Finite Group Databasebeta

← #14732296

Subgroups — #14732296

Order 2816.

1020 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079541C211yesmaximal, characteristic, complemented
2#13078616C211yesmaximal, characteristic
3#13078088C211yesmaximal, characteristic, complemented
4#13067830C214yesmaximal, complemented
5#13067688C214yesmaximal, complemented
6#13067297C211yesmaximal, characteristic, complemented
7#13067041C211yesmaximal, characteristic, complemented
8#13067011C211yesmaximal, characteristic, complemented
9C2×C11×#554C211yesmaximal, characteristic, complemented
10C11×#554—22no—
11C11×#554—22no—
12C11×#554—22no—
13C11×#554C2214yes—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#125—21no—
16C2×C11×C22⋊Q8—21no—
17C2×C11×C22⋊Q8—22no—
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×D4×C11—21no—
20C2×C4×D4×C11C2211yescharacteristic
21C22×C11×C4⋊C4—21no—
22C2×#66995—21no—
23#10623008C2211yescharacteristic
24#10622840—22no—
25#10622830—21no—
26#10622698C2212yescomplemented
27#10622696—22no—
28#10622694C2212yescomplemented
29#10622644C2212yescomplemented
30#10622641—22no—
31#10622640C2212yescomplemented
32#10622628C2212yes—
33C4×#4323—22no—
34#10622620C2212yes—
35#10622580—21no—
36#10622579—21no—
37#10622538C2211yescharacteristic
38#10622538C2211yescharacteristic
39#10622537C2211yescharacteristic
40#10622184C2214yescomplemented
41Q8⋊(C11⋊C8)C2214yescomplemented
42D4⋊(C11⋊C8)C2214yes—
43C22×Q8×C11D411yescharacteristic
44C22×Q8×C11D412yes—
45C22×D4×C11D411yescharacteristic
46C23×C4×C11—22no—
47C23×C4×C11—21no—
48C2×#4339—21no—
49C11×C4⋊Q8—21no—
50C11×C4⋊Q8—21no—
51C11×C4⋊Q8D412yes—
52C11×C4⋊Q8C2312yes—
53C11×#125—24no—
54C11×#125—24no—
55C11×C22⋊Q8—24no—
56C11×C22⋊Q8—28no—
57C11×C22⋊Q8—24no—
58C11×C22⋊Q8—28no—
59C4×Q8×C11—21no—
60C4×Q8×C11—21no—
61C4×Q8×C11D412yes—
62C4×Q8×C11C2312yes—
63C4×D4×C11—24no—
64C4×D4×C11—24no—
65C4×D4×C11—21no—
66C4×D4×C11—21no—
67C4×D4×C11D412yes—
68C4×D4×C11C2312yes—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—24no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—24no—
76C2×C11×C4⋊C4D411yescharacteristic
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—21no—
80C2×C42×C11—21no—
81C2×C42×C11C2311yescharacteristic
82C2×#4326—22no—
83#66995—44no—
84C2×#4325—22no—
85C2×#4325—24no—
86C2×#4323—22no—
87#66983—21no—
88#66983—21no—
89C2×#4318—21no—
90#66928—21no—
91#66927C2311yescharacteristic
92C4×D44—21no—
93C4×D44—21no—
94#66922C2311yescharacteristic
95#66899—24no—
96#66896—22no—
97C22⋊(C11⋊C8)—21no—
98C22⋊(C11⋊C8)—21no—
99#66874—22no—
100#66873—22no—
101#66873—22no—
102#66871—22no—
103C4⋊(C11⋊C8)—21no—
104C4⋊(C11⋊C8)—21no—
105C4⋊(C11⋊C8)C2312yes—
106C4⋊(C11⋊C8)C2312yes—
107C4×C11⋊C8—21no—
108C4×C11⋊C8C2312yes—
109#18752—111nomaximal, Sylow
110C24×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11—22no—
115C2×Q8×C11—82no—
116C2×Q8×C11C2×D412yes—
117C2×Q8×C11C2×D414yes—
118C2×D4×C11—24no—
119C2×D4×C11—21no—
120C2×D4×C11C2×D412yes—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—22no—
125C22×C4×C11—28no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—42no—
129C22×C4×C11—42no—
130C22×C4×C11—84no—
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C2×C22⋊D11—41no—
135#4339—42no—
136#4339—42no—
137C2×D44—21no—
138C2×D44—21no—
139C2×D44—21no—
140C2×C4×D11—41no—
141C2×Dic22—21no—
142C11×C4⋊C4—28no—
143C11×C4⋊C4—28no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4C2×D412yes—
153C11×C4⋊C4C2×D412yes—
154C11×C22⋊C4—28no—
155C11×C22⋊C4—22no—
156C11×C22⋊C4—22no—
157C42×C11—22no—
158C42×C11—22no—
159C42×C11C2×D411yescharacteristic
160C42×C11C2×D411yescharacteristic
161C42×C11C2×D411yescharacteristic
162C42×C11C2411yescharacteristic
163#4326—44no—
164#4325—44no—
165#4325—84no—
166#4323—44no—
167(C2×D11)⋊C4—41no—
168(C2×D11)⋊C4—41no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171#4318—42no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—22no—
175C2×#554D1111yescharacteristic, complemented
176#3206—111no—
177#3100—111no—
178#3037—111no—
179#1644—114no—
180#1622—114no—
181#1548—111no—
182#1486—111no—
183#1479—111no—
184C23×C11—24no—
185C23×C11—22no—
186C23×C11—42no—
187C23×C11—42no—
188C23×C11#12011yescharacteristic
189C22×D11—41no—
190Q8×C11—22no—
191Q8×C11—22no—
192Q8×C11—44no—
193Q8×C11—42no—
194Q8×C11—82no—
195D4×C11—24no—
196D4×C11—22no—
197D4×C11#13714yescomplemented
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—24no—
203C2×C4×C11—41no—
204C2×C4×C11—42no—
205C2×C4×C11—44no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—44no—
211C2×C4×C11—88no—
212C2×C4×C11#12011yescharacteristic
213C2×C4×C11#12011yescharacteristic
214C2×C4×C11#12011yescharacteristic
215C2×C4×C11#13512yes—
216C2×C4×C11AGL(1,ℤ/8)12yes—
217C2×C4×C11C22×D411yescharacteristic
218C2×C4×C11C22×D411yescharacteristic
219C2×C4×C11C22×D411yescharacteristic
220C22⋊D11—82no—
221C2×Dic11—41no—
222D44—42no—
223D44—41no—
224D44—41no—
225D44—42no—
226C4×D11—82no—
227Dic22—41no—
228Dic22—41no—
229C11⋊C8—42no—
230C11⋊C8—42no—
231C11⋊C8—42no—
232C2×#137—221no—
233#554—22no—
234#554—22no—
235#554—22no—
236#554C2×D1114yes—
237#532—111no—
238C2×C4⋊Q8C2×D1111yescharacteristic
239C2×#125—21no—
240C2×C22⋊Q8—21no—
241C2×C22⋊Q8—22no—
242C2×C4×Q8C2×D1111yescharacteristic
243C2×C4×D4—21no—
244C2×C4×D4C2×D1111yescharacteristic
245C22×C4⋊C4—21no—
246#492—112no—
247#487—112no—
248#480—221no—
249#474—112no—
250#464—222no—
251#462—112no—
252#461—222no—
253#460—112no—
254#459—112no—
255#448—222no—
256#447—221no—
257C4×D8—222no—
258#431—111no—
259#431—111no—
260#423—111no—
261#417—221no—
262#333—114no—
263Q8⋊C8—114no—
264D4⋊C8—114no—
265C22×C11—21no—
266C22×C11—21no—
267C22×C11—24no—
268C22×C11—48no—
269C22×C11—42no—
270C22×C11—42no—
271C22×C11#44912yes—
272C22×C11C2×#12011yescharacteristic
273C2×D11—81no—
274C2×D11—81no—
275C2×D11—81no—
276C4×C11—21no—
277C4×C11—21no—
278C4×C11—21no—
279C4×C11—42no—
280C4×C11—42no—
281C4×C11—42no—
282C4×C11—44no—
283C4×C11#44912yes—
284C4×C11C2×#13511yescharacteristic
285C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
286C4×C11C2×#13712yes—
287Dic11—81no—
288C2×#41—221no—
289C22×Q8C22⋊D1111yescharacteristic
290C22×Q8C22⋊D1112yes—
291C22×D4C22⋊D1111yescharacteristic
292C23×C4—22no—
293C23×C4—21no—
294#137—444no—
295C2×Q16—222no—
296C2×SD16—222no—
297C2×SD16—224no—
298C2×D8—222no—
299C2×M16—221no—
300C4⋊Q8—21no—
301C4⋊Q8—21no—
302C4⋊Q8—111no—
303C4⋊Q8C22⋊D1112yes—
304C4⋊Q8C22×D1112yes—
305#127—111no—
306#125—24no—
307#125—24no—
308#124—221no—
309C22⋊Q8—24no—
310C22⋊Q8—28no—
311C22⋊Q8—24no—
312C22⋊Q8—28no—
313#121—221no—
314#121—221no—
315C4×Q8—21no—
316C4×Q8—21no—
317C4×Q8C22⋊D1112yes—
318C4×Q8C22×D1112yes—
319C4×D4—24no—
320C4×D4—24no—
321C4×D4—21no—
322C4×D4—21no—
323C4×D4—221no—
324C4×D4—221no—
325C4×D4C22⋊D1112yes—
326C4×D4C22×D1112yes—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4C22⋊D1111yescharacteristic
335C2×C4⋊C4C22⋊D1111yescharacteristic
336C2×C22⋊C4—22no—
337C2×C22⋊C4—21no—
338C2×C42—21no—
339C2×C42C22×D1111yescharacteristic
340#107—222no—
341C4⋊C8—112no—
342C4⋊C8—112no—
343C4⋊C8—221no—
344C4⋊C8—221no—
345#103—224no—
346#103—222no—
347#102—222no—
348#102—222no—
349#102—222no—
350C22⋊C8—221no—
351C22⋊C8—221no—
352C4×C8—112no—
353C4×C8—221no—
354C2×C11—22no—
355C2×C11—44no—
356C2×C11C2×#44911yescharacteristic
357C2×C11#300411yescharacteristic
358C2×C11#301911yescharacteristic
359D11—161no—
360C24—21no—
361#41—442no—
362#41—442no—
363C2×Q8—21no—
364C2×Q8—22no—
365C2×Q8—22no—
366C2×Q8—22no—
367C2×Q8—82no—
368C2×Q8—221no—
369C2×Q8C2×C22⋊D1112yes—
370C2×Q8C2×C22⋊D1114yes—
371C2×D4—24no—
372C2×D4—21no—
373C2×D4—221no—
374C2×D4—221no—
375C2×D4—221no—
376C2×D4—441no—
377C2×D4C2×C22⋊D1112yes—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—22no—
382C22×C4—28no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—42no—
386C22×C4—42no—
387C22×C4—84no—
388C22×C4—441no—
389C22×C4C2×C22⋊D1111yescharacteristic
390C22×C4C2×C22⋊D1111yescharacteristic
391C22×C4C2×C22⋊D1111yescharacteristic
392Q16—444no—
393SD16—444no—
394SD16—884no—
395D8—444no—
396M16—442no—
397C2×C8—222no—
398C2×C8—222no—
399C2×C8—222no—
400C4⋊C4—28no—
401C4⋊C4—28no—
402C4⋊C4—21no—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—21no—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—221no—
411C4⋊C4—221no—
412C4⋊C4C2×C22⋊D1112yes—
413C4⋊C4C2×C22⋊D1112yes—
414C22⋊C4—28no—
415C22⋊C4—22no—
416C22⋊C4—22no—
417C22⋊C4—441no—
418C22⋊C4—441no—
419C42—22no—
420C42—22no—
421C42C2×C22⋊D1111yescharacteristic
422C42C2×C22⋊D1111yescharacteristic
423C42C2×C22⋊D1111yescharacteristic
424C42C23×D1111yescharacteristic
425C11#1875211yescharacteristic, complemented, Sylow
426C23—24no—
427C23—22no—
428C23—42no—
429C23—42no—
430C23—441no—
431C23#6700611yescharacteristic
432Q8—22no—
433Q8—22no—
434Q8—44no—
435Q8—42no—
436Q8—82no—
437Q8—441no—
438Q8—441no—
439D4—24no—
440D4—22no—
441D4—442no—
442D4—442no—
443D4—441no—
444D4—441no—
445D4—882no—
446D4#6699514yescomplemented
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—24no—
452C2×C4—41no—
453C2×C4—42no—
454C2×C4—44no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—44no—
460C2×C4—88no—
461C2×C4—441no—
462C2×C4—882no—
463C2×C4#6700212yes—
464C2×C4#6700312yes—
465C2×C4#6700611yescharacteristic
466C2×C4#6700611yescharacteristic
467C2×C4#6700611yescharacteristic
468C2×C4C22×C22⋊D1111yescharacteristic
469C2×C4C22×C22⋊D1111yescharacteristic
470C2×C4C22×C22⋊D1111yescharacteristic
471C8—442no—
472C8—442no—
473C8—442no—
474C22—21no—
475C22—21no—
476C22—24no—
477C22—48no—
478C22—42no—
479C22—42no—
480C22—881no—
481C22—881no—
482C22—881no—
483C22#1062285112yes—
484C22C2×#6700611yescharacteristic
485C4—21no—
486C4—21no—
487C4—21no—
488C4—42no—
489C4—42no—
490C4—42no—
491C4—44no—
492C4—881no—
493C4#1062285112yes—
494C4C2×#6699512yes—
495C4C2×#6700211yescharacteristic
496C4C2×#6700311yescharacteristic
497C2—22no—
498C2—44no—
499C2—1761no—
500C2C2×#1062285111yescharacteristic
501C2#1307785011yescharacteristic
502C2#1307797311yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#554C2
socleC22×C11C2×#120
prime radical#13078616C2
hypercenterC2×#554D11
hypocenterC11#18752
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #13079541C2semidirect
3. #13078088C2semidirect
4. #13067830C2semidirect
5. #13067688C2semidirect
6. #13067297C2semidirect
7. #13067041C2semidirect
8. #13067011C2semidirect
9. C2×C11×#554C2semidirect
26. #10622698C22semidirect
28. #10622694C22semidirect
29. #10622644C22semidirect
31. #10622640C22semidirect
40. #10622184C22semidirect
41. Q8⋊(C11⋊C8)C22semidirect
175. C2×#554D11semidirect
197. D4×C11#137semidirect
425. C11#18752semidirect
446. D4#66995semidirect

Maximal subgroups

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

subgroupindex
#130795412
#130786162
#130780882
#130678302
#130676882
#130672972
#130670412
#130670112
C2×C11×#5542
#1875211