristic
303C2×C11#200811yescharacteristic
304D11—162no—
305C24—222no—
306#41—41no—
307#41—41no—
308#41—41no—
309#41—41no—
310C2×Q8—21no—
311C2×Q8—21no—
312C2×Q8—21no—
313C2×Q8—21no—
314C2×Q8—21no—
315C2×Q8—21no—
316C2×Q8#432312yescomplemented
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—41no—
321C2×D4—222no—
322C2×D4—222no—
323C2×D4—444no—
324C2×D4—441no—
325C2×D4—441no—
326C2×D4—441no—
327C2×D4—441no—
328C2×D4—441no—
329C2×D4—441no—
330C2×D4—441no—
331C2×D4—441no—
332C2×D4—882no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—41no—
336C22×C4—222no—
337C22×C4D4×D1111yescharacteristic
338C22×C4D4×D1111yescharacteristic
339C22×C4C2×C22⋊D1111yescharacteristic
340Q16—44no—
341SD16—44no—
342D8—884no—
343M16—41no—
344M16—41no—
345C2×C8—22no—
346C2×C8—222no—
347C2×C8—441no—
348C4⋊C4—21no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—41no—
353C4⋊C4—41no—
354C4⋊C4—442no—
355C22⋊C4—41no—
356C22⋊C4—41no—
357C22⋊C4—448no—
358C22⋊C4—884no—
359C42—41no—
360C42—41no—
361C42—441no—
362C42—441no—
363C42D4×D1111yescharacteristic
364C42#434111yescharacteristic
365C42C2×C22⋊D1111yescharacteristic
366C42C2×C22⋊D1111yescharacteristic
367C11#1024211yescharacteristic, complemented, Sylow
368C23—41no—
369C23—444no—
370C23—444no—
371C23—442no—
372C23—442no—
373C23—442no—
374C23#6699011yescharacteristic
375Q8—22no—
376Q8—22no—
377Q8—41no—
378Q8—41no—
379Q8—41no—
380Q8—41no—
381D4—42no—
382D4—41no—
383D4—41no—
384D4—81no—
385D4—81no—
386D4—81no—
387D4—444no—
388D4—882no—
389D4—882no—
390D4—882no—
391D4—881no—
392D4—881no—
393D4—881no—
394D4—881no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—42no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—81no—
404C2×C4—81no—
405C2×C4—442no—
406C2×C4—442no—
407C2×C4—442no—
408C2×C4C2×#432311yescharacteristic
409C2×C4#6698511yescharacteristic
410C2×C4#6699011yescharacteristic
411C2×C4#6699111yescharacteristic
412C2×C4#6699211yescharacteristic
413C2×C4#6699211yescharacteristic
414C2×C4#6699311yescharacteristic
415C2×C4#6700211yescharacteristic
416C2×C4#6700311yescharacteristic
417C2×C4#6700611yescharacteristic
418C8—42no—
419C8—442no—
420C8—881no—
421C22—21no—
422C22—21no—
423C22—81no—
424C22—81no—
425C22—81no—
426C22—884no—
427C22—884no—
428C22—882no—
429C22—882no—
430C22—882no—
431C22#1062264911yescharacteristic
432C22#1062265011yescharacteristic
433C22#1062283611yescharacteristic
434C4—21no—
435C4—21no—
436C4—21no—
437C4—42no—
438C4—81no—
439C4—81no—
440C4—882no—
441C4#1062265111yescharacteristic
442C4#1062265211yescharacteristic
443C4#1062281512yes—
444C4#1062283011yescharacteristic
445C4#1062285111yescharacteristic
446C2—21no—
447C2—21no—
448C2—161no—
449C2—1762no—
450C2#1306961211yescharacteristic
451C2#1306964211yescharacteristic
452C2#1306966611yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3037C2
socleC22×C11#392
prime radical#13079531C2
hypercenter#3037D11
hypocenterC11#10242
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3037

Complements

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

NH ≅ G/Ntype
2. #13073615C2semidirect
3. #13067285C2semidirect
4. #13067111C2semidirect
5. #13067011C2semidirect
6. #13066517C2semidirect
7. C11×#3037C2semidirect
91. C2×Q8×C11D8semidirect
143. #3037D11semidirect
316. C2×Q8#4323semidirect
367. C11#10242semidirect

Maximal subgroups

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

subgroupindex
#130795312
#130736152
#130672852
#130671112
#130670112
#130665172
C11×#30372
#1024211