Finite Group Databasebeta

← #14907648

Subgroups — #14907648

Order 2816.

1098 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622792C211yesmaximal, characteristic, complemented
2C2×#10622807C211yesmaximal, characteristic, complemented
3#13078286C211yesmaximal, characteristic, complemented
4#13070556C212yesmaximal, complemented
5#13070550C212yesmaximal, complemented
6#13070539C212yesmaximal, complemented
7#13070533C212yesmaximal, complemented
8#13070328C211yesmaximal, characteristic, complemented
9C2×#10622202C211yesmaximal, characteristic, complemented
10#13070230C211yesmaximal, characteristic, complemented
11C2×C11×#578C211yesmaximal, characteristic, complemented
12C2×C11×2−1+4—21no—
13C11×#578—24no—
14C11×#578—24no—
15C2×C11×#137—21no—
16C2×C11×#137—22no—
17C2×C11×#135C2212yes—
18C2×C11×#135C2211yescharacteristic
19C22×C11×Q16C2212yes—
20C22×C11×Q16C2211yescharacteristic
21C2×C11×#131C2211yescharacteristic
22#10623364—21no—
23C2×#66957C2211yescharacteristic
24#10622807—24no—
25C2×#66893C2211yescharacteristic
26C2×#66893C2212yes—
27#10622792—24no—
28C2×#66892C2211yescharacteristic
29C2×#66892C2212yes—
30C2×#66891C2211yescharacteristic
31C2×#66890C2211yescharacteristic
32#10622747—22no—
33#10622746—21no—
34#10622729C2212yes—
35#10622728C2212yes—
36C2×#66882C2211yescharacteristic
37C2×#66876C2211yescharacteristic
38C22×C11⋊C16C2211yescharacteristic
39#10622202C2212yes—
40#10622202C2212yes—
41#10622202C2212yes—
42#10622200C2212yes—
43C22⋊(C11⋊C16)C2212yes—
44C22⋊(C11⋊C16)C2212yes—
45C11×2−1+4—28no—
46C11×2−1+4—44no—
47C2×C11×#41—22no—
48C2×C11×#41—21no—
49C2×C11×#41—41no—
50C2×C11×#41—42no—
51C2×C11×#41D411yescharacteristic
52C22×Q8×C11—22no—
53C22×Q8×C11—21no—
54C22×Q8×C11—41no—
55C2×#4339—21no—
56C11×#137—216no—
57C11×#137—28no—
58C11×#135—24no—
59C11×#135—24no—
60C11×#135—22no—
61C11×#135D414yescomplemented
62C2×C11×Q16—24no—
63C2×C11×Q16—24no—
64C2×C11×Q16—22no—
65C2×C11×Q16—21no—
66C2×C11×Q16—22no—
67C2×C11×Q16D414yescomplemented
68C2×C11×Q16C2311yescharacteristic
69C2×C11×Q16C2312yes—
70C2×C11×SD16—22no—
71C2×C11×SD16—21no—
72C2×C11×D8C2311yescharacteristic
73C11×#131—22no—
74C11×#131—22no—
75C2×C11×M16D411yescharacteristic
76C2×C11×M16D412yes—
77C22×C8×C11C2312yes—
78C22×C8×C11C2311yescharacteristic
79#66999—41no—
80#66992—42no—
81#66991—41no—
82#66983—22no—
83C2×C4⋊Dic11—21no—
84#66977—22no—
85C2×Dic44C2311yescharacteristic
86#66957—22no—
87#66957—22no—
88C2×D88C2311yescharacteristic
89C2×#4314—21no—
90#66893—24no—
91#66893—22no—
92#66892—24no—
93#66892—22no—
94#66891—22no—
95#66890—22no—
96#66885—22no—
97#66882—21no—
98#66882C2312yes—
99#66880—22no—
100#66876—22no—
101C2×C11⋊C16—22no—
102C2×C11⋊C16C2311yescharacteristic
103C2×C11⋊C16C2311yescharacteristic
104C2×C11⋊C16C2312yes—
105#33527—111nomaximal, Sylow
106C11×#41—22no—
107C11×#41—22no—
108C11×#41—28no—
109C11×#41—24no—
110C11×#41—44no—
111C11×#41—416no—
112C11×#41—48no—
113C11×#41—42no—
114C2×Q8×C11—28no—
115C2×Q8×C11—24no—
116C2×Q8×C11—22no—
117C2×Q8×C11—21no—
118C2×Q8×C11—44no—
119C2×Q8×C11—48no—
120C2×Q8×C11—42no—
121C2×Q8×C11—41no—
122C2×Q8×C11—42no—
123C2×Q8×C11D811yescharacteristic
124C2×D4×C11—21no—
125C2×D4×C11—42no—
126C2×D4×C11—41no—
127C2×D4×C11D811yescharacteristic
128C2×D4×C11D812yes—
129C22×C4×C11—42no—
130C22×C4×C11—41no—
131C22×C4×C11—42no—
132C22×C4×C11—41no—
133C22×C4×C11C2×D412yes—
134C22×C4×C11C2×D411yescharacteristic
135C2×C22⋊D11—41no—
136C2×C22⋊D11—42no—
137C22×Dic11—41no—
138#4339—42no—
139#4339—42no—
140C2×D44—21no—
141C2×C4×D11—41no—
142C2×Dic22—21no—
143C11×Q16—28no—
144C11×Q16—24no—
145C11×Q16—21no—
146C11×Q16—22no—
147C11×Q16C2×D412yes—
148C11×Q16C2×D414yes—
149C11×SD16—28no—
150C11×SD16—24no—
151C11×D8—21no—
152C11×D8C2×D412yes—
153C11×M16—24no—
154C11×M16—22no—
155C2×C8×C11—22no—
156C2×C8×C11—22no—
157C2×C8×C11C2×D412yes—
158C2×C8×C11C2×D412yes—
159C2×C8×C11C2×D412yes—
160C2×C8×C11C2×D411yescharacteristic
161C2×C8×C11C2411yescharacteristic
162C22⋊Dic11—42no—
163(C2×D11)⋊C4—42no—
164C4⋊Dic11—22no—
165C4⋊Dic11—41no—
166Dic11⋊C4—42no—
167Dic44—21no—
168Dic44—21no—
169D88—21no—
170D88—21no—
171#4314—42no—
172C11⋊C16—21no—
173C11⋊C16—21no—
174C11⋊C16—22no—
175C2×#578D1111yescharacteristic, complemented
176C2×#510—111no—
177C2×#508—111no—
178#3061—111no—
179#2189—112no—
180#2188—112no—
181#2186—112no—
182#2185—112no—
183#2139—111no—
184C2×#358—111no—
185#2113—111no—
186C23×C11—41no—
187C23×C11C2×D812yes—
188C23×C11C2×D811yescharacteristic
189C22×D11—41no—
190Q8×C11—22no—
191Q8×C11—24no—
192Q8×C11—22no—
193Q8×C11—48no—
194Q8×C11—41no—
195Q8×C11—42no—
196Q8×C11—44no—
197D4×C11—24no—
198D4×C11—22no—
199D4×C11—22no—
200D4×C11—48no—
201D4×C11—44no—
202D4×C11—41no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—48no—
206C2×C4×C11—48no—
207C2×C4×C11—42no—
208C2×C4×C11—41no—
209C2×C4×C11—44no—
210C2×C4×C11—44no—
211C2×C4×C11#12012yes—
212C2×C4×C11C2×D812yes—
213C2×C4×C11C2×D811yescharacteristic
214C2×C4×C11AGL(1,ℤ/8)12yes—
215C2×C4×C11C22×D411yescharacteristic
216C22⋊D11—82no—
217C22⋊D11—162no—
218C2×Dic11—41no—
219C2×Dic11—42no—
220C2×Dic11—161no—
221D44—41no—
222D44—41no—
223C4×D11—82no—
224Dic22—41no—
225Dic22—41no—
226C8×C11—22no—
227C8×C11#12012yes—
228C8×C11C22×D411yescharacteristic
229C8×C11C22×D411yescharacteristic
230C2×2−1+4—21no—
231#578—24no—
232#578—24no—
233C2×#137—21no—
234C2×#137—22no—
235C2×#135—111no—
236C2×#135C2×D1112yes—
237C2×#135C2×D1111yescharacteristic
238C22×Q16C2×D1112yes—
239C22×Q16C2×D1111yescharacteristic
240C2×#131C2×D1111yescharacteristic
241#537—221no—
242#510—224no—
243#508—224no—
244C2×Q32—111no—
245C2×Q32—112no—
246C2×SD32—111no—
247C2×SD32—112no—
248C2×SD32—111no—
249C2×D16—111no—
250C2×M32—111no—
251C22×C16—111no—
252#468—222no—
253#467—112no—
254#466—112no—
255C2×#107—111no—
256#417—221no—
257#358—112no—
258#358—112no—
259#358—112no—
260#357—112no—
261C22⋊C16—112no—
262C22⋊C16—112no—
263C22×C11—21no—
264C22×C11—21no—
265C22×C11—22no—
266C22×C11—22no—
267C22×C11—22no—
268C22×C11—42no—
269C22×C11—81no—
270C22×C11—81no—
271C22×C11#44712yes—
272C22×C11C22×D811yescharacteristic
273C2×D11—81no—
274C2×D11—81no—
275C2×D11—81no—
276C4×C11—22no—
277C4×C11—44no—
278C4×C11—42no—
279C4×C11#44712yes—
280C4×C11C2×#12011yescharacteristic
281C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
282Dic11—82no—
283Dic11—81no—
2842−1+4—28no—
2852−1+4—44no—
286C2×#41—22no—
287C2×#41—21no—
288C2×#41—41no—
289C2×#41—42no—
290C2×#41—221no—
291C2×#41C22⋊D1111yescharacteristic
292C22×Q8—22no—
293C22×Q8—21no—
294C22×Q8—41no—
295#137—28no—
296#137—216no—
297#135—24no—
298#135—24no—
299#135—22no—
300#135—222no—
301#135—222no—
302#135C22⋊D1114yescomplemented
303C2×Q16—24no—
304C2×Q16—24no—
305C2×Q16—22no—
306C2×Q16—21no—
307C2×Q16—22no—
308C2×Q16—111no—
309C2×Q16C22⋊D1114yescomplemented
310C2×Q16C22×D1111yescharacteristic
311C2×Q16C22×D1112yes—
312C2×SD16—22no—
313C2×SD16—21no—
314C2×SD16—221no—
315C2×D8—111no—
316C2×D8C22×D1111yescharacteristic
317#131—22no—
318#131—22no—
319C2×M16C22⋊D1111yescharacteristic
320C2×M16C22⋊D1112yes—
321C22×C8C22×D1112yes—
322C22×C8C22×D1111yescharacteristic
323C22⋊Q8—222no—
324C22⋊Q8—441no—
325#121—222no—
326#121—441no—
327#121—442no—
328C2×C4⋊C4—221no—
329Q32—222no—
330Q32—224no—
331SD32—222no—
332SD32—224no—
333SD32—222no—
334D16—222no—
335M32—222no—
336C2×C16—112no—
337C2×C16—111no—
338C2×C16—111no—
339C2×C16—222no—
340#107—112no—
341#107—221no—
342#103—222no—
343#102—222no—
344C2×C11—22no—
345C2×C11—42no—
346C2×C11—82no—
347C2×C11C2×#44711yescharacteristic
348C2×C11#341611yescharacteristic
349C2×C11#341711yescharacteristic
350D11—161no—
351#41—22no—
352#41—22no—
353#41—28no—
354#41—24no—
355#41—44no—
356#41—416no—
357#41—48no—
358#41—42no—
359#41—442no—
360#41—442no—
361C2×Q8—28no—
362C2×Q8—24no—
363C2×Q8—22no—
364C2×Q8—21no—
365C2×Q8—44no—
366C2×Q8—48no—
367C2×Q8—42no—
368C2×Q8—41no—
369C2×Q8—42no—
370C2×Q8—221no—
371C2×Q8#432311yescharacteristic
372C2×D4—21no—
373C2×D4—42no—
374C2×D4—41no—
375C2×D4—221no—
376C2×D4—441no—
377C2×D4—442no—
378C2×D4#432312yes—
379C2×D4#432311yescharacteristic
380C22×C4—42no—
381C22×C4—41no—
382C22×C4—42no—
383C22×C4—41no—
384C22×C4—441no—
385C22×C4—441no—
386C22×C4C2×C22⋊D1112yes—
387C22×C4C2×C22⋊D1111yescharacteristic
388Q16—28no—
389Q16—24no—
390Q16—21no—
391Q16—22no—
392Q16—221no—
393Q16—221no—
394Q16C2×C22⋊D1112yes—
395Q16C2×C22⋊D1114yes—
396SD16—28no—
397SD16—24no—
398SD16—442no—
399D8—21no—
400D8—221no—
401D8—221no—
402D8C2×C22⋊D1112yes—
403M16—22no—
404M16—24no—
405C2×C8—22no—
406C2×C8—22no—
407C2×C8C2×C22⋊D1112yes—
408C2×C8C2×C22⋊D1111yescharacteristic
409C2×C8C2×C22⋊D1112yes—
410C2×C8C2×C22⋊D1112yes—
411C2×C8C23×D1111yescharacteristic
412C4⋊C4—222no—
413C4⋊C4—441no—
414C4⋊C4—442no—
415C22⋊C4—442no—
416C22⋊C4—442no—
417C16—221no—
418C16—221no—
419C16—222no—
420C11#3352711yescharacteristic, complemented, Sylow
421C23—41no—
422C23—441no—
423C23C2×#432312yes—
424C23C2×#432311yescharacteristic
425Q8—22no—
426Q8—24no—
427Q8—22no—
428Q8—48no—
429Q8—41no—
430Q8—42no—
431Q8—44no—
432Q8—441no—
433Q8—441no—
434D4—24no—
435D4—22no—
436D4—22no—
437D4—48no—
438D4—44no—
439D4—41no—
440D4—441no—
441D4—441no—
442D4—882no—
443D4—1762no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—48no—
447C2×C4—48no—
448C2×C4—42no—
449C2×C4—41no—
450C2×C4—44no—
451C2×C4—44no—
452C2×C4—442no—
453C2×C4—441no—
454C2×C4—882no—
455C2×C4—1761no—
456C2×C4C2×#432312yes—
457C2×C4C2×#432311yescharacteristic
458C2×C4#6698512yes—
459C2×C4#6700612yes—
460C2×C4C22×C22⋊D1111yescharacteristic
461C8—22no—
462C8#6700612yes—
463C8C22×C22⋊D1111yescharacteristic
464C8C22×C22⋊D1111yescharacteristic
465C22—21no—
466C22—21no—
467C22—22no—
468C22—22no—
469C22—22no—
470C22—42no—
471C22—81no—
472C22—81no—
473C22—881no—
474C22—881no—
475C22—881no—
476C22#1062283012yes—
477C22C22×#432311yescharacteristic
478C4—22no—
479C4—44no—
480C4—42no—
481C4—881no—
482C4—882no—
483C4#1062283012yes—
484C4C2×#6698511yescharacteristic
485C4C2×#6700611yescharacteristic
486C2—22no—
487C2—42no—
488C2—82no—
489C2—1761no—
490C2C2×#1062283011yescharacteristic
491C2#1308176011yescharacteristic
492C2#1308176711yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#578C2
socleC22×C11C22×D8
hypercenterC2×#578D11
hypocenterC11#33527
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#131 ◁ C2×#578

Complements

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

NH ≅ G/Ntype
1. C2×#10622792C2semidirect
2. C2×#10622807C2semidirect
3. #13078286C2semidirect
4. #13070556C2semidirect
5. #13070550C2semidirect
6. #13070539C2semidirect
7. #13070533C2semidirect
8. #13070328C2semidirect
9. C2×#10622202C2semidirect
10. #13070230C2semidirect
11. C2×C11×#578C2semidirect
61. C11×#135D4semidirect
67. C2×C11×Q16D4semidirect
175. C2×#578D11semidirect
302. #135C22⋊D11semidirect
309. C2×Q16C22⋊D11semidirect
420. C11#33527semidirect

Maximal subgroups

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

subgroupindex
C2×#106227922
C2×#106228072
#130782862
#130705562
#130705502
#130705392
#130705332
#130703282
C2×#106222022
#130702302
C2×C11×#5782
#3352711