Finite Group Databasebeta

← #14907669

Subgroups — #14907669

Order 2816.

1132 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081750C212yesmaximal, complemented
2#13078225C211yesmaximal, characteristic, complemented
3#13070567C214yesmaximal, complemented
4#13070562C214yesmaximal, complemented
5#13070352C212yesmaximal, complemented
6C2×#10622191C211yesmaximal, characteristic, complemented
7C2×C11×#575C211yesmaximal, characteristic, complemented
8C22×C11×#41—21no—
9C11×#575—24no—
10C11×#575—22no—
11C11×#575C2214yes—
12C2×C11×#137—22no—
13C2×C11×AGL(1,ℤ/8)—22no—
14C2×C11×#135—21no—
15C2×C11×#135C2212yes—
16C22×C11×M16C2211yescharacteristic
17#10623322—21no—
18C2×#66957C2211yescharacteristic, complemented
19#10622808C2214yescomplemented
20#10622807—24no—
21#10622806C2214yescomplemented
22#10622792—22no—
23#10622760—22no—
24#10622750C2212yescomplemented
25#10622748C2212yescomplemented
26#10622747—22no—
27#10622726—21no—
28#10622719C2211yescharacteristic, complemented
29C2×#66876C2212yescomplemented
30#10622204C2218yescomplemented
31#10622191C2214yescomplemented
32C2×C11×#41—22no—
33C2×C11×#41—24no—
34C2×C11×#41—22no—
35C2×C11×#41—24no—
36C2×C11×#41—41no—
37C2×C11×#41—42no—
38C2×C11×#41—42no—
39C2×C11×#41—41no—
40C22×Q8×C11—21no—
41C22×D4×C11—21no—
42C22×D4×C11—41no—
43C23×C4×C11—41no—
44C23×C4×C11D411yescharacteristic
45C2×#4339—21no—
46C11×#137—28no—
47C11×#137—28no—
48C11×AGL(1,ℤ/8)—28no—
49C11×AGL(1,ℤ/8)—28no—
50C11×#135—24no—
51C11×#135—24no—
52C11×#135—22no—
53C11×#135—22no—
54C11×#135D414yescomplemented
55C11×#135C2314yes—
56C2×C11×Q16—21no—
57C2×C11×Q16D412yescomplemented
58C2×C11×SD16—22no—
59C2×C11×SD16—22no—
60C2×C11×D8—21no—
61C2×C11×D8D412yescomplemented
62C2×C11×M16—22no—
63C2×C11×M16—22no—
64C2×C11×M16D412yes—
65C2×C11×M16C2312yes—
66C22×C8×C11D411yescharacteristic
67C22×C8×C11C2311yescharacteristic
68#67006—41no—
69#66983—22no—
70#66982—41no—
71C4×C22⋊D11—42no—
72#66979—21no—
73#66977—22no—
74C2×Dic44C2311yescharacteristic, complemented
75#66957—22no—
76#66957—22no—
77C2×D88C2311yescharacteristic, complemented
78C2×#4314—21no—
79#66893—24no—
80#66892—24no—
81#66891—24no—
82#66890—24no—
83#66885—22no—
84#66882—21no—
85#66881C2312yescomplemented
86#66880—22no—
87#66876—22no—
88#66876C2314yescomplemented
89C2×C11⋊C16—22no—
90#33530—111nomaximal, Sylow
91C24×C11—41no—
92C24×C11D811yescharacteristic
93C11×#41—28no—
94C11×#41—24no—
95C11×#41—24no—
96C11×#41—44no—
97C11×#41—44no—
98C11×#41—44no—
99C11×#41—44no—
100C11×#41—44no—
101C11×#41—42no—
102C11×#41—42no—
103C2×Q8×C11—24no—
104C2×Q8×C11—22no—
105C2×Q8×C11—41no—
106C2×Q8×C11—42no—
107C2×D4×C11—24no—
108C2×D4×C11—22no—
109C2×D4×C11—41no—
110C2×D4×C11—42no—
111C2×D4×C11—44no—
112C2×D4×C11—42no—
113C2×D4×C11—44no—
114C2×D4×C11—42no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—42no—
120C22×C4×C11—44no—
121C22×C4×C11—44no—
122C22×C4×C11—41no—
123C22×C4×C11—42no—
124C22×C4×C11D812yes—
125C22×C4×C11D811yescharacteristic
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×D411yescharacteristic
128C2×C22⋊D11—42no—
129C2×C22⋊D11—41no—
130#4339—41no—
131#4339—41no—
132#4339—41no—
133#4339—41no—
134C2×D44—21no—
135C2×C4×D11—41no—
136C2×Dic22—21no—
137C11×Q16—24no—
138C11×Q16—22no—
139C11×Q16C2×D414yes—
140C11×SD16—28no—
141C11×SD16—24no—
142C11×SD16—24no—
143C11×D8—24no—
144C11×D8—22no—
145C11×D8C2×D414yes—
146C11×M16—24no—
147C11×M16—24no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11C2×D412yes—
151C2×C8×C11C2×D412yes—
152C2×C8×C11C2×D412yes—
153C2×C8×C11C2×D411yescharacteristic
154C2×C8×C11C2411yescharacteristic
155C22⋊Dic11—42no—
156C22⋊Dic11—41no—
157(C2×D11)⋊C4—42no—
158C4⋊Dic11—22no—
159Dic11⋊C4—42no—
160C4×Dic11—41no—
161Dic44—22no—
162D88—22no—
163#4314—42no—
164C11⋊C16—24no—
165C2×#575D1111yescharacteristic, complemented
166#3414—112no—
167#3054—111no—
168#2191—114no—
169#2190—114no—
170#2145—112no—
171C2×#349—111no—
172C23×C11—21no—
173C23×C11—21no—
174C23×C11—44no—
175C23×C11—42no—
176C23×C11—81no—
177C23×C11—84no—
178C23×C11C2×D812yes—
179C23×C11C2×D811yescharacteristic
180C22×D11—41no—
181Q8×C11—24no—
182Q8×C11—44no—
183Q8×C11—42no—
184D4×C11—24no—
185D4×C11—44no—
186D4×C11—48no—
187D4×C11—44no—
188D4×C11—44no—
189D4×C11—42no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—48no—
197C2×C4×C11—44no—
198C2×C4×C11—42no—
199C2×C4×C11—44no—
200C2×C4×C11—44no—
201C2×C4×C11#12011yescharacteristic
202C2×C4×C11#12011yescharacteristic
203C2×C4×C11C2×D812yes—
204C2×C4×C11C2×D811yescharacteristic
205C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
206C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
207C2×C4×C11C22×D411yescharacteristic
208C22⋊D11—84no—
209C22⋊D11—81no—
210C22⋊D11—81no—
211C2×Dic11—42no—
212C2×Dic11—41no—
213D44—41no—
214D44—41no—
215C4×D11—81no—
216C4×D11—81no—
217Dic22—41no—
218Dic22—41no—
219C8×C11—22no—
220C8×C11#12012yes—
221C8×C11C22×D412yes—
222C22×#41—21no—
223#575—24no—
224#575—22no—
225#575C2×D1114yes—
226C2×#137—22no—
227C2×AGL(1,ℤ/8)—22no—
228C2×#135—21no—
229C2×#135—111no—
230C2×#135C2×D1112yes—
231C22×M16C2×D1111yescharacteristic
232#525—221no—
233#510—114no—
234#510—222no—
235#509—114no—
236#509—222no—
237#508—224no—
238C2×M32—112no—
239#470—112no—
240#469—112no—
241#468—222no—
242#427—111no—
243#416—221no—
244#360—118no—
245#349—114no—
246C22×C11—22no—
247C22×C11—41no—
248C22×C11—42no—
249C22×C11—42no—
250C22×C11—44no—
251C22×C11—81no—
252C22×C11—84no—
253C22×C11—88no—
254C22×C11#44711yescharacteristic
255C22×C11#44711yescharacteristic
256C22×C11C22×D811yescharacteristic
257C2×D11—82no—
258C2×D11—81no—
259C4×C11—22no—
260C4×C11—44no—
261C4×C11#44711yescharacteristic
262C4×C11#44711yescharacteristic
263C4×C11C2×#12011yescharacteristic
264C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
265Dic11—82no—
266Dic11—81no—
267C2×#41—22no—
268C2×#41—24no—
269C2×#41—24no—
270C2×#41—22no—
271C2×#41—41no—
272C2×#41—42no—
273C2×#41—42no—
274C2×#41—41no—
275C2×#41—221no—
276C22×Q8—21no—
277C22×D4—21no—
278C22×D4—41no—
279C23×C4—41no—
280C23×C4C22⋊D1111yescharacteristic
281#137—28no—
282#137—28no—
283AGL(1,ℤ/8)—28no—
284AGL(1,ℤ/8)—28no—
285#135—24no—
286#135—24no—
287#135—22no—
288#135—22no—
289#135—222no—
290#135—222no—
291#135C22⋊D1114yescomplemented
292#135C22×D1114yes—
293C2×Q16—21no—
294C2×Q16—111no—
295C2×Q16C22⋊D1112yescomplemented
296C2×SD16—22no—
297C2×SD16—22no—
298C2×SD16—221no—
299C2×D8—21no—
300C2×D8—111no—
301C2×D8C22⋊D1112yescomplemented
302C2×M16—22no—
303C2×M16—22no—
304C2×M16C22⋊D1112yes—
305C2×M16C22×D1112yes—
306C22×C8C22⋊D1111yescharacteristic
307C22×C8C22×D1111yescharacteristic
308#123—441no—
309C22⋊Q8—222no—
310#121—222no—
311#120—441no—
312C4×D4—442no—
313#117—221no—
314Q32—224no—
315SD32—224no—
316SD32—224no—
317D16—224no—
318M32—114no—
319M32—222no—
320C2×C16—222no—
321#107—221no—
322#106—112no—
323#103—222no—
324#102—222no—
325C2×C11—21no—
326C2×C11—21no—
327C2×C11—21no—
328C2×C11—42no—
329C2×C11—84no—
330C2×C11C2×#44711yescharacteristic
331D11—161no—
332C24—41no—
333C24#432311yescharacteristic
334#41—28no—
335#41—24no—
336#41—24no—
337#41—44no—
338#41—44no—
339#41—44no—
340#41—44no—
341#41—44no—
342#41—42no—
343#41—42no—
344#41—441no—
345#41—441no—
346#41—441no—
347#41—441no—
348C2×Q8—24no—
349C2×Q8—22no—
350C2×Q8—41no—
351C2×Q8—42no—
352C2×Q8—221no—
353C2×D4—24no—
354C2×D4—22no—
355C2×D4—41no—
356C2×D4—42no—
357C2×D4—44no—
358C2×D4—42no—
359C2×D4—44no—
360C2×D4—42no—
361C2×D4—221no—
362C2×D4—442no—
363C2×D4—441no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—42no—
369C22×C4—44no—
370C22×C4—44no—
371C22×C4—41no—
372C22×C4—42no—
373C22×C4—441no—
374C22×C4#432312yes—
375C22×C4#432311yescharacteristic
376C22×C4C2×C22⋊D1112yes—
377C22×C4C2×C22⋊D1111yescharacteristic
378Q16—24no—
379Q16—22no—
380Q16—222no—
381Q16C2×C22⋊D1114yes—
382SD16—28no—
383SD16—24no—
384SD16—24no—
385SD16—442no—
386D8—24no—
387D8—22no—
388D8—222no—
389D8C2×C22⋊D1114yes—
390M16—24no—
391M16—24no—
392C2×C8—21no—
393C2×C8—21no—
394C2×C8C2×C22⋊D1112yes—
395C2×C8C2×C22⋊D1111yescharacteristic
396C2×C8C2×C22⋊D1112yes—
397C2×C8C2×C22⋊D1112yes—
398C2×C8C23×D1111yescharacteristic
399C4⋊C4—222no—
400C4⋊C4—442no—
401C22⋊C4—441no—
402C22⋊C4—442no—
403C22⋊C4—442no—
404C42—441no—
405C16—224no—
406C11#3353011yescharacteristic, complemented, Sylow
407C23—21no—
408C23—21no—
409C23—44no—
410C23—42no—
411C23—81no—
412C23—84no—
413C23—441no—
414C23C2×#432312yes—
415C23C2×#432311yescharacteristic
416Q8—24no—
417Q8—44no—
418Q8—42no—
419Q8—441no—
420Q8—441no—
421D4—24no—
422D4—44no—
423D4—48no—
424D4—44no—
425D4—44no—
426D4—42no—
427D4—441no—
428D4—441no—
429D4—884no—
430D4—881no—
431D4—881no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—48no—
439C2×C4—44no—
440C2×C4—42no—
441C2×C4—44no—
442C2×C4—44no—
443C2×C4—442no—
444C2×C4—441no—
445C2×C4—881no—
446C2×C4—881no—
447C2×C4C2×#432312yes—
448C2×C4C2×#432311yescharacteristic
449C2×C4#6698511yescharacteristic
450C2×C4#6698511yescharacteristic
451C2×C4#6700611yescharacteristic
452C2×C4#6700611yescharacteristic
453C2×C4C22×C22⋊D1111yescharacteristic
454C8—22no—
455C8#6700612yes—
456C8C22×C22⋊D1112yes—
457C22—22no—
458C22—41no—
459C22—42no—
460C22—42no—
461C22—44no—
462C22—81no—
463C22—84no—
464C22—88no—
465C22—882no—
466C22—881no—
467C22#1062283011yescharacteristic
468C22#1062283011yescharacteristic
469C22C22×#432311yescharacteristic
470C4—22no—
471C4—44no—
472C4—882no—
473C4—881no—
474C4#1062283011yescharacteristic
475C4#1062283011yescharacteristic
476C4C2×#6698511yescharacteristic
477C4C2×#6700611yescharacteristic
478C2—21no—
479C2—21no—
480C2—21no—
481C2—42no—
482C2—84no—
483C2—1761no—
484C2C2×#1062283011yescharacteristic
subgroupG/H
centerC4#10622830
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#575C2
socleC2×C11C2×#447
hypercenterC2×#575D11
hypocenterC11#33530
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×M16 ◁ C2×#575

Complements

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

NH ≅ G/Ntype
1. #13081750C2semidirect
2. #13078225C2semidirect
3. #13070567C2semidirect
4. #13070562C2semidirect
5. #13070352C2semidirect
6. C2×#10622191C2semidirect
7. C2×C11×#575C2semidirect
18. C2×#66957C22semidirect
19. #10622808C22semidirect
21. #10622806C22semidirect
24. #10622750C22semidirect
25. #10622748C22semidirect
28. #10622719C22semidirect
29. C2×#66876C22semidirect
30. #10622204C22semidirect
31. #10622191C22semidirect
54. C11×#135D4semidirect
57. C2×C11×Q16D4semidirect
61. C2×C11×D8D4semidirect
74. C2×Dic44C23semidirect
77. C2×D88C23semidirect
85. #66881C23semidirect
88. #66876C23semidirect
165. C2×#575D11semidirect
291. #135C22⋊D11semidirect
295. C2×Q16C22⋊D11semidirect
301. C2×D8C22⋊D11semidirect
406. C11#33530semidirect

Maximal subgroups

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

subgroupindex
#130817502
#130782252
#130705672
#130705622
#130703522
C2×#106221912
C2×C11×#5752
#3353011